TSTP Solution File: SET903+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET903+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 00:23:02 EDT 2022
% Result : Theorem 2.05s 1.20s
% Output : Proof 2.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET903+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 17:48:11 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.63/0.61 ____ _
% 0.63/0.61 ___ / __ \_____(_)___ ________ __________
% 0.63/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.61
% 0.63/0.61 A Theorem Prover for First-Order Logic
% 0.63/0.61 (ePrincess v.1.0)
% 0.63/0.61
% 0.63/0.61 (c) Philipp Rümmer, 2009-2015
% 0.63/0.61 (c) Peter Backeman, 2014-2015
% 0.63/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.61 Bug reports to peter@backeman.se
% 0.63/0.61
% 0.63/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.61
% 0.63/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.36/0.93 Prover 0: Preprocessing ...
% 1.78/1.12 Prover 0: Constructing countermodel ...
% 2.05/1.20 Prover 0: proved (541ms)
% 2.05/1.20
% 2.05/1.20 No countermodel exists, formula is valid
% 2.05/1.20 % SZS status Theorem for theBenchmark
% 2.05/1.20
% 2.05/1.20 Generating proof ... found it (size 14)
% 2.65/1.41
% 2.65/1.41 % SZS output start Proof for theBenchmark
% 2.65/1.41 Assumed formulas after preprocessing and simplification:
% 2.65/1.42 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v2 = v1) & ~ (v2 = empty_set) & ~ (v1 = empty_set) & singleton(v0) = v3 & set_union2(v1, v2) = v3 & empty(v5) & empty(empty_set) & ~ empty(v4) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v9 = v7 | v8 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v9 = v7 | v7 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v9 = v7 | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v8 = empty_set | v7 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v8 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v8 = empty_set | v7 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v7 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (set_union2(v9, v8) = v7) | ~ (set_union2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v7, v6) = v8) | ~ empty(v8) | empty(v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v7, v6) = v8) | set_union2(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | ~ empty(v8) | empty(v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | set_union2(v7, v6) = v8) & ! [v6] : ! [v7] : (v7 = v6 | ~ (set_union2(v6, v6) = v7)))
% 2.65/1.45 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 2.65/1.45 | (1) ~ (all_0_3_3 = all_0_4_4) & ~ (all_0_3_3 = empty_set) & ~ (all_0_4_4 = empty_set) & singleton(all_0_5_5) = all_0_2_2 & set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v2 = empty_set | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v2 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v2 = empty_set | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 2.89/1.46 |
% 2.89/1.46 | Applying alpha-rule on (1) yields:
% 2.89/1.46 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3))
% 2.89/1.46 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 2.89/1.46 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v2 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3))
% 2.89/1.46 | (5) ~ empty(all_0_1_1)
% 2.89/1.46 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 2.89/1.46 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 2.89/1.46 | (8) ~ (all_0_3_3 = all_0_4_4)
% 2.89/1.46 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 2.89/1.46 | (10) ~ (all_0_3_3 = empty_set)
% 2.89/1.46 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3))
% 2.89/1.46 | (12) set_union2(all_0_4_4, all_0_3_3) = all_0_2_2
% 2.89/1.46 | (13) ~ (all_0_4_4 = empty_set)
% 2.89/1.46 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.89/1.46 | (15) empty(empty_set)
% 2.89/1.46 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v2 = empty_set | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3))
% 2.89/1.47 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v2 = empty_set | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3))
% 2.89/1.47 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3))
% 2.89/1.47 | (19) singleton(all_0_5_5) = all_0_2_2
% 2.89/1.47 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3))
% 2.89/1.47 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 2.89/1.47 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 2.89/1.47 | (23) empty(all_0_0_0)
% 2.89/1.47 |
% 2.89/1.47 | Instantiating formula (4) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_2_2, set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 2.89/1.47 | (24) all_0_2_2 = all_0_3_3 | all_0_3_3 = empty_set
% 2.89/1.47 |
% 2.89/1.47 | Instantiating formula (20) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_2_2, set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 2.89/1.47 | (25) all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set
% 2.89/1.47 |
% 2.89/1.47 +-Applying beta-rule and splitting (25), into two cases.
% 2.89/1.47 |-Branch one:
% 2.89/1.47 | (26) all_0_4_4 = empty_set
% 2.89/1.47 |
% 2.89/1.47 | Equations (26) can reduce 13 to:
% 2.89/1.47 | (27) $false
% 2.89/1.47 |
% 2.89/1.47 |-The branch is then unsatisfiable
% 2.89/1.47 |-Branch two:
% 2.89/1.47 | (13) ~ (all_0_4_4 = empty_set)
% 2.89/1.47 | (29) all_0_2_2 = all_0_4_4
% 2.89/1.47 |
% 2.89/1.47 +-Applying beta-rule and splitting (24), into two cases.
% 2.89/1.47 |-Branch one:
% 2.89/1.47 | (30) all_0_3_3 = empty_set
% 2.89/1.47 |
% 2.89/1.47 | Equations (30) can reduce 10 to:
% 2.89/1.47 | (27) $false
% 2.89/1.47 |
% 2.89/1.47 |-The branch is then unsatisfiable
% 2.89/1.47 |-Branch two:
% 2.89/1.47 | (10) ~ (all_0_3_3 = empty_set)
% 2.89/1.47 | (33) all_0_2_2 = all_0_3_3
% 2.89/1.47 |
% 2.89/1.47 | Combining equations (33,29) yields a new equation:
% 2.89/1.47 | (34) all_0_3_3 = all_0_4_4
% 2.89/1.47 |
% 2.89/1.47 | Simplifying 34 yields:
% 2.89/1.47 | (35) all_0_3_3 = all_0_4_4
% 2.89/1.47 |
% 2.89/1.47 | Equations (35) can reduce 8 to:
% 2.89/1.47 | (27) $false
% 2.89/1.47 |
% 2.89/1.47 |-The branch is then unsatisfiable
% 2.89/1.47 % SZS output end Proof for theBenchmark
% 2.89/1.47
% 2.89/1.47 854ms
%------------------------------------------------------------------------------