TSTP Solution File: LCL650+1.001 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL650+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 09:37:43 EDT 2022
% Result : Theorem 2.24s 1.14s
% Output : Proof 3.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : LCL650+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.08 % Command : ePrincess-casc -timeout=%d %s
% 0.07/0.28 % Computer : n024.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 600
% 0.07/0.28 % DateTime : Sun Jul 3 10:34:29 EDT 2022
% 0.07/0.28 % CPUTime :
% 0.12/0.48 ____ _
% 0.12/0.48 ___ / __ \_____(_)___ ________ __________
% 0.12/0.48 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.12/0.48 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.12/0.48 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.12/0.48
% 0.12/0.48 A Theorem Prover for First-Order Logic
% 0.12/0.48 (ePrincess v.1.0)
% 0.12/0.48
% 0.12/0.48 (c) Philipp Rümmer, 2009-2015
% 0.12/0.48 (c) Peter Backeman, 2014-2015
% 0.12/0.48 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.12/0.48 Free software under GNU Lesser General Public License (LGPL).
% 0.12/0.48 Bug reports to peter@backeman.se
% 0.12/0.48
% 0.12/0.48 For more information, visit http://user.uu.se/~petba168/breu/
% 0.12/0.48
% 0.12/0.48 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.12/0.53 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.42/0.83 Prover 0: Preprocessing ...
% 1.66/0.96 Prover 0: Constructing countermodel ...
% 2.24/1.13 Prover 0: proved (602ms)
% 2.24/1.14
% 2.24/1.14 No countermodel exists, formula is valid
% 2.24/1.14 % SZS status Theorem for theBenchmark
% 2.24/1.14
% 2.24/1.14 Generating proof ... found it (size 19)
% 3.18/1.35
% 3.18/1.35 % SZS output start Proof for theBenchmark
% 3.18/1.35 Assumed formulas after preprocessing and simplification:
% 3.18/1.35 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (r1(v8, v9) & r1(v7, v8) & r1(v6, v7) & r1(v3, v4) & r1(v2, v3) & r1(v1, v2) & r1(v0, v6) & r1(v0, v5) & r1(v0, v1) & ~ p5(v5) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ p1(v13) | ~ p3(v13) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v0, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ p1(v13) | ~ p2(v13) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v0, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ p3(v13) | ~ p2(v13) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v0, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v0, v10) | p1(v13) | p3(v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v0, v10) | p1(v13) | p2(v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v0, v10) | p3(v13) | p2(v13)) & ! [v10] : ! [v11] : ( ~ r1(v10, v11) | ~ r1(v0, v10) | ? [v12] : (r1(v11, v12) & ~ p3(v12))) & ! [v10] : ( ~ r1(v0, v10) | ? [v11] : (r1(v10, v11) & ~ p4(v11))) & ( ~ p1(v4) | ~ p3(v4) | ~ p2(v4) | ~ p4(v4)) & (p2(v9) | p4(v9) | p6(v9) | p8(v9)))
% 3.18/1.37 | 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:
% 3.18/1.37 | (1) r1(all_0_1_1, 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_6_6, all_0_5_5) & r1(all_0_7_7, all_0_6_6) & r1(all_0_8_8, all_0_7_7) & r1(all_0_9_9, all_0_3_3) & r1(all_0_9_9, all_0_4_4) & r1(all_0_9_9, all_0_8_8) & ~ p5(all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ p1(v3) | ~ p3(v3) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ p1(v3) | ~ p2(v3) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ p3(v3) | ~ p2(v3) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0) | p1(v3) | p3(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0) | p1(v3) | p2(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0) | p3(v3) | p2(v3)) & ! [v0] : ! [v1] : ( ~ r1(v0, v1) | ~ r1(all_0_9_9, v0) | ? [v2] : (r1(v1, v2) & ~ p3(v2))) & ! [v0] : ( ~ r1(all_0_9_9, v0) | ? [v1] : (r1(v0, v1) & ~ p4(v1))) & ( ~ p1(all_0_5_5) | ~ p3(all_0_5_5) | ~ p2(all_0_5_5) | ~ p4(all_0_5_5)) & (p2(all_0_0_0) | p4(all_0_0_0) | p6(all_0_0_0) | p8(all_0_0_0))
% 3.37/1.37 |
% 3.37/1.37 | Applying alpha-rule on (1) yields:
% 3.37/1.37 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0) | p1(v3) | p2(v3))
% 3.37/1.37 | (3) r1(all_0_8_8, all_0_7_7)
% 3.37/1.37 | (4) r1(all_0_2_2, all_0_1_1)
% 3.37/1.37 | (5) r1(all_0_9_9, all_0_4_4)
% 3.37/1.37 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ p1(v3) | ~ p3(v3) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0))
