TSTP Solution File: SET587+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 00:20:29 EDT 2022
% Result : Theorem 11.57s 3.64s
% Output : Proof 14.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n021.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 : Sat Jul 9 18:22:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.53/0.58 ____ _
% 0.53/0.58 ___ / __ \_____(_)___ ________ __________
% 0.53/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.58
% 0.53/0.58 A Theorem Prover for First-Order Logic
% 0.53/0.59 (ePrincess v.1.0)
% 0.53/0.59
% 0.53/0.59 (c) Philipp Rümmer, 2009-2015
% 0.53/0.59 (c) Peter Backeman, 2014-2015
% 0.53/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.59 Bug reports to peter@backeman.se
% 0.53/0.59
% 0.53/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.59
% 0.53/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.89 Prover 0: Preprocessing ...
% 1.66/1.02 Prover 0: Warning: ignoring some quantifiers
% 1.82/1.04 Prover 0: Constructing countermodel ...
% 2.18/1.16 Prover 0: gave up
% 2.18/1.17 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.27/1.18 Prover 1: Preprocessing ...
% 2.50/1.26 Prover 1: Warning: ignoring some quantifiers
% 2.50/1.27 Prover 1: Constructing countermodel ...
% 2.50/1.31 Prover 1: gave up
% 2.50/1.32 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.70/1.34 Prover 2: Preprocessing ...
% 3.21/1.44 Prover 2: Warning: ignoring some quantifiers
% 3.21/1.45 Prover 2: Constructing countermodel ...
% 3.36/1.50 Prover 2: gave up
% 3.36/1.51 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.36/1.52 Prover 3: Preprocessing ...
% 3.62/1.54 Prover 3: Warning: ignoring some quantifiers
% 3.62/1.54 Prover 3: Constructing countermodel ...
% 3.71/1.57 Prover 3: gave up
% 3.71/1.57 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.71/1.59 Prover 4: Preprocessing ...
% 4.03/1.65 Prover 4: Warning: ignoring some quantifiers
% 4.03/1.66 Prover 4: Constructing countermodel ...
% 5.46/2.00 Prover 4: gave up
% 5.46/2.00 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.46/2.00 Prover 5: Preprocessing ...
% 5.46/2.04 Prover 5: Warning: ignoring some quantifiers
% 5.46/2.04 Prover 5: Constructing countermodel ...
% 5.83/2.07 Prover 5: gave up
% 5.83/2.07 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.83/2.08 Prover 6: Preprocessing ...
% 5.93/2.10 Prover 6: Warning: ignoring some quantifiers
% 5.93/2.10 Prover 6: Constructing countermodel ...
% 6.11/2.12 Prover 6: gave up
% 6.11/2.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 6.11/2.13 Prover 7: Preprocessing ...
% 6.11/2.14 Prover 7: Proving ...
