TSTP Solution File: MGT053+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT053+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 : Sun Jul 17 22:07:12 EDT 2022
% Result : Theorem 3.06s 1.45s
% Output : Proof 4.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.16 % Problem : MGT053+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.17 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.38 % Computer : n027.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8042.1875MB
% 0.12/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 600
% 0.12/0.38 % DateTime : Thu Jun 9 09:40:27 EDT 2022
% 0.12/0.38 % CPUTime :
% 0.45/0.62 ____ _
% 0.45/0.62 ___ / __ \_____(_)___ ________ __________
% 0.45/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.45/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.45/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.45/0.62
% 0.45/0.62 A Theorem Prover for First-Order Logic
% 0.45/0.62 (ePrincess v.1.0)
% 0.45/0.62
% 0.45/0.62 (c) Philipp Rümmer, 2009-2015
% 0.45/0.62 (c) Peter Backeman, 2014-2015
% 0.45/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.45/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.45/0.62 Bug reports to peter@backeman.se
% 0.45/0.62
% 0.45/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.45/0.62
% 0.45/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.48/0.95 Prover 0: Preprocessing ...
% 1.74/1.06 Prover 0: Warning: ignoring some quantifiers
% 1.84/1.08 Prover 0: Constructing countermodel ...
% 2.48/1.26 Prover 0: gave up
% 2.48/1.26 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.48/1.28 Prover 1: Preprocessing ...
% 2.81/1.38 Prover 1: Constructing countermodel ...
% 3.06/1.45 Prover 1: proved (187ms)
% 3.06/1.45
% 3.06/1.45 No countermodel exists, formula is valid
% 3.06/1.45 % SZS status Theorem for theBenchmark
% 3.06/1.45
% 3.06/1.45 Generating proof ... found it (size 89)
% 3.91/1.71
% 3.91/1.71 % SZS output start Proof for theBenchmark
% 3.91/1.71 Assumed formulas after preprocessing and simplification:
% 3.91/1.71 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (dissimilar(v0, v2, v1) = v4 & dissimilar(v0, v1, v2) = v3 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (dissimilar(v9, v8, v7) = v6) | ~ (dissimilar(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (dissimilar(v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (organization(v5) = v9 & is_aligned(v5, v7) = v11 & is_aligned(v5, v6) = v10 & ( ~ (v9 = 0) | (( ~ (v11 = 0) | v10 = 0) & ( ~ (v10 = 0) | v11 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (greater(v5, v7) = v8) | ~ (greater(v5, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & greater(v6, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (is_aligned(v8, v7) = v6) | ~ (is_aligned(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (greater_or_equal(v8, v7) = v6) | ~ (greater_or_equal(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (greater(v8, v7) = v6) | ~ (greater(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (smaller_or_equal(v8, v7) = v6) | ~ (smaller_or_equal(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (smaller(v8, v7) = v6) | ~ (smaller(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = v5 | ~ (smaller(v5, v6) = v7) | greater(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (greater_or_equal(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & greater(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (smaller_or_equal(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & smaller(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (smaller(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & greater(v6, v5) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (organization(v7) = v6) | ~ (organization(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (dissimilar(v5, v6, v7) = 0) | ? [v8] : ? [v9] : (organization(v5) = 0 & is_aligned(v5, v7) = v9 & is_aligned(v5, v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)) & (v9 = 0 | v8 = 0))) & ! [v5] : ! [v6] : (v6 = v5 | ~ (greater_or_equal(v5, v6) = 0) | greater(v5, v6) = 0) & ! [v5] : ! [v6] : (v6 = v5 | ~ (smaller_or_equal(v5, v6) = 0) | smaller(v5, v6) = 0) & ! [v5] : ! [v6] : (v6 = 0 | ~ (greater_or_equal(v5, v5) = v6)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (smaller_or_equal(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (greater(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & greater(v6, v5) = v7)) & ! [v5] : ! [v6] : ( ~ (smaller(v5, v6) = 0) | greater(v6, v5) = 0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))
