TSTP Solution File: LCL658+1.010 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL658+1.010 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.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 09:37:54 EDT 2022
% Result : Theorem 14.25s 4.15s
% Output : Proof 16.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL658+1.010 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n008.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 Jul 3 22:40:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.60/0.58 ____ _
% 0.60/0.58 ___ / __ \_____(_)___ ________ __________
% 0.60/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.58
% 0.60/0.58 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 ...
% 0.60/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.90/1.00 Prover 0: Preprocessing ...
% 2.40/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.56/1.21 Prover 0: Constructing countermodel ...
% 14.25/4.15 Prover 0: proved (3516ms)
% 14.25/4.15
% 14.25/4.15 No countermodel exists, formula is valid
% 14.25/4.15 % SZS status Theorem for theBenchmark
% 14.25/4.15
% 14.25/4.15 Generating proof ... Warning: ignoring some quantifiers
% 15.73/4.58 found it (size 45)
% 15.73/4.58
% 15.73/4.58 % SZS output start Proof for theBenchmark
% 15.73/4.58 Assumed formulas after preprocessing and simplification:
% 15.73/4.58 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (r1(v6, v8) & r1(v6, v7) & r1(v5, v6) & r1(v4, v5) & r1(v3, v4) & r1(v2, v3) & r1(v1, v2) & r1(v0, v1) & ~ p1(v8) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v19) | ? [v20] : (r1(v17, v20) & ~ p1(v20))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v18) | ? [v19] : (r1(v16, v19) & ~ p1(v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v17) | ? [v18] : (r1(v15, v18) & ~ p1(v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ p1(v14) | ~ r1(v14, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v16) | ? [v17] : ? [v18] : ((p1(v17) & r1(v17, v18) & r1(v15, v17) & ~ p1(v18)) | (p1(v17) & r1(v17, v18) & r1(v14, v17) & ~ p1(v18) & ! [v19] : ! [v20] : ! [v21] : ( ~ p1(v20) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v17, v19) | p1(v21) | p1(v19)) & ! [v19] : ! [v20] : ! [v21] : ( ~ p1(v20) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v17, v19) | p1(v21) | ? [v22] : (r1(v19, v22) & ~ p1(v22)))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v16) | ? [v17] : ? [v18] : ((p1(v17) & r1(v17, v18) & r1(v16, v17) & ~ p1(v18)) | (r1(v14, v17) & ~ p1(v17) & ! [v19] : ! [v20] : ( ~ p1(v19) | ~ r1(v19, v20) | ~ r1(v17, v19) | p1(v20))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v15) | ? [v16] : (r1(v13, v16) & ~ p1(v16))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v14) | ? [v16] : ((r1(v15, v16) & ~ p1(v16)) | (r1(v14, v16) & ~ p1(v16) & ! [v17] : ! [v18] : ( ~ p1(v17) | ~ r1(v17, v18) | ~ r1(v16, v17) | p1(v18))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v14) | ? [v15] : (r1(v12, v15) & ~ p1(v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v13) | ? [v14] : (r1(v11, v14) & ~ p1(v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v12) | ? [v13] : (r1(v10, v13) & ~ p1(v13))) & ! [v9] : ! [v10] : ! [v11] : ( ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v11) | ? [v12] : (r1(v9, v12) & ~ p1(v12))) & ! [v9] : ( ~ r1(v7, v9) | p1(v9)) & ! [v9] : ( ~ r1(v6, v9) | p1(v9) | ? [v10] : ? [v11] : (p1(v10) & r1(v10, v11) & r1(v9, v10) & ~ p1(v11))) & ? [v9] : r1(v9, v9))
% 15.84/4.60 | 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 yields:
% 15.84/4.60 | (1) r1(all_0_2_2, all_0_0_0) & r1(all_0_2_2, all_0_1_1) & r1(all_0_3_3, all_0_2_2) & r1(all_0_4_4, all_0_3_3) & r1(all_0_5_5, all_0_4_4) & r1(all_0_6_6, all_0_5_5) & r1(all_0_7_7, all_0_6_6) & r1(all_0_8_8, all_0_7_7) & ~ p1(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v10) | ? [v11] : (r1(v8, v11) & ~ p1(v11))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v9) | ? [v10] : (r1(v7, v10) & ~ p1(v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v8) | ? [v9] : (r1(v6, v9) & ~ p1(v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ p1(v5) | ~ r1(v5, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v7) | ? [v8] : ? [v9] : ((p1(v8) & r1(v8, v9) & r1(v6, v8) & ~ p1(v9)) | (p1(v8) & r1(v8, v9) & r1(v5, v8) & ~ p1(v9) & ! [v10] : ! [v11] : ! [v12] : ( ~ p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8, v10) | p1(v12) | p1(v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8, v10) | p1(v12) | ? [v13] : (r1(v10, v13) & ~ p1(v13)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v7) | ? [v8] : ? [v9] : ((p1(v8) & r1(v8, v9) & r1(v7, v8) & ~ p1(v9)) | (r1(v5, v8) & ~ p1(v8) & ! [v10] : ! [v11] : ( ~ p1(v10) | ~ r1(v10, v11) | ~ r1(v8, v10) | p1(v11))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v6) | ? [v7] : (r1(v4, v7) & ~ p1(v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v5) | ? [v7] : ((r1(v6, v7) & ~ p1(v7)) | (r1(v5, v7) & ~ p1(v7) & ! [v8] : ! [v9] : ( ~ p1(v8) | ~ r1(v8, v9) | ~ r1(v7, v8) | p1(v9))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v5) | ? [v6] : (r1(v3, v6) & ~ p1(v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v4) | ? [v5] : (r1(v2, v5) & ~ p1(v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v3) | ? [v4] : (r1(v1, v4) & ~ p1(v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v2) | ? [v3] : (r1(v0, v3) & ~ p1(v3))) & ! [v0] : ( ~ r1(all_0_1_1, v0) | p1(v0)) & ! [v0] : ( ~ r1(all_0_2_2, v0) | p1(v0) | ? [v1] : ? [v2] : (p1(v1) & r1(v1, v2) & r1(v0, v1) & ~ p1(v2))) & ? [v0] : r1(v0, v0)
% 15.84/4.62 |
% 15.84/4.62 | Applying alpha-rule on (1) yields:
% 15.84/4.62 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v9) | ? [v10] : (r1(v7, v10) & ~ p1(v10)))
% 15.84/4.62 | (3) r1(all_0_4_4, all_0_3_3)
% 15.84/4.62 | (4) r1(all_0_7_7, all_0_6_6)
% 15.84/4.62 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ p1(v5) | ~ r1(v5, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v7) | ? [v8] : ? [v9] : ((p1(v8) & r1(v8, v9) & r1(v6, v8) & ~ p1(v9)) | (p1(v8) & r1(v8, v9) & r1(v5, v8) & ~ p1(v9) & ! [v10] : ! [v11] : ! [v12] : ( ~ p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8, v10) | p1(v12) | p1(v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8, v10) | p1(v12) | ? [v13] : (r1(v10, v13) & ~ p1(v13))))))
% 15.84/4.62 | (6) ~ p1(all_0_0_0)
% 15.84/4.62 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v8) | ? [v9] : (r1(v6, v9) & ~ p1(v9)))
% 15.84/4.62 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v5) | ? [v7] : ((r1(v6, v7) & ~ p1(v7)) | (r1(v5, v7) & ~ p1(v7) & ! [v8] : ! [v9] : ( ~ p1(v8) | ~ r1(v8, v9) | ~ r1(v7, v8) | p1(v9)))))
% 15.84/4.62 | (9) r1(all_0_5_5, all_0_4_4)
% 15.84/4.62 | (10) r1(all_0_6_6, all_0_5_5)
% 15.84/4.62 | (11) r1(all_0_8_8, all_0_7_7)
% 15.84/4.62 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v4) | ? [v5] : (r1(v2, v5) & ~ p1(v5)))
% 15.84/4.62 | (13) r1(all_0_2_2, all_0_0_0)
% 15.84/4.62 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v7) | ? [v8] : ? [v9] : ((p1(v8) & r1(v8, v9) & r1(v7, v8) & ~ p1(v9)) | (r1(v5, v8) & ~ p1(v8) & ! [v10] : ! [v11] : ( ~ p1(v10) | ~ r1(v10, v11) | ~ r1(v8, v10) | p1(v11)))))
% 15.84/4.62 | (15) r1(all_0_2_2, all_0_1_1)
