TSTP Solution File: SEU127+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU127+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 08:46:46 EDT 2022
% Result : Theorem 4.28s 1.70s
% Output : Proof 5.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU127+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jun 19 13:42:14 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.58 (ePrincess v.1.0)
% 0.55/0.58
% 0.55/0.58 (c) Philipp Rümmer, 2009-2015
% 0.55/0.58 (c) Peter Backeman, 2014-2015
% 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.59 Bug reports to peter@backeman.se
% 0.55/0.59
% 0.55/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.59
% 0.55/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.94 Prover 0: Preprocessing ...
% 2.19/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.28/1.20 Prover 0: Constructing countermodel ...
% 3.44/1.49 Prover 0: gave up
% 3.44/1.49 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.44/1.53 Prover 1: Preprocessing ...
% 4.04/1.64 Prover 1: Warning: ignoring some quantifiers
% 4.04/1.65 Prover 1: Constructing countermodel ...
% 4.28/1.70 Prover 1: proved (203ms)
% 4.28/1.70
% 4.28/1.70 No countermodel exists, formula is valid
% 4.28/1.70 % SZS status Theorem for theBenchmark
% 4.28/1.70
% 4.28/1.70 Generating proof ... Warning: ignoring some quantifiers
% 5.41/1.93 found it (size 18)
% 5.41/1.93
% 5.41/1.93 % SZS output start Proof for theBenchmark
% 5.41/1.93 Assumed formulas after preprocessing and simplification:
% 5.41/1.93 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v3 = 0) & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & subset(v2, v0) = v3 & set_intersection2(v0, v1) = v2 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v8) = v11) | ~ (set_union2(v7, v9) = v10) | ? [v12] : ? [v13] : (subset(v9, v8) = v13 & subset(v7, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | (v13 = 0 & v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ? [v13] : (in(v10, v9) = v13 & in(v10, v8) = v12 & (v13 = 0 | ( ~ (v12 = 0) & ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v9) = v10) | ~ (subset(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v9) = v10) | ~ (set_union2(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (disjoint(v10, v9) = v8) | ~ (disjoint(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(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 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(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, v7) = 0) | ? [v11] : ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)) & (v12 = 0 | (v14 = 0 & v13 = 0)))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_union2(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v12 = 0) | ( ~ (v14 = 0) & ~ (v13 = 0))) & (v14 = 0 | v13 = 0 | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(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] : (v9 = 0 | ~ (disjoint(v7, v8) = v9) | ? [v10] : ( ~ (v10 = empty_set) & set_intersection2(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (disjoint(v7, v8) = v9) | ? [v10] : (in(v10, v8) = 0 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (disjoint(v7, v8) = 0) | ~ (in(v9, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (in(v9, v7) = 0) | in(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | set_intersection2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | ? [v10] : ? [v11] : (empty(v9) = v11 & empty(v7) = v10 & ( ~ (v11 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ? [v10] : ? [v11] : (empty(v9) = v11 & empty(v7) = v10 & ( ~ (v11 = 0) | v10 = 0))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (empty(v8) = 0) | ~ (empty(v7) = 0)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (subset(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & subset(v8, v7) = v9)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_intersection2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (set_intersection2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(empty_set, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (disjoint(v7, v8) = 0) | disjoint(v8, v7) = 0) & ! [v7] : ! [v8] : ( ~ (disjoint(v7, v8) = 0) | set_intersection2(v7, v8) = empty_set) & ! [v7] : ! [v8] : ( ~ (disjoint(v7, v8) = 0) | ? [v9] : (set_intersection2(v7, v8) = v9 & ! [v10] : ~ (in(v10, v9) = 0))) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ! [v7] : (v7 = empty_set | ~ (empty(v7) = 0)) & ! [v7] : (v7 = empty_set | ~ (subset(v7, empty_set) = 0)) & ! [v7] : ~ (in(v7, empty_set) = 0) & ? [v7] : (v7 = empty_set | ? [v8] : in(v8, v7) = 0))
% 5.71/1.97 | 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:
% 5.71/1.97 | (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 & set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [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, v2) = v3) | ~ (set_union2(v0, v1) = v2)) & ! [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, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(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, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [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_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [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 = empty_set | ~ (set_intersection2(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] : ( ~ (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] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 5.71/1.99 |
% 5.71/1.99 | Applying alpha-rule on (1) yields:
% 5.71/1.99 | (2) ~ (all_0_1_1 = 0)
% 5.71/1.99 | (3) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 5.71/1.99 | (4) empty(all_0_0_0) = 0
% 5.71/1.99 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 5.71/1.99 | (6) ! [v0] : ~ (in(v0, empty_set) = 0)
% 5.71/1.99 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 5.71/1.99 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 5.71/1.99 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 5.71/1.99 | (10) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 5.71/1.99 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0)))))
% 5.71/1.99 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 5.71/1.99 | (13) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 5.71/1.99 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 5.71/1.99 | (15) subset(all_0_4_4, all_0_6_6) = all_0_3_3
% 5.71/1.99 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 5.71/1.99 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 5.71/1.99 | (18) ~ (all_0_3_3 = 0)
% 5.71/1.99 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2))
% 5.71/1.99 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 5.71/1.99 | (21) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 5.71/2.00 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 5.71/2.00 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 5.71/2.00 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 5.71/2.00 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 5.71/2.00 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 5.71/2.00 | (27) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 5.71/2.00 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 5.71/2.00 | (29) set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4
% 5.71/2.00 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 5.71/2.00 | (31) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 5.71/2.00 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 5.71/2.00 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 5.71/2.00 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 5.71/2.00 | (35) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 5.71/2.00 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 5.71/2.00 | (37) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 5.71/2.00 | (38) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 5.71/2.00 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 5.71/2.00 | (40) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 5.71/2.00 | (41) empty(all_0_2_2) = all_0_1_1
% 5.71/2.00 | (42) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 5.71/2.00 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 5.71/2.00 | (44) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 5.71/2.00 | (45) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 5.71/2.00 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 5.71/2.00 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 5.71/2.01 | (48) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 5.71/2.01 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 5.71/2.01 | (50) empty(empty_set) = 0
% 5.71/2.01 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 5.71/2.01 |
% 5.71/2.01 | Instantiating formula (17) 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:
% 5.71/2.01 | (52) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1)
% 5.71/2.01 |
% 5.71/2.01 +-Applying beta-rule and splitting (52), into two cases.
