TSTP Solution File: SEU254+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU254+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.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 08:48:11 EDT 2022
% Result : Theorem 23.12s 6.24s
% Output : Proof 25.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU254+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 00:20:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.58/0.59 ____ _
% 0.58/0.59 ___ / __ \_____(_)___ ________ __________
% 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.59
% 0.58/0.59 A Theorem Prover for First-Order Logic
% 0.58/0.59 (ePrincess v.1.0)
% 0.58/0.59
% 0.58/0.59 (c) Philipp Rümmer, 2009-2015
% 0.58/0.59 (c) Peter Backeman, 2014-2015
% 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.59 Bug reports to peter@backeman.se
% 0.58/0.59
% 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.59
% 0.58/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.53/0.95 Prover 0: Preprocessing ...
% 2.19/1.20 Prover 0: Warning: ignoring some quantifiers
% 2.26/1.22 Prover 0: Constructing countermodel ...
% 21.64/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 21.64/5.98 Prover 1: Preprocessing ...
% 22.57/6.11 Prover 1: Warning: ignoring some quantifiers
% 22.57/6.12 Prover 1: Constructing countermodel ...
% 23.12/6.24 Prover 1: proved (301ms)
% 23.12/6.24 Prover 0: stopped
% 23.12/6.24
% 23.12/6.24 No countermodel exists, formula is valid
% 23.12/6.24 % SZS status Theorem for theBenchmark
% 23.12/6.24
% 23.12/6.24 Generating proof ... Warning: ignoring some quantifiers
% 24.97/6.69 found it (size 103)
% 24.97/6.69
% 24.97/6.69 % SZS output start Proof for theBenchmark
% 24.97/6.69 Assumed formulas after preprocessing and simplification:
% 24.97/6.69 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v6 = 0) & ~ (v3 = 0) & transitive(v2) = v3 & transitive(v1) = 0 & relation_restriction(v1, v0) = v2 & one_to_one(v4) = 0 & relation(v9) = 0 & relation(v7) = 0 & relation(v4) = 0 & relation(v1) = 0 & function(v9) = 0 & function(v7) = 0 & function(v4) = 0 & empty(v8) = 0 & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (transitive(v10) = 0) | ~ (ordered_pair(v11, v13) = v15) | ~ (ordered_pair(v11, v12) = v14) | ~ (in(v15, v10) = v16) | ~ (in(v14, v10) = 0) | ? [v17] : ? [v18] : (( ~ (v18 = 0) & ordered_pair(v12, v13) = v17 & in(v17, v10) = v18) | ( ~ (v17 = 0) & relation(v10) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ (in(v14, v15) = v16) | ? [v17] : ? [v18] : (in(v11, v13) = v18 & in(v10, v12) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ (in(v14, v15) = 0) | (in(v11, v13) = 0 & in(v10, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_restriction(v12, v11) = v13) | ~ (in(v10, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (cartesian_product2(v11, v11) = v17 & relation(v12) = v15 & in(v10, v17) = v18 & in(v10, v12) = v16 & ( ~ (v15 = 0) | (( ~ (v18 = 0) | ~ (v16 = 0) | v14 = 0) & ( ~ (v14 = 0) | (v18 = 0 & v16 = 0)))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v10) = v13) | ~ (unordered_pair(v12, v13) = v14) | ~ (unordered_pair(v10, v11) = v12) | ordered_pair(v10, v11) = v14) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (element(v13, v12) = v11) | ~ (element(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (relation_restriction(v13, v12) = v11) | ~ (relation_restriction(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_intersection2(v13, v12) = v11) | ~ (set_intersection2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v11, v11) = v12) | ~ (set_intersection2(v10, v12) = v13) | ~ (relation(v10) = 0) | relation_restriction(v10, v11) = v13) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (element(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (transitive(v12) = v11) | ~ (transitive(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (one_to_one(v12) = v11) | ~ (one_to_one(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation(v12) = v11) | ~ (relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (function(v12) = v11) | ~ (function(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_restriction(v10, v11) = v12) | ? [v13] : ? [v14] : (relation(v12) = v14 & relation(v10) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | set_intersection2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_intersection2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (empty(v11) = 0) | ~ (empty(v10) = 0)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_intersection2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (transitive(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v18 = 0 & v16 = 0 & ~ (v20 = 0) & ordered_pair(v13, v14) = v17 & ordered_pair(v12, v14) = v19 & ordered_pair(v12, v13) = v15 & in(v19, v10) = v20 & in(v17, v10) = 0 & in(v15, v10) = 0) | ( ~ (v12 = 0) & relation(v10) = v12))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (function(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v10) = v12)) & ! [v10] : ! [v11] : ( ~ (element(v10, v11) = 0) | ? [v12] : ? [v13] : (empty(v11) = v12 & in(v10, v11) = v13 & (v13 = 0 | v12 = 0))) & ! [v10] : ! [v11] : ( ~ (one_to_one(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (relation(v10) = v12 & function(v10) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | v11 = 0))) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v10] : (v10 = empty_set | ~ (empty(v10) = 0)) & ? [v10] : ? [v11] : element(v11, v10) = 0)
% 25.37/6.73 | 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 yields:
