TSTP Solution File: SEU238+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU238+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 08:48:01 EDT 2022
% Result : Theorem 4.44s 1.85s
% Output : Proof 6.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU238+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jun 18 20:55:44 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.66/0.64 ____ _
% 0.66/0.64 ___ / __ \_____(_)___ ________ __________
% 0.66/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.66/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.66/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.66/0.64
% 0.66/0.64 A Theorem Prover for First-Order Logic
% 0.66/0.64 (ePrincess v.1.0)
% 0.66/0.64
% 0.66/0.64 (c) Philipp Rümmer, 2009-2015
% 0.66/0.64 (c) Peter Backeman, 2014-2015
% 0.66/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.66/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.66/0.64 Bug reports to peter@backeman.se
% 0.66/0.64
% 0.66/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.66/0.64
% 0.66/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.79/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.66/1.05 Prover 0: Preprocessing ...
% 2.21/1.30 Prover 0: Warning: ignoring some quantifiers
% 2.50/1.33 Prover 0: Constructing countermodel ...
% 4.44/1.85 Prover 0: proved (1143ms)
% 4.44/1.85
% 4.44/1.85 No countermodel exists, formula is valid
% 4.44/1.85 % SZS status Theorem for theBenchmark
% 4.44/1.85
% 4.44/1.85 Generating proof ... Warning: ignoring some quantifiers
% 6.59/2.33 found it (size 41)
% 6.59/2.33
% 6.59/2.33 % SZS output start Proof for theBenchmark
% 6.59/2.33 Assumed formulas after preprocessing and simplification:
% 6.59/2.33 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (relation_empty_yielding(v4) & relation_empty_yielding(v3) & relation_empty_yielding(empty_set) & one_to_one(v9) & one_to_one(v6) & one_to_one(empty_set) & relation(v14) & relation(v12) & relation(v10) & relation(v9) & relation(v8) & relation(v6) & relation(v4) & relation(v3) & relation(empty_set) & epsilon_connected(v13) & epsilon_connected(v9) & epsilon_connected(v5) & epsilon_connected(empty_set) & epsilon_transitive(v13) & epsilon_transitive(v9) & epsilon_transitive(v5) & epsilon_transitive(empty_set) & ordinal(v13) & ordinal(v9) & ordinal(v5) & ordinal(v0) & ordinal(empty_set) & function(v14) & function(v10) & function(v9) & function(v6) & function(v3) & function(empty_set) & empty(v12) & empty(v11) & empty(v10) & empty(v9) & empty(empty_set) & ~ empty(v8) & ~ empty(v7) & ~ empty(v5) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (set_union2(v18, v17) = v16) | ~ (set_union2(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ empty(v17) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ in(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (powerset(v17) = v16) | ~ (powerset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (singleton(v17) = v16) | ~ (singleton(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (succ(v17) = v16) | ~ (succ(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ subset(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v15) = v16) | ~ (set_union2(v15, v16) = v17) | succ(v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (succ(v16) = v17) | ~ being_limit_ordinal(v15) | ~ ordinal(v16) | ~ ordinal(v15) | ~ in(v16, v15) | in(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (succ(v15) = v16) | ~ ordinal_subset(v16, v17) | ~ ordinal(v17) | ~ ordinal(v15) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (succ(v15) = v16) | ~ ordinal(v17) | ~ ordinal(v15) | ~ in(v15, v17) | ordinal_subset(v16, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v16, v15) = v17) | ~ empty(v17) | empty(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v16, v15) = v17) | set_union2(v15, v16) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | ~ empty(v17) | empty(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | set_union2(v16, v15) = v17) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_union2(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_union2(v15, empty_set) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ subset(v15, v16) | proper_subset(v15, v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ empty(v16) | ~ empty(v15)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ~ ordinal(v15) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ~ ordinal(v15) | epsilon_connected(v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ~ ordinal(v15) | epsilon_transitive(v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ~ ordinal(v15) | ordinal(v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ? [v17] : (singleton(v15) = v17 & set_union2(v15, v17) = v16)) & ! [v15] : ! [v16] : ( ~ element(v15, v16) | empty(v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ subset(v15, v16) | ~ ordinal(v16) | ~ ordinal(v15) | ordinal_subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ ordinal_subset(v15, v16) | ~ ordinal(v16) | ~ ordinal(v15) | subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ epsilon_transitive(v15) | ~ ordinal(v16) | ~ proper_subset(v15, v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ ordinal(v16) | ~ ordinal(v15) | ordinal_subset(v16, v15) | ordinal_subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ ordinal(v16) | ~ ordinal(v15) | ordinal_subset(v15, v15)) & ! [v15] : ! [v16] : ( ~ empty(v16) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ proper_subset(v16, v15) | ~ proper_subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ proper_subset(v15, v16) | subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v16, v15) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v15, v16) | element(v15, v16)) & ! [v15] : (v15 = empty_set | ~ empty(v15)) & ! [v15] : ( ~ relation(v15) | ~ function(v15) | ~ empty(v15) | one_to_one(v15)) & ! [v15] : ( ~ epsilon_connected(v15) | ~ epsilon_transitive(v15) | ordinal(v15)) & ! [v15] : ( ~ ordinal(v15) | being_limit_ordinal(v15) | ? [v16] : ? [v17] : (succ(v16) = v17 & ordinal(v16) & in(v16, v15) & ~ in(v17, v15))) & ! [v15] : ( ~ ordinal(v15) | epsilon_connected(v15)) & ! [v15] : ( ~ ordinal(v15) | epsilon_transitive(v15)) & ! [v15] : ( ~ empty(v15) | relation(v15)) & ! [v15] : ( ~ empty(v15) | epsilon_connected(v15)) & ! [v15] : ( ~ empty(v15) | epsilon_transitive(v15)) & ! [v15] : ( ~ empty(v15) | ordinal(v15)) & ! [v15] : ( ~ empty(v15) | function(v15)) & ! [v15] : ~ proper_subset(v15, v15) & ? [v15] : ? [v16] : element(v16, v15) & ? [v15] : subset(v15, v15) & ((v2 = v0 & succ(v1) = v0 & being_limit_ordinal(v0) & ordinal(v1)) | ( ~ being_limit_ordinal(v0) & ! [v15] : ( ~ ordinal(v15) | ? [v16] : ( ~ (v16 = v0) & succ(v15) = v16)))))
% 6.97/2.38 | 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 yields:
% 6.97/2.38 | (1) 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(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_14_14) & 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(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_12_12 = all_0_14_14 & succ(all_0_13_13) = all_0_14_14 & being_limit_ordinal(all_0_14_14) & ordinal(all_0_13_13)) | ( ~ being_limit_ordinal(all_0_14_14) & ! [v0] : ( ~ ordinal(v0) | ? [v1] : ( ~ (v1 = all_0_14_14) & succ(v0) = v1))))
% 6.97/2.41 |
% 6.97/2.41 | Applying alpha-rule on (1) yields:
% 6.97/2.41 | (2) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1))
% 6.97/2.41 | (3) one_to_one(all_0_8_8)
% 6.97/2.41 | (4) relation(all_0_11_11)
% 6.97/2.41 | (5) relation(all_0_6_6)
% 6.97/2.41 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1))
