TSTP Solution File: SET018+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET018+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 00:16:10 EDT 2022
% Result : Theorem 2.79s 1.31s
% Output : Proof 4.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET018+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n005.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 : Mon Jul 11 01:09:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.51/0.58 ____ _
% 0.51/0.58 ___ / __ \_____(_)___ ________ __________
% 0.51/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.58
% 0.51/0.58 A Theorem Prover for First-Order Logic
% 0.51/0.58 (ePrincess v.1.0)
% 0.51/0.58
% 0.51/0.58 (c) Philipp Rümmer, 2009-2015
% 0.51/0.58 (c) Peter Backeman, 2014-2015
% 0.51/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.58 Bug reports to peter@backeman.se
% 0.51/0.58
% 0.51/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.58
% 0.51/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.88 Prover 0: Preprocessing ...
% 1.96/1.07 Prover 0: Warning: ignoring some quantifiers
% 2.06/1.09 Prover 0: Constructing countermodel ...
% 2.79/1.30 Prover 0: proved (677ms)
% 2.79/1.31
% 2.79/1.31 No countermodel exists, formula is valid
% 2.79/1.31 % SZS status Theorem for theBenchmark
% 2.79/1.31
% 2.79/1.31 Generating proof ... Warning: ignoring some quantifiers
% 3.98/1.55 found it (size 78)
% 3.98/1.55
% 3.98/1.55 % SZS output start Proof for theBenchmark
% 3.98/1.55 Assumed formulas after preprocessing and simplification:
% 3.98/1.55 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v3 = v1) & unordered_pair(v7, v8) = v9 & unordered_pair(v4, v5) = v6 & unordered_pair(v2, v3) = v8 & unordered_pair(v0, v1) = v5 & singleton(v2) = v7 & singleton(v0) = v4 & equal_set(v6, v9) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v10 | v11 = v10 | ~ (unordered_pair(v11, v12) = v13) | ~ member(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (difference(v13, v12) = v11) | ~ (difference(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (union(v13, v12) = v11) | ~ (union(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (intersection(v13, v12) = v11) | ~ (intersection(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (product(v11) = v12) | ~ member(v13, v11) | ~ member(v10, v12) | member(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sum(v11) = v12) | ~ member(v13, v11) | ~ member(v10, v13) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (difference(v12, v11) = v13) | ~ member(v10, v13) | ~ member(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (difference(v12, v11) = v13) | ~ member(v10, v13) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (difference(v12, v11) = v13) | ~ member(v10, v12) | member(v10, v13) | member(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11, v12) = v13) | ~ member(v10, v13) | member(v10, v12) | member(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11, v12) = v13) | ~ member(v10, v12) | member(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11, v12) = v13) | ~ member(v10, v11) | member(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (intersection(v11, v12) = v13) | ~ member(v10, v13) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (intersection(v11, v12) = v13) | ~ member(v10, v13) | member(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (intersection(v11, v12) = v13) | ~ member(v10, v12) | ~ member(v10, v11) | member(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (product(v12) = v11) | ~ (product(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (sum(v12) = v11) | ~ (sum(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v11) = v12) | ~ member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (power_set(v12) = v11) | ~ (power_set(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sum(v11) = v12) | ~ member(v10, v12) | ? [v13] : (member(v13, v11) & member(v10, v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (power_set(v11) = v12) | ~ member(v10, v12) | subset(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (power_set(v11) = v12) | ~ subset(v10, v11) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ member(v12, v10) | ~ subset(v10, v11) | member(v12, v11)) & ? [v10] : ! [v11] : ! [v12] : ( ~ (product(v11) = v12) | member(v10, v12) | ? [v13] : (member(v13, v11) & ~ member(v10, v13))) & ! [v10] : ! [v11] : ( ~ (singleton(v10) = v11) | member(v10, v11)) & ! [v10] : ! [v11] : ( ~ equal_set(v10, v11) | subset(v11, v10)) & ! [v10] : ! [v11] : ( ~ equal_set(v10, v11) | subset(v10, v11)) & ! [v10] : ! [v11] : ( ~ subset(v11, v10) | ~ subset(v10, v11) | equal_set(v10, v11)) & ! [v10] : ~ member(v10, empty_set) & ? [v10] : ? [v11] : (subset(v10, v11) | ? [v12] : (member(v12, v10) & ~ member(v12, v11))))