% 11.57/3.64 Prover 7: proved (1520ms)
% 11.57/3.64
% 11.57/3.64 % SZS status Theorem for theBenchmark
% 11.57/3.64
% 11.57/3.64 Generating proof ... found it (size 62)
% 14.44/4.43
% 14.44/4.43 % SZS output start Proof for theBenchmark
% 14.44/4.43 Assumed formulas after preprocessing and simplification:
% 14.44/4.43 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (difference(v4, v3) = v2) | ~ (difference(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] : (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] : (difference(v1, v2) = v3 & ((v3 = v0 & ~ subset(v1, v2)) | ( ~ (v3 = v0) & subset(v1, v2)))))
% 14.73/4.45 | Instantiating (0) with all_0_0_0 yields:
% 14.73/4.45 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(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] : (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] : (difference(v0, v1) = v2 & ((v2 = all_0_0_0 & ~ subset(v0, v1)) | ( ~ (v2 = all_0_0_0) & subset(v0, v1))))
% 14.73/4.45 |
% 14.73/4.45 | Applying alpha-rule on (1) yields:
% 14.73/4.45 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1))
% 14.73/4.45 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v0) & ~ member(v2, v1)))
% 14.73/4.45 | (4) ? [v0] : ? [v1] : ? [v2] : (difference(v0, v1) = v2 & ((v2 = all_0_0_0 & ~ subset(v0, v1)) | ( ~ (v2 = all_0_0_0) & subset(v0, v1))))
% 14.73/4.45 | (5) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 14.73/4.46 | (6) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 14.73/4.46 | (7) ! [v0] : ~ member(v0, all_0_0_0)
% 14.73/4.46 | (8) ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0))
% 14.73/4.46 | (9) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1)))
% 14.73/4.46 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 14.73/4.46 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 14.84/4.46 | (12) ! [v0] : subset(v0, v0)
% 14.84/4.46 | (13) ! [v0] : (empty(v0) | ? [v1] : member(v1, v0))
% 14.84/4.46 |
% 14.84/4.46 | Instantiating (4) with all_2_0_1, all_2_1_2, all_2_2_3 yields:
% 14.84/4.46 | (14) difference(all_2_2_3, all_2_1_2) = all_2_0_1 & ((all_2_0_1 = all_0_0_0 & ~ subset(all_2_2_3, all_2_1_2)) | ( ~ (all_2_0_1 = all_0_0_0) & subset(all_2_2_3, all_2_1_2)))
% 14.84/4.46 |
% 14.84/4.46 | Applying alpha-rule on (14) yields:
% 14.84/4.46 | (15) difference(all_2_2_3, all_2_1_2) = all_2_0_1
% 14.84/4.46 | (16) (all_2_0_1 = all_0_0_0 & ~ subset(all_2_2_3, all_2_1_2)) | ( ~ (all_2_0_1 = all_0_0_0) & subset(all_2_2_3, all_2_1_2))
% 14.84/4.46 |
% 14.84/4.46 +-Applying beta-rule and splitting (16), into two cases.
% 14.84/4.46 |-Branch one:
% 14.84/4.46 | (17) all_2_0_1 = all_0_0_0 & ~ subset(all_2_2_3, all_2_1_2)
% 14.84/4.46 |
% 14.84/4.46 | Applying alpha-rule on (17) yields:
% 14.84/4.46 | (18) all_2_0_1 = all_0_0_0
% 14.84/4.46 | (19) ~ subset(all_2_2_3, all_2_1_2)
% 14.84/4.46 |
% 14.84/4.46 | From (18) and (15) follows:
% 14.84/4.46 | (20) difference(all_2_2_3, all_2_1_2) = all_0_0_0
% 14.84/4.46 |
% 14.84/4.46 | Introducing new symbol ex_26_1_8 defined by:
% 14.84/4.46 | (21) ex_26_1_8 = all_2_2_3
% 14.84/4.46 |
% 14.84/4.46 | Introducing new symbol ex_26_0_7 defined by:
% 14.84/4.46 | (22) ex_26_0_7 = all_2_1_2
% 14.84/4.46 |
% 14.84/4.46 | Instantiating formula (5) with ex_26_0_7, ex_26_1_8 yields:
% 14.84/4.46 | (23) subset(ex_26_1_8, ex_26_0_7) | ? [v0] : (member(v0, ex_26_1_8) & ~ member(v0, ex_26_0_7))
% 14.84/4.46 |
% 14.84/4.46 +-Applying beta-rule and splitting (23), into two cases.
