TSTP Solution File: SET611+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 00:20:47 EDT 2022
% Result : Theorem 21.36s 6.19s
% Output : Proof 29.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 14:35:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.67/0.63 ____ _
% 0.67/0.63 ___ / __ \_____(_)___ ________ __________
% 0.67/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.67/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.67/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.67/0.63
% 0.67/0.63 A Theorem Prover for First-Order Logic
% 0.67/0.63 (ePrincess v.1.0)
% 0.67/0.63
% 0.67/0.63 (c) Philipp Rümmer, 2009-2015
% 0.67/0.63 (c) Peter Backeman, 2014-2015
% 0.67/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.67/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.67/0.63 Bug reports to peter@backeman.se
% 0.67/0.63
% 0.67/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.67/0.63
% 0.67/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.51/0.94 Prover 0: Preprocessing ...
% 1.96/1.10 Prover 0: Warning: ignoring some quantifiers
% 1.96/1.11 Prover 0: Constructing countermodel ...
% 2.44/1.24 Prover 0: gave up
% 2.44/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.44/1.26 Prover 1: Preprocessing ...
% 2.75/1.34 Prover 1: Warning: ignoring some quantifiers
% 2.75/1.35 Prover 1: Constructing countermodel ...
% 2.75/1.38 Prover 1: gave up
% 3.03/1.39 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.03/1.40 Prover 2: Preprocessing ...
% 3.41/1.47 Prover 2: Warning: ignoring some quantifiers
% 3.47/1.48 Prover 2: Constructing countermodel ...
% 3.61/1.53 Prover 2: gave up
% 3.61/1.53 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.70/1.54 Prover 3: Preprocessing ...
% 3.70/1.56 Prover 3: Warning: ignoring some quantifiers
% 3.70/1.57 Prover 3: Constructing countermodel ...
% 3.70/1.60 Prover 3: gave up
% 3.70/1.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.70/1.61 Prover 4: Preprocessing ...
% 4.13/1.68 Prover 4: Warning: ignoring some quantifiers
% 4.13/1.69 Prover 4: Constructing countermodel ...
% 6.23/2.10 Prover 4: gave up
% 6.23/2.10 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.23/2.11 Prover 5: Preprocessing ...
% 6.33/2.15 Prover 5: Warning: ignoring some quantifiers
% 6.33/2.15 Prover 5: Constructing countermodel ...
% 6.33/2.17 Prover 5: gave up
% 6.33/2.17 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.33/2.18 Prover 6: Preprocessing ...
% 6.33/2.21 Prover 6: Warning: ignoring some quantifiers
% 6.33/2.21 Prover 6: Constructing countermodel ...
% 6.79/2.23 Prover 6: gave up
% 6.79/2.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 6.79/2.24 Prover 7: Preprocessing ...
% 6.79/2.26 Prover 7: Proving ...
% 21.36/6.19 Prover 7: proved (3957ms)
% 21.36/6.19
% 21.36/6.19 % SZS status Theorem for theBenchmark
% 21.36/6.19
% 21.36/6.19 Generating proof ... found it (size 119)
% 29.52/8.58
% 29.52/8.58 % SZS output start Proof for theBenchmark
% 29.52/8.58 Assumed formulas after preprocessing and simplification:
% 29.52/8.58 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (difference(v4, v3) = v2) | ~ (difference(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (intersection(v4, v3) = v2) | ~ (intersection(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v2) = v4) | ~ member(v3, v4) | (member(v3, v1) & ~ member(v3, v2))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v2) = v4) | ~ member(v3, v1) | member(v3, v4) | member(v3, v2)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v2) = v4) | ~ member(v3, v4) | (member(v3, v2) & member(v3, v1))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v2) = v4) | ~ member(v3, v2) | ~ member(v3, v1) | member(v3, v4)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | intersection(v2, v1) = v3) & ! [v1] : ! [v2] : (v2 = v1 | ~ subset(v2, v1) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : (v2 = v1 | ? [v3] : (( ~ member(v3, v2) | ~ member(v3, v1)) & (member(v3, v2) | member(v3, v1)))) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ! [v3] : ( ~ member(v3, v1) | member(v3, v2))) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (member(v3, v1) & ~ member(v3, v2))) & ! [v1] : ( ~ empty(v1) | ! [v2] : ~ member(v2, v1)) & ! [v1] : ~ member(v1, v0) & ! [v1] : (empty(v1) | ? [v2] : member(v2, v1)) & ! [v1] : subset(v1, v1) & ? [v1] : ? [v2] : ? [v3] : ? [v4] : (difference(v1, v2) = v4 & intersection(v1, v2) = v3 & ((v4 = v1 & ~ (v3 = v0)) | (v3 = v0 & ~ (v4 = v1)))))
