TSTP Solution File: NUN073+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 : Mon Jul 18 16:25:09 EDT 2022
% Result : Theorem 2.37s 1.24s
% Output : Proof 3.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 2 06:36:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.58/0.58 ____ _
% 0.58/0.58 ___ / __ \_____(_)___ ________ __________
% 0.58/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.58
% 0.58/0.58 A Theorem Prover for First-Order Logic
% 0.58/0.59 (ePrincess v.1.0)
% 0.58/0.59
% 0.58/0.59 (c) Philipp Rümmer, 2009-2015
% 0.58/0.59 (c) Peter Backeman, 2014-2015
% 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.59 Bug reports to peter@backeman.se
% 0.58/0.59
% 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.59
% 0.58/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.80/0.98 Prover 0: Preprocessing ...
% 1.98/1.13 Prover 0: Warning: ignoring some quantifiers
% 2.21/1.14 Prover 0: Constructing countermodel ...
% 2.37/1.24 Prover 0: proved (602ms)
% 2.37/1.24
% 2.37/1.24 No countermodel exists, formula is valid
% 2.37/1.24 % SZS status Theorem for theBenchmark
% 2.37/1.24
% 2.37/1.24 Generating proof ... Warning: ignoring some quantifiers
% 3.20/1.44 found it (size 12)
% 3.20/1.44
% 3.20/1.44 % SZS output start Proof for theBenchmark
% 3.20/1.44 Assumed formulas after preprocessing and simplification:
% 3.20/1.44 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (r2(v3, v0) & r2(v2, v1) & r2(v1, v0) & r1(v4) & r1(v3) & r1(v2) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ r2(v6, v7) | ~ r2(v5, v7)) & ! [v5] : ! [v6] : ( ~ r2(v5, v6) | ~ r1(v6)) & ! [v5] : (v5 = v4 | ~ r1(v5)) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (r4(v5, v9, v7) & r4(v5, v6, v8) & r3(v8, v5, v7) & r2(v6, v9)) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (r3(v5, v9, v7) & r3(v5, v6, v8) & r2(v8, v7) & r2(v6, v9)) & ? [v5] : ? [v6] : ? [v7] : ((v7 = v5 & r2(v6, v5)) | (v6 = v5 & r1(v5))) & ? [v5] : ? [v6] : ? [v7] : (r4(v5, v7, v6) & r1(v7) & r1(v6)) & ? [v5] : ? [v6] : ? [v7] : (r4(v5, v6, v7) & ! [v8] : (v8 = v7 | ~ r4(v5, v6, v8))) & ? [v5] : ? [v6] : ? [v7] : (r3(v5, v6, v7) & ! [v8] : (v8 = v7 | ~ r3(v5, v6, v8))) & ? [v5] : ? [v6] : (r3(v5, v6, v5) & r1(v6)) & ? [v5] : ? [v6] : (r2(v5, v6) & ! [v7] : (v7 = v6 | ~ r2(v5, v7))))
% 3.20/1.45 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.20/1.45 | (1) r2(all_0_1_1, all_0_4_4) & r2(all_0_2_2, all_0_3_3) & r2(all_0_3_3, all_0_4_4) & r1(all_0_0_0) & r1(all_0_1_1) & r1(all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ r2(v1, v2) | ~ r2(v0, v2)) & ! [v0] : ! [v1] : ( ~ r2(v0, v1) | ~ r1(v1)) & ! [v0] : (v0 = all_0_0_0 | ~ r1(v0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (r4(v0, v4, v2) & r4(v0, v1, v3) & r3(v3, v0, v2) & r2(v1, v4)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (r3(v0, v4, v2) & r3(v0, v1, v3) & r2(v3, v2) & r2(v1, v4)) & ? [v0] : ? [v1] : ? [v2] : ((v2 = v0 & r2(v1, v0)) | (v1 = v0 & r1(v0))) & ? [v0] : ? [v1] : ? [v2] : (r4(v0, v2, v1) & r1(v2) & r1(v1)) & ? [v0] : ? [v1] : ? [v2] : (r4(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r4(v0, v1, v3))) & ? [v0] : ? [v1] : ? [v2] : (r3(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r3(v0, v1, v3))) & ? [v0] : ? [v1] : (r3(v0, v1, v0) & r1(v1)) & ? [v0] : ? [v1] : (r2(v0, v1) & ! [v2] : (v2 = v1 | ~ r2(v0, v2)))
