TSTP Solution File: SET931+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 00:23:16 EDT 2022
% Result : Theorem 3.57s 1.52s
% Output : Proof 4.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 21:43:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.58 (ePrincess v.1.0)
% 0.55/0.58
% 0.55/0.58 (c) Philipp Rümmer, 2009-2015
% 0.55/0.58 (c) Peter Backeman, 2014-2015
% 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58 Bug reports to peter@backeman.se
% 0.55/0.58
% 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58
% 0.55/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.61/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.33/0.87 Prover 0: Preprocessing ...
% 1.71/1.03 Prover 0: Warning: ignoring some quantifiers
% 1.71/1.04 Prover 0: Constructing countermodel ...
% 3.02/1.42 Prover 0: gave up
% 3.02/1.42 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.02/1.44 Prover 1: Preprocessing ...
% 3.45/1.48 Prover 1: Constructing countermodel ...
% 3.57/1.52 Prover 1: proved (100ms)
% 3.57/1.52
% 3.57/1.52 No countermodel exists, formula is valid
% 3.57/1.52 % SZS status Theorem for theBenchmark
% 3.57/1.52
% 3.57/1.52 Generating proof ... found it (size 66)
% 4.30/1.75
% 4.30/1.75 % SZS output start Proof for theBenchmark
% 4.30/1.75 Assumed formulas after preprocessing and simplification:
% 4.30/1.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v8 = 0) & set_difference(v0, v3) = v4 & empty(v9) = 0 & empty(v7) = v8 & empty(empty_set) = 0 & singleton(v2) = v6 & singleton(v1) = v5 & unordered_pair(v1, v2) = v3 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v10, v13) = v14) | ~ (unordered_pair(v11, v12) = v13) | ? [v15] : ? [v16] : ( ~ (v16 = v10) & ~ (v15 = v10) & singleton(v12) = v16 & singleton(v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | v10 = empty_set | ~ (subset(v10, v13) = 0) | ~ (unordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : (singleton(v12) = v15 & singleton(v11) = v14 & (v15 = v10 | v14 = v10))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v10, v10) = v13) | ~ (unordered_pair(v11, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(empty_set, v12) = v13) | ~ (unordered_pair(v10, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_difference(v13, v12) = v11) | ~ (set_difference(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset(v13, v12) = v11) | ~ (subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_difference(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v10) = v11)) & ! [v10] : ! [v11] : ( ~ (set_difference(v10, v11) = empty_set) | subset(v10, v11) = 0) & ((v4 = empty_set & ~ (v6 = v0) & ~ (v5 = v0) & ~ (v3 = v0) & ~ (v0 = empty_set)) | ( ~ (v4 = empty_set) & (v6 = v0 | v5 = v0 | v3 = v0 | v0 = empty_set))))
% 4.78/1.78 | 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:
% 4.78/1.78 | (1) ~ (all_0_1_1 = 0) & set_difference(all_0_9_9, all_0_6_6) = all_0_5_5 & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & singleton(all_0_7_7) = all_0_3_3 & singleton(all_0_8_8) = all_0_4_4 & unordered_pair(all_0_8_8, all_0_7_7) = all_0_6_6 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (unordered_pair(v1, v2) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = v0) & ~ (v5 = v0) & singleton(v2) = v6 & singleton(v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = empty_set | ~ (subset(v0, v3) = 0) | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (singleton(v2) = v5 & singleton(v1) = v4 & (v5 = v0 | v4 = v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v0) = v3) | ~ (unordered_pair(v1, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(empty_set, v2) = v3) | ~ (unordered_pair(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [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] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ((all_0_5_5 = empty_set & ~ (all_0_3_3 = all_0_9_9) & ~ (all_0_4_4 = all_0_9_9) & ~ (all_0_6_6 = all_0_9_9) & ~ (all_0_9_9 = empty_set)) | ( ~ (all_0_5_5 = empty_set) & (all_0_3_3 = all_0_9_9 | all_0_4_4 = all_0_9_9 | all_0_6_6 = all_0_9_9 | all_0_9_9 = empty_set)))