% 29.52/8.60 | Instantiating (0) with all_0_0_0 yields:
% 29.52/8.60 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v0) & ~ member(v2, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v1) & member(v2, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1))) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0)) & ! [v0] : ~ member(v0, all_0_0_0) & ! [v0] : (empty(v0) | ? [v1] : member(v1, v0)) & ! [v0] : subset(v0, v0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (difference(v0, v1) = v3 & intersection(v0, v1) = v2 & ((v3 = v0 & ~ (v2 = all_0_0_0)) | (v2 = all_0_0_0 & ~ (v3 = v0))))
% 29.52/8.61 |
% 29.52/8.61 | Applying alpha-rule on (1) yields:
% 29.52/8.61 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1))
% 29.52/8.61 | (3) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (difference(v0, v1) = v3 & intersection(v0, v1) = v2 & ((v3 = v0 & ~ (v2 = all_0_0_0)) | (v2 = all_0_0_0 & ~ (v3 = v0))))
% 29.52/8.61 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 29.52/8.61 | (5) ! [v0] : (empty(v0) | ? [v1] : member(v1, v0))
% 29.52/8.61 | (6) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 29.52/8.61 | (7) ! [v0] : ~ member(v0, all_0_0_0)
% 29.52/8.61 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 29.52/8.61 | (9) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 29.52/8.61 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v0) & ~ member(v2, v1)))
% 29.52/8.61 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 29.52/8.61 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3))
% 29.52/8.61 | (13) ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0))
% 29.52/8.61 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v1) & member(v2, v0)))
% 29.52/8.61 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 29.52/8.61 | (16) ! [v0] : subset(v0, v0)
% 29.52/8.61 | (17) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1)))
% 29.52/8.61 |
% 29.52/8.61 | Instantiating (3) with all_2_0_1, all_2_1_2, all_2_2_3, all_2_3_4 yields:
% 29.52/8.61 | (18) difference(all_2_3_4, all_2_2_3) = all_2_0_1 & intersection(all_2_3_4, all_2_2_3) = all_2_1_2 & ((all_2_0_1 = all_2_3_4 & ~ (all_2_1_2 = all_0_0_0)) | (all_2_1_2 = all_0_0_0 & ~ (all_2_0_1 = all_2_3_4)))
% 29.52/8.62 |
% 29.52/8.62 | Applying alpha-rule on (18) yields:
% 29.52/8.62 | (19) difference(all_2_3_4, all_2_2_3) = all_2_0_1
% 29.52/8.62 | (20) intersection(all_2_3_4, all_2_2_3) = all_2_1_2
% 29.52/8.62 | (21) (all_2_0_1 = all_2_3_4 & ~ (all_2_1_2 = all_0_0_0)) | (all_2_1_2 = all_0_0_0 & ~ (all_2_0_1 = all_2_3_4))
% 29.52/8.62 |
% 29.52/8.62 +-Applying beta-rule and splitting (21), into two cases.
% 29.52/8.62 |-Branch one:
% 29.52/8.62 | (22) all_2_0_1 = all_2_3_4 & ~ (all_2_1_2 = all_0_0_0)
% 29.52/8.62 |
% 29.52/8.62 | Applying alpha-rule on (22) yields:
% 29.52/8.62 | (23) all_2_0_1 = all_2_3_4
% 29.52/8.62 | (24) ~ (all_2_1_2 = all_0_0_0)
% 29.52/8.62 |
% 29.52/8.62 | From (23) and (19) follows:
% 29.52/8.62 | (25) difference(all_2_3_4, all_2_2_3) = all_2_3_4
% 29.94/8.62 |
% 29.94/8.62 | Introducing new symbol ex_42_1_10 defined by:
% 29.94/8.62 | (26) ex_42_1_10 = all_2_1_2
% 29.94/8.62 |
% 29.94/8.62 | Introducing new symbol ex_42_0_9 defined by:
% 29.94/8.62 | (27) ex_42_0_9 = all_0_0_0
% 29.94/8.62 |
% 29.94/8.62 | Instantiating formula (6) with ex_42_0_9, ex_42_1_10 yields:
% 29.94/8.62 | (28) ex_42_0_9 = ex_42_1_10 | ? [v0] : (( ~ member(v0, ex_42_0_9) | ~ member(v0, ex_42_1_10)) & (member(v0, ex_42_0_9) | member(v0, ex_42_1_10)))
% 29.94/8.62 |
% 29.94/8.62 +-Applying beta-rule and splitting (28), into two cases.
