TSTP Solution File: SEU141+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU141+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n016.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 08:46:54 EDT 2022
% Result : Theorem 107.95s 67.62s
% Output : Proof 134.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SEU141+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jun 19 04:26:23 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.49/0.62 ____ _
% 0.49/0.62 ___ / __ \_____(_)___ ________ __________
% 0.49/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.62
% 0.49/0.62 A Theorem Prover for First-Order Logic
% 0.49/0.62 (ePrincess v.1.0)
% 0.49/0.62
% 0.49/0.62 (c) Philipp Rümmer, 2009-2015
% 0.49/0.62 (c) Peter Backeman, 2014-2015
% 0.49/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.62 Bug reports to peter@backeman.se
% 0.49/0.62
% 0.49/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.62
% 0.49/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.77/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.57/0.99 Prover 0: Preprocessing ...
% 2.23/1.26 Prover 0: Warning: ignoring some quantifiers
% 2.23/1.28 Prover 0: Constructing countermodel ...
% 2.89/1.46 Prover 0: gave up
% 2.89/1.46 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.99/1.49 Prover 1: Preprocessing ...
% 3.31/1.60 Prover 1: Warning: ignoring some quantifiers
% 3.31/1.61 Prover 1: Constructing countermodel ...
% 4.64/1.85 Prover 1: gave up
% 4.64/1.85 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.64/1.86 Prover 2: Preprocessing ...
% 4.99/1.96 Prover 2: Warning: ignoring some quantifiers
% 4.99/1.97 Prover 2: Constructing countermodel ...
% 5.76/2.12 Prover 2: gave up
% 5.76/2.12 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.97/2.14 Prover 3: Preprocessing ...
% 5.97/2.16 Prover 3: Warning: ignoring some quantifiers
% 6.15/2.16 Prover 3: Constructing countermodel ...
% 6.15/2.20 Prover 3: gave up
% 6.15/2.20 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 6.15/2.21 Prover 4: Preprocessing ...
% 6.73/2.29 Prover 4: Warning: ignoring some quantifiers
% 6.73/2.30 Prover 4: Constructing countermodel ...
% 11.09/3.38 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 11.32/3.39 Prover 5: Preprocessing ...
% 11.32/3.43 Prover 5: Warning: ignoring some quantifiers
% 11.32/3.44 Prover 5: Constructing countermodel ...
% 12.04/3.56 Prover 5: gave up
% 12.04/3.56 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 12.04/3.60 Prover 6: Preprocessing ...
% 12.65/3.68 Prover 6: Warning: ignoring some quantifiers
% 12.65/3.69 Prover 6: Constructing countermodel ...
% 13.04/3.79 Prover 6: gave up
% 13.04/3.79 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 13.04/3.80 Prover 7: Preprocessing ...
% 13.04/3.83 Prover 7: Proving ...
% 36.84/13.77 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 36.84/13.80 Prover 8: Preprocessing ...
% 37.17/13.85 Prover 8: Proving ...
% 67.99/36.15 Prover 4: gave up
% 67.99/36.15 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal
% 67.99/36.17 Prover 9: Preprocessing ...
% 67.99/36.21 Prover 9: Proving ...
% 91.18/56.31 Prover 9: stopped
% 91.38/56.51 Prover 10: Options: -triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 91.38/56.53 Prover 10: Preprocessing ...
% 91.54/56.55 Prover 10: Warning: ignoring some quantifiers
% 91.54/56.55 Prover 10: Constructing countermodel ...
% 91.70/56.58 Prover 10: gave up
% 91.70/56.58 Prover 11: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 91.70/56.60 Prover 11: Preprocessing ...
% 91.70/56.62 Prover 11: Warning: ignoring some quantifiers
% 91.70/56.62 Prover 11: Constructing countermodel ...
% 91.95/56.65 Prover 11: gave up
% 91.95/56.65 Prover 12: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 91.95/56.66 Prover 12: Preprocessing ...
% 92.08/56.68 Prover 12: Proving ...
% 96.30/59.73 Prover 12: stopped
% 96.51/59.93 Prover 13: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 96.62/59.94 Prover 13: Preprocessing ...
% 96.71/59.99 Prover 13: Warning: ignoring some quantifiers
% 96.71/59.99 Prover 13: Constructing countermodel ...
% 96.95/60.08 Prover 13: gave up
% 96.95/60.08 Prover 14: Options: -triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 96.95/60.09 Prover 14: Preprocessing ...
% 96.95/60.10 Prover 14: Warning: ignoring some quantifiers
% 96.95/60.11 Prover 14: Constructing countermodel ...
% 96.95/60.12 Prover 14: gave up
% 96.95/60.12 Prover 15: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 96.95/60.13 Prover 15: Preprocessing ...
% 97.28/60.15 Prover 15: Proving ...
