TSTP Solution File: SET014+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET014+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:16:02 EDT 2022
% Result : Theorem 4.92s 1.89s
% Output : Proof 7.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET014+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 10:21:09 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.63/0.60 ____ _
% 0.63/0.60 ___ / __ \_____(_)___ ________ __________
% 0.63/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.60
% 0.63/0.60 A Theorem Prover for First-Order Logic
% 0.63/0.60 (ePrincess v.1.0)
% 0.63/0.60
% 0.63/0.60 (c) Philipp Rümmer, 2009-2015
% 0.63/0.60 (c) Peter Backeman, 2014-2015
% 0.63/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.60 Bug reports to peter@backeman.se
% 0.63/0.60
% 0.63/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.60
% 0.63/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.95 Prover 0: Preprocessing ...
% 2.11/1.14 Prover 0: Warning: ignoring some quantifiers
% 2.11/1.17 Prover 0: Constructing countermodel ...
% 2.65/1.34 Prover 0: gave up
% 2.65/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.65/1.36 Prover 1: Preprocessing ...
% 3.27/1.47 Prover 1: Constructing countermodel ...
% 3.63/1.56 Prover 1: gave up
% 3.63/1.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.63/1.58 Prover 2: Preprocessing ...
% 4.28/1.67 Prover 2: Warning: ignoring some quantifiers
% 4.35/1.68 Prover 2: Constructing countermodel ...
% 4.92/1.89 Prover 2: proved (329ms)
% 4.92/1.89
% 4.92/1.89 No countermodel exists, formula is valid
% 4.92/1.89 % SZS status Theorem for theBenchmark
% 4.92/1.89
% 4.92/1.89 Generating proof ... Warning: ignoring some quantifiers
% 6.59/2.25 found it (size 84)
% 6.59/2.25
% 6.59/2.25 % SZS output start Proof for theBenchmark
% 6.59/2.25 Assumed formulas after preprocessing and simplification:
% 6.59/2.25 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (union(v1, v2) = v5 & subset(v5, v0) = v6 & ! [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 & (( ~ (v4 = 0) & subset(v2, v0) = v4) | ( ~ (v3 = 0) & subset(v1, v0) = v3))) | (v4 = 0 & v3 = 0 & ~ (v6 = 0) & subset(v2, v0) = 0 & subset(v1, v0) = 0)))
% 7.11/2.30 | 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:
% 7.11/2.30 | (1) union(all_0_5_5, all_0_4_4) = all_0_1_1 & subset(all_0_1_1, all_0_6_6) = 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] : ((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_2_2 = 0) & subset(all_0_4_4, all_0_6_6) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & subset(all_0_5_5, all_0_6_6) = all_0_3_3))) | (all_0_2_2 = 0 & all_0_3_3 = 0 & ~ (all_0_0_0 = 0) & subset(all_0_4_4, all_0_6_6) = 0 & subset(all_0_5_5, all_0_6_6) = 0))
% 7.20/2.31 |
% 7.20/2.31 | Applying alpha-rule on (1) yields:
% 7.20/2.31 | (2) ! [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)))
% 7.20/2.32 | (3) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 7.21/2.32 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 7.21/2.32 | (5) ! [v0] : ~ (member(v0, empty_set) = 0)
% 7.21/2.32 | (6) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 7.21/2.32 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 7.21/2.32 | (8) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 7.21/2.32 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 7.21/2.32 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 7.21/2.32 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 7.21/2.32 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 7.21/2.32 | (13) union(all_0_5_5, all_0_4_4) = all_0_1_1
% 7.21/2.32 | (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))
% 7.21/2.32 | (15) ? [v0] : ? [v1] : singleton(v0) = v1
% 7.21/2.32 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 7.21/2.32 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 7.21/2.32 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 7.21/2.32 | (19) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 7.21/2.32 | (20) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 7.21/2.32 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 7.21/2.32 | (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))
% 7.21/2.32 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 7.21/2.32 | (24) ? [v0] : ? [v1] : sum(v0) = v1