% 5.71/2.01 |-Branch one:
% 5.71/2.01 | (53) all_0_3_3 = 0
% 5.71/2.01 |
% 5.71/2.01 | Equations (53) can reduce 18 to:
% 5.71/2.01 | (54) $false
% 5.71/2.01 |
% 5.71/2.01 |-The branch is then unsatisfiable
% 5.71/2.01 |-Branch two:
% 5.71/2.01 | (18) ~ (all_0_3_3 = 0)
% 5.71/2.01 | (56) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1)
% 5.71/2.01 |
% 5.71/2.01 | Instantiating (56) with all_46_0_10, all_46_1_11 yields:
% 5.71/2.01 | (57) ~ (all_46_0_10 = 0) & in(all_46_1_11, all_0_4_4) = 0 & in(all_46_1_11, all_0_6_6) = all_46_0_10
% 5.71/2.01 |
% 5.71/2.01 | Applying alpha-rule on (57) yields:
% 5.71/2.01 | (58) ~ (all_46_0_10 = 0)
% 5.71/2.01 | (59) in(all_46_1_11, all_0_4_4) = 0
% 5.71/2.01 | (60) in(all_46_1_11, all_0_6_6) = all_46_0_10
% 5.71/2.01 |
% 5.71/2.01 | Instantiating formula (33) with all_46_0_10, all_46_1_11, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4, in(all_46_1_11, all_0_6_6) = all_46_0_10, yields:
% 5.71/2.01 | (61) ? [v0] : ? [v1] : (in(all_46_1_11, all_0_4_4) = v0 & in(all_46_1_11, all_0_5_5) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_46_0_10 = 0)))
% 5.71/2.01 |
% 5.71/2.01 | Instantiating (61) with all_53_0_12, all_53_1_13 yields:
% 5.71/2.01 | (62) in(all_46_1_11, all_0_4_4) = all_53_1_13 & in(all_46_1_11, all_0_5_5) = all_53_0_12 & ( ~ (all_53_1_13 = 0) | (all_53_0_12 = 0 & all_46_0_10 = 0))
% 5.71/2.01 |
% 5.71/2.01 | Applying alpha-rule on (62) yields:
% 5.71/2.01 | (63) in(all_46_1_11, all_0_4_4) = all_53_1_13
% 5.71/2.01 | (64) in(all_46_1_11, all_0_5_5) = all_53_0_12
% 5.71/2.01 | (65) ~ (all_53_1_13 = 0) | (all_53_0_12 = 0 & all_46_0_10 = 0)
% 5.71/2.01 |
% 5.71/2.01 +-Applying beta-rule and splitting (65), into two cases.
% 5.71/2.01 |-Branch one:
% 5.71/2.01 | (66) ~ (all_53_1_13 = 0)
% 5.71/2.01 |
% 5.71/2.01 | Instantiating formula (22) with all_46_1_11, all_0_4_4, all_53_1_13, 0 and discharging atoms in(all_46_1_11, all_0_4_4) = all_53_1_13, in(all_46_1_11, all_0_4_4) = 0, yields:
% 5.71/2.01 | (67) all_53_1_13 = 0
% 5.71/2.01 |
% 5.71/2.01 | Equations (67) can reduce 66 to:
% 5.71/2.01 | (54) $false
% 5.71/2.01 |
% 5.71/2.01 |-The branch is then unsatisfiable
% 5.71/2.01 |-Branch two:
% 5.71/2.01 | (67) all_53_1_13 = 0
% 5.71/2.01 | (70) all_53_0_12 = 0 & all_46_0_10 = 0
% 5.71/2.01 |
% 5.71/2.01 | Applying alpha-rule on (70) yields:
% 5.71/2.01 | (71) all_53_0_12 = 0
% 5.71/2.01 | (72) all_46_0_10 = 0
% 5.71/2.01 |
% 5.71/2.01 | Equations (72) can reduce 58 to:
% 5.71/2.01 | (54) $false
% 5.71/2.01 |
% 5.71/2.01 |-The branch is then unsatisfiable
% 5.71/2.01 % SZS output end Proof for theBenchmark
% 5.71/2.01
% 5.71/2.01 1419ms
%------------------------------------------------------------------------------