TSTP Solution File: SET692+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET692+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 00:21:26 EDT 2022
% Result : Theorem 3.51s 1.52s
% Output : Proof 5.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET692+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n026.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 : Sun Jul 10 09:09:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.56/0.57 ____ _
% 0.56/0.57 ___ / __ \_____(_)___ ________ __________
% 0.56/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.57
% 0.56/0.57 A Theorem Prover for First-Order Logic
% 0.56/0.58 (ePrincess v.1.0)
% 0.56/0.58
% 0.56/0.58 (c) Philipp Rümmer, 2009-2015
% 0.56/0.58 (c) Peter Backeman, 2014-2015
% 0.56/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.58 Bug reports to peter@backeman.se
% 0.56/0.58
% 0.56/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.58
% 0.56/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.56/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.43/0.91 Prover 0: Preprocessing ...
% 1.95/1.12 Prover 0: Warning: ignoring some quantifiers
% 1.95/1.14 Prover 0: Constructing countermodel ...
% 2.51/1.30 Prover 0: gave up
% 2.51/1.30 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.76/1.32 Prover 1: Preprocessing ...
% 2.98/1.43 Prover 1: Constructing countermodel ...
% 3.51/1.52 Prover 1: proved (221ms)
% 3.51/1.52
% 3.51/1.52 No countermodel exists, formula is valid
% 3.51/1.52 % SZS status Theorem for theBenchmark
% 3.51/1.52
% 3.51/1.52 Generating proof ... found it (size 74)
% 4.83/1.82
% 4.83/1.82 % SZS output start Proof for theBenchmark
% 4.83/1.82 Assumed formulas after preprocessing and simplification:
% 4.83/1.82 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (intersection(v0, v1) = v2 & equal_set(v0, v2) = v3 & subset(v0, v1) = v4 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v8) = v9) | ~ (member(v5, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v8, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : (member(v5, v7) = v10 & member(v5, v6) = v11 & ( ~ (v10 = 0) | v11 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v10 = 0) & member(v5, v7) = v11 & member(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : (member(v5, v7) = v11 & member(v5, v6) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sum(v6) = v7) | ~ (member(v5, v9) = 0) | ~ (member(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = 0 & member(v5, v9) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v6, v5) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v5, v6) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (power_set(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & subset(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | v6 = v5 | ~ (unordered_pair(v6, v7) = v8) | ~ (member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unordered_pair(v8, v7) = v6) | ~ (unordered_pair(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (difference(v8, v7) = v6) | ~ (difference(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection(v8, v7) = v6) | ~ (intersection(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equal_set(v8, v7) = v6) | ~ (equal_set(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subset(v8, v7) = v6) | ~ (subset(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (member(v8, v7) = v6) | ~ (member(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v5, v7) = 0 & member(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ? [v10] : (member(v5, v7) = v10 & member(v5, v6) = v9 & (v10 = 0 | v9 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = 0) | (member(v5, v7) = 0 & member(v5, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (singleton(v5) = v6) | ~ (member(v5, v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equal_set(v5, v6) = v7) | ? [v8] : ? [v9] : (subset(v6, v5) = v9 & subset(v5, v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (product(v7) = v6) | ~ (product(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sum(v7) = v6) | ~ (sum(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v6) = v7) | ~ (member(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (power_set(v7) = v6) | ~ (power_set(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6) = v7) | ~ (member(v5, v7) = 0) | ? [v8] : (member(v8, v6) = 0 & member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (power_set(v6) = v7) | ~ (member(v5, v7) = 0) | subset(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = 0) | ~ (member(v7, v5) = 0) | member(v7, v6) = 0) & ! [v5] : ! [v6] : ( ~ (equal_set(v5, v6) = 0) | (subset(v6, v5) = 0 & subset(v5, v6) = 0)) & ! [v5] : ~ (member(v5, empty_set) = 0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))
% 4.89/1.87 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 4.89/1.87 | (1) intersection(all_0_4_4, all_0_3_3) = all_0_2_2 & equal_set(all_0_4_4, all_0_2_2) = all_0_1_1 & subset(all_0_4_4, all_0_3_3) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [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] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [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) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0) & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))
% 4.89/1.88 |
% 4.89/1.88 | Applying alpha-rule on (1) yields:
% 4.89/1.88 | (2) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))
% 4.89/1.88 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 4.89/1.88 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 4.89/1.88 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 4.89/1.88 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 4.89/1.88 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 4.89/1.88 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 4.89/1.88 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 4.89/1.88 | (10) intersection(all_0_4_4, all_0_3_3) = all_0_2_2
% 4.89/1.88 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 4.89/1.88 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 4.89/1.88 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 4.89/1.88 | (14) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 4.89/1.88 | (15) subset(all_0_4_4, all_0_3_3) = all_0_0_0
% 4.89/1.88 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 4.89/1.88 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 4.89/1.88 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5))
% 4.89/1.89 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 4.89/1.89 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 4.89/1.89 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 4.89/1.89 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 4.89/1.89 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 4.89/1.89 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 4.89/1.89 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5))
% 4.89/1.89 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 4.89/1.89 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 4.89/1.89 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 4.89/1.89 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 4.89/1.89 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 4.89/1.89 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 4.89/1.89 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 4.89/1.89 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5))
% 4.89/1.89 | (34) equal_set(all_0_4_4, all_0_2_2) = all_0_1_1
% 4.89/1.89 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 4.89/1.89 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 4.89/1.89 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 4.89/1.89 | (38) ! [v0] : ~ (member(v0, empty_set) = 0)
% 4.89/1.89 |
% 4.89/1.89 | Instantiating formula (14) with all_0_2_2, all_0_4_4 yields:
% 4.89/1.89 | (39) ~ (equal_set(all_0_4_4, all_0_2_2) = 0) | (subset(all_0_2_2, all_0_4_4) = 0 & subset(all_0_4_4, all_0_2_2) = 0)
% 4.89/1.89 |
% 4.89/1.89 | Instantiating formula (19) with all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms equal_set(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 4.89/1.90 | (40) all_0_1_1 = 0 | ? [v0] : ? [v1] : (subset(all_0_2_2, all_0_4_4) = v1 & subset(all_0_4_4, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 4.89/1.90 |
% 4.89/1.90 | Instantiating formula (8) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_3_3) = all_0_0_0, yields:
% 4.89/1.90 | (41) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1 & member(v0, all_0_4_4) = 0)
% 4.89/1.90 |
% 4.89/1.90 +-Applying beta-rule and splitting (2), into two cases.
% 4.89/1.90 |-Branch one:
% 4.89/1.90 | (42) all_0_0_0 = 0 & ~ (all_0_1_1 = 0)
% 4.89/1.90 |
% 4.89/1.90 | Applying alpha-rule on (42) yields:
% 4.89/1.90 | (43) all_0_0_0 = 0
% 4.89/1.90 | (44) ~ (all_0_1_1 = 0)
% 4.89/1.90 |
% 4.89/1.90 | From (43) and (15) follows:
% 4.89/1.90 | (45) subset(all_0_4_4, all_0_3_3) = 0
% 4.89/1.90 |
% 4.89/1.90 +-Applying beta-rule and splitting (40), into two cases.
% 4.89/1.90 |-Branch one:
% 4.89/1.90 | (46) all_0_1_1 = 0
% 4.89/1.90 |
% 4.89/1.90 | Equations (46) can reduce 44 to:
% 4.89/1.90 | (47) $false
% 4.89/1.90 |
% 4.89/1.90 |-The branch is then unsatisfiable
% 4.89/1.90 |-Branch two:
% 4.89/1.90 | (44) ~ (all_0_1_1 = 0)
% 4.89/1.90 | (49) ? [v0] : ? [v1] : (subset(all_0_2_2, all_0_4_4) = v1 & subset(all_0_4_4, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 4.89/1.90 |
% 4.89/1.90 | Instantiating (49) with all_14_0_5, all_14_1_6 yields:
% 4.89/1.90 | (50) subset(all_0_2_2, all_0_4_4) = all_14_0_5 & subset(all_0_4_4, all_0_2_2) = all_14_1_6 & ( ~ (all_14_0_5 = 0) | ~ (all_14_1_6 = 0))
% 4.89/1.90 |
% 4.89/1.90 | Applying alpha-rule on (50) yields:
% 4.89/1.90 | (51) subset(all_0_2_2, all_0_4_4) = all_14_0_5
% 4.89/1.90 | (52) subset(all_0_4_4, all_0_2_2) = all_14_1_6
% 4.89/1.90 | (53) ~ (all_14_0_5 = 0) | ~ (all_14_1_6 = 0)
% 4.89/1.90 |
% 4.89/1.90 | Instantiating formula (35) with all_0_4_4, all_0_3_3, 0, all_14_1_6 and discharging atoms subset(all_0_4_4, all_0_3_3) = 0, yields:
% 4.89/1.90 | (54) all_14_1_6 = 0 | ~ (subset(all_0_4_4, all_0_3_3) = all_14_1_6)
% 4.89/1.90 |
% 4.89/1.90 | Instantiating formula (8) with all_14_0_5, all_0_4_4, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_4_4) = all_14_0_5, yields:
% 4.89/1.90 | (55) all_14_0_5 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = 0 & member(v0, all_0_4_4) = v1)
% 4.89/1.90 |
% 4.89/1.90 | Instantiating formula (8) with all_14_1_6, all_0_2_2, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_2_2) = all_14_1_6, yields:
% 4.89/1.90 | (56) all_14_1_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, all_0_4_4) = 0)
% 4.89/1.90 |
% 4.89/1.90 +-Applying beta-rule and splitting (54), into two cases.
