TSTP Solution File: SEU212+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU212+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 08:47:41 EDT 2022
% Result : Theorem 3.02s 1.36s
% Output : Proof 4.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU212+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 15:44:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.50/0.58 ____ _
% 0.50/0.58 ___ / __ \_____(_)___ ________ __________
% 0.50/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.58
% 0.50/0.58 A Theorem Prover for First-Order Logic
% 0.50/0.59 (ePrincess v.1.0)
% 0.50/0.59
% 0.50/0.59 (c) Philipp Rümmer, 2009-2015
% 0.50/0.59 (c) Peter Backeman, 2014-2015
% 0.50/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.59 Bug reports to peter@backeman.se
% 0.50/0.59
% 0.50/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.59
% 0.50/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.50/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.43/0.93 Prover 0: Preprocessing ...
% 2.27/1.16 Prover 0: Warning: ignoring some quantifiers
% 2.27/1.19 Prover 0: Constructing countermodel ...
% 3.02/1.36 Prover 0: proved (729ms)
% 3.02/1.36
% 3.02/1.36 No countermodel exists, formula is valid
% 3.02/1.36 % SZS status Theorem for theBenchmark
% 3.02/1.36
% 3.02/1.36 Generating proof ... Warning: ignoring some quantifiers
% 3.98/1.63 found it (size 29)
% 3.98/1.63
% 3.98/1.63 % SZS output start Proof for theBenchmark
% 3.98/1.63 Assumed formulas after preprocessing and simplification:
% 3.98/1.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_dom(v2) = v4 & ordered_pair(v0, v1) = v3 & apply(v2, v0) = v5 & relation_empty_yielding(v6) & relation_empty_yielding(empty_set) & relation(v11) & relation(v10) & relation(v8) & relation(v6) & relation(v2) & relation(empty_set) & function(v11) & function(v2) & empty(v10) & empty(v9) & empty(empty_set) & ~ empty(v8) & ~ empty(v7) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (singleton(v12) = v15) | ~ (unordered_pair(v14, v15) = v16) | ~ (unordered_pair(v12, v13) = v14) | ordered_pair(v12, v13) = v16) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v12) | ~ function(v12) | ~ in(v14, v13) | ? [v17] : (apply(v12, v14) = v17 & ( ~ (v17 = v15) | in(v16, v12)) & (v17 = v15 | ~ in(v16, v12)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v12) | ~ in(v16, v12) | in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = empty_set | ~ (relation_dom(v12) = v13) | ~ (apply(v12, v14) = v15) | ~ relation(v12) | ~ function(v12) | in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (ordered_pair(v15, v14) = v13) | ~ (ordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (apply(v15, v14) = v13) | ~ (apply(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (unordered_pair(v15, v14) = v13) | ~ (unordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ element(v13, v15) | ~ empty(v14) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ element(v13, v15) | ~ in(v12, v13) | element(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (powerset(v14) = v13) | ~ (powerset(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v14) = v13) | ~ (singleton(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_dom(v14) = v13) | ~ (relation_dom(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ subset(v12, v13) | element(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ element(v12, v14) | subset(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ~ in(v14, v13) | ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & in(v16, v12))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ~ empty(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ? [v16] : (singleton(v12) = v16 & unordered_pair(v15, v16) = v14 & unordered_pair(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v13, v12) = v14) | unordered_pair(v12, v13) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | ~ empty(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | unordered_pair(v13, v12) = v14) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (relation_dom(v13) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : ? [v17] : (( ~ in(v15, v12) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v15, v18) = v19) | ~ in(v19, v13))) & (in(v15, v12) | (ordered_pair(v15, v16) = v17 & in(v17, v13))))) & ! [v12] : ! [v13] : (v13 = v12 | ~ empty(v13) | ~ empty(v12)) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ empty(v13)) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | empty(v12) | ? [v14] : (element(v14, v13) & ~ empty(v14))) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : (element(v14, v13) & empty(v14))) & ! [v12] : ! [v13] : ( ~ (singleton(v12) = v13) | ~ empty(v13)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ~ empty(v13) | empty(v12)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ empty(v12) | relation(v13)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ empty(v12) | empty(v13)) & ! [v12] : ! [v13] : ( ~ element(v12, v13) | empty(v13) | in(v12, v13)) & ! [v12] : ! [v13] : ( ~ empty(v13) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ( ~ in(v13, v12) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ( ~ in(v12, v13) | element(v12, v13)) & ! [v12] : (v12 = empty_set | ~ empty(v12)) & ! [v12] : ( ~ empty(v12) | relation(v12)) & ! [v12] : ( ~ empty(v12) | function(v12)) & ? [v12] : ? [v13] : element(v13, v12) & ? [v12] : subset(v12, v12) & ((v5 = v1 & in(v0, v4) & ~ in(v3, v2)) | (in(v3, v2) & ( ~ (v5 = v1) | ~ in(v0, v4)))))