% 29.94/8.62 |-Branch one:
% 29.94/8.62 | (29) ex_42_0_9 = ex_42_1_10
% 29.94/8.62 |
% 29.94/8.62 | Combining equations (27,29) yields a new equation:
% 29.94/8.62 | (30) ex_42_1_10 = all_0_0_0
% 29.94/8.62 |
% 29.94/8.62 | Combining equations (30,26) yields a new equation:
% 29.94/8.62 | (31) all_2_1_2 = all_0_0_0
% 29.94/8.62 |
% 29.94/8.62 | Equations (31) can reduce 24 to:
% 29.94/8.62 | (32) $false
% 29.94/8.62 |
% 29.94/8.62 |-The branch is then unsatisfiable
% 29.94/8.62 |-Branch two:
% 29.94/8.62 | (33) ? [v0] : (( ~ member(v0, ex_42_0_9) | ~ member(v0, ex_42_1_10)) & (member(v0, ex_42_0_9) | member(v0, ex_42_1_10)))
% 29.94/8.62 |
% 29.94/8.62 | Instantiating (33) with all_45_0_11 yields:
% 29.94/8.62 | (34) ( ~ member(all_45_0_11, ex_42_0_9) | ~ member(all_45_0_11, ex_42_1_10)) & (member(all_45_0_11, ex_42_0_9) | member(all_45_0_11, ex_42_1_10))
% 29.94/8.62 |
% 29.94/8.62 | Applying alpha-rule on (34) yields:
% 29.94/8.62 | (35) ~ member(all_45_0_11, ex_42_0_9) | ~ member(all_45_0_11, ex_42_1_10)
% 29.94/8.62 | (36) member(all_45_0_11, ex_42_0_9) | member(all_45_0_11, ex_42_1_10)
% 29.94/8.62 |
% 29.94/8.62 +-Applying beta-rule and splitting (35), into two cases.
% 29.94/8.62 |-Branch one:
% 29.94/8.62 | (37) ~ member(all_45_0_11, ex_42_0_9)
% 29.94/8.62 |
% 29.94/8.62 +-Applying beta-rule and splitting (36), into two cases.
% 29.94/8.62 |-Branch one:
% 29.94/8.62 | (38) member(all_45_0_11, ex_42_0_9)
% 29.94/8.62 |
% 29.94/8.62 | Using (38) and (37) yields:
% 29.94/8.62 | (39) $false
% 29.94/8.62 |
% 29.94/8.62 |-The branch is then unsatisfiable
% 29.94/8.62 |-Branch two:
% 29.94/8.62 | (40) member(all_45_0_11, ex_42_1_10)
% 29.94/8.62 |
% 29.94/8.62 | Instantiating formula (10) with all_2_3_4, all_45_0_11, all_2_2_3, all_2_3_4 and discharging atoms difference(all_2_3_4, all_2_2_3) = all_2_3_4, yields:
% 29.94/8.62 | (41) ~ member(all_45_0_11, all_2_2_3) | ~ member(all_45_0_11, all_2_3_4)
% 29.94/8.62 |
% 29.94/8.62 | Instantiating formula (14) with all_2_1_2, all_45_0_11, all_2_2_3, all_2_3_4 and discharging atoms intersection(all_2_3_4, all_2_2_3) = all_2_1_2, yields:
% 29.94/8.62 | (42) ~ member(all_45_0_11, all_2_1_2) | (member(all_45_0_11, all_2_2_3) & member(all_45_0_11, all_2_3_4))
% 29.94/8.62 |
% 29.94/8.62 +-Applying beta-rule and splitting (41), into two cases.
% 29.94/8.62 |-Branch one:
% 29.94/8.62 | (43) ~ member(all_45_0_11, all_2_2_3)
% 29.94/8.62 |
% 29.94/8.62 +-Applying beta-rule and splitting (42), into two cases.