% 4.89/1.90 |-Branch one:
% 4.89/1.90 | (57) ~ (subset(all_0_4_4, all_0_3_3) = all_14_1_6)
% 4.89/1.90 |
% 4.89/1.90 | Using (45) and (57) yields:
% 4.89/1.90 | (58) ~ (all_14_1_6 = 0)
% 4.89/1.90 |
% 4.89/1.90 +-Applying beta-rule and splitting (56), into two cases.
% 4.89/1.90 |-Branch one:
% 4.89/1.90 | (59) all_14_1_6 = 0
% 4.89/1.90 |
% 4.89/1.90 | Equations (59) can reduce 58 to:
% 4.89/1.90 | (47) $false
% 4.89/1.90 |
% 4.89/1.90 |-The branch is then unsatisfiable
% 4.89/1.90 |-Branch two:
% 4.89/1.90 | (58) ~ (all_14_1_6 = 0)
% 4.89/1.90 | (62) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, all_0_4_4) = 0)
% 4.89/1.90 |
% 4.89/1.90 | Instantiating (62) with all_31_0_7, all_31_1_8 yields:
% 4.89/1.90 | (63) ~ (all_31_0_7 = 0) & member(all_31_1_8, all_0_2_2) = all_31_0_7 & member(all_31_1_8, all_0_4_4) = 0
% 4.89/1.90 |
% 4.89/1.90 | Applying alpha-rule on (63) yields:
% 4.89/1.90 | (64) ~ (all_31_0_7 = 0)
% 4.89/1.90 | (65) member(all_31_1_8, all_0_2_2) = all_31_0_7
% 4.89/1.90 | (66) member(all_31_1_8, all_0_4_4) = 0
% 4.89/1.90 |
% 4.89/1.90 | Instantiating formula (30) with all_31_0_7, all_0_2_2, all_0_3_3, all_0_4_4, all_31_1_8 and discharging atoms intersection(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_31_1_8, all_0_2_2) = all_31_0_7, yields:
% 4.89/1.91 | (67) all_31_0_7 = 0 | ? [v0] : ? [v1] : (member(all_31_1_8, all_0_3_3) = v1 & member(all_31_1_8, all_0_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 4.89/1.91 |
% 4.89/1.91 | Instantiating formula (37) with all_31_1_8, all_0_3_3, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_3_3) = 0, member(all_31_1_8, all_0_4_4) = 0, yields:
% 4.89/1.91 | (68) member(all_31_1_8, all_0_3_3) = 0
% 4.89/1.91 |
% 4.89/1.91 +-Applying beta-rule and splitting (67), into two cases.
