TSTP Solution File: SET700+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET700+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 00:21:29 EDT 2022
% Result : Theorem 6.20s 2.19s
% Output : Proof 8.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET700+4 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.09 % Command : ePrincess-casc -timeout=%d %s
% 0.08/0.28 % Computer : n019.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Sun Jul 10 01:35:53 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.51/0.52 ____ _
% 0.51/0.52 ___ / __ \_____(_)___ ________ __________
% 0.51/0.52 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.52 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.52 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.52
% 0.51/0.52 A Theorem Prover for First-Order Logic
% 0.51/0.53 (ePrincess v.1.0)
% 0.51/0.53
% 0.51/0.53 (c) Philipp Rümmer, 2009-2015
% 0.51/0.53 (c) Peter Backeman, 2014-2015
% 0.51/0.53 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.53 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.53 Bug reports to peter@backeman.se
% 0.51/0.53
% 0.51/0.53 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.53
% 0.51/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.53/0.59 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.35/0.92 Prover 0: Preprocessing ...
% 2.01/1.17 Prover 0: Warning: ignoring some quantifiers
% 2.01/1.21 Prover 0: Constructing countermodel ...
% 2.96/1.52 Prover 0: gave up
% 3.26/1.52 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.26/1.56 Prover 1: Preprocessing ...
% 3.91/1.72 Prover 1: Constructing countermodel ...
% 4.54/1.86 Prover 1: gave up
% 4.54/1.86 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.78/1.88 Prover 2: Preprocessing ...
% 5.30/2.01 Prover 2: Warning: ignoring some quantifiers
% 5.30/2.02 Prover 2: Constructing countermodel ...
% 6.20/2.19 Prover 2: proved (336ms)
% 6.20/2.19
% 6.20/2.19 No countermodel exists, formula is valid
% 6.20/2.19 % SZS status Theorem for theBenchmark
% 6.20/2.19
% 6.20/2.19 Generating proof ... Warning: ignoring some quantifiers
% 8.08/2.60 found it (size 70)
% 8.08/2.60
% 8.08/2.60 % SZS output start Proof for theBenchmark
% 8.08/2.60 Assumed formulas after preprocessing and simplification:
% 8.08/2.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (difference(v2, v1) = v4 & intersection(v0, v4) = v5 & subset(v5, v1) = v6 & subset(v1, v2) = 0 & subset(v0, v2) = 0 & subset(v0, v1) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v10) = v11) | ~ (member(v7, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ((v12 = 0 & member(v7, v8) = 0) | ( ~ (v12 = 0) & member(v7, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & member(v7, v9) = v13 & member(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : (( ~ (v12 = 0) & member(v7, v9) = v12) | ( ~ (v12 = 0) & member(v7, v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v11, v8) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v7, v11) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = 0 & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v8, v7) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (power_set(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v8) = 0) | ~ (member(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | v8 = v7 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (difference(v10, v9) = v8) | ~ (difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_set(v10, v9) = v8) | ~ (equal_set(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (product(v8) = v9) | ~ (member(v10, v8) = 0) | ~ (member(v7, v9) = 0) | member(v7, v10) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v7, v9) = 0 & member(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ((v11 = 0 & member(v7, v9) = 0) | (v11 = 0 & member(v7, v8) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = 0) | (member(v7, v9) = 0 & member(v7, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (singleton(v7) = v8) | ~ (member(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_set(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & subset(v8, v7) = v10) | ( ~ (v10 = 0) & subset(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & power_set(v8) = v10 & member(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (product(v9) = v8) | ~ (product(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sum(v9) = v8) | ~ (sum(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v8) = v9) | ~ (member(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (power_set(v9) = v8) | ~ (power_set(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v8) = v9) | ~ (member(v7, v9) = 0) | ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_set(v8) = v9) | ~ (member(v7, v9) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v8, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & subset(v7, v8) = 0) | ( ~ (v10 = 0) & equal_set(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & subset(v8, v7) = 0) | ( ~ (v10 = 0) & equal_set(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ( ~ (equal_set(v7, v8) = 0) | (subset(v8, v7) = 0 & subset(v7, v8) = 0)) & ! [v7] : ! [v8] : ( ~ (subset(v8, v7) = 0) | ? [v9] : ((v9 = 0 & equal_set(v7, v8) = 0) | ( ~ (v9 = 0) & subset(v7, v8) = v9))) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ? [v9] : (power_set(v8) = v9 & member(v7, v9) = 0)) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ? [v9] : ((v9 = 0 & equal_set(v7, v8) = 0) | ( ~ (v9 = 0) & subset(v8, v7) = v9))) & ! [v7] : ~ (member(v7, empty_set) = 0) & ? [v7] : ? [v8] : ? [v9] : unordered_pair(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : difference(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : union(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : intersection(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : equal_set(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : member(v8, v7) = v9 & ? [v7] : ? [v8] : product(v7) = v8 & ? [v7] : ? [v8] : sum(v7) = v8 & ? [v7] : ? [v8] : singleton(v7) = v8 & ? [v7] : ? [v8] : power_set(v7) = v8 & ((v6 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v6 = 0))))
% 8.25/2.66 | 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 yields:
% 8.25/2.66 | (1) difference(all_0_4_4, all_0_5_5) = all_0_2_2 & intersection(all_0_6_6, all_0_2_2) = all_0_1_1 & subset(all_0_1_1, all_0_5_5) = all_0_0_0 & subset(all_0_5_5, all_0_4_4) = 0 & subset(all_0_6_6, all_0_4_4) = 0 & subset(all_0_6_6, all_0_5_5) = all_0_3_3 & ! [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] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5))) & ! [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] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) & ! [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] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = 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] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0) & ! [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] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 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] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4)) & ! [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(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [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] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2))) & ! [v0] : ~ (member(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : product(v0) = v1 & ? [v0] : ? [v1] : sum(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : power_set(v0) = v1 & ((all_0_0_0 = 0 & ~ (all_0_3_3 = 0)) | (all_0_3_3 = 0 & ~ (all_0_0_0 = 0)))
% 8.25/2.68 |
% 8.25/2.68 | Applying alpha-rule on (1) yields:
% 8.25/2.68 | (2) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 8.25/2.68 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 8.25/2.68 | (4) ! [v0] : ~ (member(v0, empty_set) = 0)
% 8.25/2.68 | (5) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 8.25/2.68 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 8.25/2.68 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 8.25/2.68 | (8) intersection(all_0_6_6, all_0_2_2) = all_0_1_1
% 8.25/2.68 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 8.25/2.68 | (10) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 8.25/2.68 | (11) subset(all_0_6_6, all_0_4_4) = 0
% 8.25/2.68 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 8.25/2.68 | (13) ! [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))
% 8.25/2.68 | (14) (all_0_0_0 = 0 & ~ (all_0_3_3 = 0)) | (all_0_3_3 = 0 & ~ (all_0_0_0 = 0))
% 8.25/2.68 | (15) ! [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))
% 8.25/2.69 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0)))
% 8.25/2.69 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5)))
% 8.25/2.69 | (18) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 8.25/2.69 | (19) ! [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))
