TSTP Solution File: SET997+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET997+1 : TPTP v8.1.0. Released v3.2.0.
% 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 00:23:41 EDT 2022
% Result : Theorem 5.85s 2.13s
% Output : Proof 9.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET997+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jul 9 19:11:42 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.53/0.59 ____ _
% 0.53/0.59 ___ / __ \_____(_)___ ________ __________
% 0.53/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.59
% 0.53/0.59 A Theorem Prover for First-Order Logic
% 0.53/0.59 (ePrincess v.1.0)
% 0.53/0.59
% 0.53/0.59 (c) Philipp Rümmer, 2009-2015
% 0.53/0.59 (c) Peter Backeman, 2014-2015
% 0.53/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.59 Bug reports to peter@backeman.se
% 0.53/0.59
% 0.53/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.59
% 0.53/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.92 Prover 0: Preprocessing ...
% 2.03/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.11/1.20 Prover 0: Constructing countermodel ...
% 4.33/1.78 Prover 0: gave up
% 4.33/1.78 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.49/1.83 Prover 1: Preprocessing ...
% 4.93/1.94 Prover 1: Warning: ignoring some quantifiers
% 4.93/1.95 Prover 1: Constructing countermodel ...
% 5.85/2.13 Prover 1: proved (345ms)
% 5.85/2.13
% 5.85/2.13 No countermodel exists, formula is valid
% 5.85/2.13 % SZS status Theorem for theBenchmark
% 5.85/2.13
% 5.85/2.13 Generating proof ... Warning: ignoring some quantifiers
% 8.65/2.78 found it (size 49)
% 8.65/2.78
% 8.65/2.78 % SZS output start Proof for theBenchmark
% 8.65/2.78 Assumed formulas after preprocessing and simplification:
% 8.65/2.78 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v4 = 0) & relation_empty_yielding(v5) = 0 & relation_empty_yielding(empty_set) = 0 & relation_rng(v1) = v3 & relation_dom(v1) = v2 & subset(v0, v3) = v4 & relation(v12) = 0 & relation(v11) = 0 & relation(v8) = 0 & relation(v5) = 0 & relation(v1) = 0 & relation(empty_set) = 0 & function(v12) = 0 & function(v1) = 0 & empty(v11) = 0 & empty(v10) = 0 & empty(v8) = v9 & empty(v6) = v7 & empty(empty_set) = 0 & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (powerset(v15) = v16) | ~ (element(v14, v16) = 0) | ~ (element(v13, v15) = v17) | ? [v18] : ( ~ (v18 = 0) & in(v13, v14) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (powerset(v14) = v15) | ~ (element(v13, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & subset(v13, v14) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (element(v16, v15) = v14) | ~ (element(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (apply(v16, v15) = v14) | ~ (apply(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (subset(v16, v15) = v14) | ~ (subset(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (in(v16, v15) = v14) | ~ (in(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ (element(v14, v16) = 0) | ~ (in(v13, v14) = 0) | ? [v17] : ( ~ (v17 = 0) & empty(v15) = v17)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (element(v13, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v13, v14) = v15) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & in(v16, v14) = v17 & in(v16, v13) = 0)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (relation_empty_yielding(v15) = v14) | ~ (relation_empty_yielding(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (powerset(v15) = v14) | ~ (powerset(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (relation_rng(v15) = v14) | ~ (relation_rng(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (relation_dom(v15) = v14) | ~ (relation_dom(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (relation(v15) = v14) | ~ (relation(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (function(v15) = v14) | ~ (function(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (empty(v15) = v14) | ~ (empty(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | subset(v13, v14) = 0) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset(v13, v14) = 0) | ~ (in(v15, v13) = 0) | in(v15, v14) = 0) & ! [v13] : ! [v14] : (v14 = v13 | ~ (empty(v14) = 0) | ~ (empty(v13) = 0)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (relation(v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (function(v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) & ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v16 = 0 & ~ (v17 = 0) & element(v15, v14) = 0 & empty(v15) = v17) | (v15 = 0 & empty(v13) = 0))) & ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v14) = v15)) & ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ? [v15] : (element(v15, v14) = 0 & empty(v15) = 0)) & ! [v13] : ! [v14] : ( ~ (element(v13, v14) = 0) | ? [v15] : ? [v16] : (empty(v14) = v15 & in(v13, v14) = v16 & (v16 = 0 | v15 = 0))) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (relation(v14) = v17 & empty(v14) = v16 & empty(v13) = v15 & ( ~ (v15 = 0) | (v17 = 0 & v16 = 0)))) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (relation(v13) = v16 & empty(v14) = v17 & empty(v13) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | v15 = 0))) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (relation(v14) = v17 & empty(v14) = v16 & empty(v13) = v15 & ( ~ (v15 = 0) | (v17 = 0 & v16 = 0)))) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (relation(v13) = v16 & empty(v14) = v17 & empty(v13) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | v15 = 0))) & ! [v13] : ! [v14] : ( ~ (in(v13, v14) = 0) | ? [v15] : ( ~ (v15 = 0) & empty(v14) = v15)) & ! [v13] : ! [v14] : ( ~ (in(v13, v14) = 0) | ? [v15] : ( ~ (v15 = 0) & in(v14, v13) = v15)) & ! [v13] : (v13 = empty_set | ~ (empty(v13) = 0)) & ! [v13] : ( ~ (function(v13) = 0) | ? [v14] : ? [v15] : ? [v16] : (relation_rng(v13) = v15 & relation_dom(v13) = v16 & relation(v13) = v14 & ( ~ (v14 = 0) | ( ! [v17] : ! [v18] : ! [v19] : (v18 = 0 | ~ (in(v19, v16) = 0) | ~ (in(v17, v15) = v18) | ? [v20] : ( ~ (v20 = v17) & apply(v13, v19) = v20)) & ! [v17] : ( ~ (in(v17, v15) = 0) | ? [v18] : (apply(v13, v18) = v17 & in(v18, v16) = 0)) & ? [v17] : (v17 = v15 | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (in(v18, v17) = v19 & ( ~ (v19 = 0) | ! [v23] : ( ~ (in(v23, v16) = 0) | ? [v24] : ( ~ (v24 = v18) & apply(v13, v23) = v24))) & (v19 = 0 | (v22 = v18 & v21 = 0 & apply(v13, v20) = v18 & in(v20, v16) = 0)))))))) & ! [v13] : ( ~ (in(v13, v0) = 0) | ? [v14] : (apply(v1, v14) = v13 & in(v14, v2) = 0)) & ? [v13] : ? [v14] : element(v14, v13) = 0)
% 8.65/2.83 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 yields:
% 8.65/2.83 | (1) ~ (all_0_3_3 = 0) & ~ (all_0_5_5 = 0) & ~ (all_0_8_8 = 0) & relation_empty_yielding(all_0_7_7) = 0 & relation_empty_yielding(empty_set) = 0 & relation_rng(all_0_11_11) = all_0_9_9 & relation_dom(all_0_11_11) = all_0_10_10 & subset(all_0_12_12, all_0_9_9) = all_0_8_8 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_4_4) = 0 & relation(all_0_7_7) = 0 & relation(all_0_11_11) = 0 & relation(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_11_11) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_4_4) = all_0_3_3 & empty(all_0_6_6) = all_0_5_5 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [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 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(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] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 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] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (in(v6, v3) = 0) | ~ (in(v4, v2) = v5) | ? [v7] : ( ~ (v7 = v4) & apply(v0, v6) = v7)) & ! [v4] : ( ~ (in(v4, v2) = 0) | ? [v5] : (apply(v0, v5) = v4 & in(v5, v3) = 0)) & ? [v4] : (v4 = v2 | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v5, v4) = v6 & ( ~ (v6 = 0) | ! [v10] : ( ~ (in(v10, v3) = 0) | ? [v11] : ( ~ (v11 = v5) & apply(v0, v10) = v11))) & (v6 = 0 | (v9 = v5 & v8 = 0 & apply(v0, v7) = v5 & in(v7, v3) = 0)))))))) & ! [v0] : ( ~ (in(v0, all_0_12_12) = 0) | ? [v1] : (apply(all_0_11_11, v1) = v0 & in(v1, all_0_10_10) = 0)) & ? [v0] : ? [v1] : element(v1, v0) = 0
