TSTP Solution File: SET584+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET584+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.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 00:20:27 EDT 2022
% Result : Theorem 2.65s 1.41s
% Output : Proof 4.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET584+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n018.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 : Sun Jul 10 03:02:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.62/0.64 ____ _
% 0.62/0.64 ___ / __ \_____(_)___ ________ __________
% 0.62/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.62/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.62/0.64
% 0.62/0.64 A Theorem Prover for First-Order Logic
% 0.62/0.64 (ePrincess v.1.0)
% 0.62/0.64
% 0.62/0.64 (c) Philipp Rümmer, 2009-2015
% 0.62/0.64 (c) Peter Backeman, 2014-2015
% 0.62/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.64 Bug reports to peter@backeman.se
% 0.62/0.64
% 0.62/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.64
% 0.62/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.40/0.94 Prover 0: Preprocessing ...
% 1.69/1.08 Prover 0: Warning: ignoring some quantifiers
% 1.78/1.10 Prover 0: Constructing countermodel ...
% 2.21/1.25 Prover 0: gave up
% 2.21/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.27/1.27 Prover 1: Preprocessing ...
% 2.55/1.33 Prover 1: Warning: ignoring some quantifiers
% 2.55/1.34 Prover 1: Constructing countermodel ...
% 2.65/1.41 Prover 1: proved (159ms)
% 2.65/1.41
% 2.65/1.41 No countermodel exists, formula is valid
% 2.65/1.41 % SZS status Theorem for theBenchmark
% 2.65/1.41
% 2.65/1.41 Generating proof ... Warning: ignoring some quantifiers
% 4.07/1.76 found it (size 46)
% 4.07/1.76
% 4.07/1.76 % SZS output start Proof for theBenchmark
% 4.07/1.76 Assumed formulas after preprocessing and simplification:
% 4.07/1.76 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset(v3, v4) = v5 & subset(v0, v1) = 0 & union(v1, v2) = v4 & union(v0, v2) = v3 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (union(v6, v7) = v9) | ~ (member(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & ~ (v11 = 0) & member(v8, v7) = v12 & member(v8, v6) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (subset(v9, v8) = v7) | ~ (subset(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (union(v9, v8) = v7) | ~ (union(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (member(v9, v8) = v7) | ~ (member(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : ? [v11] : (member(v8, v7) = v11 & member(v8, v6) = v10 & (v11 = 0 | v10 = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v7) = v10 & member(v9, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v6, v7) = 0) | ~ (member(v8, v6) = 0) | member(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v6, v7) = v8) | union(v7, v6) = v8) & ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v6, v6) = v7)) & ? [v6] : ? [v7] : (v7 = v6 | ? [v8] : ? [v9] : ? [v10] : (member(v8, v7) = v10 & member(v8, v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)) & (v10 = 0 | v9 = 0))))
% 4.11/1.79 | 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:
% 4.11/1.79 | (1) ~ (all_0_0_0 = 0) & subset(all_0_2_2, all_0_1_1) = all_0_0_0 & subset(all_0_5_5, all_0_4_4) = 0 & union(all_0_4_4, all_0_3_3) = all_0_1_1 & union(all_0_5_5, all_0_3_3) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 4.11/1.80 |
% 4.11/1.80 | Applying alpha-rule on (1) yields:
% 4.11/1.80 | (2) union(all_0_5_5, all_0_3_3) = all_0_2_2
% 4.11/1.80 | (3) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 4.11/1.80 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5))
% 4.11/1.80 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 4.11/1.80 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 4.11/1.80 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 4.11/1.80 | (8) subset(all_0_2_2, all_0_1_1) = all_0_0_0
% 4.11/1.80 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 4.11/1.80 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 4.11/1.80 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 4.11/1.80 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 4.11/1.80 | (13) subset(all_0_5_5, all_0_4_4) = 0
% 4.11/1.80 | (14) union(all_0_4_4, all_0_3_3) = all_0_1_1
% 4.11/1.80 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 4.11/1.80 | (16) ~ (all_0_0_0 = 0)
% 4.11/1.80 |
% 4.11/1.80 | Instantiating formula (7) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 4.11/1.80 | (17) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 4.11/1.80 |
% 4.11/1.80 | Instantiating formula (10) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms union(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 4.11/1.80 | (18) union(all_0_3_3, all_0_4_4) = all_0_1_1
% 4.11/1.80 |
% 4.11/1.80 | Instantiating formula (10) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms union(all_0_5_5, all_0_3_3) = all_0_2_2, yields:
% 4.11/1.80 | (19) union(all_0_3_3, all_0_5_5) = all_0_2_2
% 4.11/1.81 |
% 4.11/1.81 +-Applying beta-rule and splitting (17), into two cases.
