TSTP Solution File: SET917+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET917+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Jul 19 00:23:08 EDT 2022
% Result : Theorem 2.41s 1.30s
% Output : Proof 3.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET917+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 10 12:21:38 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.61/0.60 ____ _
% 0.61/0.60 ___ / __ \_____(_)___ ________ __________
% 0.61/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.60
% 0.61/0.60 A Theorem Prover for First-Order Logic
% 0.61/0.60 (ePrincess v.1.0)
% 0.61/0.60
% 0.61/0.60 (c) Philipp Rümmer, 2009-2015
% 0.61/0.60 (c) Peter Backeman, 2014-2015
% 0.61/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.60 Bug reports to peter@backeman.se
% 0.61/0.60
% 0.61/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.60
% 0.61/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.35/0.91 Prover 0: Preprocessing ...
% 1.62/1.03 Prover 0: Warning: ignoring some quantifiers
% 1.62/1.04 Prover 0: Constructing countermodel ...
% 2.20/1.18 Prover 0: gave up
% 2.20/1.18 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.20/1.20 Prover 1: Preprocessing ...
% 2.41/1.26 Prover 1: Constructing countermodel ...
% 2.41/1.30 Prover 1: proved (117ms)
% 2.41/1.30
% 2.41/1.30 No countermodel exists, formula is valid
% 2.41/1.30 % SZS status Theorem for theBenchmark
% 2.41/1.30
% 2.41/1.30 Generating proof ... found it (size 16)
% 3.13/1.47
% 3.13/1.47 % SZS output start Proof for theBenchmark
% 3.13/1.47 Assumed formulas after preprocessing and simplification:
% 3.13/1.47 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & ~ (v4 = v2) & ~ (v3 = 0) & empty(v7) = 0 & empty(v5) = v6 & singleton(v0) = v2 & disjoint(v2, v1) = v3 & set_intersection2(v2, v1) = v4 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (singleton(v8) = v10) | ~ (set_intersection2(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (singleton(v8) = v10) | ~ (disjoint(v10, v9) = v11) | in(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (disjoint(v11, v10) = v9) | ~ (disjoint(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_intersection2(v11, v10) = v9) | ~ (set_intersection2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (in(v11, v10) = v9) | ~ (in(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (empty(v10) = v9) | ~ (empty(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | set_intersection2(v9, v8) = v10) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_intersection2(v8, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | disjoint(v9, v8) = 0) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)))
% 3.13/1.50 | 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 yields:
% 3.13/1.50 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = all_0_5_5) & ~ (all_0_4_4 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & singleton(all_0_7_7) = all_0_5_5 & disjoint(all_0_5_5, all_0_6_6) = all_0_4_4 & set_intersection2(all_0_5_5, all_0_6_6) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (singleton(v0) = v2) | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (disjoint(v2, v1) = v3) | in(v0, v1) = 0) & ! [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 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 3.28/1.51 |
% 3.28/1.51 | Applying alpha-rule on (1) yields:
% 3.28/1.51 | (2) ~ (all_0_4_4 = 0)
% 3.28/1.51 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 3.28/1.51 | (4) singleton(all_0_7_7) = all_0_5_5
% 3.28/1.51 | (5) empty(all_0_0_0) = 0
% 3.28/1.51 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 3.28/1.51 | (7) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 3.28/1.51 | (8) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 3.28/1.51 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 3.28/1.51 | (10) empty(all_0_2_2) = all_0_1_1
% 3.28/1.51 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (disjoint(v2, v1) = v3) | in(v0, v1) = 0)
% 3.28/1.51 | (12) ~ (all_0_1_1 = 0)
% 3.28/1.51 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 3.28/1.51 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 3.28/1.51 | (15) set_intersection2(all_0_5_5, all_0_6_6) = all_0_3_3
% 3.28/1.51 | (16) disjoint(all_0_5_5, all_0_6_6) = all_0_4_4
% 3.28/1.51 | (17) ~ (all_0_3_3 = all_0_5_5)
% 3.28/1.51 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 3.28/1.51 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (singleton(v0) = v2) | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 3.28/1.51 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 3.28/1.51 |
% 3.28/1.51 | Instantiating formula (11) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms singleton(all_0_7_7) = all_0_5_5, disjoint(all_0_5_5, all_0_6_6) = all_0_4_4, yields:
% 3.28/1.51 | (21) all_0_4_4 = 0 | in(all_0_7_7, all_0_6_6) = 0
% 3.28/1.51 |
% 3.28/1.51 | Instantiating formula (3) with all_0_3_3, all_0_6_6, all_0_5_5 and discharging atoms set_intersection2(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 3.28/1.51 | (22) set_intersection2(all_0_6_6, all_0_5_5) = all_0_3_3
% 3.28/1.52 |
% 3.28/1.52 +-Applying beta-rule and splitting (21), into two cases.