% 7.21/2.32 | (25) ! [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)))
% 7.21/2.32 | (26) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 7.21/2.32 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 7.21/2.33 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 7.21/2.33 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 7.21/2.33 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 7.21/2.33 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 7.21/2.33 | (32) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 7.21/2.33 | (33) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 7.21/2.33 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 7.21/2.33 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 7.21/2.33 | (36) ! [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)))
% 7.21/2.33 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 7.21/2.33 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 7.21/2.33 | (39) ? [v0] : ? [v1] : power_set(v0) = v1
% 7.21/2.33 | (40) (all_0_0_0 = 0 & (( ~ (all_0_2_2 = 0) & subset(all_0_4_4, all_0_6_6) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & subset(all_0_5_5, all_0_6_6) = all_0_3_3))) | (all_0_2_2 = 0 & all_0_3_3 = 0 & ~ (all_0_0_0 = 0) & subset(all_0_4_4, all_0_6_6) = 0 & subset(all_0_5_5, all_0_6_6) = 0)
% 7.21/2.33 | (41) subset(all_0_1_1, all_0_6_6) = all_0_0_0
% 7.21/2.33 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 7.21/2.33 | (43) ! [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))
% 7.21/2.33 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 7.21/2.33 | (45) ? [v0] : ? [v1] : product(v0) = v1
% 7.21/2.33 | (46) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 7.21/2.33 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 7.21/2.33 | (48) ! [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))
% 7.21/2.33 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 7.21/2.33 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 7.21/2.33 | (51) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 7.21/2.33 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 7.21/2.34 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 7.21/2.34 | (54) ! [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))
% 7.21/2.34 | (55) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 7.21/2.34 | (56) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 7.21/2.34 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 7.21/2.34 |
% 7.21/2.34 | Instantiating formula (28) with all_0_0_0, all_0_6_6, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_6_6) = all_0_0_0, yields:
% 7.21/2.34 | (58) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_6_6) = v0 & member(all_0_1_1, v0) = v1)
% 7.21/2.34 |
% 7.21/2.34 | Instantiating formula (23) with all_0_0_0, all_0_6_6, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_6_6) = all_0_0_0, yields:
% 7.21/2.34 | (59) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_6_6) = v1)
% 7.21/2.34 |
% 7.21/2.34 +-Applying beta-rule and splitting (40), into two cases.
% 7.21/2.34 |-Branch one:
% 7.21/2.34 | (60) all_0_0_0 = 0 & (( ~ (all_0_2_2 = 0) & subset(all_0_4_4, all_0_6_6) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & subset(all_0_5_5, all_0_6_6) = all_0_3_3))
% 7.21/2.34 |
% 7.21/2.34 | Applying alpha-rule on (60) yields:
% 7.21/2.34 | (61) all_0_0_0 = 0
% 7.21/2.34 | (62) ( ~ (all_0_2_2 = 0) & subset(all_0_4_4, all_0_6_6) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & subset(all_0_5_5, all_0_6_6) = all_0_3_3)
% 7.21/2.34 |
% 7.21/2.34 | From (61) and (41) follows:
% 7.21/2.34 | (63) subset(all_0_1_1, all_0_6_6) = 0
% 7.21/2.34 |
% 7.21/2.34 +-Applying beta-rule and splitting (62), into two cases.
% 7.21/2.34 |-Branch one:
% 7.21/2.34 | (64) ~ (all_0_2_2 = 0) & subset(all_0_4_4, all_0_6_6) = all_0_2_2
% 7.21/2.34 |
% 7.21/2.34 | Applying alpha-rule on (64) yields:
% 7.21/2.34 | (65) ~ (all_0_2_2 = 0)
% 7.21/2.34 | (66) subset(all_0_4_4, all_0_6_6) = all_0_2_2
% 7.21/2.34 |
% 7.21/2.34 | Instantiating formula (23) with all_0_2_2, all_0_6_6, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_6_6) = all_0_2_2, yields:
% 7.21/2.34 | (67) all_0_2_2 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_4_4) = 0 & member(v0, all_0_6_6) = v1)
% 7.21/2.34 |
% 7.21/2.34 +-Applying beta-rule and splitting (67), into two cases.
