TSTP Solution File: SEU019+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU019+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:46:13 EDT 2022
% Result : Theorem 3.95s 1.69s
% Output : Proof 6.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU019+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jun 19 14:02:14 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.57/0.62 ____ _
% 0.57/0.62 ___ / __ \_____(_)___ ________ __________
% 0.57/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.62
% 0.57/0.62 A Theorem Prover for First-Order Logic
% 0.57/0.62 (ePrincess v.1.0)
% 0.57/0.62
% 0.57/0.62 (c) Philipp Rümmer, 2009-2015
% 0.57/0.62 (c) Peter Backeman, 2014-2015
% 0.57/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.62 Bug reports to peter@backeman.se
% 0.57/0.62
% 0.57/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.62
% 0.57/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/0.99 Prover 0: Preprocessing ...
% 2.18/1.21 Prover 0: Warning: ignoring some quantifiers
% 2.27/1.23 Prover 0: Constructing countermodel ...
% 2.88/1.40 Prover 0: gave up
% 2.88/1.40 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.88/1.43 Prover 1: Preprocessing ...
% 3.57/1.56 Prover 1: Warning: ignoring some quantifiers
% 3.57/1.56 Prover 1: Constructing countermodel ...
% 3.95/1.68 Prover 1: proved (281ms)
% 3.95/1.68
% 3.95/1.68 No countermodel exists, formula is valid
% 3.95/1.69 % SZS status Theorem for theBenchmark
% 3.95/1.69
% 3.95/1.69 Generating proof ... Warning: ignoring some quantifiers
% 6.23/2.21 found it (size 57)
% 6.23/2.21
% 6.23/2.21 % SZS output start Proof for theBenchmark
% 6.23/2.22 Assumed formulas after preprocessing and simplification:
% 6.23/2.22 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v7 = 0) & ~ (v5 = 0) & ~ (v2 = 0) & relation_empty_yielding(v3) = 0 & relation_empty_yielding(empty_set) = 0 & identity_relation(v0) = v1 & one_to_one(v1) = v2 & relation(v10) = 0 & relation(v9) = 0 & relation(v6) = 0 & relation(v3) = 0 & relation(empty_set) = 0 & function(v10) = 0 & empty(v9) = 0 & empty(v8) = 0 & empty(v6) = v7 & empty(v4) = v5 & empty(empty_set) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ~ (element(v11, v13) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (element(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (element(v14, v13) = v12) | ~ (element(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (apply(v14, v13) = v12) | ~ (apply(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (in(v14, v13) = v12) | ~ (in(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ~ (in(v11, v12) = 0) | ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (element(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_empty_yielding(v13) = v12) | ~ (relation_empty_yielding(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (identity_relation(v13) = v12) | ~ (identity_relation(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (one_to_one(v13) = v12) | ~ (one_to_one(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_dom(v13) = v12) | ~ (relation_dom(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation(v13) = v12) | ~ (relation(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (function(v13) = v12) | ~ (function(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (empty(v13) = v12) | ~ (empty(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (identity_relation(v11) = v13) | ~ (function(v12) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (relation_dom(v12) = v15 & relation(v12) = v14 & ( ~ (v14 = 0) | (( ~ (v15 = v11) | v13 = v12 | (v17 = 0 & ~ (v18 = v16) & apply(v12, v16) = v18 & in(v16, v11) = 0)) & ( ~ (v13 = v12) | (v15 = v11 & ! [v19] : ! [v20] : (v20 = v19 | ~ (apply(v12, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & in(v19, v11) = v21)))))))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (empty(v12) = 