% 4.13/1.59 | 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 yields:
% 4.13/1.59 | (1) ~ (all_0_6_6 = all_0_8_8) & unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0 & unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3 & unordered_pair(all_0_7_7, all_0_6_6) = all_0_1_1 & unordered_pair(all_0_9_9, all_0_8_8) = all_0_4_4 & singleton(all_0_7_7) = all_0_2_2 & singleton(all_0_9_9) = all_0_5_5 & equal_set(all_0_3_3, all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v2) | member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v3) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | ~ member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v2) | member(v0, v3) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v2) | member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v1) | member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v2) | ~ member(v0, v1) | member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ member(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ subset(v0, v1) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ? [v0] : ! [v1] : ! [v2] : ( ~ (product(v1) = v2) | member(v0, v2) | ? [v3] : (member(v3, v1) & ~ member(v0, v3))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | member(v0, v1)) & ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v1, v0) | ~ subset(v0, v1) | equal_set(v0, v1)) & ! [v0] : ~ member(v0, empty_set) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 4.13/1.60 |
% 4.13/1.60 | Applying alpha-rule on (1) yields:
% 4.13/1.60 | (2) equal_set(all_0_3_3, all_0_0_0)
% 4.13/1.60 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 4.13/1.61 | (4) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | member(v0, v1))
% 4.13/1.61 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 4.13/1.61 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ subset(v0, v1) | member(v0, v2))
% 4.13/1.61 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ member(v0, v2) | subset(v0, v1))
% 4.13/1.61 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 4.13/1.61 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v2) | member(v0, v3))
% 4.13/1.61 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v2) | ~ member(v0, v1) | member(v0, v3))
% 4.13/1.61 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 4.13/1.61 | (12) singleton(all_0_9_9) = all_0_5_5
% 4.13/1.61 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3)))
% 4.13/1.61 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2))
% 4.13/1.61 | (15) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 4.13/1.61 | (16) singleton(all_0_7_7) = all_0_2_2
% 4.13/1.61 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v3) | member(v0, v2))
% 4.13/1.61 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 4.13/1.61 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v1) | member(v0, v3))
% 4.13/1.61 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v1))
% 4.13/1.61 | (21) ! [v0] : ~ member(v0, empty_set)
% 4.13/1.61 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2) | member(v0, v1))
% 4.13/1.61 | (23) ~ (all_0_6_6 = all_0_8_8)
% 4.13/1.61 | (24) unordered_pair(all_0_9_9, all_0_8_8) = all_0_4_4
% 4.13/1.61 | (25) ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | subset(v1, v0))
% 4.13/1.61 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 4.13/1.61 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3))
% 4.13/1.61 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 4.13/1.61 | (29) unordered_pair(all_0_7_7, all_0_6_6) = all_0_1_1
% 4.13/1.61 | (30) ? [v0] : ! [v1] : ! [v2] : ( ~ (product(v1) = v2) | member(v0, v2) | ? [v3] : (member(v3, v1) & ~ member(v0, v3)))
% 4.13/1.61 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1))
% 4.13/1.61 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v2) | member(v0, v3))
% 4.13/1.61 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v0, v2))
% 4.13/1.62 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | member(v0, v2))
% 4.13/1.62 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ member(v0, v2))
% 4.13/1.62 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v2) | member(v0, v3) | member(v0, v1))