% 7.21/2.34 |-Branch one:
% 7.21/2.34 | (68) all_0_2_2 = 0
% 7.21/2.34 |
% 7.21/2.34 | Equations (68) can reduce 65 to:
% 7.21/2.34 | (69) $false
% 7.21/2.34 |
% 7.21/2.34 |-The branch is then unsatisfiable
% 7.21/2.34 |-Branch two:
% 7.21/2.34 | (65) ~ (all_0_2_2 = 0)
% 7.21/2.34 | (71) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_4_4) = 0 & member(v0, all_0_6_6) = v1)
% 7.21/2.34 |
% 7.21/2.34 | Instantiating (71) with all_85_0_44, all_85_1_45 yields:
% 7.21/2.34 | (72) ~ (all_85_0_44 = 0) & member(all_85_1_45, all_0_4_4) = 0 & member(all_85_1_45, all_0_6_6) = all_85_0_44
% 7.21/2.34 |
% 7.21/2.34 | Applying alpha-rule on (72) yields:
% 7.21/2.34 | (73) ~ (all_85_0_44 = 0)
% 7.21/2.34 | (74) member(all_85_1_45, all_0_4_4) = 0
% 7.21/2.34 | (75) member(all_85_1_45, all_0_6_6) = all_85_0_44
% 7.21/2.34 |
% 7.21/2.34 | Instantiating formula (49) with all_85_0_44, all_85_1_45, all_0_6_6, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_6_6) = 0, member(all_85_1_45, all_0_6_6) = all_85_0_44, yields:
% 7.21/2.34 | (76) all_85_0_44 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_85_1_45, all_0_1_1) = v0)
% 7.21/2.34 |
% 7.21/2.34 +-Applying beta-rule and splitting (76), into two cases.
% 7.21/2.34 |-Branch one:
% 7.21/2.34 | (77) all_85_0_44 = 0
% 7.21/2.34 |
% 7.21/2.35 | Equations (77) can reduce 73 to:
% 7.21/2.35 | (69) $false
% 7.21/2.35 |
% 7.21/2.35 |-The branch is then unsatisfiable
% 7.21/2.35 |-Branch two:
% 7.21/2.35 | (73) ~ (all_85_0_44 = 0)
% 7.21/2.35 | (80) ? [v0] : ( ~ (v0 = 0) & member(all_85_1_45, all_0_1_1) = v0)
% 7.21/2.35 |
% 7.21/2.35 | Instantiating (80) with all_111_0_48 yields:
% 7.21/2.35 | (81) ~ (all_111_0_48 = 0) & member(all_85_1_45, all_0_1_1) = all_111_0_48
% 7.21/2.35 |
% 7.21/2.35 | Applying alpha-rule on (81) yields:
% 7.21/2.35 | (82) ~ (all_111_0_48 = 0)
% 7.21/2.35 | (83) member(all_85_1_45, all_0_1_1) = all_111_0_48
% 7.21/2.35 |
% 7.21/2.35 | Instantiating formula (14) with all_111_0_48, all_0_1_1, all_0_4_4, all_0_5_5, all_85_1_45 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_1_1, member(all_85_1_45, all_0_1_1) = all_111_0_48, yields:
% 7.21/2.35 | (84) all_111_0_48 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_85_1_45, all_0_4_4) = v1 & member(all_85_1_45, all_0_5_5) = v0)
% 7.21/2.35 |
% 7.21/2.35 +-Applying beta-rule and splitting (84), into two cases.