% 15.84/4.62 | (16) ! [v0] : ( ~ r1(all_0_1_1, v0) | p1(v0))
% 15.84/4.62 | (17) ! [v0] : ( ~ r1(all_0_2_2, v0) | p1(v0) | ? [v1] : ? [v2] : (p1(v1) & r1(v1, v2) & r1(v0, v1) & ~ p1(v2)))
% 15.84/4.62 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v10) | ? [v11] : (r1(v8, v11) & ~ p1(v11)))
% 15.84/4.62 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v3) | ? [v4] : (r1(v1, v4) & ~ p1(v4)))
% 15.84/4.62 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v5) | ? [v6] : (r1(v3, v6) & ~ p1(v6)))
% 15.84/4.63 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v6) | ? [v7] : (r1(v4, v7) & ~ p1(v7)))
% 15.84/4.63 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_8_8, v0) | p1(v2) | ? [v3] : (r1(v0, v3) & ~ p1(v3)))
% 15.84/4.63 | (23) ? [v0] : r1(v0, v0)
% 15.84/4.63 | (24) r1(all_0_3_3, all_0_2_2)
% 15.84/4.63 |
% 15.84/4.63 | Instantiating formula (8) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms r1(all_0_2_2, all_0_0_0), r1(all_0_3_3, all_0_2_2), r1(all_0_4_4, all_0_3_3), r1(all_0_5_5, all_0_4_4), r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), yields:
% 15.84/4.63 | (25) p1(all_0_2_2) | ? [v0] : ((r1(all_0_0_0, v0) & ~ p1(v0)) | (r1(all_0_2_2, v0) & ~ p1(v0) & ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | p1(v2))))
% 15.84/4.63 |
% 15.84/4.63 | Instantiating formula (8) with 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 and discharging atoms r1(all_0_2_2, all_0_1_1), r1(all_0_3_3, all_0_2_2), r1(all_0_4_4, all_0_3_3), r1(all_0_5_5, all_0_4_4), r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), yields:
% 15.84/4.63 | (26) p1(all_0_2_2) | ? [v0] : ((r1(all_0_1_1, v0) & ~ p1(v0)) | (r1(all_0_2_2, v0) & ~ p1(v0) & ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | p1(v2))))
% 15.84/4.63 |
% 15.84/4.63 | Instantiating formula (20) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms r1(all_0_3_3, all_0_2_2), r1(all_0_4_4, all_0_3_3), r1(all_0_5_5, all_0_4_4), r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), yields:
% 15.84/4.63 | (27) p1(all_0_2_2) | ? [v0] : (r1(all_0_4_4, v0) & ~ p1(v0))
% 15.84/4.63 |
% 15.84/4.63 +-Applying beta-rule and splitting (27), into two cases.
% 15.84/4.63 |-Branch one:
% 15.84/4.63 | (28) p1(all_0_2_2)
% 15.84/4.63 |
% 15.84/4.63 | Instantiating formula (5) 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 and discharging atoms p1(all_0_2_2), r1(all_0_2_2, all_0_0_0), r1(all_0_2_2, all_0_1_1), r1(all_0_3_3, all_0_2_2), r1(all_0_4_4, all_0_3_3), r1(all_0_5_5, all_0_4_4), r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), ~ p1(all_0_0_0), yields:
% 15.84/4.63 | (29) ? [v0] : ? [v1] : ((p1(v0) & r1(v0, v1) & r1(all_0_1_1, v0) & ~ p1(v1)) | (p1(v0) & r1(v0, v1) & r1(all_0_2_2, v0) & ~ p1(v1) & ! [v2] : ! [v3] : ! [v4] : ( ~ p1(v3) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | p1(v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ p1(v3) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | ? [v5] : (r1(v2, v5) & ~ p1(v5)))))
% 15.84/4.63 |
% 15.84/4.63 | Instantiating (29) with all_57_0_20, all_57_1_21 yields:
% 15.84/4.63 | (30) (p1(all_57_1_21) & r1(all_57_1_21, all_57_0_20) & r1(all_0_1_1, all_57_1_21) & ~ p1(all_57_0_20)) | (p1(all_57_1_21) & r1(all_57_1_21, all_57_0_20) & r1(all_0_2_2, all_57_1_21) & ~ p1(all_57_0_20) & ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_57_1_21, v0) | p1(v2) | p1(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_57_1_21, v0) | p1(v2) | ? [v3] : (r1(v0, v3) & ~ p1(v3))))
% 15.84/4.63 |
% 15.84/4.63 +-Applying beta-rule and splitting (30), into two cases.
