TSTP Solution File: SEU125+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU125+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 08:46:45 EDT 2022
% Result : Theorem 6.68s 2.29s
% Output : Proof 8.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU125+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 00:46:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.59 ____ _
% 0.55/0.59 ___ / __ \_____(_)___ ________ __________
% 0.55/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.59
% 0.55/0.59 A Theorem Prover for First-Order Logic
% 0.55/0.60 (ePrincess v.1.0)
% 0.55/0.60
% 0.55/0.60 (c) Philipp Rümmer, 2009-2015
% 0.55/0.60 (c) Peter Backeman, 2014-2015
% 0.55/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.60 Bug reports to peter@backeman.se
% 0.55/0.60
% 0.55/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.60
% 0.55/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.59/0.96 Prover 0: Preprocessing ...
% 2.24/1.19 Prover 0: Warning: ignoring some quantifiers
% 2.34/1.22 Prover 0: Constructing countermodel ...
% 4.32/1.70 Prover 0: gave up
% 4.32/1.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.32/1.73 Prover 1: Preprocessing ...
% 4.90/1.83 Prover 1: Warning: ignoring some quantifiers
% 4.90/1.84 Prover 1: Constructing countermodel ...
% 6.22/2.12 Prover 1: gave up
% 6.22/2.12 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.22/2.14 Prover 2: Preprocessing ...
% 6.68/2.23 Prover 2: Warning: ignoring some quantifiers
% 6.68/2.24 Prover 2: Constructing countermodel ...
% 6.68/2.29 Prover 2: proved (173ms)
% 6.68/2.29
% 6.68/2.29 No countermodel exists, formula is valid
% 6.68/2.29 % SZS status Theorem for theBenchmark
% 6.68/2.29
% 6.68/2.29 Generating proof ... Warning: ignoring some quantifiers
% 7.95/2.57 found it (size 32)
% 7.95/2.57
% 7.95/2.57 % SZS output start Proof for theBenchmark
% 7.95/2.58 Assumed formulas after preprocessing and simplification:
% 7.95/2.58 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & ~ (v4 = 0) & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & subset(v3, v1) = v4 & subset(v2, v1) = 0 & subset(v0, v1) = 0 & set_union2(v0, v2) = v3 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v10) = v12) | ? [v13] : (( ~ (v13 = 0) & in(v11, v9) = v13) | ( ~ (v13 = 0) & in(v11, v8) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v10) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & in(v11, v9) = v14 & in(v11, v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v9) = v12) | ? [v13] : ((v13 = 0 & in(v11, v8) = 0) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ((v13 = 0 & in(v11, v9) = 0) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v9) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & in(v11, v8) = 0) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & in(v11, v9) = 0) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v9) = v12) | ? [v13] : ((v13 = 0 & in(v11, v10) = 0) | ( ~ (v13 = 0) & ~ (v12 = 0) & in(v11, v8) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ((v13 = 0 & in(v11, v10) = 0) | ( ~ (v13 = 0) & ~ (v12 = 0) & in(v11, v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v9, v10) = 0) | ~ (subset(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v8, v10) = v11) | ~ (subset(v8, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v8, v9) = 0) | ~ (in(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v10, v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (disjoint(v11, v10) = v9) | ~ (disjoint(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_intersection2(v11, v10) = v9) | ~ (set_intersection2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_union2(v11, v10) = v9) | ~ (set_union2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (in(v11, v10) = v9) | ~ (in(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & disjoint(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v10) = 0) | (in(v11, v9) = 0 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v9) = 0) | ? [v12] : ((v12 = 0 & in(v11, v10) = 0) | ( ~ (v12 = 0) & in(v11, v8) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v8) = 0) | ? [v12] : ((v12 = 0 & in(v11, v10) = 0) | ( ~ (v12 = 0) & in(v11, v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v10) = 0) | ? [v12] : ((v12 = 0 & in(v11, v9) = 0) | (v12 = 0 & in(v11, v8) = 0))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_intersection2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & v14 = 0 & in(v12, v10) = 0 & in(v12, v9) = 0) | (v13 = 0 & in(v12, v8) = 0)) & (( ~ (v15 = 0) & in(v12, v10) = v15) | ( ~ (v14 = 0) & in(v12, v9) = v14) | ( ~ (v13 = 0) & in(v12, v8) = v13)))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_union2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & in(v12, v10) = 0) | (v14 = 0 & in(v12, v9) = 0) | (v13 = 0 & in(v12, v8) = 0)) & (( ~ (v15 = 0) & ~ (v14 = 0) & in(v12, v10) = v15 & in(v12, v9) = v14) | ( ~ (v13 = 0) & in(v12, v8) = v13)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & disjoint(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & disjoint(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : ? [v12] : (set_intersection2(v8, v9) = v11 & in(v12, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : ( ~ (v11 = empty_set) & set_intersection2(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : (in(v11, v9) = 0 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (empty(v10) = v9) | ~ (empty(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v8, v9) = 0) | ~ (in(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v8, v9) = 0) | ~ (in(v10, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v9, v10) = 0) | ~ (subset(v8, v9) = 0) | subset(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (in(v10, v8) = 0) | in(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v9, v8) = v10) | set_intersection2(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | set_intersection2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & in(v11, v10) = 0) | (v11 = 0 & disjoint(v8, v9) = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | set_union2(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | ? [v11] : ((v11 = 0 & empty(v8) = 0) | ( ~ (v11 = 0) & empty(v10) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | subset(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | set_union2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ? [v11] : ((v11 = 0 & empty(v8) = 0) | ( ~ (v11 = 0) & empty(v10) = v11))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (empty(v9) = 0) | ~ (empty(v8) = 0)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (subset(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & subset(v8, v9) = v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (subset(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & subset(v9, v8) = v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_intersection2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(empty_set, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | disjoint(v9, v8) = 0) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | set_intersection2(v8, v9) = empty_set) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | ? [v10] : (set_intersection2(v8, v9) = v10 & ! [v11] : ~ (in(v11, v10) = 0))) & ! [v8] : ! [v9] : ( ~ (set_intersection2(v8, v9) = empty_set) | disjoint(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (in(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & empty(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) & ! [v8] : (v8 = empty_set | ~ (empty(v8) = 0)) & ! [v8] : (v8 = empty_set | ~ (subset(v8, empty_set) = 0)) & ! [v8] : ~ (in(v8, empty_set) = 0) & ? [v8] : ? [v9] : ? [v10] : disjoint(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : subset(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : set_intersection2(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : set_union2(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : in(v9, v8) = v10 & ? [v8] : ? [v9] : empty(v8) = v9 & ? [v8] : (v8 = empty_set | ? [v9] : in(v9, v8) = 0))
% 8.38/2.62 | 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, all_0_7_7 yields:
% 8.38/2.62 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & subset(all_0_4_4, all_0_6_6) = all_0_3_3 & subset(all_0_5_5, all_0_6_6) = 0 & subset(all_0_7_7, all_0_6_6) = 0 & set_union2(all_0_7_7, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : ~ (in(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 8.38/2.64 |
% 8.38/2.64 | Applying alpha-rule on (1) yields:
% 8.38/2.64 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 8.38/2.64 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 8.38/2.64 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 8.38/2.64 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 8.38/2.64 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5)))
% 8.38/2.64 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 8.38/2.64 | (8) empty(all_0_2_2) = all_0_1_1
% 8.38/2.64 | (9) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0)
% 8.38/2.64 | (10) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 8.38/2.64 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5)))
% 8.38/2.64 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3))
% 8.38/2.64 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5)))
% 8.38/2.64 | (14) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 8.38/2.64 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 8.38/2.64 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 8.38/2.64 | (17) subset(all_0_4_4, all_0_6_6) = all_0_3_3
% 8.38/2.64 | (18) subset(all_0_7_7, all_0_6_6) = 0
% 8.38/2.64 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 8.38/2.65 | (20) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 8.38/2.65 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4)))
% 8.38/2.65 | (22) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 8.38/2.65 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 8.38/2.65 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 8.38/2.65 | (25) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 8.38/2.65 | (26) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 8.38/2.65 | (27) ? [v0] : ? [v1] : empty(v0) = v1
% 8.38/2.65 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 8.38/2.65 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 8.38/2.65 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 8.38/2.65 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 8.38/2.65 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 8.38/2.65 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 8.38/2.65 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 8.38/2.65 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)))
