TSTP Solution File: SEU238+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU238+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n003.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 08:48:02 EDT 2022
% Result : Theorem 4.19s 1.67s
% Output : Proof 6.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU238+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.32 % Computer : n003.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sun Jun 19 09:33:28 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.55/0.56 ____ _
% 0.55/0.56 ___ / __ \_____(_)___ ________ __________
% 0.55/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.56
% 0.55/0.56 A Theorem Prover for First-Order Logic
% 0.55/0.56 (ePrincess v.1.0)
% 0.55/0.56
% 0.55/0.56 (c) Philipp Rümmer, 2009-2015
% 0.55/0.56 (c) Peter Backeman, 2014-2015
% 0.55/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.57 Bug reports to peter@backeman.se
% 0.55/0.57
% 0.55/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.57
% 0.55/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.55/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/0.94 Prover 0: Preprocessing ...
% 2.31/1.19 Prover 0: Warning: ignoring some quantifiers
% 2.31/1.21 Prover 0: Constructing countermodel ...
% 4.19/1.67 Prover 0: proved (1050ms)
% 4.19/1.67
% 4.19/1.67 No countermodel exists, formula is valid
% 4.19/1.67 % SZS status Theorem for theBenchmark
% 4.19/1.67
% 4.19/1.67 Generating proof ... Warning: ignoring some quantifiers
% 6.43/2.21 found it (size 41)
% 6.43/2.21
% 6.43/2.21 % SZS output start Proof for theBenchmark
% 6.43/2.21 Assumed formulas after preprocessing and simplification:
% 6.43/2.21 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (relation_non_empty(v3) & relation_empty_yielding(v5) & relation_empty_yielding(v4) & relation_empty_yielding(empty_set) & one_to_one(v10) & one_to_one(v7) & one_to_one(empty_set) & relation(v15) & relation(v13) & relation(v11) & relation(v10) & relation(v9) & relation(v7) & relation(v5) & relation(v4) & relation(v3) & relation(empty_set) & epsilon_connected(v14) & epsilon_connected(v10) & epsilon_connected(v6) & epsilon_connected(empty_set) & epsilon_transitive(v14) & epsilon_transitive(v10) & epsilon_transitive(v6) & epsilon_transitive(empty_set) & ordinal(v14) & ordinal(v10) & ordinal(v6) & ordinal(v0) & ordinal(empty_set) & function(v15) & function(v11) & function(v10) & function(v7) & function(v4) & function(v3) & function(empty_set) & empty(v13) & empty(v12) & empty(v11) & empty(v10) & empty(empty_set) & ~ empty(v9) & ~ empty(v8) & ~ empty(v6) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (set_union2(v19, v18) = v17) | ~ (set_union2(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ element(v17, v19) | ~ empty(v18) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ element(v17, v19) | ~ in(v16, v17) | element(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (powerset(v18) = v17) | ~ (powerset(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (singleton(v18) = v17) | ~ (singleton(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (succ(v18) = v17) | ~ (succ(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | subset(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ subset(v16, v17) | element(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (singleton(v16) = v17) | ~ (set_union2(v16, v17) = v18) | succ(v16) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (succ(v17) = v18) | ~ being_limit_ordinal(v16) | ~ ordinal(v17) | ~ ordinal(v16) | ~ in(v17, v16) | in(v18, v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (succ(v16) = v17) | ~ ordinal_subset(v17, v18) | ~ ordinal(v18) | ~ ordinal(v16) | in(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (succ(v16) = v17) | ~ ordinal(v18) | ~ ordinal(v16) | ~ in(v16, v18) | ordinal_subset(v17, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v17, v16) = v18) | ~ empty(v18) | empty(v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v17, v16) = v18) | set_union2(v16, v17) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | ~ empty(v18) | empty(v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | set_union2(v17, v16) = v18) & ! [v16] : ! [v17] : (v17 = v16 | ~ (set_union2(v16, v16) = v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ (set_union2(v16, empty_set) = v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ subset(v16, v17) | proper_subset(v16, v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ empty(v17) | ~ empty(v16)) & ! [v16] : ! [v17] : ( ~ (succ(v16) = v17) | ~ ordinal(v16) | ~ empty(v17)) & ! [v16] : ! [v17] : ( ~ (succ(v16) = v17) | ~ ordinal(v16) | epsilon_connected(v17)) & ! [v16] : ! [v17] : ( ~ (succ(v16) = v17) | ~ ordinal(v16) | epsilon_transitive(v17)) & ! [v16] : ! [v17] : ( ~ (succ(v16) = v17) | ~ ordinal(v16) | ordinal(v17)) & ! [v16] : ! [v17] : ( ~ (succ(v16) = v17) | ~ empty(v17)) & ! [v16] : ! [v17] : ( ~ (succ(v16) = v17) | in(v16, v17)) & ! [v16] : ! [v17] : ( ~ (succ(v16) = v17) | ? [v18] : (singleton(v16) = v18 & set_union2(v16, v18) = v17)) & ! [v16] : ! [v17] : ( ~ element(v16, v17) | empty(v17) | in(v16, v17)) & ! [v16] : ! [v17] : ( ~ subset(v16, v17) | ~ ordinal(v17) | ~ ordinal(v16) | ordinal_subset(v16, v17)) & ! [v16] : ! [v17] : ( ~ ordinal_subset(v16, v17) | ~ ordinal(v17) | ~ ordinal(v16) | subset(v16, v17)) & ! [v16] : ! [v17] : ( ~ epsilon_transitive(v16) | ~ ordinal(v17) | ~ proper_subset(v16, v17) | in(v16, v17)) & ! [v16] : ! [v17] : ( ~ ordinal(v17) | ~ ordinal(v16) | ordinal_subset(v17, v16) | ordinal_subset(v16, v17)) & ! [v16] : ! [v17] : ( ~ ordinal(v17) | ~ ordinal(v16) | ordinal_subset(v16, v16)) & ! [v16] : ! [v17] : ( ~ empty(v17) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ( ~ proper_subset(v17, v16) | ~ proper_subset(v16, v17)) & ! [v16] : ! [v17] : ( ~ proper_subset(v16, v17) | subset(v16, v17)) & ! [v16] : ! [v17] : ( ~ in(v17, v16) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ( ~ in(v16, v17) | element(v16, v17)) & ! [v16] : (v16 = empty_set | ~ empty(v16)) & ! [v16] : ( ~ relation(v16) | ~ function(v16) | ~ empty(v16) | one_to_one(v16)) & ! [v16] : ( ~ epsilon_connected(v16) | ~ epsilon_transitive(v16) | ordinal(v16)) & ! [v16] : ( ~ ordinal(v16) | being_limit_ordinal(v16) | ? [v17] : ? [v18] : (succ(v17) = v18 & ordinal(v17) & in(v17, v16) & ~ in(v18, v16))) & ! [v16] : ( ~ ordinal(v16) | epsilon_connected(v16)) & ! [v16] : ( ~ ordinal(v16) | epsilon_transitive(v16)) & ! [v16] : ( ~ empty(v16) | relation(v16)) & ! [v16] : ( ~ empty(v16) | epsilon_connected(v16)) & ! [v16] : ( ~ empty(v16) | epsilon_transitive(v16)) & ! [v16] : ( ~ empty(v16) | ordinal(v16)) & ! [v16] : ( ~ empty(v16) | function(v16)) & ! [v16] : ~ proper_subset(v16, v16) & ? [v16] : ? [v17] : element(v17, v16) & ? [v16] : subset(v16, v16) & ((v2 = v0 & succ(v1) = v0 & being_limit_ordinal(v0) & ordinal(v1)) | ( ~ being_limit_ordinal(v0) & ! [v16] : ( ~ ordinal(v16) | ? [v17] : ( ~ (v17 = v0) & succ(v16) = v17)))))