% 15.84/4.63 |-Branch one:
% 15.84/4.63 | (31) p1(all_57_1_21) & r1(all_57_1_21, all_57_0_20) & r1(all_0_1_1, all_57_1_21) & ~ p1(all_57_0_20)
% 15.84/4.63 |
% 15.84/4.63 | Applying alpha-rule on (31) yields:
% 15.84/4.63 | (32) p1(all_57_1_21)
% 15.84/4.63 | (33) r1(all_57_1_21, all_57_0_20)
% 15.84/4.63 | (34) r1(all_0_1_1, all_57_1_21)
% 15.84/4.63 | (35) ~ p1(all_57_0_20)
% 15.84/4.63 |
% 15.84/4.63 | Instantiating formula (7) with all_57_0_20, all_57_1_21, 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 and discharging atoms r1(all_57_1_21, all_57_0_20), r1(all_0_1_1, all_57_1_21), r1(all_0_2_2, all_0_1_1), r1(all_0_3_3, all_0_2_2), r1(all_0_4_4, all_0_3_3), r1(all_0_5_5, all_0_4_4), r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), ~ p1(all_57_0_20), yields:
% 15.84/4.63 | (36) ? [v0] : (r1(all_0_1_1, v0) & ~ p1(v0))
% 15.84/4.63 |
% 15.84/4.63 | Instantiating (36) with all_116_0_28 yields:
% 15.84/4.63 | (37) r1(all_0_1_1, all_116_0_28) & ~ p1(all_116_0_28)
% 15.84/4.63 |
% 15.84/4.63 | Applying alpha-rule on (37) yields:
% 15.84/4.63 | (38) r1(all_0_1_1, all_116_0_28)
% 15.84/4.63 | (39) ~ p1(all_116_0_28)
% 15.84/4.63 |
% 15.84/4.63 | Instantiating formula (16) with all_116_0_28 and discharging atoms r1(all_0_1_1, all_116_0_28), ~ p1(all_116_0_28), yields:
% 15.84/4.63 | (40) $false
% 15.84/4.63 |
% 15.84/4.63 |-The branch is then unsatisfiable
% 15.84/4.63 |-Branch two:
% 15.84/4.63 | (41) p1(all_57_1_21) & r1(all_57_1_21, all_57_0_20) & r1(all_0_2_2, all_57_1_21) & ~ p1(all_57_0_20) & ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_57_1_21, v0) | p1(v2) | p1(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_57_1_21, v0) | p1(v2) | ? [v3] : (r1(v0, v3) & ~ p1(v3)))
% 16.10/4.64 |
% 16.10/4.64 | Applying alpha-rule on (41) yields:
% 16.10/4.64 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_57_1_21, v0) | p1(v2) | ? [v3] : (r1(v0, v3) & ~ p1(v3)))
% 16.10/4.64 | (33) r1(all_57_1_21, all_57_0_20)
% 16.10/4.64 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_57_1_21, v0) | p1(v2) | p1(v0))
% 16.10/4.64 | (32) p1(all_57_1_21)
% 16.10/4.64 | (46) r1(all_0_2_2, all_57_1_21)
% 16.10/4.64 | (35) ~ p1(all_57_0_20)
% 16.10/4.64 |
% 16.10/4.64 | Instantiating formula (14) with all_57_0_20, all_57_1_21, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms r1(all_57_1_21, all_57_0_20), r1(all_0_2_2, all_57_1_21), r1(all_0_3_3, all_0_2_2), r1(all_0_4_4, all_0_3_3), r1(all_0_5_5, all_0_4_4), r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), ~ p1(all_57_0_20), yields:
% 16.10/4.64 | (48) ? [v0] : ? [v1] : ((p1(v0) & r1(v0, v1) & r1(all_57_0_20, v0) & ~ p1(v1)) | (r1(all_0_2_2, v0) & ~ p1(v0) & ! [v2] : ! [v3] : ( ~ p1(v2) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v3))))
% 16.10/4.64 |
% 16.10/4.64 | Instantiating (48) with all_118_0_31, all_118_1_32 yields:
% 16.10/4.64 | (49) (p1(all_118_1_32) & r1(all_118_1_32, all_118_0_31) & r1(all_57_0_20, all_118_1_32) & ~ p1(all_118_0_31)) | (r1(all_0_2_2, all_118_1_32) & ~ p1(all_118_1_32) & ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_118_1_32, v0) | p1(v1)))
% 16.10/4.64 |
% 16.10/4.64 +-Applying beta-rule and splitting (49), into two cases.
