TSTP Solution File: SET628+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 00:20:59 EDT 2022
% Result : Theorem 13.13s 4.56s
% Output : Proof 20.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n023.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 : Mon Jul 11 02:48:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.60 ____ _
% 0.57/0.60 ___ / __ \_____(_)___ ________ __________
% 0.57/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.60
% 0.57/0.60 A Theorem Prover for First-Order Logic
% 0.57/0.60 (ePrincess v.1.0)
% 0.57/0.60
% 0.57/0.60 (c) Philipp Rümmer, 2009-2015
% 0.57/0.60 (c) Peter Backeman, 2014-2015
% 0.57/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.61 Bug reports to peter@backeman.se
% 0.57/0.61
% 0.57/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.61
% 0.57/0.61 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
% 1.38/0.91 Prover 0: Preprocessing ...
% 1.50/1.01 Prover 0: Warning: ignoring some quantifiers
% 1.67/1.02 Prover 0: Constructing countermodel ...
% 1.85/1.13 Prover 0: gave up
% 1.85/1.13 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.85/1.15 Prover 1: Preprocessing ...
% 2.46/1.23 Prover 1: Warning: ignoring some quantifiers
% 2.46/1.24 Prover 1: Constructing countermodel ...
% 2.46/1.29 Prover 1: gave up
% 2.46/1.29 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.46/1.30 Prover 2: Preprocessing ...
% 2.77/1.36 Prover 2: Warning: ignoring some quantifiers
% 2.77/1.37 Prover 2: Constructing countermodel ...
% 3.00/1.42 Prover 2: gave up
% 3.00/1.43 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.00/1.44 Prover 3: Preprocessing ...
% 3.00/1.45 Prover 3: Warning: ignoring some quantifiers
% 3.00/1.45 Prover 3: Constructing countermodel ...
% 3.00/1.47 Prover 3: gave up
% 3.00/1.47 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.28/1.48 Prover 4: Preprocessing ...
% 3.28/1.54 Prover 4: Warning: ignoring some quantifiers
% 3.28/1.54 Prover 4: Constructing countermodel ...
% 4.43/1.76 Prover 4: gave up
% 4.43/1.76 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.43/1.77 Prover 5: Preprocessing ...
% 4.43/1.79 Prover 5: Warning: ignoring some quantifiers
% 4.43/1.79 Prover 5: Constructing countermodel ...
% 4.83/1.83 Prover 5: gave up
% 4.83/1.83 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.83/1.84 Prover 6: Preprocessing ...
% 4.83/1.86 Prover 6: Warning: ignoring some quantifiers
% 4.83/1.86 Prover 6: Constructing countermodel ...
% 5.17/1.89 Prover 6: gave up
% 5.17/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 5.17/1.89 Prover 7: Preprocessing ...
% 5.17/1.90 Prover 7: Proving ...
% 13.13/4.56 Prover 7: proved (2669ms)
% 13.13/4.56
% 13.13/4.56 % SZS status Theorem for theBenchmark
% 13.13/4.56
% 13.13/4.56 Generating proof ... found it (size 84)
% 20.89/7.48
% 20.89/7.48 % SZS output start Proof for theBenchmark
% 20.89/7.48 Assumed formulas after preprocessing and simplification:
% 20.89/7.48 | (0) ? [v0] : ( ! [v1] : ! [v2] : (v2 = v1 | not_equal(v1, v2)) & ! [v1] : ! [v2] : (v2 = v1 | ? [v3] : (( ~ member(v3, v2) | ~ member(v3, v1)) & (member(v3, v2) | member(v3, v1)))) & ! [v1] : ! [v2] : ( ~ intersect(v1, v2) | intersect(v2, v1)) & ! [v1] : ! [v2] : ( ~ intersect(v1, v2) | ? [v3] : (member(v3, v2) & member(v3, v1))) & ! [v1] : ! [v2] : (intersect(v1, v2) | ! [v3] : ( ~ member(v3, v2) | ~ member(v3, v1))) & ! [v1] : ( ~ empty(v1) | ! [v2] : ~ member(v2, v1)) & ! [v1] : ~ not_equal(v1, v1) & ! [v1] : ~ member(v1, v0) & ! [v1] : (empty(v1) | ? [v2] : member(v2, v1)) & ? [v1] : ((not_equal(v1, v0) & ~ intersect(v1, v1)) | (intersect(v1, v1) & ~ not_equal(v1, v0))))
% 20.89/7.48 | Instantiating (0) with all_0_0_0 yields:
% 20.89/7.48 | (1) ! [v0] : ! [v1] : (v1 = v0 | not_equal(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | intersect(v1, v0)) & ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0))) & ! [v0] : ! [v1] : (intersect(v0, v1) | ! [v2] : ( ~ member(v2, v1) | ~ member(v2, v0))) & ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0)) & ! [v0] : ~ not_equal(v0, v0) & ! [v0] : ~ member(v0, all_0_0_0) & ! [v0] : (empty(v0) | ? [v1] : member(v1, v0)) & ? [v0] : ((not_equal(v0, all_0_0_0) & ~ intersect(v0, v0)) | (intersect(v0, v0) & ~ not_equal(v0, all_0_0_0)))
% 20.89/7.48 |
% 20.89/7.48 | Applying alpha-rule on (1) yields:
% 20.89/7.48 | (2) ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | intersect(v1, v0))
% 20.89/7.48 | (3) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 20.89/7.48 | (4) ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0))
% 20.89/7.49 | (5) ! [v0] : ~ member(v0, all_0_0_0)
% 20.89/7.49 | (6) ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0)))
% 20.89/7.49 | (7) ! [v0] : (empty(v0) | ? [v1] : member(v1, v0))
% 20.89/7.49 | (8) ? [v0] : ((not_equal(v0, all_0_0_0) & ~ intersect(v0, v0)) | (intersect(v0, v0) & ~ not_equal(v0, all_0_0_0)))
% 20.89/7.49 | (9) ! [v0] : ! [v1] : (v1 = v0 | not_equal(v0, v1))
% 20.89/7.49 | (10) ! [v0] : ! [v1] : (intersect(v0, v1) | ! [v2] : ( ~ member(v2, v1) | ~ member(v2, v0)))
% 20.89/7.49 | (11) ! [v0] : ~ not_equal(v0, v0)
% 20.89/7.49 |
% 20.89/7.49 | Instantiating (8) with all_2_0_1 yields:
% 20.89/7.49 | (12) (not_equal(all_2_0_1, all_0_0_0) & ~ intersect(all_2_0_1, all_2_0_1)) | (intersect(all_2_0_1, all_2_0_1) & ~ not_equal(all_2_0_1, all_0_0_0))
% 20.89/7.49 |
% 20.89/7.49 +-Applying beta-rule and splitting (12), into two cases.
% 20.89/7.49 |-Branch one:
% 20.89/7.49 | (13) not_equal(all_2_0_1, all_0_0_0) & ~ intersect(all_2_0_1, all_2_0_1)
% 20.89/7.49 |
% 20.89/7.49 | Applying alpha-rule on (13) yields:
% 20.89/7.49 | (14) not_equal(all_2_0_1, all_0_0_0)
% 20.89/7.49 | (15) ~ intersect(all_2_0_1, all_2_0_1)
% 20.89/7.49 |
% 20.89/7.49 | Instantiating formula (11) with all_0_0_0 yields:
% 20.89/7.49 | (16) ~ not_equal(all_0_0_0, all_0_0_0)
% 20.89/7.49 |
% 20.89/7.49 | Introducing new symbol ex_18_1_3 defined by:
% 20.89/7.49 | (17) ex_18_1_3 = all_2_0_1
% 20.89/7.49 |
% 20.89/7.49 | Introducing new symbol ex_18_0_2 defined by:
% 20.89/7.49 | (18) ex_18_0_2 = all_2_0_1
% 20.89/7.49 |
% 20.89/7.49 | Instantiating formula (10) with ex_18_0_2, ex_18_1_3 yields:
% 20.89/7.49 | (19) intersect(ex_18_1_3, ex_18_0_2) | ! [v0] : ( ~ member(v0, ex_18_0_2) | ~ member(v0, ex_18_1_3))
% 20.89/7.49 |
% 20.89/7.49 +-Applying beta-rule and splitting (19), into two cases.