% 4.13/1.62 | (37) unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0
% 4.13/1.62 | (38) ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | subset(v0, v1))
% 4.13/1.62 | (39) unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3
% 4.13/1.62 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | member(v0, v2))
% 4.13/1.62 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | ~ member(v0, v1))
% 4.13/1.62 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 4.13/1.62 | (43) ! [v0] : ! [v1] : ( ~ subset(v1, v0) | ~ subset(v0, v1) | equal_set(v0, v1))
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (34) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 4.13/1.62 | (44) member(all_0_1_1, all_0_0_0)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (33) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 4.13/1.62 | (45) member(all_0_2_2, all_0_0_0)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (34) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 4.13/1.62 | (46) member(all_0_4_4, all_0_3_3)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (33) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 4.13/1.62 | (47) member(all_0_5_5, all_0_3_3)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (34) with all_0_1_1, all_0_7_7, all_0_6_6 and discharging atoms unordered_pair(all_0_7_7, all_0_6_6) = all_0_1_1, yields:
% 4.13/1.62 | (48) member(all_0_6_6, all_0_1_1)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (33) with all_0_1_1, all_0_6_6, all_0_7_7 and discharging atoms unordered_pair(all_0_7_7, all_0_6_6) = all_0_1_1, yields:
% 4.13/1.62 | (49) member(all_0_7_7, all_0_1_1)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (34) with all_0_4_4, all_0_9_9, all_0_8_8 and discharging atoms unordered_pair(all_0_9_9, all_0_8_8) = all_0_4_4, yields:
% 4.13/1.62 | (50) member(all_0_8_8, all_0_4_4)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (4) with all_0_2_2, all_0_7_7 and discharging atoms singleton(all_0_7_7) = all_0_2_2, yields:
% 4.13/1.62 | (51) member(all_0_7_7, all_0_2_2)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (25) with all_0_0_0, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_0_0), yields:
% 4.13/1.62 | (52) subset(all_0_0_0, all_0_3_3)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (38) with all_0_0_0, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_0_0), yields:
% 4.13/1.62 | (53) subset(all_0_3_3, all_0_0_0)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (31) with all_0_1_1, all_0_3_3, all_0_0_0 and discharging atoms member(all_0_1_1, all_0_0_0), subset(all_0_0_0, all_0_3_3), yields:
% 4.13/1.62 | (54) member(all_0_1_1, all_0_3_3)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (31) with all_0_2_2, all_0_3_3, all_0_0_0 and discharging atoms member(all_0_2_2, all_0_0_0), subset(all_0_0_0, all_0_3_3), yields:
% 4.13/1.62 | (55) member(all_0_2_2, all_0_3_3)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (31) with all_0_4_4, all_0_0_0, all_0_3_3 and discharging atoms member(all_0_4_4, all_0_3_3), subset(all_0_3_3, all_0_0_0), yields:
% 4.13/1.62 | (56) member(all_0_4_4, all_0_0_0)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (31) with all_0_5_5, all_0_0_0, all_0_3_3 and discharging atoms member(all_0_5_5, all_0_3_3), subset(all_0_3_3, all_0_0_0), yields:
% 4.13/1.62 | (57) member(all_0_5_5, all_0_0_0)
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (27) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_1_1 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3, member(all_0_1_1, all_0_3_3), yields:
% 4.13/1.62 | (58) all_0_1_1 = all_0_4_4 | all_0_1_1 = all_0_5_5
% 4.13/1.62 |
% 4.13/1.62 | Instantiating formula (27) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_2_2 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3, member(all_0_2_2, all_0_3_3), yields:
% 4.13/1.63 | (59) all_0_2_2 = all_0_4_4 | all_0_2_2 = all_0_5_5
% 4.13/1.63 |
% 4.13/1.63 | Instantiating formula (27) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0, member(all_0_4_4, all_0_0_0), yields:
% 4.13/1.63 | (60) all_0_1_1 = all_0_4_4 | all_0_2_2 = all_0_4_4
% 4.13/1.63 |
% 4.13/1.63 | Instantiating formula (27) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_5_5 and discharging atoms unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0, member(all_0_5_5, all_0_0_0), yields:
% 4.13/1.63 | (61) all_0_1_1 = all_0_5_5 | all_0_2_2 = all_0_5_5
% 4.13/1.63 |
% 4.13/1.63 +-Applying beta-rule and splitting (60), into two cases.