% 8.25/2.69 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 8.25/2.69 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 8.25/2.69 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 8.25/2.69 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 8.25/2.69 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 8.25/2.69 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 8.25/2.69 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 8.25/2.69 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 8.25/2.69 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 8.25/2.69 | (29) ? [v0] : ? [v1] : singleton(v0) = v1
% 8.25/2.69 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 8.25/2.69 | (31) subset(all_0_1_1, all_0_5_5) = all_0_0_0
% 8.25/2.69 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 8.25/2.69 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 8.25/2.70 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 8.25/2.70 | (35) ? [v0] : ? [v1] : sum(v0) = v1
% 8.25/2.70 | (36) difference(all_0_4_4, all_0_5_5) = all_0_2_2
% 8.25/2.70 | (37) ? [v0] : ? [v1] : power_set(v0) = v1
% 8.25/2.70 | (38) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 8.25/2.70 | (39) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 8.25/2.70 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 8.25/2.70 | (41) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 8.25/2.70 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 8.25/2.70 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 8.25/2.70 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 8.25/2.70 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 8.25/2.70 | (46) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 8.25/2.70 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5))
% 8.25/2.70 | (48) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 8.25/2.70 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 8.25/2.70 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5)))
% 8.25/2.70 | (51) subset(all_0_5_5, all_0_4_4) = 0
% 8.25/2.70 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 8.25/2.71 | (53) ? [v0] : ? [v1] : product(v0) = v1
% 8.25/2.71 | (54) ! [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))
% 8.25/2.71 | (55) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 8.25/2.71 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 8.25/2.71 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 8.25/2.71 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 8.25/2.71 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 8.25/2.71 | (60) subset(all_0_6_6, all_0_5_5) = all_0_3_3
% 8.25/2.71 | (61) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 8.25/2.71 |
% 8.25/2.71 | Instantiating formula (30) with all_0_0_0, all_0_5_5, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 8.25/2.71 | (62) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_5_5) = v0 & member(all_0_1_1, v0) = v1)
% 8.25/2.71 |
% 8.25/2.71 | Instantiating formula (40) with all_0_0_0, all_0_5_5, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 8.25/2.71 | (63) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_5_5) = v1)
% 8.25/2.71 |
% 8.25/2.71 | Instantiating formula (30) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 8.25/2.71 | (64) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_5_5) = v0 & member(all_0_6_6, v0) = v1)
% 8.25/2.71 |
% 8.25/2.71 | Instantiating formula (40) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 8.25/2.71 | (65) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_5_5) = v1 & member(v0, all_0_6_6) = 0)
% 8.25/2.71 |
% 8.25/2.71 +-Applying beta-rule and splitting (14), into two cases.
% 8.25/2.71 |-Branch one:
% 8.25/2.71 | (66) all_0_0_0 = 0 & ~ (all_0_3_3 = 0)
% 8.25/2.71 |
% 8.25/2.71 | Applying alpha-rule on (66) yields:
% 8.25/2.71 | (67) all_0_0_0 = 0
% 8.25/2.71 | (68) ~ (all_0_3_3 = 0)
% 8.25/2.71 |
% 8.25/2.71 | From (67) and (31) follows:
% 8.25/2.71 | (69) subset(all_0_1_1, all_0_5_5) = 0
% 8.25/2.72 |
% 8.25/2.72 +-Applying beta-rule and splitting (64), into two cases.
% 8.25/2.72 |-Branch one:
% 8.25/2.72 | (70) all_0_3_3 = 0
% 8.25/2.72 |
% 8.25/2.72 | Equations (70) can reduce 68 to:
% 8.25/2.72 | (71) $false
% 8.25/2.72 |
% 8.65/2.72 |-The branch is then unsatisfiable
% 8.65/2.72 |-Branch two:
% 8.65/2.72 | (68) ~ (all_0_3_3 = 0)
% 8.65/2.72 | (73) ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_5_5) = v0 & member(all_0_6_6, v0) = v1)
% 8.65/2.72 |
% 8.65/2.72 +-Applying beta-rule and splitting (65), into two cases.