% 7.21/2.35 |-Branch one:
% 7.21/2.35 | (85) all_111_0_48 = 0
% 7.21/2.35 |
% 7.21/2.35 | Equations (85) can reduce 82 to:
% 7.21/2.35 | (69) $false
% 7.21/2.35 |
% 7.21/2.35 |-The branch is then unsatisfiable
% 7.21/2.35 |-Branch two:
% 7.21/2.35 | (82) ~ (all_111_0_48 = 0)
% 7.21/2.35 | (88) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_85_1_45, all_0_4_4) = v1 & member(all_85_1_45, all_0_5_5) = v0)
% 7.21/2.35 |
% 7.21/2.35 | Instantiating (88) with all_133_0_51, all_133_1_52 yields:
% 7.21/2.35 | (89) ~ (all_133_0_51 = 0) & ~ (all_133_1_52 = 0) & member(all_85_1_45, all_0_4_4) = all_133_0_51 & member(all_85_1_45, all_0_5_5) = all_133_1_52
% 7.21/2.35 |
% 7.21/2.35 | Applying alpha-rule on (89) yields:
% 7.21/2.35 | (90) ~ (all_133_0_51 = 0)
% 7.21/2.35 | (91) ~ (all_133_1_52 = 0)
% 7.21/2.35 | (92) member(all_85_1_45, all_0_4_4) = all_133_0_51
% 7.21/2.35 | (93) member(all_85_1_45, all_0_5_5) = all_133_1_52
% 7.21/2.35 |
% 7.21/2.35 | Instantiating formula (18) with all_85_1_45, all_0_4_4, all_133_0_51, 0 and discharging atoms member(all_85_1_45, all_0_4_4) = all_133_0_51, member(all_85_1_45, all_0_4_4) = 0, yields:
% 7.21/2.35 | (94) all_133_0_51 = 0
% 7.21/2.35 |
% 7.21/2.35 | Equations (94) can reduce 90 to:
% 7.21/2.35 | (69) $false
% 7.21/2.35 |
% 7.21/2.35 |-The branch is then unsatisfiable
% 7.21/2.35 |-Branch two:
% 7.21/2.35 | (96) ~ (all_0_3_3 = 0) & subset(all_0_5_5, all_0_6_6) = all_0_3_3
% 7.21/2.35 |
% 7.21/2.35 | Applying alpha-rule on (96) yields:
% 7.21/2.35 | (97) ~ (all_0_3_3 = 0)
% 7.21/2.35 | (98) subset(all_0_5_5, all_0_6_6) = all_0_3_3
% 7.21/2.35 |
% 7.21/2.35 | Instantiating formula (23) with all_0_3_3, all_0_6_6, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 7.21/2.35 | (99) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_5_5) = 0 & member(v0, all_0_6_6) = v1)
% 7.21/2.35 |
% 7.21/2.35 +-Applying beta-rule and splitting (99), into two cases.
% 7.21/2.35 |-Branch one:
% 7.21/2.35 | (100) all_0_3_3 = 0
% 7.21/2.35 |
% 7.21/2.35 | Equations (100) can reduce 97 to:
% 7.21/2.35 | (69) $false
% 7.21/2.35 |
% 7.21/2.35 |-The branch is then unsatisfiable
% 7.21/2.35 |-Branch two:
% 7.21/2.35 | (97) ~ (all_0_3_3 = 0)
% 7.21/2.35 | (103) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_5_5) = 0 & member(v0, all_0_6_6) = v1)
% 7.21/2.35 |
% 7.21/2.35 | Instantiating (103) with all_85_0_55, all_85_1_56 yields:
% 7.21/2.35 | (104) ~ (all_85_0_55 = 0) & member(all_85_1_56, all_0_5_5) = 0 & member(all_85_1_56, all_0_6_6) = all_85_0_55
% 7.21/2.35 |
% 7.21/2.35 | Applying alpha-rule on (104) yields:
% 7.21/2.35 | (105) ~ (all_85_0_55 = 0)
% 7.21/2.35 | (106) member(all_85_1_56, all_0_5_5) = 0
% 7.21/2.35 | (107) member(all_85_1_56, all_0_6_6) = all_85_0_55
% 7.21/2.35 |
% 7.21/2.35 | Instantiating formula (49) with all_85_0_55, all_85_1_56, all_0_6_6, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_6_6) = 0, member(all_85_1_56, all_0_6_6) = all_85_0_55, yields:
% 7.21/2.35 | (108) all_85_0_55 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_85_1_56, all_0_1_1) = v0)
% 7.21/2.36 |
% 7.21/2.36 +-Applying beta-rule and splitting (108), into two cases.