% 107.95/67.62 Prover 15: proved (7500ms)
% 107.95/67.62 Prover 7: stopped
% 107.95/67.62 Prover 8: stopped
% 107.95/67.62
% 107.95/67.62 % SZS status Theorem for theBenchmark
% 107.95/67.62
% 107.95/67.62 Generating proof ... found it (size 119)
% 134.63/86.15
% 134.63/86.15 % SZS output start Proof for theBenchmark
% 134.63/86.15 Assumed formulas after preprocessing and simplification:
% 134.63/86.15 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & empty(v7) = 0 & empty(v5) = v6 & empty(v0) = 0 & disjoint(v1, v2) = v3 & set_difference(v1, v2) = v4 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ((v12 = 0 & ~ (v13 = 0) & in(v11, v9) = v13) | ( ~ (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] : (v9 = v8 | ~ (disjoint(v11, v10) = v9) | ~ (disjoint(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_difference(v11, v10) = v9) | ~ (set_difference(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 | ~ (in(v11, v10) = v9) | ~ (in(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v8) = 0) | ? [v12] : ((v12 = 0 & in(v11, v10) = 0) | (v12 = 0 & in(v11, v9) = 0))) & ! [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] : (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 = v0) & set_intersection2(v8, v9) = v11)) & ! [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] : ( ~ (set_difference(v8, v9) = v10) | ! [v11] : (v11 = v10 | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & in(v12, v9) = 0) | ( ~ (v14 = 0) & in(v12, v8) = v14) | ( ~ (v13 = 0) & in(v12, v11) = v13)) & ((v14 = 0 & ~ (v15 = 0) & in(v12, v9) = v15 & in(v12, v8) = 0) | (v13 = 0 & in(v12, v11) = 0))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (in(v10, v8) = 0) | in(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | set_intersection2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | ! [v11] : (v11 = v10 | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & v14 = 0 & in(v12, v9) = 0 & in(v12, v8) = 0) | (v13 = 0 & in(v12, v11) = 0)) & (( ~ (v15 = 0) & in(v12, v9) = v15) | ( ~ (v14 = 0) & in(v12, v8) = v14) | ( ~ (v13 = 0) & in(v12, v11) = v13))))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (empty(v9) = 0) | ~ (empty(v8) = 0)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_difference(v8, v0) = v9)) & ! [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 = v0 | ~ (set_difference(v0, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v0 | ~ (set_intersection2(v8, v0) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v8, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | disjoint(v9, v8) = 0) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | set_intersection2(v8, v9) = v0) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | ? [v10] : (set_intersection2(v8, v9) = v10 & ! [v11] : ~ (in(v11, v10) = 0))) & ! [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 = v0 | ~ (empty(v8) = 0)) & ((v4 = v1 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = v1))))
% 134.72/86.18 | 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:
% 134.72/86.18 | (1) ~ (all_0_1_1 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(all_0_7_7) = 0 & disjoint(all_0_6_6, all_0_5_5) = all_0_4_4 & set_difference(all_0_6_6, all_0_5_5) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v4 = 0 & ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (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] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(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 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v4 = 0 & in(v3, v1) = 0))) & ! [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] : (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 = all_0_7_7) & set_intersection2(v0, v1) = v3)) & ! [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] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v1) = 0) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v5 = 0) & in(v4, v3) = v5)) & ((v6 = 0 & ~ (v7 = 0) & in(v4, v1) = v7 & in(v4, v0) = 0) | (v5 = 0 & in(v4, v3) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v1) = 0 & in(v4, v0) = 0) | (v5 = 0 & in(v4, v3) = 0)) & (( ~ (v7 = 0) & in(v4, v1) = v7) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v5 = 0) & in(v4, v3) = v5))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_7_7) = v1)) & ! [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 = all_0_7_7 | ~ (set_difference(all_0_7_7, v0) = v1)) & ! [v0] : ! [v1] : (v1 = all_0_7_7 | ~ (set_intersection2(v0, all_0_7_7) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = all_0_7_7) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [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 = all_0_7_7 | ~ (empty(v0) = 0)) & ((all_0_3_3 = all_0_6_6 & ~ (all_0_4_4 = 0)) | (all_0_4_4 = 0 & ~ (all_0_3_3 = all_0_6_6)))
% 134.72/86.19 |
% 134.72/86.19 | Applying alpha-rule on (1) yields:
% 134.72/86.19 | (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)))
% 134.72/86.19 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 134.72/86.19 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v1) = 0) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v5 = 0) & in(v4, v3) = v5)) & ((v6 = 0 & ~ (v7 = 0) & in(v4, v1) = v7 & in(v4, v0) = 0) | (v5 = 0 & in(v4, v3) = 0)))))
% 134.72/86.19 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 134.72/86.19 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 134.72/86.19 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 134.72/86.19 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 134.72/86.19 | (9) ! [v0] : (v0 = all_0_7_7 | ~ (empty(v0) = 0))
