TSTP Solution File: SET581+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET581+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.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 00:20:25 EDT 2022
% Result : Theorem 4.76s 1.81s
% Output : Proof 6.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET581+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 17:15:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.50/0.59 ____ _
% 0.50/0.59 ___ / __ \_____(_)___ ________ __________
% 0.50/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.59
% 0.50/0.59 A Theorem Prover for First-Order Logic
% 0.50/0.60 (ePrincess v.1.0)
% 0.50/0.60
% 0.50/0.60 (c) Philipp Rümmer, 2009-2015
% 0.50/0.60 (c) Peter Backeman, 2014-2015
% 0.50/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.60 Bug reports to peter@backeman.se
% 0.50/0.60
% 0.50/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.60
% 0.50/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.33/0.88 Prover 0: Preprocessing ...
% 1.63/1.02 Prover 0: Warning: ignoring some quantifiers
% 1.63/1.03 Prover 0: Constructing countermodel ...
% 2.25/1.19 Prover 0: gave up
% 2.25/1.19 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.25/1.21 Prover 1: Preprocessing ...
% 2.58/1.27 Prover 1: Warning: ignoring some quantifiers
% 2.58/1.28 Prover 1: Constructing countermodel ...
% 2.58/1.33 Prover 1: gave up
% 2.58/1.33 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.85/1.34 Prover 2: Preprocessing ...
% 3.00/1.39 Prover 2: Warning: ignoring some quantifiers
% 3.00/1.39 Prover 2: Constructing countermodel ...
% 3.32/1.45 Prover 2: gave up
% 3.32/1.45 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.32/1.46 Prover 3: Preprocessing ...
% 3.46/1.48 Prover 3: Warning: ignoring some quantifiers
% 3.46/1.48 Prover 3: Constructing countermodel ...
% 3.78/1.53 Prover 3: gave up
% 3.78/1.53 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.78/1.54 Prover 4: Preprocessing ...
% 3.94/1.59 Prover 4: Warning: ignoring some quantifiers
% 3.94/1.59 Prover 4: Constructing countermodel ...
% 4.39/1.73 Prover 4: gave up
% 4.39/1.73 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.39/1.74 Prover 5: Preprocessing ...
% 4.76/1.77 Prover 5: Warning: ignoring some quantifiers
% 4.76/1.77 Prover 5: Constructing countermodel ...
% 4.76/1.81 Prover 5: proved (74ms)
% 4.76/1.81
% 4.76/1.81 No countermodel exists, formula is valid
% 4.76/1.81 % SZS status Theorem for theBenchmark
% 4.76/1.81
% 4.76/1.81 Generating proof ... Warning: ignoring some quantifiers
% 5.73/2.04 found it (size 16)
% 5.73/2.04
% 5.73/2.04 % SZS output start Proof for theBenchmark
% 5.73/2.04 Assumed formulas after preprocessing and simplification:
% 5.73/2.04 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v1) = v4) | ? [v5] : ? [v6] : (member(v2, v3) = v5 & member(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v0) = v4) | ? [v5] : ? [v6] : (member(v2, v3) = v5 & member(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (member(v2, v1) = v4) | ~ (member(v2, v0) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & intersection(v0, v1) = v5 & member(v2, v5) = v6) | (v4 = 0 & v3 = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (not_equal(v3, v2) = v1) | ~ (not_equal(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v1) = 0) | ? [v4] : ? [v5] : (member(v2, v3) = v5 & member(v2, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v0) = 0) | ? [v4] : ? [v5] : (member(v2, v3) = v5 & member(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (not_equal(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v2, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : (intersection(v0, v1) = v3 & member(v2, v3) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ! [v1] : ~ (member(v1, v0) = 0)) & ! [v0] : ~ (not_equal(v0, v0) = 0) & ! [v0] : ~ (member(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & not_equal(v3, empty_set) = v4 & intersection(v1, v2) = v3 & member(v0, v2) = 0 & member(v0, v1) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 6.12/2.07 | Applying alpha-rule on (0) yields:
% 6.12/2.07 | (1) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (not_equal(v0, v1) = v2))
% 6.12/2.07 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (not_equal(v3, v2) = v1) | ~ (not_equal(v3, v2) = v0))
% 6.12/2.07 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 6.12/2.07 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0)
% 6.12/2.07 | (5) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & not_equal(v3, empty_set) = v4 & intersection(v1, v2) = v3 & member(v0, v2) = 0 & member(v0, v1) = 0)
