TSTP Solution File: SET916+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET916+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 00:23:08 EDT 2022
% Result : Theorem 4.94s 1.89s
% Output : Proof 6.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET916+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n012.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 : Mon Jul 11 08:16:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.53/0.57 ____ _
% 0.53/0.57 ___ / __ \_____(_)___ ________ __________
% 0.53/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.57
% 0.53/0.57 A Theorem Prover for First-Order Logic
% 0.53/0.57 (ePrincess v.1.0)
% 0.53/0.57
% 0.53/0.57 (c) Philipp Rümmer, 2009-2015
% 0.53/0.57 (c) Peter Backeman, 2014-2015
% 0.53/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.57 Bug reports to peter@backeman.se
% 0.53/0.57
% 0.53/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.57
% 0.53/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.53/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.89 Prover 0: Preprocessing ...
% 1.75/1.07 Prover 0: Warning: ignoring some quantifiers
% 1.82/1.09 Prover 0: Constructing countermodel ...
% 2.11/1.24 Prover 0: gave up
% 2.11/1.24 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.32/1.26 Prover 1: Preprocessing ...
% 2.67/1.33 Prover 1: Warning: ignoring some quantifiers
% 2.67/1.33 Prover 1: Constructing countermodel ...
% 3.68/1.60 Prover 1: gave up
% 3.68/1.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.68/1.62 Prover 2: Preprocessing ...
% 4.17/1.68 Prover 2: Warning: ignoring some quantifiers
% 4.17/1.69 Prover 2: Constructing countermodel ...
% 4.94/1.89 Prover 2: proved (283ms)
% 4.94/1.89
% 4.94/1.89 No countermodel exists, formula is valid
% 4.94/1.89 % SZS status Theorem for theBenchmark
% 4.94/1.89
% 4.94/1.89 Generating proof ... Warning: ignoring some quantifiers
% 6.33/2.24 found it (size 20)
% 6.33/2.24
% 6.33/2.24 % SZS output start Proof for theBenchmark
% 6.33/2.24 Assumed formulas after preprocessing and simplification:
% 6.33/2.24 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = 0) & ~ (v3 = 0) & disjoint(v5, v1) = v6 & empty(v9) = 0 & empty(v7) = v8 & unordered_pair(v0, v2) = v5 & in(v2, v1) = v4 & in(v0, v1) = v3 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v12) = v14) | ? [v15] : (( ~ (v15 = 0) & in(v13, v11) = v15) | ( ~ (v15 = 0) & in(v13, v10) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v11) = v14) | ? [v15] : ((v15 = 0 & v14 = 0 & in(v13, v10) = 0) | ( ~ (v15 = 0) & in(v13, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ((v15 = 0 & v14 = 0 & in(v13, v11) = 0) | ( ~ (v15 = 0) & in(v13, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | v13 = v10 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v13, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v10, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (disjoint(v13, v12) = v11) | ~ (disjoint(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_intersection2(v13, v12) = v11) | ~ (set_intersection2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v12) = 0) | ? [v14] : ( ~ (v14 = 0) & disjoint(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v12) = 0) | (in(v13, v11) = 0 & in(v13, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v11) = 0) | ? [v14] : ((v14 = 0 & in(v13, v12) = 0) | ( ~ (v14 = 0) & in(v13, v10) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v10) = 0) | ? [v14] : ((v14 = 0 & in(v13, v12) = 0) | ( ~ (v14 = 0) & in(v13, v11) = v14))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_intersection2(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (((v17 = 0 & v16 = 0 & in(v14, v12) = 0 & in(v14, v11) = 0) | (v15 = 0 & in(v14, v10) = 0)) & (( ~ (v17 = 0) & in(v14, v12) = v17) | ( ~ (v16 = 0) & in(v14, v11) = v16) | ( ~ (v15 = 0) & in(v14, v10) = v15)))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (unordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : ((v14 = v12 | v14 = v11 | (v15 = 0 & in(v14, v10) = 0)) & (( ~ (v15 = 0) & in(v14, v10) = v15) | ( ~ (v14 = v12) & ~ (v14 = v11))))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (disjoint(v11, v10) = v12) | ? [v13] : ( ~ (v13 = 0) & disjoint(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (disjoint(v10, v11) = v12) | ? [v13] : ? [v14] : (set_intersection2(v10, v11) = v13 & in(v14, v13) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v11, v10) = v12) | set_intersection2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | set_intersection2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | ? [v13] : ? [v14] : ((v14 = 0 & in(v13, v12) = 0) | (v13 = 0 & disjoint(v10, v11) = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | unordered_pair(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_intersection2(v10, v10) = v11)) & ! [v10] : ! [v11] : ( ~ (disjoint(v10, v11) = 0) | disjoint(v11, v10) = 0) & ! [v10] : ! [v11] : ( ~ (disjoint(v10, v11) = 0) | ? [v12] : (set_intersection2(v10, v11) = v12 & ! [v13] : ~ (in(v13, v12) = 0))) & ! [v10] : ! [v11] : ( ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ? [v10] : ? [v11] : ? [v12] : disjoint(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : set_intersection2(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : unordered_pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : in(v11, v10) = v12 & ? [v10] : ? [v11] : empty(v10) = v11)