0) | ~ (empty(v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (relation(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (function(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v11) = v13)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v14 = 0 & ~ (v15 = 0) & element(v13, v12) = 0 & empty(v13) = v15) | (v13 = 0 & empty(v11) = 0))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (element(v13, v12) = 0 & empty(v13) = 0)) & ! [v11] : ! [v12] : ( ~ (element(v11, v12) = 0) | ? [v13] : ? [v14] : (empty(v12) = v13 & in(v11, v12) = v14 & (v14 = 0 | v13 = 0))) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | relation(v12) = 0) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | function(v12) = 0) & ! [v11] : ! [v12] : ( ~ (one_to_one(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (relation_dom(v11) = v15 & relation(v11) = v13 & function(v11) = v14 & ( ~ (v14 = 0) | ~ (v13 = 0) | (( ~ (v12 = 0) | ! [v22] : ! [v23] : (v23 = v22 | ~ (in(v23, v15) = 0) | ~ (in(v22, v15) = 0) | ? [v24] : ? [v25] : ( ~ (v25 = v24) & apply(v11, v23) = v25 & apply(v11, v22) = v24))) & (v12 = 0 | (v21 = v20 & v19 = 0 & v18 = 0 & ~ (v17 = v16) & apply(v11, v17) = v20 & apply(v11, v16) = v20 & in(v17, v15) = 0 & in(v16, v15) = 0)))))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (relation(v12) = v15 & empty(v12) = v14 & empty(v11) = v13 & ( ~ (v13 = 0) | (v15 = 0 & v14 = 0)))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (relation(v11) = v14 & empty(v12) = v15 & empty(v11) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | v13 = 0))) & ! [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] : ? [v12] : element(v12, v11) = 0)
% 6.65/2.25 | 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:
% 6.65/2.25 | (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 & identity_relation(all_0_10_10) = all_0_9_9 & one_to_one(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(empty_set) = 0 & function(all_0_0_0) = 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 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(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] : (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 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(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] : ( ~ (identity_relation(v0) = v2) | ~ (function(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v1) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v0) | v2 = v1 | (v6 = 0 & ~ (v7 = v5) & apply(v1, v5) = v7 & in(v5, v0) = 0)) & ( ~ (v2 = v1) | (v4 = v0 & ! [v8] : ! [v9] : (v9 = v8 | ~ (apply(v1, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v0) = v10)))))))) & ! [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] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1) = 0) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v11] : ! [v12] : (v12 = v11 | ~ (in(v12, v4) = 0) | ~ (in(v11, v4) = 0) | ? [v13] : ? [v14] : ( ~ (v14 = v13) & apply(v0, v12) = v14 & apply(v0, v11) = v13))) & (v1 = 0 | (v10 = v9 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v6) = v9 & apply(v0, v5) = v9 & in(v6, v4) = 0 & in(v5, v4) = 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] : ? [v1] : element(v1, v0) = 0
% 6.65/2.26 |
% 6.65/2.26 | Applying alpha-rule on (1) yields:
% 6.65/2.26 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 6.65/2.26 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 6.65/2.26 | (4) ? [v0] : ? [v1] : element(v1, v0) = 0
% 6.65/2.26 | (5) function(all_0_0_0) = 0
% 6.65/2.26 | (6) relation_empty_yielding(all_0_7_7) = 0
% 6.65/2.26 | (7) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1) = 0)
% 6.65/2.26 | (8) relation(all_0_7_7) = 0
% 6.65/2.26 | (9) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 6.65/2.26 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 6.65/2.26 | (11) empty(empty_set) = 0