% 134.72/86.19 | (10) ~ (all_0_1_1 = 0)
% 134.72/86.19 | (11) ! [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)))
% 134.72/86.19 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 134.72/86.19 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v4 = 0 & in(v3, v1) = 0)))
% 134.72/86.19 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v1) = 0 & in(v4, v0) = 0) | (v5 = 0 & in(v4, v3) = 0)) & (( ~ (v7 = 0) & in(v4, v1) = v7) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v5 = 0) & in(v4, v3) = v5)))))
% 134.72/86.19 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v4 = 0 & ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 134.72/86.19 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = all_0_7_7) & set_intersection2(v0, v1) = v3))
% 134.72/86.19 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 134.72/86.19 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 134.72/86.19 | (19) empty(all_0_7_7) = 0
% 134.72/86.19 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 134.72/86.20 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 134.72/86.20 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 134.72/86.20 | (23) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_7_7) = v1))
% 134.72/86.20 | (24) ! [v0] : ! [v1] : (v1 = all_0_7_7 | ~ (set_difference(all_0_7_7, v0) = v1))
% 134.72/86.20 | (25) (all_0_3_3 = all_0_6_6 & ~ (all_0_4_4 = 0)) | (all_0_4_4 = 0 & ~ (all_0_3_3 = all_0_6_6))
% 134.72/86.20 | (26) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 134.72/86.20 | (27) set_difference(all_0_6_6, all_0_5_5) = all_0_3_3
% 134.72/86.20 | (28) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = all_0_7_7)
% 134.72/86.20 | (29) disjoint(all_0_6_6, all_0_5_5) = all_0_4_4
% 134.72/86.20 | (30) empty(all_0_2_2) = all_0_1_1
% 134.72/86.20 | (31) empty(all_0_0_0) = 0
% 134.72/86.20 | (32) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 134.72/86.20 | (33) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 134.72/86.20 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 134.72/86.20 | (35) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 134.72/86.20 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 134.72/86.20 | (37) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 134.72/86.20 | (38) ! [v0] : ! [v1] : (v1 = all_0_7_7 | ~ (set_intersection2(v0, all_0_7_7) = v1))
% 134.72/86.20 |
% 134.72/86.20 | Instantiating formula (18) with all_0_7_7, all_0_0_0 and discharging atoms empty(all_0_0_0) = 0, empty(all_0_7_7) = 0, yields:
% 134.72/86.20 | (39) all_0_0_0 = all_0_7_7
% 134.72/86.20 |
% 134.72/86.20 | Instantiating formula (28) with all_0_5_5, all_0_6_6 yields:
% 134.72/86.20 | (40) ~ (disjoint(all_0_6_6, all_0_5_5) = 0) | set_intersection2(all_0_6_6, all_0_5_5) = all_0_7_7
% 134.72/86.20 |
% 134.72/86.20 | Instantiating formula (37) with all_0_5_5, all_0_6_6 yields:
% 134.72/86.20 | (41) ~ (disjoint(all_0_6_6, all_0_5_5) = 0) | ? [v0] : (set_intersection2(all_0_6_6, all_0_5_5) = v0 & ! [v1] : ~ (in(v1, v0) = 0))
% 134.72/86.20 |
% 134.72/86.20 | Instantiating formula (6) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms disjoint(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 134.72/86.20 | (42) all_0_4_4 = 0 | ? [v0] : ? [v1] : (set_intersection2(all_0_6_6, all_0_5_5) = v0 & in(v1, v0) = 0)
% 134.72/86.20 |
% 134.72/86.20 | Instantiating formula (16) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms disjoint(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 134.72/86.20 | (43) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = all_0_7_7) & set_intersection2(all_0_6_6, all_0_5_5) = v0)
% 134.72/86.20 |
% 134.72/86.20 | Instantiating formula (4) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 134.72/86.20 | (44) ! [v0] : (v0 = all_0_3_3 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & in(v1, all_0_5_5) = 0) | ( ~ (v3 = 0) & in(v1, all_0_6_6) = v3) | ( ~ (v2 = 0) & in(v1, v0) = v2)) & ((v3 = 0 & ~ (v4 = 0) & in(v1, all_0_5_5) = v4 & in(v1, all_0_6_6) = 0) | (v2 = 0 & in(v1, v0) = 0))))
% 134.72/86.20 |
% 134.72/86.20 +-Applying beta-rule and splitting (25), into two cases.
% 134.72/86.20 |-Branch one:
% 134.72/86.20 | (45) all_0_3_3 = all_0_6_6 & ~ (all_0_4_4 = 0)
% 134.72/86.20 |
% 134.72/86.20 | Applying alpha-rule on (45) yields:
% 134.72/86.20 | (46) all_0_3_3 = all_0_6_6
% 134.72/86.20 | (47) ~ (all_0_4_4 = 0)
% 134.72/86.20 |
% 134.72/86.20 | From (46) and (27) follows:
% 134.72/86.20 | (48) set_difference(all_0_6_6, all_0_5_5) = all_0_6_6
% 134.72/86.20 |
% 134.72/86.20 +-Applying beta-rule and splitting (42), into two cases.
% 134.72/86.20 |-Branch one:
% 134.72/86.20 | (49) all_0_4_4 = 0
% 134.72/86.20 |
% 134.72/86.20 | Equations (49) can reduce 47 to:
% 134.72/86.20 | (50) $false
% 134.72/86.20 |
% 134.72/86.20 |-The branch is then unsatisfiable
% 134.72/86.20 |-Branch two:
% 134.72/86.20 | (51) ? [v0] : ? [v1] : (set_intersection2(all_0_6_6, all_0_5_5) = v0 & in(v1, v0) = 0)
% 134.72/86.20 |
% 134.72/86.20 | Instantiating (51) with all_18_0_8, all_18_1_9 yields:
% 134.72/86.20 | (52) set_intersection2(all_0_6_6, all_0_5_5) = all_18_1_9 & in(all_18_0_8, all_18_1_9) = 0
% 134.72/86.20 |
% 134.72/86.20 | Applying alpha-rule on (52) yields:
% 134.72/86.20 | (53) set_intersection2(all_0_6_6, all_0_5_5) = all_18_1_9
% 134.72/86.20 | (54) in(all_18_0_8, all_18_1_9) = 0
% 134.72/86.20 |
% 134.72/86.20 +-Applying beta-rule and splitting (43), into two cases.