% 3.91/1.75 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.91/1.75 | (1) dissimilar(all_0_4_4, all_0_2_2, all_0_3_3) = all_0_0_0 & dissimilar(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (dissimilar(v4, v3, v2) = v1) | ~ (dissimilar(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (dissimilar(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (organization(v0) = v4 & is_aligned(v0, v2) = v6 & is_aligned(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (greater(v0, v2) = v3) | ~ (greater(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & greater(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (is_aligned(v3, v2) = v1) | ~ (is_aligned(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (smaller_or_equal(v3, v2) = v1) | ~ (smaller_or_equal(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (smaller(v3, v2) = v1) | ~ (smaller(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (smaller(v0, v1) = v2) | greater(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (greater_or_equal(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (smaller_or_equal(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & smaller(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (smaller(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (organization(v2) = v1) | ~ (organization(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (dissimilar(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (organization(v0) = 0 & is_aligned(v0, v2) = v4 & is_aligned(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (greater_or_equal(v0, v1) = 0) | greater(v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (smaller_or_equal(v0, v1) = 0) | smaller(v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (greater_or_equal(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (smaller_or_equal(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (greater(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & greater(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (smaller(v0, v1) = 0) | greater(v1, v0) = 0) & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))
% 3.91/1.76 |
% 3.91/1.76 | Applying alpha-rule on (1) yields:
% 3.91/1.76 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (smaller_or_equal(v3, v2) = v1) | ~ (smaller_or_equal(v3, v2) = v0))
% 3.91/1.76 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (greater(v0, v2) = v3) | ~ (greater(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & greater(v1, v2) = v4))
% 3.91/1.76 | (4) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))
% 3.91/1.76 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (dissimilar(v4, v3, v2) = v1) | ~ (dissimilar(v4, v3, v2) = v0))
% 3.91/1.76 | (6) dissimilar(all_0_4_4, all_0_2_2, all_0_3_3) = all_0_0_0
% 3.91/1.76 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (greater_or_equal(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3))
% 3.91/1.76 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) = v0))
% 3.91/1.76 | (9) dissimilar(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1
% 3.91/1.76 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (smaller_or_equal(v0, v1) = 0) | smaller(v0, v1) = 0)
% 3.91/1.76 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (smaller(v3, v2) = v1) | ~ (smaller(v3, v2) = v0))
% 3.91/1.76 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (greater_or_equal(v0, v0) = v1))
% 3.91/1.76 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (smaller(v0, v1) = v2) | greater(v0, v1) = 0)
% 4.20/1.76 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (smaller(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3))
% 4.20/1.76 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (dissimilar(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (organization(v0) = 0 & is_aligned(v0, v2) = v4 & is_aligned(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 4.20/1.76 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (organization(v2) = v1) | ~ (organization(v2) = v0))