% 4.78/1.79 |
% 4.78/1.79 | Applying alpha-rule on (1) yields:
% 4.78/1.79 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 4.78/1.79 | (3) ~ (all_0_1_1 = 0)
% 4.78/1.79 | (4) singleton(all_0_7_7) = all_0_3_3
% 4.78/1.79 | (5) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 4.78/1.79 | (6) set_difference(all_0_9_9, all_0_6_6) = all_0_5_5
% 4.78/1.79 | (7) singleton(all_0_8_8) = all_0_4_4
% 4.78/1.79 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 4.78/1.79 | (9) unordered_pair(all_0_8_8, all_0_7_7) = all_0_6_6
% 4.78/1.79 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 4.78/1.79 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 4.78/1.79 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 4.78/1.80 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = empty_set | ~ (subset(v0, v3) = 0) | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (singleton(v2) = v5 & singleton(v1) = v4 & (v5 = v0 | v4 = v0)))
% 4.86/1.80 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (unordered_pair(v1, v2) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = v0) & ~ (v5 = v0) & singleton(v2) = v6 & singleton(v1) = v5))
% 4.86/1.80 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 4.86/1.80 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 4.86/1.80 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(empty_set, v2) = v3) | ~ (unordered_pair(v0, v1) = v2))
% 4.86/1.80 | (18) empty(empty_set) = 0
% 4.86/1.80 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 4.86/1.80 | (20) empty(all_0_2_2) = all_0_1_1
% 4.86/1.80 | (21) empty(all_0_0_0) = 0
% 4.86/1.80 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v0) = v3) | ~ (unordered_pair(v1, v2) = v0))
% 4.86/1.80 | (23) (all_0_5_5 = empty_set & ~ (all_0_3_3 = all_0_9_9) & ~ (all_0_4_4 = all_0_9_9) & ~ (all_0_6_6 = all_0_9_9) & ~ (all_0_9_9 = empty_set)) | ( ~ (all_0_5_5 = empty_set) & (all_0_3_3 = all_0_9_9 | all_0_4_4 = all_0_9_9 | all_0_6_6 = all_0_9_9 | all_0_9_9 = empty_set))
% 4.86/1.80 |
% 4.86/1.80 | Instantiating formula (5) with all_0_6_6, all_0_9_9 yields:
% 4.86/1.80 | (24) ~ (set_difference(all_0_9_9, all_0_6_6) = empty_set) | subset(all_0_9_9, all_0_6_6) = 0
% 4.86/1.80 |
% 4.86/1.80 | Instantiating formula (12) with all_0_5_5, all_0_6_6, all_0_9_9 and discharging atoms set_difference(all_0_9_9, all_0_6_6) = all_0_5_5, yields:
% 4.86/1.80 | (25) all_0_5_5 = empty_set | ? [v0] : ( ~ (v0 = 0) & subset(all_0_9_9, all_0_6_6) = v0)
% 4.86/1.80 |
% 4.86/1.80 +-Applying beta-rule and splitting (23), into two cases.
% 4.86/1.80 |-Branch one:
% 4.86/1.80 | (26) all_0_5_5 = empty_set & ~ (all_0_3_3 = all_0_9_9) & ~ (all_0_4_4 = all_0_9_9) & ~ (all_0_6_6 = all_0_9_9) & ~ (all_0_9_9 = empty_set)
% 4.86/1.80 |
% 4.86/1.80 | Applying alpha-rule on (26) yields:
% 4.86/1.80 | (27) ~ (all_0_6_6 = all_0_9_9)
% 4.86/1.80 | (28) ~ (all_0_4_4 = all_0_9_9)
% 4.86/1.80 | (29) ~ (all_0_3_3 = all_0_9_9)
% 4.86/1.80 | (30) ~ (all_0_9_9 = empty_set)
% 4.86/1.80 | (31) all_0_5_5 = empty_set
% 4.86/1.80 |
% 4.86/1.80 | From (31) and (6) follows:
% 4.86/1.80 | (32) set_difference(all_0_9_9, all_0_6_6) = empty_set
% 4.86/1.80 |
% 4.86/1.80 +-Applying beta-rule and splitting (24), into two cases.