% 4.89/1.91 |-Branch one:
% 4.89/1.91 | (69) all_31_0_7 = 0
% 4.89/1.91 |
% 4.89/1.91 | Equations (69) can reduce 64 to:
% 4.89/1.91 | (47) $false
% 4.89/1.91 |
% 4.89/1.91 |-The branch is then unsatisfiable
% 4.89/1.91 |-Branch two:
% 4.89/1.91 | (64) ~ (all_31_0_7 = 0)
% 4.89/1.91 | (72) ? [v0] : ? [v1] : (member(all_31_1_8, all_0_3_3) = v1 & member(all_31_1_8, all_0_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 4.89/1.91 |
% 4.89/1.91 | Instantiating (72) with all_51_0_9, all_51_1_10 yields:
% 4.89/1.91 | (73) member(all_31_1_8, all_0_3_3) = all_51_0_9 & member(all_31_1_8, all_0_4_4) = all_51_1_10 & ( ~ (all_51_0_9 = 0) | ~ (all_51_1_10 = 0))
% 4.89/1.91 |
% 4.89/1.91 | Applying alpha-rule on (73) yields:
% 4.89/1.91 | (74) member(all_31_1_8, all_0_3_3) = all_51_0_9
% 4.89/1.91 | (75) member(all_31_1_8, all_0_4_4) = all_51_1_10
% 4.89/1.91 | (76) ~ (all_51_0_9 = 0) | ~ (all_51_1_10 = 0)
% 4.89/1.91 |
% 4.89/1.91 | Instantiating formula (21) with all_31_1_8, all_0_3_3, 0, all_51_0_9 and discharging atoms member(all_31_1_8, all_0_3_3) = all_51_0_9, member(all_31_1_8, all_0_3_3) = 0, yields:
% 4.89/1.91 | (77) all_51_0_9 = 0
% 4.89/1.91 |
% 4.89/1.91 | Instantiating formula (21) with all_31_1_8, all_0_4_4, all_51_1_10, 0 and discharging atoms member(all_31_1_8, all_0_4_4) = all_51_1_10, member(all_31_1_8, all_0_4_4) = 0, yields:
% 4.89/1.91 | (78) all_51_1_10 = 0
% 4.89/1.91 |
% 4.89/1.91 +-Applying beta-rule and splitting (76), into two cases.
% 4.89/1.91 |-Branch one:
% 4.89/1.91 | (79) ~ (all_51_0_9 = 0)
% 4.89/1.91 |
% 4.89/1.91 | Equations (77) can reduce 79 to:
% 4.89/1.91 | (47) $false
% 4.89/1.91 |
% 4.89/1.91 |-The branch is then unsatisfiable
% 4.89/1.91 |-Branch two:
% 4.89/1.91 | (77) all_51_0_9 = 0
% 4.89/1.91 | (82) ~ (all_51_1_10 = 0)
% 4.89/1.91 |
% 4.89/1.91 | Equations (78) can reduce 82 to:
% 4.89/1.91 | (47) $false
% 4.89/1.91 |
% 4.89/1.91 |-The branch is then unsatisfiable
% 4.89/1.91 |-Branch two:
% 4.89/1.91 | (84) subset(all_0_4_4, all_0_3_3) = all_14_1_6
% 4.89/1.91 | (59) all_14_1_6 = 0
% 4.89/1.91 |
% 4.89/1.91 +-Applying beta-rule and splitting (53), into two cases.
% 4.89/1.91 |-Branch one:
% 4.89/1.91 | (86) ~ (all_14_0_5 = 0)
% 5.19/1.91 |
% 5.19/1.91 +-Applying beta-rule and splitting (55), into two cases.