% 4.30/1.67 | 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:
% 4.30/1.67 | (1) relation_dom(all_0_9_9) = all_0_7_7 & ordered_pair(all_0_11_11, all_0_10_10) = all_0_8_8 & apply(all_0_9_9, all_0_11_11) = all_0_6_6 & relation_empty_yielding(all_0_5_5) & relation_empty_yielding(empty_set) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_5_5) & relation(all_0_9_9) & relation(empty_set) & function(all_0_0_0) & function(all_0_9_9) & empty(all_0_1_1) & empty(all_0_2_2) & empty(empty_set) & ~ empty(all_0_3_3) & ~ empty(all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) & ((all_0_6_6 = all_0_10_10 & in(all_0_11_11, all_0_7_7) & ~ in(all_0_8_8, all_0_9_9)) | (in(all_0_8_8, all_0_9_9) & ( ~ (all_0_6_6 = all_0_10_10) | ~ in(all_0_11_11, all_0_7_7))))
% 4.45/1.68 |
% 4.45/1.68 | Applying alpha-rule on (1) yields:
% 4.45/1.68 | (2) function(all_0_0_0)
% 4.45/1.68 | (3) ~ empty(all_0_4_4)
% 4.45/1.68 | (4) empty(all_0_2_2)
% 4.45/1.68 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 4.45/1.68 | (6) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 4.45/1.68 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 4.45/1.68 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 4.45/1.68 | (9) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 4.45/1.68 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 4.45/1.68 | (11) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 4.45/1.68 | (12) relation_dom(all_0_9_9) = all_0_7_7
% 4.45/1.68 | (13) relation(all_0_0_0)
% 4.45/1.68 | (14) empty(all_0_1_1)
% 4.45/1.68 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1))
% 4.45/1.68 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0)))
% 4.45/1.69 | (17) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.45/1.69 | (18) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 4.45/1.69 | (19) relation_empty_yielding(empty_set)
% 4.45/1.69 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 4.45/1.69 | (21) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 4.45/1.69 | (22) relation(all_0_3_3)
% 4.45/1.69 | (23) ordered_pair(all_0_11_11, all_0_10_10) = all_0_8_8
% 4.45/1.69 | (24) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1)))))
% 4.45/1.69 | (25) relation(all_0_5_5)
% 4.45/1.69 | (26) ! [v0] : ( ~ empty(v0) | relation(v0))
% 4.45/1.69 | (27) relation_empty_yielding(all_0_5_5)
% 4.45/1.69 | (28) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 4.45/1.69 | (29) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 4.45/1.69 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0))))
% 4.45/1.69 | (31) apply(all_0_9_9, all_0_11_11) = all_0_6_6
% 4.45/1.69 | (32) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1))
% 4.45/1.69 | (33) relation(empty_set)
% 4.45/1.69 | (34) empty(empty_set)
% 4.45/1.69 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 4.45/1.69 | (36) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 4.45/1.69 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 4.45/1.69 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 4.45/1.69 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 4.45/1.69 | (40) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.45/1.69 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 4.45/1.69 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 4.45/1.69 | (43) ? [v0] : ? [v1] : element(v1, v0)
% 4.45/1.69 | (44) function(all_0_9_9)
% 4.45/1.69 | (45) (all_0_6_6 = all_0_10_10 & in(all_0_11_11, all_0_7_7) & ~ in(all_0_8_8, all_0_9_9)) | (in(all_0_8_8, all_0_9_9) & ( ~ (all_0_6_6 = all_0_10_10) | ~ in(all_0_11_11, all_0_7_7)))
% 4.45/1.69 | (46) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 4.45/1.69 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 4.45/1.69 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 4.45/1.69 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 4.45/1.69 | (50) relation(all_0_9_9)
% 4.45/1.69 | (51) ! [v0] : ( ~ empty(v0) | function(v0))
% 4.45/1.69 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 4.45/1.69 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2))
% 4.45/1.70 | (54) relation(all_0_1_1)
% 4.45/1.70 | (55) ~ empty(all_0_3_3)
% 4.45/1.70 | (56) ? [v0] : subset(v0, v0)
% 4.45/1.70 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 4.45/1.70 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 4.45/1.70 |
% 4.45/1.70 +-Applying beta-rule and splitting (45), into two cases.