% 4.86/1.80 |-Branch one:
% 4.86/1.80 | (33) ~ (set_difference(all_0_9_9, all_0_6_6) = empty_set)
% 4.86/1.80 |
% 4.86/1.80 | Using (32) and (33) yields:
% 4.86/1.80 | (34) $false
% 4.86/1.80 |
% 4.86/1.80 |-The branch is then unsatisfiable
% 4.86/1.80 |-Branch two:
% 4.86/1.80 | (32) set_difference(all_0_9_9, all_0_6_6) = empty_set
% 4.86/1.80 | (36) subset(all_0_9_9, all_0_6_6) = 0
% 4.86/1.80 |
% 4.86/1.80 | Instantiating formula (13) with all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_6_6) = 0, unordered_pair(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 4.86/1.81 | (37) all_0_6_6 = all_0_9_9 | all_0_9_9 = empty_set | ? [v0] : ? [v1] : (singleton(all_0_7_7) = v1 & singleton(all_0_8_8) = v0 & (v1 = all_0_9_9 | v0 = all_0_9_9))
% 4.86/1.81 |
% 4.86/1.81 +-Applying beta-rule and splitting (37), into two cases.
% 4.86/1.81 |-Branch one:
% 4.86/1.81 | (38) all_0_9_9 = empty_set
% 4.86/1.81 |
% 4.86/1.81 | Equations (38) can reduce 30 to:
% 4.86/1.81 | (39) $false
% 4.86/1.81 |
% 4.86/1.81 |-The branch is then unsatisfiable
% 4.86/1.81 |-Branch two:
% 4.86/1.81 | (30) ~ (all_0_9_9 = empty_set)
% 4.86/1.81 | (41) all_0_6_6 = all_0_9_9 | ? [v0] : ? [v1] : (singleton(all_0_7_7) = v1 & singleton(all_0_8_8) = v0 & (v1 = all_0_9_9 | v0 = all_0_9_9))
% 4.86/1.81 |
% 4.86/1.81 +-Applying beta-rule and splitting (41), into two cases.
% 4.86/1.81 |-Branch one:
% 4.86/1.81 | (42) all_0_6_6 = all_0_9_9
% 4.86/1.81 |
% 4.86/1.81 | Equations (42) can reduce 27 to:
% 4.86/1.81 | (39) $false
% 4.86/1.81 |
% 4.86/1.81 |-The branch is then unsatisfiable
% 4.86/1.81 |-Branch two:
% 4.86/1.81 | (27) ~ (all_0_6_6 = all_0_9_9)
% 4.86/1.81 | (45) ? [v0] : ? [v1] : (singleton(all_0_7_7) = v1 & singleton(all_0_8_8) = v0 & (v1 = all_0_9_9 | v0 = all_0_9_9))
% 4.86/1.81 |
% 4.86/1.81 | Instantiating (45) with all_39_0_10, all_39_1_11 yields:
% 4.86/1.81 | (46) singleton(all_0_7_7) = all_39_0_10 & singleton(all_0_8_8) = all_39_1_11 & (all_39_0_10 = all_0_9_9 | all_39_1_11 = all_0_9_9)
% 4.86/1.81 |
% 4.86/1.81 | Applying alpha-rule on (46) yields:
% 4.86/1.81 | (47) singleton(all_0_7_7) = all_39_0_10
% 4.86/1.81 | (48) singleton(all_0_8_8) = all_39_1_11
% 4.86/1.81 | (49) all_39_0_10 = all_0_9_9 | all_39_1_11 = all_0_9_9
% 4.86/1.81 |
% 4.86/1.81 | Instantiating formula (15) with all_0_7_7, all_39_0_10, all_0_3_3 and discharging atoms singleton(all_0_7_7) = all_39_0_10, singleton(all_0_7_7) = all_0_3_3, yields:
% 4.86/1.81 | (50) all_39_0_10 = all_0_3_3
% 4.86/1.81 |
% 4.86/1.81 | Instantiating formula (15) with all_0_8_8, all_39_1_11, all_0_4_4 and discharging atoms singleton(all_0_8_8) = all_39_1_11, singleton(all_0_8_8) = all_0_4_4, yields:
% 4.86/1.81 | (51) all_39_1_11 = all_0_4_4
% 4.86/1.81 |
% 4.86/1.81 +-Applying beta-rule and splitting (49), into two cases.