% 4.20/1.76 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (dissimilar(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (organization(v0) = v4 & is_aligned(v0, v2) = v6 & is_aligned(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0)))))
% 4.20/1.76 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0))
% 4.20/1.77 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (smaller_or_equal(v0, v0) = v1))
% 4.20/1.77 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (is_aligned(v3, v2) = v1) | ~ (is_aligned(v3, v2) = v0))
% 4.20/1.77 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (greater_or_equal(v0, v1) = 0) | greater(v0, v1) = 0)
% 4.20/1.77 | (22) ! [v0] : ! [v1] : ( ~ (smaller(v0, v1) = 0) | greater(v1, v0) = 0)
% 4.20/1.77 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (smaller_or_equal(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & smaller(v0, v1) = v3))
% 4.20/1.77 | (24) ! [v0] : ! [v1] : ( ~ (greater(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & greater(v1, v0) = v2))
% 4.20/1.77 |
% 4.20/1.77 | Instantiating formula (15) with all_0_3_3, all_0_2_2, all_0_4_4 yields:
% 4.20/1.77 | (25) ~ (dissimilar(all_0_4_4, all_0_2_2, all_0_3_3) = 0) | ? [v0] : ? [v1] : (organization(all_0_4_4) = 0 & is_aligned(all_0_4_4, all_0_2_2) = v0 & is_aligned(all_0_4_4, all_0_3_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)) & (v1 = 0 | v0 = 0))
% 4.20/1.77 |
% 4.20/1.77 | Instantiating formula (17) with all_0_0_0, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms dissimilar(all_0_4_4, all_0_2_2, all_0_3_3) = all_0_0_0, yields:
% 4.20/1.77 | (26) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (organization(all_0_4_4) = v0 & is_aligned(all_0_4_4, all_0_2_2) = v1 & is_aligned(all_0_4_4, all_0_3_3) = v2 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0))))
% 4.20/1.77 |
% 4.20/1.77 | Instantiating formula (15) with all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 4.20/1.77 | (27) ~ (dissimilar(all_0_4_4, all_0_3_3, all_0_2_2) = 0) | ? [v0] : ? [v1] : (organization(all_0_4_4) = 0 & is_aligned(all_0_4_4, all_0_2_2) = v1 & is_aligned(all_0_4_4, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)) & (v1 = 0 | v0 = 0))
% 4.20/1.77 |
% 4.20/1.77 | Instantiating formula (17) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms dissimilar(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 4.20/1.77 | (28) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (organization(all_0_4_4) = v0 & is_aligned(all_0_4_4, all_0_2_2) = v2 & is_aligned(all_0_4_4, all_0_3_3) = v1 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0))))
% 4.20/1.77 |
% 4.20/1.77 +-Applying beta-rule and splitting (4), into two cases.
% 4.20/1.77 |-Branch one:
% 4.20/1.77 | (29) all_0_0_0 = 0 & ~ (all_0_1_1 = 0)
% 4.20/1.77 |
% 4.20/1.77 | Applying alpha-rule on (29) yields:
% 4.20/1.77 | (30) all_0_0_0 = 0
% 4.20/1.77 | (31) ~ (all_0_1_1 = 0)
% 4.20/1.77 |
% 4.20/1.77 | From (30) and (6) follows:
% 4.20/1.77 | (32) dissimilar(all_0_4_4, all_0_2_2, all_0_3_3) = 0
% 4.20/1.77 |
% 4.20/1.77 +-Applying beta-rule and splitting (25), into two cases.
% 4.20/1.77 |-Branch one:
% 4.20/1.77 | (33) ~ (dissimilar(all_0_4_4, all_0_2_2, all_0_3_3) = 0)
% 4.20/1.77 |
% 4.20/1.77 | Using (32) and (33) yields:
% 4.20/1.77 | (34) $false
% 4.20/1.77 |
% 4.20/1.77 |-The branch is then unsatisfiable
% 4.20/1.77 |-Branch two:
% 4.20/1.77 | (32) dissimilar(all_0_4_4, all_0_2_2, all_0_3_3) = 0
% 4.20/1.77 | (36) ? [v0] : ? [v1] : (organization(all_0_4_4) = 0 & is_aligned(all_0_4_4, all_0_2_2) = v0 & is_aligned(all_0_4_4, all_0_3_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)) & (v1 = 0 | v0 = 0))
% 4.20/1.78 |
% 4.20/1.78 | Instantiating (36) with all_14_0_5, all_14_1_6 yields:
% 4.20/1.78 | (37) organization(all_0_4_4) = 0 & is_aligned(all_0_4_4, all_0_2_2) = all_14_1_6 & is_aligned(all_0_4_4, all_0_3_3) = all_14_0_5 & ( ~ (all_14_0_5 = 0) | ~ (all_14_1_6 = 0)) & (all_14_0_5 = 0 | all_14_1_6 = 0)
% 4.20/1.78 |
% 4.20/1.78 | Applying alpha-rule on (37) yields:
% 4.20/1.78 | (38) ~ (all_14_0_5 = 0) | ~ (all_14_1_6 = 0)
% 4.20/1.78 | (39) is_aligned(all_0_4_4, all_0_3_3) = all_14_0_5
% 4.20/1.78 | (40) is_aligned(all_0_4_4, all_0_2_2) = all_14_1_6
% 4.20/1.78 | (41) organization(all_0_4_4) = 0
% 4.20/1.78 | (42) all_14_0_5 = 0 | all_14_1_6 = 0
% 4.20/1.78 |
% 4.20/1.78 +-Applying beta-rule and splitting (28), into two cases.