% 6.66/2.28 | 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, all_0_8_8, all_0_9_9 yields:
% 6.66/2.28 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & ~ (all_0_5_5 = 0) & ~ (all_0_6_6 = 0) & disjoint(all_0_4_4, all_0_8_8) = all_0_3_3 & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & unordered_pair(all_0_9_9, all_0_7_7) = all_0_4_4 & in(all_0_7_7, all_0_8_8) = all_0_5_5 & in(all_0_9_9, all_0_8_8) = all_0_6_6 & ! [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] : ( ~ (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] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) & ! [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 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(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] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = v2 | v4 = v1 | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [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] : ( ~ (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] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [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] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1
% 6.88/2.29 |
% 6.88/2.29 | Applying alpha-rule on (1) yields:
% 6.88/2.29 | (2) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 6.88/2.29 | (3) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 6.88/2.29 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 6.88/2.29 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 6.88/2.29 | (6) in(all_0_9_9, all_0_8_8) = all_0_6_6
% 6.88/2.29 | (7) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2
% 6.88/2.29 | (8) ! [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)))
% 6.88/2.29 | (9) ~ (all_0_3_3 = 0)
% 6.88/2.29 | (10) ! [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)))
% 6.88/2.29 | (11) ~ (all_0_5_5 = 0)
% 6.88/2.29 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 6.88/2.29 | (13) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = v2 | v4 = v1 | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v4 = v2) & ~ (v4 = v1)))))
% 6.88/2.29 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 6.88/2.30 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 6.88/2.30 | (16) unordered_pair(all_0_9_9, all_0_7_7) = all_0_4_4
% 6.88/2.30 | (17) ~ (all_0_6_6 = 0)
% 6.88/2.30 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 6.88/2.30 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 6.88/2.30 | (20) ~ (all_0_1_1 = 0)
% 6.88/2.30 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 6.88/2.30 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 6.88/2.30 | (23) ! [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)))
% 6.88/2.30 | (24) empty(all_0_0_0) = 0
% 6.88/2.30 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 6.88/2.30 | (26) empty(all_0_2_2) = all_0_1_1
% 6.88/2.30 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 6.88/2.30 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 6.88/2.30 | (29) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2
% 6.88/2.30 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 6.88/2.30 | (31) in(all_0_7_7, all_0_8_8) = all_0_5_5
% 6.88/2.30 | (32) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 6.88/2.30 | (33) disjoint(all_0_4_4, all_0_8_8) = all_0_3_3
% 6.88/2.30 | (34) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 6.88/2.30 | (35) ? [v0] : ? [v1] : empty(v0) = v1
% 6.88/2.30 | (36) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 6.88/2.30 | (37) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 6.88/2.30 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 6.88/2.30 | (39) ! [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)))
% 6.88/2.30 | (40) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 6.88/2.30 | (41) ? [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))))
% 6.88/2.30 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.88/2.30 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 6.88/2.30 | (44) ! [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)))
% 6.88/2.31 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 6.88/2.31 |
% 6.88/2.31 | Instantiating formula (19) with all_0_3_3, all_0_8_8, all_0_4_4 and discharging atoms disjoint(all_0_4_4, all_0_8_8) = all_0_3_3, yields:
% 6.88/2.31 | (46) all_0_3_3 = 0 | ? [v0] : ? [v1] : (set_intersection2(all_0_4_4, all_0_8_8) = v0 & in(v1, v0) = 0)
% 6.88/2.31 |
% 6.88/2.31 +-Applying beta-rule and splitting (46), into two cases.