% 6.84/2.25 | 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, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15 yields:
% 6.84/2.25 | (1) relation_non_empty(all_0_12_12) & relation_empty_yielding(all_0_10_10) & relation_empty_yielding(all_0_11_11) & relation_empty_yielding(empty_set) & one_to_one(all_0_5_5) & one_to_one(all_0_8_8) & one_to_one(empty_set) & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_4_4) & relation(all_0_5_5) & relation(all_0_6_6) & relation(all_0_8_8) & relation(all_0_10_10) & relation(all_0_11_11) & relation(all_0_12_12) & relation(empty_set) & epsilon_connected(all_0_1_1) & epsilon_connected(all_0_5_5) & epsilon_connected(all_0_9_9) & epsilon_connected(empty_set) & epsilon_transitive(all_0_1_1) & epsilon_transitive(all_0_5_5) & epsilon_transitive(all_0_9_9) & epsilon_transitive(empty_set) & ordinal(all_0_1_1) & ordinal(all_0_5_5) & ordinal(all_0_9_9) & ordinal(all_0_15_15) & ordinal(empty_set) & function(all_0_0_0) & function(all_0_4_4) & function(all_0_5_5) & function(all_0_8_8) & function(all_0_11_11) & function(all_0_12_12) & function(empty_set) & empty(all_0_2_2) & empty(all_0_3_3) & empty(all_0_4_4) & empty(all_0_5_5) & empty(empty_set) & ~ empty(all_0_6_6) & ~ empty(all_0_7_7) & ~ empty(all_0_9_9) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(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 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0) | ~ in(v1, v0) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal_subset(v1, v2) | ~ ordinal(v2) | ~ ordinal(v0) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) | ordinal_subset(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_connected(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_transitive(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ordinal(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(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] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) & ! [v0] : ( ~ ordinal(v0) | being_limit_ordinal(v0) | ? [v1] : ? [v2] : (succ(v1) = v2 & ordinal(v1) & in(v1, v0) & ~ in(v2, v0))) & ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | ordinal(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ~ proper_subset(v0, v0) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) & ((all_0_13_13 = all_0_15_15 & succ(all_0_14_14) = all_0_15_15 & being_limit_ordinal(all_0_15_15) & ordinal(all_0_14_14)) | ( ~ being_limit_ordinal(all_0_15_15) & ! [v0] : ( ~ ordinal(v0) | ? [v1] : ( ~ (v1 = all_0_15_15) & succ(v0) = v1))))
% 6.84/2.26 |
% 6.84/2.26 | Applying alpha-rule on (1) yields:
% 6.84/2.26 | (2) empty(all_0_2_2)
% 6.84/2.26 | (3) ~ empty(all_0_6_6)
% 6.84/2.26 | (4) ordinal(all_0_15_15)
% 6.84/2.26 | (5) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 6.84/2.26 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 6.84/2.26 | (7) ordinal(all_0_1_1)
% 6.84/2.26 | (8) epsilon_transitive(all_0_5_5)
% 6.84/2.26 | (9) relation_non_empty(all_0_12_12)
% 6.84/2.26 | (10) function(all_0_11_11)
% 6.84/2.26 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.84/2.26 | (12) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ empty(v1))
% 6.84/2.26 | (13) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1))
% 6.84/2.26 | (14) (all_0_13_13 = all_0_15_15 & succ(all_0_14_14) = all_0_15_15 & being_limit_ordinal(all_0_15_15) & ordinal(all_0_14_14)) | ( ~ being_limit_ordinal(all_0_15_15) & ! [v0] : ( ~ ordinal(v0) | ? [v1] : ( ~ (v1 = all_0_15_15) & succ(v0) = v1)))
% 6.84/2.26 | (15) relation_empty_yielding(all_0_10_10)
