TSTP Solution File: SET901+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET901+1 : TPTP v8.1.0. Released v3.2.0.
% 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 00:23:01 EDT 2022
% Result : Theorem 3.98s 1.67s
% Output : Proof 5.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET901+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 13:54:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.59/0.61 ____ _
% 0.59/0.61 ___ / __ \_____(_)___ ________ __________
% 0.59/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.61
% 0.59/0.61 A Theorem Prover for First-Order Logic
% 0.59/0.61 (ePrincess v.1.0)
% 0.59/0.61
% 0.59/0.61 (c) Philipp Rümmer, 2009-2015
% 0.59/0.61 (c) Peter Backeman, 2014-2015
% 0.59/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.61 Bug reports to peter@backeman.se
% 0.59/0.61
% 0.59/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.61
% 0.59/0.61 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
% 1.35/0.91 Prover 0: Preprocessing ...
% 1.60/1.06 Prover 0: Warning: ignoring some quantifiers
% 1.60/1.08 Prover 0: Constructing countermodel ...
% 3.03/1.45 Prover 0: gave up
% 3.03/1.45 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.35/1.47 Prover 1: Preprocessing ...
% 3.53/1.51 Prover 1: Constructing countermodel ...
% 3.60/1.58 Prover 1: Exception: f.bc cannot be cast to f.aV
% 3.60/1.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.60/1.59 Prover 2: Preprocessing ...
% 3.98/1.63 Prover 2: Warning: ignoring some quantifiers
% 3.98/1.63 Prover 2: Constructing countermodel ...
% 3.98/1.67 Prover 2: proved (89ms)
% 3.98/1.67
% 3.98/1.67 No countermodel exists, formula is valid
% 3.98/1.67 % SZS status Theorem for theBenchmark
% 3.98/1.67
% 3.98/1.67 Generating proof ... Warning: ignoring some quantifiers
% 4.83/1.87 found it (size 62)
% 4.83/1.87
% 4.83/1.87 % SZS output start Proof for theBenchmark
% 4.83/1.87 Assumed formulas after preprocessing and simplification:
% 4.83/1.87 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v8 = 0) & empty(v9) = 0 & empty(v7) = v8 & empty(empty_set) = 0 & subset(v0, v3) = v4 & unordered_pair(v1, v2) = v3 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v10, v13) = v14) | ~ (unordered_pair(v11, v12) = v13) | ? [v15] : ? [v16] : ( ~ (v16 = v10) & ~ (v15 = v10) & singleton(v12) = v16 & singleton(v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | v10 = empty_set | ~ (subset(v10, v13) = 0) | ~ (unordered_pair(v11, v12) = v13) | ? [v14] : ((v14 = v10 & singleton(v12) = v10) | (v14 = v10 & singleton(v11) = v10))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v10, v10) = v13) | ~ (unordered_pair(v11, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(empty_set, v12) = v13) | ~ (unordered_pair(v10, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset(v13, v12) = v11) | ~ (subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | unordered_pair(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v10) = v11)) & ? [v10] : ? [v11] : ? [v12] : subset(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : unordered_pair(v11, v10) = v12 & ? [v10] : ? [v11] : singleton(v10) = v11 & ? [v10] : ? [v11] : empty(v10) = v11 & ((v4 = 0 & ~ (v6 = v0) & ~ (v5 = v0) & ~ (v3 = v0) & ~ (v0 = empty_set) & singleton(v2) = v6 & singleton(v1) = v5) | ( ~ (v4 = 0) & (v3 = v0 | v0 = empty_set | (v6 = v0 & singleton(v2) = v0) | (v5 = v0 & singleton(v1) = v0)))))
% 4.83/1.90 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 4.83/1.90 | (1) ~ (all_0_1_1 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & subset(all_0_9_9, all_0_6_6) = all_0_5_5 & unordered_pair(all_0_8_8, all_0_7_7) = all_0_6_6 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (unordered_pair(v1, v2) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = v0) & ~ (v5 = v0) & singleton(v2) = v6 & singleton(v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = empty_set | ~ (subset(v0, v3) = 0) | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v0 & singleton(v2) = v0) | (v4 = v0 & singleton(v1) = v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v0) = v3) | ~ (unordered_pair(v1, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(empty_set, v2) = v3) | ~ (unordered_pair(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1 & ((all_0_5_5 = 0 & ~ (all_0_3_3 = all_0_9_9) & ~ (all_0_4_4 = all_0_9_9) & ~ (all_0_6_6 = all_0_9_9) & ~ (all_0_9_9 = empty_set) & singleton(all_0_7_7) = all_0_3_3 & singleton(all_0_8_8) = all_0_4_4) | ( ~ (all_0_5_5 = 0) & (all_0_6_6 = all_0_9_9 | all_0_9_9 = empty_set | (all_0_3_3 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9) | (all_0_4_4 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9))))