% 25.37/6.73 | (1) ~ (all_0_3_3 = 0) & ~ (all_0_6_6 = 0) & transitive(all_0_7_7) = all_0_6_6 & transitive(all_0_8_8) = 0 & relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7 & one_to_one(all_0_5_5) = 0 & relation(all_0_0_0) = 0 & relation(all_0_2_2) = 0 & relation(all_0_5_5) = 0 & relation(all_0_8_8) = 0 & function(all_0_0_0) = 0 & function(all_0_2_2) = 0 & function(all_0_5_5) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_4_4) = all_0_3_3 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (transitive(v0) = 0) | ~ (ordered_pair(v1, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ (in(v5, v0) = v6) | ~ (in(v4, v0) = 0) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & ordered_pair(v2, v3) = v7 & in(v7, v0) = v8) | ( ~ (v7 = 0) & relation(v0) = v7))) & ! [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] : ( ~ (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] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cartesian_product2(v1, v1) = v7 & relation(v2) = v5 & in(v0, v7) = v8 & in(v0, v2) = v6 & ( ~ (v5 = 0) | (( ~ (v8 = 0) | ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v8 = 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] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(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 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(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 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(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 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (set_intersection2(v0, v2) = v3) | ~ (relation(v0) = 0) | relation_restriction(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [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 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (transitive(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & v6 = 0 & ~ (v10 = 0) & ordered_pair(v3, v4) = v7 & ordered_pair(v2, v4) = v9 & ordered_pair(v2, v3) = v5 & in(v9, v0) = v10 & in(v7, v0) = 0 & in(v5, v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | 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] : ? [v1] : element(v1, v0) = 0
% 25.37/6.74 |
% 25.37/6.74 | Applying alpha-rule on (1) yields:
% 25.37/6.74 | (2) ~ (all_0_3_3 = 0)
% 25.37/6.74 | (3) empty(empty_set) = 0
% 25.37/6.74 | (4) empty(all_0_1_1) = 0
% 25.37/6.74 | (5) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 25.37/6.74 | (6) relation(all_0_8_8) = 0
% 25.37/6.74 | (7) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 25.37/6.74 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 25.37/6.74 | (9) transitive(all_0_8_8) = 0
% 25.37/6.74 | (10) empty(all_0_4_4) = all_0_3_3
% 25.37/6.74 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 25.37/6.74 | (12) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 25.37/6.74 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 25.37/6.74 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 25.37/6.74 | (15) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 25.37/6.74 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 25.37/6.74 | (17) transitive(all_0_7_7) = all_0_6_6
% 25.37/6.74 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cartesian_product2(v1, v1) = v7 & relation(v2) = v5 & in(v0, v7) = v8 & in(v0, v2) = v6 & ( ~ (v5 = 0) | (( ~ (v8 = 0) | ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0))))))
% 25.37/6.74 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (transitive(v0) = 0) | ~ (ordered_pair(v1, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ (in(v5, v0) = v6) | ~ (in(v4, v0) = 0) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & ordered_pair(v2, v3) = v7 & in(v7, v0) = v8) | ( ~ (v7 = 0) & relation(v0) = v7)))
% 25.37/6.74 | (20) function(all_0_2_2) = 0
% 25.37/6.75 | (21) function(all_0_0_0) = 0
% 25.37/6.75 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 25.37/6.75 | (23) ? [v0] : ? [v1] : element(v1, v0) = 0
% 25.37/6.75 | (24) empty(all_0_2_2) = 0
% 25.37/6.75 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0))
% 25.37/6.75 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 25.37/6.75 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 25.37/6.75 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 25.37/6.75 | (29) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 25.37/6.75 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 25.37/6.75 | (31) relation(all_0_2_2) = 0
% 25.37/6.75 | (32) relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7
% 25.37/6.75 | (33) one_to_one(all_0_5_5) = 0
% 25.37/6.75 | (34) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 25.37/6.75 | (35) ! [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))
% 25.37/6.75 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 25.37/6.75 | (37) ! [v0] : ! [v1] : (v1 = 0 | ~ (transitive(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & v6 = 0 & ~ (v10 = 0) & ordered_pair(v3, v4) = v7 & ordered_pair(v2, v4) = v9 & ordered_pair(v2, v3) = v5 & in(v9, v0) = v10 & in(v7, v0) = 0 & in(v5, v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 25.37/6.75 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 25.37/6.75 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 25.37/6.75 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 25.37/6.75 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 25.37/6.75 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = v0))
% 25.37/6.75 | (43) function(all_0_5_5) = 0
% 25.37/6.75 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 25.37/6.75 | (45) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 25.37/6.75 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (set_intersection2(v0, v2) = v3) | ~ (relation(v0) = 0) | relation_restriction(v0, v1) = v3)
% 25.37/6.75 | (47) ~ (all_0_6_6 = 0)
% 25.37/6.75 | (48) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 25.37/6.75 | (49) relation(all_0_5_5) = 0
% 25.37/6.75 | (50) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 25.37/6.75 | (51) ! [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))))
% 25.37/6.75 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 25.37/6.75 | (53) relation(all_0_0_0) = 0
% 25.37/6.75 |
% 25.37/6.75 | Instantiating formula (37) with all_0_6_6, all_0_7_7 and discharging atoms transitive(all_0_7_7) = all_0_6_6, yields:
% 25.37/6.75 | (54) all_0_6_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v4 = 0 & ~ (v8 = 0) & ordered_pair(v1, v2) = v5 & ordered_pair(v0, v2) = v7 & ordered_pair(v0, v1) = v3 & in(v7, all_0_7_7) = v8 & in(v5, all_0_7_7) = 0 & in(v3, all_0_7_7) = 0) | ( ~ (v0 = 0) & relation(all_0_7_7) = v0))
% 25.37/6.75 |
% 25.37/6.75 | Instantiating formula (8) with all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, yields:
% 25.37/6.75 | (55) ? [v0] : ? [v1] : (relation(all_0_7_7) = v1 & relation(all_0_8_8) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 25.37/6.75 |
% 25.37/6.75 | Instantiating (55) with all_16_0_15, all_16_1_16 yields:
% 25.37/6.75 | (56) relation(all_0_7_7) = all_16_0_15 & relation(all_0_8_8) = all_16_1_16 & ( ~ (all_16_1_16 = 0) | all_16_0_15 = 0)
% 25.37/6.75 |
% 25.37/6.75 | Applying alpha-rule on (56) yields:
% 25.37/6.75 | (57) relation(all_0_7_7) = all_16_0_15
% 25.37/6.75 | (58) relation(all_0_8_8) = all_16_1_16
% 25.37/6.75 | (59) ~ (all_16_1_16 = 0) | all_16_0_15 = 0
% 25.37/6.75 |
% 25.37/6.75 +-Applying beta-rule and splitting (54), into two cases.