% 16.10/4.64 |-Branch one:
% 16.10/4.64 | (50) p1(all_118_1_32) & r1(all_118_1_32, all_118_0_31) & r1(all_57_0_20, all_118_1_32) & ~ p1(all_118_0_31)
% 16.10/4.64 |
% 16.10/4.64 | Applying alpha-rule on (50) yields:
% 16.10/4.64 | (51) p1(all_118_1_32)
% 16.10/4.64 | (52) r1(all_118_1_32, all_118_0_31)
% 16.10/4.64 | (53) r1(all_57_0_20, all_118_1_32)
% 16.10/4.64 | (54) ~ p1(all_118_0_31)
% 16.10/4.64 |
% 16.10/4.64 | Instantiating formula (44) with all_118_0_31, all_118_1_32, all_57_0_20 and discharging atoms p1(all_118_1_32), r1(all_118_1_32, all_118_0_31), r1(all_57_0_20, all_118_1_32), r1(all_57_1_21, all_57_0_20), ~ p1(all_118_0_31), ~ p1(all_57_0_20), yields:
% 16.10/4.64 | (40) $false
% 16.10/4.64 |
% 16.10/4.64 |-The branch is then unsatisfiable
% 16.10/4.64 |-Branch two:
% 16.10/4.64 | (56) r1(all_0_2_2, all_118_1_32) & ~ p1(all_118_1_32) & ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_118_1_32, v0) | p1(v1))
% 16.10/4.64 |
% 16.10/4.64 | Applying alpha-rule on (56) yields:
% 16.10/4.64 | (57) r1(all_0_2_2, all_118_1_32)
% 16.10/4.64 | (58) ~ p1(all_118_1_32)
% 16.10/4.64 | (59) ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_118_1_32, v0) | p1(v1))
% 16.10/4.64 |
% 16.10/4.64 | Instantiating formula (17) with all_118_1_32 and discharging atoms r1(all_0_2_2, all_118_1_32), ~ p1(all_118_1_32), yields:
% 16.10/4.64 | (60) ? [v0] : ? [v1] : (p1(v0) & r1(v0, v1) & r1(all_118_1_32, v0) & ~ p1(v1))
% 16.10/4.64 |
% 16.10/4.64 | Instantiating (60) with all_179_0_43, all_179_1_44 yields:
% 16.10/4.64 | (61) p1(all_179_1_44) & r1(all_179_1_44, all_179_0_43) & r1(all_118_1_32, all_179_1_44) & ~ p1(all_179_0_43)
% 16.10/4.64 |
% 16.10/4.64 | Applying alpha-rule on (61) yields:
% 16.10/4.64 | (62) p1(all_179_1_44)
% 16.10/4.64 | (63) r1(all_179_1_44, all_179_0_43)
% 16.10/4.64 | (64) r1(all_118_1_32, all_179_1_44)
% 16.10/4.64 | (65) ~ p1(all_179_0_43)
% 16.10/4.64 |
% 16.10/4.64 | Instantiating formula (59) with all_179_0_43, all_179_1_44 and discharging atoms p1(all_179_1_44), r1(all_179_1_44, all_179_0_43), r1(all_118_1_32, all_179_1_44), ~ p1(all_179_0_43), yields:
% 16.10/4.64 | (40) $false
% 16.10/4.64 |
% 16.10/4.64 |-The branch is then unsatisfiable
% 16.10/4.64 |-Branch two:
% 16.10/4.64 | (67) ~ p1(all_0_2_2)
% 16.10/4.64 | (68) ? [v0] : (r1(all_0_4_4, v0) & ~ p1(v0))
% 16.10/4.64 |
% 16.10/4.64 +-Applying beta-rule and splitting (25), into two cases.
% 16.10/4.64 |-Branch one:
% 16.10/4.64 | (28) p1(all_0_2_2)
% 16.10/4.64 |
% 16.10/4.64 | Using (28) and (67) yields:
% 16.10/4.64 | (40) $false
% 16.10/4.64 |
% 16.10/4.64 |-The branch is then unsatisfiable
% 16.10/4.64 |-Branch two:
% 16.10/4.64 | (67) ~ p1(all_0_2_2)
% 16.10/4.64 | (72) ? [v0] : ((r1(all_0_0_0, v0) & ~ p1(v0)) | (r1(all_0_2_2, v0) & ~ p1(v0) & ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | p1(v2))))
% 16.10/4.64 |
% 16.10/4.64 +-Applying beta-rule and splitting (26), into two cases.