% 7.21/2.36 |-Branch one:
% 7.21/2.36 | (109) all_85_0_55 = 0
% 7.21/2.36 |
% 7.21/2.36 | Equations (109) can reduce 105 to:
% 7.21/2.36 | (69) $false
% 7.21/2.36 |
% 7.21/2.36 |-The branch is then unsatisfiable
% 7.21/2.36 |-Branch two:
% 7.21/2.36 | (105) ~ (all_85_0_55 = 0)
% 7.21/2.36 | (112) ? [v0] : ( ~ (v0 = 0) & member(all_85_1_56, all_0_1_1) = v0)
% 7.21/2.36 |
% 7.21/2.36 | Instantiating (112) with all_111_0_59 yields:
% 7.21/2.36 | (113) ~ (all_111_0_59 = 0) & member(all_85_1_56, all_0_1_1) = all_111_0_59
% 7.21/2.36 |
% 7.21/2.36 | Applying alpha-rule on (113) yields:
% 7.21/2.36 | (114) ~ (all_111_0_59 = 0)
% 7.21/2.36 | (115) member(all_85_1_56, all_0_1_1) = all_111_0_59
% 7.21/2.36 |
% 7.21/2.36 | Instantiating formula (14) with all_111_0_59, all_0_1_1, all_0_4_4, all_0_5_5, all_85_1_56 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_1_1, member(all_85_1_56, all_0_1_1) = all_111_0_59, yields:
% 7.21/2.36 | (116) all_111_0_59 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_85_1_56, all_0_4_4) = v1 & member(all_85_1_56, all_0_5_5) = v0)
% 7.21/2.36 |
% 7.21/2.36 +-Applying beta-rule and splitting (116), into two cases.
% 7.21/2.36 |-Branch one:
% 7.21/2.36 | (117) all_111_0_59 = 0
% 7.21/2.36 |
% 7.21/2.36 | Equations (117) can reduce 114 to:
% 7.21/2.36 | (69) $false
% 7.21/2.36 |
% 7.21/2.36 |-The branch is then unsatisfiable
% 7.21/2.36 |-Branch two:
% 7.21/2.36 | (114) ~ (all_111_0_59 = 0)
% 7.21/2.36 | (120) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_85_1_56, all_0_4_4) = v1 & member(all_85_1_56, all_0_5_5) = v0)
% 7.21/2.36 |
% 7.21/2.36 | Instantiating (120) with all_133_0_62, all_133_1_63 yields:
% 7.21/2.36 | (121) ~ (all_133_0_62 = 0) & ~ (all_133_1_63 = 0) & member(all_85_1_56, all_0_4_4) = all_133_0_62 & member(all_85_1_56, all_0_5_5) = all_133_1_63
% 7.21/2.36 |
% 7.21/2.36 | Applying alpha-rule on (121) yields:
% 7.21/2.36 | (122) ~ (all_133_0_62 = 0)
% 7.21/2.36 | (123) ~ (all_133_1_63 = 0)
% 7.21/2.36 | (124) member(all_85_1_56, all_0_4_4) = all_133_0_62
% 7.21/2.36 | (125) member(all_85_1_56, all_0_5_5) = all_133_1_63
% 7.21/2.36 |
% 7.21/2.36 | Instantiating formula (18) with all_85_1_56, all_0_5_5, all_133_1_63, 0 and discharging atoms member(all_85_1_56, all_0_5_5) = all_133_1_63, member(all_85_1_56, all_0_5_5) = 0, yields:
% 7.21/2.36 | (126) all_133_1_63 = 0
% 7.21/2.36 |
% 7.21/2.36 | Equations (126) can reduce 123 to:
% 7.21/2.36 | (69) $false
% 7.21/2.36 |
% 7.21/2.36 |-The branch is then unsatisfiable
% 7.21/2.36 |-Branch two:
% 7.21/2.36 | (128) all_0_2_2 = 0 & all_0_3_3 = 0 & ~ (all_0_0_0 = 0) & subset(all_0_4_4, all_0_6_6) = 0 & subset(all_0_5_5, all_0_6_6) = 0
% 7.21/2.36 |
% 7.21/2.36 | Applying alpha-rule on (128) yields:
% 7.21/2.36 | (129) subset(all_0_4_4, all_0_6_6) = 0
% 7.21/2.36 | (100) all_0_3_3 = 0
% 7.21/2.36 | (131) ~ (all_0_0_0 = 0)
% 7.21/2.36 | (132) subset(all_0_5_5, all_0_6_6) = 0
% 7.21/2.36 | (68) all_0_2_2 = 0
% 7.21/2.36 |
% 7.21/2.36 +-Applying beta-rule and splitting (58), into two cases.