% 29.94/8.62 |-Branch one:
% 29.94/8.62 | (44) ~ member(all_45_0_11, all_2_1_2)
% 29.94/8.62 |
% 29.94/8.62 | From (26) and (40) follows:
% 29.94/8.62 | (45) member(all_45_0_11, all_2_1_2)
% 29.94/8.62 |
% 29.94/8.62 | Using (45) and (44) yields:
% 29.94/8.62 | (39) $false
% 29.94/8.62 |
% 29.94/8.62 |-The branch is then unsatisfiable
% 29.94/8.62 |-Branch two:
% 29.94/8.62 | (47) member(all_45_0_11, all_2_2_3) & member(all_45_0_11, all_2_3_4)
% 29.94/8.62 |
% 29.94/8.62 | Applying alpha-rule on (47) yields:
% 29.94/8.62 | (48) member(all_45_0_11, all_2_2_3)
% 29.94/8.62 | (49) member(all_45_0_11, all_2_3_4)
% 29.94/8.62 |
% 29.94/8.62 | Using (48) and (43) yields:
% 29.94/8.62 | (39) $false
% 29.94/8.62 |
% 29.94/8.62 |-The branch is then unsatisfiable
% 29.94/8.62 |-Branch two:
% 29.94/8.62 | (51) ~ member(all_45_0_11, all_2_3_4)
% 29.94/8.62 |
% 29.94/8.62 +-Applying beta-rule and splitting (42), into two cases.
% 29.94/8.62 |-Branch one:
% 29.94/8.62 | (44) ~ member(all_45_0_11, all_2_1_2)
% 29.94/8.62 |
% 29.94/8.62 | From (26) and (40) follows:
% 29.94/8.62 | (45) member(all_45_0_11, all_2_1_2)
% 29.94/8.62 |
% 29.94/8.62 | Using (45) and (44) yields:
% 29.94/8.62 | (39) $false
% 29.94/8.62 |
% 29.94/8.62 |-The branch is then unsatisfiable
% 29.94/8.62 |-Branch two:
% 29.94/8.62 | (47) member(all_45_0_11, all_2_2_3) & member(all_45_0_11, all_2_3_4)
% 29.94/8.62 |
% 29.94/8.62 | Applying alpha-rule on (47) yields:
% 29.94/8.62 | (48) member(all_45_0_11, all_2_2_3)
% 29.94/8.62 | (49) member(all_45_0_11, all_2_3_4)
% 29.94/8.62 |
% 29.94/8.62 | Using (49) and (51) yields:
% 29.94/8.62 | (39) $false
% 29.94/8.62 |
% 29.94/8.62 |-The branch is then unsatisfiable
% 29.94/8.62 |-Branch two:
% 29.94/8.62 | (38) member(all_45_0_11, ex_42_0_9)
% 29.94/8.62 | (60) ~ member(all_45_0_11, ex_42_1_10)
% 29.94/8.63 |
% 29.94/8.63 | Instantiating formula (7) with all_45_0_11 yields:
% 29.94/8.63 | (61) ~ member(all_45_0_11, all_0_0_0)
% 29.94/8.63 |
% 29.94/8.63 | From (27) and (38) follows:
% 29.94/8.63 | (62) member(all_45_0_11, all_0_0_0)
% 29.94/8.63 |
% 29.94/8.63 | Using (62) and (61) yields:
% 29.94/8.63 | (39) $false
% 29.94/8.63 |
% 29.94/8.63 |-The branch is then unsatisfiable
% 29.94/8.63 |-Branch two:
% 29.94/8.63 | (64) all_2_1_2 = all_0_0_0 & ~ (all_2_0_1 = all_2_3_4)
% 29.94/8.63 |
% 29.94/8.63 | Applying alpha-rule on (64) yields:
% 29.94/8.63 | (31) all_2_1_2 = all_0_0_0
% 29.94/8.63 | (66) ~ (all_2_0_1 = all_2_3_4)
% 29.94/8.63 |
% 29.94/8.63 | From (31) and (20) follows:
% 29.94/8.63 | (67) intersection(all_2_3_4, all_2_2_3) = all_0_0_0
% 29.94/8.63 |
% 29.94/8.63 | Introducing new symbol ex_31_1_17 defined by:
% 29.94/8.63 | (68) ex_31_1_17 = all_2_3_4
% 29.94/8.63 |
% 29.94/8.63 | Introducing new symbol ex_31_0_16 defined by:
% 29.94/8.63 | (69) ex_31_0_16 = all_2_3_4
% 29.94/8.63 |
% 29.94/8.63 | Instantiating formula (9) with ex_31_0_16, ex_31_1_17 yields:
% 29.94/8.63 | (70) subset(ex_31_1_17, ex_31_0_16) | ? [v0] : (member(v0, ex_31_1_17) & ~ member(v0, ex_31_0_16))
% 29.94/8.63 |
% 29.94/8.63 +-Applying beta-rule and splitting (70), into two cases.