% 14.84/4.46 |-Branch one:
% 14.84/4.46 | (24) subset(ex_26_1_8, ex_26_0_7)
% 14.84/4.46 |
% 14.84/4.46 | From (21)(22) and (24) follows:
% 14.84/4.46 | (25) subset(all_2_2_3, all_2_1_2)
% 14.84/4.46 |
% 14.84/4.46 | Using (25) and (19) yields:
% 14.84/4.46 | (26) $false
% 14.84/4.46 |
% 14.84/4.46 |-The branch is then unsatisfiable
% 14.84/4.46 |-Branch two:
% 14.84/4.46 | (27) ? [v0] : (member(v0, ex_26_1_8) & ~ member(v0, ex_26_0_7))
% 14.84/4.46 |
% 14.84/4.46 | Instantiating (27) with all_28_0_9 yields:
% 14.84/4.46 | (28) member(all_28_0_9, ex_26_1_8) & ~ member(all_28_0_9, ex_26_0_7)
% 14.84/4.46 |
% 14.84/4.46 | Applying alpha-rule on (28) yields:
% 14.84/4.46 | (29) member(all_28_0_9, ex_26_1_8)
% 14.84/4.46 | (30) ~ member(all_28_0_9, ex_26_0_7)
% 14.84/4.46 |
% 14.84/4.46 | Instantiating formula (7) with all_28_0_9 yields:
% 14.84/4.46 | (31) ~ member(all_28_0_9, all_0_0_0)
% 14.84/4.46 |
% 14.84/4.46 | Instantiating formula (2) with all_0_0_0, all_28_0_9, all_2_1_2, all_2_2_3 and discharging atoms difference(all_2_2_3, all_2_1_2) = all_0_0_0, ~ member(all_28_0_9, all_0_0_0), yields:
% 14.84/4.47 | (32) ~ member(all_28_0_9, all_2_2_3) | member(all_28_0_9, all_2_1_2)
% 14.84/4.47 |
% 14.84/4.47 +-Applying beta-rule and splitting (32), into two cases.
% 14.84/4.47 |-Branch one:
% 14.84/4.47 | (33) ~ member(all_28_0_9, all_2_2_3)
% 14.84/4.47 |
% 14.84/4.47 | From (21) and (29) follows:
% 14.84/4.47 | (34) member(all_28_0_9, all_2_2_3)
% 14.84/4.47 |
% 14.84/4.47 | Using (34) and (33) yields:
% 14.84/4.47 | (26) $false
% 14.84/4.47 |
% 14.84/4.47 |-The branch is then unsatisfiable
% 14.84/4.47 |-Branch two:
% 14.84/4.47 | (36) member(all_28_0_9, all_2_1_2)
% 14.84/4.47 |
% 14.84/4.47 | From (22) and (30) follows:
% 14.84/4.47 | (37) ~ member(all_28_0_9, all_2_1_2)
% 14.84/4.47 |
% 14.84/4.47 | Using (36) and (37) yields:
% 14.84/4.47 | (26) $false
% 14.84/4.47 |
% 14.84/4.47 |-The branch is then unsatisfiable
% 14.84/4.47 |-Branch two:
% 14.84/4.47 | (39) ~ (all_2_0_1 = all_0_0_0) & subset(all_2_2_3, all_2_1_2)
% 14.84/4.47 |
% 14.84/4.47 | Applying alpha-rule on (39) yields:
% 14.84/4.47 | (40) ~ (all_2_0_1 = all_0_0_0)
% 14.84/4.47 | (25) subset(all_2_2_3, all_2_1_2)
% 14.84/4.47 |
% 14.84/4.47 | Instantiating formula (9) with all_2_1_2, all_2_2_3 and discharging atoms subset(all_2_2_3, all_2_1_2), yields:
% 14.84/4.47 | (42) ! [v0] : ( ~ member(v0, all_2_2_3) | member(v0, all_2_1_2))
% 14.84/4.47 |
% 14.84/4.47 | Introducing new symbol ex_19_1_11 defined by:
% 14.84/4.47 | (43) ex_19_1_11 = all_2_0_1
% 14.84/4.47 |
% 14.84/4.47 | Introducing new symbol ex_19_0_10 defined by:
% 14.84/4.47 | (44) ex_19_0_10 = all_0_0_0
% 14.84/4.47 |
% 14.84/4.47 | Instantiating formula (6) with ex_19_0_10, ex_19_1_11 yields:
% 14.84/4.47 | (45) ex_19_0_10 = ex_19_1_11 | ? [v0] : (( ~ member(v0, ex_19_0_10) | ~ member(v0, ex_19_1_11)) & (member(v0, ex_19_0_10) | member(v0, ex_19_1_11)))
% 14.84/4.47 |
% 14.84/4.47 +-Applying beta-rule and splitting (45), into two cases.
