TSTP Solution File: SET696+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET696+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 00:21:28 EDT 2022
% Result : Theorem 3.76s 1.49s
% Output : Proof 5.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET696+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n027.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 : Sat Jul 9 21:21:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.57/0.90 Prover 0: Preprocessing ...
% 1.93/1.08 Prover 0: Warning: ignoring some quantifiers
% 2.11/1.10 Prover 0: Constructing countermodel ...
% 2.69/1.28 Prover 0: gave up
% 2.69/1.28 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.69/1.30 Prover 1: Preprocessing ...
% 3.22/1.42 Prover 1: Constructing countermodel ...
% 3.76/1.49 Prover 1: proved (215ms)
% 3.76/1.49
% 3.76/1.49 No countermodel exists, formula is valid
% 3.76/1.49 % SZS status Theorem for theBenchmark
% 3.76/1.49
% 3.76/1.49 Generating proof ... found it (size 34)
% 4.49/1.75
% 4.49/1.75 % SZS output start Proof for theBenchmark
% 4.49/1.75 Assumed formulas after preprocessing and simplification:
% 4.49/1.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & difference(v1, v0) = v2 & intersection(v2, v0) = v3 & equal_set(v3, empty_set) = v4 & subset(v0, v1) = 0 & ! [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))
% 4.88/1.79 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 4.88/1.79 | (1) ~ (all_0_0_0 = 0) & difference(all_0_3_3, all_0_4_4) = all_0_2_2 & intersection(all_0_2_2, all_0_4_4) = all_0_1_1 & equal_set(all_0_1_1, empty_set) = all_0_0_0 & subset(all_0_4_4, all_0_3_3) = 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)
% 4.88/1.80 |
% 4.88/1.80 | Applying alpha-rule on (1) yields:
% 4.88/1.80 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 4.88/1.80 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 4.88/1.80 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 4.88/1.80 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 4.88/1.80 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 4.88/1.80 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 4.88/1.80 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 4.88/1.80 | (9) difference(all_0_3_3, all_0_4_4) = all_0_2_2
% 4.88/1.80 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 4.88/1.81 | (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)))
% 4.88/1.81 | (12) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 4.88/1.81 | (13) ! [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)))
% 4.88/1.81 | (14) ! [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))
% 4.88/1.81 | (15) ~ (all_0_0_0 = 0)
% 4.88/1.81 | (16) ! [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))))
% 4.88/1.81 | (17) ! [v0] : ~ (member(v0, empty_set) = 0)
% 4.88/1.81 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 4.88/1.81 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 4.88/1.81 | (20) ! [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))
% 5.02/1.81 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 5.02/1.81 | (22) ! [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))
% 5.02/1.81 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 5.02/1.81 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 5.02/1.81 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 5.02/1.81 | (26) ! [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))
% 5.02/1.81 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 5.02/1.81 | (28) subset(all_0_4_4, all_0_3_3) = 0
% 5.02/1.81 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 5.02/1.82 | (30) intersection(all_0_2_2, all_0_4_4) = all_0_1_1
% 5.02/1.82 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 5.02/1.82 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 5.02/1.82 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 5.02/1.82 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 5.02/1.82 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 5.02/1.82 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 5.02/1.82 | (37) equal_set(all_0_1_1, empty_set) = all_0_0_0
% 5.02/1.82 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 5.02/1.82 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 5.02/1.82 |
% 5.02/1.82 | Instantiating formula (31) with all_0_0_0, empty_set, all_0_1_1 and discharging atoms equal_set(all_0_1_1, empty_set) = all_0_0_0, yields:
% 5.02/1.82 | (40) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, empty_set) = v0 & subset(empty_set, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 5.02/1.82 |
% 5.02/1.82 +-Applying beta-rule and splitting (40), into two cases.