% 9.05/2.86 |
% 9.05/2.86 | Applying alpha-rule on (1) yields:
% 9.05/2.86 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 9.05/2.86 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 9.05/2.86 | (4) relation(empty_set) = 0
% 9.05/2.86 | (5) ? [v0] : ? [v1] : element(v1, v0) = 0
% 9.05/2.86 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 9.05/2.86 | (7) relation_empty_yielding(all_0_7_7) = 0
% 9.05/2.86 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 9.05/2.86 | (9) relation_dom(all_0_11_11) = all_0_10_10
% 9.05/2.86 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 9.05/2.86 | (11) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 9.05/2.86 | (12) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 9.05/2.87 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 9.05/2.87 | (14) relation_rng(all_0_11_11) = all_0_9_9
% 9.05/2.87 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 9.05/2.87 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 9.05/2.87 | (17) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 9.05/2.87 | (18) ~ (all_0_3_3 = 0)
% 9.05/2.87 | (19) relation(all_0_1_1) = 0
% 9.05/2.87 | (20) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (in(v6, v3) = 0) | ~ (in(v4, v2) = v5) | ? [v7] : ( ~ (v7 = v4) & apply(v0, v6) = v7)) & ! [v4] : ( ~ (in(v4, v2) = 0) | ? [v5] : (apply(v0, v5) = v4 & in(v5, v3) = 0)) & ? [v4] : (v4 = v2 | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v5, v4) = v6 & ( ~ (v6 = 0) | ! [v10] : ( ~ (in(v10, v3) = 0) | ? [v11] : ( ~ (v11 = v5) & apply(v0, v10) = v11))) & (v6 = 0 | (v9 = v5 & v8 = 0 & apply(v0, v7) = v5 & in(v7, v3) = 0))))))))
% 9.05/2.87 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 9.05/2.87 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 9.05/2.87 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 9.05/2.88 | (24) function(all_0_11_11) = 0
% 9.05/2.88 | (25) relation(all_0_11_11) = 0
% 9.05/2.88 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 9.05/2.88 | (27) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 9.05/2.88 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 9.05/2.88 | (29) ! [v0] : ( ~ (in(v0, all_0_12_12) = 0) | ? [v1] : (apply(all_0_11_11, v1) = v0 & in(v1, all_0_10_10) = 0))
% 9.05/2.88 | (30) ~ (all_0_8_8 = 0)
% 9.05/2.88 | (31) relation_empty_yielding(empty_set) = 0
% 9.05/2.88 | (32) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 9.05/2.88 | (33) relation(all_0_4_4) = 0
% 9.05/2.88 | (34) ~ (all_0_5_5 = 0)
% 9.05/2.88 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 9.05/2.88 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 9.05/2.88 | (37) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 9.05/2.88 | (38) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 9.05/2.88 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 9.05/2.88 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 9.27/2.88 | (41) empty(all_0_1_1) = 0
% 9.27/2.89 | (42) empty(all_0_4_4) = all_0_3_3
% 9.27/2.89 | (43) relation(all_0_0_0) = 0
% 9.27/2.89 | (44) empty(all_0_2_2) = 0
% 9.27/2.89 | (45) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 9.27/2.89 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 9.27/2.89 | (47) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 9.27/2.89 | (48) subset(all_0_12_12, all_0_9_9) = all_0_8_8