% 25.37/6.75 |-Branch one:
% 25.37/6.75 | (60) all_0_6_6 = 0
% 25.37/6.75 |
% 25.37/6.76 | Equations (60) can reduce 47 to:
% 25.37/6.76 | (61) $false
% 25.37/6.76 |
% 25.37/6.76 |-The branch is then unsatisfiable
% 25.37/6.76 |-Branch two:
% 25.37/6.76 | (47) ~ (all_0_6_6 = 0)
% 25.37/6.76 | (63) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v4 = 0 & ~ (v8 = 0) & ordered_pair(v1, v2) = v5 & ordered_pair(v0, v2) = v7 & ordered_pair(v0, v1) = v3 & in(v7, all_0_7_7) = v8 & in(v5, all_0_7_7) = 0 & in(v3, all_0_7_7) = 0) | ( ~ (v0 = 0) & relation(all_0_7_7) = v0))
% 25.37/6.76 |
% 25.37/6.76 | Instantiating (63) with all_24_0_19, all_24_1_20, all_24_2_21, all_24_3_22, all_24_4_23, all_24_5_24, all_24_6_25, all_24_7_26, all_24_8_27 yields:
% 25.37/6.76 | (64) (all_24_2_21 = 0 & all_24_4_23 = 0 & ~ (all_24_0_19 = 0) & ordered_pair(all_24_7_26, all_24_6_25) = all_24_3_22 & ordered_pair(all_24_8_27, all_24_6_25) = all_24_1_20 & ordered_pair(all_24_8_27, all_24_7_26) = all_24_5_24 & in(all_24_1_20, all_0_7_7) = all_24_0_19 & in(all_24_3_22, all_0_7_7) = 0 & in(all_24_5_24, all_0_7_7) = 0) | ( ~ (all_24_8_27 = 0) & relation(all_0_7_7) = all_24_8_27)
% 25.37/6.76 |
% 25.37/6.76 | Instantiating formula (26) with all_0_8_8, all_16_1_16, 0 and discharging atoms relation(all_0_8_8) = all_16_1_16, relation(all_0_8_8) = 0, yields:
% 25.37/6.76 | (65) all_16_1_16 = 0
% 25.37/6.76 |
% 25.37/6.76 | From (65) and (58) follows:
% 25.37/6.76 | (6) relation(all_0_8_8) = 0
% 25.37/6.76 |
% 25.37/6.76 +-Applying beta-rule and splitting (59), into two cases.
% 25.37/6.76 |-Branch one:
% 25.37/6.76 | (67) ~ (all_16_1_16 = 0)
% 25.37/6.76 |
% 25.37/6.76 | Equations (65) can reduce 67 to:
% 25.37/6.76 | (61) $false
% 25.37/6.76 |
% 25.37/6.76 |-The branch is then unsatisfiable
% 25.37/6.76 |-Branch two:
% 25.37/6.76 | (65) all_16_1_16 = 0
% 25.37/6.76 | (70) all_16_0_15 = 0
% 25.37/6.76 |
% 25.37/6.76 | From (70) and (57) follows:
% 25.37/6.76 | (71) relation(all_0_7_7) = 0
% 25.37/6.76 |
% 25.37/6.76 +-Applying beta-rule and splitting (64), into two cases.