% 8.38/2.65 | (36) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 8.38/2.65 | (37) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5))))
% 8.38/2.65 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 8.38/2.65 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 8.38/2.65 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 8.38/2.65 | (41) ~ (all_0_3_3 = 0)
% 8.38/2.65 | (42) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 8.38/2.65 | (43) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 8.38/2.65 | (44) ~ (all_0_1_1 = 0)
% 8.38/2.65 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0)
% 8.38/2.65 | (46) subset(all_0_5_5, all_0_6_6) = 0
% 8.38/2.65 | (47) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2
% 8.38/2.65 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 8.38/2.65 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4)))
% 8.38/2.65 | (50) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2
% 8.38/2.65 | (51) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 8.38/2.65 | (52) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 8.38/2.65 | (53) set_union2(all_0_7_7, all_0_5_5) = all_0_4_4
% 8.38/2.65 | (54) empty(all_0_0_0) = 0
% 8.38/2.65 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 8.38/2.65 | (56) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 8.38/2.66 | (57) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 8.38/2.66 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 8.38/2.66 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5))
% 8.38/2.66 | (60) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 8.38/2.66 | (61) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 8.38/2.66 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 8.38/2.66 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 8.38/2.66 | (64) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 8.38/2.66 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 8.38/2.66 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0)
% 8.38/2.66 | (67) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 8.38/2.66 | (68) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 8.38/2.66 | (69) empty(empty_set) = 0
% 8.38/2.66 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 8.38/2.66 | (71) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 8.38/2.66 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 8.38/2.66 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 8.38/2.66 | (74) ! [v0] : ~ (in(v0, empty_set) = 0)
% 8.38/2.66 | (75) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5))))
% 8.38/2.66 | (76) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 8.38/2.66 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 8.38/2.66 |
% 8.38/2.66 | Instantiating formula (67) with all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_6_6) = all_0_3_3, yields:
% 8.38/2.66 | (78) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1)
% 8.38/2.66 |
% 8.38/2.66 | Instantiating formula (24) with all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms set_union2(all_0_7_7, all_0_5_5) = all_0_4_4, yields:
% 8.38/2.66 | (79) set_union2(all_0_5_5, all_0_7_7) = all_0_4_4
% 8.38/2.66 |
% 8.38/2.66 +-Applying beta-rule and splitting (78), into two cases.
% 8.38/2.66 |-Branch one:
% 8.38/2.66 | (80) all_0_3_3 = 0
% 8.38/2.66 |
% 8.38/2.66 | Equations (80) can reduce 41 to:
% 8.38/2.66 | (81) $false
% 8.38/2.66 |
% 8.38/2.67 |-The branch is then unsatisfiable
% 8.38/2.67 |-Branch two:
% 8.38/2.67 | (41) ~ (all_0_3_3 = 0)
% 8.38/2.67 | (83) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1)
% 8.38/2.67 |
% 8.38/2.67 | Instantiating (83) with all_36_0_30, all_36_1_31 yields:
% 8.38/2.67 | (84) ~ (all_36_0_30 = 0) & in(all_36_1_31, all_0_4_4) = 0 & in(all_36_1_31, all_0_6_6) = all_36_0_30
% 8.38/2.67 |
% 8.38/2.67 | Applying alpha-rule on (84) yields:
% 8.38/2.67 | (85) ~ (all_36_0_30 = 0)
% 8.38/2.67 | (86) in(all_36_1_31, all_0_4_4) = 0
% 8.38/2.67 | (87) in(all_36_1_31, all_0_6_6) = all_36_0_30
% 8.38/2.67 |
% 8.38/2.67 | Instantiating formula (35) with all_36_1_31, all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms set_union2(all_0_5_5, all_0_7_7) = all_0_4_4, in(all_36_1_31, all_0_4_4) = 0, yields:
% 8.38/2.67 | (88) ? [v0] : ((v0 = 0 & in(all_36_1_31, all_0_5_5) = 0) | (v0 = 0 & in(all_36_1_31, all_0_7_7) = 0))
% 8.38/2.67 |
% 8.38/2.67 | Instantiating formula (16) with all_36_0_30, all_36_1_31, all_0_6_6, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_6_6) = 0, in(all_36_1_31, all_0_6_6) = all_36_0_30, yields:
% 8.38/2.67 | (89) all_36_0_30 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_36_1_31, all_0_5_5) = v0)
% 8.38/2.67 |
% 8.38/2.67 | Instantiating formula (16) with all_36_0_30, all_36_1_31, all_0_6_6, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_6_6) = 0, in(all_36_1_31, all_0_6_6) = all_36_0_30, yields:
% 8.38/2.67 | (90) all_36_0_30 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_36_1_31, all_0_7_7) = v0)
% 8.38/2.67 |
% 8.38/2.67 | Instantiating (88) with all_59_0_37 yields:
% 8.38/2.67 | (91) (all_59_0_37 = 0 & in(all_36_1_31, all_0_5_5) = 0) | (all_59_0_37 = 0 & in(all_36_1_31, all_0_7_7) = 0)
% 8.38/2.67 |
% 8.38/2.67 +-Applying beta-rule and splitting (90), into two cases.