% 6.65/2.26 | (12) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.65/2.26 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 6.65/2.26 | (14) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.65/2.26 | (15) one_to_one(all_0_9_9) = all_0_8_8
% 6.65/2.26 | (16) ~ (all_0_8_8 = 0)
% 6.65/2.26 | (17) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 6.65/2.27 | (18) empty(all_0_6_6) = all_0_5_5
% 6.65/2.27 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 6.65/2.27 | (20) ! [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))
% 6.65/2.27 | (21) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 6.65/2.27 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 6.65/2.27 | (23) relation(all_0_1_1) = 0
% 6.65/2.27 | (24) identity_relation(all_0_10_10) = all_0_9_9
% 6.65/2.27 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 6.65/2.27 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 6.65/2.27 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 6.65/2.27 | (28) relation(empty_set) = 0
% 6.65/2.27 | (29) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 6.65/2.27 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 6.65/2.27 | (31) relation(all_0_0_0) = 0
% 6.65/2.27 | (32) empty(all_0_2_2) = 0
% 6.65/2.27 | (33) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0)
% 6.65/2.27 | (34) empty(all_0_4_4) = all_0_3_3
% 6.65/2.27 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 6.65/2.27 | (36) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 6.65/2.27 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 6.65/2.27 | (38) relation_empty_yielding(empty_set) = 0
% 6.65/2.27 | (39) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 6.65/2.27 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 6.65/2.27 | (41) empty(all_0_1_1) = 0
% 6.65/2.27 | (42) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 6.65/2.27 | (43) ~ (all_0_3_3 = 0)
% 6.65/2.27 | (44) ~ (all_0_5_5 = 0)
% 6.65/2.27 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 6.65/2.27 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 6.65/2.27 | (47) relation(all_0_4_4) = 0
% 6.65/2.27 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity_relation(v0) = v2) | ~ (function(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v1) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v0) | v2 = v1 | (v6 = 0 & ~ (v7 = v5) & apply(v1, v5) = v7 & in(v5, v0) = 0)) & ( ~ (v2 = v1) | (v4 = v0 & ! [v8] : ! [v9] : (v9 = v8 | ~ (apply(v1, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v0) = v10))))))))
% 6.65/2.27 | (49) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 6.65/2.27 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 6.65/2.28 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.65/2.28 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 6.65/2.28 | (53) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 6.65/2.28 | (54) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v11] : ! [v12] : (v12 = v11 | ~ (in(v12, v4) = 0) | ~ (in(v11, v4) = 0) | ? [v13] : ? [v14] : ( ~ (v14 = v13) & apply(v0, v12) = v14 & apply(v0, v11) = v13))) & (v1 = 0 | (v10 = v9 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v6) = v9 & apply(v0, v5) = v9 & in(v6, v4) = 0 & in(v5, v4) = 0))))))
% 6.65/2.28 |
% 6.65/2.28 | Instantiating formula (33) with all_0_9_9, all_0_10_10 and discharging atoms identity_relation(all_0_10_10) = all_0_9_9, yields:
% 6.65/2.28 | (55) relation(all_0_9_9) = 0
% 6.65/2.28 |
% 6.65/2.28 | Instantiating formula (7) with all_0_9_9, all_0_10_10 and discharging atoms identity_relation(all_0_10_10) = all_0_9_9, yields:
% 6.65/2.28 | (56) function(all_0_9_9) = 0
% 6.65/2.28 |
% 6.65/2.28 | Instantiating formula (54) with all_0_8_8, all_0_9_9 and discharging atoms one_to_one(all_0_9_9) = all_0_8_8, yields:
% 6.65/2.28 | (57) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(all_0_9_9) = v2 & relation(all_0_9_9) = v0 & function(all_0_9_9) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (all_0_8_8 = 0) | ! [v9] : ! [v10] : (v10 = v9 | ~ (in(v10, v2) = 0) | ~ (in(v9, v2) = 0) | ? [v11] : ? [v12] : ( ~ (v12 = v11) & apply(all_0_9_9, v10) = v12 & apply(all_0_9_9, v9) = v11))) & (all_0_8_8 = 0 | (v8 = v7 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & apply(all_0_9_9, v4) = v7 & apply(all_0_9_9, v3) = v7 & in(v4, v2) = 0 & in(v3, v2) = 0)))))
% 6.65/2.28 |
% 6.65/2.28 | Instantiating (57) with all_19_0_20, all_19_1_21, all_19_2_22, all_19_3_23, all_19_4_24, all_19_5_25, all_19_6_26, all_19_7_27, all_19_8_28 yields:
% 6.65/2.28 | (58) relation_dom(all_0_9_9) = all_19_6_26 & relation(all_0_9_9) = all_19_8_28 & function(all_0_9_9) = all_19_7_27 & ( ~ (all_19_7_27 = 0) | ~ (all_19_8_28 = 0) | (( ~ (all_0_8_8 = 0) | ! [v0] : ! [v1] : (v1 = v0 | ~ (in(v1, all_19_6_26) = 0) | ~ (in(v0, all_19_6_26) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = v2) & apply(all_0_9_9, v1) = v3 & apply(all_0_9_9, v0) = v2))) & (all_0_8_8 = 0 | (all_19_0_20 = all_19_1_21 & all_19_2_22 = 0 & all_19_3_23 = 0 & ~ (all_19_4_24 = all_19_5_25) & apply(all_0_9_9, all_19_4_24) = all_19_1_21 & apply(all_0_9_9, all_19_5_25) = all_19_1_21 & in(all_19_4_24, all_19_6_26) = 0 & in(all_19_5_25, all_19_6_26) = 0))))
% 6.65/2.28 |
% 6.65/2.28 | Applying alpha-rule on (58) yields:
% 6.65/2.28 | (59) relation_dom(all_0_9_9) = all_19_6_26
% 6.65/2.28 | (60) relation(all_0_9_9) = all_19_8_28
% 6.65/2.28 | (61) function(all_0_9_9) = all_19_7_27
% 6.65/2.28 | (62) ~ (all_19_7_27 = 0) | ~ (all_19_8_28 = 0) | (( ~ (all_0_8_8 = 0) | ! [v0] : ! [v1] : (v1 = v0 | ~ (in(v1, all_19_6_26) = 0) | ~ (in(v0, all_19_6_26) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = v2) & apply(all_0_9_9, v1) = v3 & apply(all_0_9_9, v0) = v2))) & (all_0_8_8 = 0 | (all_19_0_20 = all_19_1_21 & all_19_2_22 = 0 & all_19_3_23 = 0 & ~ (all_19_4_24 = all_19_5_25) & apply(all_0_9_9, all_19_4_24) = all_19_1_21 & apply(all_0_9_9, all_19_5_25) = all_19_1_21 & in(all_19_4_24, all_19_6_26) = 0 & in(all_19_5_25, all_19_6_26) = 0)))
% 6.65/2.28 |
% 6.65/2.28 | Instantiating formula (52) with all_0_9_9, all_19_8_28, 0 and discharging atoms relation(all_0_9_9) = all_19_8_28, relation(all_0_9_9) = 0, yields:
% 6.65/2.28 | (63) all_19_8_28 = 0
% 6.65/2.28 |
% 6.65/2.28 | Instantiating formula (26) with all_0_9_9, all_19_7_27, 0 and discharging atoms function(all_0_9_9) = all_19_7_27, function(all_0_9_9) = 0, yields:
% 6.65/2.28 | (64) all_19_7_27 = 0
% 6.65/2.28 |
% 6.65/2.29 | From (63) and (60) follows:
% 6.65/2.29 | (55) relation(all_0_9_9) = 0
% 6.65/2.29 |
% 6.65/2.29 | From (64) and (61) follows:
% 6.65/2.29 | (56) function(all_0_9_9) = 0
% 6.65/2.29 |
% 6.65/2.29 +-Applying beta-rule and splitting (62), into two cases.
% 6.65/2.29 |-Branch one:
% 6.65/2.29 | (67) ~ (all_19_7_27 = 0)
% 6.65/2.29 |
% 6.65/2.29 | Equations (64) can reduce 67 to:
% 6.65/2.29 | (68) $false
% 6.65/2.29 |
% 6.65/2.29 |-The branch is then unsatisfiable
% 6.65/2.29 |-Branch two:
% 6.65/2.29 | (64) all_19_7_27 = 0
% 6.65/2.29 | (70) ~ (all_19_8_28 = 0) | (( ~ (all_0_8_8 = 0) | ! [v0] : ! [v1] : (v1 = v0 | ~ (in(v1, all_19_6_26) = 0) | ~ (in(v0, all_19_6_26) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = v2) & apply(all_0_9_9, v1) = v3 & apply(all_0_9_9, v0) = v2))) & (all_0_8_8 = 0 | (all_19_0_20 = all_19_1_21 & all_19_2_22 = 0 & all_19_3_23 = 0 & ~ (all_19_4_24 = all_19_5_25) & apply(all_0_9_9, all_19_4_24) = all_19_1_21 & apply(all_0_9_9, all_19_5_25) = all_19_1_21 & in(all_19_4_24, all_19_6_26) = 0 & in(all_19_5_25, all_19_6_26) = 0)))
% 6.65/2.29 |
% 6.65/2.29 +-Applying beta-rule and splitting (70), into two cases.