% 9.27/2.89 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 9.27/2.89 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 9.27/2.89 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 9.27/2.89 | (52) empty(all_0_6_6) = all_0_5_5
% 9.27/2.89 | (53) empty(empty_set) = 0
% 9.27/2.89 | (54) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 9.27/2.89 | (55) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 9.27/2.89 | (56) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 9.27/2.89 | (57) function(all_0_0_0) = 0
% 9.27/2.89 | (58) relation(all_0_7_7) = 0
% 9.27/2.89 |
% 9.27/2.89 | Instantiating formula (54) with all_0_9_9, all_0_11_11 and discharging atoms relation_rng(all_0_11_11) = all_0_9_9, yields:
% 9.27/2.90 | (59) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_11_11) = v1 & empty(all_0_9_9) = v2 & empty(all_0_11_11) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0))
% 9.27/2.90 |
% 9.27/2.90 | Instantiating formula (12) with all_0_10_10, all_0_11_11 and discharging atoms relation_dom(all_0_11_11) = all_0_10_10, yields:
% 9.27/2.90 | (60) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_11_11) = v1 & empty(all_0_10_10) = v2 & empty(all_0_11_11) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0))
% 9.27/2.90 |
% 9.27/2.90 | Instantiating formula (49) with all_0_8_8, all_0_9_9, all_0_12_12 and discharging atoms subset(all_0_12_12, all_0_9_9) = all_0_8_8, yields:
% 9.27/2.90 | (61) all_0_8_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_9_9) = v1 & in(v0, all_0_12_12) = 0)
% 9.27/2.90 |
% 9.27/2.90 | Instantiating formula (20) with all_0_11_11 and discharging atoms function(all_0_11_11) = 0, yields:
% 9.27/2.90 | (62) ? [v0] : ? [v1] : ? [v2] : (relation_rng(all_0_11_11) = v1 & relation_dom(all_0_11_11) = v2 & relation(all_0_11_11) = v0 & ( ~ (v0 = 0) | ( ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (in(v5, v2) = 0) | ~ (in(v3, v1) = v4) | ? [v6] : ( ~ (v6 = v3) & apply(all_0_11_11, v5) = v6)) & ! [v3] : ( ~ (in(v3, v1) = 0) | ? [v4] : (apply(all_0_11_11, v4) = v3 & in(v4, v2) = 0)) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (in(v4, v3) = v5 & ( ~ (v5 = 0) | ! [v9] : ( ~ (in(v9, v2) = 0) | ? [v10] : ( ~ (v10 = v4) & apply(all_0_11_11, v9) = v10))) & (v5 = 0 | (v8 = v4 & v7 = 0 & apply(all_0_11_11, v6) = v4 & in(v6, v2) = 0)))))))
% 9.27/2.90 |
% 9.27/2.90 | Instantiating (62) with all_22_0_15, all_22_1_16, all_22_2_17 yields:
% 9.27/2.90 | (63) relation_rng(all_0_11_11) = all_22_1_16 & relation_dom(all_0_11_11) = all_22_0_15 & relation(all_0_11_11) = all_22_2_17 & ( ~ (all_22_2_17 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (in(v2, all_22_0_15) = 0) | ~ (in(v0, all_22_1_16) = v1) | ? [v3] : ( ~ (v3 = v0) & apply(all_0_11_11, v2) = v3)) & ! [v0] : ( ~ (in(v0, all_22_1_16) = 0) | ? [v1] : (apply(all_0_11_11, v1) = v0 & in(v1, all_22_0_15) = 0)) & ? [v0] : (v0 = all_22_1_16 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ! [v6] : ( ~ (in(v6, all_22_0_15) = 0) | ? [v7] : ( ~ (v7 = v1) & apply(all_0_11_11, v6) = v7))) & (v2 = 0 | (v5 = v1 & v4 = 0 & apply(all_0_11_11, v3) = v1 & in(v3, all_22_0_15) = 0))))))
% 9.27/2.90 |
% 9.27/2.90 | Applying alpha-rule on (63) yields:
% 9.27/2.90 | (64) relation_rng(all_0_11_11) = all_22_1_16
% 9.27/2.90 | (65) relation_dom(all_0_11_11) = all_22_0_15
% 9.27/2.90 | (66) relation(all_0_11_11) = all_22_2_17
% 9.27/2.90 | (67) ~ (all_22_2_17 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (in(v2, all_22_0_15) = 0) | ~ (in(v0, all_22_1_16) = v1) | ? [v3] : ( ~ (v3 = v0) & apply(all_0_11_11, v2) = v3)) & ! [v0] : ( ~ (in(v0, all_22_1_16) = 0) | ? [v1] : (apply(all_0_11_11, v1) = v0 & in(v1, all_22_0_15) = 0)) & ? [v0] : (v0 = all_22_1_16 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ! [v6] : ( ~ (in(v6, all_22_0_15) = 0) | ? [v7] : ( ~ (v7 = v1) & apply(all_0_11_11, v6) = v7))) & (v2 = 0 | (v5 = v1 & v4 = 0 & apply(all_0_11_11, v3) = v1 & in(v3, all_22_0_15) = 0)))))