% 6.84/2.26 | (16) ? [v0] : ? [v1] : element(v1, v0)
% 6.84/2.26 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 6.84/2.26 | (18) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1))
% 6.84/2.26 | (19) epsilon_connected(all_0_5_5)
% 6.84/2.26 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 6.84/2.26 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0) | ~ in(v1, v0) | in(v2, v0))
% 6.84/2.26 | (22) ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0))
% 6.84/2.26 | (23) ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0))
% 6.84/2.26 | (24) relation(all_0_11_11)
% 6.84/2.26 | (25) one_to_one(empty_set)
% 6.84/2.26 | (26) function(empty_set)
% 6.84/2.26 | (27) epsilon_connected(empty_set)
% 6.84/2.26 | (28) epsilon_transitive(all_0_9_9)
% 6.84/2.26 | (29) relation(all_0_10_10)
% 6.84/2.26 | (30) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 6.84/2.26 | (31) relation_empty_yielding(all_0_11_11)
% 6.84/2.26 | (32) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ordinal(v1))
% 6.84/2.26 | (33) empty(empty_set)
% 6.84/2.26 | (34) ! [v0] : ~ proper_subset(v0, v0)
% 6.84/2.26 | (35) empty(all_0_3_3)
% 6.84/2.27 | (36) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_connected(v1))
% 6.84/2.27 | (37) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1))
% 6.84/2.27 | (38) empty(all_0_5_5)
% 6.84/2.27 | (39) relation(all_0_12_12)
% 6.84/2.27 | (40) ? [v0] : subset(v0, v0)
% 6.84/2.27 | (41) ordinal(all_0_5_5)
% 6.84/2.27 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 6.84/2.27 | (43) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1))
% 6.84/2.27 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 6.84/2.27 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 6.84/2.27 | (46) relation(all_0_2_2)
% 6.84/2.27 | (47) relation(all_0_8_8)
% 6.84/2.27 | (48) function(all_0_5_5)
% 6.84/2.27 | (49) function(all_0_4_4)
% 6.84/2.27 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) | ordinal_subset(v1, v2))
% 6.84/2.27 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 6.84/2.27 | (52) relation(empty_set)
% 6.84/2.27 | (53) epsilon_connected(all_0_9_9)
% 6.84/2.27 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 6.84/2.27 | (55) relation_empty_yielding(empty_set)
% 6.84/2.27 | (56) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 6.84/2.27 | (57) ! [v0] : ! [v1] : ( ~ ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, v1))
% 6.84/2.27 | (58) ! [v0] : ( ~ empty(v0) | epsilon_connected(v0))
% 6.84/2.27 | (59) epsilon_transitive(all_0_1_1)
% 6.84/2.27 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 6.84/2.27 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 6.84/2.27 | (62) one_to_one(all_0_8_8)
% 6.84/2.27 | (63) relation(all_0_4_4)
% 6.84/2.27 | (64) ordinal(all_0_9_9)
% 6.84/2.27 | (65) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1))
% 6.84/2.27 | (66) ! [v0] : ( ~ empty(v0) | function(v0))
% 6.84/2.27 | (67) ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1))
% 6.84/2.27 | (68) ~ empty(all_0_9_9)
% 6.84/2.27 | (69) ! [v0] : ( ~ empty(v0) | relation(v0))
% 6.84/2.27 | (70) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1))
% 6.84/2.27 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 6.84/2.27 | (72) relation(all_0_0_0)
% 6.84/2.27 | (73) empty(all_0_4_4)
% 6.84/2.27 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 6.84/2.27 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 6.84/2.27 | (76) ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 6.84/2.27 | (77) ~ empty(all_0_7_7)
