TSTP Solution File: SET945+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET945+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 00:23:21 EDT 2022
% Result : Theorem 4.99s 1.82s
% Output : Proof 7.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET945+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n029.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 : Sun Jul 10 01:52:46 EDT 2022
% 0.20/0.34 % CPUTime :
% 0.58/0.59 ____ _
% 0.58/0.59 ___ / __ \_____(_)___ ________ __________
% 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.59
% 0.58/0.59 A Theorem Prover for First-Order Logic
% 0.58/0.59 (ePrincess v.1.0)
% 0.58/0.59
% 0.58/0.59 (c) Philipp Rümmer, 2009-2015
% 0.58/0.59 (c) Peter Backeman, 2014-2015
% 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.59 Bug reports to peter@backeman.se
% 0.58/0.59
% 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.59
% 0.58/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.78/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.44/0.92 Prover 0: Preprocessing ...
% 1.89/1.11 Prover 0: Warning: ignoring some quantifiers
% 1.89/1.13 Prover 0: Constructing countermodel ...
% 2.39/1.24 Prover 0: gave up
% 2.39/1.24 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.39/1.27 Prover 1: Preprocessing ...
% 2.80/1.35 Prover 1: Warning: ignoring some quantifiers
% 2.80/1.36 Prover 1: Constructing countermodel ...
% 3.70/1.60 Prover 1: gave up
% 3.70/1.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.70/1.61 Prover 2: Preprocessing ...
% 4.15/1.68 Prover 2: Warning: ignoring some quantifiers
% 4.15/1.69 Prover 2: Constructing countermodel ...
% 4.99/1.82 Prover 2: proved (226ms)
% 4.99/1.82
% 4.99/1.82 No countermodel exists, formula is valid
% 4.99/1.82 % SZS status Theorem for theBenchmark
% 4.99/1.82
% 4.99/1.82 Generating proof ... Warning: ignoring some quantifiers
% 6.71/2.23 found it (size 27)
% 6.71/2.23
% 6.71/2.23 % SZS output start Proof for theBenchmark
% 6.71/2.23 Assumed formulas after preprocessing and simplification:
% 6.71/2.24 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v3 = 0) & disjoint(v2, v1) = v3 & empty(v6) = 0 & empty(v4) = v5 & union(v0) = v2 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v9) = v11) | ? [v12] : (( ~ (v12 = 0) & in(v10, v8) = v12) | ( ~ (v12 = 0) & in(v10, v7) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (union(v7) = v8) | ~ (in(v11, v7) = 0) | ~ (in(v9, v8) = v10) | ? [v12] : ( ~ (v12 = 0) & in(v9, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (union(v7) = v8) | ~ (in(v9, v11) = 0) | ~ (in(v9, v8) = v10) | ? [v12] : ( ~ (v12 = 0) & in(v11, v7) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v8) = v11) | ? [v12] : ((v12 = 0 & v11 = 0 & in(v10, v7) = 0) | ( ~ (v12 = 0) & in(v10, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ((v12 = 0 & v11 = 0 & in(v10, v8) = 0) | ( ~ (v12 = 0) & in(v10, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (disjoint(v10, v9) = v8) | ~ (disjoint(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_intersection2(v10, v9) = v8) | ~ (set_intersection2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & disjoint(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v9) = 0) | (in(v10, v8) = 0 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v8) = 0) | ? [v11] : ((v11 = 0 & in(v10, v9) = 0) | ( ~ (v11 = 0) & in(v10, v7) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v7) = 0) | ? [v11] : ((v11 = 0 & in(v10, v9) = 0) | ( ~ (v11 = 0) & in(v10, v8) = v11))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (((v14 = 0 & v13 = 0 & in(v11, v9) = 0 & in(v11, v8) = 0) | (v12 = 0 & in(v11, v7) = 0)) & (( ~ (v14 = 0) & in(v11, v9) = v14) | ( ~ (v13 = 0) & in(v11, v8) = v13) | ( ~ (v12 = 0) & in(v11, v7) = v12)))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (disjoint(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & disjoint(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (disjoint(v7, v8) = v9) | ? [v10] : ? [v11] : (set_intersection2(v7, v8) = v10 & in(v11, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (union(v9) = v8) | ~ (union(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v7) = v8) | ~ (in(v9, v8) = 0) | ? [v10] : (in(v10, v7) = 0 & in(v9, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v8, v7) = v9) | set_intersection2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | set_intersection2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & in(v10, v9) = 0) | (v10 = 0 & disjoint(v7, v8) = 0))) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (union(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (((v14 = 0 & v13 = 0 & in(v12, v8) = 0 & in(v10, v12) = 0) | (v11 = 0 & in(v10, v7) = 0)) & (( ~ (v11 = 0) & in(v10, v7) = v11) | ( ! [v15] : ( ~ (in(v15, v8) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v10, v15) = v16)) & ! [v15] : ( ~ (in(v10, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v15, v8) = v16)))))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_intersection2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (disjoint(v7, v1) = v8) | ? [v9] : ( ~ (v9 = 0) & in(v7, v0) = v9)) & ! [v7] : ! [v8] : ( ~ (disjoint(v7, v8) = 0) | disjoint(v8, v7) = 0) & ! [v7] : ! [v8] : ( ~ (disjoint(v7, v8) = 0) | ? [v9] : (set_intersection2(v7, v8) = v9 & ! [v10] : ~ (in(v10, v9) = 0))) & ! [v7] : ! [v8] : ( ~ (in(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ! [v7] : ( ~ (in(v7, v0) = 0) | disjoint(v7, v1) = 0) & ? [v7] : ? [v8] : ? [v9] : disjoint(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : set_intersection2(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : in(v8, v7) = v9 & ? [v7] : ? [v8] : empty(v7) = v8 & ? [v7] : ? [v8] : union(v7) = v8)