% 25.37/6.76 |-Branch one:
% 25.37/6.76 | (72) all_24_2_21 = 0 & all_24_4_23 = 0 & ~ (all_24_0_19 = 0) & ordered_pair(all_24_7_26, all_24_6_25) = all_24_3_22 & ordered_pair(all_24_8_27, all_24_6_25) = all_24_1_20 & ordered_pair(all_24_8_27, all_24_7_26) = all_24_5_24 & in(all_24_1_20, all_0_7_7) = all_24_0_19 & in(all_24_3_22, all_0_7_7) = 0 & in(all_24_5_24, all_0_7_7) = 0
% 25.37/6.76 |
% 25.37/6.76 | Applying alpha-rule on (72) yields:
% 25.37/6.76 | (73) ordered_pair(all_24_8_27, all_24_6_25) = all_24_1_20
% 25.37/6.76 | (74) in(all_24_3_22, all_0_7_7) = 0
% 25.37/6.76 | (75) all_24_4_23 = 0
% 25.37/6.76 | (76) ordered_pair(all_24_7_26, all_24_6_25) = all_24_3_22
% 25.37/6.76 | (77) in(all_24_5_24, all_0_7_7) = 0
% 25.37/6.76 | (78) all_24_2_21 = 0
% 25.37/6.76 | (79) ~ (all_24_0_19 = 0)
% 25.37/6.76 | (80) ordered_pair(all_24_8_27, all_24_7_26) = all_24_5_24
% 25.37/6.76 | (81) in(all_24_1_20, all_0_7_7) = all_24_0_19
% 25.37/6.76 |
% 25.37/6.76 | Instantiating formula (18) with all_24_0_19, all_0_7_7, all_0_8_8, all_0_9_9, all_24_1_20 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, in(all_24_1_20, all_0_7_7) = all_24_0_19, yields:
% 25.37/6.76 | (82) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (cartesian_product2(all_0_9_9, all_0_9_9) = v2 & relation(all_0_8_8) = v0 & in(all_24_1_20, v2) = v3 & in(all_24_1_20, all_0_8_8) = v1 & ( ~ (v0 = 0) | (( ~ (v3 = 0) | ~ (v1 = 0) | all_24_0_19 = 0) & ( ~ (all_24_0_19 = 0) | (v3 = 0 & v1 = 0)))))
% 25.37/6.76 |
% 25.37/6.76 | Instantiating formula (18) with 0, all_0_7_7, all_0_8_8, all_0_9_9, all_24_3_22 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, in(all_24_3_22, all_0_7_7) = 0, yields:
% 25.37/6.76 | (83) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (cartesian_product2(all_0_9_9, all_0_9_9) = v2 & relation(all_0_8_8) = v0 & in(all_24_3_22, v2) = v3 & in(all_24_3_22, all_0_8_8) = v1 & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0)))
% 25.37/6.76 |
% 25.37/6.76 | Instantiating formula (18) with 0, all_0_7_7, all_0_8_8, all_0_9_9, all_24_5_24 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, in(all_24_5_24, all_0_7_7) = 0, yields:
% 25.37/6.76 | (84) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (cartesian_product2(all_0_9_9, all_0_9_9) = v2 & relation(all_0_8_8) = v0 & in(all_24_5_24, v2) = v3 & in(all_24_5_24, all_0_8_8) = v1 & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0)))
% 25.37/6.76 |
% 25.37/6.76 | Instantiating (84) with all_44_0_29, all_44_1_30, all_44_2_31, all_44_3_32 yields:
% 25.37/6.76 | (85) cartesian_product2(all_0_9_9, all_0_9_9) = all_44_1_30 & relation(all_0_8_8) = all_44_3_32 & in(all_24_5_24, all_44_1_30) = all_44_0_29 & in(all_24_5_24, all_0_8_8) = all_44_2_31 & ( ~ (all_44_3_32 = 0) | (all_44_0_29 = 0 & all_44_2_31 = 0))
% 25.37/6.76 |
% 25.37/6.76 | Applying alpha-rule on (85) yields:
% 25.37/6.76 | (86) in(all_24_5_24, all_44_1_30) = all_44_0_29
% 25.37/6.76 | (87) ~ (all_44_3_32 = 0) | (all_44_0_29 = 0 & all_44_2_31 = 0)
% 25.37/6.76 | (88) relation(all_0_8_8) = all_44_3_32
% 25.37/6.76 | (89) in(all_24_5_24, all_0_8_8) = all_44_2_31
% 25.37/6.76 | (90) cartesian_product2(all_0_9_9, all_0_9_9) = all_44_1_30
% 25.37/6.76 |
% 25.37/6.76 | Instantiating (82) with all_48_0_34, all_48_1_35, all_48_2_36, all_48_3_37 yields:
% 25.37/6.76 | (91) cartesian_product2(all_0_9_9, all_0_9_9) = all_48_1_35 & relation(all_0_8_8) = all_48_3_37 & in(all_24_1_20, all_48_1_35) = all_48_0_34 & in(all_24_1_20, all_0_8_8) = all_48_2_36 & ( ~ (all_48_3_37 = 0) | (( ~ (all_48_0_34 = 0) | ~ (all_48_2_36 = 0) | all_24_0_19 = 0) & ( ~ (all_24_0_19 = 0) | (all_48_0_34 = 0 & all_48_2_36 = 0))))
% 25.37/6.76 |
% 25.37/6.76 | Applying alpha-rule on (91) yields:
% 25.37/6.76 | (92) in(all_24_1_20, all_48_1_35) = all_48_0_34
% 25.37/6.76 | (93) in(all_24_1_20, all_0_8_8) = all_48_2_36
% 25.37/6.76 | (94) relation(all_0_8_8) = all_48_3_37
% 25.37/6.76 | (95) ~ (all_48_3_37 = 0) | (( ~ (all_48_0_34 = 0) | ~ (all_48_2_36 = 0) | all_24_0_19 = 0) & ( ~ (all_24_0_19 = 0) | (all_48_0_34 = 0 & all_48_2_36 = 0)))
% 25.37/6.76 | (96) cartesian_product2(all_0_9_9, all_0_9_9) = all_48_1_35
% 25.37/6.76 |
