TSTP Solution File: SET347+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET347+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 00:19:08 EDT 2022
% Result : Theorem 3.51s 1.47s
% Output : Proof 4.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET347+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 03:07:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.59 ____ _
% 0.20/0.59 ___ / __ \_____(_)___ ________ __________
% 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic
% 0.20/0.60 (ePrincess v.1.0)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2015
% 0.20/0.60 (c) Peter Backeman, 2014-2015
% 0.20/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.60 Bug reports to peter@backeman.se
% 0.20/0.60
% 0.20/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.60
% 0.62/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.53/0.91 Prover 0: Preprocessing ...
% 2.02/1.10 Prover 0: Warning: ignoring some quantifiers
% 2.02/1.13 Prover 0: Constructing countermodel ...
% 2.62/1.25 Prover 0: gave up
% 2.62/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.62/1.27 Prover 1: Preprocessing ...
% 3.09/1.39 Prover 1: Constructing countermodel ...
% 3.51/1.46 Prover 1: proved (212ms)
% 3.51/1.47
% 3.51/1.47 No countermodel exists, formula is valid
% 3.51/1.47 % SZS status Theorem for theBenchmark
% 3.51/1.47
% 3.51/1.47 Generating proof ... found it (size 28)
% 4.43/1.72
% 4.43/1.72 % SZS output start Proof for theBenchmark
% 4.43/1.72 Assumed formulas after preprocessing and simplification:
% 4.43/1.72 | (0) ? [v0] : ? [v1] : ( ~ (v1 = 0) & sum(empty_set) = v0 & equal_set(v0, empty_set) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (product(v3) = v4) | ~ (member(v2, v5) = v6) | ~ (member(v2, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & member(v5, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (difference(v4, v3) = v5) | ~ (member(v2, v5) = v6) | ? [v7] : ? [v8] : (member(v2, v4) = v7 & member(v2, v3) = v8 & ( ~ (v7 = 0) | v8 = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (union(v3, v4) = v5) | ~ (member(v2, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v7 = 0) & member(v2, v4) = v8 & member(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (intersection(v3, v4) = v5) | ~ (member(v2, v5) = v6) | ? [v7] : ? [v8] : (member(v2, v4) = v8 & member(v2, v3) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (sum(v3) = v4) | ~ (member(v2, v6) = 0) | ~ (member(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & member(v6, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (product(v3) = v4) | ~ (member(v2, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & member(v6, v3) = 0 & member(v2, v6) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unordered_pair(v3, v2) = v4) | ~ (member(v2, v4) = v5)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unordered_pair(v2, v3) = v4) | ~ (member(v2, v4) = v5)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (power_set(v3) = v4) | ~ (member(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v2, v3) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v2 | v3 = v2 | ~ (unordered_pair(v3, v4) = v5) | ~ (member(v2, v5) = 0)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (unordered_pair(v5, v4) = v3) | ~ (unordered_pair(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (difference(v5, v4) = v3) | ~ (difference(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (union(v5, v4) = v3) | ~ (union(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (intersection(v5, v4) = v3) | ~ (intersection(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (equal_set(v5, v4) = v3) | ~ (equal_set(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (subset(v5, v4) = v3) | ~ (subset(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (member(v5, v4) = v3) | ~ (member(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (difference(v4, v3) = v5) | ~ (member(v2, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & member(v2, v4) = 0 & member(v2, v3) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (union(v3, v4) = v5) | ~ (member(v2, v5) = 0) | ? [v6] : ? [v7] : (member(v2, v4) = v7 & member(v2, v3) = v6 & (v7 = 0 | v6 = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection(v3, v4) = v5) | ~ (member(v2, v5) = 0) | (member(v2, v4) = 0 & member(v2, v3) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (singleton(v2) = v3) | ~ (member(v2, v3) = v4)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equal_set(v2, v3) = v4) | ? [v5] : ? [v6] : (subset(v3, v2) = v6 & subset(v2, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & member(v5, v3) = v6 & member(v5, v2) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (product(v4) = v3) | ~ (product(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (sum(v4) = v3) | ~ (sum(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (singleton(v4) = v3) | ~ (singleton(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (singleton(v3) = v4) | ~ (member(v2, v4) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (power_set(v4) = v3) | ~ (power_set(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v3) = v4) | ~ (member(v2, v4) = 0) | ? [v5] : (member(v5, v3) = 0 & member(v2, v5) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (power_set(v3) = v4) | ~ (member(v2, v4) = 0) | subset(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ( ~ (subset(v2, v3) = 0) | ~ (member(v4, v2) = 0) | member(v4, v3) = 0) & ! [v2] : ! [v3] : ( ~ (equal_set(v2, v3) = 0) | (subset(v3, v2) = 0 & subset(v2, v3) = 0)) & ! [v2] : ~ (member(v2, empty_set) = 0))