% 6.65/2.29 |-Branch one:
% 6.65/2.29 | (71) ~ (all_19_8_28 = 0)
% 6.65/2.29 |
% 6.65/2.29 | Equations (63) can reduce 71 to:
% 6.65/2.29 | (68) $false
% 6.65/2.29 |
% 6.65/2.29 |-The branch is then unsatisfiable
% 6.65/2.29 |-Branch two:
% 6.65/2.29 | (63) all_19_8_28 = 0
% 6.65/2.29 | (74) ( ~ (all_0_8_8 = 0) | ! [v0] : ! [v1] : (v1 = v0 | ~ (in(v1, all_19_6_26) = 0) | ~ (in(v0, all_19_6_26) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = v2) & apply(all_0_9_9, v1) = v3 & apply(all_0_9_9, v0) = v2))) & (all_0_8_8 = 0 | (all_19_0_20 = all_19_1_21 & all_19_2_22 = 0 & all_19_3_23 = 0 & ~ (all_19_4_24 = all_19_5_25) & apply(all_0_9_9, all_19_4_24) = all_19_1_21 & apply(all_0_9_9, all_19_5_25) = all_19_1_21 & in(all_19_4_24, all_19_6_26) = 0 & in(all_19_5_25, all_19_6_26) = 0))
% 6.65/2.29 |
% 6.65/2.29 | Applying alpha-rule on (74) yields:
% 6.65/2.29 | (75) ~ (all_0_8_8 = 0) | ! [v0] : ! [v1] : (v1 = v0 | ~ (in(v1, all_19_6_26) = 0) | ~ (in(v0, all_19_6_26) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = v2) & apply(all_0_9_9, v1) = v3 & apply(all_0_9_9, v0) = v2))
% 6.65/2.29 | (76) all_0_8_8 = 0 | (all_19_0_20 = all_19_1_21 & all_19_2_22 = 0 & all_19_3_23 = 0 & ~ (all_19_4_24 = all_19_5_25) & apply(all_0_9_9, all_19_4_24) = all_19_1_21 & apply(all_0_9_9, all_19_5_25) = all_19_1_21 & in(all_19_4_24, all_19_6_26) = 0 & in(all_19_5_25, all_19_6_26) = 0)
% 6.65/2.29 |
% 6.65/2.29 +-Applying beta-rule and splitting (76), into two cases.
% 6.65/2.29 |-Branch one:
% 6.65/2.29 | (77) all_0_8_8 = 0
% 6.65/2.29 |
% 6.65/2.29 | Equations (77) can reduce 16 to:
% 6.65/2.29 | (68) $false
% 6.65/2.29 |
% 6.65/2.29 |-The branch is then unsatisfiable
% 6.65/2.29 |-Branch two:
% 6.65/2.29 | (16) ~ (all_0_8_8 = 0)
% 6.65/2.29 | (80) all_19_0_20 = all_19_1_21 & all_19_2_22 = 0 & all_19_3_23 = 0 & ~ (all_19_4_24 = all_19_5_25) & apply(all_0_9_9, all_19_4_24) = all_19_1_21 & apply(all_0_9_9, all_19_5_25) = all_19_1_21 & in(all_19_4_24, all_19_6_26) = 0 & in(all_19_5_25, all_19_6_26) = 0
% 6.65/2.29 |
% 6.65/2.29 | Applying alpha-rule on (80) yields:
% 6.65/2.29 | (81) ~ (all_19_4_24 = all_19_5_25)
% 6.65/2.29 | (82) in(all_19_5_25, all_19_6_26) = 0
% 6.65/2.29 | (83) all_19_3_23 = 0
% 6.65/2.29 | (84) all_19_0_20 = all_19_1_21
% 6.65/2.29 | (85) apply(all_0_9_9, all_19_5_25) = all_19_1_21
% 6.65/2.29 | (86) apply(all_0_9_9, all_19_4_24) = all_19_1_21
% 6.65/2.29 | (87) all_19_2_22 = 0
% 6.65/2.29 | (88) in(all_19_4_24, all_19_6_26) = 0
% 6.65/2.29 |
% 6.65/2.29 | Instantiating formula (29) with all_19_6_26, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_19_6_26, yields:
% 6.65/2.29 | (89) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_9_9) = v1 & empty(all_19_6_26) = v2 & empty(all_0_9_9) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0))
% 6.65/2.29 |
% 6.65/2.29 | Instantiating formula (48) with all_0_9_9, all_0_9_9, all_0_10_10 and discharging atoms identity_relation(all_0_10_10) = all_0_9_9, function(all_0_9_9) = 0, yields:
% 6.65/2.29 | (90) ? [v0] : ? [v1] : (relation_dom(all_0_9_9) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | (v1 = all_0_10_10 & ! [v2] : ! [v3] : (v3 = v2 | ~ (apply(all_0_9_9, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, all_0_10_10) = v4)))))
% 6.65/2.29 |
% 6.65/2.29 | Instantiating (89) with all_46_0_31, all_46_1_32, all_46_2_33 yields:
% 6.65/2.29 | (91) relation(all_0_9_9) = all_46_1_32 & empty(all_19_6_26) = all_46_0_31 & empty(all_0_9_9) = all_46_2_33 & ( ~ (all_46_0_31 = 0) | ~ (all_46_1_32 = 0) | all_46_2_33 = 0)
