TSTP Solution File: SET603+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET603+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n016.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 00:20:40 EDT 2022
% Result : Theorem 11.04s 3.26s
% Output : Proof 13.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET603+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 14:59:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.51/0.60 ____ _
% 0.51/0.60 ___ / __ \_____(_)___ ________ __________
% 0.51/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.60
% 0.51/0.60 A Theorem Prover for First-Order Logic
% 0.51/0.60 (ePrincess v.1.0)
% 0.51/0.60
% 0.51/0.60 (c) Philipp Rümmer, 2009-2015
% 0.51/0.60 (c) Peter Backeman, 2014-2015
% 0.51/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.60 Bug reports to peter@backeman.se
% 0.51/0.60
% 0.51/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.60
% 0.51/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.29/0.91 Prover 0: Preprocessing ...
% 1.69/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.69/1.07 Prover 0: Constructing countermodel ...
% 2.12/1.19 Prover 0: gave up
% 2.12/1.19 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.12/1.21 Prover 1: Preprocessing ...
% 2.40/1.28 Prover 1: Warning: ignoring some quantifiers
% 2.40/1.29 Prover 1: Constructing countermodel ...
% 2.40/1.31 Prover 1: gave up
% 2.40/1.31 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.58/1.33 Prover 2: Preprocessing ...
% 2.79/1.39 Prover 2: Warning: ignoring some quantifiers
% 2.79/1.40 Prover 2: Constructing countermodel ...
% 2.79/1.43 Prover 2: gave up
% 2.79/1.43 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.79/1.44 Prover 3: Preprocessing ...
% 3.18/1.46 Prover 3: Warning: ignoring some quantifiers
% 3.18/1.46 Prover 3: Constructing countermodel ...
% 3.34/1.49 Prover 3: gave up
% 3.34/1.49 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.34/1.50 Prover 4: Preprocessing ...
% 3.69/1.57 Prover 4: Warning: ignoring some quantifiers
% 3.69/1.57 Prover 4: Constructing countermodel ...
% 4.90/1.89 Prover 4: gave up
% 4.90/1.89 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.90/1.90 Prover 5: Preprocessing ...
% 5.27/1.94 Prover 5: Warning: ignoring some quantifiers
% 5.27/1.94 Prover 5: Constructing countermodel ...
% 5.27/1.95 Prover 5: gave up
% 5.27/1.95 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.27/1.96 Prover 6: Preprocessing ...
% 5.56/1.99 Prover 6: Warning: ignoring some quantifiers
% 5.56/1.99 Prover 6: Constructing countermodel ...
% 5.56/2.01 Prover 6: gave up
% 5.56/2.01 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 5.56/2.02 Prover 7: Preprocessing ...
% 5.56/2.03 Prover 7: Proving ...
% 11.04/3.26 Prover 7: proved (1252ms)
% 11.04/3.26
% 11.04/3.26 % SZS status Theorem for theBenchmark
% 11.04/3.26
% 11.04/3.26 Generating proof ... found it (size 43)
% 13.12/3.79
% 13.12/3.79 % SZS output start Proof for theBenchmark
% 13.12/3.79 Assumed formulas after preprocessing and simplification:
% 13.12/3.79 | (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] : ( ~ (v2 = v1) & difference(v1, v0) = v2))
% 13.12/3.81 | Instantiating (0) with all_0_0_0 yields:
% 13.12/3.81 | (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] : ( ~ (v1 = v0) & difference(v0, all_0_0_0) = v1)
% 13.47/3.82 |
% 13.47/3.82 | Applying alpha-rule on (1) yields:
% 13.47/3.82 | (2) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 13.47/3.82 | (3) ! [v0] : (empty(v0) | ? [v1] : member(v1, v0))
% 13.47/3.82 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1))
% 13.47/3.82 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 13.47/3.82 | (6) ! [v0] : subset(v0, v0)
% 13.47/3.82 | (7) ? [v0] : ? [v1] : ( ~ (v1 = v0) & difference(v0, all_0_0_0) = v1)
% 13.47/3.82 | (8) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1)))
% 13.47/3.82 | (9) ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0))
% 13.47/3.82 | (10) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 13.47/3.82 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v0) & ~ member(v2, v1)))
% 13.47/3.82 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 13.47/3.82 | (13) ! [v0] : ~ member(v0, all_0_0_0)
% 13.47/3.82 |
% 13.47/3.82 | Instantiating (7) with all_2_0_1, all_2_1_2 yields:
% 13.47/3.82 | (14) ~ (all_2_0_1 = all_2_1_2) & difference(all_2_1_2, all_0_0_0) = all_2_0_1
% 13.47/3.82 |
% 13.47/3.82 | Applying alpha-rule on (14) yields:
% 13.47/3.82 | (15) ~ (all_2_0_1 = all_2_1_2)
% 13.47/3.82 | (16) difference(all_2_1_2, all_0_0_0) = all_2_0_1
% 13.47/3.82 |
% 13.47/3.82 | Introducing new symbol ex_10_1_4 defined by:
% 13.47/3.82 | (17) ex_10_1_4 = all_2_1_2
% 13.47/3.82 |
% 13.47/3.82 | Introducing new symbol ex_10_0_3 defined by:
% 13.47/3.82 | (18) ex_10_0_3 = all_2_0_1
% 13.47/3.82 |
% 13.47/3.83 | Instantiating formula (2) with ex_10_0_3, ex_10_1_4 yields:
% 13.47/3.83 | (19) ex_10_0_3 = ex_10_1_4 | ? [v0] : (( ~ member(v0, ex_10_0_3) | ~ member(v0, ex_10_1_4)) & (member(v0, ex_10_0_3) | member(v0, ex_10_1_4)))
% 13.47/3.83 |
% 13.47/3.83 +-Applying beta-rule and splitting (19), into two cases.