% 25.37/6.76 | Instantiating (83) with all_58_0_42, all_58_1_43, all_58_2_44, all_58_3_45 yields:
% 25.37/6.76 | (97) cartesian_product2(all_0_9_9, all_0_9_9) = all_58_1_43 & relation(all_0_8_8) = all_58_3_45 & in(all_24_3_22, all_58_1_43) = all_58_0_42 & in(all_24_3_22, all_0_8_8) = all_58_2_44 & ( ~ (all_58_3_45 = 0) | (all_58_0_42 = 0 & all_58_2_44 = 0))
% 25.37/6.76 |
% 25.37/6.77 | Applying alpha-rule on (97) yields:
% 25.37/6.77 | (98) cartesian_product2(all_0_9_9, all_0_9_9) = all_58_1_43
% 25.37/6.77 | (99) in(all_24_3_22, all_58_1_43) = all_58_0_42
% 25.37/6.77 | (100) in(all_24_3_22, all_0_8_8) = all_58_2_44
% 25.37/6.77 | (101) ~ (all_58_3_45 = 0) | (all_58_0_42 = 0 & all_58_2_44 = 0)
% 25.37/6.77 | (102) relation(all_0_8_8) = all_58_3_45
% 25.37/6.77 |
% 25.37/6.77 | Instantiating formula (30) with all_0_9_9, all_0_9_9, all_48_1_35, all_58_1_43 and discharging atoms cartesian_product2(all_0_9_9, all_0_9_9) = all_58_1_43, cartesian_product2(all_0_9_9, all_0_9_9) = all_48_1_35, yields:
% 25.37/6.77 | (103) all_58_1_43 = all_48_1_35
% 25.37/6.77 |
% 25.37/6.77 | Instantiating formula (30) with all_0_9_9, all_0_9_9, all_44_1_30, all_58_1_43 and discharging atoms cartesian_product2(all_0_9_9, all_0_9_9) = all_58_1_43, cartesian_product2(all_0_9_9, all_0_9_9) = all_44_1_30, yields:
% 25.37/6.77 | (104) all_58_1_43 = all_44_1_30
% 25.37/6.77 |
% 25.37/6.77 | Instantiating formula (26) with all_0_8_8, all_48_3_37, 0 and discharging atoms relation(all_0_8_8) = all_48_3_37, relation(all_0_8_8) = 0, yields:
% 25.37/6.77 | (105) all_48_3_37 = 0
% 25.37/6.77 |
% 25.37/6.77 | Instantiating formula (26) with all_0_8_8, all_48_3_37, all_58_3_45 and discharging atoms relation(all_0_8_8) = all_58_3_45, relation(all_0_8_8) = all_48_3_37, yields:
% 25.37/6.77 | (106) all_58_3_45 = all_48_3_37
% 25.37/6.77 |
% 25.37/6.77 | Instantiating formula (26) with all_0_8_8, all_44_3_32, all_58_3_45 and discharging atoms relation(all_0_8_8) = all_58_3_45, relation(all_0_8_8) = all_44_3_32, yields:
% 25.37/6.77 | (107) all_58_3_45 = all_44_3_32
% 25.37/6.77 |
% 25.37/6.77 | Combining equations (103,104) yields a new equation:
% 25.37/6.77 | (108) all_48_1_35 = all_44_1_30
% 25.37/6.77 |
% 25.37/6.77 | Simplifying 108 yields:
% 25.37/6.77 | (109) all_48_1_35 = all_44_1_30
% 25.37/6.77 |
% 25.37/6.77 | Combining equations (106,107) yields a new equation:
% 25.37/6.77 | (110) all_48_3_37 = all_44_3_32
% 25.37/6.77 |
% 25.37/6.77 | Simplifying 110 yields:
% 25.37/6.77 | (111) all_48_3_37 = all_44_3_32
% 25.37/6.77 |
% 25.37/6.77 | Combining equations (105,111) yields a new equation:
% 25.37/6.77 | (112) all_44_3_32 = 0
% 25.37/6.77 |
% 25.37/6.77 | Combining equations (112,111) yields a new equation:
% 25.37/6.77 | (105) all_48_3_37 = 0
% 25.37/6.77 |
% 25.37/6.77 | Combining equations (112,107) yields a new equation:
% 25.37/6.77 | (114) all_58_3_45 = 0
% 25.37/6.77 |
% 25.37/6.77 | From (109) and (96) follows:
% 25.37/6.77 | (90) cartesian_product2(all_0_9_9, all_0_9_9) = all_44_1_30
% 25.37/6.77 |
% 25.37/6.77 | From (112) and (88) follows:
% 25.37/6.77 | (6) relation(all_0_8_8) = 0
% 25.37/6.77 |
% 25.37/6.77 | From (109) and (92) follows:
% 25.37/6.77 | (117) in(all_24_1_20, all_44_1_30) = all_48_0_34
% 25.37/6.77 |
% 25.37/6.77 | From (104) and (99) follows:
% 25.37/6.77 | (118) in(all_24_3_22, all_44_1_30) = all_58_0_42
% 25.37/6.77 |
% 25.37/6.77 +-Applying beta-rule and splitting (101), into two cases.
% 25.37/6.77 |-Branch one:
% 25.37/6.77 | (119) ~ (all_58_3_45 = 0)
% 25.37/6.77 |
% 25.37/6.77 | Equations (114) can reduce 119 to:
% 25.37/6.77 | (61) $false
% 25.37/6.77 |
% 25.37/6.77 |-The branch is then unsatisfiable
% 25.37/6.77 |-Branch two:
% 25.37/6.77 | (114) all_58_3_45 = 0
% 25.37/6.77 | (122) all_58_0_42 = 0 & all_58_2_44 = 0
% 25.37/6.77 |
% 25.37/6.77 | Applying alpha-rule on (122) yields:
% 25.37/6.77 | (123) all_58_0_42 = 0
% 25.37/6.77 | (124) all_58_2_44 = 0
% 25.37/6.77 |
% 25.37/6.77 | From (123) and (118) follows:
% 25.37/6.77 | (125) in(all_24_3_22, all_44_1_30) = 0
% 25.37/6.77 |
% 25.37/6.77 | From (124) and (100) follows:
% 25.37/6.77 | (126) in(all_24_3_22, all_0_8_8) = 0
% 25.37/6.77 |
% 25.37/6.77 +-Applying beta-rule and splitting (87), into two cases.
