TSTP Solution File: SET995+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET995+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 3.25s 1.46s
% Output : Proof 5.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET995+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n027.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 : Sat Jul 9 17:43:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.48/0.58 ____ _
% 0.48/0.58 ___ / __ \_____(_)___ ________ __________
% 0.48/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.58
% 0.48/0.58 A Theorem Prover for First-Order Logic
% 0.48/0.58 (ePrincess v.1.0)
% 0.48/0.58
% 0.48/0.58 (c) Philipp Rümmer, 2009-2015
% 0.48/0.58 (c) Peter Backeman, 2014-2015
% 0.48/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.58 Bug reports to peter@backeman.se
% 0.48/0.58
% 0.48/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.58
% 0.48/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.58/0.96 Prover 0: Preprocessing ...
% 2.38/1.24 Prover 0: Warning: ignoring some quantifiers
% 2.38/1.26 Prover 0: Constructing countermodel ...
% 3.25/1.45 Prover 0: proved (823ms)
% 3.25/1.46
% 3.25/1.46 No countermodel exists, formula is valid
% 3.25/1.46 % SZS status Theorem for theBenchmark
% 3.25/1.46
% 3.25/1.46 Generating proof ... Warning: ignoring some quantifiers
% 4.82/1.84 found it (size 24)
% 4.82/1.84
% 4.82/1.84 % SZS output start Proof for theBenchmark
% 4.82/1.84 Assumed formulas after preprocessing and simplification:
% 4.82/1.84 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v4 = v1) & relation_rng(v4) = v3 & relation_rng(v1) = v3 & relation_dom(v4) = v2 & relation_dom(v1) = v2 & singleton(v0) = v3 & relation_empty_yielding(v5) & relation_empty_yielding(empty_set) & relation(v10) & relation(v9) & relation(v7) & relation(v5) & relation(v4) & relation(v1) & relation(empty_set) & function(v10) & function(v4) & function(v1) & empty(v9) & empty(v8) & empty(empty_set) & ~ empty(v7) & ~ empty(v6) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (apply(v14, v13) = v12) | ~ (apply(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ element(v12, v14) | ~ empty(v13) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ element(v12, v14) | ~ in(v11, v12) | element(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (relation_dom(v13) = v12) | ~ (relation_dom(v11) = v12) | ~ relation(v13) | ~ relation(v11) | ~ function(v13) | ~ function(v11) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = v15) & apply(v13, v14) = v16 & apply(v11, v14) = v15 & in(v14, v12))) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v11) = v12) | ~ in(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_rng(v13) = v12) | ~ (relation_rng(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_dom(v13) = v12) | ~ (relation_dom(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v13) = v12) | ~ (singleton(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ subset(v11, v12) | element(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ element(v11, v13) | subset(v11, v12)) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v12) = v13) | ? [v14] : (( ~ (v14 = v12) | ~ in(v12, v11)) & (v14 = v12 | in(v14, v11)))) & ! [v11] : ! [v12] : (v12 = v11 | ~ empty(v12) | ~ empty(v11)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | empty(v11) | ? [v13] : (element(v13, v12) & ~ empty(v13))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (element(v13, v12) & empty(v13))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ~ function(v11) | ? [v13] : (relation_dom(v11) = v13 & ! [v14] : ! [v15] : ( ~ (apply(v11, v15) = v14) | ~ in(v15, v13) | in(v14, v12)) & ! [v14] : ( ~ in(v14, v12) | ? [v15] : (apply(v11, v15) = v14 & in(v15, v13))) & ? [v14] : (v14 = v12 | ? [v15] : ? [v16] : ? [v17] : (( ~ in(v15, v14) | ! [v18] : ( ~ (apply(v11, v18) = v15) | ~ in(v18, v13))) & (in(v15, v14) | (v17 = v15 & apply(v11, v16) = v15 & in(v16, v13))))))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ~ empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ~ function(v11) | ? [v13] : (relation_rng(v11) = v13 & ! [v14] : ! [v15] : ( ~ (apply(v11, v15) = v14) | ~ in(v15, v12) | in(v14, v13)) & ! [v14] : ( ~ in(v14, v13) | ? [v15] : (apply(v11, v15) = v14 & in(v15, v12))) & ? [v14] : (v14 = v13 | ? [v15] : ? [v16] : ? [v17] : (( ~ in(v15, v14) | ! [v18] : ( ~ (apply(v11, v18) = v15) | ~ in(v18, v12))) & (in(v15, v14) | (v17 = v15 & apply(v11, v16) = v15 & in(v16, v12))))))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ~ empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ empty(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ element(v11, v12) | empty(v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ empty(v12) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v12, v11) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v11, v12) | element(v11, v12)) & ! [v11] : (v11 = empty_set | ~ empty(v11)) & ! [v11] : ( ~ empty(v11) | relation(v11)) & ! [v11] : ( ~ empty(v11) | function(v11)) & ? [v11] : ? [v12] : element(v12, v11) & ? [v11] : subset(v11, v11))