% 6.97/2.41 | (7) ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1))
% 6.97/2.41 | (8) ordinal(all_0_9_9)
% 6.97/2.41 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 6.97/2.41 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 6.97/2.41 | (11) ordinal(empty_set)
% 6.97/2.41 | (12) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 6.97/2.41 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 6.97/2.41 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 6.97/2.41 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0) | ~ in(v1, v0) | in(v2, v0))
% 6.97/2.41 | (16) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ordinal(v1))
% 6.97/2.41 | (17) function(all_0_11_11)
% 6.97/2.41 | (18) empty(all_0_3_3)
% 6.97/2.41 | (19) relation_empty_yielding(all_0_10_10)
% 6.97/2.41 | (20) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 6.97/2.41 | (21) relation(all_0_4_4)
% 6.97/2.41 | (22) relation(all_0_0_0)
% 6.97/2.41 | (23) empty(empty_set)
% 6.97/2.41 | (24) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 6.97/2.42 | (25) epsilon_connected(all_0_9_9)
% 6.97/2.42 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 6.97/2.42 | (27) ordinal(all_0_1_1)
% 6.97/2.42 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 6.97/2.42 | (29) ! [v0] : ( ~ empty(v0) | relation(v0))
% 6.97/2.42 | (30) relation_empty_yielding(all_0_11_11)
% 6.97/2.42 | (31) empty(all_0_4_4)
% 6.97/2.42 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 6.97/2.42 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 6.97/2.42 | (34) ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0))
% 6.97/2.42 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 6.97/2.42 | (36) ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 6.97/2.42 | (37) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 6.97/2.42 | (38) ~ empty(all_0_9_9)
% 6.97/2.42 | (39) function(all_0_0_0)
% 6.97/2.42 | (40) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 6.97/2.42 | (41) ! [v0] : ( ~ empty(v0) | ordinal(v0))
% 6.97/2.42 | (42) function(empty_set)
% 6.97/2.42 | (43) epsilon_transitive(all_0_1_1)
% 6.97/2.42 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 6.97/2.42 | (45) relation(all_0_10_10)
% 6.97/2.42 | (46) function(all_0_8_8)
% 6.97/2.42 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2)
% 6.97/2.42 | (48) ! [v0] : ! [v1] : ( ~ ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, v1))
% 6.97/2.42 | (49) ! [v0] : ( ~ empty(v0) | epsilon_connected(v0))
% 6.97/2.42 | (50) ordinal(all_0_14_14)
% 6.97/2.42 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 6.97/2.42 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 6.97/2.43 | (53) function(all_0_5_5)
% 6.97/2.43 | (54) epsilon_connected(empty_set)
% 6.97/2.43 | (55) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v0))
% 6.97/2.43 | (56) epsilon_transitive(empty_set)
% 6.97/2.43 | (57) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 6.97/2.43 | (58) relation(all_0_5_5)
% 6.97/2.43 | (59) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1))
% 6.97/2.43 | (60) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 6.97/2.43 | (61) epsilon_transitive(all_0_5_5)
% 6.97/2.43 | (62) ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 6.97/2.43 | (63) ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0))
% 6.97/2.43 | (64) empty(all_0_5_5)
% 6.97/2.43 | (65) one_to_one(all_0_5_5)
% 6.97/2.43 | (66) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 6.97/2.43 | (67) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 6.97/2.43 | (68) ! [v0] : ~ proper_subset(v0, v0)
% 6.97/2.43 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) | ordinal_subset(v1, v2))
% 6.97/2.43 | (70) ~ empty(all_0_6_6)
% 6.97/2.43 | (71) ordinal(all_0_5_5)
% 6.97/2.43 | (72) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_connected(v1))