% 25.37/6.77 |-Branch one:
% 25.37/6.77 | (127) ~ (all_44_3_32 = 0)
% 25.37/6.77 |
% 25.37/6.77 | Equations (112) can reduce 127 to:
% 25.37/6.77 | (61) $false
% 25.37/6.77 |
% 25.37/6.77 |-The branch is then unsatisfiable
% 25.37/6.77 |-Branch two:
% 25.37/6.77 | (112) all_44_3_32 = 0
% 25.37/6.77 | (130) all_44_0_29 = 0 & all_44_2_31 = 0
% 25.37/6.77 |
% 25.37/6.77 | Applying alpha-rule on (130) yields:
% 25.37/6.77 | (131) all_44_0_29 = 0
% 25.37/6.77 | (132) all_44_2_31 = 0
% 25.37/6.77 |
% 25.37/6.77 | From (131) and (86) follows:
% 25.37/6.77 | (133) in(all_24_5_24, all_44_1_30) = 0
% 25.37/6.77 |
% 25.37/6.77 | From (132) and (89) follows:
% 25.37/6.77 | (134) in(all_24_5_24, all_0_8_8) = 0
% 25.37/6.77 |
% 25.37/6.77 | Instantiating formula (51) with all_48_0_34, all_44_1_30, all_24_1_20, all_0_9_9, all_0_9_9, all_24_6_25, all_24_8_27 and discharging atoms cartesian_product2(all_0_9_9, all_0_9_9) = all_44_1_30, ordered_pair(all_24_8_27, all_24_6_25) = all_24_1_20, in(all_24_1_20, all_44_1_30) = all_48_0_34, yields:
% 25.37/6.77 | (135) all_48_0_34 = 0 | ? [v0] : ? [v1] : (in(all_24_6_25, all_0_9_9) = v1 & in(all_24_8_27, all_0_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 25.37/6.77 |
% 25.37/6.77 | Instantiating formula (35) with all_44_1_30, all_24_3_22, all_0_9_9, all_0_9_9, all_24_6_25, all_24_7_26 and discharging atoms cartesian_product2(all_0_9_9, all_0_9_9) = all_44_1_30, ordered_pair(all_24_7_26, all_24_6_25) = all_24_3_22, in(all_24_3_22, all_44_1_30) = 0, yields:
% 25.37/6.77 | (136) in(all_24_6_25, all_0_9_9) = 0 & in(all_24_7_26, all_0_9_9) = 0
% 25.37/6.77 |
% 25.37/6.77 | Applying alpha-rule on (136) yields:
% 25.37/6.77 | (137) in(all_24_6_25, all_0_9_9) = 0
% 25.37/6.77 | (138) in(all_24_7_26, all_0_9_9) = 0
% 25.37/6.77 |
% 25.37/6.77 | Instantiating formula (35) with all_44_1_30, all_24_5_24, all_0_9_9, all_0_9_9, all_24_7_26, all_24_8_27 and discharging atoms cartesian_product2(all_0_9_9, all_0_9_9) = all_44_1_30, ordered_pair(all_24_8_27, all_24_7_26) = all_24_5_24, in(all_24_5_24, all_44_1_30) = 0, yields:
% 25.37/6.77 | (139) in(all_24_7_26, all_0_9_9) = 0 & in(all_24_8_27, all_0_9_9) = 0
% 25.37/6.77 |
% 25.37/6.77 | Applying alpha-rule on (139) yields:
% 25.37/6.77 | (138) in(all_24_7_26, all_0_9_9) = 0
% 25.37/6.77 | (141) in(all_24_8_27, all_0_9_9) = 0
% 25.37/6.77 |
% 25.37/6.77 | Instantiating formula (19) with all_48_2_36, all_24_1_20, all_24_5_24, all_24_6_25, all_24_7_26, all_24_8_27, all_0_8_8 and discharging atoms transitive(all_0_8_8) = 0, ordered_pair(all_24_8_27, all_24_6_25) = all_24_1_20, ordered_pair(all_24_8_27, all_24_7_26) = all_24_5_24, in(all_24_1_20, all_0_8_8) = all_48_2_36, in(all_24_5_24, all_0_8_8) = 0, yields:
% 25.37/6.77 | (142) all_48_2_36 = 0 | ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_24_7_26, all_24_6_25) = v0 & in(v0, all_0_8_8) = v1) | ( ~ (v0 = 0) & relation(all_0_8_8) = v0))
% 25.37/6.77 |
% 25.37/6.77 +-Applying beta-rule and splitting (135), into two cases.
% 25.37/6.77 |-Branch one:
% 25.37/6.77 | (143) all_48_0_34 = 0
% 25.37/6.77 |
% 25.37/6.77 +-Applying beta-rule and splitting (142), into two cases.
% 25.37/6.77 |-Branch one:
% 25.37/6.77 | (144) all_48_2_36 = 0
% 25.37/6.78 |
% 25.37/6.78 +-Applying beta-rule and splitting (95), into two cases.