% 4.11/1.81 |-Branch one:
% 4.11/1.81 | (20) all_0_0_0 = 0
% 4.11/1.81 |
% 4.11/1.81 | Equations (20) can reduce 16 to:
% 4.11/1.81 | (21) $false
% 4.11/1.81 |
% 4.11/1.81 |-The branch is then unsatisfiable
% 4.11/1.81 |-Branch two:
% 4.11/1.81 | (16) ~ (all_0_0_0 = 0)
% 4.11/1.81 | (23) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 4.26/1.81 |
% 4.26/1.81 | Instantiating (23) with all_18_0_8, all_18_1_9 yields:
% 4.26/1.81 | (24) ~ (all_18_0_8 = 0) & member(all_18_1_9, all_0_1_1) = all_18_0_8 & member(all_18_1_9, all_0_2_2) = 0
% 4.26/1.81 |
% 4.26/1.81 | Applying alpha-rule on (24) yields:
% 4.26/1.81 | (25) ~ (all_18_0_8 = 0)
% 4.26/1.81 | (26) member(all_18_1_9, all_0_1_1) = all_18_0_8
% 4.26/1.81 | (27) member(all_18_1_9, all_0_2_2) = 0
% 4.26/1.81 |
% 4.26/1.81 | Instantiating formula (4) with all_18_0_8, all_0_1_1, all_18_1_9, all_0_3_3, all_0_4_4 and discharging atoms union(all_0_4_4, all_0_3_3) = all_0_1_1, member(all_18_1_9, all_0_1_1) = all_18_0_8, yields:
% 4.26/1.81 | (28) all_18_0_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_18_1_9, all_0_3_3) = v1 & member(all_18_1_9, all_0_4_4) = v0)
% 4.26/1.81 |
% 4.26/1.81 | Instantiating formula (4) with all_18_0_8, all_0_1_1, all_18_1_9, all_0_4_4, all_0_3_3 and discharging atoms union(all_0_3_3, all_0_4_4) = all_0_1_1, member(all_18_1_9, all_0_1_1) = all_18_0_8, yields:
% 4.26/1.81 | (29) all_18_0_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_18_1_9, all_0_3_3) = v0 & member(all_18_1_9, all_0_4_4) = v1)
% 4.26/1.81 |
% 4.26/1.81 | Instantiating formula (9) with all_0_2_2, all_18_1_9, all_0_3_3, all_0_5_5 and discharging atoms union(all_0_5_5, all_0_3_3) = all_0_2_2, member(all_18_1_9, all_0_2_2) = 0, yields:
% 4.26/1.81 | (30) ? [v0] : ? [v1] : (member(all_18_1_9, all_0_3_3) = v1 & member(all_18_1_9, all_0_5_5) = v0 & (v1 = 0 | v0 = 0))
% 4.26/1.81 |
% 4.26/1.81 | Instantiating formula (9) with all_0_2_2, all_18_1_9, all_0_5_5, all_0_3_3 and discharging atoms union(all_0_3_3, all_0_5_5) = all_0_2_2, member(all_18_1_9, all_0_2_2) = 0, yields:
% 4.26/1.81 | (31) ? [v0] : ? [v1] : (member(all_18_1_9, all_0_3_3) = v0 & member(all_18_1_9, all_0_5_5) = v1 & (v1 = 0 | v0 = 0))
% 4.26/1.81 |
% 4.26/1.81 | Instantiating formula (11) with all_18_1_9, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = 0, yields:
% 4.26/1.81 | (32) ~ (member(all_18_1_9, all_0_5_5) = 0) | member(all_18_1_9, all_0_4_4) = 0
% 4.26/1.81 |
% 4.26/1.81 | Instantiating (31) with all_29_0_10, all_29_1_11 yields:
% 4.26/1.81 | (33) member(all_18_1_9, all_0_3_3) = all_29_1_11 & member(all_18_1_9, all_0_5_5) = all_29_0_10 & (all_29_0_10 = 0 | all_29_1_11 = 0)
% 4.26/1.81 |
% 4.26/1.81 | Applying alpha-rule on (33) yields:
% 4.26/1.81 | (34) member(all_18_1_9, all_0_3_3) = all_29_1_11
% 4.26/1.81 | (35) member(all_18_1_9, all_0_5_5) = all_29_0_10
% 4.26/1.81 | (36) all_29_0_10 = 0 | all_29_1_11 = 0
% 4.26/1.81 |
% 4.26/1.81 | Instantiating (30) with all_31_0_12, all_31_1_13 yields:
% 4.26/1.81 | (37) member(all_18_1_9, all_0_3_3) = all_31_0_12 & member(all_18_1_9, all_0_5_5) = all_31_1_13 & (all_31_0_12 = 0 | all_31_1_13 = 0)
% 4.26/1.81 |
% 4.26/1.81 | Applying alpha-rule on (37) yields:
% 4.26/1.81 | (38) member(all_18_1_9, all_0_3_3) = all_31_0_12
% 4.26/1.81 | (39) member(all_18_1_9, all_0_5_5) = all_31_1_13
% 4.26/1.81 | (40) all_31_0_12 = 0 | all_31_1_13 = 0
% 4.26/1.81 |
% 4.26/1.81 +-Applying beta-rule and splitting (28), into two cases.
% 4.26/1.81 |-Branch one:
% 4.26/1.81 | (41) all_18_0_8 = 0
% 4.26/1.81 |
% 4.26/1.81 | Equations (41) can reduce 25 to:
% 4.26/1.81 | (21) $false
% 4.26/1.81 |
% 4.26/1.81 |-The branch is then unsatisfiable
% 4.26/1.81 |-Branch two:
% 4.26/1.81 | (25) ~ (all_18_0_8 = 0)
% 4.26/1.81 | (44) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_18_1_9, all_0_3_3) = v1 & member(all_18_1_9, all_0_4_4) = v0)
% 4.26/1.81 |
% 4.26/1.81 | Instantiating (44) with all_37_0_14, all_37_1_15 yields:
% 4.26/1.81 | (45) ~ (all_37_0_14 = 0) & ~ (all_37_1_15 = 0) & member(all_18_1_9, all_0_3_3) = all_37_0_14 & member(all_18_1_9, all_0_4_4) = all_37_1_15
% 4.26/1.81 |
% 4.26/1.81 | Applying alpha-rule on (45) yields:
% 4.26/1.81 | (46) ~ (all_37_0_14 = 0)
% 4.26/1.81 | (47) ~ (all_37_1_15 = 0)
% 4.26/1.81 | (48) member(all_18_1_9, all_0_3_3) = all_37_0_14
% 4.26/1.81 | (49) member(all_18_1_9, all_0_4_4) = all_37_1_15
% 4.26/1.82 |
% 4.26/1.82 +-Applying beta-rule and splitting (29), into two cases.
% 4.26/1.82 |-Branch one:
% 4.26/1.82 | (41) all_18_0_8 = 0
% 4.26/1.82 |
% 4.26/1.82 | Equations (41) can reduce 25 to:
% 4.26/1.82 | (21) $false
% 4.26/1.82 |
% 4.26/1.82 |-The branch is then unsatisfiable
% 4.26/1.82 |-Branch two:
% 4.26/1.82 | (25) ~ (all_18_0_8 = 0)
% 4.26/1.82 | (53) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_18_1_9, all_0_3_3) = v0 & member(all_18_1_9, all_0_4_4) = v1)
% 4.26/1.82 |
% 4.26/1.82 | Instantiating (53) with all_42_0_16, all_42_1_17 yields:
% 4.26/1.82 | (54) ~ (all_42_0_16 = 0) & ~ (all_42_1_17 = 0) & member(all_18_1_9, all_0_3_3) = all_42_1_17 & member(all_18_1_9, all_0_4_4) = all_42_0_16
% 4.26/1.82 |
% 4.26/1.82 | Applying alpha-rule on (54) yields:
% 4.26/1.82 | (55) ~ (all_42_0_16 = 0)
% 4.26/1.82 | (56) ~ (all_42_1_17 = 0)
% 4.26/1.82 | (57) member(all_18_1_9, all_0_3_3) = all_42_1_17
% 4.26/1.82 | (58) member(all_18_1_9, all_0_4_4) = all_42_0_16
% 4.26/1.82 |
% 4.26/1.82 +-Applying beta-rule and splitting (32), into two cases.