% 5.03/1.89 | 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:
% 5.03/1.89 | (1) ~ (all_0_6_6 = all_0_9_9) & relation_rng(all_0_6_6) = all_0_7_7 & relation_rng(all_0_9_9) = all_0_7_7 & relation_dom(all_0_6_6) = all_0_8_8 & relation_dom(all_0_9_9) = all_0_8_8 & singleton(all_0_10_10) = all_0_7_7 & 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_6_6) & relation(all_0_9_9) & relation(empty_set) & function(all_0_0_0) & function(all_0_6_6) & 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] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(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] : (v2 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & apply(v2, v3) = v5 & apply(v0, v3) = v4 & in(v3, v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [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 | ~ (singleton(v2) = v1) | ~ (singleton(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] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [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] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, 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] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, 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)
% 5.03/1.90 |
% 5.03/1.90 | Applying alpha-rule on (1) yields:
% 5.03/1.90 | (2) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 5.03/1.90 | (3) relation_dom(all_0_6_6) = all_0_8_8
% 5.03/1.90 | (4) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2)))))))
% 5.03/1.90 | (5) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1))
% 5.03/1.90 | (6) relation_dom(all_0_9_9) = all_0_8_8
% 5.03/1.90 | (7) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 5.03/1.91 | (8) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 5.03/1.91 | (9) relation(all_0_0_0)
% 5.03/1.91 | (10) relation(all_0_5_5)
% 5.03/1.91 | (11) relation_empty_yielding(all_0_5_5)
% 5.03/1.91 | (12) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 5.03/1.91 | (13) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1)))))))
% 5.03/1.91 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 5.03/1.91 | (15) relation(empty_set)
% 5.03/1.91 | (16) ! [v0] : ( ~ empty(v0) | relation(v0))
% 5.03/1.91 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 5.03/1.91 | (18) ~ empty(all_0_3_3)
% 5.03/1.91 | (19) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 5.03/1.91 | (20) relation_empty_yielding(empty_set)
% 5.03/1.91 | (21) empty(all_0_2_2)
% 5.03/1.91 | (22) ~ (all_0_6_6 = all_0_9_9)
% 5.03/1.91 | (23) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 5.03/1.91 | (24) relation_rng(all_0_9_9) = all_0_7_7
% 5.03/1.91 | (25) empty(empty_set)
% 5.03/1.91 | (26) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 5.03/1.91 | (27) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 5.03/1.91 | (28) relation_rng(all_0_6_6) = all_0_7_7
% 5.03/1.91 | (29) relation(all_0_9_9)
% 5.03/1.91 | (30) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 5.03/1.91 | (31) empty(all_0_1_1)
% 5.03/1.91 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 5.03/1.91 | (33) relation(all_0_1_1)
% 5.03/1.91 | (34) ? [v0] : ? [v1] : element(v1, v0)
% 5.03/1.91 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 5.03/1.91 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 5.03/1.91 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 5.03/1.91 | (38) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 5.03/1.91 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 5.03/1.91 | (40) function(all_0_6_6)
% 5.03/1.92 | (41) ! [v0] : ( ~ empty(v0) | function(v0))
% 5.03/1.92 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 5.03/1.92 | (43) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 5.03/1.92 | (44) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 5.03/1.92 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 5.03/1.92 | (46) ? [v0] : subset(v0, v0)
% 5.03/1.92 | (47) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 5.03/1.92 | (48) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 5.03/1.92 | (49) function(all_0_9_9)