% 25.37/6.78 |-Branch one:
% 25.37/6.78 | (145) ~ (all_48_3_37 = 0)
% 25.37/6.78 |
% 25.37/6.78 | Equations (105) can reduce 145 to:
% 25.37/6.78 | (61) $false
% 25.37/6.78 |
% 25.37/6.78 |-The branch is then unsatisfiable
% 25.37/6.78 |-Branch two:
% 25.37/6.78 | (105) all_48_3_37 = 0
% 25.37/6.78 | (148) ( ~ (all_48_0_34 = 0) | ~ (all_48_2_36 = 0) | all_24_0_19 = 0) & ( ~ (all_24_0_19 = 0) | (all_48_0_34 = 0 & all_48_2_36 = 0))
% 25.37/6.78 |
% 25.37/6.78 | Applying alpha-rule on (148) yields:
% 25.37/6.78 | (149) ~ (all_48_0_34 = 0) | ~ (all_48_2_36 = 0) | all_24_0_19 = 0
% 25.37/6.78 | (150) ~ (all_24_0_19 = 0) | (all_48_0_34 = 0 & all_48_2_36 = 0)
% 25.37/6.78 |
% 25.37/6.78 +-Applying beta-rule and splitting (149), into two cases.
% 25.37/6.78 |-Branch one:
% 25.37/6.78 | (151) ~ (all_48_0_34 = 0)
% 25.37/6.78 |
% 25.37/6.78 | Equations (143) can reduce 151 to:
% 25.37/6.78 | (61) $false
% 25.37/6.78 |
% 25.37/6.78 |-The branch is then unsatisfiable
% 25.37/6.78 |-Branch two:
% 25.37/6.78 | (143) all_48_0_34 = 0
% 25.37/6.78 | (154) ~ (all_48_2_36 = 0) | all_24_0_19 = 0
% 25.37/6.78 |
% 25.37/6.78 +-Applying beta-rule and splitting (154), into two cases.
% 25.37/6.78 |-Branch one:
% 25.37/6.78 | (155) ~ (all_48_2_36 = 0)
% 25.37/6.78 |
% 25.37/6.78 | Equations (144) can reduce 155 to:
% 25.37/6.78 | (61) $false
% 25.37/6.78 |
% 25.37/6.78 |-The branch is then unsatisfiable
% 25.37/6.78 |-Branch two:
% 25.37/6.78 | (144) all_48_2_36 = 0
% 25.37/6.78 | (158) all_24_0_19 = 0
% 25.37/6.78 |
% 25.37/6.78 | Equations (158) can reduce 79 to:
% 25.37/6.78 | (61) $false
% 25.37/6.78 |
% 25.37/6.78 |-The branch is then unsatisfiable
% 25.37/6.78 |-Branch two:
% 25.37/6.78 | (155) ~ (all_48_2_36 = 0)
% 25.37/6.78 | (161) ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_24_7_26, all_24_6_25) = v0 & in(v0, all_0_8_8) = v1) | ( ~ (v0 = 0) & relation(all_0_8_8) = v0))
% 25.37/6.78 |
% 25.37/6.78 | Instantiating (161) with all_98_0_54, all_98_1_55 yields:
% 25.37/6.78 | (162) ( ~ (all_98_0_54 = 0) & ordered_pair(all_24_7_26, all_24_6_25) = all_98_1_55 & in(all_98_1_55, all_0_8_8) = all_98_0_54) | ( ~ (all_98_1_55 = 0) & relation(all_0_8_8) = all_98_1_55)
% 25.37/6.78 |
% 25.37/6.78 +-Applying beta-rule and splitting (162), into two cases.
% 25.37/6.78 |-Branch one:
% 25.37/6.78 | (163) ~ (all_98_0_54 = 0) & ordered_pair(all_24_7_26, all_24_6_25) = all_98_1_55 & in(all_98_1_55, all_0_8_8) = all_98_0_54
% 25.37/6.78 |
% 25.37/6.78 | Applying alpha-rule on (163) yields:
% 25.37/6.78 | (164) ~ (all_98_0_54 = 0)
% 25.37/6.78 | (165) ordered_pair(all_24_7_26, all_24_6_25) = all_98_1_55
% 25.37/6.78 | (166) in(all_98_1_55, all_0_8_8) = all_98_0_54
% 25.37/6.78 |
% 25.37/6.78 | Instantiating formula (13) with all_24_7_26, all_24_6_25, all_98_1_55, all_24_3_22 and discharging atoms ordered_pair(all_24_7_26, all_24_6_25) = all_98_1_55, ordered_pair(all_24_7_26, all_24_6_25) = all_24_3_22, yields:
% 25.37/6.78 | (167) all_98_1_55 = all_24_3_22
% 25.37/6.78 |
% 25.37/6.78 | Instantiating formula (22) with all_24_3_22, all_0_8_8, all_98_0_54, 0 and discharging atoms in(all_24_3_22, all_0_8_8) = 0, yields:
% 25.37/6.78 | (168) all_98_0_54 = 0 | ~ (in(all_24_3_22, all_0_8_8) = all_98_0_54)
% 25.37/6.78 |
% 25.37/6.78 | From (167) and (166) follows:
% 25.37/6.78 | (169) in(all_24_3_22, all_0_8_8) = all_98_0_54
% 25.37/6.78 |
% 25.37/6.78 +-Applying beta-rule and splitting (168), into two cases.