% 6.65/2.29 |
% 6.65/2.29 | Applying alpha-rule on (91) yields:
% 6.65/2.29 | (92) relation(all_0_9_9) = all_46_1_32
% 6.65/2.29 | (93) empty(all_19_6_26) = all_46_0_31
% 6.65/2.29 | (94) empty(all_0_9_9) = all_46_2_33
% 6.65/2.29 | (95) ~ (all_46_0_31 = 0) | ~ (all_46_1_32 = 0) | all_46_2_33 = 0
% 6.65/2.29 |
% 6.65/2.29 | Instantiating (90) with all_52_0_38, all_52_1_39 yields:
% 6.65/2.29 | (96) relation_dom(all_0_9_9) = all_52_0_38 & relation(all_0_9_9) = all_52_1_39 & ( ~ (all_52_1_39 = 0) | (all_52_0_38 = all_0_10_10 & ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_10_10) = v2))))
% 6.65/2.29 |
% 6.65/2.29 | Applying alpha-rule on (96) yields:
% 6.65/2.29 | (97) relation_dom(all_0_9_9) = all_52_0_38
% 6.65/2.29 | (98) relation(all_0_9_9) = all_52_1_39
% 6.65/2.29 | (99) ~ (all_52_1_39 = 0) | (all_52_0_38 = all_0_10_10 & ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_10_10) = v2)))
% 6.65/2.29 |
% 6.65/2.29 | Instantiating formula (40) with all_0_9_9, all_52_0_38, all_19_6_26 and discharging atoms relation_dom(all_0_9_9) = all_52_0_38, relation_dom(all_0_9_9) = all_19_6_26, yields:
% 6.65/2.29 | (100) all_52_0_38 = all_19_6_26
% 6.65/2.29 |
% 6.65/2.29 | Instantiating formula (52) with all_0_9_9, all_52_1_39, 0 and discharging atoms relation(all_0_9_9) = all_52_1_39, relation(all_0_9_9) = 0, yields:
% 6.65/2.30 | (101) all_52_1_39 = 0
% 6.65/2.30 |
% 6.65/2.30 | Instantiating formula (52) with all_0_9_9, all_46_1_32, all_52_1_39 and discharging atoms relation(all_0_9_9) = all_52_1_39, relation(all_0_9_9) = all_46_1_32, yields:
% 6.65/2.30 | (102) all_52_1_39 = all_46_1_32
% 6.65/2.30 |
% 6.65/2.30 | Combining equations (101,102) yields a new equation:
% 6.65/2.30 | (103) all_46_1_32 = 0
% 6.65/2.30 |
% 6.65/2.30 | Combining equations (103,102) yields a new equation:
% 6.65/2.30 | (101) all_52_1_39 = 0
% 6.65/2.30 |
% 6.65/2.30 +-Applying beta-rule and splitting (99), into two cases.
% 6.65/2.30 |-Branch one:
% 6.65/2.30 | (105) ~ (all_52_1_39 = 0)
% 6.65/2.30 |
% 6.65/2.30 | Equations (101) can reduce 105 to:
% 6.65/2.30 | (68) $false
% 6.65/2.30 |
% 6.65/2.30 |-The branch is then unsatisfiable
% 6.65/2.30 |-Branch two:
% 6.65/2.30 | (101) all_52_1_39 = 0
% 6.65/2.30 | (108) all_52_0_38 = all_0_10_10 & ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_10_10) = v2))
% 6.65/2.30 |
% 6.65/2.30 | Applying alpha-rule on (108) yields:
% 6.65/2.30 | (109) all_52_0_38 = all_0_10_10
% 6.65/2.30 | (110) ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_10_10) = v2))
% 6.65/2.30 |
% 6.65/2.30 | Combining equations (109,100) yields a new equation:
% 6.65/2.30 | (111) all_19_6_26 = all_0_10_10
% 6.65/2.30 |
% 6.65/2.30 | Instantiating formula (110) with all_19_1_21, all_19_4_24 and discharging atoms apply(all_0_9_9, all_19_4_24) = all_19_1_21, yields:
% 6.65/2.30 | (112) all_19_1_21 = all_19_4_24 | ? [v0] : ( ~ (v0 = 0) & in(all_19_4_24, all_0_10_10) = v0)
% 6.65/2.30 |
% 6.65/2.30 | Instantiating formula (110) with all_19_1_21, all_19_5_25 and discharging atoms apply(all_0_9_9, all_19_5_25) = all_19_1_21, yields:
% 6.65/2.30 | (113) all_19_1_21 = all_19_5_25 | ? [v0] : ( ~ (v0 = 0) & in(all_19_5_25, all_0_10_10) = v0)
% 6.65/2.30 |
% 6.65/2.30 | From (111) and (88) follows:
% 6.65/2.30 | (114) in(all_19_4_24, all_0_10_10) = 0
% 6.65/2.30 |
% 6.65/2.30 | From (111) and (82) follows:
% 6.65/2.30 | (115) in(all_19_5_25, all_0_10_10) = 0
% 6.65/2.30 |
% 6.65/2.30 +-Applying beta-rule and splitting (113), into two cases.
