TSTP Solution File: NUM393+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM393+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.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 : Mon Jul 18 08:44:07 EDT 2022
% Result : Theorem 2.91s 1.38s
% Output : Proof 4.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM393+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n008.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 : Wed Jul 6 00:26:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.56 ____ _
% 0.18/0.56 ___ / __ \_____(_)___ ________ __________
% 0.18/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.57
% 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57
% 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.44/0.92 Prover 0: Preprocessing ...
% 1.75/1.08 Prover 0: Warning: ignoring some quantifiers
% 1.95/1.10 Prover 0: Constructing countermodel ...
% 2.91/1.38 Prover 0: proved (767ms)
% 2.91/1.38
% 2.91/1.38 No countermodel exists, formula is valid
% 2.91/1.38 % SZS status Theorem for theBenchmark
% 2.91/1.38
% 2.91/1.39 Generating proof ... Warning: ignoring some quantifiers
% 4.21/1.63 found it (size 10)
% 4.21/1.63
% 4.21/1.63 % SZS output start Proof for theBenchmark
% 4.21/1.63 Assumed formulas after preprocessing and simplification:
% 4.21/1.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (relation_non_empty(v2) & relation_empty_yielding(v4) & relation_empty_yielding(v3) & relation_empty_yielding(empty_set) & one_to_one(v5) & relation(v12) & relation(v10) & relation(v8) & relation(v7) & relation(v5) & relation(v4) & relation(v3) & relation(v2) & relation(empty_set) & epsilon_connected(v11) & epsilon_transitive(v11) & ordinal(v11) & ordinal(v1) & ordinal(v0) & function(v12) & function(v8) & function(v5) & function(v3) & function(v2) & empty(v10) & empty(v9) & empty(v8) & empty(empty_set) & ~ inclusion_comparable(v0, v1) & ~ empty(v7) & ~ empty(v6) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ element(v14, v16) | ~ empty(v15) | ~ in(v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ element(v14, v16) | ~ in(v13, v14) | element(v13, v15)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (powerset(v15) = v14) | ~ (powerset(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ element(v13, v15) | subset(v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ subset(v13, v14) | element(v13, v15)) & ! [v13] : ! [v14] : (v14 = v13 | ~ empty(v14) | ~ empty(v13)) & ! [v13] : ! [v14] : ( ~ element(v13, v14) | empty(v14) | in(v13, v14)) & ! [v13] : ! [v14] : ( ~ subset(v14, v13) | inclusion_comparable(v13, v14)) & ! [v13] : ! [v14] : ( ~ subset(v13, v14) | ~ ordinal(v14) | ~ ordinal(v13) | ordinal_subset(v13, v14)) & ! [v13] : ! [v14] : ( ~ subset(v13, v14) | inclusion_comparable(v13, v14)) & ! [v13] : ! [v14] : ( ~ inclusion_comparable(v13, v14) | subset(v14, v13) | subset(v13, v14)) & ! [v13] : ! [v14] : ( ~ inclusion_comparable(v13, v14) | inclusion_comparable(v14, v13)) & ! [v13] : ! [v14] : ( ~ ordinal_subset(v13, v14) | ~ ordinal(v14) | ~ ordinal(v13) | subset(v13, v14)) & ! [v13] : ! [v14] : ( ~ ordinal(v14) | ~ ordinal(v13) | ordinal_subset(v14, v13) | ordinal_subset(v13, v14)) & ! [v13] : ! [v14] : ( ~ ordinal(v14) | ~ ordinal(v13) | ordinal_subset(v13, v13)) & ! [v13] : ! [v14] : ( ~ empty(v14) | ~ in(v13, v14)) & ! [v13] : ! [v14] : ( ~ in(v14, v13) | ~ in(v13, v14)) & ! [v13] : ! [v14] : ( ~ in(v13, v14) | element(v13, v14)) & ! [v13] : (v13 = empty_set | ~ empty(v13)) & ! [v13] : ( ~ relation(v13) | ~ function(v13) | ~ empty(v13) | one_to_one(v13)) & ! [v13] : ( ~ epsilon_connected(v13) | ~ epsilon_transitive(v13) | ordinal(v13)) & ! [v13] : ( ~ ordinal(v13) | epsilon_connected(v13)) & ! [v13] : ( ~ ordinal(v13) | epsilon_transitive(v13)) & ! [v13] : ( ~ empty(v13) | relation(v13)) & ! [v13] : ( ~ empty(v13) | function(v13)) & ? [v13] : ? [v14] : element(v14, v13) & ? [v13] : subset(v13, v13) & ? [v13] : inclusion_comparable(v13, v13))