% 8.65/2.72 |-Branch one:
% 8.65/2.72 | (70) all_0_3_3 = 0
% 8.65/2.72 |
% 8.65/2.72 | Equations (70) can reduce 68 to:
% 8.65/2.72 | (71) $false
% 8.65/2.72 |
% 8.65/2.72 |-The branch is then unsatisfiable
% 8.65/2.72 |-Branch two:
% 8.65/2.72 | (68) ~ (all_0_3_3 = 0)
% 8.65/2.72 | (77) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_5_5) = v1 & member(v0, all_0_6_6) = 0)
% 8.65/2.72 |
% 8.65/2.72 | Instantiating (77) with all_73_0_52, all_73_1_53 yields:
% 8.65/2.72 | (78) ~ (all_73_0_52 = 0) & member(all_73_1_53, all_0_5_5) = all_73_0_52 & member(all_73_1_53, all_0_6_6) = 0
% 8.65/2.72 |
% 8.65/2.72 | Applying alpha-rule on (78) yields:
% 8.65/2.72 | (79) ~ (all_73_0_52 = 0)
% 8.65/2.72 | (80) member(all_73_1_53, all_0_5_5) = all_73_0_52
% 8.65/2.72 | (81) member(all_73_1_53, all_0_6_6) = 0
% 8.65/2.72 |
% 8.65/2.72 | Instantiating formula (12) with all_73_0_52, all_73_1_53, all_0_5_5, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_5_5) = 0, member(all_73_1_53, all_0_5_5) = all_73_0_52, yields:
% 8.65/2.72 | (82) all_73_0_52 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_73_1_53, all_0_1_1) = v0)
% 8.65/2.72 |
% 8.65/2.72 | Instantiating formula (27) with all_73_1_53, all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = 0, member(all_73_1_53, all_0_6_6) = 0, yields:
% 8.65/2.72 | (83) member(all_73_1_53, all_0_4_4) = 0
% 8.65/2.72 |
% 8.65/2.72 +-Applying beta-rule and splitting (82), into two cases.
% 8.65/2.72 |-Branch one:
% 8.65/2.72 | (84) all_73_0_52 = 0
% 8.65/2.72 |
% 8.65/2.72 | Equations (84) can reduce 79 to:
% 8.65/2.72 | (71) $false
% 8.65/2.72 |
% 8.65/2.72 |-The branch is then unsatisfiable
% 8.65/2.72 |-Branch two:
% 8.65/2.72 | (79) ~ (all_73_0_52 = 0)
% 8.65/2.72 | (87) ? [v0] : ( ~ (v0 = 0) & member(all_73_1_53, all_0_1_1) = v0)
% 8.65/2.72 |
% 8.65/2.72 | Instantiating (87) with all_89_0_57 yields:
% 8.65/2.72 | (88) ~ (all_89_0_57 = 0) & member(all_73_1_53, all_0_1_1) = all_89_0_57
% 8.65/2.72 |
% 8.65/2.72 | Applying alpha-rule on (88) yields:
% 8.65/2.72 | (89) ~ (all_89_0_57 = 0)
% 8.65/2.72 | (90) member(all_73_1_53, all_0_1_1) = all_89_0_57
% 8.65/2.72 |
% 8.65/2.72 | Instantiating formula (50) with all_89_0_57, all_0_1_1, all_0_2_2, all_0_6_6, all_73_1_53 and discharging atoms intersection(all_0_6_6, all_0_2_2) = all_0_1_1, member(all_73_1_53, all_0_1_1) = all_89_0_57, yields:
% 8.65/2.72 | (91) all_89_0_57 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_73_1_53, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_73_1_53, all_0_6_6) = v0))
% 8.65/2.72 |
% 8.65/2.72 +-Applying beta-rule and splitting (91), into two cases.
% 8.65/2.72 |-Branch one:
% 8.65/2.72 | (92) all_89_0_57 = 0
% 8.65/2.72 |
% 8.65/2.72 | Equations (92) can reduce 89 to:
% 8.65/2.72 | (71) $false
% 8.65/2.72 |
% 8.65/2.72 |-The branch is then unsatisfiable
% 8.65/2.72 |-Branch two:
% 8.65/2.72 | (89) ~ (all_89_0_57 = 0)
% 8.65/2.72 | (95) ? [v0] : (( ~ (v0 = 0) & member(all_73_1_53, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_73_1_53, all_0_6_6) = v0))
% 8.65/2.72 |
% 8.65/2.72 | Instantiating (95) with all_117_0_60 yields:
% 8.65/2.72 | (96) ( ~ (all_117_0_60 = 0) & member(all_73_1_53, all_0_2_2) = all_117_0_60) | ( ~ (all_117_0_60 = 0) & member(all_73_1_53, all_0_6_6) = all_117_0_60)
% 8.65/2.73 |
% 8.65/2.73 +-Applying beta-rule and splitting (96), into two cases.