% 5.02/1.82 |-Branch one:
% 5.02/1.82 | (41) all_0_0_0 = 0
% 5.02/1.82 |
% 5.02/1.82 | Equations (41) can reduce 15 to:
% 5.02/1.82 | (42) $false
% 5.02/1.82 |
% 5.02/1.82 |-The branch is then unsatisfiable
% 5.02/1.82 |-Branch two:
% 5.02/1.82 | (15) ~ (all_0_0_0 = 0)
% 5.02/1.82 | (44) ? [v0] : ? [v1] : (subset(all_0_1_1, empty_set) = v0 & subset(empty_set, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 5.02/1.82 |
% 5.02/1.82 | Instantiating (44) with all_10_0_5, all_10_1_6 yields:
% 5.02/1.82 | (45) subset(all_0_1_1, empty_set) = all_10_1_6 & subset(empty_set, all_0_1_1) = all_10_0_5 & ( ~ (all_10_0_5 = 0) | ~ (all_10_1_6 = 0))
% 5.02/1.82 |
% 5.02/1.82 | Applying alpha-rule on (45) yields:
% 5.02/1.82 | (46) subset(all_0_1_1, empty_set) = all_10_1_6
% 5.02/1.82 | (47) subset(empty_set, all_0_1_1) = all_10_0_5
% 5.02/1.82 | (48) ~ (all_10_0_5 = 0) | ~ (all_10_1_6 = 0)
% 5.02/1.82 |
% 5.02/1.82 | Instantiating formula (21) with all_10_1_6, empty_set, all_0_1_1 and discharging atoms subset(all_0_1_1, empty_set) = all_10_1_6, yields:
% 5.02/1.82 | (49) all_10_1_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, empty_set) = v1)
% 5.02/1.83 |
% 5.02/1.83 | Instantiating formula (21) with all_10_0_5, all_0_1_1, empty_set and discharging atoms subset(empty_set, all_0_1_1) = all_10_0_5, yields:
% 5.02/1.83 | (50) all_10_0_5 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, empty_set) = 0)
% 5.02/1.83 |
% 5.02/1.83 +-Applying beta-rule and splitting (48), into two cases.
% 5.02/1.83 |-Branch one:
% 5.02/1.83 | (51) ~ (all_10_0_5 = 0)
% 5.02/1.83 |
% 5.02/1.83 +-Applying beta-rule and splitting (50), into two cases.
% 5.02/1.83 |-Branch one:
% 5.02/1.83 | (52) all_10_0_5 = 0
% 5.02/1.83 |
% 5.02/1.83 | Equations (52) can reduce 51 to:
% 5.02/1.83 | (42) $false
% 5.02/1.83 |
% 5.02/1.83 |-The branch is then unsatisfiable
% 5.02/1.83 |-Branch two:
% 5.02/1.83 | (51) ~ (all_10_0_5 = 0)
% 5.02/1.83 | (55) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, empty_set) = 0)
% 5.02/1.83 |
% 5.02/1.83 | Instantiating (55) with all_23_0_7, all_23_1_8 yields:
% 5.02/1.83 | (56) ~ (all_23_0_7 = 0) & member(all_23_1_8, all_0_1_1) = all_23_0_7 & member(all_23_1_8, empty_set) = 0
% 5.02/1.83 |
% 5.02/1.83 | Applying alpha-rule on (56) yields:
% 5.02/1.83 | (57) ~ (all_23_0_7 = 0)
% 5.09/1.83 | (58) member(all_23_1_8, all_0_1_1) = all_23_0_7
% 5.09/1.83 | (59) member(all_23_1_8, empty_set) = 0
% 5.09/1.83 |
% 5.09/1.83 | Instantiating formula (17) with all_23_1_8 and discharging atoms member(all_23_1_8, empty_set) = 0, yields:
% 5.09/1.83 | (60) $false
% 5.09/1.83 |
% 5.09/1.83 |-The branch is then unsatisfiable
% 5.09/1.83 |-Branch two:
% 5.09/1.83 | (52) all_10_0_5 = 0
% 5.09/1.83 | (62) ~ (all_10_1_6 = 0)
% 5.09/1.83 |
% 5.09/1.83 +-Applying beta-rule and splitting (49), into two cases.