% 6.97/2.43 | (73) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1))
% 6.97/2.43 | (74) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1))
% 6.97/2.43 | (75) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ empty(v1))
% 6.97/2.43 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal_subset(v1, v2) | ~ ordinal(v2) | ~ ordinal(v0) | in(v0, v2))
% 6.97/2.44 | (77) one_to_one(empty_set)
% 6.97/2.44 | (78) relation_empty_yielding(empty_set)
% 6.97/2.44 | (79) ! [v0] : ( ~ ordinal(v0) | being_limit_ordinal(v0) | ? [v1] : ? [v2] : (succ(v1) = v2 & ordinal(v1) & in(v1, v0) & ~ in(v2, v0)))
% 6.97/2.44 | (80) ! [v0] : ( ~ empty(v0) | function(v0))
% 6.97/2.44 | (81) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_transitive(v1))
% 6.97/2.44 | (82) relation(all_0_2_2)
% 6.97/2.44 | (83) empty(all_0_2_2)
% 6.97/2.44 | (84) relation(empty_set)
% 6.97/2.44 | (85) relation(all_0_8_8)
% 6.97/2.44 | (86) function(all_0_4_4)
% 6.97/2.44 | (87) ~ empty(all_0_7_7)
% 6.97/2.44 | (88) epsilon_connected(all_0_1_1)
% 6.97/2.44 | (89) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1))
% 6.97/2.44 | (90) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1))
% 6.97/2.44 | (91) ? [v0] : subset(v0, v0)
% 6.97/2.44 | (92) epsilon_connected(all_0_5_5)
% 6.97/2.44 | (93) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.97/2.44 | (94) ? [v0] : ? [v1] : element(v1, v0)
% 6.97/2.44 | (95) (all_0_12_12 = all_0_14_14 & succ(all_0_13_13) = all_0_14_14 & being_limit_ordinal(all_0_14_14) & ordinal(all_0_13_13)) | ( ~ being_limit_ordinal(all_0_14_14) & ! [v0] : ( ~ ordinal(v0) | ? [v1] : ( ~ (v1 = all_0_14_14) & succ(v0) = v1)))
% 6.97/2.44 | (96) epsilon_transitive(all_0_9_9)
% 6.97/2.44 | (97) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1))
% 6.97/2.44 |
% 6.97/2.44 | Instantiating formula (33) with all_0_3_3, all_0_2_2 and discharging atoms empty(all_0_2_2), empty(all_0_3_3), yields:
% 6.97/2.44 | (98) all_0_2_2 = all_0_3_3
% 6.97/2.44 |
% 6.97/2.44 | Instantiating formula (33) with all_0_4_4, all_0_2_2 and discharging atoms empty(all_0_2_2), empty(all_0_4_4), yields:
% 6.97/2.44 | (99) all_0_2_2 = all_0_4_4
% 6.97/2.44 |
% 6.97/2.44 | Instantiating formula (33) with all_0_5_5, all_0_3_3 and discharging atoms empty(all_0_3_3), empty(all_0_5_5), yields:
% 6.97/2.45 | (100) all_0_3_3 = all_0_5_5
% 6.97/2.45 |
% 6.97/2.45 | Instantiating formula (33) with empty_set, all_0_3_3 and discharging atoms empty(all_0_3_3), empty(empty_set), yields:
% 6.97/2.45 | (101) all_0_3_3 = empty_set
% 6.97/2.45 |
% 6.97/2.45 | Combining equations (98,99) yields a new equation:
% 6.97/2.45 | (102) all_0_3_3 = all_0_4_4
% 6.97/2.45 |
% 6.97/2.45 | Simplifying 102 yields:
% 6.97/2.45 | (103) all_0_3_3 = all_0_4_4
% 6.97/2.45 |
% 6.97/2.45 | Combining equations (101,103) yields a new equation:
% 6.97/2.45 | (104) all_0_4_4 = empty_set
% 6.97/2.45 |
% 6.97/2.45 | Combining equations (100,103) yields a new equation:
% 6.97/2.45 | (105) all_0_4_4 = all_0_5_5
% 6.97/2.45 |
% 6.97/2.45 | Combining equations (104,105) yields a new equation:
% 6.97/2.45 | (106) all_0_5_5 = empty_set
% 6.97/2.45 |
% 6.97/2.45 | From (106) and (71) follows:
% 6.97/2.45 | (11) ordinal(empty_set)
% 6.97/2.45 |
% 6.97/2.45 | Instantiating formula (79) with all_0_14_14 and discharging atoms ordinal(all_0_14_14), yields:
% 6.97/2.45 | (108) being_limit_ordinal(all_0_14_14) | ? [v0] : ? [v1] : (succ(v0) = v1 & ordinal(v0) & in(v0, all_0_14_14) & ~ in(v1, all_0_14_14))
% 6.97/2.45 |
% 6.97/2.45 | Instantiating formula (55) with empty_set, all_0_14_14 and discharging atoms ordinal(all_0_14_14), ordinal(empty_set), yields:
% 6.97/2.45 | (109) ordinal_subset(all_0_14_14, all_0_14_14)
% 6.97/2.45 |
% 6.97/2.45 +-Applying beta-rule and splitting (95), into two cases.