% 6.12/2.08 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v1) = 0) | ? [v4] : ? [v5] : (member(v2, v3) = v5 & member(v2, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 6.12/2.08 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 6.12/2.08 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v2, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : (intersection(v0, v1) = v3 & member(v2, v3) = 0))
% 6.12/2.08 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 6.12/2.08 | (10) ! [v0] : ~ (member(v0, empty_set) = 0)
% 6.12/2.08 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v0) = 0) | ? [v4] : ? [v5] : (member(v2, v3) = v5 & member(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 6.12/2.08 | (12) ! [v0] : ( ~ (empty(v0) = 0) | ! [v1] : ~ (member(v1, v0) = 0))
% 6.12/2.08 | (13) ! [v0] : ~ (not_equal(v0, v0) = 0)
% 6.12/2.08 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 6.12/2.08 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 6.12/2.08 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2)
% 6.12/2.08 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 6.12/2.08 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v1) = v4) | ? [v5] : ? [v6] : (member(v2, v3) = v5 & member(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 6.12/2.08 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (member(v2, v1) = v4) | ~ (member(v2, v0) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & intersection(v0, v1) = v5 & member(v2, v5) = v6) | (v4 = 0 & v3 = 0))
% 6.12/2.08 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v0) = v4) | ? [v5] : ? [v6] : (member(v2, v3) = v5 & member(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 6.12/2.08 | (21) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 6.12/2.08 |
% 6.12/2.08 | Instantiating (5) with all_2_0_2, all_2_1_3, all_2_2_4, all_2_3_5, all_2_4_6 yields:
% 6.12/2.08 | (22) ~ (all_2_0_2 = 0) & not_equal(all_2_1_3, empty_set) = all_2_0_2 & intersection(all_2_3_5, all_2_2_4) = all_2_1_3 & member(all_2_4_6, all_2_2_4) = 0 & member(all_2_4_6, all_2_3_5) = 0
% 6.12/2.08 |
% 6.12/2.08 | Applying alpha-rule on (22) yields:
% 6.12/2.08 | (23) member(all_2_4_6, all_2_3_5) = 0
% 6.12/2.09 | (24) member(all_2_4_6, all_2_2_4) = 0
% 6.12/2.09 | (25) ~ (all_2_0_2 = 0)
% 6.12/2.09 | (26) not_equal(all_2_1_3, empty_set) = all_2_0_2
% 6.12/2.09 | (27) intersection(all_2_3_5, all_2_2_4) = all_2_1_3
% 6.12/2.09 |
% 6.12/2.09 | Instantiating formula (1) with all_2_0_2, empty_set, all_2_1_3 and discharging atoms not_equal(all_2_1_3, empty_set) = all_2_0_2, yields:
% 6.12/2.09 | (28) all_2_0_2 = 0 | all_2_1_3 = empty_set
% 6.12/2.09 |
% 6.12/2.09 | Instantiating formula (10) with all_2_4_6 yields:
% 6.12/2.09 | (29) ~ (member(all_2_4_6, empty_set) = 0)
% 6.12/2.09 |
% 6.12/2.09 +-Applying beta-rule and splitting (28), into two cases.
% 6.12/2.09 |-Branch one:
% 6.12/2.09 | (30) all_2_1_3 = empty_set
% 6.12/2.09 |
% 6.12/2.09 | From (30) and (27) follows:
% 6.12/2.09 | (31) intersection(all_2_3_5, all_2_2_4) = empty_set
% 6.12/2.09 |
% 6.12/2.09 | Instantiating formula (8) with all_2_4_6, all_2_2_4, all_2_3_5 and discharging atoms member(all_2_4_6, all_2_2_4) = 0, member(all_2_4_6, all_2_3_5) = 0, yields:
% 6.12/2.09 | (32) ? [v0] : (intersection(all_2_3_5, all_2_2_4) = v0 & member(all_2_4_6, v0) = 0)
% 6.12/2.09 |
% 6.12/2.09 | Instantiating (32) with all_24_0_8 yields:
% 6.12/2.09 | (33) intersection(all_2_3_5, all_2_2_4) = all_24_0_8 & member(all_2_4_6, all_24_0_8) = 0
% 6.12/2.09 |
% 6.12/2.09 | Applying alpha-rule on (33) yields:
% 6.12/2.09 | (34) intersection(all_2_3_5, all_2_2_4) = all_24_0_8
% 6.12/2.09 | (35) member(all_2_4_6, all_24_0_8) = 0
% 6.12/2.09 |
% 6.12/2.09 | Instantiating formula (3) with all_2_3_5, all_2_2_4, all_24_0_8, empty_set and discharging atoms intersection(all_2_3_5, all_2_2_4) = all_24_0_8, intersection(all_2_3_5, all_2_2_4) = empty_set, yields:
% 6.12/2.09 | (36) all_24_0_8 = empty_set
% 6.12/2.09 |
% 6.12/2.09 | Using (35) and (29) yields:
% 6.12/2.09 | (37) ~ (all_24_0_8 = empty_set)
% 6.12/2.09 |
% 6.12/2.09 | Equations (36) can reduce 37 to:
% 6.12/2.09 | (38) $false
% 6.12/2.09 |
% 6.12/2.09 |-The branch is then unsatisfiable
% 6.12/2.09 |-Branch two:
% 6.12/2.09 | (39) ~ (all_2_1_3 = empty_set)
% 6.12/2.09 | (40) all_2_0_2 = 0
% 6.12/2.09 |
% 6.12/2.09 | Equations (40) can reduce 25 to:
% 6.12/2.09 | (38) $false
% 6.12/2.09 |
% 6.12/2.09 |-The branch is then unsatisfiable
% 6.12/2.09 % SZS output end Proof for theBenchmark
% 6.12/2.09
% 6.12/2.09 1487ms
%------------------------------------------------------------------------------