% 6.84/2.27 | (78) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_transitive(v1))
% 6.84/2.27 | (79) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 6.84/2.27 | (80) ordinal(empty_set)
% 6.84/2.27 | (81) relation(all_0_5_5)
% 6.84/2.27 | (82) epsilon_transitive(empty_set)
% 6.84/2.27 | (83) ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 6.84/2.27 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2)
% 6.84/2.27 | (85) function(all_0_8_8)
% 6.84/2.27 | (86) one_to_one(all_0_5_5)
% 6.84/2.27 | (87) function(all_0_12_12)
% 6.84/2.27 | (88) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1))
% 6.84/2.27 | (89) ! [v0] : ( ~ ordinal(v0) | being_limit_ordinal(v0) | ? [v1] : ? [v2] : (succ(v1) = v2 & ordinal(v1) & in(v1, v0) & ~ in(v2, v0)))
% 6.84/2.27 | (90) epsilon_connected(all_0_1_1)
% 6.84/2.27 | (91) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 6.84/2.27 | (92) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1))
% 6.84/2.28 | (93) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 6.84/2.28 | (94) function(all_0_0_0)
% 6.84/2.28 | (95) ! [v0] : ( ~ empty(v0) | ordinal(v0))
% 6.84/2.28 | (96) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 6.84/2.28 | (97) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 6.84/2.28 | (98) relation(all_0_6_6)
% 6.84/2.28 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal_subset(v1, v2) | ~ ordinal(v2) | ~ ordinal(v0) | in(v0, v2))
% 6.84/2.28 | (100) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v0))
% 6.84/2.28 |
% 6.84/2.28 | Instantiating formula (93) with all_0_3_3, all_0_2_2 and discharging atoms empty(all_0_2_2), empty(all_0_3_3), yields:
% 6.84/2.28 | (101) all_0_2_2 = all_0_3_3
% 6.84/2.28 |
% 6.84/2.28 | Instantiating formula (93) with all_0_4_4, all_0_2_2 and discharging atoms empty(all_0_2_2), empty(all_0_4_4), yields:
% 6.84/2.28 | (102) all_0_2_2 = all_0_4_4
% 6.84/2.28 |
% 6.84/2.28 | Instantiating formula (93) with all_0_5_5, all_0_3_3 and discharging atoms empty(all_0_3_3), empty(all_0_5_5), yields:
% 6.84/2.28 | (103) all_0_3_3 = all_0_5_5
% 6.84/2.28 |
% 6.84/2.28 | Instantiating formula (93) with empty_set, all_0_3_3 and discharging atoms empty(all_0_3_3), empty(empty_set), yields:
% 6.84/2.28 | (104) all_0_3_3 = empty_set
% 6.84/2.28 |
% 6.84/2.28 | Combining equations (101,102) yields a new equation:
% 6.84/2.28 | (105) all_0_3_3 = all_0_4_4
% 6.84/2.28 |
% 6.84/2.28 | Simplifying 105 yields:
% 6.84/2.28 | (106) all_0_3_3 = all_0_4_4
% 6.84/2.28 |
% 6.84/2.28 | Combining equations (104,106) yields a new equation:
% 6.84/2.28 | (107) all_0_4_4 = empty_set
% 6.84/2.28 |
% 6.84/2.28 | Combining equations (103,106) yields a new equation:
% 6.84/2.28 | (108) all_0_4_4 = all_0_5_5
% 6.84/2.28 |
% 6.84/2.28 | Combining equations (107,108) yields a new equation:
% 6.84/2.28 | (109) all_0_5_5 = empty_set
% 6.84/2.28 |
% 6.84/2.28 | From (109) and (41) follows:
% 6.84/2.28 | (80) ordinal(empty_set)
% 6.84/2.28 |
% 6.84/2.28 | Instantiating formula (89) with all_0_15_15 and discharging atoms ordinal(all_0_15_15), yields:
% 6.84/2.28 | (111) being_limit_ordinal(all_0_15_15) | ? [v0] : ? [v1] : (succ(v0) = v1 & ordinal(v0) & in(v0, all_0_15_15) & ~ in(v1, all_0_15_15))
% 6.84/2.28 |
% 6.84/2.28 | Instantiating formula (100) with empty_set, all_0_15_15 and discharging atoms ordinal(all_0_15_15), ordinal(empty_set), yields:
% 6.84/2.28 | (112) ordinal_subset(all_0_15_15, all_0_15_15)
% 6.84/2.28 |
% 6.84/2.28 +-Applying beta-rule and splitting (14), into two cases.