% 8.38/2.67 |-Branch one:
% 8.38/2.67 | (92) all_36_0_30 = 0
% 8.38/2.67 |
% 8.38/2.67 | Equations (92) can reduce 85 to:
% 8.38/2.67 | (81) $false
% 8.38/2.67 |
% 8.38/2.67 |-The branch is then unsatisfiable
% 8.38/2.67 |-Branch two:
% 8.38/2.67 | (85) ~ (all_36_0_30 = 0)
% 8.38/2.67 | (95) ? [v0] : ( ~ (v0 = 0) & in(all_36_1_31, all_0_7_7) = v0)
% 8.38/2.67 |
% 8.38/2.67 | Instantiating (95) with all_75_0_43 yields:
% 8.38/2.67 | (96) ~ (all_75_0_43 = 0) & in(all_36_1_31, all_0_7_7) = all_75_0_43
% 8.38/2.67 |
% 8.38/2.67 | Applying alpha-rule on (96) yields:
% 8.38/2.67 | (97) ~ (all_75_0_43 = 0)
% 8.38/2.67 | (98) in(all_36_1_31, all_0_7_7) = all_75_0_43
% 8.38/2.67 |
% 8.38/2.67 +-Applying beta-rule and splitting (89), into two cases.
% 8.38/2.67 |-Branch one:
% 8.38/2.67 | (92) all_36_0_30 = 0
% 8.38/2.67 |
% 8.38/2.67 | Equations (92) can reduce 85 to:
% 8.38/2.67 | (81) $false
% 8.38/2.67 |
% 8.38/2.67 |-The branch is then unsatisfiable
% 8.38/2.67 |-Branch two:
% 8.38/2.67 | (85) ~ (all_36_0_30 = 0)
% 8.38/2.67 | (102) ? [v0] : ( ~ (v0 = 0) & in(all_36_1_31, all_0_5_5) = v0)
% 8.38/2.67 |
% 8.38/2.67 | Instantiating (102) with all_80_0_44 yields:
% 8.38/2.67 | (103) ~ (all_80_0_44 = 0) & in(all_36_1_31, all_0_5_5) = all_80_0_44
% 8.38/2.67 |
% 8.38/2.67 | Applying alpha-rule on (103) yields:
% 8.38/2.67 | (104) ~ (all_80_0_44 = 0)
% 8.38/2.67 | (105) in(all_36_1_31, all_0_5_5) = all_80_0_44
% 8.38/2.67 |
% 8.38/2.67 +-Applying beta-rule and splitting (91), into two cases.
% 8.38/2.67 |-Branch one:
% 8.38/2.67 | (106) all_59_0_37 = 0 & in(all_36_1_31, all_0_5_5) = 0
% 8.38/2.67 |
% 8.38/2.67 | Applying alpha-rule on (106) yields:
% 8.38/2.67 | (107) all_59_0_37 = 0
% 8.38/2.67 | (108) in(all_36_1_31, all_0_5_5) = 0
% 8.38/2.67 |
% 8.38/2.67 | Instantiating formula (32) with all_36_1_31, all_0_5_5, 0, all_80_0_44 and discharging atoms in(all_36_1_31, all_0_5_5) = all_80_0_44, in(all_36_1_31, all_0_5_5) = 0, yields:
% 8.38/2.67 | (109) all_80_0_44 = 0
% 8.38/2.67 |
% 8.38/2.67 | Equations (109) can reduce 104 to:
% 8.38/2.67 | (81) $false
% 8.38/2.67 |
% 8.38/2.67 |-The branch is then unsatisfiable
% 8.38/2.67 |-Branch two:
% 8.38/2.67 | (111) all_59_0_37 = 0 & in(all_36_1_31, all_0_7_7) = 0
% 8.38/2.67 |
% 8.38/2.67 | Applying alpha-rule on (111) yields:
% 8.38/2.67 | (107) all_59_0_37 = 0
% 8.38/2.68 | (113) in(all_36_1_31, all_0_7_7) = 0
% 8.38/2.68 |
% 8.38/2.68 | Instantiating formula (32) with all_36_1_31, all_0_7_7, 0, all_75_0_43 and discharging atoms in(all_36_1_31, all_0_7_7) = all_75_0_43, in(all_36_1_31, all_0_7_7) = 0, yields:
% 8.38/2.68 | (114) all_75_0_43 = 0
% 8.38/2.68 |
% 8.38/2.68 | Equations (114) can reduce 97 to:
% 8.38/2.68 | (81) $false
% 8.38/2.68 |
% 8.38/2.68 |-The branch is then unsatisfiable
% 8.38/2.68 % SZS output end Proof for theBenchmark
% 8.38/2.68
% 8.38/2.68 2069ms
%------------------------------------------------------------------------------