% 13.47/3.83 |-Branch one:
% 13.47/3.83 | (20) ex_10_0_3 = ex_10_1_4
% 13.47/3.83 |
% 13.47/3.83 | Combining equations (20,18) yields a new equation:
% 13.47/3.83 | (21) ex_10_1_4 = all_2_0_1
% 13.47/3.83 |
% 13.47/3.83 | Simplifying 21 yields:
% 13.47/3.83 | (22) ex_10_1_4 = all_2_0_1
% 13.47/3.83 |
% 13.47/3.83 | Combining equations (22,17) yields a new equation:
% 13.47/3.83 | (23) all_2_0_1 = all_2_1_2
% 13.47/3.83 |
% 13.47/3.83 | Simplifying 23 yields:
% 13.47/3.83 | (24) all_2_0_1 = all_2_1_2
% 13.47/3.83 |
% 13.47/3.83 | Equations (24) can reduce 15 to:
% 13.47/3.83 | (25) $false
% 13.47/3.83 |
% 13.47/3.83 |-The branch is then unsatisfiable
% 13.47/3.83 |-Branch two:
% 13.47/3.83 | (26) ? [v0] : (( ~ member(v0, ex_10_0_3) | ~ member(v0, ex_10_1_4)) & (member(v0, ex_10_0_3) | member(v0, ex_10_1_4)))
% 13.47/3.83 |
% 13.47/3.83 | Instantiating (26) with all_13_0_5 yields:
% 13.47/3.83 | (27) ( ~ member(all_13_0_5, ex_10_0_3) | ~ member(all_13_0_5, ex_10_1_4)) & (member(all_13_0_5, ex_10_0_3) | member(all_13_0_5, ex_10_1_4))
% 13.47/3.83 |
% 13.47/3.83 | Applying alpha-rule on (27) yields:
% 13.47/3.83 | (28) ~ member(all_13_0_5, ex_10_0_3) | ~ member(all_13_0_5, ex_10_1_4)
% 13.47/3.83 | (29) member(all_13_0_5, ex_10_0_3) | member(all_13_0_5, ex_10_1_4)
% 13.47/3.83 |
% 13.47/3.83 +-Applying beta-rule and splitting (28), into two cases.
% 13.47/3.83 |-Branch one:
% 13.47/3.83 | (30) ~ member(all_13_0_5, ex_10_0_3)
% 13.47/3.83 |
% 13.47/3.83 +-Applying beta-rule and splitting (29), into two cases.
% 13.47/3.83 |-Branch one:
% 13.47/3.83 | (31) member(all_13_0_5, ex_10_0_3)
% 13.47/3.83 |
% 13.47/3.83 | Using (31) and (30) yields:
% 13.47/3.83 | (32) $false
% 13.47/3.83 |
% 13.47/3.83 |-The branch is then unsatisfiable
% 13.47/3.83 |-Branch two:
% 13.47/3.83 | (33) member(all_13_0_5, ex_10_1_4)
% 13.47/3.83 |
% 13.47/3.83 | Instantiating formula (13) with all_13_0_5 yields:
% 13.47/3.83 | (34) ~ member(all_13_0_5, all_0_0_0)
% 13.47/3.83 |
% 13.47/3.83 | Instantiating formula (4) with all_2_0_1, all_13_0_5, all_0_0_0, all_2_1_2 and discharging atoms difference(all_2_1_2, all_0_0_0) = all_2_0_1, ~ member(all_13_0_5, all_0_0_0), yields:
% 13.47/3.83 | (35) ~ member(all_13_0_5, all_2_1_2) | member(all_13_0_5, all_2_0_1)
% 13.47/3.83 |
% 13.47/3.83 +-Applying beta-rule and splitting (35), into two cases.