% 4.13/1.63 |-Branch one:
% 4.13/1.63 | (62) all_0_1_1 = all_0_4_4
% 4.13/1.63 |
% 4.13/1.63 | From (62) and (29) follows:
% 4.13/1.63 | (63) unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4
% 4.13/1.63 |
% 4.13/1.63 | From (62) and (48) follows:
% 4.13/1.63 | (64) member(all_0_6_6, all_0_4_4)
% 4.13/1.63 |
% 4.13/1.63 | Instantiating formula (27) with all_0_4_4, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4, member(all_0_8_8, all_0_4_4), yields:
% 4.13/1.63 | (65) all_0_6_6 = all_0_8_8 | all_0_7_7 = all_0_8_8
% 4.13/1.63 |
% 4.13/1.63 | Instantiating formula (27) with all_0_4_4, all_0_8_8, all_0_9_9, all_0_6_6 and discharging atoms unordered_pair(all_0_9_9, all_0_8_8) = all_0_4_4, member(all_0_6_6, all_0_4_4), yields:
% 4.13/1.63 | (66) all_0_6_6 = all_0_8_8 | all_0_6_6 = all_0_9_9
% 4.13/1.63 |
% 4.13/1.63 +-Applying beta-rule and splitting (61), into two cases.
% 4.13/1.63 |-Branch one:
% 4.13/1.63 | (67) all_0_1_1 = all_0_5_5
% 4.13/1.63 |
% 4.13/1.63 | Combining equations (67,62) yields a new equation:
% 4.13/1.63 | (68) all_0_4_4 = all_0_5_5
% 4.13/1.63 |
% 4.13/1.63 +-Applying beta-rule and splitting (59), into two cases.
% 4.13/1.63 |-Branch one:
% 4.13/1.63 | (69) all_0_2_2 = all_0_4_4
% 4.13/1.63 |
% 4.13/1.63 | Combining equations (68,69) yields a new equation:
% 4.13/1.63 | (70) all_0_2_2 = all_0_5_5
% 4.13/1.63 |
% 4.13/1.63 | From (70) and (51) follows:
% 4.13/1.63 | (71) member(all_0_7_7, all_0_5_5)
% 4.13/1.63 |
% 4.13/1.63 +-Applying beta-rule and splitting (66), into two cases.
% 4.13/1.63 |-Branch one:
% 4.13/1.63 | (72) all_0_6_6 = all_0_8_8
% 4.13/1.63 |
% 4.13/1.63 | Equations (72) can reduce 23 to:
% 4.13/1.63 | (73) $false
% 4.13/1.63 |
% 4.13/1.63 |-The branch is then unsatisfiable
% 4.13/1.63 |-Branch two:
% 4.13/1.63 | (23) ~ (all_0_6_6 = all_0_8_8)
% 4.13/1.63 | (75) all_0_6_6 = all_0_9_9
% 4.13/1.63 |
% 4.13/1.63 | Equations (75) can reduce 23 to:
% 4.13/1.63 | (76) ~ (all_0_8_8 = all_0_9_9)
% 4.13/1.63 |
% 4.13/1.63 | Simplifying 76 yields:
% 4.13/1.63 | (77) ~ (all_0_8_8 = all_0_9_9)
% 4.13/1.63 |
% 4.13/1.63 +-Applying beta-rule and splitting (65), into two cases.