% 4.20/1.78 |-Branch one:
% 4.20/1.78 | (43) all_0_1_1 = 0
% 4.20/1.78 |
% 4.20/1.78 | Equations (43) can reduce 31 to:
% 4.20/1.78 | (44) $false
% 4.20/1.78 |
% 4.20/1.78 |-The branch is then unsatisfiable
% 4.20/1.78 |-Branch two:
% 4.20/1.78 | (31) ~ (all_0_1_1 = 0)
% 4.20/1.78 | (46) ? [v0] : ? [v1] : ? [v2] : (organization(all_0_4_4) = v0 & is_aligned(all_0_4_4, all_0_2_2) = v2 & is_aligned(all_0_4_4, all_0_3_3) = v1 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0))))
% 4.20/1.78 |
% 4.20/1.78 | Instantiating (46) with all_19_0_7, all_19_1_8, all_19_2_9 yields:
% 4.20/1.78 | (47) organization(all_0_4_4) = all_19_2_9 & is_aligned(all_0_4_4, all_0_2_2) = all_19_0_7 & is_aligned(all_0_4_4, all_0_3_3) = all_19_1_8 & ( ~ (all_19_2_9 = 0) | (( ~ (all_19_0_7 = 0) | all_19_1_8 = 0) & ( ~ (all_19_1_8 = 0) | all_19_0_7 = 0)))
% 4.27/1.78 |
% 4.27/1.78 | Applying alpha-rule on (47) yields:
% 4.27/1.78 | (48) organization(all_0_4_4) = all_19_2_9
% 4.27/1.78 | (49) is_aligned(all_0_4_4, all_0_2_2) = all_19_0_7
% 4.27/1.78 | (50) is_aligned(all_0_4_4, all_0_3_3) = all_19_1_8
% 4.27/1.78 | (51) ~ (all_19_2_9 = 0) | (( ~ (all_19_0_7 = 0) | all_19_1_8 = 0) & ( ~ (all_19_1_8 = 0) | all_19_0_7 = 0))
% 4.27/1.78 |
% 4.27/1.78 | Instantiating formula (16) with all_0_4_4, 0, all_19_2_9 and discharging atoms organization(all_0_4_4) = all_19_2_9, organization(all_0_4_4) = 0, yields:
% 4.27/1.78 | (52) all_19_2_9 = 0
% 4.27/1.78 |
% 4.27/1.78 | Instantiating formula (20) with all_0_4_4, all_0_2_2, all_14_1_6, all_19_0_7 and discharging atoms is_aligned(all_0_4_4, all_0_2_2) = all_19_0_7, is_aligned(all_0_4_4, all_0_2_2) = all_14_1_6, yields:
% 4.27/1.78 | (53) all_19_0_7 = all_14_1_6
% 4.27/1.78 |
% 4.27/1.78 | Instantiating formula (20) with all_0_4_4, all_0_3_3, all_14_0_5, all_19_1_8 and discharging atoms is_aligned(all_0_4_4, all_0_3_3) = all_19_1_8, is_aligned(all_0_4_4, all_0_3_3) = all_14_0_5, yields:
% 4.27/1.78 | (54) all_19_1_8 = all_14_0_5
% 4.27/1.78 |
% 4.27/1.78 +-Applying beta-rule and splitting (38), into two cases.
% 4.27/1.78 |-Branch one:
% 4.27/1.78 | (55) ~ (all_14_0_5 = 0)
% 4.27/1.78 |
% 4.27/1.78 +-Applying beta-rule and splitting (42), into two cases.
% 4.27/1.78 |-Branch one:
% 4.27/1.78 | (56) all_14_0_5 = 0
% 4.27/1.78 |
% 4.27/1.78 | Equations (56) can reduce 55 to:
% 4.27/1.78 | (44) $false
% 4.27/1.78 |
% 4.27/1.78 |-The branch is then unsatisfiable
% 4.27/1.78 |-Branch two:
% 4.27/1.78 | (55) ~ (all_14_0_5 = 0)
% 4.27/1.78 | (59) all_14_1_6 = 0
% 4.27/1.78 |
% 4.27/1.78 | Combining equations (59,53) yields a new equation:
% 4.27/1.78 | (60) all_19_0_7 = 0
% 4.27/1.78 |
% 4.27/1.78 +-Applying beta-rule and splitting (51), into two cases.