% 6.84/2.28 |-Branch one:
% 6.84/2.28 | (113) all_0_13_13 = all_0_15_15 & succ(all_0_14_14) = all_0_15_15 & being_limit_ordinal(all_0_15_15) & ordinal(all_0_14_14)
% 6.84/2.28 |
% 6.84/2.28 | Applying alpha-rule on (113) yields:
% 6.84/2.28 | (114) all_0_13_13 = all_0_15_15
% 6.84/2.28 | (115) succ(all_0_14_14) = all_0_15_15
% 6.84/2.28 | (116) being_limit_ordinal(all_0_15_15)
% 6.84/2.28 | (117) ordinal(all_0_14_14)
% 6.84/2.28 |
% 6.84/2.28 | Instantiating formula (99) with all_0_15_15, all_0_15_15, all_0_14_14 and discharging atoms succ(all_0_14_14) = all_0_15_15, ordinal_subset(all_0_15_15, all_0_15_15), ordinal(all_0_14_14), ordinal(all_0_15_15), yields:
% 6.84/2.28 | (118) in(all_0_14_14, all_0_15_15)
% 6.84/2.28 |
% 6.84/2.28 | Instantiating formula (21) with all_0_15_15, all_0_14_14, all_0_15_15 and discharging atoms succ(all_0_14_14) = all_0_15_15, being_limit_ordinal(all_0_15_15), ordinal(all_0_14_14), ordinal(all_0_15_15), in(all_0_14_14, all_0_15_15), yields:
% 6.84/2.28 | (119) in(all_0_15_15, all_0_15_15)
% 6.84/2.28 |
% 6.84/2.28 | Instantiating formula (30) with all_0_15_15, all_0_15_15 and discharging atoms in(all_0_15_15, all_0_15_15), yields:
% 6.84/2.28 | (120) $false
% 6.84/2.28 |
% 6.84/2.28 |-The branch is then unsatisfiable
% 6.84/2.28 |-Branch two:
% 6.84/2.28 | (121) ~ being_limit_ordinal(all_0_15_15) & ! [v0] : ( ~ ordinal(v0) | ? [v1] : ( ~ (v1 = all_0_15_15) & succ(v0) = v1))
% 6.84/2.28 |
% 6.84/2.29 | Applying alpha-rule on (121) yields:
% 6.84/2.29 | (122) ~ being_limit_ordinal(all_0_15_15)
% 6.84/2.29 | (123) ! [v0] : ( ~ ordinal(v0) | ? [v1] : ( ~ (v1 = all_0_15_15) & succ(v0) = v1))
% 6.84/2.29 |
% 6.84/2.29 +-Applying beta-rule and splitting (111), into two cases.
% 6.84/2.29 |-Branch one:
% 6.84/2.29 | (116) being_limit_ordinal(all_0_15_15)
% 6.84/2.29 |
% 6.84/2.29 | Using (116) and (122) yields:
% 6.84/2.29 | (120) $false
% 6.84/2.29 |
% 6.84/2.29 |-The branch is then unsatisfiable
% 6.84/2.29 |-Branch two:
% 6.84/2.29 | (122) ~ being_limit_ordinal(all_0_15_15)
% 6.84/2.29 | (127) ? [v0] : ? [v1] : (succ(v0) = v1 & ordinal(v0) & in(v0, all_0_15_15) & ~ in(v1, all_0_15_15))
% 6.84/2.29 |
% 6.84/2.29 | Instantiating (127) with all_43_0_24, all_43_1_25 yields:
% 6.84/2.29 | (128) succ(all_43_1_25) = all_43_0_24 & ordinal(all_43_1_25) & in(all_43_1_25, all_0_15_15) & ~ in(all_43_0_24, all_0_15_15)
% 6.84/2.29 |
% 6.84/2.29 | Applying alpha-rule on (128) yields:
% 6.84/2.29 | (129) succ(all_43_1_25) = all_43_0_24
% 6.84/2.29 | (130) ordinal(all_43_1_25)
% 6.84/2.29 | (131) in(all_43_1_25, all_0_15_15)
% 6.84/2.29 | (132) ~ in(all_43_0_24, all_0_15_15)
% 6.84/2.29 |
% 6.84/2.29 | Instantiating formula (78) with all_43_0_24, all_43_1_25 and discharging atoms succ(all_43_1_25) = all_43_0_24, ordinal(all_43_1_25), yields:
% 6.84/2.29 | (133) epsilon_transitive(all_43_0_24)