% 6.65/2.30 |-Branch one:
% 6.65/2.30 | (116) all_19_1_21 = all_19_5_25
% 6.65/2.30 |
% 6.65/2.30 +-Applying beta-rule and splitting (112), into two cases.
% 6.65/2.30 |-Branch one:
% 6.65/2.30 | (117) all_19_1_21 = all_19_4_24
% 6.65/2.30 |
% 6.65/2.30 | Combining equations (116,117) yields a new equation:
% 6.65/2.30 | (118) all_19_4_24 = all_19_5_25
% 6.65/2.30 |
% 6.65/2.30 | Equations (118) can reduce 81 to:
% 6.65/2.30 | (68) $false
% 6.65/2.30 |
% 6.65/2.30 |-The branch is then unsatisfiable
% 6.65/2.30 |-Branch two:
% 6.65/2.30 | (120) ~ (all_19_1_21 = all_19_4_24)
% 6.65/2.30 | (121) ? [v0] : ( ~ (v0 = 0) & in(all_19_4_24, all_0_10_10) = v0)
% 6.65/2.30 |
% 6.65/2.30 | Instantiating (121) with all_79_0_46 yields:
% 6.65/2.30 | (122) ~ (all_79_0_46 = 0) & in(all_19_4_24, all_0_10_10) = all_79_0_46
% 6.65/2.30 |
% 6.65/2.30 | Applying alpha-rule on (122) yields:
% 6.65/2.30 | (123) ~ (all_79_0_46 = 0)
% 6.65/2.30 | (124) in(all_19_4_24, all_0_10_10) = all_79_0_46
% 6.65/2.30 |
% 6.65/2.30 | Instantiating formula (51) with all_19_4_24, all_0_10_10, 0, all_79_0_46 and discharging atoms in(all_19_4_24, all_0_10_10) = all_79_0_46, in(all_19_4_24, all_0_10_10) = 0, yields:
% 6.65/2.30 | (125) all_79_0_46 = 0
% 6.65/2.30 |
% 6.65/2.30 | Equations (125) can reduce 123 to:
% 6.65/2.30 | (68) $false
% 6.65/2.30 |
% 6.65/2.30 |-The branch is then unsatisfiable
% 6.65/2.30 |-Branch two:
% 6.65/2.30 | (127) ~ (all_19_1_21 = all_19_5_25)
% 6.65/2.30 | (128) ? [v0] : ( ~ (v0 = 0) & in(all_19_5_25, all_0_10_10) = v0)
% 6.65/2.30 |
% 6.65/2.30 | Instantiating (128) with all_75_0_47 yields:
% 6.65/2.30 | (129) ~ (all_75_0_47 = 0) & in(all_19_5_25, all_0_10_10) = all_75_0_47
% 6.65/2.30 |
% 6.65/2.30 | Applying alpha-rule on (129) yields:
% 6.65/2.30 | (130) ~ (all_75_0_47 = 0)
% 6.65/2.30 | (131) in(all_19_5_25, all_0_10_10) = all_75_0_47
% 6.65/2.30 |
% 6.65/2.30 | Instantiating formula (51) with all_19_5_25, all_0_10_10, 0, all_75_0_47 and discharging atoms in(all_19_5_25, all_0_10_10) = all_75_0_47, in(all_19_5_25, all_0_10_10) = 0, yields:
% 6.65/2.30 | (132) all_75_0_47 = 0
% 6.65/2.30 |
% 6.65/2.30 | Equations (132) can reduce 130 to:
% 6.65/2.30 | (68) $false
% 6.65/2.30 |
% 6.65/2.30 |-The branch is then unsatisfiable
% 6.65/2.30 % SZS output end Proof for theBenchmark
% 6.65/2.30
% 6.65/2.30 1667ms
%------------------------------------------------------------------------------