% 4.27/1.78 |-Branch one:
% 4.27/1.78 | (61) ~ (all_19_2_9 = 0)
% 4.27/1.78 |
% 4.27/1.78 | Equations (52) can reduce 61 to:
% 4.27/1.78 | (44) $false
% 4.27/1.78 |
% 4.27/1.78 |-The branch is then unsatisfiable
% 4.27/1.78 |-Branch two:
% 4.27/1.78 | (52) all_19_2_9 = 0
% 4.27/1.78 | (64) ( ~ (all_19_0_7 = 0) | all_19_1_8 = 0) & ( ~ (all_19_1_8 = 0) | all_19_0_7 = 0)
% 4.27/1.78 |
% 4.27/1.78 | Applying alpha-rule on (64) yields:
% 4.27/1.78 | (65) ~ (all_19_0_7 = 0) | all_19_1_8 = 0
% 4.27/1.78 | (66) ~ (all_19_1_8 = 0) | all_19_0_7 = 0
% 4.27/1.78 |
% 4.27/1.78 +-Applying beta-rule and splitting (65), into two cases.
% 4.27/1.78 |-Branch one:
% 4.27/1.78 | (67) ~ (all_19_0_7 = 0)
% 4.27/1.78 |
% 4.27/1.78 | Equations (60) can reduce 67 to:
% 4.27/1.78 | (44) $false
% 4.27/1.78 |
% 4.27/1.78 |-The branch is then unsatisfiable
% 4.27/1.78 |-Branch two:
% 4.27/1.78 | (60) all_19_0_7 = 0
% 4.27/1.79 | (70) all_19_1_8 = 0
% 4.27/1.79 |
% 4.27/1.79 | Combining equations (70,54) yields a new equation:
% 4.27/1.79 | (56) all_14_0_5 = 0
% 4.27/1.79 |
% 4.27/1.79 | Equations (56) can reduce 55 to:
% 4.27/1.79 | (44) $false
% 4.27/1.79 |
% 4.27/1.79 |-The branch is then unsatisfiable
% 4.27/1.79 |-Branch two:
% 4.27/1.79 | (56) all_14_0_5 = 0
% 4.27/1.79 | (74) ~ (all_14_1_6 = 0)
% 4.27/1.79 |
% 4.27/1.79 | Combining equations (56,54) yields a new equation:
% 4.27/1.79 | (70) all_19_1_8 = 0
% 4.27/1.79 |
% 4.27/1.79 +-Applying beta-rule and splitting (51), into two cases.
% 4.27/1.79 |-Branch one:
% 4.27/1.79 | (61) ~ (all_19_2_9 = 0)
% 4.27/1.79 |
% 4.27/1.79 | Equations (52) can reduce 61 to:
% 4.27/1.79 | (44) $false
% 4.27/1.79 |
% 4.27/1.79 |-The branch is then unsatisfiable
% 4.27/1.79 |-Branch two:
% 4.27/1.79 | (52) all_19_2_9 = 0
% 4.27/1.79 | (64) ( ~ (all_19_0_7 = 0) | all_19_1_8 = 0) & ( ~ (all_19_1_8 = 0) | all_19_0_7 = 0)
% 4.27/1.79 |
% 4.27/1.79 | Applying alpha-rule on (64) yields:
% 4.27/1.79 | (65) ~ (all_19_0_7 = 0) | all_19_1_8 = 0
% 4.27/1.79 | (66) ~ (all_19_1_8 = 0) | all_19_0_7 = 0
% 4.27/1.79 |
% 4.27/1.79 +-Applying beta-rule and splitting (66), into two cases.