% 4.13/1.63 |-Branch one:
% 4.13/1.63 | (72) all_0_6_6 = all_0_8_8
% 4.13/1.63 |
% 4.13/1.63 | Combining equations (72,75) yields a new equation:
% 4.13/1.63 | (79) all_0_8_8 = all_0_9_9
% 4.13/1.63 |
% 4.13/1.63 | Simplifying 79 yields:
% 4.13/1.63 | (80) all_0_8_8 = all_0_9_9
% 4.13/1.63 |
% 4.13/1.63 | Equations (80) can reduce 77 to:
% 4.13/1.63 | (73) $false
% 4.13/1.63 |
% 4.13/1.63 |-The branch is then unsatisfiable
% 4.13/1.63 |-Branch two:
% 4.13/1.63 | (23) ~ (all_0_6_6 = all_0_8_8)
% 4.13/1.63 | (83) all_0_7_7 = all_0_8_8
% 4.13/1.63 |
% 4.13/1.63 | Equations (75) can reduce 23 to:
% 4.13/1.63 | (76) ~ (all_0_8_8 = all_0_9_9)
% 4.13/1.63 |
% 4.13/1.63 | Simplifying 76 yields:
% 4.13/1.63 | (77) ~ (all_0_8_8 = all_0_9_9)
% 4.13/1.63 |
% 4.13/1.63 | From (83) and (71) follows:
% 4.13/1.63 | (86) member(all_0_8_8, all_0_5_5)
% 4.13/1.63 |
% 4.13/1.63 | Instantiating formula (35) with all_0_5_5, all_0_9_9, all_0_8_8 and discharging atoms singleton(all_0_9_9) = all_0_5_5, member(all_0_8_8, all_0_5_5), yields:
% 4.13/1.63 | (80) all_0_8_8 = all_0_9_9
% 4.13/1.64 |
% 4.13/1.64 | Equations (80) can reduce 77 to:
% 4.13/1.64 | (73) $false
% 4.13/1.64 |
% 4.13/1.64 |-The branch is then unsatisfiable
% 4.13/1.64 |-Branch two:
% 4.13/1.64 | (89) ~ (all_0_2_2 = all_0_4_4)
% 4.13/1.64 | (70) all_0_2_2 = all_0_5_5
% 4.13/1.64 |
% 4.13/1.64 | Equations (70,68) can reduce 89 to:
% 4.13/1.64 | (73) $false
% 4.13/1.64 |
% 4.13/1.64 |-The branch is then unsatisfiable
% 4.13/1.64 |-Branch two:
% 4.13/1.64 | (92) ~ (all_0_1_1 = all_0_5_5)
% 4.13/1.64 | (70) all_0_2_2 = all_0_5_5
% 4.13/1.64 |
% 4.13/1.64 | From (70) and (51) follows:
% 4.13/1.64 | (71) member(all_0_7_7, all_0_5_5)
% 4.13/1.64 |
% 4.13/1.64 +-Applying beta-rule and splitting (66), into two cases.
% 4.13/1.64 |-Branch one:
% 4.13/1.64 | (72) all_0_6_6 = all_0_8_8
% 4.13/1.64 |
% 4.13/1.64 | Equations (72) can reduce 23 to:
% 4.13/1.64 | (73) $false
% 4.13/1.64 |
% 4.13/1.64 |-The branch is then unsatisfiable
% 4.13/1.64 |-Branch two:
% 4.13/1.64 | (23) ~ (all_0_6_6 = all_0_8_8)
% 4.13/1.64 | (75) all_0_6_6 = all_0_9_9
% 4.13/1.64 |
% 4.13/1.64 | Equations (75) can reduce 23 to:
% 4.13/1.64 | (76) ~ (all_0_8_8 = all_0_9_9)
% 4.13/1.64 |
% 4.13/1.64 | Simplifying 76 yields:
% 4.13/1.64 | (77) ~ (all_0_8_8 = all_0_9_9)
% 4.13/1.64 |
% 4.13/1.64 +-Applying beta-rule and splitting (65), into two cases.