% 5.03/1.92 | (50) function(all_0_0_0)
% 5.03/1.92 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & apply(v2, v3) = v5 & apply(v0, v3) = v4 & in(v3, v1)))
% 5.03/1.92 | (52) relation(all_0_6_6)
% 5.03/1.92 | (53) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 5.03/1.92 | (54) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 5.03/1.92 | (55) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 5.03/1.92 | (56) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 5.03/1.92 | (57) singleton(all_0_10_10) = all_0_7_7
% 5.03/1.92 | (58) relation(all_0_3_3)
% 5.03/1.92 | (59) ~ empty(all_0_4_4)
% 5.03/1.92 |
% 5.03/1.92 | Instantiating formula (13) with all_0_8_8, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_8_8, relation(all_0_6_6), function(all_0_6_6), yields:
% 5.03/1.92 | (60) ? [v0] : (relation_rng(all_0_6_6) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_6_6, v2) = v1) | ~ in(v2, all_0_8_8) | in(v1, v0)) & ! [v1] : ( ~ in(v1, v0) | ? [v2] : (apply(all_0_6_6, v2) = v1 & in(v2, all_0_8_8))) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_6_6, v5) = v2) | ~ in(v5, all_0_8_8))) & (in(v2, v1) | (v4 = v2 & apply(all_0_6_6, v3) = v2 & in(v3, all_0_8_8))))))
% 5.03/1.92 |
% 5.03/1.92 | Instantiating formula (51) with all_0_9_9, all_0_8_8, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_8_8, relation_dom(all_0_9_9) = all_0_8_8, relation(all_0_6_6), relation(all_0_9_9), function(all_0_6_6), function(all_0_9_9), yields:
% 5.03/1.92 | (61) all_0_6_6 = all_0_9_9 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_6_6, v0) = v1 & apply(all_0_9_9, v0) = v2 & in(v0, all_0_8_8))
% 5.03/1.92 |
% 5.03/1.92 | Instantiating formula (13) with all_0_8_8, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_8_8, relation(all_0_9_9), function(all_0_9_9), yields:
% 5.03/1.93 | (62) ? [v0] : (relation_rng(all_0_9_9) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_9_9, v2) = v1) | ~ in(v2, all_0_8_8) | in(v1, v0)) & ! [v1] : ( ~ in(v1, v0) | ? [v2] : (apply(all_0_9_9, v2) = v1 & in(v2, all_0_8_8))) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_9_9, v5) = v2) | ~ in(v5, all_0_8_8))) & (in(v2, v1) | (v4 = v2 & apply(all_0_9_9, v3) = v2 & in(v3, all_0_8_8))))))
% 5.03/1.93 |
% 5.03/1.93 | Instantiating (60) with all_19_0_15 yields:
% 5.03/1.93 | (63) relation_rng(all_0_6_6) = all_19_0_15 & ! [v0] : ! [v1] : ( ~ (apply(all_0_6_6, v1) = v0) | ~ in(v1, all_0_8_8) | in(v0, all_19_0_15)) & ! [v0] : ( ~ in(v0, all_19_0_15) | ? [v1] : (apply(all_0_6_6, v1) = v0 & in(v1, all_0_8_8))) & ? [v0] : (v0 = all_19_0_15 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_6_6, v4) = v1) | ~ in(v4, all_0_8_8))) & (in(v1, v0) | (v3 = v1 & apply(all_0_6_6, v2) = v1 & in(v2, all_0_8_8)))))
% 5.03/1.93 |
% 5.03/1.93 | Applying alpha-rule on (63) yields:
% 5.03/1.93 | (64) relation_rng(all_0_6_6) = all_19_0_15
% 5.03/1.93 | (65) ! [v0] : ! [v1] : ( ~ (apply(all_0_6_6, v1) = v0) | ~ in(v1, all_0_8_8) | in(v0, all_19_0_15))
% 5.03/1.93 | (66) ! [v0] : ( ~ in(v0, all_19_0_15) | ? [v1] : (apply(all_0_6_6, v1) = v0 & in(v1, all_0_8_8)))
% 5.03/1.93 | (67) ? [v0] : (v0 = all_19_0_15 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_6_6, v4) = v1) | ~ in(v4, all_0_8_8))) & (in(v1, v0) | (v3 = v1 & apply(all_0_6_6, v2) = v1 & in(v2, all_0_8_8)))))
% 5.03/1.93 |
% 5.03/1.93 | Instantiating (62) with all_22_0_16 yields:
% 5.03/1.93 | (68) relation_rng(all_0_9_9) = all_22_0_16 & ! [v0] : ! [v1] : ( ~ (apply(all_0_9_9, v1) = v0) | ~ in(v1, all_0_8_8) | in(v0, all_22_0_16)) & ! [v0] : ( ~ in(v0, all_22_0_16) | ? [v1] : (apply(all_0_9_9, v1) = v0 & in(v1, all_0_8_8))) & ? [v0] : (v0 = all_22_0_16 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_9_9, v4) = v1) | ~ in(v4, all_0_8_8))) & (in(v1, v0) | (v3 = v1 & apply(all_0_9_9, v2) = v1 & in(v2, all_0_8_8)))))
% 5.03/1.93 |
% 5.03/1.93 | Applying alpha-rule on (68) yields:
% 5.03/1.93 | (69) relation_rng(all_0_9_9) = all_22_0_16
% 5.03/1.93 | (70) ! [v0] : ! [v1] : ( ~ (apply(all_0_9_9, v1) = v0) | ~ in(v1, all_0_8_8) | in(v0, all_22_0_16))
% 5.03/1.93 | (71) ! [v0] : ( ~ in(v0, all_22_0_16) | ? [v1] : (apply(all_0_9_9, v1) = v0 & in(v1, all_0_8_8)))
% 5.03/1.93 | (72) ? [v0] : (v0 = all_22_0_16 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_9_9, v4) = v1) | ~ in(v4, all_0_8_8))) & (in(v1, v0) | (v3 = v1 & apply(all_0_9_9, v2) = v1 & in(v2, all_0_8_8)))))
% 5.03/1.93 |
% 5.03/1.93 +-Applying beta-rule and splitting (61), into two cases.