% 13.47/3.83 |-Branch one:
% 13.47/3.83 | (36) ~ member(all_13_0_5, all_2_1_2)
% 13.47/3.83 |
% 13.47/3.83 | From (17) and (33) follows:
% 13.47/3.83 | (37) member(all_13_0_5, all_2_1_2)
% 13.47/3.83 |
% 13.47/3.83 | Using (37) and (36) yields:
% 13.47/3.83 | (32) $false
% 13.47/3.83 |
% 13.47/3.83 |-The branch is then unsatisfiable
% 13.47/3.83 |-Branch two:
% 13.47/3.83 | (39) member(all_13_0_5, all_2_0_1)
% 13.47/3.83 |
% 13.47/3.83 | From (18) and (30) follows:
% 13.47/3.83 | (40) ~ member(all_13_0_5, all_2_0_1)
% 13.47/3.83 |
% 13.47/3.83 | Using (39) and (40) yields:
% 13.47/3.83 | (32) $false
% 13.47/3.83 |
% 13.47/3.83 |-The branch is then unsatisfiable
% 13.47/3.83 |-Branch two:
% 13.47/3.83 | (31) member(all_13_0_5, ex_10_0_3)
% 13.47/3.83 | (43) ~ member(all_13_0_5, ex_10_1_4)
% 13.47/3.83 |
% 13.47/3.83 | Instantiating formula (13) with all_13_0_5 yields:
% 13.47/3.83 | (34) ~ member(all_13_0_5, all_0_0_0)
% 13.47/3.83 |
% 13.47/3.83 | Instantiating formula (11) with all_2_0_1, all_13_0_5, all_0_0_0, all_2_1_2 and discharging atoms difference(all_2_1_2, all_0_0_0) = all_2_0_1, yields:
% 13.47/3.83 | (45) ~ member(all_13_0_5, all_2_0_1) | (member(all_13_0_5, all_2_1_2) & ~ member(all_13_0_5, all_0_0_0))
% 13.47/3.83 |
% 13.47/3.83 | Instantiating formula (4) with all_2_0_1, all_13_0_5, all_0_0_0, all_2_1_2 and discharging atoms difference(all_2_1_2, all_0_0_0) = all_2_0_1, ~ member(all_13_0_5, all_0_0_0), yields:
% 13.47/3.83 | (35) ~ member(all_13_0_5, all_2_1_2) | member(all_13_0_5, all_2_0_1)
% 13.47/3.83 |
% 13.47/3.83 +-Applying beta-rule and splitting (35), into two cases.
% 13.47/3.83 |-Branch one:
% 13.47/3.83 | (36) ~ member(all_13_0_5, all_2_1_2)
% 13.47/3.83 |
% 13.47/3.83 +-Applying beta-rule and splitting (45), into two cases.
% 13.47/3.83 |-Branch one:
% 13.47/3.83 | (40) ~ member(all_13_0_5, all_2_0_1)
% 13.47/3.83 |
% 13.47/3.83 | From (18) and (31) follows:
% 13.47/3.83 | (39) member(all_13_0_5, all_2_0_1)
% 13.47/3.83 |
% 13.47/3.83 | Using (39) and (40) yields:
% 13.47/3.83 | (32) $false
% 13.47/3.83 |
% 13.47/3.83 |-The branch is then unsatisfiable
% 13.47/3.83 |-Branch two:
% 13.47/3.83 | (51) member(all_13_0_5, all_2_1_2) & ~ member(all_13_0_5, all_0_0_0)
% 13.47/3.83 |
% 13.47/3.83 | Applying alpha-rule on (51) yields:
% 13.47/3.83 | (37) member(all_13_0_5, all_2_1_2)
% 13.47/3.83 | (34) ~ member(all_13_0_5, all_0_0_0)
% 13.47/3.83 |
% 13.47/3.83 | Using (37) and (36) yields:
% 13.47/3.83 | (32) $false
% 13.47/3.83 |
% 13.47/3.83 |-The branch is then unsatisfiable
% 13.47/3.83 |-Branch two:
% 13.47/3.83 | (37) member(all_13_0_5, all_2_1_2)
% 13.47/3.83 | (39) member(all_13_0_5, all_2_0_1)
% 13.47/3.83 |
% 13.47/3.83 | From (17) and (43) follows:
% 13.47/3.83 | (36) ~ member(all_13_0_5, all_2_1_2)
% 13.47/3.83 |
% 13.47/3.83 | Using (37) and (36) yields:
% 13.47/3.83 | (32) $false
% 13.47/3.83 |
% 13.47/3.83 |-The branch is then unsatisfiable
% 13.47/3.83 % SZS output end Proof for theBenchmark
% 13.47/3.84
% 13.47/3.84 3226ms
%------------------------------------------------------------------------------