% 4.45/1.70 |-Branch one:
% 4.45/1.70 | (59) all_0_6_6 = all_0_10_10 & in(all_0_11_11, all_0_7_7) & ~ in(all_0_8_8, all_0_9_9)
% 4.45/1.70 |
% 4.45/1.70 | Applying alpha-rule on (59) yields:
% 4.45/1.70 | (60) all_0_6_6 = all_0_10_10
% 4.45/1.70 | (61) in(all_0_11_11, all_0_7_7)
% 4.45/1.70 | (62) ~ in(all_0_8_8, all_0_9_9)
% 4.45/1.70 |
% 4.45/1.70 | From (60) and (31) follows:
% 4.45/1.70 | (63) apply(all_0_9_9, all_0_11_11) = all_0_10_10
% 4.45/1.70 |
% 4.45/1.70 | Instantiating formula (30) with all_0_8_8, all_0_10_10, all_0_11_11, all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, ordered_pair(all_0_11_11, all_0_10_10) = all_0_8_8, relation(all_0_9_9), function(all_0_9_9), in(all_0_11_11, all_0_7_7), yields:
% 4.45/1.70 | (64) ? [v0] : (apply(all_0_9_9, all_0_11_11) = v0 & ( ~ (v0 = all_0_10_10) | in(all_0_8_8, all_0_9_9)) & (v0 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9)))
% 4.45/1.70 |
% 4.45/1.70 | Instantiating (64) with all_42_0_20 yields:
% 4.45/1.70 | (65) apply(all_0_9_9, all_0_11_11) = all_42_0_20 & ( ~ (all_42_0_20 = all_0_10_10) | in(all_0_8_8, all_0_9_9)) & (all_42_0_20 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9))
% 4.45/1.70 |
% 4.45/1.70 | Applying alpha-rule on (65) yields:
% 4.45/1.70 | (66) apply(all_0_9_9, all_0_11_11) = all_42_0_20
% 4.45/1.70 | (67) ~ (all_42_0_20 = all_0_10_10) | in(all_0_8_8, all_0_9_9)
% 4.45/1.70 | (68) all_42_0_20 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9)
% 4.45/1.70 |
% 4.45/1.70 +-Applying beta-rule and splitting (67), into two cases.
% 4.45/1.70 |-Branch one:
% 4.45/1.70 | (69) in(all_0_8_8, all_0_9_9)
% 4.45/1.70 |
% 4.45/1.70 | Using (69) and (62) yields:
% 4.45/1.70 | (70) $false
% 4.45/1.70 |
% 4.45/1.70 |-The branch is then unsatisfiable
% 4.45/1.70 |-Branch two:
% 4.45/1.70 | (62) ~ in(all_0_8_8, all_0_9_9)
% 4.45/1.70 | (72) ~ (all_42_0_20 = all_0_10_10)
% 4.45/1.70 |
% 4.45/1.70 | Instantiating formula (39) with all_0_9_9, all_0_11_11, all_42_0_20, all_0_10_10 and discharging atoms apply(all_0_9_9, all_0_11_11) = all_42_0_20, apply(all_0_9_9, all_0_11_11) = all_0_10_10, yields:
% 4.45/1.70 | (73) all_42_0_20 = all_0_10_10
% 4.45/1.70 |
% 4.45/1.70 | Equations (73) can reduce 72 to:
% 4.45/1.70 | (74) $false
% 4.45/1.70 |
% 4.45/1.70 |-The branch is then unsatisfiable
% 4.45/1.70 |-Branch two:
% 4.45/1.70 | (75) in(all_0_8_8, all_0_9_9) & ( ~ (all_0_6_6 = all_0_10_10) | ~ in(all_0_11_11, all_0_7_7))
% 4.45/1.70 |
% 4.45/1.70 | Applying alpha-rule on (75) yields:
% 4.45/1.70 | (69) in(all_0_8_8, all_0_9_9)
% 4.45/1.70 | (77) ~ (all_0_6_6 = all_0_10_10) | ~ in(all_0_11_11, all_0_7_7)
% 4.45/1.70 |
% 4.45/1.70 | Instantiating formula (49) with all_0_8_8, all_0_10_10, all_0_11_11, all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, ordered_pair(all_0_11_11, all_0_10_10) = all_0_8_8, relation(all_0_9_9), in(all_0_8_8, all_0_9_9), yields:
% 4.45/1.70 | (61) in(all_0_11_11, all_0_7_7)
% 4.45/1.70 |
% 4.45/1.70 +-Applying beta-rule and splitting (77), into two cases.