% 29.94/8.63 |-Branch one:
% 29.94/8.63 | (71) subset(ex_31_1_17, ex_31_0_16)
% 29.94/8.63 |
% 29.94/8.63 | Instantiating formula (17) with ex_31_0_16, ex_31_1_17 and discharging atoms subset(ex_31_1_17, ex_31_0_16), yields:
% 29.94/8.63 | (72) ! [v0] : ( ~ member(v0, ex_31_1_17) | member(v0, ex_31_0_16))
% 29.94/8.63 |
% 29.94/8.63 | Introducing new symbol ex_42_1_20 defined by:
% 29.94/8.63 | (73) ex_42_1_20 = all_2_0_1
% 29.94/8.63 |
% 29.94/8.63 | Introducing new symbol ex_42_0_19 defined by:
% 29.94/8.63 | (74) ex_42_0_19 = all_2_3_4
% 29.94/8.63 |
% 29.94/8.63 | Instantiating formula (6) with ex_42_0_19, ex_42_1_20 yields:
% 29.94/8.63 | (75) ex_42_0_19 = ex_42_1_20 | ? [v0] : (( ~ member(v0, ex_42_0_19) | ~ member(v0, ex_42_1_20)) & (member(v0, ex_42_0_19) | member(v0, ex_42_1_20)))
% 29.94/8.63 |
% 29.94/8.63 +-Applying beta-rule and splitting (75), into two cases.
% 29.94/8.63 |-Branch one:
% 29.94/8.63 | (76) ex_42_0_19 = ex_42_1_20
% 29.94/8.63 |
% 29.94/8.63 | Combining equations (76,74) yields a new equation:
% 29.94/8.63 | (77) ex_42_1_20 = all_2_3_4
% 29.94/8.63 |
% 29.94/8.63 | Simplifying 77 yields:
% 29.94/8.63 | (78) ex_42_1_20 = all_2_3_4
% 29.94/8.63 |
% 29.94/8.63 | Combining equations (78,73) yields a new equation:
% 29.94/8.63 | (23) all_2_0_1 = all_2_3_4
% 29.94/8.63 |
% 29.94/8.63 | Equations (23) can reduce 66 to:
% 29.94/8.63 | (32) $false
% 29.94/8.63 |
% 29.94/8.63 |-The branch is then unsatisfiable
% 29.94/8.63 |-Branch two:
% 29.94/8.63 | (81) ? [v0] : (( ~ member(v0, ex_42_0_19) | ~ member(v0, ex_42_1_20)) & (member(v0, ex_42_0_19) | member(v0, ex_42_1_20)))
% 29.94/8.63 |
% 29.94/8.63 | Instantiating (81) with all_45_0_21 yields:
% 29.94/8.63 | (82) ( ~ member(all_45_0_21, ex_42_0_19) | ~ member(all_45_0_21, ex_42_1_20)) & (member(all_45_0_21, ex_42_0_19) | member(all_45_0_21, ex_42_1_20))
% 29.94/8.63 |
% 29.94/8.63 | Applying alpha-rule on (82) yields:
% 29.94/8.63 | (83) ~ member(all_45_0_21, ex_42_0_19) | ~ member(all_45_0_21, ex_42_1_20)
% 29.94/8.63 | (84) member(all_45_0_21, ex_42_0_19) | member(all_45_0_21, ex_42_1_20)
% 29.94/8.63 |
% 29.94/8.63 +-Applying beta-rule and splitting (83), into two cases.
% 29.94/8.63 |-Branch one:
% 29.94/8.63 | (85) ~ member(all_45_0_21, ex_42_0_19)
% 29.94/8.63 |
% 29.94/8.63 +-Applying beta-rule and splitting (84), into two cases.