% 20.89/7.49 |-Branch one:
% 20.89/7.49 | (20) intersect(ex_18_1_3, ex_18_0_2)
% 20.89/7.49 |
% 20.89/7.49 | From (17)(18) and (20) follows:
% 20.89/7.49 | (21) intersect(all_2_0_1, all_2_0_1)
% 20.89/7.49 |
% 20.89/7.49 | Using (21) and (15) yields:
% 20.89/7.49 | (22) $false
% 20.89/7.49 |
% 20.89/7.49 |-The branch is then unsatisfiable
% 20.89/7.49 |-Branch two:
% 20.89/7.49 | (23) ! [v0] : ( ~ member(v0, ex_18_0_2) | ~ member(v0, ex_18_1_3))
% 20.89/7.49 |
% 20.89/7.49 | Introducing new symbol ex_47_1_9 defined by:
% 20.89/7.49 | (24) ex_47_1_9 = all_2_0_1
% 20.89/7.49 |
% 20.89/7.49 | Introducing new symbol ex_47_0_8 defined by:
% 20.89/7.49 | (25) ex_47_0_8 = all_0_0_0
% 20.89/7.49 |
% 20.89/7.49 | Instantiating formula (3) with ex_47_0_8, ex_47_1_9 yields:
% 20.89/7.49 | (26) ex_47_0_8 = ex_47_1_9 | ? [v0] : (( ~ member(v0, ex_47_0_8) | ~ member(v0, ex_47_1_9)) & (member(v0, ex_47_0_8) | member(v0, ex_47_1_9)))
% 20.89/7.49 |
% 20.89/7.49 +-Applying beta-rule and splitting (26), into two cases.
% 20.89/7.49 |-Branch one:
% 20.89/7.49 | (27) ex_47_0_8 = ex_47_1_9
% 20.89/7.49 |
% 20.89/7.49 | Combining equations (25,27) yields a new equation:
% 20.89/7.49 | (28) ex_47_1_9 = all_0_0_0
% 20.89/7.49 |
% 20.89/7.49 | Combining equations (28,24) yields a new equation:
% 20.89/7.49 | (29) all_2_0_1 = all_0_0_0
% 20.89/7.49 |
% 20.89/7.49 | From (29) and (14) follows:
% 20.89/7.49 | (30) not_equal(all_0_0_0, all_0_0_0)
% 20.89/7.49 |
% 20.89/7.49 | Using (30) and (16) yields:
% 20.89/7.49 | (22) $false
% 20.89/7.49 |
% 20.89/7.49 |-The branch is then unsatisfiable
% 20.89/7.49 |-Branch two:
% 20.89/7.49 | (32) ? [v0] : (( ~ member(v0, ex_47_0_8) | ~ member(v0, ex_47_1_9)) & (member(v0, ex_47_0_8) | member(v0, ex_47_1_9)))
% 20.89/7.49 |
% 20.89/7.49 | Instantiating (32) with all_50_0_12 yields:
% 20.89/7.49 | (33) ( ~ member(all_50_0_12, ex_47_0_8) | ~ member(all_50_0_12, ex_47_1_9)) & (member(all_50_0_12, ex_47_0_8) | member(all_50_0_12, ex_47_1_9))
% 20.89/7.49 |
% 20.89/7.49 | Applying alpha-rule on (33) yields:
% 20.89/7.49 | (34) ~ member(all_50_0_12, ex_47_0_8) | ~ member(all_50_0_12, ex_47_1_9)
% 20.89/7.49 | (35) member(all_50_0_12, ex_47_0_8) | member(all_50_0_12, ex_47_1_9)
% 20.89/7.49 |
% 20.89/7.49 +-Applying beta-rule and splitting (34), into two cases.
% 20.89/7.49 |-Branch one:
% 20.89/7.49 | (36) ~ member(all_50_0_12, ex_47_0_8)
% 20.89/7.49 |
% 20.89/7.49 +-Applying beta-rule and splitting (35), into two cases.
