TSTP Solution File: SEU217+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU217+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:47:45 EDT 2022
% Result : Theorem 3.41s 1.48s
% Output : Proof 4.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU217+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 13:54:59 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.53/0.60 ____ _
% 0.53/0.60 ___ / __ \_____(_)___ ________ __________
% 0.53/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.60
% 0.53/0.60 A Theorem Prover for First-Order Logic
% 0.53/0.60 (ePrincess v.1.0)
% 0.53/0.60
% 0.53/0.60 (c) Philipp Rümmer, 2009-2015
% 0.53/0.60 (c) Peter Backeman, 2014-2015
% 0.53/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.60 Bug reports to peter@backeman.se
% 0.53/0.60
% 0.53/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.60
% 0.53/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.55/0.93 Prover 0: Preprocessing ...
% 1.82/1.08 Prover 0: Warning: ignoring some quantifiers
% 1.97/1.10 Prover 0: Constructing countermodel ...
% 2.58/1.26 Prover 0: gave up
% 2.58/1.26 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.58/1.29 Prover 1: Preprocessing ...
% 2.86/1.37 Prover 1: Warning: ignoring some quantifiers
% 2.86/1.37 Prover 1: Constructing countermodel ...
% 3.41/1.48 Prover 1: proved (215ms)
% 3.41/1.48
% 3.41/1.48 No countermodel exists, formula is valid
% 3.41/1.48 % SZS status Theorem for theBenchmark
% 3.41/1.48
% 3.41/1.48 Generating proof ... Warning: ignoring some quantifiers
% 4.80/1.83 found it (size 21)
% 4.80/1.83
% 4.80/1.83 % SZS output start Proof for theBenchmark
% 4.80/1.83 Assumed formulas after preprocessing and simplification:
% 4.80/1.83 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v9 = 0) & ~ (v6 = 0) & ~ (v3 = v1) & apply(v2, v1) = v3 & identity_relation(v0) = v2 & in(v1, v0) = 0 & function(v4) = 0 & empty(v10) = 0 & empty(v8) = v9 & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & relation(v11) = 0 & relation(v10) = 0 & relation(v8) = 0 & relation(v4) = 0 & relation(empty_set) = 0 & relation_empty_yielding(v11) = 0 & relation_empty_yielding(empty_set) = 0 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (apply(v15, v14) = v13) | ~ (apply(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (in(v15, v14) = v13) | ~ (in(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (element(v15, v14) = v13) | ~ (element(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (element(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (identity_relation(v14) = v13) | ~ (identity_relation(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_dom(v14) = v13) | ~ (relation_dom(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (function(v14) = v13) | ~ (function(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (empty(v14) = v13) | ~ (empty(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation(v14) = v13) | ~ (relation(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_empty_yielding(v14) = v13) | ~ (relation_empty_yielding(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (identity_relation(v12) = v14) | ~ (function(v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (relation_dom(v13) = v16 & relation(v13) = v15 & ( ~ (v15 = 0) | (( ~ (v16 = v12) | v14 = v13 | (v18 = 0 & ~ (v19 = v17) & apply(v13, v17) = v19 & in(v17, v12) = 0)) & ( ~ (v14 = v13) | (v16 = v12 & ! [v20] : ! [v21] : (v21 = v20 | ~ (apply(v13, v20) = v21) | ? [v22] : ( ~ (v22 = 0) & in(v20, v12) = v22)))))))) & ! [v12] : ! [v13] : (v13 = v12 | ~ (empty(v13) = 0) | ~ (empty(v12) = 0)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (function(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (relation(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v12] : ! [v13] : ( ~ (identity_relation(v12) = v13) | function(v13) = 0) & ! [v12] : ! [v13] : ( ~ (identity_relation(v12) = v13) | relation(v13) = 0) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (empty(v13) = v16 & empty(v12) = v14 & relation(v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v14 = 0))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (empty(v13) = v15 & empty(v12) = v14 & relation(v13) = v16 & ( ~ (v14 = 0) | (v16 = 0 & v15 = 0)))) & ! [v12] : ! [v13] : ( ~ (element(v12, v13) = 0) | ? [v14] : ? [v15] : (in(v12, v13) = v15 & empty(v13) = v14 & (v15 = 0 | v14 = 0))) & ! [v12] : (v12 = empty_set | ~ (empty(v12) = 0)) & ? [v12] : ? [v13] : element(v13, v12) = 0)
% 4.80/1.87 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11 yields:
% 4.80/1.87 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_5_5 = 0) & ~ (all_0_8_8 = all_0_10_10) & apply(all_0_9_9, all_0_10_10) = all_0_8_8 & identity_relation(all_0_11_11) = all_0_9_9 & in(all_0_10_10, all_0_11_11) = 0 & function(all_0_7_7) = 0 & empty(all_0_1_1) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(empty_set) = 0 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_3_3) = 0 & relation(all_0_7_7) = 0 & relation(empty_set) = 0 & relation_empty_yielding(all_0_0_0) = 0 & relation_empty_yielding(empty_set) = 0 & ! [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] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(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] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [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 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1) = 0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v3 & empty(v0) = v2 & relation(v1) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (in(v0, v1) = v3 & empty(v1) = v2 & (v3 = 0 | v2 = 0))) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ? [v0] : ? [v1] : element(v1, v0) = 0
% 4.80/1.88 |
% 4.80/1.88 | Applying alpha-rule on (1) yields:
% 4.80/1.88 | (2) ~ (all_0_2_2 = 0)
% 4.80/1.88 | (3) empty(all_0_1_1) = 0
% 4.80/1.88 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 4.80/1.88 | (5) relation(empty_set) = 0
% 4.80/1.88 | (6) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 4.80/1.88 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 4.80/1.88 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 4.80/1.88 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 4.80/1.88 | (10) empty(all_0_4_4) = 0
% 4.80/1.88 | (11) relation(all_0_0_0) = 0
% 4.80/1.88 | (12) empty(all_0_3_3) = all_0_2_2
% 4.80/1.88 | (13) ~ (all_0_5_5 = 0)
% 4.80/1.88 | (14) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 4.80/1.88 | (15) empty(empty_set) = 0
% 4.80/1.88 | (16) relation_empty_yielding(all_0_0_0) = 0
% 4.80/1.88 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 4.80/1.88 | (18) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0)
% 4.80/1.88 | (19) ! [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))))))))
% 4.80/1.88 | (20) in(all_0_10_10, all_0_11_11) = 0
% 4.80/1.88 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 4.80/1.89 | (22) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 4.80/1.89 | (23) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1) = 0)
% 4.80/1.89 | (24) identity_relation(all_0_11_11) = all_0_9_9
% 4.80/1.89 | (25) ? [v0] : ? [v1] : element(v1, v0) = 0
% 4.80/1.89 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 4.80/1.89 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 4.80/1.89 | (28) empty(all_0_6_6) = all_0_5_5
% 4.80/1.89 | (29) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (in(v0, v1) = v3 & empty(v1) = v2 & (v3 = 0 | v2 = 0)))
% 4.80/1.89 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.80/1.89 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 4.80/1.89 | (32) ~ (all_0_8_8 = all_0_10_10)
% 4.80/1.89 | (33) relation_empty_yielding(empty_set) = 0
% 4.80/1.89 | (34) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v3 & empty(v0) = v2 & relation(v1) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 4.80/1.89 | (35) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 4.80/1.89 | (36) relation(all_0_3_3) = 0
% 4.80/1.89 | (37) apply(all_0_9_9, all_0_10_10) = all_0_8_8
% 4.80/1.89 | (38) relation(all_0_1_1) = 0
% 4.80/1.89 | (39) relation(all_0_7_7) = 0
% 4.80/1.89 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 4.80/1.89 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 4.80/1.89 | (42) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 4.80/1.89 | (43) function(all_0_7_7) = 0
% 4.80/1.89 |
% 4.80/1.89 | Instantiating formula (23) with all_0_9_9, all_0_11_11 and discharging atoms identity_relation(all_0_11_11) = all_0_9_9, yields:
% 4.80/1.89 | (44) function(all_0_9_9) = 0
% 4.80/1.89 |
% 4.80/1.89 | Instantiating formula (18) with all_0_9_9, all_0_11_11 and discharging atoms identity_relation(all_0_11_11) = all_0_9_9, yields:
% 4.80/1.89 | (45) relation(all_0_9_9) = 0
% 4.80/1.89 |
% 4.80/1.89 | Instantiating formula (19) with all_0_9_9, all_0_9_9, all_0_11_11 and discharging atoms identity_relation(all_0_11_11) = all_0_9_9, function(all_0_9_9) = 0, yields:
% 4.80/1.89 | (46) ? [v0] : ? [v1] : (relation_dom(all_0_9_9) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | (v1 = all_0_11_11 & ! [v2] : ! [v3] : (v3 = v2 | ~ (apply(all_0_9_9, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, all_0_11_11) = v4)))))
% 4.80/1.89 |
% 4.80/1.89 | Instantiating (46) with all_32_0_23, all_32_1_24 yields:
% 4.80/1.89 | (47) relation_dom(all_0_9_9) = all_32_0_23 & relation(all_0_9_9) = all_32_1_24 & ( ~ (all_32_1_24 = 0) | (all_32_0_23 = all_0_11_11 & ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_11_11) = v2))))
% 4.80/1.90 |
% 4.80/1.90 | Applying alpha-rule on (47) yields:
% 4.80/1.90 | (48) relation_dom(all_0_9_9) = all_32_0_23
% 4.80/1.90 | (49) relation(all_0_9_9) = all_32_1_24
% 4.80/1.90 | (50) ~ (all_32_1_24 = 0) | (all_32_0_23 = all_0_11_11 & ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_11_11) = v2)))
% 4.80/1.90 |
% 4.80/1.90 | Instantiating formula (41) with all_0_9_9, all_32_1_24, 0 and discharging atoms relation(all_0_9_9) = all_32_1_24, relation(all_0_9_9) = 0, yields:
% 4.80/1.90 | (51) all_32_1_24 = 0
% 4.80/1.90 |
% 4.80/1.90 +-Applying beta-rule and splitting (50), into two cases.