% 5.19/1.91 |-Branch one:
% 5.19/1.91 | (87) all_14_0_5 = 0
% 5.19/1.91 |
% 5.19/1.91 | Equations (87) can reduce 86 to:
% 5.19/1.91 | (47) $false
% 5.19/1.91 |
% 5.19/1.91 |-The branch is then unsatisfiable
% 5.19/1.91 |-Branch two:
% 5.19/1.91 | (86) ~ (all_14_0_5 = 0)
% 5.19/1.91 | (90) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = 0 & member(v0, all_0_4_4) = v1)
% 5.19/1.91 |
% 5.19/1.91 | Instantiating (90) with all_31_0_11, all_31_1_12 yields:
% 5.19/1.91 | (91) ~ (all_31_0_11 = 0) & member(all_31_1_12, all_0_2_2) = 0 & member(all_31_1_12, all_0_4_4) = all_31_0_11
% 5.19/1.91 |
% 5.19/1.91 | Applying alpha-rule on (91) yields:
% 5.19/1.91 | (92) ~ (all_31_0_11 = 0)
% 5.19/1.91 | (93) member(all_31_1_12, all_0_2_2) = 0
% 5.19/1.91 | (94) member(all_31_1_12, all_0_4_4) = all_31_0_11
% 5.19/1.91 |
% 5.19/1.91 | Instantiating formula (21) with all_31_1_12, all_0_4_4, all_31_0_11, 0 and discharging atoms member(all_31_1_12, all_0_4_4) = all_31_0_11, yields:
% 5.19/1.91 | (95) all_31_0_11 = 0 | ~ (member(all_31_1_12, all_0_4_4) = 0)
% 5.19/1.91 |
% 5.19/1.91 | Instantiating formula (17) with all_0_2_2, all_0_3_3, all_0_4_4, all_31_1_12 and discharging atoms intersection(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_31_1_12, all_0_2_2) = 0, yields:
% 5.19/1.91 | (96) member(all_31_1_12, all_0_3_3) = 0 & member(all_31_1_12, all_0_4_4) = 0
% 5.19/1.91 |
% 5.19/1.91 | Applying alpha-rule on (96) yields:
% 5.19/1.91 | (97) member(all_31_1_12, all_0_3_3) = 0
% 5.19/1.91 | (98) member(all_31_1_12, all_0_4_4) = 0
% 5.19/1.91 |
% 5.19/1.91 +-Applying beta-rule and splitting (95), into two cases.
% 5.19/1.91 |-Branch one:
% 5.19/1.91 | (99) ~ (member(all_31_1_12, all_0_4_4) = 0)
% 5.19/1.91 |
% 5.19/1.91 | Using (98) and (99) yields:
% 5.19/1.91 | (100) $false
% 5.19/1.91 |
% 5.19/1.91 |-The branch is then unsatisfiable
% 5.19/1.91 |-Branch two:
% 5.19/1.92 | (98) member(all_31_1_12, all_0_4_4) = 0
% 5.19/1.92 | (102) all_31_0_11 = 0
% 5.19/1.92 |
% 5.19/1.92 | Equations (102) can reduce 92 to:
% 5.19/1.92 | (47) $false
% 5.19/1.92 |
% 5.19/1.92 |-The branch is then unsatisfiable
% 5.19/1.92 |-Branch two:
% 5.19/1.92 | (87) all_14_0_5 = 0
% 5.19/1.92 | (58) ~ (all_14_1_6 = 0)
% 5.19/1.92 |
% 5.19/1.92 | Equations (59) can reduce 58 to:
% 5.19/1.92 | (47) $false
% 5.19/1.92 |
% 5.19/1.92 |-The branch is then unsatisfiable
% 5.19/1.92 |-Branch two:
% 5.19/1.92 | (107) all_0_1_1 = 0 & ~ (all_0_0_0 = 0)
% 5.19/1.92 |
% 5.19/1.92 | Applying alpha-rule on (107) yields:
% 5.19/1.92 | (46) all_0_1_1 = 0
% 5.19/1.92 | (109) ~ (all_0_0_0 = 0)
% 5.19/1.92 |
% 5.19/1.92 | From (46) and (34) follows:
% 5.19/1.92 | (110) equal_set(all_0_4_4, all_0_2_2) = 0
% 5.19/1.92 |
% 5.19/1.92 +-Applying beta-rule and splitting (39), into two cases.
% 5.19/1.92 |-Branch one:
% 5.19/1.92 | (111) ~ (equal_set(all_0_4_4, all_0_2_2) = 0)
% 5.19/1.92 |
% 5.19/1.92 | Using (110) and (111) yields:
% 5.19/1.92 | (100) $false
% 5.19/1.92 |
% 5.19/1.92 |-The branch is then unsatisfiable
% 5.19/1.92 |-Branch two:
% 5.19/1.92 | (110) equal_set(all_0_4_4, all_0_2_2) = 0
% 5.19/1.92 | (114) subset(all_0_2_2, all_0_4_4) = 0 & subset(all_0_4_4, all_0_2_2) = 0
% 5.19/1.92 |
% 5.19/1.92 | Applying alpha-rule on (114) yields:
% 5.19/1.92 | (115) subset(all_0_2_2, all_0_4_4) = 0
% 5.19/1.92 | (116) subset(all_0_4_4, all_0_2_2) = 0
% 5.19/1.92 |
% 5.19/1.92 +-Applying beta-rule and splitting (41), into two cases.