% 8.65/2.73 |-Branch one:
% 8.65/2.73 | (97) ~ (all_117_0_60 = 0) & member(all_73_1_53, all_0_2_2) = all_117_0_60
% 8.65/2.73 |
% 8.65/2.73 | Applying alpha-rule on (97) yields:
% 8.65/2.73 | (98) ~ (all_117_0_60 = 0)
% 8.65/2.73 | (99) member(all_73_1_53, all_0_2_2) = all_117_0_60
% 8.65/2.73 |
% 8.65/2.73 | Instantiating formula (17) with all_117_0_60, all_0_2_2, all_0_4_4, all_0_5_5, all_73_1_53 and discharging atoms difference(all_0_4_4, all_0_5_5) = all_0_2_2, member(all_73_1_53, all_0_2_2) = all_117_0_60, yields:
% 8.65/2.73 | (100) all_117_0_60 = 0 | ? [v0] : ((v0 = 0 & member(all_73_1_53, all_0_5_5) = 0) | ( ~ (v0 = 0) & member(all_73_1_53, all_0_4_4) = v0))
% 8.65/2.73 |
% 8.65/2.73 +-Applying beta-rule and splitting (100), into two cases.
% 8.65/2.73 |-Branch one:
% 8.65/2.73 | (101) all_117_0_60 = 0
% 8.65/2.73 |
% 8.65/2.73 | Equations (101) can reduce 98 to:
% 8.65/2.73 | (71) $false
% 8.65/2.73 |
% 8.65/2.73 |-The branch is then unsatisfiable
% 8.65/2.73 |-Branch two:
% 8.65/2.73 | (98) ~ (all_117_0_60 = 0)
% 8.65/2.73 | (104) ? [v0] : ((v0 = 0 & member(all_73_1_53, all_0_5_5) = 0) | ( ~ (v0 = 0) & member(all_73_1_53, all_0_4_4) = v0))
% 8.65/2.73 |
% 8.65/2.73 | Instantiating (104) with all_141_0_62 yields:
% 8.65/2.73 | (105) (all_141_0_62 = 0 & member(all_73_1_53, all_0_5_5) = 0) | ( ~ (all_141_0_62 = 0) & member(all_73_1_53, all_0_4_4) = all_141_0_62)
% 8.65/2.73 |
% 8.65/2.73 +-Applying beta-rule and splitting (105), into two cases.