% 6.88/2.31 |-Branch one:
% 6.88/2.31 | (47) all_0_3_3 = 0
% 6.88/2.31 |
% 6.88/2.31 | Equations (47) can reduce 9 to:
% 6.88/2.31 | (48) $false
% 6.88/2.31 |
% 6.88/2.31 |-The branch is then unsatisfiable
% 6.88/2.31 |-Branch two:
% 6.88/2.31 | (9) ~ (all_0_3_3 = 0)
% 6.88/2.31 | (50) ? [v0] : ? [v1] : (set_intersection2(all_0_4_4, all_0_8_8) = v0 & in(v1, v0) = 0)
% 6.88/2.31 |
% 6.88/2.31 | Instantiating (50) with all_27_0_26, all_27_1_27 yields:
% 6.88/2.31 | (51) set_intersection2(all_0_4_4, all_0_8_8) = all_27_1_27 & in(all_27_0_26, all_27_1_27) = 0
% 6.88/2.31 |
% 6.88/2.31 | Applying alpha-rule on (51) yields:
% 6.88/2.31 | (52) set_intersection2(all_0_4_4, all_0_8_8) = all_27_1_27
% 6.88/2.31 | (53) in(all_27_0_26, all_27_1_27) = 0
% 6.88/2.31 |
% 6.88/2.31 | Instantiating formula (5) with all_27_0_26, all_27_1_27, all_0_8_8, all_0_4_4 and discharging atoms set_intersection2(all_0_4_4, all_0_8_8) = all_27_1_27, in(all_27_0_26, all_27_1_27) = 0, yields:
% 6.88/2.31 | (54) in(all_27_0_26, all_0_4_4) = 0 & in(all_27_0_26, all_0_8_8) = 0
% 6.88/2.31 |
% 6.88/2.31 | Applying alpha-rule on (54) yields:
% 6.88/2.31 | (55) in(all_27_0_26, all_0_4_4) = 0
% 6.88/2.31 | (56) in(all_27_0_26, all_0_8_8) = 0
% 6.88/2.31 |
% 6.88/2.31 | Instantiating formula (14) with all_27_0_26, all_0_4_4, all_0_7_7, all_0_9_9 and discharging atoms unordered_pair(all_0_9_9, all_0_7_7) = all_0_4_4, in(all_27_0_26, all_0_4_4) = 0, yields:
% 6.88/2.31 | (57) all_27_0_26 = all_0_7_7 | all_27_0_26 = all_0_9_9
% 6.88/2.31 |
% 6.88/2.31 +-Applying beta-rule and splitting (57), into two cases.
% 6.88/2.31 |-Branch one:
% 6.88/2.31 | (58) all_27_0_26 = all_0_7_7
% 6.88/2.31 |
% 6.88/2.31 | From (58) and (56) follows:
% 6.88/2.31 | (59) in(all_0_7_7, all_0_8_8) = 0
% 6.88/2.31 |
% 6.88/2.31 | Instantiating formula (42) with all_0_7_7, all_0_8_8, 0, all_0_5_5 and discharging atoms in(all_0_7_7, all_0_8_8) = all_0_5_5, in(all_0_7_7, all_0_8_8) = 0, yields:
% 6.88/2.31 | (60) all_0_5_5 = 0
% 6.88/2.31 |
% 6.88/2.31 | Equations (60) can reduce 11 to:
% 6.88/2.31 | (48) $false
% 6.88/2.31 |
% 6.88/2.31 |-The branch is then unsatisfiable
% 6.88/2.31 |-Branch two:
% 6.88/2.31 | (62) ~ (all_27_0_26 = all_0_7_7)
% 6.88/2.31 | (63) all_27_0_26 = all_0_9_9
% 6.88/2.31 |
% 6.88/2.31 | From (63) and (56) follows:
% 6.88/2.31 | (64) in(all_0_9_9, all_0_8_8) = 0
% 6.88/2.31 |
% 6.88/2.31 | Instantiating formula (42) with all_0_9_9, all_0_8_8, 0, all_0_6_6 and discharging atoms in(all_0_9_9, all_0_8_8) = all_0_6_6, in(all_0_9_9, all_0_8_8) = 0, yields:
% 6.88/2.31 | (65) all_0_6_6 = 0
% 6.88/2.31 |
% 6.88/2.31 | Equations (65) can reduce 17 to:
% 6.88/2.31 | (48) $false
% 6.88/2.31 |
% 6.88/2.31 |-The branch is then unsatisfiable
% 6.88/2.31 % SZS output end Proof for theBenchmark
% 6.88/2.31
% 6.88/2.31 1732ms
%------------------------------------------------------------------------------