% 7.21/2.36 |-Branch one:
% 7.21/2.36 | (61) all_0_0_0 = 0
% 7.21/2.36 |
% 7.21/2.36 | Equations (61) can reduce 131 to:
% 7.21/2.36 | (69) $false
% 7.21/2.36 |
% 7.21/2.36 |-The branch is then unsatisfiable
% 7.21/2.36 |-Branch two:
% 7.21/2.36 | (131) ~ (all_0_0_0 = 0)
% 7.21/2.36 | (137) ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_6_6) = v0 & member(all_0_1_1, v0) = v1)
% 7.21/2.36 |
% 7.21/2.36 +-Applying beta-rule and splitting (59), into two cases.
% 7.21/2.36 |-Branch one:
% 7.21/2.36 | (61) all_0_0_0 = 0
% 7.21/2.36 |
% 7.21/2.36 | Equations (61) can reduce 131 to:
% 7.21/2.36 | (69) $false
% 7.21/2.36 |
% 7.21/2.36 |-The branch is then unsatisfiable
% 7.21/2.36 |-Branch two:
% 7.21/2.36 | (131) ~ (all_0_0_0 = 0)
% 7.21/2.36 | (141) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_6_6) = v1)
% 7.21/2.36 |
% 7.21/2.36 | Instantiating (141) with all_50_0_66, all_50_1_67 yields:
% 7.21/2.36 | (142) ~ (all_50_0_66 = 0) & member(all_50_1_67, all_0_1_1) = 0 & member(all_50_1_67, all_0_6_6) = all_50_0_66
% 7.21/2.36 |
% 7.21/2.36 | Applying alpha-rule on (142) yields:
% 7.21/2.36 | (143) ~ (all_50_0_66 = 0)
% 7.21/2.36 | (144) member(all_50_1_67, all_0_1_1) = 0
% 7.21/2.36 | (145) member(all_50_1_67, all_0_6_6) = all_50_0_66
% 7.21/2.36 |
% 7.21/2.36 | Instantiating formula (36) with all_0_1_1, all_0_4_4, all_0_5_5, all_50_1_67 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_1_1, member(all_50_1_67, all_0_1_1) = 0, yields:
% 7.21/2.36 | (146) ? [v0] : ((v0 = 0 & member(all_50_1_67, all_0_4_4) = 0) | (v0 = 0 & member(all_50_1_67, all_0_5_5) = 0))
% 7.21/2.36 |
% 7.21/2.36 | Instantiating formula (49) with all_50_0_66, all_50_1_67, all_0_6_6, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_6_6) = 0, member(all_50_1_67, all_0_6_6) = all_50_0_66, yields:
% 7.21/2.36 | (147) all_50_0_66 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_50_1_67, all_0_4_4) = v0)
% 7.21/2.36 |
% 7.21/2.36 | Instantiating formula (49) with all_50_0_66, all_50_1_67, all_0_6_6, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_6_6) = 0, member(all_50_1_67, all_0_6_6) = all_50_0_66, yields:
% 7.21/2.36 | (148) all_50_0_66 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_50_1_67, all_0_5_5) = v0)
% 7.21/2.36 |
% 7.21/2.36 | Instantiating (146) with all_57_0_68 yields:
% 7.21/2.36 | (149) (all_57_0_68 = 0 & member(all_50_1_67, all_0_4_4) = 0) | (all_57_0_68 = 0 & member(all_50_1_67, all_0_5_5) = 0)
% 7.21/2.36 |
% 7.21/2.36 +-Applying beta-rule and splitting (148), into two cases.