% 9.27/2.91 |
% 9.27/2.91 | Instantiating (60) with all_24_0_18, all_24_1_19, all_24_2_20 yields:
% 9.27/2.91 | (68) relation(all_0_11_11) = all_24_1_19 & empty(all_0_10_10) = all_24_0_18 & empty(all_0_11_11) = all_24_2_20 & ( ~ (all_24_0_18 = 0) | ~ (all_24_1_19 = 0) | all_24_2_20 = 0)
% 9.27/2.91 |
% 9.27/2.91 | Applying alpha-rule on (68) yields:
% 9.27/2.91 | (69) relation(all_0_11_11) = all_24_1_19
% 9.27/2.91 | (70) empty(all_0_10_10) = all_24_0_18
% 9.27/2.91 | (71) empty(all_0_11_11) = all_24_2_20
% 9.27/2.91 | (72) ~ (all_24_0_18 = 0) | ~ (all_24_1_19 = 0) | all_24_2_20 = 0
% 9.27/2.91 |
% 9.27/2.91 | Instantiating (59) with all_30_0_27, all_30_1_28, all_30_2_29 yields:
% 9.27/2.91 | (73) relation(all_0_11_11) = all_30_1_28 & empty(all_0_9_9) = all_30_0_27 & empty(all_0_11_11) = all_30_2_29 & ( ~ (all_30_0_27 = 0) | ~ (all_30_1_28 = 0) | all_30_2_29 = 0)
% 9.27/2.91 |
% 9.27/2.91 | Applying alpha-rule on (73) yields:
% 9.27/2.91 | (74) relation(all_0_11_11) = all_30_1_28
% 9.27/2.91 | (75) empty(all_0_9_9) = all_30_0_27
% 9.27/2.91 | (76) empty(all_0_11_11) = all_30_2_29
% 9.27/2.91 | (77) ~ (all_30_0_27 = 0) | ~ (all_30_1_28 = 0) | all_30_2_29 = 0
% 9.27/2.91 |
% 9.27/2.91 +-Applying beta-rule and splitting (61), into two cases.
% 9.27/2.91 |-Branch one:
% 9.27/2.91 | (78) all_0_8_8 = 0
% 9.27/2.91 |
% 9.27/2.91 | Equations (78) can reduce 30 to:
% 9.27/2.91 | (79) $false
% 9.27/2.91 |
% 9.27/2.91 |-The branch is then unsatisfiable
% 9.27/2.91 |-Branch two:
% 9.27/2.91 | (30) ~ (all_0_8_8 = 0)
% 9.27/2.91 | (81) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_9_9) = v1 & in(v0, all_0_12_12) = 0)
% 9.27/2.91 |
% 9.27/2.91 | Instantiating (81) with all_40_0_35, all_40_1_36 yields:
% 9.27/2.91 | (82) ~ (all_40_0_35 = 0) & in(all_40_1_36, all_0_9_9) = all_40_0_35 & in(all_40_1_36, all_0_12_12) = 0
% 9.27/2.91 |
% 9.27/2.91 | Applying alpha-rule on (82) yields:
% 9.27/2.91 | (83) ~ (all_40_0_35 = 0)
% 9.27/2.91 | (84) in(all_40_1_36, all_0_9_9) = all_40_0_35
% 9.27/2.91 | (85) in(all_40_1_36, all_0_12_12) = 0
% 9.27/2.91 |
% 9.27/2.91 | Instantiating formula (15) with all_0_11_11, all_22_1_16, all_0_9_9 and discharging atoms relation_rng(all_0_11_11) = all_22_1_16, relation_rng(all_0_11_11) = all_0_9_9, yields:
% 9.27/2.91 | (86) all_22_1_16 = all_0_9_9
% 9.27/2.91 |
% 9.27/2.91 | Instantiating formula (21) with all_0_11_11, all_22_0_15, all_0_10_10 and discharging atoms relation_dom(all_0_11_11) = all_22_0_15, relation_dom(all_0_11_11) = all_0_10_10, yields:
% 9.27/2.91 | (87) all_22_0_15 = all_0_10_10
% 9.27/2.91 |
% 9.27/2.91 | Instantiating formula (46) with all_0_11_11, all_30_1_28, 0 and discharging atoms relation(all_0_11_11) = all_30_1_28, relation(all_0_11_11) = 0, yields:
% 9.27/2.92 | (88) all_30_1_28 = 0
% 9.27/2.92 |
% 9.27/2.92 | Instantiating formula (46) with all_0_11_11, all_24_1_19, all_30_1_28 and discharging atoms relation(all_0_11_11) = all_30_1_28, relation(all_0_11_11) = all_24_1_19, yields:
% 9.27/2.92 | (89) all_30_1_28 = all_24_1_19
% 9.27/2.92 |
% 9.27/2.92 | Instantiating formula (46) with all_0_11_11, all_22_2_17, all_24_1_19 and discharging atoms relation(all_0_11_11) = all_24_1_19, relation(all_0_11_11) = all_22_2_17, yields:
% 9.27/2.92 | (90) all_24_1_19 = all_22_2_17
% 9.27/2.92 |
% 9.27/2.92 | Combining equations (89,88) yields a new equation:
% 9.27/2.92 | (91) all_24_1_19 = 0
% 9.27/2.92 |
% 9.27/2.92 | Simplifying 91 yields:
% 9.27/2.92 | (92) all_24_1_19 = 0
% 9.27/2.92 |
% 9.27/2.92 | Combining equations (92,90) yields a new equation:
% 9.27/2.92 | (93) all_22_2_17 = 0
% 9.27/2.92 |
% 9.27/2.92 +-Applying beta-rule and splitting (67), into two cases.