% 29.94/8.63 |-Branch one:
% 29.94/8.63 | (86) member(all_45_0_21, ex_42_0_19)
% 29.94/8.63 |
% 29.94/8.63 | Using (86) and (85) yields:
% 29.94/8.63 | (39) $false
% 29.94/8.63 |
% 29.94/8.63 |-The branch is then unsatisfiable
% 29.94/8.63 |-Branch two:
% 29.94/8.63 | (88) member(all_45_0_21, ex_42_1_20)
% 29.94/8.63 |
% 29.94/8.63 | Instantiating formula (7) with all_45_0_21 yields:
% 29.94/8.63 | (89) ~ member(all_45_0_21, all_0_0_0)
% 29.94/8.63 |
% 29.94/8.63 | Instantiating formula (10) with all_2_0_1, all_45_0_21, all_2_2_3, all_2_3_4 and discharging atoms difference(all_2_3_4, all_2_2_3) = all_2_0_1, yields:
% 29.94/8.63 | (90) ~ member(all_45_0_21, all_2_0_1) | (member(all_45_0_21, all_2_3_4) & ~ member(all_45_0_21, all_2_2_3))
% 29.94/8.63 |
% 29.94/8.63 | Instantiating formula (12) with all_0_0_0, all_45_0_21, all_2_3_4, all_2_3_4 and discharging atoms ~ member(all_45_0_21, all_0_0_0), yields:
% 29.94/8.63 | (91) ~ (intersection(all_2_3_4, all_2_3_4) = all_0_0_0) | ~ member(all_45_0_21, all_2_3_4)
% 29.94/8.63 |
% 29.94/8.63 | Instantiating formula (72) with all_45_0_21 yields:
% 29.94/8.63 | (92) ~ member(all_45_0_21, ex_31_1_17) | member(all_45_0_21, ex_31_0_16)
% 29.94/8.63 |
% 29.94/8.63 +-Applying beta-rule and splitting (92), into two cases.
% 29.94/8.63 |-Branch one:
% 29.94/8.63 | (93) ~ member(all_45_0_21, ex_31_1_17)
% 29.94/8.63 |
% 29.94/8.63 +-Applying beta-rule and splitting (91), into two cases.
% 29.94/8.63 |-Branch one:
% 29.94/8.63 | (94) ~ member(all_45_0_21, all_2_3_4)
% 29.94/8.63 |
% 29.94/8.63 +-Applying beta-rule and splitting (90), into two cases.
% 29.94/8.63 |-Branch one:
% 29.94/8.63 | (95) ~ member(all_45_0_21, all_2_0_1)
% 29.94/8.63 |
% 29.94/8.63 | From (73) and (88) follows:
% 29.94/8.63 | (96) member(all_45_0_21, all_2_0_1)
% 29.94/8.63 |
% 29.94/8.63 | Using (96) and (95) yields:
% 29.94/8.63 | (39) $false
% 29.94/8.63 |
% 29.94/8.63 |-The branch is then unsatisfiable
% 29.94/8.63 |-Branch two:
% 29.94/8.63 | (98) member(all_45_0_21, all_2_3_4) & ~ member(all_45_0_21, all_2_2_3)
% 29.94/8.63 |
% 29.94/8.63 | Applying alpha-rule on (98) yields:
% 29.94/8.63 | (99) member(all_45_0_21, all_2_3_4)
% 29.94/8.63 | (100) ~ member(all_45_0_21, all_2_2_3)
% 29.94/8.63 |
% 29.94/8.63 | Using (99) and (94) yields:
% 29.94/8.63 | (39) $false
% 29.94/8.63 |
% 29.94/8.63 |-The branch is then unsatisfiable
% 29.94/8.63 |-Branch two:
% 29.94/8.63 | (99) member(all_45_0_21, all_2_3_4)
% 29.94/8.63 | (103) ~ (intersection(all_2_3_4, all_2_3_4) = all_0_0_0)
% 29.94/8.63 |
% 29.94/8.63 | From (68) and (93) follows:
% 29.94/8.63 | (94) ~ member(all_45_0_21, all_2_3_4)
% 29.94/8.63 |
% 29.94/8.63 | Using (99) and (94) yields:
% 29.94/8.63 | (39) $false
% 29.94/8.63 |
% 29.94/8.63 |-The branch is then unsatisfiable
% 29.94/8.63 |-Branch two:
% 29.94/8.63 | (106) member(all_45_0_21, ex_31_0_16)
% 29.94/8.63 |
% 29.94/8.63 +-Applying beta-rule and splitting (91), into two cases.