% 4.21/1.68 | 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 yields:
% 4.21/1.68 | (1) relation_non_empty(all_0_10_10) & relation_empty_yielding(all_0_8_8) & relation_empty_yielding(all_0_9_9) & relation_empty_yielding(empty_set) & one_to_one(all_0_7_7) & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_4_4) & relation(all_0_5_5) & relation(all_0_7_7) & relation(all_0_8_8) & relation(all_0_9_9) & relation(all_0_10_10) & relation(empty_set) & epsilon_connected(all_0_1_1) & epsilon_transitive(all_0_1_1) & ordinal(all_0_1_1) & ordinal(all_0_11_11) & ordinal(all_0_12_12) & function(all_0_0_0) & function(all_0_4_4) & function(all_0_7_7) & function(all_0_9_9) & function(all_0_10_10) & empty(all_0_2_2) & empty(all_0_3_3) & empty(all_0_4_4) & empty(empty_set) & ~ inclusion_comparable(all_0_12_12, all_0_11_11) & ~ empty(all_0_5_5) & ~ empty(all_0_6_6) & ! [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] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v1, v0) | inclusion_comparable(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | inclusion_comparable(v0, v1)) & ! [v0] : ! [v1] : ( ~ inclusion_comparable(v0, v1) | subset(v1, v0) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ inclusion_comparable(v0, v1) | inclusion_comparable(v1, v0)) & ! [v0] : ! [v1] : ( ~ ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(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] : ( ~ 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) | epsilon_connected(v0)) & ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) & ? [v0] : inclusion_comparable(v0, v0)
% 4.21/1.68 |
% 4.21/1.68 | Applying alpha-rule on (1) yields:
% 4.21/1.68 | (2) relation(all_0_4_4)
% 4.21/1.68 | (3) empty(all_0_3_3)
% 4.21/1.68 | (4) ordinal(all_0_12_12)
% 4.21/1.68 | (5) function(all_0_10_10)
% 4.21/1.69 | (6) one_to_one(all_0_7_7)
% 4.21/1.69 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 4.21/1.69 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 4.21/1.69 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 4.21/1.69 | (10) relation(all_0_8_8)
% 4.21/1.69 | (11) ! [v0] : ( ~ empty(v0) | function(v0))
% 4.21/1.69 | (12) relation(all_0_9_9)
% 4.21/1.69 | (13) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 4.21/1.69 | (14) ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 4.21/1.69 | (15) ~ empty(all_0_5_5)
% 4.21/1.69 | (16) function(all_0_7_7)
% 4.21/1.69 | (17) ! [v0] : ( ~ empty(v0) | relation(v0))
% 4.21/1.69 | (18) relation(all_0_2_2)
% 4.21/1.69 | (19) relation_empty_yielding(all_0_9_9)
% 4.21/1.69 | (20) relation_empty_yielding(all_0_8_8)
% 4.21/1.69 | (21) ! [v0] : ! [v1] : ( ~ ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, v1))
% 4.21/1.69 | (22) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 4.21/1.69 | (23) ! [v0] : ! [v1] : ( ~ inclusion_comparable(v0, v1) | inclusion_comparable(v1, v0))
% 4.21/1.69 | (24) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.21/1.69 | (25) empty(all_0_2_2)
% 4.21/1.69 | (26) ? [v0] : ? [v1] : element(v1, v0)
% 4.21/1.69 | (27) empty(all_0_4_4)
% 4.21/1.69 | (28) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 4.21/1.69 | (29) ? [v0] : inclusion_comparable(v0, v0)