% 4.86/1.81 |-Branch one:
% 4.86/1.81 | (52) all_39_0_10 = all_0_9_9
% 4.86/1.81 |
% 4.86/1.81 | Combining equations (52,50) yields a new equation:
% 4.86/1.81 | (53) all_0_3_3 = all_0_9_9
% 4.86/1.81 |
% 4.86/1.81 | Equations (53) can reduce 29 to:
% 4.86/1.81 | (39) $false
% 4.86/1.81 |
% 4.86/1.81 |-The branch is then unsatisfiable
% 4.86/1.81 |-Branch two:
% 4.86/1.81 | (55) ~ (all_39_0_10 = all_0_9_9)
% 4.86/1.81 | (56) all_39_1_11 = all_0_9_9
% 4.86/1.81 |
% 4.86/1.81 | Combining equations (51,56) yields a new equation:
% 4.86/1.81 | (57) all_0_4_4 = all_0_9_9
% 4.86/1.81 |
% 4.86/1.81 | Simplifying 57 yields:
% 4.86/1.81 | (58) all_0_4_4 = all_0_9_9
% 4.86/1.81 |
% 4.86/1.81 | Equations (58) can reduce 28 to:
% 4.86/1.81 | (39) $false
% 4.86/1.81 |
% 4.86/1.81 |-The branch is then unsatisfiable
% 4.86/1.81 |-Branch two:
% 4.86/1.81 | (60) ~ (all_0_5_5 = empty_set) & (all_0_3_3 = all_0_9_9 | all_0_4_4 = all_0_9_9 | all_0_6_6 = all_0_9_9 | all_0_9_9 = empty_set)
% 4.86/1.81 |
% 4.86/1.81 | Applying alpha-rule on (60) yields:
% 4.86/1.81 | (61) ~ (all_0_5_5 = empty_set)
% 4.86/1.81 | (62) all_0_3_3 = all_0_9_9 | all_0_4_4 = all_0_9_9 | all_0_6_6 = all_0_9_9 | all_0_9_9 = empty_set
% 4.86/1.81 |
% 4.86/1.81 +-Applying beta-rule and splitting (25), into two cases.
% 4.86/1.81 |-Branch one:
% 4.86/1.81 | (31) all_0_5_5 = empty_set
% 4.86/1.81 |
% 4.86/1.81 | Equations (31) can reduce 61 to:
% 4.86/1.81 | (39) $false
% 4.86/1.81 |
% 4.86/1.81 |-The branch is then unsatisfiable
% 4.86/1.81 |-Branch two:
% 4.86/1.81 | (61) ~ (all_0_5_5 = empty_set)
% 4.86/1.81 | (66) ? [v0] : ( ~ (v0 = 0) & subset(all_0_9_9, all_0_6_6) = v0)
% 4.86/1.81 |
% 4.86/1.81 | Instantiating (66) with all_20_0_14 yields:
% 4.86/1.81 | (67) ~ (all_20_0_14 = 0) & subset(all_0_9_9, all_0_6_6) = all_20_0_14
% 4.86/1.81 |
% 4.86/1.81 | Applying alpha-rule on (67) yields:
% 4.86/1.81 | (68) ~ (all_20_0_14 = 0)
% 4.86/1.81 | (69) subset(all_0_9_9, all_0_6_6) = all_20_0_14
% 4.86/1.81 |
% 4.86/1.81 | Instantiating formula (19) with all_20_0_14, all_0_9_9 yields:
% 4.86/1.81 | (70) all_20_0_14 = 0 | ~ (subset(all_0_9_9, all_0_9_9) = all_20_0_14)
% 4.86/1.81 |
% 4.86/1.81 | Instantiating formula (17) with all_20_0_14, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms unordered_pair(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 4.86/1.81 | (71) all_20_0_14 = 0 | ~ (subset(empty_set, all_0_6_6) = all_20_0_14)
% 4.86/1.81 |
% 4.86/1.81 | Instantiating formula (14) with all_20_0_14, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_6_6) = all_20_0_14, unordered_pair(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 4.86/1.81 | (72) all_20_0_14 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = all_0_9_9) & ~ (v0 = all_0_9_9) & singleton(all_0_7_7) = v1 & singleton(all_0_8_8) = v0)
% 4.86/1.82 |
% 4.86/1.82 +-Applying beta-rule and splitting (71), into two cases.