% 6.97/2.45 |-Branch one:
% 6.97/2.45 | (110) all_0_12_12 = all_0_14_14 & succ(all_0_13_13) = all_0_14_14 & being_limit_ordinal(all_0_14_14) & ordinal(all_0_13_13)
% 6.97/2.45 |
% 6.97/2.45 | Applying alpha-rule on (110) yields:
% 6.97/2.45 | (111) all_0_12_12 = all_0_14_14
% 6.97/2.45 | (112) succ(all_0_13_13) = all_0_14_14
% 6.97/2.45 | (113) being_limit_ordinal(all_0_14_14)
% 6.97/2.45 | (114) ordinal(all_0_13_13)
% 6.97/2.45 |
% 6.97/2.45 | Instantiating formula (76) with all_0_14_14, all_0_14_14, all_0_13_13 and discharging atoms succ(all_0_13_13) = all_0_14_14, ordinal_subset(all_0_14_14, all_0_14_14), ordinal(all_0_13_13), ordinal(all_0_14_14), yields:
% 6.97/2.45 | (115) in(all_0_13_13, all_0_14_14)
% 6.97/2.45 |
% 6.97/2.45 | Instantiating formula (15) with all_0_14_14, all_0_13_13, all_0_14_14 and discharging atoms succ(all_0_13_13) = all_0_14_14, being_limit_ordinal(all_0_14_14), ordinal(all_0_13_13), ordinal(all_0_14_14), in(all_0_13_13, all_0_14_14), yields:
% 6.97/2.45 | (116) in(all_0_14_14, all_0_14_14)
% 6.97/2.45 |
% 6.97/2.45 | Instantiating formula (37) with all_0_14_14, all_0_14_14 and discharging atoms in(all_0_14_14, all_0_14_14), yields:
% 6.97/2.45 | (117) $false
% 6.97/2.45 |
% 6.97/2.45 |-The branch is then unsatisfiable
% 6.97/2.45 |-Branch two:
% 6.97/2.45 | (118) ~ being_limit_ordinal(all_0_14_14) & ! [v0] : ( ~ ordinal(v0) | ? [v1] : ( ~ (v1 = all_0_14_14) & succ(v0) = v1))
% 6.97/2.46 |
% 6.97/2.46 | Applying alpha-rule on (118) yields:
% 6.97/2.46 | (119) ~ being_limit_ordinal(all_0_14_14)
% 6.97/2.46 | (120) ! [v0] : ( ~ ordinal(v0) | ? [v1] : ( ~ (v1 = all_0_14_14) & succ(v0) = v1))
% 6.97/2.46 |
% 6.97/2.46 +-Applying beta-rule and splitting (108), into two cases.
% 6.97/2.46 |-Branch one:
% 6.97/2.46 | (113) being_limit_ordinal(all_0_14_14)
% 6.97/2.46 |
% 6.97/2.46 | Using (113) and (119) yields:
% 6.97/2.46 | (117) $false
% 6.97/2.46 |
% 6.97/2.46 |-The branch is then unsatisfiable
% 6.97/2.46 |-Branch two:
% 6.97/2.46 | (119) ~ being_limit_ordinal(all_0_14_14)
% 6.97/2.46 | (124) ? [v0] : ? [v1] : (succ(v0) = v1 & ordinal(v0) & in(v0, all_0_14_14) & ~ in(v1, all_0_14_14))
% 6.97/2.46 |
% 6.97/2.46 | Instantiating (124) with all_43_0_23, all_43_1_24 yields:
% 6.97/2.46 | (125) succ(all_43_1_24) = all_43_0_23 & ordinal(all_43_1_24) & in(all_43_1_24, all_0_14_14) & ~ in(all_43_0_23, all_0_14_14)
% 6.97/2.46 |
% 6.97/2.46 | Applying alpha-rule on (125) yields:
% 6.97/2.46 | (126) succ(all_43_1_24) = all_43_0_23
% 6.97/2.46 | (127) ordinal(all_43_1_24)
% 6.97/2.46 | (128) in(all_43_1_24, all_0_14_14)
% 6.97/2.46 | (129) ~ in(all_43_0_23, all_0_14_14)
% 6.97/2.46 |
% 6.97/2.46 | Instantiating formula (81) with all_43_0_23, all_43_1_24 and discharging atoms succ(all_43_1_24) = all_43_0_23, ordinal(all_43_1_24), yields:
% 6.97/2.46 | (130) epsilon_transitive(all_43_0_23)