% 5.19/1.92 |-Branch one:
% 5.19/1.92 | (43) all_0_0_0 = 0
% 5.19/1.92 |
% 5.19/1.92 | Equations (43) can reduce 109 to:
% 5.19/1.92 | (47) $false
% 5.19/1.92 |
% 5.19/1.92 |-The branch is then unsatisfiable
% 5.19/1.92 |-Branch two:
% 5.19/1.92 | (109) ~ (all_0_0_0 = 0)
% 5.19/1.92 | (120) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1 & member(v0, all_0_4_4) = 0)
% 5.19/1.92 |
% 5.19/1.92 | Instantiating (120) with all_17_0_13, all_17_1_14 yields:
% 5.19/1.92 | (121) ~ (all_17_0_13 = 0) & member(all_17_1_14, all_0_3_3) = all_17_0_13 & member(all_17_1_14, all_0_4_4) = 0
% 5.19/1.92 |
% 5.19/1.92 | Applying alpha-rule on (121) yields:
% 5.19/1.92 | (122) ~ (all_17_0_13 = 0)
% 5.19/1.92 | (123) member(all_17_1_14, all_0_3_3) = all_17_0_13
% 5.19/1.92 | (124) member(all_17_1_14, all_0_4_4) = 0
% 5.19/1.92 |
% 5.19/1.92 | Instantiating formula (17) with all_0_4_4, all_0_3_3, all_0_4_4, all_17_1_14 and discharging atoms member(all_17_1_14, all_0_4_4) = 0, yields:
% 5.19/1.92 | (125) ~ (intersection(all_0_4_4, all_0_3_3) = all_0_4_4) | member(all_17_1_14, all_0_3_3) = 0
% 5.19/1.92 |
% 5.19/1.92 | Instantiating formula (37) with all_17_1_14, all_0_2_2, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_2_2) = 0, member(all_17_1_14, all_0_4_4) = 0, yields:
% 5.19/1.92 | (126) member(all_17_1_14, all_0_2_2) = 0
% 5.19/1.92 |
% 5.19/1.92 +-Applying beta-rule and splitting (125), into two cases.
% 5.19/1.92 |-Branch one:
% 5.19/1.92 | (127) member(all_17_1_14, all_0_3_3) = 0
% 5.19/1.92 |
% 5.19/1.92 | Instantiating formula (21) with all_17_1_14, all_0_3_3, 0, all_17_0_13 and discharging atoms member(all_17_1_14, all_0_3_3) = all_17_0_13, member(all_17_1_14, all_0_3_3) = 0, yields:
% 5.19/1.92 | (128) all_17_0_13 = 0
% 5.19/1.92 |
% 5.19/1.92 | Equations (128) can reduce 122 to:
% 5.19/1.92 | (47) $false
% 5.19/1.92 |
% 5.19/1.92 |-The branch is then unsatisfiable
% 5.19/1.92 |-Branch two:
% 5.19/1.92 | (130) ~ (member(all_17_1_14, all_0_3_3) = 0)
% 5.19/1.93 | (131) ~ (intersection(all_0_4_4, all_0_3_3) = all_0_4_4)
% 5.19/1.93 |
% 5.19/1.93 | Instantiating formula (17) with all_0_2_2, all_0_3_3, all_0_4_4, all_17_1_14 and discharging atoms intersection(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_17_1_14, all_0_2_2) = 0, yields:
% 5.19/1.93 | (132) member(all_17_1_14, all_0_3_3) = 0 & member(all_17_1_14, all_0_4_4) = 0
% 5.19/1.93 |
% 5.19/1.93 | Applying alpha-rule on (132) yields:
% 5.19/1.93 | (127) member(all_17_1_14, all_0_3_3) = 0
% 5.19/1.93 | (124) member(all_17_1_14, all_0_4_4) = 0
% 5.19/1.93 |
% 5.19/1.93 | Using (127) and (130) yields:
% 5.19/1.93 | (100) $false
% 5.19/1.93 |
% 5.19/1.93 |-The branch is then unsatisfiable
% 5.19/1.93 % SZS output end Proof for theBenchmark
% 5.19/1.93
% 5.19/1.93 1341ms
%------------------------------------------------------------------------------