% 4.27/1.79 |-Branch one:
% 4.27/1.79 | (82) ~ (all_19_1_8 = 0)
% 4.27/1.79 |
% 4.27/1.79 | Equations (70) can reduce 82 to:
% 4.27/1.79 | (44) $false
% 4.27/1.79 |
% 4.27/1.79 |-The branch is then unsatisfiable
% 4.27/1.79 |-Branch two:
% 4.27/1.79 | (70) all_19_1_8 = 0
% 4.27/1.79 | (60) all_19_0_7 = 0
% 4.27/1.79 |
% 4.27/1.79 | Combining equations (60,53) yields a new equation:
% 4.27/1.79 | (59) all_14_1_6 = 0
% 4.27/1.79 |
% 4.27/1.79 | Equations (59) can reduce 74 to:
% 4.27/1.79 | (44) $false
% 4.27/1.79 |
% 4.27/1.79 |-The branch is then unsatisfiable
% 4.27/1.79 |-Branch two:
% 4.27/1.79 | (88) all_0_1_1 = 0 & ~ (all_0_0_0 = 0)
% 4.27/1.79 |
% 4.27/1.79 | Applying alpha-rule on (88) yields:
% 4.27/1.79 | (43) all_0_1_1 = 0
% 4.27/1.79 | (90) ~ (all_0_0_0 = 0)
% 4.27/1.79 |
% 4.27/1.79 | From (43) and (9) follows:
% 4.27/1.79 | (91) dissimilar(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 4.27/1.79 |
% 4.27/1.79 +-Applying beta-rule and splitting (27), into two cases.
% 4.27/1.79 |-Branch one:
% 4.27/1.79 | (92) ~ (dissimilar(all_0_4_4, all_0_3_3, all_0_2_2) = 0)
% 4.27/1.79 |
% 4.27/1.79 | Using (91) and (92) yields:
% 4.27/1.79 | (34) $false
% 4.27/1.79 |
% 4.27/1.79 |-The branch is then unsatisfiable
% 4.27/1.79 |-Branch two:
% 4.27/1.79 | (91) dissimilar(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 4.27/1.79 | (95) ? [v0] : ? [v1] : (organization(all_0_4_4) = 0 & is_aligned(all_0_4_4, all_0_2_2) = v1 & is_aligned(all_0_4_4, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)) & (v1 = 0 | v0 = 0))
% 4.27/1.79 |
% 4.27/1.79 | Instantiating (95) with all_14_0_10, all_14_1_11 yields:
% 4.27/1.79 | (96) organization(all_0_4_4) = 0 & is_aligned(all_0_4_4, all_0_2_2) = all_14_0_10 & is_aligned(all_0_4_4, all_0_3_3) = all_14_1_11 & ( ~ (all_14_0_10 = 0) | ~ (all_14_1_11 = 0)) & (all_14_0_10 = 0 | all_14_1_11 = 0)
% 4.27/1.79 |
% 4.27/1.79 | Applying alpha-rule on (96) yields:
% 4.27/1.79 | (97) is_aligned(all_0_4_4, all_0_3_3) = all_14_1_11
% 4.27/1.79 | (98) all_14_0_10 = 0 | all_14_1_11 = 0
% 4.27/1.79 | (99) is_aligned(all_0_4_4, all_0_2_2) = all_14_0_10
% 4.27/1.79 | (100) ~ (all_14_0_10 = 0) | ~ (all_14_1_11 = 0)
% 4.27/1.79 | (41) organization(all_0_4_4) = 0
% 4.27/1.79 |
% 4.27/1.79 +-Applying beta-rule and splitting (26), into two cases.
