TSTP Solution File: SET629+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET629+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 2.76s 1.42s
% Output : Proof 3.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET629+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n029.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 10:05:01 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.60/0.61 ____ _
% 0.60/0.61 ___ / __ \_____(_)___ ________ __________
% 0.60/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.61
% 0.60/0.61 A Theorem Prover for First-Order Logic
% 0.60/0.61 (ePrincess v.1.0)
% 0.60/0.61
% 0.60/0.61 (c) Philipp Rümmer, 2009-2015
% 0.60/0.61 (c) Peter Backeman, 2014-2015
% 0.60/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.61 Bug reports to peter@backeman.se
% 0.60/0.61
% 0.60/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.61
% 0.60/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.40/0.94 Prover 0: Preprocessing ...
% 1.81/1.10 Prover 0: Warning: ignoring some quantifiers
% 1.81/1.13 Prover 0: Constructing countermodel ...
% 2.27/1.25 Prover 0: gave up
% 2.27/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.27/1.27 Prover 1: Preprocessing ...
% 2.56/1.36 Prover 1: Warning: ignoring some quantifiers
% 2.56/1.36 Prover 1: Constructing countermodel ...
% 2.76/1.42 Prover 1: proved (168ms)
% 2.76/1.42
% 2.76/1.42 No countermodel exists, formula is valid
% 2.76/1.42 % SZS status Theorem for theBenchmark
% 2.76/1.42
% 2.76/1.42 Generating proof ... Warning: ignoring some quantifiers
% 3.69/1.67 found it (size 17)
% 3.69/1.67
% 3.69/1.67 % SZS output start Proof for theBenchmark
% 3.69/1.67 Assumed formulas after preprocessing and simplification:
% 3.69/1.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & disjoint(v2, v3) = v4 & difference(v0, v1) = v3 & intersection(v0, v1) = v2 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (difference(v5, v6) = v8) | ~ (member(v7, v8) = v9) | ? [v10] : ? [v11] : (member(v7, v6) = v11 & member(v7, v5) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection(v5, v6) = v8) | ~ (member(v7, v8) = v9) | ? [v10] : ? [v11] : (member(v7, v6) = v11 & member(v7, v5) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (intersect(v5, v6) = v7) | ~ (member(v8, v5) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (disjoint(v8, v7) = v6) | ~ (disjoint(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersect(v8, v7) = v6) | ~ (intersect(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (difference(v8, v7) = v6) | ~ (difference(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection(v8, v7) = v6) | ~ (intersection(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (member(v8, v7) = v6) | ~ (member(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (difference(v5, v6) = v8) | ~ (member(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v7, v6) = v9 & member(v7, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v5, v6) = v8) | ~ (member(v7, v8) = 0) | (member(v7, v6) = 0 & member(v7, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (disjoint(v5, v6) = v7) | intersect(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v5, v6) = v7) | intersection(v6, v5) = v7) & ! [v5] : ! [v6] : ( ~ (disjoint(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & intersect(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (intersect(v5, v6) = 0) | intersect(v6, v5) = 0) & ! [v5] : ! [v6] : ( ~ (intersect(v5, v6) = 0) | ? [v7] : (member(v7, v6) = 0 & member(v7, v5) = 0)) & ? [v5] : ? [v6] : (v6 = v5 | ? [v7] : ? [v8] : ? [v9] : (member(v7, v6) = v9 & member(v7, v5) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)) & (v9 = 0 | v8 = 0))))
% 3.97/1.70 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.97/1.70 | (1) ~ (all_0_0_0 = 0) & disjoint(all_0_2_2, all_0_1_1) = all_0_0_0 & difference(all_0_4_4, all_0_3_3) = all_0_1_1 & intersection(all_0_4_4, all_0_3_3) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 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] : (v2 = 0 | ~ (intersect(v0, v1) = v2) | ~ (member(v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = v0)) & ! [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] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | intersect(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & intersect(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | intersect(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | ? [v2] : (member(v2, v1) = 0 & member(v2, v0) = 0)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 3.97/1.72 |
% 3.97/1.72 | Applying alpha-rule on (1) yields:
% 3.97/1.72 | (2) ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | intersect(v1, v0) = 0)
% 3.97/1.72 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 3.97/1.72 | (4) intersection(all_0_4_4, all_0_3_3) = all_0_2_2
% 3.97/1.72 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 3.97/1.72 | (6) ~ (all_0_0_0 = 0)
% 3.97/1.72 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0))
% 3.97/1.72 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 3.97/1.72 | (9) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 3.97/1.72 | (10) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & intersect(v0, v1) = v2))
% 3.97/1.72 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = v0))
% 3.97/1.72 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 3.97/1.72 | (13) ! [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))))
% 3.97/1.72 | (14) difference(all_0_4_4, all_0_3_3) = all_0_1_1
% 3.97/1.72 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | intersect(v0, v1) = 0)
% 3.97/1.72 | (16) disjoint(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.97/1.72 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 3.97/1.72 | (18) ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | ? [v2] : (member(v2, v1) = 0 & member(v2, v0) = 0))
% 3.97/1.73 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 3.97/1.73 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (intersect(v0, v1) = v2) | ~ (member(v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4))
% 3.97/1.73 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 3.97/1.73 |
% 3.97/1.73 | Instantiating formula (15) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms disjoint(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 3.97/1.73 | (22) all_0_0_0 = 0 | intersect(all_0_2_2, all_0_1_1) = 0
% 3.97/1.73 |
% 3.97/1.73 +-Applying beta-rule and splitting (22), into two cases.