% 20.89/7.49 |-Branch one:
% 20.89/7.49 | (37) member(all_50_0_12, ex_47_0_8)
% 20.89/7.49 |
% 20.89/7.49 | Using (37) and (36) yields:
% 20.89/7.49 | (22) $false
% 20.89/7.49 |
% 20.89/7.49 |-The branch is then unsatisfiable
% 20.89/7.49 |-Branch two:
% 20.89/7.49 | (39) member(all_50_0_12, ex_47_1_9)
% 20.89/7.49 |
% 20.89/7.49 | Instantiating formula (23) with all_50_0_12 yields:
% 20.89/7.49 | (40) ~ member(all_50_0_12, ex_18_0_2) | ~ member(all_50_0_12, ex_18_1_3)
% 20.89/7.49 |
% 20.89/7.49 +-Applying beta-rule and splitting (40), into two cases.
% 20.89/7.49 |-Branch one:
% 20.89/7.49 | (41) ~ member(all_50_0_12, ex_18_0_2)
% 20.89/7.49 |
% 20.89/7.49 | From (24) and (39) follows:
% 20.89/7.49 | (42) member(all_50_0_12, all_2_0_1)
% 20.89/7.49 |
% 20.89/7.49 | From (18) and (41) follows:
% 20.89/7.49 | (43) ~ member(all_50_0_12, all_2_0_1)
% 20.89/7.49 |
% 20.89/7.49 | Using (42) and (43) yields:
% 20.89/7.49 | (22) $false
% 20.89/7.49 |
% 20.89/7.49 |-The branch is then unsatisfiable
% 20.89/7.49 |-Branch two:
% 20.89/7.50 | (45) ~ member(all_50_0_12, ex_18_1_3)
% 20.89/7.50 |
% 20.89/7.50 | From (24) and (39) follows:
% 20.89/7.50 | (42) member(all_50_0_12, all_2_0_1)
% 20.89/7.50 |
% 20.89/7.50 | From (17) and (45) follows:
% 20.89/7.50 | (43) ~ member(all_50_0_12, all_2_0_1)
% 20.89/7.50 |
% 20.89/7.50 | Using (42) and (43) yields:
% 20.89/7.50 | (22) $false
% 20.89/7.50 |
% 20.89/7.50 |-The branch is then unsatisfiable
% 20.89/7.50 |-Branch two:
% 20.89/7.50 | (37) member(all_50_0_12, ex_47_0_8)
% 20.89/7.50 | (50) ~ member(all_50_0_12, ex_47_1_9)
% 20.89/7.50 |
% 20.89/7.50 | Instantiating formula (5) with all_50_0_12 yields:
% 20.89/7.50 | (51) ~ member(all_50_0_12, all_0_0_0)
% 20.89/7.50 |
% 20.89/7.50 | From (25) and (37) follows:
% 20.89/7.50 | (52) member(all_50_0_12, all_0_0_0)
% 20.89/7.50 |
% 20.89/7.50 | Using (52) and (51) yields:
% 20.89/7.50 | (22) $false
% 20.89/7.50 |
% 20.89/7.50 |-The branch is then unsatisfiable
% 20.89/7.50 |-Branch two:
% 20.89/7.50 | (54) intersect(all_2_0_1, all_2_0_1) & ~ not_equal(all_2_0_1, all_0_0_0)
% 20.89/7.50 |
% 20.89/7.50 | Applying alpha-rule on (54) yields:
% 20.89/7.50 | (21) intersect(all_2_0_1, all_2_0_1)
% 20.89/7.50 | (56) ~ not_equal(all_2_0_1, all_0_0_0)
% 20.89/7.50 |
% 20.89/7.50 | Instantiating formula (6) with all_2_0_1, all_2_0_1 and discharging atoms intersect(all_2_0_1, all_2_0_1), yields:
% 20.89/7.50 | (57) ? [v0] : member(v0, all_2_0_1)
% 20.89/7.50 |
% 20.89/7.50 | Instantiating (57) with all_13_0_20 yields:
% 20.89/7.50 | (58) member(all_13_0_20, all_2_0_1)
% 20.89/7.50 |
% 20.89/7.50 | Introducing new symbol ex_25_1_22 defined by:
% 20.89/7.50 | (59) ex_25_1_22 = all_2_0_1
% 20.89/7.50 |
% 20.89/7.50 | Introducing new symbol ex_25_0_21 defined by:
% 20.89/7.50 | (60) ex_25_0_21 = all_2_0_1
% 20.89/7.50 |
% 20.89/7.50 | Instantiating formula (10) with ex_25_0_21, ex_25_1_22 yields:
% 20.89/7.50 | (61) intersect(ex_25_1_22, ex_25_0_21) | ! [v0] : ( ~ member(v0, ex_25_0_21) | ~ member(v0, ex_25_1_22))
% 20.89/7.50 |
% 20.89/7.50 +-Applying beta-rule and splitting (61), into two cases.
