TSTP Solution File: SEU128+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU128+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 08:46:47 EDT 2022
% Result : Theorem 5.46s 2.00s
% Output : Proof 7.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU128+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n004.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
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 22:20:23 EDT 2022
% 0.12/0.33 % 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
% 0.60/0.59 (ePrincess v.1.0)
% 0.60/0.59
% 0.60/0.59 (c) Philipp Rümmer, 2009-2015
% 0.60/0.59 (c) Peter Backeman, 2014-2015
% 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.59 Bug reports to peter@backeman.se
% 0.60/0.59
% 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.59
% 0.60/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.94 Prover 0: Preprocessing ...
% 1.90/1.17 Prover 0: Warning: ignoring some quantifiers
% 2.16/1.19 Prover 0: Constructing countermodel ...
% 4.20/1.71 Prover 0: gave up
% 4.20/1.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.20/1.76 Prover 1: Preprocessing ...
% 5.09/1.90 Prover 1: Warning: ignoring some quantifiers
% 5.09/1.91 Prover 1: Constructing countermodel ...
% 5.46/2.00 Prover 1: proved (288ms)
% 5.46/2.00
% 5.46/2.00 No countermodel exists, formula is valid
% 5.46/2.00 % SZS status Theorem for theBenchmark
% 5.46/2.00
% 5.46/2.00 Generating proof ... Warning: ignoring some quantifiers
% 6.98/2.39 found it (size 34)
% 6.98/2.39
% 6.98/2.39 % SZS output start Proof for theBenchmark
% 6.98/2.39 Assumed formulas after preprocessing and simplification:
% 6.98/2.39 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & ~ (v4 = 0) & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & subset(v0, v3) = v4 & subset(v0, v2) = 0 & subset(v0, v1) = 0 & set_intersection2(v1, v2) = v3 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v9) = v12) | ~ (set_union2(v8, v10) = v11) | ? [v13] : ? [v14] : (subset(v10, v9) = v14 & subset(v8, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | (v14 = 0 & v12 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ? [v14] : (in(v11, v10) = v14 & in(v11, v9) = v13 & (v14 = 0 | ( ~ (v13 = 0) & ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v8) = v11) | ~ (set_intersection2(v8, v9) = v10)) & ! [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, v10) = v11) | ~ (set_union2(v8, v9) = v10)) & ! [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, v8) = 0) | ? [v12] : ? [v13] : (in(v11, v10) = v13 & in(v11, v9) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_intersection2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)) & (v13 = 0 | (v15 = 0 & v14 = 0)))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_union2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v13 = 0) | ( ~ (v15 = 0) & ~ (v14 = 0))) & (v15 = 0 | v14 = 0 | v13 = 0))) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (set_union2(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(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, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)) & ! [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_union2(v9, v8) = v10) | ? [v11] : ? [v12] : (empty(v10) = v12 & empty(v8) = v11 & ( ~ (v12 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | set_union2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ? [v11] : ? [v12] : (empty(v10) = v12 & empty(v8) = v11 & ( ~ (v12 = 0) | v11 = 0))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (empty(v9) = 0) | ~ (empty(v8) = 0)) & ! [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 = empty_set | ~ (set_intersection2(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] : ( ~ (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] : (v8 = empty_set | ? [v9] : in(v9, v8) = 0))
% 7.42/2.42 | 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:
% 7.42/2.42 | (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_7_7, all_0_4_4) = all_0_3_3 & subset(all_0_7_7, all_0_5_5) = 0 & subset(all_0_7_7, all_0_6_6) = 0 & 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(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) & ! [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)
% 7.42/2.44 |
% 7.42/2.44 | Applying alpha-rule on (1) yields:
% 7.42/2.44 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 7.42/2.44 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 7.42/2.44 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 7.42/2.44 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 7.42/2.44 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 7.42/2.44 | (7) ? [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))))
% 7.42/2.44 | (8) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 7.42/2.44 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 7.42/2.44 | (10) empty(all_0_2_2) = all_0_1_1
% 7.42/2.44 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 7.42/2.44 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 7.42/2.44 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 7.42/2.44 | (14) ! [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))))
% 7.42/2.44 | (15) ! [v0] : ~ (in(v0, empty_set) = 0)
% 7.42/2.44 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 7.42/2.44 | (17) subset(all_0_7_7, all_0_4_4) = all_0_3_3
% 7.42/2.44 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 7.42/2.44 | (19) ! [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)))))
% 7.42/2.44 | (20) ~ (all_0_1_1 = 0)
% 7.42/2.44 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 7.42/2.44 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 7.42/2.44 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 7.42/2.44 | (24) ~ (all_0_3_3 = 0)