% 8.65/2.73 |-Branch one:
% 8.65/2.73 | (106) all_141_0_62 = 0 & member(all_73_1_53, all_0_5_5) = 0
% 8.65/2.73 |
% 8.65/2.73 | Applying alpha-rule on (106) yields:
% 8.65/2.73 | (107) all_141_0_62 = 0
% 8.65/2.73 | (108) member(all_73_1_53, all_0_5_5) = 0
% 8.65/2.73 |
% 8.65/2.73 | Instantiating formula (44) with all_73_1_53, all_0_5_5, 0, all_73_0_52 and discharging atoms member(all_73_1_53, all_0_5_5) = all_73_0_52, member(all_73_1_53, all_0_5_5) = 0, yields:
% 8.65/2.73 | (84) all_73_0_52 = 0
% 8.65/2.73 |
% 8.65/2.73 | Equations (84) can reduce 79 to:
% 8.65/2.73 | (71) $false
% 8.65/2.73 |
% 8.65/2.73 |-The branch is then unsatisfiable
% 8.65/2.73 |-Branch two:
% 8.65/2.73 | (111) ~ (all_141_0_62 = 0) & member(all_73_1_53, all_0_4_4) = all_141_0_62
% 8.65/2.73 |
% 8.65/2.73 | Applying alpha-rule on (111) yields:
% 8.65/2.73 | (112) ~ (all_141_0_62 = 0)
% 8.65/2.73 | (113) member(all_73_1_53, all_0_4_4) = all_141_0_62
% 8.65/2.73 |
% 8.65/2.73 | Instantiating formula (44) with all_73_1_53, all_0_4_4, all_141_0_62, 0 and discharging atoms member(all_73_1_53, all_0_4_4) = all_141_0_62, member(all_73_1_53, all_0_4_4) = 0, yields:
% 8.65/2.74 | (107) all_141_0_62 = 0
% 8.65/2.74 |
% 8.65/2.74 | Equations (107) can reduce 112 to:
% 8.65/2.74 | (71) $false
% 8.65/2.74 |
% 8.65/2.74 |-The branch is then unsatisfiable
% 8.65/2.74 |-Branch two:
% 8.65/2.74 | (116) ~ (all_117_0_60 = 0) & member(all_73_1_53, all_0_6_6) = all_117_0_60
% 8.65/2.74 |
% 8.65/2.74 | Applying alpha-rule on (116) yields:
% 8.65/2.74 | (98) ~ (all_117_0_60 = 0)
% 8.65/2.74 | (118) member(all_73_1_53, all_0_6_6) = all_117_0_60
% 8.65/2.74 |
% 8.65/2.74 | Instantiating formula (44) with all_73_1_53, all_0_6_6, all_117_0_60, 0 and discharging atoms member(all_73_1_53, all_0_6_6) = all_117_0_60, member(all_73_1_53, all_0_6_6) = 0, yields:
% 8.65/2.74 | (101) all_117_0_60 = 0
% 8.65/2.74 |
% 8.65/2.74 | Equations (101) can reduce 98 to:
% 8.65/2.74 | (71) $false
% 8.65/2.74 |
% 8.65/2.74 |-The branch is then unsatisfiable
% 8.65/2.74 |-Branch two:
% 8.65/2.74 | (121) all_0_3_3 = 0 & ~ (all_0_0_0 = 0)
% 8.65/2.74 |
% 8.65/2.74 | Applying alpha-rule on (121) yields:
% 8.65/2.74 | (70) all_0_3_3 = 0
% 8.65/2.74 | (123) ~ (all_0_0_0 = 0)
% 8.65/2.74 |
% 8.65/2.74 | From (70) and (60) follows:
% 8.65/2.74 | (124) subset(all_0_6_6, all_0_5_5) = 0
% 8.65/2.74 |
% 8.65/2.74 +-Applying beta-rule and splitting (62), into two cases.
% 8.65/2.74 |-Branch one:
% 8.65/2.74 | (67) all_0_0_0 = 0
% 8.65/2.74 |
% 8.65/2.74 | Equations (67) can reduce 123 to:
% 8.65/2.74 | (71) $false
% 8.65/2.74 |
% 8.65/2.74 |-The branch is then unsatisfiable
% 8.65/2.74 |-Branch two:
% 8.65/2.74 | (123) ~ (all_0_0_0 = 0)
% 8.65/2.74 | (128) ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_5_5) = v0 & member(all_0_1_1, v0) = v1)
% 8.65/2.74 |
% 8.65/2.74 +-Applying beta-rule and splitting (63), into two cases.