% 20.89/7.50 |-Branch one:
% 20.89/7.50 | (62) intersect(ex_25_1_22, ex_25_0_21)
% 20.89/7.50 |
% 20.89/7.50 | Instantiating formula (6) with ex_25_0_21, ex_25_1_22 and discharging atoms intersect(ex_25_1_22, ex_25_0_21), yields:
% 20.89/7.50 | (63) ? [v0] : (member(v0, ex_25_0_21) & member(v0, ex_25_1_22))
% 20.89/7.50 |
% 20.89/7.50 | Instantiating (63) with all_45_0_24 yields:
% 20.89/7.50 | (64) member(all_45_0_24, ex_25_0_21) & member(all_45_0_24, ex_25_1_22)
% 20.89/7.50 |
% 20.89/7.50 | Applying alpha-rule on (64) yields:
% 20.89/7.50 | (65) member(all_45_0_24, ex_25_0_21)
% 20.89/7.50 | (66) member(all_45_0_24, ex_25_1_22)
% 20.89/7.50 |
% 20.89/7.50 | Introducing new symbol ex_57_0_27 defined by:
% 20.89/7.50 | (67) ex_57_0_27 = all_2_0_1
% 20.89/7.50 |
% 20.89/7.50 | Instantiating formula (7) with ex_57_0_27 yields:
% 20.89/7.50 | (68) empty(ex_57_0_27) | ? [v0] : member(v0, ex_57_0_27)
% 20.89/7.50 |
% 20.89/7.50 +-Applying beta-rule and splitting (68), into two cases.
% 20.89/7.50 |-Branch one:
% 20.89/7.50 | (69) empty(ex_57_0_27)
% 20.89/7.50 |
% 20.89/7.50 | Instantiating formula (4) with ex_57_0_27 and discharging atoms empty(ex_57_0_27), yields:
% 20.89/7.50 | (70) ! [v0] : ~ member(v0, ex_57_0_27)
% 20.89/7.50 |
% 20.89/7.50 | Instantiating formula (70) with all_45_0_24 yields:
% 20.89/7.50 | (71) ~ member(all_45_0_24, ex_57_0_27)
% 20.89/7.50 |
% 20.89/7.50 | From (59) and (66) follows:
% 20.89/7.50 | (72) member(all_45_0_24, all_2_0_1)
% 20.89/7.50 |
% 20.89/7.50 | From (67) and (71) follows:
% 20.89/7.50 | (73) ~ member(all_45_0_24, all_2_0_1)
% 20.89/7.50 |
% 20.89/7.50 | Using (72) and (73) yields:
% 20.89/7.50 | (22) $false
% 20.89/7.50 |
% 20.89/7.50 |-The branch is then unsatisfiable
% 20.89/7.50 |-Branch two:
% 20.89/7.50 | (75) ? [v0] : member(v0, ex_57_0_27)
% 20.89/7.50 |
% 20.89/7.50 | Instantiating (75) with all_59_0_30 yields:
% 20.89/7.50 | (76) member(all_59_0_30, ex_57_0_27)
% 20.89/7.50 |
% 20.89/7.50 | Instantiating formula (5) with all_59_0_30 yields:
% 20.89/7.50 | (77) ~ member(all_59_0_30, all_0_0_0)
% 20.89/7.50 |
% 20.89/7.50 | Introducing new symbol ex_80_1_53 defined by:
% 20.89/7.50 | (78) ex_80_1_53 = all_2_0_1
% 20.89/7.50 |
% 20.89/7.50 | Introducing new symbol ex_80_0_52 defined by:
% 20.89/7.50 | (79) ex_80_0_52 = all_0_0_0
% 20.89/7.50 |
% 20.89/7.50 | Instantiating formula (9) with ex_80_0_52, ex_80_1_53 yields:
% 20.89/7.50 | (80) ex_80_0_52 = ex_80_1_53 | not_equal(ex_80_1_53, ex_80_0_52)
% 20.89/7.50 |
% 20.89/7.50 +-Applying beta-rule and splitting (80), into two cases.