% 4.21/1.69 | (30) ! [v0] : ! [v1] : ( ~ inclusion_comparable(v0, v1) | subset(v1, v0) | subset(v0, v1))
% 4.21/1.69 | (31) ordinal(all_0_1_1)
% 4.21/1.69 | (32) relation(all_0_5_5)
% 4.21/1.69 | (33) epsilon_connected(all_0_1_1)
% 4.21/1.69 | (34) relation(empty_set)
% 4.21/1.69 | (35) relation(all_0_0_0)
% 4.21/1.69 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 4.21/1.69 | (37) ! [v0] : ! [v1] : ( ~ subset(v1, v0) | inclusion_comparable(v0, v1))
% 4.21/1.69 | (38) ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 4.21/1.69 | (39) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 4.21/1.69 | (40) ~ inclusion_comparable(all_0_12_12, all_0_11_11)
% 4.21/1.69 | (41) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v0))
% 4.21/1.69 | (42) epsilon_transitive(all_0_1_1)
% 4.21/1.69 | (43) function(all_0_9_9)
% 4.21/1.69 | (44) ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0))
% 4.21/1.69 | (45) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1))
% 4.21/1.69 | (46) relation(all_0_7_7)
% 4.21/1.69 | (47) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 4.21/1.70 | (48) empty(empty_set)
% 4.21/1.70 | (49) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.21/1.70 | (50) ? [v0] : subset(v0, v0)
% 4.21/1.70 | (51) ~ empty(all_0_6_6)
% 4.21/1.70 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 4.21/1.70 | (53) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | inclusion_comparable(v0, v1))
% 4.21/1.70 | (54) ordinal(all_0_11_11)
% 4.21/1.70 | (55) relation_non_empty(all_0_10_10)
% 4.21/1.70 | (56) function(all_0_4_4)
% 4.21/1.70 | (57) relation(all_0_10_10)
% 4.21/1.70 | (58) function(all_0_0_0)
% 4.21/1.70 | (59) relation_empty_yielding(empty_set)
% 4.21/1.70 | (60) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1))
% 4.21/1.70 |
% 4.21/1.70 | Instantiating formula (60) with all_0_12_12, all_0_11_11 and discharging atoms ordinal(all_0_11_11), ordinal(all_0_12_12), yields:
% 4.21/1.70 | (61) ordinal_subset(all_0_11_11, all_0_12_12) | ordinal_subset(all_0_12_12, all_0_11_11)
% 4.21/1.70 |
% 4.21/1.70 +-Applying beta-rule and splitting (61), into two cases.
% 4.21/1.70 |-Branch one:
% 4.21/1.70 | (62) ordinal_subset(all_0_11_11, all_0_12_12)
% 4.21/1.70 |
% 4.21/1.70 | Instantiating formula (21) with all_0_12_12, all_0_11_11 and discharging atoms ordinal_subset(all_0_11_11, all_0_12_12), ordinal(all_0_11_11), ordinal(all_0_12_12), yields:
% 4.21/1.70 | (63) subset(all_0_11_11, all_0_12_12)
% 4.21/1.70 |
% 4.21/1.70 | Instantiating formula (37) with all_0_11_11, all_0_12_12 and discharging atoms subset(all_0_11_11, all_0_12_12), ~ inclusion_comparable(all_0_12_12, all_0_11_11), yields:
% 4.21/1.70 | (64) $false
% 4.21/1.70 |
% 4.21/1.70 |-The branch is then unsatisfiable
% 4.21/1.70 |-Branch two:
% 4.21/1.70 | (65) ~ ordinal_subset(all_0_11_11, all_0_12_12)
% 4.21/1.70 | (66) ordinal_subset(all_0_12_12, all_0_11_11)
% 4.21/1.70 |
% 4.21/1.70 | Instantiating formula (21) with all_0_11_11, all_0_12_12 and discharging atoms ordinal_subset(all_0_12_12, all_0_11_11), ordinal(all_0_11_11), ordinal(all_0_12_12), yields:
% 4.21/1.70 | (67) subset(all_0_12_12, all_0_11_11)
% 4.21/1.70 |
% 4.21/1.70 | Instantiating formula (53) with all_0_11_11, all_0_12_12 and discharging atoms subset(all_0_12_12, all_0_11_11), ~ inclusion_comparable(all_0_12_12, all_0_11_11), yields:
% 4.21/1.70 | (64) $false
% 4.21/1.70 |
% 4.21/1.70 |-The branch is then unsatisfiable
% 4.21/1.70 % SZS output end Proof for theBenchmark
% 4.21/1.70
% 4.21/1.70 1126ms
%------------------------------------------------------------------------------