% 6.71/2.27 | 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:
% 6.71/2.27 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & disjoint(all_0_4_4, all_0_5_5) = all_0_3_3 & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & union(all_0_6_6) = 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] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v2, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = 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] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(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_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] : (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] : (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] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 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] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v4 = 0) & in(v3, v0) = v4) | ( ! [v8] : ( ~ (in(v8, v1) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v3, v8) = v9)) & ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9)))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (disjoint(v0, all_0_5_5) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_6_6) = v2)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : ( ~ (in(v0, all_0_6_6) = 0) | disjoint(v0, all_0_5_5) = 0) & ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : union(v0) = v1
% 6.71/2.29 |
% 6.71/2.29 | Applying alpha-rule on (1) yields:
% 6.71/2.29 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 6.71/2.29 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 6.71/2.29 | (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)))
% 6.71/2.29 | (5) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2
% 6.71/2.29 | (6) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2
% 6.71/2.29 | (7) disjoint(all_0_4_4, all_0_5_5) = all_0_3_3
% 6.71/2.29 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5))
% 6.71/2.29 | (9) ~ (all_0_3_3 = 0)
% 6.71/2.29 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v2, v4) = v5))
% 6.71/2.29 | (11) ~ (all_0_1_1 = 0)
% 6.71/2.29 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 6.71/2.29 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 6.71/2.29 | (14) ? [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))))
% 6.71/2.29 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 6.71/2.29 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 6.71/2.29 | (17) ! [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)))
% 6.71/2.29 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 6.71/2.29 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 6.71/2.29 | (20) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 6.71/2.29 | (21) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 6.71/2.29 | (22) ? [v0] : ? [v1] : empty(v0) = v1
% 6.71/2.29 | (23) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v4 = 0) & in(v3, v0) = v4) | ( ! [v8] : ( ~ (in(v8, v1) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v3, v8) = v9)) & ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))))))
% 6.71/2.30 | (24) empty(all_0_2_2) = all_0_1_1
% 6.71/2.30 | (25) ! [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)))
% 6.71/2.30 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 6.71/2.30 | (27) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 6.71/2.30 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 6.71/2.30 | (29) ? [v0] : ? [v1] : union(v0) = v1
% 6.71/2.30 | (30) ! [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)))
% 6.71/2.30 | (31) ! [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)))
% 6.71/2.30 | (32) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 6.71/2.30 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 6.71/2.30 | (34) ! [v0] : ! [v1] : (v1 = 0 | ~ (disjoint(v0, all_0_5_5) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_6_6) = v2))
% 6.71/2.30 | (35) ! [v0] : ( ~ (in(v0, all_0_6_6) = 0) | disjoint(v0, all_0_5_5) = 0)
% 6.71/2.30 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 6.71/2.30 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 6.71/2.30 | (38) union(all_0_6_6) = all_0_4_4
% 6.71/2.30 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.71/2.30 | (40) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 6.71/2.30 | (41) empty(all_0_0_0) = 0
% 6.71/2.30 |
% 6.71/2.30 | Instantiating formula (16) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms disjoint(all_0_4_4, all_0_5_5) = all_0_3_3, yields:
% 6.71/2.30 | (42) all_0_3_3 = 0 | ? [v0] : ? [v1] : (set_intersection2(all_0_4_4, all_0_5_5) = v0 & in(v1, v0) = 0)
% 6.71/2.30 |
% 6.71/2.30 +-Applying beta-rule and splitting (42), into two cases.