% 134.72/86.20 |-Branch one:
% 134.72/86.20 | (49) all_0_4_4 = 0
% 134.72/86.20 |
% 134.72/86.20 | Equations (49) can reduce 47 to:
% 134.72/86.20 | (50) $false
% 134.72/86.20 |
% 134.72/86.20 |-The branch is then unsatisfiable
% 134.72/86.20 |-Branch two:
% 134.72/86.20 | (57) ? [v0] : ( ~ (v0 = all_0_7_7) & set_intersection2(all_0_6_6, all_0_5_5) = v0)
% 134.72/86.21 |
% 134.72/86.21 | Instantiating (57) with all_23_0_10 yields:
% 134.72/86.21 | (58) ~ (all_23_0_10 = all_0_7_7) & set_intersection2(all_0_6_6, all_0_5_5) = all_23_0_10
% 134.72/86.21 |
% 134.72/86.21 | Applying alpha-rule on (58) yields:
% 134.72/86.21 | (59) ~ (all_23_0_10 = all_0_7_7)
% 134.72/86.21 | (60) set_intersection2(all_0_6_6, all_0_5_5) = all_23_0_10
% 134.72/86.21 |
% 134.72/86.21 | Instantiating formula (20) with all_0_6_6, all_0_5_5, all_18_1_9, all_23_0_10 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_23_0_10, set_intersection2(all_0_6_6, all_0_5_5) = all_18_1_9, yields:
% 134.72/86.21 | (61) all_23_0_10 = all_18_1_9
% 134.72/86.21 |
% 134.72/86.21 | Equations (61) can reduce 59 to:
% 134.72/86.21 | (62) ~ (all_18_1_9 = all_0_7_7)
% 134.72/86.21 |
% 134.72/86.21 | Instantiating formula (14) with all_18_1_9, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_18_1_9, yields:
% 134.72/86.21 | (63) ! [v0] : (v0 = all_18_1_9 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & v3 = 0 & in(v1, all_0_5_5) = 0 & in(v1, all_0_6_6) = 0) | (v2 = 0 & in(v1, v0) = 0)) & (( ~ (v4 = 0) & in(v1, all_0_5_5) = v4) | ( ~ (v3 = 0) & in(v1, all_0_6_6) = v3) | ( ~ (v2 = 0) & in(v1, v0) = v2))))
% 134.72/86.21 |
% 134.72/86.21 | Introducing new symbol ex_104_0_27 defined by:
% 134.72/86.21 | (64) ex_104_0_27 = all_0_0_0
% 134.72/86.21 |
% 134.72/86.21 | Instantiating formula (63) with ex_104_0_27 yields:
% 134.72/86.21 | (65) ex_104_0_27 = all_18_1_9 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & v2 = 0 & in(v0, all_0_5_5) = 0 & in(v0, all_0_6_6) = 0) | (v1 = 0 & in(v0, ex_104_0_27) = 0)) & (( ~ (v3 = 0) & in(v0, all_0_5_5) = v3) | ( ~ (v2 = 0) & in(v0, all_0_6_6) = v2) | ( ~ (v1 = 0) & in(v0, ex_104_0_27) = v1)))
% 134.72/86.21 |
% 134.72/86.21 +-Applying beta-rule and splitting (65), into two cases.
% 134.72/86.21 |-Branch one:
% 134.72/86.21 | (66) ex_104_0_27 = all_18_1_9
% 134.72/86.21 |
% 134.72/86.21 | Combining equations (66,64) yields a new equation:
% 134.72/86.21 | (67) all_18_1_9 = all_0_0_0
% 134.72/86.21 |
% 134.72/86.21 | Simplifying 67 yields:
% 134.72/86.21 | (68) all_18_1_9 = all_0_0_0
% 134.72/86.21 |
% 134.72/86.21 | Combining equations (39,68) yields a new equation:
% 134.72/86.21 | (69) all_18_1_9 = all_0_7_7
% 134.72/86.21 |
% 134.72/86.21 | Equations (69) can reduce 62 to:
% 134.72/86.21 | (50) $false
% 134.72/86.21 |
% 134.72/86.21 |-The branch is then unsatisfiable
% 134.72/86.21 |-Branch two:
% 134.72/86.21 | (71) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & v2 = 0 & in(v0, all_0_5_5) = 0 & in(v0, all_0_6_6) = 0) | (v1 = 0 & in(v0, ex_104_0_27) = 0)) & (( ~ (v3 = 0) & in(v0, all_0_5_5) = v3) | ( ~ (v2 = 0) & in(v0, all_0_6_6) = v2) | ( ~ (v1 = 0) & in(v0, ex_104_0_27) = v1)))
% 134.72/86.21 |
% 134.72/86.21 | Instantiating (71) with all_107_0_28, all_107_1_29, all_107_2_30, all_107_3_31 yields:
% 134.72/86.21 | (72) ((all_107_0_28 = 0 & all_107_1_29 = 0 & in(all_107_3_31, all_0_5_5) = 0 & in(all_107_3_31, all_0_6_6) = 0) | (all_107_2_30 = 0 & in(all_107_3_31, ex_104_0_27) = 0)) & (( ~ (all_107_0_28 = 0) & in(all_107_3_31, all_0_5_5) = all_107_0_28) | ( ~ (all_107_1_29 = 0) & in(all_107_3_31, all_0_6_6) = all_107_1_29) | ( ~ (all_107_2_30 = 0) & in(all_107_3_31, ex_104_0_27) = all_107_2_30))
% 134.72/86.21 |
% 134.72/86.21 | Applying alpha-rule on (72) yields:
% 134.72/86.21 | (73) (all_107_0_28 = 0 & all_107_1_29 = 0 & in(all_107_3_31, all_0_5_5) = 0 & in(all_107_3_31, all_0_6_6) = 0) | (all_107_2_30 = 0 & in(all_107_3_31, ex_104_0_27) = 0)
% 134.72/86.21 | (74) ( ~ (all_107_0_28 = 0) & in(all_107_3_31, all_0_5_5) = all_107_0_28) | ( ~ (all_107_1_29 = 0) & in(all_107_3_31, all_0_6_6) = all_107_1_29) | ( ~ (all_107_2_30 = 0) & in(all_107_3_31, ex_104_0_27) = all_107_2_30)
% 134.72/86.21 |
% 134.72/86.21 +-Applying beta-rule and splitting (73), into two cases.
% 134.72/86.21 |-Branch one:
% 134.72/86.21 | (75) all_107_0_28 = 0 & all_107_1_29 = 0 & in(all_107_3_31, all_0_5_5) = 0 & in(all_107_3_31, all_0_6_6) = 0
% 134.72/86.21 |
% 134.72/86.21 | Applying alpha-rule on (75) yields:
% 134.72/86.21 | (76) all_107_0_28 = 0
% 134.72/86.21 | (77) all_107_1_29 = 0
% 134.72/86.21 | (78) in(all_107_3_31, all_0_5_5) = 0
% 134.72/86.21 | (79) in(all_107_3_31, all_0_6_6) = 0
% 134.72/86.21 |
% 134.72/86.21 | Instantiating formula (15) with 0, all_107_3_31, all_0_6_6, all_0_5_5, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_5_5) = all_0_6_6, in(all_107_3_31, all_0_6_6) = 0, yields:
% 134.72/86.21 | (80) ? [v0] : (( ~ (v0 = 0) & in(all_107_3_31, all_0_5_5) = v0) | ( ~ (v0 = 0) & in(all_107_3_31, all_0_6_6) = v0))
% 134.72/86.21 |
% 134.72/86.21 | Instantiating (80) with all_134_0_51 yields:
% 134.72/86.21 | (81) ( ~ (all_134_0_51 = 0) & in(all_107_3_31, all_0_5_5) = all_134_0_51) | ( ~ (all_134_0_51 = 0) & in(all_107_3_31, all_0_6_6) = all_134_0_51)
% 134.72/86.21 |
% 134.72/86.21 +-Applying beta-rule and splitting (81), into two cases.