% 5.03/1.93 |-Branch one:
% 5.03/1.93 | (73) all_0_6_6 = all_0_9_9
% 5.03/1.93 |
% 5.03/1.93 | Equations (73) can reduce 22 to:
% 5.03/1.94 | (74) $false
% 5.03/1.94 |
% 5.03/1.94 |-The branch is then unsatisfiable
% 5.03/1.94 |-Branch two:
% 5.03/1.94 | (22) ~ (all_0_6_6 = all_0_9_9)
% 5.03/1.94 | (76) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_6_6, v0) = v1 & apply(all_0_9_9, v0) = v2 & in(v0, all_0_8_8))
% 5.03/1.94 |
% 5.03/1.94 | Instantiating (76) with all_39_0_23, all_39_1_24, all_39_2_25 yields:
% 5.03/1.94 | (77) ~ (all_39_0_23 = all_39_1_24) & apply(all_0_6_6, all_39_2_25) = all_39_1_24 & apply(all_0_9_9, all_39_2_25) = all_39_0_23 & in(all_39_2_25, all_0_8_8)
% 5.03/1.94 |
% 5.03/1.94 | Applying alpha-rule on (77) yields:
% 5.03/1.94 | (78) ~ (all_39_0_23 = all_39_1_24)
% 5.03/1.94 | (79) apply(all_0_6_6, all_39_2_25) = all_39_1_24
% 5.03/1.94 | (80) apply(all_0_9_9, all_39_2_25) = all_39_0_23
% 5.03/1.94 | (81) in(all_39_2_25, all_0_8_8)
% 5.03/1.94 |
% 5.03/1.94 | Instantiating formula (42) with all_0_6_6, all_19_0_15, all_0_7_7 and discharging atoms relation_rng(all_0_6_6) = all_19_0_15, relation_rng(all_0_6_6) = all_0_7_7, yields:
% 5.03/1.94 | (82) all_19_0_15 = all_0_7_7
% 5.03/1.94 |
% 5.03/1.94 | Instantiating formula (42) with all_0_9_9, all_22_0_16, all_0_7_7 and discharging atoms relation_rng(all_0_9_9) = all_22_0_16, relation_rng(all_0_9_9) = all_0_7_7, yields:
% 5.03/1.94 | (83) all_22_0_16 = all_0_7_7
% 5.03/1.94 |
% 5.03/1.94 | Instantiating formula (65) with all_39_2_25, all_39_1_24 and discharging atoms apply(all_0_6_6, all_39_2_25) = all_39_1_24, in(all_39_2_25, all_0_8_8), yields:
% 5.03/1.94 | (84) in(all_39_1_24, all_19_0_15)
% 5.03/1.94 |
% 5.03/1.94 | Instantiating formula (70) with all_39_2_25, all_39_0_23 and discharging atoms apply(all_0_9_9, all_39_2_25) = all_39_0_23, in(all_39_2_25, all_0_8_8), yields:
% 5.03/1.94 | (85) in(all_39_0_23, all_22_0_16)
% 5.03/1.94 |
% 5.03/1.94 | From (83) and (85) follows:
% 5.37/1.94 | (86) in(all_39_0_23, all_0_7_7)
% 5.37/1.94 |
% 5.37/1.94 | From (82) and (84) follows:
% 5.37/1.94 | (87) in(all_39_1_24, all_0_7_7)
% 5.37/1.94 |
% 5.37/1.94 | Instantiating formula (53) with all_39_0_23, all_0_7_7, all_0_10_10 and discharging atoms singleton(all_0_10_10) = all_0_7_7, in(all_39_0_23, all_0_7_7), yields:
% 5.37/1.94 | (88) all_39_0_23 = all_0_10_10
% 5.37/1.94 |
% 5.37/1.94 | Instantiating formula (53) with all_39_1_24, all_0_7_7, all_0_10_10 and discharging atoms singleton(all_0_10_10) = all_0_7_7, in(all_39_1_24, all_0_7_7), yields:
% 5.37/1.94 | (89) all_39_1_24 = all_0_10_10
% 5.37/1.94 |
% 5.37/1.94 | Equations (88,89) can reduce 78 to:
% 5.37/1.94 | (74) $false
% 5.37/1.94 |
% 5.37/1.94 |-The branch is then unsatisfiable
% 5.37/1.94 % SZS output end Proof for theBenchmark
% 5.37/1.94
% 5.37/1.94 1353ms
%------------------------------------------------------------------------------