% 4.86/1.82 |-Branch one:
% 4.86/1.82 | (73) ~ (subset(empty_set, all_0_6_6) = all_20_0_14)
% 4.86/1.82 |
% 4.86/1.82 +-Applying beta-rule and splitting (70), into two cases.
% 4.86/1.82 |-Branch one:
% 4.86/1.82 | (74) ~ (subset(all_0_9_9, all_0_9_9) = all_20_0_14)
% 4.86/1.82 |
% 4.86/1.82 +-Applying beta-rule and splitting (72), into two cases.
% 4.86/1.82 |-Branch one:
% 4.93/1.82 | (75) all_20_0_14 = 0
% 4.93/1.82 |
% 4.93/1.82 | Equations (75) can reduce 68 to:
% 4.93/1.82 | (39) $false
% 4.93/1.82 |
% 4.93/1.82 |-The branch is then unsatisfiable
% 4.93/1.82 |-Branch two:
% 4.93/1.82 | (68) ~ (all_20_0_14 = 0)
% 4.93/1.82 | (78) ? [v0] : ? [v1] : ( ~ (v1 = all_0_9_9) & ~ (v0 = all_0_9_9) & singleton(all_0_7_7) = v1 & singleton(all_0_8_8) = v0)
% 4.93/1.82 |
% 4.93/1.82 | Instantiating (78) with all_41_0_15, all_41_1_16 yields:
% 4.93/1.82 | (79) ~ (all_41_0_15 = all_0_9_9) & ~ (all_41_1_16 = all_0_9_9) & singleton(all_0_7_7) = all_41_0_15 & singleton(all_0_8_8) = all_41_1_16
% 4.93/1.82 |
% 4.93/1.82 | Applying alpha-rule on (79) yields:
% 4.93/1.82 | (80) ~ (all_41_0_15 = all_0_9_9)
% 4.93/1.82 | (81) ~ (all_41_1_16 = all_0_9_9)
% 4.93/1.82 | (82) singleton(all_0_7_7) = all_41_0_15
% 4.93/1.82 | (83) singleton(all_0_8_8) = all_41_1_16
% 4.93/1.82 |
% 4.93/1.82 | Instantiating formula (15) with all_0_7_7, all_41_0_15, all_0_3_3 and discharging atoms singleton(all_0_7_7) = all_41_0_15, singleton(all_0_7_7) = all_0_3_3, yields:
% 4.93/1.82 | (84) all_41_0_15 = all_0_3_3
% 4.93/1.82 |
% 4.93/1.82 | Instantiating formula (15) with all_0_8_8, all_41_1_16, all_0_4_4 and discharging atoms singleton(all_0_8_8) = all_41_1_16, singleton(all_0_8_8) = all_0_4_4, yields:
% 4.93/1.82 | (85) all_41_1_16 = all_0_4_4
% 4.93/1.82 |
% 4.93/1.82 | Using (69) and (74) yields:
% 4.93/1.82 | (27) ~ (all_0_6_6 = all_0_9_9)
% 4.93/1.82 |
% 4.93/1.82 | Using (69) and (73) yields:
% 4.93/1.82 | (30) ~ (all_0_9_9 = empty_set)
% 4.93/1.82 |
% 4.93/1.82 | Equations (84) can reduce 80 to:
% 4.93/1.82 | (29) ~ (all_0_3_3 = all_0_9_9)
% 4.93/1.82 |
% 4.93/1.82 | Equations (85) can reduce 81 to:
% 4.93/1.82 | (28) ~ (all_0_4_4 = all_0_9_9)
% 4.93/1.82 |
% 4.93/1.82 +-Applying beta-rule and splitting (62), into two cases.