% 134.72/86.21 |-Branch one:
% 134.72/86.21 | (82) ~ (all_134_0_51 = 0) & in(all_107_3_31, all_0_5_5) = all_134_0_51
% 134.72/86.21 |
% 134.72/86.21 | Applying alpha-rule on (82) yields:
% 134.72/86.21 | (83) ~ (all_134_0_51 = 0)
% 134.72/86.21 | (84) in(all_107_3_31, all_0_5_5) = all_134_0_51
% 134.72/86.21 |
% 134.72/86.21 | Instantiating formula (17) with all_107_3_31, all_0_5_5, all_134_0_51, 0 and discharging atoms in(all_107_3_31, all_0_5_5) = all_134_0_51, in(all_107_3_31, all_0_5_5) = 0, yields:
% 134.72/86.21 | (85) all_134_0_51 = 0
% 134.72/86.21 |
% 134.72/86.21 | Equations (85) can reduce 83 to:
% 134.72/86.21 | (50) $false
% 134.72/86.21 |
% 134.72/86.21 |-The branch is then unsatisfiable
% 134.72/86.21 |-Branch two:
% 134.72/86.21 | (87) ~ (all_134_0_51 = 0) & in(all_107_3_31, all_0_6_6) = all_134_0_51
% 134.72/86.21 |
% 134.72/86.21 | Applying alpha-rule on (87) yields:
% 134.72/86.21 | (83) ~ (all_134_0_51 = 0)
% 134.72/86.21 | (89) in(all_107_3_31, all_0_6_6) = all_134_0_51
% 134.72/86.21 |
% 134.72/86.21 | Instantiating formula (17) with all_107_3_31, all_0_6_6, all_134_0_51, 0 and discharging atoms in(all_107_3_31, all_0_6_6) = all_134_0_51, in(all_107_3_31, all_0_6_6) = 0, yields:
% 134.72/86.21 | (85) all_134_0_51 = 0
% 134.72/86.21 |
% 134.72/86.21 | Equations (85) can reduce 83 to:
% 134.72/86.21 | (50) $false
% 134.72/86.21 |
% 134.72/86.21 |-The branch is then unsatisfiable
% 134.72/86.21 |-Branch two:
% 134.72/86.21 | (92) all_107_2_30 = 0 & in(all_107_3_31, ex_104_0_27) = 0
% 134.72/86.21 |
% 134.72/86.21 | Applying alpha-rule on (92) yields:
% 134.72/86.21 | (93) all_107_2_30 = 0
% 134.72/86.21 | (94) in(all_107_3_31, ex_104_0_27) = 0
% 134.72/86.21 |
% 134.72/86.21 | Instantiating formula (33) with ex_104_0_27, all_107_3_31 and discharging atoms in(all_107_3_31, ex_104_0_27) = 0, yields:
% 134.72/86.21 | (95) ? [v0] : ( ~ (v0 = 0) & empty(ex_104_0_27) = v0)
% 134.72/86.22 |
% 134.72/86.22 | Instantiating (95) with all_122_0_55 yields:
% 134.72/86.22 | (96) ~ (all_122_0_55 = 0) & empty(ex_104_0_27) = all_122_0_55
% 134.72/86.22 |
% 134.72/86.22 | Applying alpha-rule on (96) yields:
% 134.72/86.22 | (97) ~ (all_122_0_55 = 0)
% 134.72/86.22 | (98) empty(ex_104_0_27) = all_122_0_55
% 134.72/86.22 |
% 134.72/86.22 | Combining equations (39,64) yields a new equation:
% 134.72/86.22 | (99) ex_104_0_27 = all_0_7_7
% 134.72/86.22 |
% 134.72/86.22 | From (99) and (98) follows:
% 134.72/86.22 | (100) empty(all_0_7_7) = all_122_0_55
% 134.72/86.22 |
% 134.72/86.22 | Instantiating formula (21) with all_0_7_7, 0, all_122_0_55 and discharging atoms empty(all_0_7_7) = all_122_0_55, empty(all_0_7_7) = 0, yields:
% 134.72/86.22 | (101) all_122_0_55 = 0
% 134.72/86.22 |
% 134.72/86.22 | Equations (101) can reduce 97 to:
% 134.72/86.22 | (50) $false
% 134.72/86.22 |
% 134.72/86.22 |-The branch is then unsatisfiable
% 134.72/86.22 |-Branch two:
% 134.72/86.22 | (103) all_0_4_4 = 0 & ~ (all_0_3_3 = all_0_6_6)
% 134.72/86.22 |
% 134.72/86.22 | Applying alpha-rule on (103) yields:
% 134.72/86.22 | (49) all_0_4_4 = 0
% 134.72/86.22 | (105) ~ (all_0_3_3 = all_0_6_6)
% 134.72/86.22 |
% 134.72/86.22 | From (49) and (29) follows:
% 134.72/86.22 | (106) disjoint(all_0_6_6, all_0_5_5) = 0
% 134.72/86.22 |
% 134.72/86.22 +-Applying beta-rule and splitting (40), into two cases.