% 3.20/1.46 |
% 3.20/1.46 | Applying alpha-rule on (1) yields:
% 3.20/1.46 | (2) ? [v0] : ? [v1] : ? [v2] : (r3(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r3(v0, v1, v3)))
% 3.20/1.46 | (3) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (r4(v0, v4, v2) & r4(v0, v1, v3) & r3(v3, v0, v2) & r2(v1, v4))
% 3.20/1.46 | (4) ? [v0] : ? [v1] : ? [v2] : ((v2 = v0 & r2(v1, v0)) | (v1 = v0 & r1(v0)))
% 3.20/1.46 | (5) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (r3(v0, v4, v2) & r3(v0, v1, v3) & r2(v3, v2) & r2(v1, v4))
% 3.20/1.46 | (6) r2(all_0_2_2, all_0_3_3)
% 3.20/1.46 | (7) ! [v0] : (v0 = all_0_0_0 | ~ r1(v0))
% 3.20/1.46 | (8) r2(all_0_3_3, all_0_4_4)
% 3.20/1.46 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ r2(v1, v2) | ~ r2(v0, v2))
% 3.20/1.46 | (10) ? [v0] : ? [v1] : (r3(v0, v1, v0) & r1(v1))
% 3.20/1.46 | (11) r1(all_0_0_0)
% 3.20/1.46 | (12) ? [v0] : ? [v1] : ? [v2] : (r4(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r4(v0, v1, v3)))
% 3.20/1.46 | (13) r2(all_0_1_1, all_0_4_4)
% 3.20/1.46 | (14) ? [v0] : ? [v1] : ? [v2] : (r4(v0, v2, v1) & r1(v2) & r1(v1))
% 3.20/1.46 | (15) ? [v0] : ? [v1] : (r2(v0, v1) & ! [v2] : (v2 = v1 | ~ r2(v0, v2)))
% 3.20/1.46 | (16) r1(all_0_2_2)
% 3.20/1.46 | (17) ! [v0] : ! [v1] : ( ~ r2(v0, v1) | ~ r1(v1))
% 3.20/1.46 | (18) r1(all_0_1_1)
% 3.20/1.46 |
% 3.20/1.46 | Instantiating formula (9) with all_0_4_4, all_0_3_3, all_0_1_1 and discharging atoms r2(all_0_1_1, all_0_4_4), r2(all_0_3_3, all_0_4_4), yields:
% 3.20/1.46 | (19) all_0_1_1 = all_0_3_3
% 3.20/1.46 |
% 3.20/1.46 | Instantiating formula (7) with all_0_1_1 and discharging atoms r1(all_0_1_1), yields:
% 3.20/1.46 | (20) all_0_0_0 = all_0_1_1
% 3.20/1.46 |
% 3.20/1.46 | Instantiating formula (7) with all_0_2_2 and discharging atoms r1(all_0_2_2), yields:
% 3.20/1.46 | (21) all_0_0_0 = all_0_2_2
% 3.20/1.46 |
% 3.20/1.46 | Combining equations (21,20) yields a new equation:
% 3.20/1.46 | (22) all_0_1_1 = all_0_2_2
% 3.20/1.46 |
% 3.20/1.46 | Combining equations (22,19) yields a new equation:
% 3.20/1.46 | (23) all_0_2_2 = all_0_3_3
% 3.20/1.46 |
% 3.20/1.46 | Simplifying 23 yields:
% 3.20/1.46 | (24) all_0_2_2 = all_0_3_3
% 3.20/1.46 |
% 3.20/1.46 | From (24) and (6) follows:
% 3.20/1.47 | (25) r2(all_0_3_3, all_0_3_3)
% 3.20/1.47 |
% 3.20/1.47 | From (24) and (16) follows:
% 3.20/1.47 | (26) r1(all_0_3_3)
% 3.20/1.47 |
% 3.20/1.47 | Instantiating formula (17) with all_0_3_3, all_0_3_3 and discharging atoms r2(all_0_3_3, all_0_3_3), r1(all_0_3_3), yields:
% 3.20/1.47 | (27) $false
% 3.20/1.47 |
% 3.20/1.47 |-The branch is then unsatisfiable
% 3.20/1.47 % SZS output end Proof for theBenchmark
% 3.20/1.47
% 3.20/1.47 871ms
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