% 8.65/2.74 |-Branch one:
% 8.65/2.74 | (67) all_0_0_0 = 0
% 8.65/2.74 |
% 8.65/2.74 | Equations (67) can reduce 123 to:
% 8.65/2.74 | (71) $false
% 8.65/2.74 |
% 8.65/2.74 |-The branch is then unsatisfiable
% 8.65/2.74 |-Branch two:
% 8.65/2.74 | (123) ~ (all_0_0_0 = 0)
% 8.65/2.74 | (132) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_5_5) = v1)
% 8.65/2.74 |
% 8.65/2.74 | Instantiating (132) with all_69_0_65, all_69_1_66 yields:
% 8.65/2.74 | (133) ~ (all_69_0_65 = 0) & member(all_69_1_66, all_0_1_1) = 0 & member(all_69_1_66, all_0_5_5) = all_69_0_65
% 8.65/2.74 |
% 8.65/2.74 | Applying alpha-rule on (133) yields:
% 8.65/2.74 | (134) ~ (all_69_0_65 = 0)
% 8.65/2.74 | (135) member(all_69_1_66, all_0_1_1) = 0
% 8.65/2.74 | (136) member(all_69_1_66, all_0_5_5) = all_69_0_65
% 8.65/2.74 |
% 8.65/2.74 | Instantiating formula (26) with all_0_1_1, all_0_2_2, all_0_6_6, all_69_1_66 and discharging atoms intersection(all_0_6_6, all_0_2_2) = all_0_1_1, member(all_69_1_66, all_0_1_1) = 0, yields:
% 8.65/2.74 | (137) member(all_69_1_66, all_0_2_2) = 0 & member(all_69_1_66, all_0_6_6) = 0
% 8.65/2.74 |
% 8.65/2.74 | Applying alpha-rule on (137) yields:
% 8.65/2.74 | (138) member(all_69_1_66, all_0_2_2) = 0
% 8.65/2.74 | (139) member(all_69_1_66, all_0_6_6) = 0
% 8.65/2.74 |
% 8.65/2.74 | Instantiating formula (12) with all_69_0_65, all_69_1_66, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = 0, member(all_69_1_66, all_0_5_5) = all_69_0_65, yields:
% 8.65/2.74 | (140) all_69_0_65 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_69_1_66, all_0_6_6) = v0)
% 8.65/2.74 |
% 8.65/2.74 +-Applying beta-rule and splitting (140), into two cases.
% 8.65/2.74 |-Branch one:
% 8.65/2.74 | (141) all_69_0_65 = 0
% 8.65/2.74 |
% 8.65/2.74 | Equations (141) can reduce 134 to:
% 8.65/2.74 | (71) $false
% 8.65/2.74 |
% 8.65/2.74 |-The branch is then unsatisfiable
% 8.65/2.74 |-Branch two:
% 8.65/2.75 | (134) ~ (all_69_0_65 = 0)
% 8.65/2.75 | (144) ? [v0] : ( ~ (v0 = 0) & member(all_69_1_66, all_0_6_6) = v0)
% 8.65/2.75 |
% 8.65/2.75 | Instantiating (144) with all_89_0_70 yields:
% 8.65/2.75 | (145) ~ (all_89_0_70 = 0) & member(all_69_1_66, all_0_6_6) = all_89_0_70
% 8.65/2.75 |
% 8.65/2.75 | Applying alpha-rule on (145) yields:
% 8.65/2.75 | (146) ~ (all_89_0_70 = 0)
% 8.65/2.75 | (147) member(all_69_1_66, all_0_6_6) = all_89_0_70
% 8.65/2.75 |
% 8.65/2.75 | Instantiating formula (44) with all_69_1_66, all_0_6_6, 0, all_89_0_70 and discharging atoms member(all_69_1_66, all_0_6_6) = all_89_0_70, member(all_69_1_66, all_0_6_6) = 0, yields:
% 8.65/2.75 | (148) all_89_0_70 = 0
% 8.65/2.75 |
% 8.65/2.75 | Equations (148) can reduce 146 to:
% 8.65/2.75 | (71) $false
% 8.65/2.75 |
% 8.65/2.75 |-The branch is then unsatisfiable
% 8.65/2.75 % SZS output end Proof for theBenchmark
% 8.65/2.75
% 8.65/2.75 2209ms
%------------------------------------------------------------------------------