% 3.37/1.37 | (7) r1(all_0_7_7, all_0_6_6)
% 3.37/1.37 | (8) r1(all_0_6_6, all_0_5_5)
% 3.37/1.38 | (9) ! [v0] : ( ~ r1(all_0_9_9, v0) | ? [v1] : (r1(v0, v1) & ~ p4(v1)))
% 3.37/1.38 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0) | p1(v3) | p3(v3))
% 3.37/1.38 | (11) r1(all_0_9_9, all_0_3_3)
% 3.37/1.38 | (12) ~ p5(all_0_4_4)
% 3.37/1.38 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ p1(v3) | ~ p2(v3) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0))
% 3.37/1.38 | (14) r1(all_0_3_3, all_0_2_2)
% 3.37/1.38 | (15) ~ p1(all_0_5_5) | ~ p3(all_0_5_5) | ~ p2(all_0_5_5) | ~ p4(all_0_5_5)
% 3.37/1.38 | (16) r1(all_0_9_9, all_0_8_8)
% 3.37/1.38 | (17) ! [v0] : ! [v1] : ( ~ r1(v0, v1) | ~ r1(all_0_9_9, v0) | ? [v2] : (r1(v1, v2) & ~ p3(v2)))
% 3.37/1.38 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ p3(v3) | ~ p2(v3) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0))
% 3.37/1.38 | (19) p2(all_0_0_0) | p4(all_0_0_0) | p6(all_0_0_0) | p8(all_0_0_0)
% 3.37/1.38 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_9_9, v0) | p3(v3) | p2(v3))
% 3.37/1.38 | (21) r1(all_0_1_1, all_0_0_0)
% 3.37/1.38 |
% 3.37/1.38 | Instantiating formula (10) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms 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), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.38 | (22) p1(all_0_5_5) | p3(all_0_5_5)
% 3.37/1.38 |
% 3.37/1.38 | Instantiating formula (2) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms 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), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.38 | (23) p1(all_0_5_5) | p2(all_0_5_5)
% 3.37/1.38 |
% 3.37/1.38 | Instantiating formula (20) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms 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), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.38 | (24) p3(all_0_5_5) | p2(all_0_5_5)
% 3.37/1.38 |
% 3.37/1.38 +-Applying beta-rule and splitting (15), into two cases.
% 3.37/1.38 |-Branch one:
% 3.37/1.38 | (25) ~ p1(all_0_5_5)
% 3.37/1.38 |
% 3.37/1.38 +-Applying beta-rule and splitting (23), into two cases.
% 3.37/1.38 |-Branch one:
% 3.37/1.38 | (26) p1(all_0_5_5)
% 3.37/1.38 |
% 3.37/1.38 | Using (26) and (25) yields:
% 3.37/1.38 | (27) $false
% 3.37/1.38 |
% 3.37/1.38 |-The branch is then unsatisfiable
% 3.37/1.38 |-Branch two:
% 3.37/1.38 | (25) ~ p1(all_0_5_5)
% 3.37/1.38 | (29) p2(all_0_5_5)
% 3.37/1.38 |
% 3.37/1.38 +-Applying beta-rule and splitting (22), into two cases.
% 3.37/1.38 |-Branch one:
% 3.37/1.38 | (26) p1(all_0_5_5)
% 3.37/1.38 |
% 3.37/1.38 | Using (26) and (25) yields:
% 3.37/1.39 | (27) $false
% 3.37/1.39 |
% 3.37/1.39 |-The branch is then unsatisfiable
% 3.37/1.39 |-Branch two:
% 3.37/1.39 | (25) ~ p1(all_0_5_5)
% 3.37/1.39 | (33) p3(all_0_5_5)
% 3.37/1.39 |
% 3.37/1.39 | Instantiating formula (18) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms p3(all_0_5_5), p2(all_0_5_5), 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), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.39 | (27) $false
% 3.37/1.39 |
% 3.37/1.39 |-The branch is then unsatisfiable
% 3.37/1.39 |-Branch two:
% 3.37/1.39 | (26) p1(all_0_5_5)
% 3.37/1.39 | (36) ~ p3(all_0_5_5) | ~ p2(all_0_5_5) | ~ p4(all_0_5_5)
% 3.37/1.39 |
% 3.37/1.39 +-Applying beta-rule and splitting (24), into two cases.
% 3.37/1.39 |-Branch one:
% 3.37/1.39 | (33) p3(all_0_5_5)
% 3.37/1.39 |
% 3.37/1.39 | Instantiating formula (6) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms p1(all_0_5_5), p3(all_0_5_5), 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), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.39 | (27) $false
% 3.37/1.39 |
% 3.37/1.39 |-The branch is then unsatisfiable
% 3.37/1.39 |-Branch two:
% 3.37/1.39 | (39) ~ p3(all_0_5_5)
% 3.37/1.39 | (29) p2(all_0_5_5)
% 3.37/1.39 |
% 3.37/1.39 | Instantiating formula (13) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms p1(all_0_5_5), p2(all_0_5_5), 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), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.39 | (27) $false
% 3.37/1.39 |
% 3.37/1.39 |-The branch is then unsatisfiable
% 3.37/1.39 % SZS output end Proof for theBenchmark
% 3.37/1.39
% 3.37/1.39 900ms
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