% 4.93/1.82 |-Branch one:
% 4.93/1.82 | (38) all_0_9_9 = empty_set
% 4.93/1.82 |
% 4.93/1.82 | Equations (38) can reduce 30 to:
% 4.93/1.82 | (39) $false
% 4.93/1.82 |
% 4.93/1.82 |-The branch is then unsatisfiable
% 4.93/1.82 |-Branch two:
% 4.93/1.82 | (30) ~ (all_0_9_9 = empty_set)
% 4.93/1.82 | (93) all_0_3_3 = all_0_9_9 | all_0_4_4 = all_0_9_9 | all_0_6_6 = all_0_9_9
% 4.93/1.82 |
% 4.93/1.82 +-Applying beta-rule and splitting (93), into two cases.
% 4.93/1.82 |-Branch one:
% 4.93/1.82 | (53) all_0_3_3 = all_0_9_9
% 4.93/1.82 |
% 4.93/1.82 | Equations (53) can reduce 29 to:
% 4.93/1.82 | (39) $false
% 4.93/1.82 |
% 4.93/1.82 |-The branch is then unsatisfiable
% 4.93/1.82 |-Branch two:
% 4.93/1.82 | (29) ~ (all_0_3_3 = all_0_9_9)
% 4.93/1.82 | (97) all_0_4_4 = all_0_9_9 | all_0_6_6 = all_0_9_9
% 4.93/1.82 |
% 4.93/1.82 +-Applying beta-rule and splitting (97), into two cases.
% 4.93/1.82 |-Branch one:
% 4.93/1.82 | (58) all_0_4_4 = all_0_9_9
% 4.93/1.82 |
% 4.93/1.82 | Equations (58) can reduce 28 to:
% 4.93/1.82 | (39) $false
% 4.93/1.82 |
% 4.93/1.82 |-The branch is then unsatisfiable
% 4.93/1.82 |-Branch two:
% 4.93/1.82 | (28) ~ (all_0_4_4 = all_0_9_9)
% 4.93/1.82 | (42) all_0_6_6 = all_0_9_9
% 4.93/1.82 |
% 4.93/1.82 | Equations (42) can reduce 27 to:
% 4.93/1.82 | (39) $false
% 4.93/1.82 |
% 4.93/1.82 |-The branch is then unsatisfiable
% 4.93/1.82 |-Branch two:
% 4.93/1.82 | (103) subset(all_0_9_9, all_0_9_9) = all_20_0_14
% 4.93/1.82 | (75) all_20_0_14 = 0
% 4.93/1.82 |
% 4.93/1.82 | Equations (75) can reduce 68 to:
% 4.93/1.82 | (39) $false
% 4.93/1.82 |
% 4.93/1.82 |-The branch is then unsatisfiable
% 4.93/1.82 |-Branch two:
% 4.93/1.82 | (106) subset(empty_set, all_0_6_6) = all_20_0_14
% 4.93/1.82 | (75) all_20_0_14 = 0
% 4.93/1.82 |
% 4.93/1.82 | Equations (75) can reduce 68 to:
% 4.93/1.82 | (39) $false
% 4.93/1.82 |
% 4.93/1.82 |-The branch is then unsatisfiable
% 4.93/1.82 % SZS output end Proof for theBenchmark
% 4.93/1.83
% 4.93/1.83 1234ms
%------------------------------------------------------------------------------