% 29.94/8.63 |-Branch one:
% 29.94/8.63 | (94) ~ member(all_45_0_21, all_2_3_4)
% 29.94/8.63 |
% 29.94/8.63 | From (69) and (106) follows:
% 29.94/8.63 | (99) member(all_45_0_21, all_2_3_4)
% 29.94/8.63 |
% 29.94/8.63 | Using (99) and (94) yields:
% 29.94/8.63 | (39) $false
% 29.94/8.63 |
% 29.94/8.63 |-The branch is then unsatisfiable
% 29.94/8.63 |-Branch two:
% 29.94/8.63 | (99) member(all_45_0_21, all_2_3_4)
% 29.94/8.63 | (103) ~ (intersection(all_2_3_4, all_2_3_4) = all_0_0_0)
% 29.94/8.63 |
% 29.94/8.63 | From (74) and (85) follows:
% 29.94/8.63 | (94) ~ member(all_45_0_21, all_2_3_4)
% 29.94/8.63 |
% 29.94/8.63 | Using (99) and (94) yields:
% 29.94/8.63 | (39) $false
% 29.94/8.63 |
% 29.94/8.63 |-The branch is then unsatisfiable
% 29.94/8.64 |-Branch two:
% 29.94/8.64 | (86) member(all_45_0_21, ex_42_0_19)
% 29.94/8.64 | (115) ~ member(all_45_0_21, ex_42_1_20)
% 29.94/8.64 |
% 29.94/8.64 | Instantiating formula (7) with all_45_0_21 yields:
% 29.94/8.64 | (89) ~ member(all_45_0_21, all_0_0_0)
% 29.94/8.64 |
% 29.94/8.64 | Instantiating formula (10) with all_2_0_1, all_45_0_21, all_2_2_3, all_2_3_4 and discharging atoms difference(all_2_3_4, all_2_2_3) = all_2_0_1, yields:
% 29.94/8.64 | (90) ~ member(all_45_0_21, all_2_0_1) | (member(all_45_0_21, all_2_3_4) & ~ member(all_45_0_21, all_2_2_3))
% 29.94/8.64 |
% 29.94/8.64 | Instantiating formula (2) with all_2_0_1, all_45_0_21, all_2_2_3, all_2_3_4 and discharging atoms difference(all_2_3_4, all_2_2_3) = all_2_0_1, yields:
% 29.94/8.64 | (118) ~ member(all_45_0_21, all_2_3_4) | member(all_45_0_21, all_2_0_1) | member(all_45_0_21, all_2_2_3)
% 29.94/8.64 |
% 29.94/8.64 | Instantiating formula (12) with all_0_0_0, all_45_0_21, all_2_3_4, all_2_3_4 and discharging atoms ~ member(all_45_0_21, all_0_0_0), yields:
% 29.94/8.64 | (91) ~ (intersection(all_2_3_4, all_2_3_4) = all_0_0_0) | ~ member(all_45_0_21, all_2_3_4)
% 29.94/8.64 |
% 29.94/8.64 +-Applying beta-rule and splitting (91), into two cases.
% 29.94/8.64 |-Branch one:
% 29.94/8.64 | (94) ~ member(all_45_0_21, all_2_3_4)
% 29.94/8.64 |
% 29.94/8.64 | From (74) and (86) follows:
% 29.94/8.64 | (99) member(all_45_0_21, all_2_3_4)
% 29.94/8.64 |
% 29.94/8.64 | Using (99) and (94) yields:
% 29.94/8.64 | (39) $false
% 29.94/8.64 |
% 29.94/8.64 |-The branch is then unsatisfiable
% 29.94/8.64 |-Branch two:
% 29.94/8.64 | (99) member(all_45_0_21, all_2_3_4)
% 29.94/8.64 | (103) ~ (intersection(all_2_3_4, all_2_3_4) = all_0_0_0)
% 29.94/8.64 |
% 29.94/8.64 +-Applying beta-rule and splitting (118), into two cases.
% 29.94/8.64 |-Branch one:
% 29.94/8.64 | (94) ~ member(all_45_0_21, all_2_3_4)
% 29.94/8.64 |
% 29.94/8.64 | Using (99) and (94) yields:
% 29.94/8.64 | (39) $false
% 29.94/8.64 |
% 29.94/8.64 |-The branch is then unsatisfiable
% 29.94/8.64 |-Branch two:
% 29.94/8.64 | (127) member(all_45_0_21, all_2_0_1) | member(all_45_0_21, all_2_2_3)
% 29.94/8.64 |
% 29.94/8.64 +-Applying beta-rule and splitting (90), into two cases.
% 29.94/8.64 |-Branch one:
% 29.94/8.64 | (95) ~ member(all_45_0_21, all_2_0_1)
% 29.94/8.64 |
% 29.94/8.64 +-Applying beta-rule and splitting (127), into two cases.