% 9.27/2.92 |-Branch one:
% 9.27/2.92 | (94) ~ (all_22_2_17 = 0)
% 9.27/2.92 |
% 9.27/2.92 | Equations (93) can reduce 94 to:
% 9.27/2.92 | (79) $false
% 9.27/2.92 |
% 9.27/2.92 |-The branch is then unsatisfiable
% 9.27/2.92 |-Branch two:
% 9.27/2.92 | (93) all_22_2_17 = 0
% 9.27/2.92 | (97) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (in(v2, all_22_0_15) = 0) | ~ (in(v0, all_22_1_16) = v1) | ? [v3] : ( ~ (v3 = v0) & apply(all_0_11_11, v2) = v3)) & ! [v0] : ( ~ (in(v0, all_22_1_16) = 0) | ? [v1] : (apply(all_0_11_11, v1) = v0 & in(v1, all_22_0_15) = 0)) & ? [v0] : (v0 = all_22_1_16 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ! [v6] : ( ~ (in(v6, all_22_0_15) = 0) | ? [v7] : ( ~ (v7 = v1) & apply(all_0_11_11, v6) = v7))) & (v2 = 0 | (v5 = v1 & v4 = 0 & apply(all_0_11_11, v3) = v1 & in(v3, all_22_0_15) = 0))))
% 9.27/2.92 |
% 9.27/2.92 | Applying alpha-rule on (97) yields:
% 9.27/2.92 | (98) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (in(v2, all_22_0_15) = 0) | ~ (in(v0, all_22_1_16) = v1) | ? [v3] : ( ~ (v3 = v0) & apply(all_0_11_11, v2) = v3))
% 9.27/2.92 | (99) ! [v0] : ( ~ (in(v0, all_22_1_16) = 0) | ? [v1] : (apply(all_0_11_11, v1) = v0 & in(v1, all_22_0_15) = 0))
% 9.27/2.92 | (100) ? [v0] : (v0 = all_22_1_16 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ! [v6] : ( ~ (in(v6, all_22_0_15) = 0) | ? [v7] : ( ~ (v7 = v1) & apply(all_0_11_11, v6) = v7))) & (v2 = 0 | (v5 = v1 & v4 = 0 & apply(all_0_11_11, v3) = v1 & in(v3, all_22_0_15) = 0))))
% 9.27/2.92 |
% 9.27/2.92 | Instantiating formula (29) with all_40_1_36 and discharging atoms in(all_40_1_36, all_0_12_12) = 0, yields:
% 9.27/2.92 | (101) ? [v0] : (apply(all_0_11_11, v0) = all_40_1_36 & in(v0, all_0_10_10) = 0)
% 9.27/2.92 |
% 9.27/2.92 | Instantiating (101) with all_66_0_42 yields:
% 9.27/2.92 | (102) apply(all_0_11_11, all_66_0_42) = all_40_1_36 & in(all_66_0_42, all_0_10_10) = 0
% 9.27/2.92 |
% 9.27/2.92 | Applying alpha-rule on (102) yields:
% 9.27/2.92 | (103) apply(all_0_11_11, all_66_0_42) = all_40_1_36
% 9.27/2.92 | (104) in(all_66_0_42, all_0_10_10) = 0
% 9.27/2.92 |
% 9.27/2.92 | Instantiating formula (98) with all_66_0_42, all_40_0_35, all_40_1_36 yields:
% 9.27/2.92 | (105) all_40_0_35 = 0 | ~ (in(all_66_0_42, all_22_0_15) = 0) | ~ (in(all_40_1_36, all_22_1_16) = all_40_0_35) | ? [v0] : ( ~ (v0 = all_40_1_36) & apply(all_0_11_11, all_66_0_42) = v0)
% 9.27/2.92 |
% 9.27/2.92 +-Applying beta-rule and splitting (105), into two cases.