% 134.72/86.22 |-Branch one:
% 134.72/86.22 | (107) ~ (disjoint(all_0_6_6, all_0_5_5) = 0)
% 134.72/86.22 |
% 134.72/86.22 | Using (106) and (107) yields:
% 134.72/86.22 | (108) $false
% 134.72/86.22 |
% 134.72/86.22 |-The branch is then unsatisfiable
% 134.72/86.22 |-Branch two:
% 134.72/86.22 | (109) set_intersection2(all_0_6_6, all_0_5_5) = all_0_7_7
% 134.72/86.22 |
% 134.72/86.22 +-Applying beta-rule and splitting (41), into two cases.
% 134.72/86.22 |-Branch one:
% 134.72/86.22 | (107) ~ (disjoint(all_0_6_6, all_0_5_5) = 0)
% 134.72/86.22 |
% 134.72/86.22 | Using (106) and (107) yields:
% 134.72/86.22 | (108) $false
% 134.72/86.22 |
% 134.72/86.22 |-The branch is then unsatisfiable
% 134.72/86.22 |-Branch two:
% 134.72/86.22 | (112) ? [v0] : (set_intersection2(all_0_6_6, all_0_5_5) = v0 & ! [v1] : ~ (in(v1, v0) = 0))
% 134.72/86.22 |
% 134.72/86.22 | Instantiating (112) with all_21_0_11 yields:
% 134.72/86.22 | (113) set_intersection2(all_0_6_6, all_0_5_5) = all_21_0_11 & ! [v0] : ~ (in(v0, all_21_0_11) = 0)
% 134.72/86.22 |
% 134.72/86.22 | Applying alpha-rule on (113) yields:
% 134.72/86.22 | (114) set_intersection2(all_0_6_6, all_0_5_5) = all_21_0_11
% 134.72/86.22 | (115) ! [v0] : ~ (in(v0, all_21_0_11) = 0)
% 134.72/86.22 |
% 134.72/86.22 | Instantiating formula (20) with all_0_6_6, all_0_5_5, all_0_7_7, all_21_0_11 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_21_0_11, set_intersection2(all_0_6_6, all_0_5_5) = all_0_7_7, yields:
% 134.72/86.22 | (116) all_21_0_11 = all_0_7_7
% 134.72/86.22 |
% 134.72/86.22 | Introducing new symbol ex_65_0_155 defined by:
% 134.72/86.22 | (117) ex_65_0_155 = all_0_6_6
% 134.72/86.22 |
% 134.72/86.22 | Instantiating formula (44) with ex_65_0_155 yields:
% 134.72/86.22 | (118) ex_65_0_155 = all_0_3_3 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & in(v0, all_0_5_5) = 0) | ( ~ (v2 = 0) & in(v0, all_0_6_6) = v2) | ( ~ (v1 = 0) & in(v0, ex_65_0_155) = v1)) & ((v2 = 0 & ~ (v3 = 0) & in(v0, all_0_5_5) = v3 & in(v0, all_0_6_6) = 0) | (v1 = 0 & in(v0, ex_65_0_155) = 0)))
% 134.72/86.22 |
% 134.72/86.22 +-Applying beta-rule and splitting (118), into two cases.
% 134.72/86.22 |-Branch one:
% 134.72/86.22 | (119) ex_65_0_155 = all_0_3_3
% 134.72/86.22 |
% 134.72/86.22 | Combining equations (119,117) yields a new equation:
% 134.72/86.22 | (120) all_0_3_3 = all_0_6_6
% 134.72/86.22 |
% 134.72/86.22 | Simplifying 120 yields:
% 134.72/86.22 | (46) all_0_3_3 = all_0_6_6
% 134.72/86.22 |
% 134.72/86.22 | Equations (46) can reduce 105 to:
% 134.72/86.22 | (50) $false
% 134.72/86.22 |
% 134.72/86.22 |-The branch is then unsatisfiable
% 134.72/86.22 |-Branch two:
% 134.72/86.22 | (123) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & in(v0, all_0_5_5) = 0) | ( ~ (v2 = 0) & in(v0, all_0_6_6) = v2) | ( ~ (v1 = 0) & in(v0, ex_65_0_155) = v1)) & ((v2 = 0 & ~ (v3 = 0) & in(v0, all_0_5_5) = v3 & in(v0, all_0_6_6) = 0) | (v1 = 0 & in(v0, ex_65_0_155) = 0)))
% 134.72/86.22 |
% 134.72/86.22 | Instantiating (123) with all_68_0_156, all_68_1_157, all_68_2_158, all_68_3_159 yields:
% 134.72/86.22 | (124) ((all_68_0_156 = 0 & in(all_68_3_159, all_0_5_5) = 0) | ( ~ (all_68_1_157 = 0) & in(all_68_3_159, all_0_6_6) = all_68_1_157) | ( ~ (all_68_2_158 = 0) & in(all_68_3_159, ex_65_0_155) = all_68_2_158)) & ((all_68_1_157 = 0 & ~ (all_68_0_156 = 0) & in(all_68_3_159, all_0_5_5) = all_68_0_156 & in(all_68_3_159, all_0_6_6) = 0) | (all_68_2_158 = 0 & in(all_68_3_159, ex_65_0_155) = 0))
% 134.72/86.22 |
% 134.72/86.22 | Applying alpha-rule on (124) yields:
% 134.72/86.22 | (125) (all_68_0_156 = 0 & in(all_68_3_159, all_0_5_5) = 0) | ( ~ (all_68_1_157 = 0) & in(all_68_3_159, all_0_6_6) = all_68_1_157) | ( ~ (all_68_2_158 = 0) & in(all_68_3_159, ex_65_0_155) = all_68_2_158)
% 134.72/86.22 | (126) (all_68_1_157 = 0 & ~ (all_68_0_156 = 0) & in(all_68_3_159, all_0_5_5) = all_68_0_156 & in(all_68_3_159, all_0_6_6) = 0) | (all_68_2_158 = 0 & in(all_68_3_159, ex_65_0_155) = 0)
% 134.72/86.22 |
% 134.72/86.22 +-Applying beta-rule and splitting (126), into two cases.