% 14.84/4.47 |-Branch one:
% 14.84/4.47 | (46) ex_19_0_10 = ex_19_1_11
% 14.84/4.47 |
% 14.84/4.47 | Combining equations (44,46) yields a new equation:
% 14.84/4.47 | (47) ex_19_1_11 = all_0_0_0
% 14.84/4.47 |
% 14.84/4.47 | Combining equations (47,43) yields a new equation:
% 14.84/4.47 | (18) all_2_0_1 = all_0_0_0
% 14.84/4.47 |
% 14.84/4.47 | Equations (18) can reduce 40 to:
% 14.84/4.47 | (49) $false
% 14.84/4.47 |
% 14.84/4.47 |-The branch is then unsatisfiable
% 14.84/4.47 |-Branch two:
% 14.84/4.47 | (50) ? [v0] : (( ~ member(v0, ex_19_0_10) | ~ member(v0, ex_19_1_11)) & (member(v0, ex_19_0_10) | member(v0, ex_19_1_11)))
% 14.84/4.47 |
% 14.84/4.47 | Instantiating (50) with all_22_0_12 yields:
% 14.84/4.47 | (51) ( ~ member(all_22_0_12, ex_19_0_10) | ~ member(all_22_0_12, ex_19_1_11)) & (member(all_22_0_12, ex_19_0_10) | member(all_22_0_12, ex_19_1_11))
% 14.84/4.47 |
% 14.84/4.47 | Applying alpha-rule on (51) yields:
% 14.84/4.47 | (52) ~ member(all_22_0_12, ex_19_0_10) | ~ member(all_22_0_12, ex_19_1_11)
% 14.84/4.47 | (53) member(all_22_0_12, ex_19_0_10) | member(all_22_0_12, ex_19_1_11)
% 14.84/4.47 |
% 14.84/4.47 +-Applying beta-rule and splitting (52), into two cases.
% 14.84/4.47 |-Branch one:
% 14.84/4.47 | (54) ~ member(all_22_0_12, ex_19_0_10)
% 14.84/4.47 |
% 14.84/4.47 +-Applying beta-rule and splitting (53), into two cases.
% 14.84/4.47 |-Branch one:
% 14.84/4.47 | (55) member(all_22_0_12, ex_19_0_10)
% 14.84/4.47 |
% 14.84/4.47 | Using (55) and (54) yields:
% 14.84/4.47 | (26) $false
% 14.84/4.47 |
% 14.84/4.47 |-The branch is then unsatisfiable
% 14.84/4.47 |-Branch two:
% 14.84/4.47 | (57) member(all_22_0_12, ex_19_1_11)
% 14.84/4.47 |
% 14.84/4.47 | Instantiating formula (3) with all_2_0_1, all_22_0_12, all_2_1_2, all_2_2_3 and discharging atoms difference(all_2_2_3, all_2_1_2) = all_2_0_1, yields:
% 14.84/4.47 | (58) ~ member(all_22_0_12, all_2_0_1) | (member(all_22_0_12, all_2_2_3) & ~ member(all_22_0_12, all_2_1_2))
% 14.84/4.47 |
% 14.84/4.47 | Instantiating formula (42) with all_22_0_12 yields:
% 14.84/4.47 | (59) ~ member(all_22_0_12, all_2_2_3) | member(all_22_0_12, all_2_1_2)
% 14.84/4.47 |
% 14.84/4.47 +-Applying beta-rule and splitting (59), into two cases.