% 4.26/1.82 |-Branch one:
% 4.26/1.82 | (59) ~ (member(all_18_1_9, all_0_5_5) = 0)
% 4.26/1.82 |
% 4.26/1.82 | Instantiating formula (6) with all_18_1_9, all_0_3_3, all_29_1_11, all_37_0_14 and discharging atoms member(all_18_1_9, all_0_3_3) = all_37_0_14, member(all_18_1_9, all_0_3_3) = all_29_1_11, yields:
% 4.26/1.82 | (60) all_37_0_14 = all_29_1_11
% 4.26/1.82 |
% 4.26/1.82 | Instantiating formula (6) with all_18_1_9, all_0_5_5, all_29_0_10, all_31_1_13 and discharging atoms member(all_18_1_9, all_0_5_5) = all_31_1_13, member(all_18_1_9, all_0_5_5) = all_29_0_10, yields:
% 4.26/1.82 | (61) all_31_1_13 = all_29_0_10
% 4.26/1.82 |
% 4.26/1.82 | Using (39) and (59) yields:
% 4.26/1.82 | (62) ~ (all_31_1_13 = 0)
% 4.26/1.82 |
% 4.26/1.82 | Equations (60) can reduce 46 to:
% 4.26/1.82 | (63) ~ (all_29_1_11 = 0)
% 4.26/1.82 |
% 4.26/1.82 | Equations (61) can reduce 62 to:
% 4.26/1.82 | (64) ~ (all_29_0_10 = 0)
% 4.26/1.82 |
% 4.26/1.82 +-Applying beta-rule and splitting (36), into two cases.
% 4.26/1.82 |-Branch one:
% 4.26/1.82 | (65) all_29_0_10 = 0
% 4.26/1.82 |
% 4.26/1.82 | Equations (65) can reduce 64 to:
% 4.26/1.82 | (21) $false
% 4.26/1.82 |
% 4.26/1.82 |-The branch is then unsatisfiable
% 4.26/1.82 |-Branch two:
% 4.26/1.82 | (64) ~ (all_29_0_10 = 0)
% 4.26/1.82 | (68) all_29_1_11 = 0
% 4.26/1.82 |
% 4.26/1.82 | Equations (68) can reduce 63 to:
% 4.26/1.82 | (21) $false
% 4.26/1.82 |
% 4.26/1.82 |-The branch is then unsatisfiable
% 4.26/1.82 |-Branch two:
% 4.26/1.82 | (70) member(all_18_1_9, all_0_5_5) = 0
% 4.26/1.82 | (71) member(all_18_1_9, all_0_4_4) = 0
% 4.26/1.82 |
% 4.26/1.82 | Instantiating formula (6) with all_18_1_9, all_0_4_4, all_42_0_16, 0 and discharging atoms member(all_18_1_9, all_0_4_4) = all_42_0_16, member(all_18_1_9, all_0_4_4) = 0, yields:
% 4.26/1.82 | (72) all_42_0_16 = 0
% 4.26/1.82 |
% 4.26/1.82 | Instantiating formula (6) with all_18_1_9, all_0_4_4, all_37_1_15, all_42_0_16 and discharging atoms member(all_18_1_9, all_0_4_4) = all_42_0_16, member(all_18_1_9, all_0_4_4) = all_37_1_15, yields:
% 4.26/1.82 | (73) all_42_0_16 = all_37_1_15
% 4.26/1.82 |
% 4.26/1.82 | Combining equations (73,72) yields a new equation:
% 4.26/1.82 | (74) all_37_1_15 = 0
% 4.26/1.82 |
% 4.26/1.82 | Simplifying 74 yields:
% 4.26/1.82 | (75) all_37_1_15 = 0
% 4.26/1.82 |
% 4.26/1.82 | Equations (75) can reduce 47 to:
% 4.26/1.82 | (21) $false
% 4.26/1.82 |
% 4.26/1.82 |-The branch is then unsatisfiable
% 4.26/1.82 % SZS output end Proof for theBenchmark
% 4.26/1.82
% 4.26/1.82 1173ms
%------------------------------------------------------------------------------