% 25.37/6.78 |-Branch one:
% 25.37/6.78 | (170) ~ (in(all_24_3_22, all_0_8_8) = all_98_0_54)
% 25.37/6.78 |
% 25.37/6.78 | Using (169) and (170) yields:
% 25.37/6.78 | (171) $false
% 25.37/6.78 |
% 25.37/6.78 |-The branch is then unsatisfiable
% 25.37/6.78 |-Branch two:
% 25.37/6.78 | (169) in(all_24_3_22, all_0_8_8) = all_98_0_54
% 25.37/6.78 | (173) all_98_0_54 = 0
% 25.37/6.78 |
% 25.37/6.78 | Equations (173) can reduce 164 to:
% 25.37/6.78 | (61) $false
% 25.37/6.78 |
% 25.37/6.78 |-The branch is then unsatisfiable
% 25.37/6.78 |-Branch two:
% 25.37/6.78 | (175) ~ (all_98_1_55 = 0) & relation(all_0_8_8) = all_98_1_55
% 25.37/6.78 |
% 25.37/6.78 | Applying alpha-rule on (175) yields:
% 25.37/6.78 | (176) ~ (all_98_1_55 = 0)
% 25.37/6.78 | (177) relation(all_0_8_8) = all_98_1_55
% 25.37/6.78 |
% 25.37/6.78 | Instantiating formula (26) with all_0_8_8, all_98_1_55, 0 and discharging atoms relation(all_0_8_8) = all_98_1_55, relation(all_0_8_8) = 0, yields:
% 25.37/6.78 | (178) all_98_1_55 = 0
% 25.37/6.78 |
% 25.37/6.78 | Equations (178) can reduce 176 to:
% 25.37/6.78 | (61) $false
% 25.37/6.78 |
% 25.37/6.78 |-The branch is then unsatisfiable
% 25.37/6.78 |-Branch two:
% 25.37/6.78 | (151) ~ (all_48_0_34 = 0)
% 25.37/6.78 | (181) ? [v0] : ? [v1] : (in(all_24_6_25, all_0_9_9) = v1 & in(all_24_8_27, all_0_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 25.37/6.78 |
% 25.37/6.78 | Instantiating (181) with all_94_0_58, all_94_1_59 yields:
% 25.37/6.78 | (182) in(all_24_6_25, all_0_9_9) = all_94_0_58 & in(all_24_8_27, all_0_9_9) = all_94_1_59 & ( ~ (all_94_0_58 = 0) | ~ (all_94_1_59 = 0))
% 25.37/6.78 |
% 25.37/6.78 | Applying alpha-rule on (182) yields:
% 25.37/6.78 | (183) in(all_24_6_25, all_0_9_9) = all_94_0_58
% 25.37/6.78 | (184) in(all_24_8_27, all_0_9_9) = all_94_1_59
% 25.37/6.78 | (185) ~ (all_94_0_58 = 0) | ~ (all_94_1_59 = 0)
% 25.37/6.78 |
% 25.37/6.78 | Instantiating formula (22) with all_24_6_25, all_0_9_9, 0, all_94_0_58 and discharging atoms in(all_24_6_25, all_0_9_9) = all_94_0_58, in(all_24_6_25, all_0_9_9) = 0, yields:
% 25.37/6.78 | (186) all_94_0_58 = 0
% 25.37/6.78 |
% 25.37/6.78 | Instantiating formula (22) with all_24_8_27, all_0_9_9, all_94_1_59, 0 and discharging atoms in(all_24_8_27, all_0_9_9) = all_94_1_59, in(all_24_8_27, all_0_9_9) = 0, yields:
% 25.37/6.78 | (187) all_94_1_59 = 0
% 25.37/6.78 |
% 25.37/6.78 +-Applying beta-rule and splitting (185), into two cases.
% 25.37/6.78 |-Branch one:
% 25.37/6.78 | (188) ~ (all_94_0_58 = 0)
% 25.37/6.78 |
% 25.37/6.78 | Equations (186) can reduce 188 to:
% 25.37/6.78 | (61) $false
% 25.37/6.78 |
% 25.37/6.78 |-The branch is then unsatisfiable
% 25.37/6.78 |-Branch two:
% 25.37/6.78 | (186) all_94_0_58 = 0
% 25.37/6.78 | (191) ~ (all_94_1_59 = 0)
% 25.37/6.78 |
% 25.37/6.78 | Equations (187) can reduce 191 to:
% 25.37/6.78 | (61) $false
% 25.37/6.78 |
% 25.37/6.78 |-The branch is then unsatisfiable
% 25.37/6.78 |-Branch two:
% 25.37/6.78 | (193) ~ (all_24_8_27 = 0) & relation(all_0_7_7) = all_24_8_27
% 25.37/6.78 |
% 25.37/6.78 | Applying alpha-rule on (193) yields:
% 25.37/6.78 | (194) ~ (all_24_8_27 = 0)
% 25.37/6.78 | (195) relation(all_0_7_7) = all_24_8_27
% 25.37/6.78 |
% 25.37/6.78 | Instantiating formula (26) with all_0_7_7, all_24_8_27, 0 and discharging atoms relation(all_0_7_7) = all_24_8_27, relation(all_0_7_7) = 0, yields:
% 25.37/6.78 | (196) all_24_8_27 = 0
% 25.37/6.78 |
% 25.37/6.78 | Equations (196) can reduce 194 to:
% 25.37/6.78 | (61) $false
% 25.37/6.78 |
% 25.37/6.78 |-The branch is then unsatisfiable
% 25.37/6.78 % SZS output end Proof for theBenchmark
% 25.37/6.78
% 25.37/6.78 6178ms
%------------------------------------------------------------------------------