% 4.75/1.76 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 4.75/1.76 | (1) ~ (all_0_0_0 = 0) & sum(empty_set) = all_0_1_1 & equal_set(all_0_1_1, empty_set) = 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)
% 4.75/1.78 |
% 4.75/1.78 | Applying alpha-rule on (1) yields:
% 4.75/1.78 | (2) ! [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)))
% 4.75/1.78 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 4.75/1.78 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 4.75/1.78 | (5) ! [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))
% 4.75/1.78 | (6) ! [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)))
% 4.75/1.78 | (7) sum(empty_set) = all_0_1_1
% 4.75/1.78 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 4.75/1.78 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 4.75/1.78 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 4.75/1.78 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 4.75/1.79 | (12) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 4.75/1.79 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 4.75/1.79 | (14) ! [v0] : ~ (member(v0, empty_set) = 0)
% 4.75/1.79 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 4.75/1.79 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 4.75/1.79 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 4.75/1.79 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 4.75/1.79 | (19) ! [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))))
% 4.75/1.79 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 4.75/1.79 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 4.75/1.79 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 4.75/1.79 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 4.75/1.79 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 4.75/1.79 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 4.75/1.79 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 4.75/1.79 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 4.75/1.79 | (28) ! [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))
% 4.75/1.79 | (29) equal_set(all_0_1_1, empty_set) = all_0_0_0
% 4.75/1.79 | (30) ~ (all_0_0_0 = 0)
% 4.75/1.79 | (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))))
% 4.75/1.79 | (32) ! [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))
% 4.75/1.79 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 4.75/1.80 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 4.75/1.80 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 4.75/1.80 | (36) ! [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))
% 4.75/1.80 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 4.75/1.80 |
% 4.75/1.80 | 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:
% 4.75/1.80 | (38) 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)))
% 4.75/1.80 |
% 4.75/1.80 +-Applying beta-rule and splitting (38), into two cases.
% 4.75/1.80 |-Branch one:
% 4.75/1.80 | (39) all_0_0_0 = 0
% 4.75/1.80 |
% 4.75/1.80 | Equations (39) can reduce 30 to:
% 4.75/1.80 | (40) $false
% 4.75/1.80 |
% 4.75/1.80 |-The branch is then unsatisfiable
% 4.75/1.80 |-Branch two:
% 4.75/1.80 | (30) ~ (all_0_0_0 = 0)
% 4.75/1.80 | (42) ? [v0] : ? [v1] : (subset(all_0_1_1, empty_set) = v0 & subset(empty_set, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 4.75/1.80 |
% 4.75/1.80 | Instantiating (42) with all_10_0_2, all_10_1_3 yields:
% 4.75/1.80 | (43) subset(all_0_1_1, empty_set) = all_10_1_3 & subset(empty_set, all_0_1_1) = all_10_0_2 & ( ~ (all_10_0_2 = 0) | ~ (all_10_1_3 = 0))
% 4.75/1.80 |
% 4.75/1.80 | Applying alpha-rule on (43) yields:
% 4.75/1.80 | (44) subset(all_0_1_1, empty_set) = all_10_1_3
% 4.75/1.80 | (45) subset(empty_set, all_0_1_1) = all_10_0_2
% 4.75/1.80 | (46) ~ (all_10_0_2 = 0) | ~ (all_10_1_3 = 0)
% 4.75/1.80 |
% 4.75/1.80 | Instantiating formula (15) with all_10_1_3, empty_set, all_0_1_1 and discharging atoms subset(all_0_1_1, empty_set) = all_10_1_3, yields:
% 4.75/1.80 | (47) all_10_1_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, empty_set) = v1)
% 4.75/1.80 |
% 4.75/1.80 | Instantiating formula (15) with all_10_0_2, all_0_1_1, empty_set and discharging atoms subset(empty_set, all_0_1_1) = all_10_0_2, yields:
% 4.75/1.80 | (48) all_10_0_2 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, empty_set) = 0)
% 4.75/1.80 |
% 4.75/1.80 +-Applying beta-rule and splitting (46), into two cases.
% 4.75/1.80 |-Branch one:
% 4.75/1.80 | (49) ~ (all_10_0_2 = 0)
% 4.75/1.80 |
% 4.75/1.80 +-Applying beta-rule and splitting (48), into two cases.