% 4.27/1.79 |-Branch one:
% 4.27/1.79 | (30) all_0_0_0 = 0
% 4.27/1.79 |
% 4.27/1.79 | Equations (30) can reduce 90 to:
% 4.27/1.79 | (44) $false
% 4.27/1.79 |
% 4.27/1.79 |-The branch is then unsatisfiable
% 4.27/1.79 |-Branch two:
% 4.27/1.79 | (90) ~ (all_0_0_0 = 0)
% 4.27/1.79 | (105) ? [v0] : ? [v1] : ? [v2] : (organization(all_0_4_4) = v0 & is_aligned(all_0_4_4, all_0_2_2) = v1 & is_aligned(all_0_4_4, all_0_3_3) = v2 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0))))
% 4.27/1.79 |
% 4.27/1.79 | Instantiating (105) with all_19_0_12, all_19_1_13, all_19_2_14 yields:
% 4.27/1.79 | (106) organization(all_0_4_4) = all_19_2_14 & is_aligned(all_0_4_4, all_0_2_2) = all_19_1_13 & is_aligned(all_0_4_4, all_0_3_3) = all_19_0_12 & ( ~ (all_19_2_14 = 0) | (( ~ (all_19_0_12 = 0) | all_19_1_13 = 0) & ( ~ (all_19_1_13 = 0) | all_19_0_12 = 0)))
% 4.27/1.80 |
% 4.27/1.80 | Applying alpha-rule on (106) yields:
% 4.27/1.80 | (107) organization(all_0_4_4) = all_19_2_14
% 4.27/1.80 | (108) is_aligned(all_0_4_4, all_0_2_2) = all_19_1_13
% 4.27/1.80 | (109) is_aligned(all_0_4_4, all_0_3_3) = all_19_0_12
% 4.27/1.80 | (110) ~ (all_19_2_14 = 0) | (( ~ (all_19_0_12 = 0) | all_19_1_13 = 0) & ( ~ (all_19_1_13 = 0) | all_19_0_12 = 0))
% 4.27/1.80 |
% 4.27/1.80 | Instantiating formula (16) with all_0_4_4, 0, all_19_2_14 and discharging atoms organization(all_0_4_4) = all_19_2_14, organization(all_0_4_4) = 0, yields:
% 4.27/1.80 | (111) all_19_2_14 = 0
% 4.27/1.80 |
% 4.27/1.80 | Instantiating formula (20) with all_0_4_4, all_0_2_2, all_14_0_10, all_19_1_13 and discharging atoms is_aligned(all_0_4_4, all_0_2_2) = all_19_1_13, is_aligned(all_0_4_4, all_0_2_2) = all_14_0_10, yields:
% 4.27/1.80 | (112) all_19_1_13 = all_14_0_10
% 4.27/1.80 |
% 4.27/1.80 | Instantiating formula (20) with all_0_4_4, all_0_3_3, all_14_1_11, all_19_0_12 and discharging atoms is_aligned(all_0_4_4, all_0_3_3) = all_19_0_12, is_aligned(all_0_4_4, all_0_3_3) = all_14_1_11, yields:
% 4.27/1.80 | (113) all_19_0_12 = all_14_1_11
% 4.27/1.80 |
% 4.27/1.80 +-Applying beta-rule and splitting (100), into two cases.
% 4.27/1.80 |-Branch one:
% 4.27/1.80 | (114) ~ (all_14_0_10 = 0)
% 4.27/1.80 |
% 4.27/1.80 +-Applying beta-rule and splitting (98), into two cases.
% 4.27/1.80 |-Branch one:
% 4.27/1.80 | (115) all_14_0_10 = 0
% 4.27/1.80 |
% 4.27/1.80 | Equations (115) can reduce 114 to:
% 4.27/1.80 | (44) $false
% 4.27/1.80 |
% 4.27/1.80 |-The branch is then unsatisfiable
% 4.27/1.80 |-Branch two:
% 4.27/1.80 | (114) ~ (all_14_0_10 = 0)
% 4.27/1.80 | (118) all_14_1_11 = 0
% 4.27/1.80 |
% 4.27/1.80 | Combining equations (118,113) yields a new equation:
% 4.27/1.80 | (119) all_19_0_12 = 0
% 4.27/1.80 |
% 4.27/1.80 +-Applying beta-rule and splitting (110), into two cases.
% 4.27/1.80 |-Branch one:
% 4.27/1.80 | (120) ~ (all_19_2_14 = 0)
% 4.27/1.80 |
% 4.27/1.80 | Equations (111) can reduce 120 to:
% 4.27/1.80 | (44) $false
% 4.27/1.80 |
% 4.27/1.80 |-The branch is then unsatisfiable
% 4.27/1.80 |-Branch two:
% 4.27/1.80 | (111) all_19_2_14 = 0
% 4.27/1.80 | (123) ( ~ (all_19_0_12 = 0) | all_19_1_13 = 0) & ( ~ (all_19_1_13 = 0) | all_19_0_12 = 0)
% 4.27/1.80 |
% 4.27/1.80 | Applying alpha-rule on (123) yields:
% 4.27/1.80 | (124) ~ (all_19_0_12 = 0) | all_19_1_13 = 0
% 4.27/1.80 | (125) ~ (all_19_1_13 = 0) | all_19_0_12 = 0
% 4.27/1.80 |
% 4.27/1.80 +-Applying beta-rule and splitting (124), into two cases.