% 20.89/7.50 |-Branch one:
% 20.89/7.50 | (81) not_equal(ex_80_1_53, ex_80_0_52)
% 20.89/7.50 |
% 20.89/7.50 | From (78)(79) and (81) follows:
% 20.89/7.50 | (14) not_equal(all_2_0_1, all_0_0_0)
% 20.89/7.50 |
% 20.89/7.50 | Using (14) and (56) yields:
% 20.89/7.50 | (22) $false
% 20.89/7.50 |
% 20.89/7.50 |-The branch is then unsatisfiable
% 20.89/7.50 |-Branch two:
% 20.89/7.50 | (84) ex_80_0_52 = ex_80_1_53
% 20.89/7.50 |
% 20.89/7.50 | Combining equations (79,84) yields a new equation:
% 20.89/7.50 | (85) ex_80_1_53 = all_0_0_0
% 20.89/7.50 |
% 20.89/7.50 | Combining equations (85,78) yields a new equation:
% 20.89/7.50 | (29) all_2_0_1 = all_0_0_0
% 20.89/7.50 |
% 20.89/7.50 | Combining equations (29,67) yields a new equation:
% 20.89/7.50 | (87) ex_57_0_27 = all_0_0_0
% 20.89/7.50 |
% 20.89/7.50 | From (87) and (76) follows:
% 20.89/7.50 | (88) member(all_59_0_30, all_0_0_0)
% 20.89/7.50 |
% 20.89/7.50 | Using (88) and (77) yields:
% 20.89/7.50 | (22) $false
% 20.89/7.50 |
% 20.89/7.50 |-The branch is then unsatisfiable
% 20.89/7.50 |-Branch two:
% 20.89/7.50 | (90) ! [v0] : ( ~ member(v0, ex_25_0_21) | ~ member(v0, ex_25_1_22))
% 20.89/7.50 |
% 20.89/7.50 | Instantiating formula (90) with all_13_0_20 yields:
% 20.89/7.50 | (91) ~ member(all_13_0_20, ex_25_0_21) | ~ member(all_13_0_20, ex_25_1_22)
% 20.89/7.50 |
% 20.89/7.50 +-Applying beta-rule and splitting (91), into two cases.
% 20.89/7.50 |-Branch one:
% 20.89/7.50 | (92) ~ member(all_13_0_20, ex_25_0_21)
% 20.89/7.50 |
% 20.89/7.50 | From (60) and (92) follows:
% 20.89/7.50 | (93) ~ member(all_13_0_20, all_2_0_1)
% 20.89/7.50 |
% 20.89/7.50 | Using (58) and (93) yields:
% 20.89/7.50 | (22) $false
% 20.89/7.50 |
% 20.89/7.50 |-The branch is then unsatisfiable
% 20.89/7.50 |-Branch two:
% 20.89/7.50 | (95) ~ member(all_13_0_20, ex_25_1_22)
% 20.89/7.50 |
% 20.89/7.50 | From (59) and (95) follows:
% 20.89/7.50 | (93) ~ member(all_13_0_20, all_2_0_1)
% 20.89/7.50 |
% 20.89/7.50 | Using (58) and (93) yields:
% 20.89/7.50 | (22) $false
% 20.89/7.50 |
% 20.89/7.50 |-The branch is then unsatisfiable
% 20.89/7.50 % SZS output end Proof for theBenchmark
% 20.89/7.50
% 20.89/7.50 6886ms
%------------------------------------------------------------------------------