% 7.42/2.44 | (25) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 7.42/2.44 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 7.42/2.44 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 7.42/2.44 | (28) ! [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))))
% 7.42/2.44 | (29) subset(all_0_7_7, all_0_6_6) = 0
% 7.42/2.44 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2))
% 7.42/2.45 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2))
% 7.42/2.45 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 7.42/2.45 | (33) set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4
% 7.42/2.45 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 7.42/2.45 | (35) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 7.42/2.45 | (36) ! [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)))
% 7.42/2.45 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 7.42/2.45 | (38) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 7.42/2.45 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 7.42/2.45 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 7.42/2.45 | (41) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 7.42/2.45 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 7.42/2.45 | (43) ? [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)))
% 7.42/2.45 | (44) ! [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)))
% 7.42/2.45 | (45) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 7.42/2.45 | (46) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 7.42/2.45 | (47) empty(empty_set) = 0
% 7.42/2.45 | (48) empty(all_0_0_0) = 0
% 7.42/2.45 | (49) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 7.42/2.45 | (50) subset(all_0_7_7, all_0_5_5) = 0
% 7.42/2.45 | (51) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 7.42/2.45 | (52) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 7.42/2.45 | (53) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 7.42/2.45 | (54) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 7.42/2.45 |
% 7.42/2.45 | Instantiating formula (40) with all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_4_4) = all_0_3_3, yields:
% 7.42/2.45 | (55) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_7_7) = 0)
% 7.42/2.45 |
% 7.42/2.45 | Instantiating formula (42) with 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, yields:
% 7.42/2.45 | (56) set_intersection2(all_0_5_5, all_0_6_6) = all_0_4_4
% 7.42/2.45 |
% 7.42/2.45 +-Applying beta-rule and splitting (55), into two cases.
% 7.42/2.45 |-Branch one:
% 7.42/2.45 | (57) all_0_3_3 = 0
% 7.42/2.45 |
% 7.42/2.45 | Equations (57) can reduce 24 to:
% 7.42/2.45 | (58) $false
% 7.42/2.45 |
% 7.42/2.45 |-The branch is then unsatisfiable
% 7.42/2.45 |-Branch two:
% 7.42/2.45 | (24) ~ (all_0_3_3 = 0)
% 7.42/2.45 | (60) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_7_7) = 0)
% 7.42/2.45 |
% 7.42/2.45 | Instantiating (60) with all_42_0_11, all_42_1_12 yields:
% 7.42/2.45 | (61) ~ (all_42_0_11 = 0) & in(all_42_1_12, all_0_4_4) = all_42_0_11 & in(all_42_1_12, all_0_7_7) = 0
% 7.42/2.46 |
% 7.42/2.46 | Applying alpha-rule on (61) yields:
% 7.42/2.46 | (62) ~ (all_42_0_11 = 0)
% 7.42/2.46 | (63) in(all_42_1_12, all_0_4_4) = all_42_0_11
% 7.42/2.46 | (64) in(all_42_1_12, all_0_7_7) = 0
% 7.42/2.46 |
% 7.42/2.46 | Instantiating formula (27) with all_42_1_12, all_0_5_5, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_5_5) = 0, in(all_42_1_12, all_0_7_7) = 0, yields:
% 7.42/2.46 | (65) in(all_42_1_12, all_0_5_5) = 0
% 7.42/2.46 |
% 7.42/2.46 | Instantiating formula (27) with all_42_1_12, all_0_6_6, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_6_6) = 0, in(all_42_1_12, all_0_7_7) = 0, yields:
% 7.42/2.46 | (66) in(all_42_1_12, all_0_6_6) = 0
% 7.42/2.46 |
% 7.42/2.46 | Instantiating formula (16) with all_42_1_12, all_0_5_5, 0, all_42_0_11 and discharging atoms in(all_42_1_12, all_0_5_5) = 0, yields:
% 7.42/2.46 | (67) all_42_0_11 = 0 | ~ (in(all_42_1_12, all_0_5_5) = all_42_0_11)
% 7.42/2.46 |
% 7.42/2.46 | Instantiating formula (36) with all_42_1_12, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms set_intersection2(all_0_5_5, all_0_6_6) = all_0_4_4, in(all_42_1_12, all_0_5_5) = 0, yields:
% 7.42/2.46 | (68) ? [v0] : ? [v1] : (in(all_42_1_12, all_0_4_4) = v1 & in(all_42_1_12, all_0_6_6) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 7.42/2.46 |
% 7.42/2.46 | Instantiating formula (36) with all_42_1_12, 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_42_1_12, all_0_6_6) = 0, yields:
% 7.42/2.46 | (69) ? [v0] : ? [v1] : (in(all_42_1_12, all_0_4_4) = v1 & in(all_42_1_12, all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 7.42/2.46 |
% 7.42/2.46 | Instantiating (69) with all_120_0_24, all_120_1_25 yields:
% 7.42/2.46 | (70) in(all_42_1_12, all_0_4_4) = all_120_0_24 & in(all_42_1_12, all_0_5_5) = all_120_1_25 & ( ~ (all_120_1_25 = 0) | all_120_0_24 = 0)
% 7.42/2.46 |
% 7.42/2.46 | Applying alpha-rule on (70) yields:
% 7.42/2.46 | (71) in(all_42_1_12, all_0_4_4) = all_120_0_24
% 7.42/2.46 | (72) in(all_42_1_12, all_0_5_5) = all_120_1_25
% 7.42/2.46 | (73) ~ (all_120_1_25 = 0) | all_120_0_24 = 0
% 7.42/2.46 |
% 7.42/2.46 | Instantiating (68) with all_124_0_27, all_124_1_28 yields:
% 7.42/2.46 | (74) in(all_42_1_12, all_0_4_4) = all_124_0_27 & in(all_42_1_12, all_0_6_6) = all_124_1_28 & ( ~ (all_124_1_28 = 0) | all_124_0_27 = 0)
% 7.42/2.46 |
% 7.42/2.46 | Applying alpha-rule on (74) yields:
% 7.42/2.46 | (75) in(all_42_1_12, all_0_4_4) = all_124_0_27
% 7.42/2.46 | (76) in(all_42_1_12, all_0_6_6) = all_124_1_28
% 7.42/2.46 | (77) ~ (all_124_1_28 = 0) | all_124_0_27 = 0
% 7.42/2.46 |
% 7.42/2.46 +-Applying beta-rule and splitting (67), into two cases.