% 16.10/4.64 |-Branch one:
% 16.10/4.64 | (28) p1(all_0_2_2)
% 16.10/4.64 |
% 16.10/4.64 | Using (28) and (67) yields:
% 16.10/4.64 | (40) $false
% 16.10/4.64 |
% 16.10/4.64 |-The branch is then unsatisfiable
% 16.10/4.64 |-Branch two:
% 16.10/4.65 | (67) ~ p1(all_0_2_2)
% 16.10/4.65 | (76) ? [v0] : ((r1(all_0_1_1, v0) & ~ p1(v0)) | (r1(all_0_2_2, v0) & ~ p1(v0) & ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | p1(v2))))
% 16.10/4.65 |
% 16.10/4.65 | Instantiating (76) with all_62_0_56 yields:
% 16.10/4.65 | (77) (r1(all_0_1_1, all_62_0_56) & ~ p1(all_62_0_56)) | (r1(all_0_2_2, all_62_0_56) & ~ p1(all_62_0_56) & ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_62_0_56, v0) | p1(v1)))
% 16.10/4.65 |
% 16.10/4.65 +-Applying beta-rule and splitting (77), into two cases.
% 16.10/4.65 |-Branch one:
% 16.10/4.65 | (78) r1(all_0_1_1, all_62_0_56) & ~ p1(all_62_0_56)
% 16.10/4.65 |
% 16.10/4.65 | Applying alpha-rule on (78) yields:
% 16.10/4.65 | (79) r1(all_0_1_1, all_62_0_56)
% 16.10/4.65 | (80) ~ p1(all_62_0_56)
% 16.10/4.65 |
% 16.10/4.65 | Instantiating formula (16) with all_62_0_56 and discharging atoms r1(all_0_1_1, all_62_0_56), ~ p1(all_62_0_56), yields:
% 16.10/4.65 | (40) $false
% 16.10/4.65 |
% 16.10/4.65 |-The branch is then unsatisfiable
% 16.10/4.65 |-Branch two:
% 16.10/4.65 | (82) r1(all_0_2_2, all_62_0_56) & ~ p1(all_62_0_56) & ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_62_0_56, v0) | p1(v1))
% 16.10/4.65 |
% 16.10/4.65 | Applying alpha-rule on (82) yields:
% 16.10/4.65 | (83) r1(all_0_2_2, all_62_0_56)
% 16.10/4.65 | (80) ~ p1(all_62_0_56)
% 16.10/4.65 | (85) ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_62_0_56, v0) | p1(v1))
% 16.10/4.65 |
% 16.10/4.65 | Instantiating formula (17) with all_62_0_56 and discharging atoms r1(all_0_2_2, all_62_0_56), ~ p1(all_62_0_56), yields:
% 16.10/4.65 | (86) ? [v0] : ? [v1] : (p1(v0) & r1(v0, v1) & r1(all_62_0_56, v0) & ~ p1(v1))
% 16.10/4.65 |
% 16.10/4.65 | Instantiating (86) with all_155_0_66, all_155_1_67 yields:
% 16.10/4.65 | (87) p1(all_155_1_67) & r1(all_155_1_67, all_155_0_66) & r1(all_62_0_56, all_155_1_67) & ~ p1(all_155_0_66)
% 16.10/4.65 |
% 16.10/4.65 | Applying alpha-rule on (87) yields:
% 16.10/4.65 | (88) p1(all_155_1_67)
% 16.10/4.65 | (89) r1(all_155_1_67, all_155_0_66)
% 16.10/4.65 | (90) r1(all_62_0_56, all_155_1_67)
% 16.10/4.65 | (91) ~ p1(all_155_0_66)
% 16.10/4.65 |
% 16.10/4.65 | Instantiating formula (85) with all_155_0_66, all_155_1_67 and discharging atoms p1(all_155_1_67), r1(all_155_1_67, all_155_0_66), r1(all_62_0_56, all_155_1_67), ~ p1(all_155_0_66), yields:
% 16.10/4.65 | (40) $false
% 16.10/4.65 |
% 16.10/4.65 |-The branch is then unsatisfiable
% 16.10/4.65 % SZS output end Proof for theBenchmark
% 16.17/4.65
% 16.17/4.65 4054ms
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