% 4.27/1.80 |-Branch one:
% 4.27/1.80 | (126) ~ (all_19_0_12 = 0)
% 4.27/1.80 |
% 4.27/1.80 | Equations (119) can reduce 126 to:
% 4.27/1.80 | (44) $false
% 4.27/1.80 |
% 4.27/1.80 |-The branch is then unsatisfiable
% 4.27/1.80 |-Branch two:
% 4.27/1.80 | (119) all_19_0_12 = 0
% 4.27/1.80 | (129) all_19_1_13 = 0
% 4.27/1.80 |
% 4.27/1.80 | Combining equations (129,112) yields a new equation:
% 4.27/1.80 | (115) all_14_0_10 = 0
% 4.27/1.80 |
% 4.27/1.80 | Equations (115) can reduce 114 to:
% 4.27/1.80 | (44) $false
% 4.27/1.80 |
% 4.27/1.80 |-The branch is then unsatisfiable
% 4.27/1.80 |-Branch two:
% 4.27/1.80 | (115) all_14_0_10 = 0
% 4.27/1.80 | (133) ~ (all_14_1_11 = 0)
% 4.27/1.80 |
% 4.27/1.80 | Combining equations (115,112) yields a new equation:
% 4.27/1.80 | (129) all_19_1_13 = 0
% 4.27/1.80 |
% 4.27/1.80 +-Applying beta-rule and splitting (110), into two cases.
% 4.27/1.80 |-Branch one:
% 4.27/1.80 | (120) ~ (all_19_2_14 = 0)
% 4.27/1.80 |
% 4.27/1.80 | Equations (111) can reduce 120 to:
% 4.27/1.80 | (44) $false
% 4.27/1.80 |
% 4.27/1.80 |-The branch is then unsatisfiable
% 4.27/1.80 |-Branch two:
% 4.27/1.80 | (111) all_19_2_14 = 0
% 4.27/1.80 | (123) ( ~ (all_19_0_12 = 0) | all_19_1_13 = 0) & ( ~ (all_19_1_13 = 0) | all_19_0_12 = 0)
% 4.27/1.80 |
% 4.27/1.80 | Applying alpha-rule on (123) yields:
% 4.27/1.80 | (124) ~ (all_19_0_12 = 0) | all_19_1_13 = 0
% 4.27/1.81 | (125) ~ (all_19_1_13 = 0) | all_19_0_12 = 0
% 4.27/1.81 |
% 4.27/1.81 +-Applying beta-rule and splitting (125), into two cases.
% 4.27/1.81 |-Branch one:
% 4.27/1.81 | (141) ~ (all_19_1_13 = 0)
% 4.27/1.81 |
% 4.27/1.81 | Equations (129) can reduce 141 to:
% 4.27/1.81 | (44) $false
% 4.27/1.81 |
% 4.27/1.81 |-The branch is then unsatisfiable
% 4.27/1.81 |-Branch two:
% 4.27/1.81 | (129) all_19_1_13 = 0
% 4.27/1.81 | (119) all_19_0_12 = 0
% 4.27/1.81 |
% 4.27/1.81 | Combining equations (119,113) yields a new equation:
% 4.27/1.81 | (118) all_14_1_11 = 0
% 4.27/1.81 |
% 4.27/1.81 | Equations (118) can reduce 133 to:
% 4.27/1.81 | (44) $false
% 4.27/1.81 |
% 4.27/1.81 |-The branch is then unsatisfiable
% 4.27/1.81 % SZS output end Proof for theBenchmark
% 4.27/1.81
% 4.27/1.81 1173ms
%------------------------------------------------------------------------------