% 14.84/4.47 |-Branch one:
% 14.84/4.47 | (60) ~ member(all_22_0_12, all_2_2_3)
% 14.84/4.47 |
% 14.84/4.47 +-Applying beta-rule and splitting (58), into two cases.
% 14.84/4.47 |-Branch one:
% 14.84/4.47 | (61) ~ member(all_22_0_12, all_2_0_1)
% 14.84/4.47 |
% 14.84/4.47 | From (43) and (57) follows:
% 14.84/4.47 | (62) member(all_22_0_12, all_2_0_1)
% 14.84/4.47 |
% 14.84/4.47 | Using (62) and (61) yields:
% 14.84/4.47 | (26) $false
% 14.84/4.47 |
% 14.84/4.47 |-The branch is then unsatisfiable
% 14.84/4.47 |-Branch two:
% 14.84/4.48 | (64) member(all_22_0_12, all_2_2_3) & ~ member(all_22_0_12, all_2_1_2)
% 14.84/4.48 |
% 14.84/4.48 | Applying alpha-rule on (64) yields:
% 14.84/4.48 | (65) member(all_22_0_12, all_2_2_3)
% 14.84/4.48 | (66) ~ member(all_22_0_12, all_2_1_2)
% 14.84/4.48 |
% 14.84/4.48 | Using (65) and (60) yields:
% 14.84/4.48 | (26) $false
% 14.84/4.48 |
% 14.84/4.48 |-The branch is then unsatisfiable
% 14.84/4.48 |-Branch two:
% 14.84/4.48 | (68) member(all_22_0_12, all_2_1_2)
% 14.84/4.48 |
% 14.84/4.48 +-Applying beta-rule and splitting (58), into two cases.
% 14.84/4.48 |-Branch one:
% 14.84/4.48 | (61) ~ member(all_22_0_12, all_2_0_1)
% 14.84/4.48 |
% 14.84/4.48 | From (43) and (57) follows:
% 14.84/4.48 | (62) member(all_22_0_12, all_2_0_1)
% 14.84/4.48 |
% 14.84/4.48 | Using (62) and (61) yields:
% 14.84/4.48 | (26) $false
% 14.84/4.48 |
% 14.84/4.48 |-The branch is then unsatisfiable
% 14.84/4.48 |-Branch two:
% 14.84/4.48 | (64) member(all_22_0_12, all_2_2_3) & ~ member(all_22_0_12, all_2_1_2)
% 14.84/4.48 |
% 14.84/4.48 | Applying alpha-rule on (64) yields:
% 14.84/4.48 | (65) member(all_22_0_12, all_2_2_3)
% 14.84/4.48 | (66) ~ member(all_22_0_12, all_2_1_2)
% 14.84/4.48 |
% 14.84/4.48 | Using (68) and (66) yields:
% 14.84/4.48 | (26) $false
% 14.84/4.48 |
% 14.84/4.48 |-The branch is then unsatisfiable
% 14.84/4.48 |-Branch two:
% 14.84/4.48 | (55) member(all_22_0_12, ex_19_0_10)
% 14.84/4.48 | (77) ~ member(all_22_0_12, ex_19_1_11)
% 14.84/4.48 |
% 14.84/4.48 | Instantiating formula (7) with all_22_0_12 yields:
% 14.84/4.48 | (78) ~ member(all_22_0_12, all_0_0_0)
% 14.84/4.48 |
% 14.84/4.48 | From (44) and (55) follows:
% 14.84/4.48 | (79) member(all_22_0_12, all_0_0_0)
% 14.84/4.48 |
% 14.84/4.48 | Using (79) and (78) yields:
% 14.84/4.48 | (26) $false
% 14.84/4.48 |
% 14.84/4.48 |-The branch is then unsatisfiable
% 14.84/4.48 % SZS output end Proof for theBenchmark
% 14.84/4.48
% 14.84/4.48 3883ms
%------------------------------------------------------------------------------