% 9.27/2.92 |-Branch one:
% 9.27/2.92 | (106) ~ (in(all_66_0_42, all_22_0_15) = 0)
% 9.27/2.92 |
% 9.27/2.92 | From (87) and (106) follows:
% 9.27/2.93 | (107) ~ (in(all_66_0_42, all_0_10_10) = 0)
% 9.27/2.93 |
% 9.27/2.93 | Using (104) and (107) yields:
% 9.27/2.93 | (108) $false
% 9.27/2.93 |
% 9.27/2.93 |-The branch is then unsatisfiable
% 9.27/2.93 |-Branch two:
% 9.27/2.93 | (109) in(all_66_0_42, all_22_0_15) = 0
% 9.27/2.93 | (110) all_40_0_35 = 0 | ~ (in(all_40_1_36, all_22_1_16) = all_40_0_35) | ? [v0] : ( ~ (v0 = all_40_1_36) & apply(all_0_11_11, all_66_0_42) = v0)
% 9.27/2.93 |
% 9.27/2.93 +-Applying beta-rule and splitting (110), into two cases.
% 9.27/2.93 |-Branch one:
% 9.27/2.93 | (111) ~ (in(all_40_1_36, all_22_1_16) = all_40_0_35)
% 9.27/2.93 |
% 9.27/2.93 | From (86) and (111) follows:
% 9.27/2.93 | (112) ~ (in(all_40_1_36, all_0_9_9) = all_40_0_35)
% 9.27/2.93 |
% 9.27/2.93 | Using (84) and (112) yields:
% 9.27/2.93 | (108) $false
% 9.27/2.93 |
% 9.27/2.93 |-The branch is then unsatisfiable
% 9.27/2.93 |-Branch two:
% 9.27/2.93 | (114) in(all_40_1_36, all_22_1_16) = all_40_0_35
% 9.27/2.93 | (115) all_40_0_35 = 0 | ? [v0] : ( ~ (v0 = all_40_1_36) & apply(all_0_11_11, all_66_0_42) = v0)
% 9.27/2.93 |
% 9.27/2.93 +-Applying beta-rule and splitting (115), into two cases.
% 9.27/2.93 |-Branch one:
% 9.27/2.93 | (116) all_40_0_35 = 0
% 9.27/2.93 |
% 9.27/2.93 | Equations (116) can reduce 83 to:
% 9.27/2.93 | (79) $false
% 9.27/2.93 |
% 9.27/2.93 |-The branch is then unsatisfiable
% 9.27/2.93 |-Branch two:
% 9.27/2.93 | (83) ~ (all_40_0_35 = 0)
% 9.27/2.93 | (119) ? [v0] : ( ~ (v0 = all_40_1_36) & apply(all_0_11_11, all_66_0_42) = v0)
% 9.27/2.93 |
% 9.27/2.93 | Instantiating (119) with all_101_0_57 yields:
% 9.27/2.93 | (120) ~ (all_101_0_57 = all_40_1_36) & apply(all_0_11_11, all_66_0_42) = all_101_0_57
% 9.27/2.93 |
% 9.27/2.93 | Applying alpha-rule on (120) yields:
% 9.27/2.93 | (121) ~ (all_101_0_57 = all_40_1_36)
% 9.27/2.93 | (122) apply(all_0_11_11, all_66_0_42) = all_101_0_57
% 9.27/2.93 |
% 9.27/2.93 | Instantiating formula (40) with all_0_11_11, all_66_0_42, all_101_0_57, all_40_1_36 and discharging atoms apply(all_0_11_11, all_66_0_42) = all_101_0_57, apply(all_0_11_11, all_66_0_42) = all_40_1_36, yields:
% 9.27/2.93 | (123) all_101_0_57 = all_40_1_36
% 9.27/2.93 |
% 9.27/2.93 | Equations (123) can reduce 121 to:
% 9.27/2.93 | (79) $false
% 9.27/2.93 |
% 9.27/2.93 |-The branch is then unsatisfiable
% 9.27/2.93 % SZS output end Proof for theBenchmark
% 9.27/2.93
% 9.27/2.93 2329ms
%------------------------------------------------------------------------------