% 6.97/2.46 |
% 6.97/2.46 | Instantiating formula (16) with all_43_0_23, all_43_1_24 and discharging atoms succ(all_43_1_24) = all_43_0_23, ordinal(all_43_1_24), yields:
% 6.97/2.46 | (131) ordinal(all_43_0_23)
% 6.97/2.46 |
% 6.97/2.46 | Instantiating formula (120) with all_43_1_24 and discharging atoms ordinal(all_43_1_24), yields:
% 6.97/2.46 | (132) ? [v0] : ( ~ (v0 = all_0_14_14) & succ(all_43_1_24) = v0)
% 6.97/2.47 |
% 6.97/2.47 | Instantiating formula (69) with all_0_14_14, all_43_0_23, all_43_1_24 and discharging atoms succ(all_43_1_24) = all_43_0_23, ordinal(all_43_1_24), ordinal(all_0_14_14), in(all_43_1_24, all_0_14_14), yields:
% 6.97/2.47 | (133) ordinal_subset(all_43_0_23, all_0_14_14)
% 6.97/2.47 |
% 6.97/2.47 | Instantiating (132) with all_55_0_27 yields:
% 6.97/2.47 | (134) ~ (all_55_0_27 = all_0_14_14) & succ(all_43_1_24) = all_55_0_27
% 6.97/2.47 |
% 6.97/2.47 | Applying alpha-rule on (134) yields:
% 6.97/2.47 | (135) ~ (all_55_0_27 = all_0_14_14)
% 6.97/2.47 | (136) succ(all_43_1_24) = all_55_0_27
% 6.97/2.47 |
% 6.97/2.47 | Instantiating formula (67) with all_43_1_24, all_55_0_27, all_43_0_23 and discharging atoms succ(all_43_1_24) = all_55_0_27, succ(all_43_1_24) = all_43_0_23, yields:
% 6.97/2.47 | (137) all_55_0_27 = all_43_0_23
% 6.97/2.47 |
% 6.97/2.47 | Equations (137) can reduce 135 to:
% 6.97/2.47 | (138) ~ (all_43_0_23 = all_0_14_14)
% 6.97/2.47 |
% 6.97/2.47 | Instantiating formula (48) with all_0_14_14, all_43_0_23 and discharging atoms ordinal_subset(all_43_0_23, all_0_14_14), ordinal(all_43_0_23), ordinal(all_0_14_14), yields:
% 6.97/2.47 | (139) subset(all_43_0_23, all_0_14_14)
% 6.97/2.47 |
% 6.97/2.47 | Instantiating formula (6) with all_0_14_14, all_43_0_23 and discharging atoms subset(all_43_0_23, all_0_14_14), yields:
% 6.97/2.47 | (140) all_43_0_23 = all_0_14_14 | proper_subset(all_43_0_23, all_0_14_14)
% 6.97/2.47 |
% 6.97/2.47 +-Applying beta-rule and splitting (140), into two cases.
% 6.97/2.47 |-Branch one:
% 6.97/2.47 | (141) proper_subset(all_43_0_23, all_0_14_14)
% 6.97/2.47 |
% 6.97/2.47 | Instantiating formula (7) with all_0_14_14, all_43_0_23 and discharging atoms epsilon_transitive(all_43_0_23), ordinal(all_0_14_14), proper_subset(all_43_0_23, all_0_14_14), ~ in(all_43_0_23, all_0_14_14), yields:
% 6.97/2.47 | (117) $false
% 6.97/2.47 |
% 6.97/2.47 |-The branch is then unsatisfiable
% 6.97/2.47 |-Branch two:
% 6.97/2.47 | (143) ~ proper_subset(all_43_0_23, all_0_14_14)
% 6.97/2.47 | (144) all_43_0_23 = all_0_14_14
% 6.97/2.47 |
% 6.97/2.47 | Equations (144) can reduce 138 to:
% 6.97/2.47 | (145) $false
% 6.97/2.47 |
% 6.97/2.47 |-The branch is then unsatisfiable
% 6.97/2.47 % SZS output end Proof for theBenchmark
% 6.97/2.47
% 6.97/2.47 1822ms
%------------------------------------------------------------------------------