% 4.13/1.64 |-Branch one:
% 4.13/1.64 | (72) all_0_6_6 = all_0_8_8
% 4.13/1.64 |
% 4.13/1.64 | Combining equations (72,75) yields a new equation:
% 4.13/1.64 | (79) all_0_8_8 = all_0_9_9
% 4.13/1.64 |
% 4.13/1.64 | Simplifying 79 yields:
% 4.13/1.64 | (80) all_0_8_8 = all_0_9_9
% 4.13/1.64 |
% 4.13/1.64 | Equations (80) can reduce 77 to:
% 4.13/1.64 | (73) $false
% 4.13/1.64 |
% 4.13/1.64 |-The branch is then unsatisfiable
% 4.13/1.64 |-Branch two:
% 4.13/1.64 | (23) ~ (all_0_6_6 = all_0_8_8)
% 4.13/1.64 | (83) all_0_7_7 = all_0_8_8
% 4.13/1.64 |
% 4.13/1.64 | Equations (75) can reduce 23 to:
% 4.13/1.64 | (76) ~ (all_0_8_8 = all_0_9_9)
% 4.13/1.64 |
% 4.13/1.64 | Simplifying 76 yields:
% 4.13/1.64 | (77) ~ (all_0_8_8 = all_0_9_9)
% 4.13/1.64 |
% 4.13/1.64 | From (83) and (71) follows:
% 4.13/1.64 | (86) member(all_0_8_8, all_0_5_5)
% 4.13/1.64 |
% 4.13/1.64 | Instantiating formula (35) with all_0_5_5, all_0_9_9, all_0_8_8 and discharging atoms singleton(all_0_9_9) = all_0_5_5, member(all_0_8_8, all_0_5_5), yields:
% 4.13/1.64 | (80) all_0_8_8 = all_0_9_9
% 4.13/1.64 |
% 4.13/1.64 | Equations (80) can reduce 77 to:
% 4.13/1.64 | (73) $false
% 4.13/1.64 |
% 4.13/1.64 |-The branch is then unsatisfiable
% 4.13/1.64 |-Branch two:
% 4.13/1.64 | (112) ~ (all_0_1_1 = all_0_4_4)
% 4.13/1.64 | (69) all_0_2_2 = all_0_4_4
% 4.13/1.64 |
% 4.13/1.64 | From (69) and (16) follows:
% 4.13/1.64 | (114) singleton(all_0_7_7) = all_0_4_4
% 4.13/1.64 |
% 4.13/1.64 +-Applying beta-rule and splitting (58), into two cases.
% 4.13/1.64 |-Branch one:
% 4.13/1.64 | (62) all_0_1_1 = all_0_4_4
% 4.13/1.64 |
% 4.13/1.64 | Equations (62) can reduce 112 to:
% 4.13/1.64 | (73) $false
% 4.13/1.64 |
% 4.13/1.64 |-The branch is then unsatisfiable
% 4.13/1.64 |-Branch two:
% 4.13/1.64 | (112) ~ (all_0_1_1 = all_0_4_4)
% 4.13/1.64 | (67) all_0_1_1 = all_0_5_5
% 4.13/1.64 |
% 4.13/1.64 | From (67) and (48) follows:
% 4.13/1.64 | (119) member(all_0_6_6, all_0_5_5)
% 4.13/1.64 |
% 4.13/1.64 | From (67) and (49) follows:
% 4.13/1.64 | (71) member(all_0_7_7, all_0_5_5)
% 4.13/1.64 |
% 4.13/1.64 | Instantiating formula (35) with all_0_4_4, all_0_7_7, all_0_8_8 and discharging atoms singleton(all_0_7_7) = all_0_4_4, member(all_0_8_8, all_0_4_4), yields:
% 4.13/1.64 | (83) all_0_7_7 = all_0_8_8
% 4.13/1.64 |
% 4.13/1.64 | Instantiating formula (35) with all_0_5_5, all_0_9_9, all_0_6_6 and discharging atoms singleton(all_0_9_9) = all_0_5_5, member(all_0_6_6, all_0_5_5), yields:
% 4.46/1.64 | (75) all_0_6_6 = all_0_9_9
% 4.46/1.64 |
% 4.46/1.64 | Instantiating formula (35) with all_0_5_5, all_0_9_9, all_0_7_7 and discharging atoms singleton(all_0_9_9) = all_0_5_5, member(all_0_7_7, all_0_5_5), yields:
% 4.46/1.64 | (123) all_0_7_7 = all_0_9_9
% 4.46/1.64 |
% 4.46/1.64 | Combining equations (83,123) yields a new equation:
% 4.46/1.64 | (79) all_0_8_8 = all_0_9_9
% 4.46/1.64 |
% 4.46/1.64 | Simplifying 79 yields:
% 4.46/1.64 | (80) all_0_8_8 = all_0_9_9
% 4.46/1.64 |
% 4.46/1.64 | Equations (75,80) can reduce 23 to:
% 4.46/1.64 | (73) $false
% 4.46/1.64 |
% 4.46/1.64 |-The branch is then unsatisfiable
% 4.46/1.64 % SZS output end Proof for theBenchmark
% 4.46/1.65
% 4.46/1.65 1055ms
%------------------------------------------------------------------------------