% 6.71/2.30 |-Branch one:
% 6.71/2.30 | (43) all_0_3_3 = 0
% 6.71/2.30 |
% 6.71/2.31 | Equations (43) can reduce 9 to:
% 6.71/2.31 | (44) $false
% 6.71/2.31 |
% 6.71/2.31 |-The branch is then unsatisfiable
% 6.71/2.31 |-Branch two:
% 6.71/2.31 | (9) ~ (all_0_3_3 = 0)
% 6.71/2.31 | (46) ? [v0] : ? [v1] : (set_intersection2(all_0_4_4, all_0_5_5) = v0 & in(v1, v0) = 0)
% 6.71/2.31 |
% 6.71/2.31 | Instantiating (46) with all_28_0_22, all_28_1_23 yields:
% 6.71/2.31 | (47) set_intersection2(all_0_4_4, all_0_5_5) = all_28_1_23 & in(all_28_0_22, all_28_1_23) = 0
% 6.71/2.31 |
% 6.71/2.31 | Applying alpha-rule on (47) yields:
% 6.71/2.31 | (48) set_intersection2(all_0_4_4, all_0_5_5) = all_28_1_23
% 6.71/2.31 | (49) in(all_28_0_22, all_28_1_23) = 0
% 6.71/2.31 |
% 6.71/2.31 | Instantiating formula (28) with all_28_0_22, all_28_1_23, all_0_5_5, all_0_4_4 and discharging atoms set_intersection2(all_0_4_4, all_0_5_5) = all_28_1_23, in(all_28_0_22, all_28_1_23) = 0, yields:
% 6.71/2.31 | (50) in(all_28_0_22, all_0_4_4) = 0 & in(all_28_0_22, all_0_5_5) = 0
% 6.71/2.31 |
% 6.71/2.31 | Applying alpha-rule on (50) yields:
% 6.71/2.31 | (51) in(all_28_0_22, all_0_4_4) = 0
% 6.71/2.31 | (52) in(all_28_0_22, all_0_5_5) = 0
% 6.71/2.31 |
% 6.71/2.31 | Instantiating formula (26) with all_28_0_22, all_0_4_4, all_0_6_6 and discharging atoms union(all_0_6_6) = all_0_4_4, in(all_28_0_22, all_0_4_4) = 0, yields:
% 6.71/2.31 | (53) ? [v0] : (in(v0, all_0_6_6) = 0 & in(all_28_0_22, v0) = 0)
% 6.71/2.31 |
% 6.71/2.31 | Instantiating (53) with all_73_0_33 yields:
% 6.71/2.31 | (54) in(all_73_0_33, all_0_6_6) = 0 & in(all_28_0_22, all_73_0_33) = 0
% 6.71/2.31 |
% 6.71/2.31 | Applying alpha-rule on (54) yields:
% 6.71/2.31 | (55) in(all_73_0_33, all_0_6_6) = 0
% 6.71/2.31 | (56) in(all_28_0_22, all_73_0_33) = 0
% 6.71/2.31 |
% 6.71/2.31 | Instantiating formula (35) with all_73_0_33 and discharging atoms in(all_73_0_33, all_0_6_6) = 0, yields:
% 6.71/2.31 | (57) disjoint(all_73_0_33, all_0_5_5) = 0
% 6.71/2.31 |
% 6.71/2.31 | Instantiating formula (40) with all_0_5_5, all_73_0_33 and discharging atoms disjoint(all_73_0_33, all_0_5_5) = 0, yields:
% 6.71/2.31 | (58) ? [v0] : (set_intersection2(all_73_0_33, all_0_5_5) = v0 & ! [v1] : ~ (in(v1, v0) = 0))
% 6.71/2.31 |
% 6.71/2.31 | Instantiating (58) with all_118_0_49 yields:
% 6.71/2.31 | (59) set_intersection2(all_73_0_33, all_0_5_5) = all_118_0_49 & ! [v0] : ~ (in(v0, all_118_0_49) = 0)
% 6.71/2.31 |
% 6.71/2.31 | Applying alpha-rule on (59) yields:
% 6.71/2.31 | (60) set_intersection2(all_73_0_33, all_0_5_5) = all_118_0_49
% 6.71/2.31 | (61) ! [v0] : ~ (in(v0, all_118_0_49) = 0)
% 6.71/2.31 |
% 6.71/2.31 | Instantiating formula (17) with all_28_0_22, all_118_0_49, all_0_5_5, all_73_0_33 and discharging atoms set_intersection2(all_73_0_33, all_0_5_5) = all_118_0_49, in(all_28_0_22, all_0_5_5) = 0, yields:
% 6.71/2.31 | (62) ? [v0] : ((v0 = 0 & in(all_28_0_22, all_118_0_49) = 0) | ( ~ (v0 = 0) & in(all_28_0_22, all_73_0_33) = v0))
% 6.71/2.31 |
% 6.71/2.31 | Instantiating (62) with all_142_0_59 yields:
% 6.71/2.31 | (63) (all_142_0_59 = 0 & in(all_28_0_22, all_118_0_49) = 0) | ( ~ (all_142_0_59 = 0) & in(all_28_0_22, all_73_0_33) = all_142_0_59)
% 6.71/2.31 |
% 6.71/2.31 +-Applying beta-rule and splitting (63), into two cases.
% 6.71/2.31 |-Branch one:
% 6.71/2.31 | (64) all_142_0_59 = 0 & in(all_28_0_22, all_118_0_49) = 0
% 6.71/2.31 |
% 7.13/2.31 | Applying alpha-rule on (64) yields:
% 7.13/2.31 | (65) all_142_0_59 = 0
% 7.13/2.31 | (66) in(all_28_0_22, all_118_0_49) = 0
% 7.13/2.31 |
% 7.13/2.31 | Instantiating formula (61) with all_28_0_22 and discharging atoms in(all_28_0_22, all_118_0_49) = 0, yields:
% 7.13/2.31 | (67) $false
% 7.13/2.31 |
% 7.13/2.31 |-The branch is then unsatisfiable
% 7.13/2.31 |-Branch two:
% 7.13/2.31 | (68) ~ (all_142_0_59 = 0) & in(all_28_0_22, all_73_0_33) = all_142_0_59
% 7.13/2.31 |
% 7.13/2.31 | Applying alpha-rule on (68) yields:
% 7.13/2.31 | (69) ~ (all_142_0_59 = 0)
% 7.13/2.31 | (70) in(all_28_0_22, all_73_0_33) = all_142_0_59
% 7.13/2.31 |
% 7.13/2.31 | Instantiating formula (39) with all_28_0_22, all_73_0_33, all_142_0_59, 0 and discharging atoms in(all_28_0_22, all_73_0_33) = all_142_0_59, in(all_28_0_22, all_73_0_33) = 0, yields:
% 7.13/2.31 | (65) all_142_0_59 = 0
% 7.13/2.31 |
% 7.13/2.31 | Equations (65) can reduce 69 to:
% 7.13/2.31 | (44) $false
% 7.13/2.31 |
% 7.13/2.31 |-The branch is then unsatisfiable
% 7.13/2.31 % SZS output end Proof for theBenchmark
% 7.13/2.31
% 7.13/2.31 1708ms
%------------------------------------------------------------------------------