% 134.72/86.22 |-Branch one:
% 134.72/86.22 | (127) all_68_1_157 = 0 & ~ (all_68_0_156 = 0) & in(all_68_3_159, all_0_5_5) = all_68_0_156 & in(all_68_3_159, all_0_6_6) = 0
% 134.72/86.22 |
% 134.72/86.22 | Applying alpha-rule on (127) yields:
% 134.72/86.22 | (128) all_68_1_157 = 0
% 134.72/86.22 | (129) ~ (all_68_0_156 = 0)
% 134.72/86.22 | (130) in(all_68_3_159, all_0_5_5) = all_68_0_156
% 134.72/86.22 | (131) in(all_68_3_159, all_0_6_6) = 0
% 134.72/86.22 |
% 134.72/86.22 +-Applying beta-rule and splitting (125), into two cases.
% 134.72/86.22 |-Branch one:
% 134.72/86.22 | (132) (all_68_0_156 = 0 & in(all_68_3_159, all_0_5_5) = 0) | ( ~ (all_68_1_157 = 0) & in(all_68_3_159, all_0_6_6) = all_68_1_157)
% 134.72/86.22 |
% 134.72/86.22 +-Applying beta-rule and splitting (132), into two cases.
% 134.72/86.22 |-Branch one:
% 134.72/86.22 | (133) all_68_0_156 = 0 & in(all_68_3_159, all_0_5_5) = 0
% 134.72/86.22 |
% 134.72/86.22 | Applying alpha-rule on (133) yields:
% 134.72/86.22 | (134) all_68_0_156 = 0
% 134.72/86.22 | (135) in(all_68_3_159, all_0_5_5) = 0
% 134.72/86.22 |
% 134.72/86.22 | Equations (134) can reduce 129 to:
% 134.72/86.22 | (50) $false
% 134.72/86.22 |
% 134.72/86.22 |-The branch is then unsatisfiable
% 134.72/86.22 |-Branch two:
% 134.72/86.22 | (137) ~ (all_68_1_157 = 0) & in(all_68_3_159, all_0_6_6) = all_68_1_157
% 134.72/86.22 |
% 134.72/86.22 | Applying alpha-rule on (137) yields:
% 134.72/86.22 | (138) ~ (all_68_1_157 = 0)
% 134.72/86.23 | (139) in(all_68_3_159, all_0_6_6) = all_68_1_157
% 134.72/86.23 |
% 134.72/86.23 | Equations (128) can reduce 138 to:
% 134.72/86.23 | (50) $false
% 134.72/86.23 |
% 134.72/86.23 |-The branch is then unsatisfiable
% 134.72/86.23 |-Branch two:
% 134.72/86.23 | (141) ~ (all_68_2_158 = 0) & in(all_68_3_159, ex_65_0_155) = all_68_2_158
% 134.72/86.23 |
% 134.72/86.23 | Applying alpha-rule on (141) yields:
% 134.72/86.23 | (142) ~ (all_68_2_158 = 0)
% 134.72/86.23 | (143) in(all_68_3_159, ex_65_0_155) = all_68_2_158
% 134.72/86.23 |
% 134.72/86.23 | From (117) and (143) follows:
% 134.72/86.23 | (144) in(all_68_3_159, all_0_6_6) = all_68_2_158
% 134.72/86.23 |
% 134.72/86.23 | Instantiating formula (17) with all_68_3_159, all_0_6_6, 0, all_68_2_158 and discharging atoms in(all_68_3_159, all_0_6_6) = all_68_2_158, in(all_68_3_159, all_0_6_6) = 0, yields:
% 134.72/86.23 | (145) all_68_2_158 = 0
% 134.72/86.23 |
% 134.72/86.23 | Equations (145) can reduce 142 to:
% 134.72/86.23 | (50) $false
% 134.72/86.23 |
% 134.72/86.23 |-The branch is then unsatisfiable
% 134.72/86.23 |-Branch two:
% 134.72/86.23 | (147) all_68_2_158 = 0 & in(all_68_3_159, ex_65_0_155) = 0
% 134.72/86.23 |
% 134.72/86.23 | Applying alpha-rule on (147) yields:
% 134.72/86.23 | (145) all_68_2_158 = 0
% 134.72/86.23 | (149) in(all_68_3_159, ex_65_0_155) = 0
% 134.72/86.23 |
% 134.72/86.23 | Instantiating formula (115) with all_68_3_159 yields:
% 134.72/86.23 | (150) ~ (in(all_68_3_159, all_21_0_11) = 0)
% 134.72/86.23 |
% 134.72/86.23 | From (116) and (150) follows:
% 134.72/86.23 | (151) ~ (in(all_68_3_159, all_0_7_7) = 0)
% 134.72/86.23 |
% 134.72/86.23 | Instantiating formula (11) with all_68_3_159, all_0_7_7, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_0_7_7, yields:
% 134.72/86.23 | (152) ~ (in(all_68_3_159, all_0_6_6) = 0) | ? [v0] : ((v0 = 0 & in(all_68_3_159, all_0_7_7) = 0) | ( ~ (v0 = 0) & in(all_68_3_159, all_0_5_5) = v0))
% 134.72/86.23 |
% 134.72/86.23 +-Applying beta-rule and splitting (125), into two cases.
% 134.72/86.23 |-Branch one:
% 134.72/86.23 | (132) (all_68_0_156 = 0 & in(all_68_3_159, all_0_5_5) = 0) | ( ~ (all_68_1_157 = 0) & in(all_68_3_159, all_0_6_6) = all_68_1_157)
% 134.72/86.23 |
% 134.72/86.23 +-Applying beta-rule and splitting (132), into two cases.