% 3.28/1.52 |-Branch one:
% 3.28/1.52 | (23) in(all_0_7_7, all_0_6_6) = 0
% 3.28/1.52 |
% 3.28/1.52 | Instantiating formula (19) with all_0_3_3, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms singleton(all_0_7_7) = all_0_5_5, set_intersection2(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 3.28/1.52 | (24) all_0_3_3 = all_0_5_5 | ? [v0] : ( ~ (v0 = 0) & in(all_0_7_7, all_0_6_6) = v0)
% 3.28/1.52 |
% 3.28/1.52 +-Applying beta-rule and splitting (24), into two cases.
% 3.28/1.52 |-Branch one:
% 3.28/1.52 | (25) all_0_3_3 = all_0_5_5
% 3.28/1.52 |
% 3.28/1.52 | Equations (25) can reduce 17 to:
% 3.28/1.52 | (26) $false
% 3.28/1.52 |
% 3.28/1.52 |-The branch is then unsatisfiable
% 3.28/1.52 |-Branch two:
% 3.28/1.52 | (17) ~ (all_0_3_3 = all_0_5_5)
% 3.28/1.52 | (28) ? [v0] : ( ~ (v0 = 0) & in(all_0_7_7, all_0_6_6) = v0)
% 3.28/1.52 |
% 3.28/1.52 | Instantiating (28) with all_24_0_9 yields:
% 3.28/1.52 | (29) ~ (all_24_0_9 = 0) & in(all_0_7_7, all_0_6_6) = all_24_0_9
% 3.28/1.52 |
% 3.28/1.52 | Applying alpha-rule on (29) yields:
% 3.28/1.52 | (30) ~ (all_24_0_9 = 0)
% 3.28/1.52 | (31) in(all_0_7_7, all_0_6_6) = all_24_0_9
% 3.28/1.52 |
% 3.28/1.52 | Instantiating formula (13) with all_0_7_7, all_0_6_6, all_24_0_9, 0 and discharging atoms in(all_0_7_7, all_0_6_6) = all_24_0_9, in(all_0_7_7, all_0_6_6) = 0, yields:
% 3.28/1.52 | (32) all_24_0_9 = 0
% 3.28/1.52 |
% 3.28/1.52 | Equations (32) can reduce 30 to:
% 3.28/1.52 | (26) $false
% 3.28/1.52 |
% 3.28/1.52 |-The branch is then unsatisfiable
% 3.28/1.52 |-Branch two:
% 3.28/1.52 | (34) ~ (in(all_0_7_7, all_0_6_6) = 0)
% 3.28/1.52 | (35) all_0_4_4 = 0
% 3.28/1.52 |
% 3.28/1.52 | Equations (35) can reduce 2 to:
% 3.28/1.52 | (26) $false
% 3.28/1.52 |
% 3.28/1.52 |-The branch is then unsatisfiable
% 3.28/1.52 % SZS output end Proof for theBenchmark
% 3.28/1.52
% 3.28/1.52 901ms
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