% 6.84/2.29 |
% 6.84/2.29 | Instantiating formula (32) with all_43_0_24, all_43_1_25 and discharging atoms succ(all_43_1_25) = all_43_0_24, ordinal(all_43_1_25), yields:
% 6.84/2.29 | (134) ordinal(all_43_0_24)
% 6.84/2.29 |
% 6.84/2.29 | Instantiating formula (123) with all_43_1_25 and discharging atoms ordinal(all_43_1_25), yields:
% 6.84/2.29 | (135) ? [v0] : ( ~ (v0 = all_0_15_15) & succ(all_43_1_25) = v0)
% 6.84/2.29 |
% 6.84/2.29 | Instantiating formula (50) with all_0_15_15, all_43_0_24, all_43_1_25 and discharging atoms succ(all_43_1_25) = all_43_0_24, ordinal(all_43_1_25), ordinal(all_0_15_15), in(all_43_1_25, all_0_15_15), yields:
% 6.84/2.29 | (136) ordinal_subset(all_43_0_24, all_0_15_15)
% 6.84/2.29 |
% 6.84/2.29 | Instantiating (135) with all_55_0_28 yields:
% 6.84/2.29 | (137) ~ (all_55_0_28 = all_0_15_15) & succ(all_43_1_25) = all_55_0_28
% 6.84/2.29 |
% 6.84/2.29 | Applying alpha-rule on (137) yields:
% 6.84/2.29 | (138) ~ (all_55_0_28 = all_0_15_15)
% 6.84/2.29 | (139) succ(all_43_1_25) = all_55_0_28
% 6.84/2.29 |
% 6.84/2.29 | Instantiating formula (6) with all_43_1_25, all_55_0_28, all_43_0_24 and discharging atoms succ(all_43_1_25) = all_55_0_28, succ(all_43_1_25) = all_43_0_24, yields:
% 6.84/2.29 | (140) all_55_0_28 = all_43_0_24
% 6.84/2.29 |
% 6.84/2.29 | Equations (140) can reduce 138 to:
% 6.84/2.29 | (141) ~ (all_43_0_24 = all_0_15_15)
% 6.84/2.29 |
% 6.84/2.29 | Instantiating formula (57) with all_0_15_15, all_43_0_24 and discharging atoms ordinal_subset(all_43_0_24, all_0_15_15), ordinal(all_43_0_24), ordinal(all_0_15_15), yields:
% 6.84/2.29 | (142) subset(all_43_0_24, all_0_15_15)
% 6.84/2.29 |
% 6.84/2.29 | Instantiating formula (65) with all_0_15_15, all_43_0_24 and discharging atoms subset(all_43_0_24, all_0_15_15), yields:
% 6.84/2.29 | (143) all_43_0_24 = all_0_15_15 | proper_subset(all_43_0_24, all_0_15_15)
% 6.84/2.29 |
% 6.84/2.29 +-Applying beta-rule and splitting (143), into two cases.
% 6.84/2.29 |-Branch one:
% 6.84/2.29 | (144) proper_subset(all_43_0_24, all_0_15_15)
% 6.84/2.29 |
% 6.84/2.29 | Instantiating formula (67) with all_0_15_15, all_43_0_24 and discharging atoms epsilon_transitive(all_43_0_24), ordinal(all_0_15_15), proper_subset(all_43_0_24, all_0_15_15), ~ in(all_43_0_24, all_0_15_15), yields:
% 6.84/2.29 | (120) $false
% 6.84/2.29 |
% 6.84/2.29 |-The branch is then unsatisfiable
% 6.84/2.29 |-Branch two:
% 6.84/2.29 | (146) ~ proper_subset(all_43_0_24, all_0_15_15)
% 6.84/2.29 | (147) all_43_0_24 = all_0_15_15
% 6.84/2.29 |
% 6.84/2.29 | Equations (147) can reduce 141 to:
% 6.84/2.29 | (148) $false
% 6.84/2.29 |
% 6.84/2.29 |-The branch is then unsatisfiable
% 6.84/2.29 % SZS output end Proof for theBenchmark
% 6.84/2.29
% 6.84/2.29 1719ms
%------------------------------------------------------------------------------