% 5.09/1.83 |-Branch one:
% 5.09/1.83 | (63) all_10_1_6 = 0
% 5.09/1.83 |
% 5.09/1.83 | Equations (63) can reduce 62 to:
% 5.09/1.83 | (42) $false
% 5.09/1.83 |
% 5.09/1.83 |-The branch is then unsatisfiable
% 5.09/1.83 |-Branch two:
% 5.09/1.83 | (62) ~ (all_10_1_6 = 0)
% 5.09/1.83 | (66) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, empty_set) = v1)
% 5.09/1.83 |
% 5.09/1.83 | Instantiating (66) with all_23_0_9, all_23_1_10 yields:
% 5.09/1.83 | (67) ~ (all_23_0_9 = 0) & member(all_23_1_10, all_0_1_1) = 0 & member(all_23_1_10, empty_set) = all_23_0_9
% 5.09/1.83 |
% 5.09/1.83 | Applying alpha-rule on (67) yields:
% 5.09/1.83 | (68) ~ (all_23_0_9 = 0)
% 5.09/1.83 | (69) member(all_23_1_10, all_0_1_1) = 0
% 5.09/1.83 | (70) member(all_23_1_10, empty_set) = all_23_0_9
% 5.09/1.83 |
% 5.09/1.83 | Instantiating formula (8) with all_0_2_2, all_0_3_3, all_0_4_4, all_23_1_10 and discharging atoms difference(all_0_3_3, all_0_4_4) = all_0_2_2, yields:
% 5.09/1.83 | (71) ~ (member(all_23_1_10, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_23_1_10, all_0_3_3) = 0 & member(all_23_1_10, all_0_4_4) = v0)
% 5.09/1.83 |
% 5.09/1.83 | Instantiating formula (39) with all_0_1_1, all_0_4_4, all_0_2_2, all_23_1_10 and discharging atoms intersection(all_0_2_2, all_0_4_4) = all_0_1_1, member(all_23_1_10, all_0_1_1) = 0, yields:
% 5.09/1.83 | (72) member(all_23_1_10, all_0_2_2) = 0 & member(all_23_1_10, all_0_4_4) = 0
% 5.09/1.83 |
% 5.09/1.83 | Applying alpha-rule on (72) yields:
% 5.09/1.83 | (73) member(all_23_1_10, all_0_2_2) = 0
% 5.09/1.83 | (74) member(all_23_1_10, all_0_4_4) = 0
% 5.09/1.83 |
% 5.09/1.83 +-Applying beta-rule and splitting (71), into two cases.
% 5.09/1.83 |-Branch one:
% 5.09/1.83 | (75) ~ (member(all_23_1_10, all_0_2_2) = 0)
% 5.09/1.83 |
% 5.09/1.83 | Using (73) and (75) yields:
% 5.09/1.83 | (60) $false
% 5.09/1.83 |
% 5.09/1.83 |-The branch is then unsatisfiable
% 5.09/1.83 |-Branch two:
% 5.09/1.83 | (73) member(all_23_1_10, all_0_2_2) = 0
% 5.09/1.83 | (78) ? [v0] : ( ~ (v0 = 0) & member(all_23_1_10, all_0_3_3) = 0 & member(all_23_1_10, all_0_4_4) = v0)
% 5.09/1.83 |
% 5.09/1.83 | Instantiating (78) with all_43_0_11 yields:
% 5.09/1.83 | (79) ~ (all_43_0_11 = 0) & member(all_23_1_10, all_0_3_3) = 0 & member(all_23_1_10, all_0_4_4) = all_43_0_11
% 5.09/1.84 |
% 5.09/1.84 | Applying alpha-rule on (79) yields:
% 5.09/1.84 | (80) ~ (all_43_0_11 = 0)
% 5.09/1.84 | (81) member(all_23_1_10, all_0_3_3) = 0
% 5.09/1.84 | (82) member(all_23_1_10, all_0_4_4) = all_43_0_11
% 5.09/1.84 |
% 5.09/1.84 | Instantiating formula (25) with all_23_1_10, all_0_4_4, all_43_0_11, 0 and discharging atoms member(all_23_1_10, all_0_4_4) = all_43_0_11, member(all_23_1_10, all_0_4_4) = 0, yields:
% 5.09/1.84 | (83) all_43_0_11 = 0
% 5.09/1.84 |
% 5.09/1.84 | Equations (83) can reduce 80 to:
% 5.09/1.84 | (42) $false
% 5.09/1.84 |
% 5.09/1.84 |-The branch is then unsatisfiable
% 5.09/1.84 % SZS output end Proof for theBenchmark
% 5.09/1.84
% 5.09/1.84 1247ms
%------------------------------------------------------------------------------