% 29.94/8.64 |-Branch one:
% 29.94/8.64 | (96) member(all_45_0_21, all_2_0_1)
% 29.94/8.64 |
% 29.94/8.64 | Using (96) and (95) yields:
% 29.94/8.64 | (39) $false
% 29.94/8.64 |
% 29.94/8.64 |-The branch is then unsatisfiable
% 29.94/8.64 |-Branch two:
% 29.94/8.64 | (131) member(all_45_0_21, all_2_2_3)
% 29.94/8.64 |
% 29.94/8.64 | Instantiating formula (12) with all_0_0_0, all_45_0_21, all_2_2_3, all_2_3_4 and discharging atoms intersection(all_2_3_4, all_2_2_3) = all_0_0_0, member(all_45_0_21, all_2_2_3), ~ member(all_45_0_21, all_0_0_0), yields:
% 29.94/8.64 | (94) ~ member(all_45_0_21, all_2_3_4)
% 29.94/8.64 |
% 29.94/8.64 | Using (99) and (94) yields:
% 29.94/8.64 | (39) $false
% 29.94/8.64 |
% 29.94/8.64 |-The branch is then unsatisfiable
% 29.94/8.64 |-Branch two:
% 29.94/8.64 | (96) member(all_45_0_21, all_2_0_1)
% 29.94/8.64 | (98) member(all_45_0_21, all_2_3_4) & ~ member(all_45_0_21, all_2_2_3)
% 29.94/8.64 |
% 29.94/8.64 | From (73) and (115) follows:
% 29.94/8.64 | (95) ~ member(all_45_0_21, all_2_0_1)
% 29.94/8.64 |
% 29.94/8.64 | Using (96) and (95) yields:
% 29.94/8.64 | (39) $false
% 29.94/8.64 |
% 29.94/8.64 |-The branch is then unsatisfiable
% 29.94/8.64 |-Branch two:
% 29.94/8.64 | (138) ? [v0] : (member(v0, ex_31_1_17) & ~ member(v0, ex_31_0_16))
% 29.94/8.64 |
% 29.94/8.64 | Instantiating (138) with all_33_0_18 yields:
% 29.94/8.64 | (139) member(all_33_0_18, ex_31_1_17) & ~ member(all_33_0_18, ex_31_0_16)
% 29.94/8.64 |
% 29.94/8.64 | Applying alpha-rule on (139) yields:
% 29.94/8.64 | (140) member(all_33_0_18, ex_31_1_17)
% 29.94/8.64 | (141) ~ member(all_33_0_18, ex_31_0_16)
% 29.94/8.64 |
% 29.94/8.64 | Instantiating formula (7) with all_33_0_18 yields:
% 29.94/8.64 | (142) ~ member(all_33_0_18, all_0_0_0)
% 29.94/8.64 |
% 29.94/8.64 | Instantiating formula (12) with all_0_0_0, all_33_0_18, all_2_3_4, all_2_3_4 and discharging atoms ~ member(all_33_0_18, all_0_0_0), yields:
% 29.94/8.64 | (143) ~ (intersection(all_2_3_4, all_2_3_4) = all_0_0_0) | ~ member(all_33_0_18, all_2_3_4)
% 29.94/8.64 |
% 29.94/8.64 +-Applying beta-rule and splitting (143), into two cases.
% 29.94/8.64 |-Branch one:
% 29.94/8.64 | (144) ~ member(all_33_0_18, all_2_3_4)
% 29.94/8.64 |
% 29.94/8.64 | From (68) and (140) follows:
% 29.94/8.64 | (145) member(all_33_0_18, all_2_3_4)
% 29.94/8.64 |
% 29.94/8.64 | Using (145) and (144) yields:
% 29.94/8.64 | (39) $false
% 29.94/8.64 |
% 29.94/8.64 |-The branch is then unsatisfiable
% 29.94/8.64 |-Branch two:
% 29.94/8.64 | (145) member(all_33_0_18, all_2_3_4)
% 29.94/8.64 | (103) ~ (intersection(all_2_3_4, all_2_3_4) = all_0_0_0)
% 29.94/8.64 |
% 29.94/8.64 | From (69) and (141) follows:
% 29.94/8.64 | (144) ~ member(all_33_0_18, all_2_3_4)
% 29.94/8.64 |
% 29.94/8.64 | Using (145) and (144) yields:
% 29.94/8.64 | (39) $false
% 29.94/8.64 |
% 29.94/8.64 |-The branch is then unsatisfiable
% 29.94/8.64 % SZS output end Proof for theBenchmark
% 29.94/8.64
% 29.94/8.64 8002ms
%------------------------------------------------------------------------------