% 7.42/2.46 |-Branch one:
% 7.42/2.46 | (78) ~ (in(all_42_1_12, all_0_5_5) = all_42_0_11)
% 7.42/2.46 |
% 7.42/2.46 | Instantiating formula (16) with all_42_1_12, all_0_4_4, all_124_0_27, all_42_0_11 and discharging atoms in(all_42_1_12, all_0_4_4) = all_124_0_27, in(all_42_1_12, all_0_4_4) = all_42_0_11, yields:
% 7.42/2.46 | (79) all_124_0_27 = all_42_0_11
% 7.42/2.46 |
% 7.42/2.46 | Instantiating formula (16) with all_42_1_12, all_0_5_5, all_120_1_25, 0 and discharging atoms in(all_42_1_12, all_0_5_5) = all_120_1_25, in(all_42_1_12, all_0_5_5) = 0, yields:
% 7.42/2.46 | (80) all_120_1_25 = 0
% 7.42/2.46 |
% 7.42/2.46 | Instantiating formula (16) with all_42_1_12, all_0_6_6, all_124_1_28, 0 and discharging atoms in(all_42_1_12, all_0_6_6) = all_124_1_28, in(all_42_1_12, all_0_6_6) = 0, yields:
% 7.42/2.46 | (81) all_124_1_28 = 0
% 7.42/2.46 |
% 7.42/2.46 | Using (72) and (78) yields:
% 7.42/2.46 | (82) ~ (all_120_1_25 = all_42_0_11)
% 7.42/2.46 |
% 7.42/2.46 | Equations (80) can reduce 82 to:
% 7.42/2.46 | (83) ~ (all_42_0_11 = 0)
% 7.42/2.46 |
% 7.42/2.46 | Simplifying 83 yields:
% 7.42/2.46 | (62) ~ (all_42_0_11 = 0)
% 7.42/2.46 |
% 7.42/2.46 +-Applying beta-rule and splitting (77), into two cases.
% 7.42/2.46 |-Branch one:
% 7.42/2.46 | (85) ~ (all_124_1_28 = 0)
% 7.42/2.46 |
% 7.42/2.46 | Equations (81) can reduce 85 to:
% 7.42/2.46 | (58) $false
% 7.42/2.46 |
% 7.42/2.46 |-The branch is then unsatisfiable
% 7.42/2.46 |-Branch two:
% 7.42/2.46 | (81) all_124_1_28 = 0
% 7.42/2.46 | (88) all_124_0_27 = 0
% 7.42/2.46 |
% 7.42/2.46 | Combining equations (79,88) yields a new equation:
% 7.42/2.46 | (89) all_42_0_11 = 0
% 7.42/2.46 |
% 7.42/2.46 | Simplifying 89 yields:
% 7.42/2.46 | (90) all_42_0_11 = 0
% 7.42/2.46 |
% 7.42/2.46 | Equations (90) can reduce 62 to:
% 7.42/2.46 | (58) $false
% 7.42/2.46 |
% 7.42/2.46 |-The branch is then unsatisfiable
% 7.42/2.46 |-Branch two:
% 7.42/2.46 | (92) in(all_42_1_12, all_0_5_5) = all_42_0_11
% 7.42/2.46 | (90) all_42_0_11 = 0
% 7.42/2.46 |
% 7.42/2.46 | Equations (90) can reduce 62 to:
% 7.42/2.46 | (58) $false
% 7.42/2.46 |
% 7.42/2.46 |-The branch is then unsatisfiable
% 7.42/2.46 % SZS output end Proof for theBenchmark
% 7.42/2.46
% 7.42/2.46 1859ms
%------------------------------------------------------------------------------