% 3.97/1.73 |-Branch one:
% 3.97/1.73 | (23) intersect(all_0_2_2, all_0_1_1) = 0
% 3.97/1.73 |
% 3.97/1.73 | Instantiating formula (18) with all_0_1_1, all_0_2_2 and discharging atoms intersect(all_0_2_2, all_0_1_1) = 0, yields:
% 3.97/1.73 | (24) ? [v0] : (member(v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = 0)
% 3.97/1.73 |
% 3.97/1.73 | Instantiating (24) with all_20_0_7 yields:
% 3.97/1.73 | (25) member(all_20_0_7, all_0_1_1) = 0 & member(all_20_0_7, all_0_2_2) = 0
% 3.97/1.73 |
% 3.97/1.73 | Applying alpha-rule on (25) yields:
% 3.97/1.73 | (26) member(all_20_0_7, all_0_1_1) = 0
% 3.97/1.73 | (27) member(all_20_0_7, all_0_2_2) = 0
% 3.97/1.73 |
% 3.97/1.73 | Instantiating formula (7) with all_0_1_1, all_20_0_7, all_0_3_3, all_0_4_4 and discharging atoms difference(all_0_4_4, all_0_3_3) = all_0_1_1, member(all_20_0_7, all_0_1_1) = 0, yields:
% 3.97/1.73 | (28) ? [v0] : ( ~ (v0 = 0) & member(all_20_0_7, all_0_3_3) = v0 & member(all_20_0_7, all_0_4_4) = 0)
% 3.97/1.73 |
% 3.97/1.73 | Instantiating formula (5) with all_0_2_2, all_20_0_7, all_0_3_3, all_0_4_4 and discharging atoms intersection(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_20_0_7, all_0_2_2) = 0, yields:
% 3.97/1.73 | (29) member(all_20_0_7, all_0_3_3) = 0 & member(all_20_0_7, all_0_4_4) = 0
% 3.97/1.73 |
% 3.97/1.73 | Applying alpha-rule on (29) yields:
% 3.97/1.73 | (30) member(all_20_0_7, all_0_3_3) = 0
% 3.97/1.73 | (31) member(all_20_0_7, all_0_4_4) = 0
% 3.97/1.73 |
% 3.97/1.73 | Instantiating (28) with all_28_0_8 yields:
% 3.97/1.73 | (32) ~ (all_28_0_8 = 0) & member(all_20_0_7, all_0_3_3) = all_28_0_8 & member(all_20_0_7, all_0_4_4) = 0
% 3.97/1.73 |
% 3.97/1.73 | Applying alpha-rule on (32) yields:
% 3.97/1.73 | (33) ~ (all_28_0_8 = 0)
% 3.97/1.73 | (34) member(all_20_0_7, all_0_3_3) = all_28_0_8
% 3.97/1.73 | (31) member(all_20_0_7, all_0_4_4) = 0
% 3.97/1.73 |
% 3.97/1.73 | Instantiating formula (12) with all_20_0_7, all_0_3_3, all_28_0_8, 0 and discharging atoms member(all_20_0_7, all_0_3_3) = all_28_0_8, member(all_20_0_7, all_0_3_3) = 0, yields:
% 3.97/1.73 | (36) all_28_0_8 = 0
% 3.97/1.73 |
% 3.97/1.73 | Equations (36) can reduce 33 to:
% 3.97/1.73 | (37) $false
% 3.97/1.73 |
% 3.97/1.73 |-The branch is then unsatisfiable
% 3.97/1.73 |-Branch two:
% 3.97/1.73 | (38) ~ (intersect(all_0_2_2, all_0_1_1) = 0)
% 3.97/1.74 | (39) all_0_0_0 = 0
% 3.97/1.74 |
% 3.97/1.74 | Equations (39) can reduce 6 to:
% 3.97/1.74 | (37) $false
% 3.97/1.74 |
% 3.97/1.74 |-The branch is then unsatisfiable
% 3.97/1.74 % SZS output end Proof for theBenchmark
% 3.97/1.74
% 3.97/1.74 1116ms
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