% 4.75/1.80 |-Branch one:
% 4.75/1.80 | (50) all_10_0_2 = 0
% 4.75/1.80 |
% 4.75/1.80 | Equations (50) can reduce 49 to:
% 4.75/1.80 | (40) $false
% 4.75/1.80 |
% 4.75/1.80 |-The branch is then unsatisfiable
% 4.75/1.80 |-Branch two:
% 4.75/1.80 | (49) ~ (all_10_0_2 = 0)
% 4.75/1.80 | (53) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, empty_set) = 0)
% 4.75/1.81 |
% 4.75/1.81 | Instantiating (53) with all_23_0_4, all_23_1_5 yields:
% 4.75/1.81 | (54) ~ (all_23_0_4 = 0) & member(all_23_1_5, all_0_1_1) = all_23_0_4 & member(all_23_1_5, empty_set) = 0
% 4.75/1.81 |
% 4.75/1.81 | Applying alpha-rule on (54) yields:
% 4.75/1.81 | (55) ~ (all_23_0_4 = 0)
% 4.75/1.81 | (56) member(all_23_1_5, all_0_1_1) = all_23_0_4
% 4.75/1.81 | (57) member(all_23_1_5, empty_set) = 0
% 4.75/1.81 |
% 4.75/1.81 | Instantiating formula (14) with all_23_1_5 and discharging atoms member(all_23_1_5, empty_set) = 0, yields:
% 4.90/1.81 | (58) $false
% 4.90/1.81 |
% 4.90/1.81 |-The branch is then unsatisfiable
% 4.90/1.81 |-Branch two:
% 4.90/1.81 | (50) all_10_0_2 = 0
% 4.90/1.81 | (60) ~ (all_10_1_3 = 0)
% 4.90/1.81 |
% 4.90/1.81 +-Applying beta-rule and splitting (47), into two cases.
% 4.90/1.81 |-Branch one:
% 4.90/1.81 | (61) all_10_1_3 = 0
% 4.90/1.81 |
% 4.90/1.81 | Equations (61) can reduce 60 to:
% 4.90/1.81 | (40) $false
% 4.90/1.81 |
% 4.90/1.81 |-The branch is then unsatisfiable
% 4.90/1.81 |-Branch two:
% 4.90/1.81 | (60) ~ (all_10_1_3 = 0)
% 4.90/1.81 | (64) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, empty_set) = v1)
% 4.90/1.81 |
% 4.90/1.81 | Instantiating (64) with all_23_0_6, all_23_1_7 yields:
% 4.90/1.81 | (65) ~ (all_23_0_6 = 0) & member(all_23_1_7, all_0_1_1) = 0 & member(all_23_1_7, empty_set) = all_23_0_6
% 4.90/1.81 |
% 4.90/1.81 | Applying alpha-rule on (65) yields:
% 4.90/1.81 | (66) ~ (all_23_0_6 = 0)
% 4.90/1.81 | (67) member(all_23_1_7, all_0_1_1) = 0
% 4.90/1.81 | (68) member(all_23_1_7, empty_set) = all_23_0_6
% 4.90/1.81 |
% 4.90/1.81 | Instantiating formula (10) with all_0_1_1, empty_set, all_23_1_7 and discharging atoms sum(empty_set) = all_0_1_1, member(all_23_1_7, all_0_1_1) = 0, yields:
% 4.90/1.81 | (69) ? [v0] : (member(v0, empty_set) = 0 & member(all_23_1_7, v0) = 0)
% 4.90/1.81 |
% 4.90/1.81 | Instantiating (69) with all_38_0_8 yields:
% 4.90/1.81 | (70) member(all_38_0_8, empty_set) = 0 & member(all_23_1_7, all_38_0_8) = 0
% 4.90/1.81 |
% 4.90/1.81 | Applying alpha-rule on (70) yields:
% 4.90/1.81 | (71) member(all_38_0_8, empty_set) = 0
% 4.90/1.81 | (72) member(all_23_1_7, all_38_0_8) = 0
% 4.90/1.81 |
% 4.90/1.81 | Instantiating formula (14) with all_38_0_8 and discharging atoms member(all_38_0_8, empty_set) = 0, yields:
% 4.90/1.81 | (58) $false
% 4.90/1.81 |
% 4.90/1.81 |-The branch is then unsatisfiable
% 4.90/1.81 % SZS output end Proof for theBenchmark
% 4.90/1.81
% 4.90/1.81 1205ms
%------------------------------------------------------------------------------