% 4.80/1.90 |-Branch one:
% 4.80/1.90 | (52) ~ (all_32_1_24 = 0)
% 4.80/1.90 |
% 4.80/1.90 | Equations (51) can reduce 52 to:
% 4.80/1.90 | (53) $false
% 4.80/1.90 |
% 4.80/1.90 |-The branch is then unsatisfiable
% 4.80/1.90 |-Branch two:
% 4.80/1.90 | (51) all_32_1_24 = 0
% 4.80/1.90 | (55) all_32_0_23 = all_0_11_11 & ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_11_11) = v2))
% 4.80/1.90 |
% 4.80/1.90 | Applying alpha-rule on (55) yields:
% 4.80/1.90 | (56) all_32_0_23 = all_0_11_11
% 4.80/1.90 | (57) ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_11_11) = v2))
% 4.80/1.90 |
% 4.80/1.90 | Instantiating formula (57) with all_0_8_8, all_0_10_10 and discharging atoms apply(all_0_9_9, all_0_10_10) = all_0_8_8, yields:
% 4.80/1.90 | (58) all_0_8_8 = all_0_10_10 | ? [v0] : ( ~ (v0 = 0) & in(all_0_10_10, all_0_11_11) = v0)
% 4.80/1.90 |
% 4.80/1.90 +-Applying beta-rule and splitting (58), into two cases.
% 4.80/1.90 |-Branch one:
% 4.80/1.90 | (59) all_0_8_8 = all_0_10_10
% 4.80/1.90 |
% 4.80/1.90 | Equations (59) can reduce 32 to:
% 4.80/1.90 | (53) $false
% 4.80/1.90 |
% 4.80/1.90 |-The branch is then unsatisfiable
% 4.80/1.90 |-Branch two:
% 4.80/1.90 | (32) ~ (all_0_8_8 = all_0_10_10)
% 4.80/1.90 | (62) ? [v0] : ( ~ (v0 = 0) & in(all_0_10_10, all_0_11_11) = v0)
% 4.80/1.90 |
% 4.80/1.90 | Instantiating (62) with all_51_0_31 yields:
% 4.80/1.90 | (63) ~ (all_51_0_31 = 0) & in(all_0_10_10, all_0_11_11) = all_51_0_31
% 4.80/1.90 |
% 4.80/1.90 | Applying alpha-rule on (63) yields:
% 4.80/1.90 | (64) ~ (all_51_0_31 = 0)
% 4.80/1.90 | (65) in(all_0_10_10, all_0_11_11) = all_51_0_31
% 4.80/1.90 |
% 4.80/1.90 | Instantiating formula (30) with all_0_10_10, all_0_11_11, all_51_0_31, 0 and discharging atoms in(all_0_10_10, all_0_11_11) = all_51_0_31, in(all_0_10_10, all_0_11_11) = 0, yields:
% 4.80/1.90 | (66) all_51_0_31 = 0
% 4.80/1.90 |
% 4.80/1.90 | Equations (66) can reduce 64 to:
% 4.80/1.90 | (53) $false
% 4.80/1.90 |
% 4.80/1.90 |-The branch is then unsatisfiable
% 4.80/1.90 % SZS output end Proof for theBenchmark
% 4.80/1.90
% 4.80/1.90 1289ms
%------------------------------------------------------------------------------