% 4.45/1.70 |-Branch one:
% 4.45/1.70 | (79) ~ in(all_0_11_11, all_0_7_7)
% 4.45/1.70 |
% 4.45/1.70 | Using (61) and (79) yields:
% 4.45/1.70 | (70) $false
% 4.45/1.70 |
% 4.45/1.70 |-The branch is then unsatisfiable
% 4.45/1.70 |-Branch two:
% 4.45/1.70 | (61) in(all_0_11_11, all_0_7_7)
% 4.45/1.70 | (82) ~ (all_0_6_6 = all_0_10_10)
% 4.45/1.70 |
% 4.45/1.70 | Instantiating formula (30) with all_0_8_8, all_0_10_10, all_0_11_11, all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, ordered_pair(all_0_11_11, all_0_10_10) = all_0_8_8, relation(all_0_9_9), function(all_0_9_9), in(all_0_11_11, all_0_7_7), yields:
% 4.45/1.71 | (64) ? [v0] : (apply(all_0_9_9, all_0_11_11) = v0 & ( ~ (v0 = all_0_10_10) | in(all_0_8_8, all_0_9_9)) & (v0 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9)))
% 4.45/1.71 |
% 4.45/1.71 | Instantiating (64) with all_52_0_23 yields:
% 4.45/1.71 | (84) apply(all_0_9_9, all_0_11_11) = all_52_0_23 & ( ~ (all_52_0_23 = all_0_10_10) | in(all_0_8_8, all_0_9_9)) & (all_52_0_23 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9))
% 4.45/1.71 |
% 4.45/1.71 | Applying alpha-rule on (84) yields:
% 4.45/1.71 | (85) apply(all_0_9_9, all_0_11_11) = all_52_0_23
% 4.45/1.71 | (86) ~ (all_52_0_23 = all_0_10_10) | in(all_0_8_8, all_0_9_9)
% 4.45/1.71 | (87) all_52_0_23 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9)
% 4.45/1.71 |
% 4.45/1.71 +-Applying beta-rule and splitting (87), into two cases.
% 4.45/1.71 |-Branch one:
% 4.45/1.71 | (62) ~ in(all_0_8_8, all_0_9_9)
% 4.45/1.71 |
% 4.45/1.71 | Using (69) and (62) yields:
% 4.45/1.71 | (70) $false
% 4.45/1.71 |
% 4.45/1.71 |-The branch is then unsatisfiable
% 4.45/1.71 |-Branch two:
% 4.45/1.71 | (69) in(all_0_8_8, all_0_9_9)
% 4.45/1.71 | (91) all_52_0_23 = all_0_10_10
% 4.45/1.71 |
% 4.45/1.71 | From (91) and (85) follows:
% 4.45/1.71 | (63) apply(all_0_9_9, all_0_11_11) = all_0_10_10
% 4.45/1.71 |
% 4.45/1.71 | Instantiating formula (39) with all_0_9_9, all_0_11_11, all_0_10_10, all_0_6_6 and discharging atoms apply(all_0_9_9, all_0_11_11) = all_0_6_6, apply(all_0_9_9, all_0_11_11) = all_0_10_10, yields:
% 4.45/1.71 | (60) all_0_6_6 = all_0_10_10
% 4.45/1.71 |
% 4.45/1.71 | Equations (60) can reduce 82 to:
% 4.45/1.71 | (74) $false
% 4.45/1.71 |
% 4.45/1.71 |-The branch is then unsatisfiable
% 4.45/1.71 % SZS output end Proof for theBenchmark
% 4.45/1.71
% 4.45/1.71 1113ms
%------------------------------------------------------------------------------