% 134.72/86.23 |-Branch one:
% 134.72/86.23 | (133) all_68_0_156 = 0 & in(all_68_3_159, all_0_5_5) = 0
% 134.72/86.23 |
% 134.72/86.23 | Applying alpha-rule on (133) yields:
% 134.72/86.23 | (134) all_68_0_156 = 0
% 134.72/86.23 | (135) in(all_68_3_159, all_0_5_5) = 0
% 134.72/86.23 |
% 134.72/86.23 +-Applying beta-rule and splitting (152), into two cases.
% 134.72/86.23 |-Branch one:
% 134.72/86.23 | (157) ~ (in(all_68_3_159, all_0_6_6) = 0)
% 134.72/86.23 |
% 134.72/86.23 | From (117) and (149) follows:
% 134.72/86.23 | (131) in(all_68_3_159, all_0_6_6) = 0
% 134.72/86.23 |
% 134.72/86.23 | Using (131) and (157) yields:
% 134.72/86.23 | (108) $false
% 134.72/86.23 |
% 134.72/86.23 |-The branch is then unsatisfiable
% 134.72/86.23 |-Branch two:
% 134.72/86.23 | (160) ? [v0] : ((v0 = 0 & in(all_68_3_159, all_0_7_7) = 0) | ( ~ (v0 = 0) & in(all_68_3_159, all_0_5_5) = v0))
% 134.72/86.23 |
% 134.72/86.23 | Instantiating (160) with all_99_0_179 yields:
% 134.72/86.23 | (161) (all_99_0_179 = 0 & in(all_68_3_159, all_0_7_7) = 0) | ( ~ (all_99_0_179 = 0) & in(all_68_3_159, all_0_5_5) = all_99_0_179)
% 134.72/86.23 |
% 134.72/86.23 +-Applying beta-rule and splitting (161), into two cases.
% 134.72/86.23 |-Branch one:
% 134.72/86.23 | (162) all_99_0_179 = 0 & in(all_68_3_159, all_0_7_7) = 0
% 134.72/86.23 |
% 134.72/86.23 | Applying alpha-rule on (162) yields:
% 134.72/86.23 | (163) all_99_0_179 = 0
% 134.72/86.23 | (164) in(all_68_3_159, all_0_7_7) = 0
% 134.72/86.23 |
% 134.72/86.23 | Using (164) and (151) yields:
% 134.72/86.23 | (108) $false
% 134.72/86.23 |
% 134.72/86.23 |-The branch is then unsatisfiable
% 134.72/86.23 |-Branch two:
% 134.72/86.23 | (166) ~ (all_99_0_179 = 0) & in(all_68_3_159, all_0_5_5) = all_99_0_179
% 134.72/86.23 |
% 134.72/86.23 | Applying alpha-rule on (166) yields:
% 134.72/86.23 | (167) ~ (all_99_0_179 = 0)
% 134.72/86.23 | (168) in(all_68_3_159, all_0_5_5) = all_99_0_179
% 134.72/86.23 |
% 134.72/86.23 | Instantiating formula (17) with all_68_3_159, all_0_5_5, all_99_0_179, 0 and discharging atoms in(all_68_3_159, all_0_5_5) = all_99_0_179, in(all_68_3_159, all_0_5_5) = 0, yields:
% 134.72/86.23 | (163) all_99_0_179 = 0
% 134.72/86.23 |
% 134.72/86.23 | Equations (163) can reduce 167 to:
% 134.72/86.23 | (50) $false
% 134.72/86.23 |
% 134.72/86.23 |-The branch is then unsatisfiable
% 134.72/86.23 |-Branch two:
% 134.72/86.23 | (137) ~ (all_68_1_157 = 0) & in(all_68_3_159, all_0_6_6) = all_68_1_157
% 134.72/86.23 |
% 134.72/86.23 | Applying alpha-rule on (137) yields:
% 134.72/86.23 | (138) ~ (all_68_1_157 = 0)
% 134.72/86.23 | (139) in(all_68_3_159, all_0_6_6) = all_68_1_157
% 134.72/86.23 |
% 134.72/86.23 | From (117) and (149) follows:
% 134.72/86.23 | (131) in(all_68_3_159, all_0_6_6) = 0
% 134.72/86.23 |
% 134.72/86.23 | Instantiating formula (17) with all_68_3_159, all_0_6_6, 0, all_68_1_157 and discharging atoms in(all_68_3_159, all_0_6_6) = all_68_1_157, in(all_68_3_159, all_0_6_6) = 0, yields:
% 134.72/86.23 | (128) all_68_1_157 = 0
% 134.72/86.23 |
% 134.72/86.23 | Equations (128) can reduce 138 to:
% 134.72/86.23 | (50) $false
% 134.72/86.23 |
% 134.72/86.23 |-The branch is then unsatisfiable
% 134.72/86.23 |-Branch two:
% 134.72/86.23 | (141) ~ (all_68_2_158 = 0) & in(all_68_3_159, ex_65_0_155) = all_68_2_158
% 134.72/86.23 |
% 134.72/86.23 | Applying alpha-rule on (141) yields:
% 134.72/86.23 | (142) ~ (all_68_2_158 = 0)
% 134.72/86.23 | (143) in(all_68_3_159, ex_65_0_155) = all_68_2_158
% 134.72/86.23 |
% 134.72/86.23 | Equations (145) can reduce 142 to:
% 134.72/86.23 | (50) $false
% 134.72/86.23 |
% 134.72/86.23 |-The branch is then unsatisfiable
% 134.72/86.23 % SZS output end Proof for theBenchmark
% 134.72/86.23
% 134.72/86.23 85598ms
%------------------------------------------------------------------------------