% 7.21/2.36 |-Branch one:
% 7.21/2.36 | (150) all_50_0_66 = 0
% 7.21/2.36 |
% 7.21/2.36 | Equations (150) can reduce 143 to:
% 7.21/2.36 | (69) $false
% 7.21/2.36 |
% 7.21/2.36 |-The branch is then unsatisfiable
% 7.21/2.36 |-Branch two:
% 7.21/2.36 | (143) ~ (all_50_0_66 = 0)
% 7.21/2.36 | (153) ? [v0] : ( ~ (v0 = 0) & member(all_50_1_67, all_0_5_5) = v0)
% 7.21/2.37 |
% 7.21/2.37 | Instantiating (153) with all_74_0_79 yields:
% 7.21/2.37 | (154) ~ (all_74_0_79 = 0) & member(all_50_1_67, all_0_5_5) = all_74_0_79
% 7.21/2.37 |
% 7.21/2.37 | Applying alpha-rule on (154) yields:
% 7.21/2.37 | (155) ~ (all_74_0_79 = 0)
% 7.21/2.37 | (156) member(all_50_1_67, all_0_5_5) = all_74_0_79
% 7.21/2.37 |
% 7.21/2.37 +-Applying beta-rule and splitting (147), into two cases.
% 7.21/2.37 |-Branch one:
% 7.21/2.37 | (150) all_50_0_66 = 0
% 7.21/2.37 |
% 7.21/2.37 | Equations (150) can reduce 143 to:
% 7.21/2.37 | (69) $false
% 7.21/2.37 |
% 7.21/2.37 |-The branch is then unsatisfiable
% 7.21/2.37 |-Branch two:
% 7.21/2.37 | (143) ~ (all_50_0_66 = 0)
% 7.21/2.37 | (160) ? [v0] : ( ~ (v0 = 0) & member(all_50_1_67, all_0_4_4) = v0)
% 7.21/2.37 |
% 7.21/2.37 | Instantiating (160) with all_79_0_80 yields:
% 7.21/2.37 | (161) ~ (all_79_0_80 = 0) & member(all_50_1_67, all_0_4_4) = all_79_0_80
% 7.21/2.37 |
% 7.21/2.37 | Applying alpha-rule on (161) yields:
% 7.21/2.37 | (162) ~ (all_79_0_80 = 0)
% 7.21/2.37 | (163) member(all_50_1_67, all_0_4_4) = all_79_0_80
% 7.21/2.37 |
% 7.21/2.37 +-Applying beta-rule and splitting (149), into two cases.
% 7.21/2.37 |-Branch one:
% 7.21/2.37 | (164) all_57_0_68 = 0 & member(all_50_1_67, all_0_4_4) = 0
% 7.21/2.37 |
% 7.21/2.37 | Applying alpha-rule on (164) yields:
% 7.21/2.37 | (165) all_57_0_68 = 0
% 7.21/2.37 | (166) member(all_50_1_67, all_0_4_4) = 0
% 7.21/2.37 |
% 7.21/2.37 | Instantiating formula (18) with all_50_1_67, all_0_4_4, 0, all_79_0_80 and discharging atoms member(all_50_1_67, all_0_4_4) = all_79_0_80, member(all_50_1_67, all_0_4_4) = 0, yields:
% 7.21/2.37 | (167) all_79_0_80 = 0
% 7.21/2.37 |
% 7.21/2.37 | Equations (167) can reduce 162 to:
% 7.21/2.37 | (69) $false
% 7.21/2.37 |
% 7.21/2.37 |-The branch is then unsatisfiable
% 7.21/2.37 |-Branch two:
% 7.21/2.37 | (169) all_57_0_68 = 0 & member(all_50_1_67, all_0_5_5) = 0
% 7.21/2.37 |
% 7.21/2.37 | Applying alpha-rule on (169) yields:
% 7.21/2.37 | (165) all_57_0_68 = 0
% 7.21/2.37 | (171) member(all_50_1_67, all_0_5_5) = 0
% 7.21/2.37 |
% 7.21/2.37 | Instantiating formula (18) with all_50_1_67, all_0_5_5, 0, all_74_0_79 and discharging atoms member(all_50_1_67, all_0_5_5) = all_74_0_79, member(all_50_1_67, all_0_5_5) = 0, yields:
% 7.21/2.37 | (172) all_74_0_79 = 0
% 7.21/2.37 |
% 7.21/2.37 | Equations (172) can reduce 155 to:
% 7.21/2.37 | (69) $false
% 7.21/2.37 |
% 7.21/2.37 |-The branch is then unsatisfiable
% 7.21/2.37 % SZS output end Proof for theBenchmark
% 7.21/2.37
% 7.21/2.37 1754ms
%------------------------------------------------------------------------------