% 5.20/1.91 |
% 5.20/1.91 | Applying alpha-rule on (1) yields:
% 5.20/1.91 | (2) (all_0_5_5 = 0 & ~ (all_0_3_3 = all_0_9_9) & ~ (all_0_4_4 = all_0_9_9) & ~ (all_0_6_6 = all_0_9_9) & ~ (all_0_9_9 = empty_set) & singleton(all_0_7_7) = all_0_3_3 & singleton(all_0_8_8) = all_0_4_4) | ( ~ (all_0_5_5 = 0) & (all_0_6_6 = all_0_9_9 | all_0_9_9 = empty_set | (all_0_3_3 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9) | (all_0_4_4 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9)))
% 5.20/1.91 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 5.20/1.91 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 5.20/1.91 | (5) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 5.20/1.91 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(empty_set, v2) = v3) | ~ (unordered_pair(v0, v1) = v2))
% 5.20/1.91 | (7) ~ (all_0_1_1 = 0)
% 5.20/1.91 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = empty_set | ~ (subset(v0, v3) = 0) | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v0 & singleton(v2) = v0) | (v4 = v0 & singleton(v1) = v0)))
% 5.20/1.91 | (9) empty(all_0_2_2) = all_0_1_1
% 5.20/1.91 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (unordered_pair(v1, v2) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = v0) & ~ (v5 = v0) & singleton(v2) = v6 & singleton(v1) = v5))
% 5.20/1.91 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 5.20/1.91 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 5.20/1.91 | (13) empty(all_0_0_0) = 0
% 5.20/1.91 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v0) = v3) | ~ (unordered_pair(v1, v2) = v0))
% 5.20/1.91 | (15) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 5.20/1.91 | (16) ? [v0] : ? [v1] : empty(v0) = v1
% 5.20/1.91 | (17) unordered_pair(all_0_8_8, all_0_7_7) = all_0_6_6
% 5.20/1.91 | (18) subset(all_0_9_9, all_0_6_6) = all_0_5_5
% 5.20/1.91 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 5.20/1.91 | (20) ? [v0] : ? [v1] : singleton(v0) = v1
% 5.20/1.91 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 5.20/1.91 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 5.20/1.91 | (23) empty(empty_set) = 0
% 5.20/1.91 |
% 5.20/1.91 | Instantiating formula (10) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_6_6) = all_0_5_5, unordered_pair(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 5.20/1.91 | (24) all_0_5_5 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = all_0_9_9) & ~ (v0 = all_0_9_9) & singleton(all_0_7_7) = v1 & singleton(all_0_8_8) = v0)
% 5.20/1.92 |
% 5.20/1.92 | Instantiating formula (4) with all_0_6_6, all_0_8_8, all_0_7_7 and discharging atoms unordered_pair(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 5.20/1.92 | (25) unordered_pair(all_0_7_7, all_0_8_8) = all_0_6_6
% 5.20/1.92 |
% 5.20/1.92 | Instantiating formula (10) with all_0_5_5, all_0_6_6, all_0_8_8, all_0_7_7, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_6_6) = all_0_5_5, unordered_pair(all_0_7_7, all_0_8_8) = all_0_6_6, yields:
% 5.20/1.92 | (26) all_0_5_5 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = all_0_9_9) & ~ (v0 = all_0_9_9) & singleton(all_0_7_7) = v0 & singleton(all_0_8_8) = v1)
% 5.20/1.92 |
% 5.20/1.92 +-Applying beta-rule and splitting (2), into two cases.
% 5.20/1.92 |-Branch one:
% 5.20/1.92 | (27) all_0_5_5 = 0 & ~ (all_0_3_3 = all_0_9_9) & ~ (all_0_4_4 = all_0_9_9) & ~ (all_0_6_6 = all_0_9_9) & ~ (all_0_9_9 = empty_set) & singleton(all_0_7_7) = all_0_3_3 & singleton(all_0_8_8) = all_0_4_4
% 5.20/1.92 |
% 5.20/1.92 | Applying alpha-rule on (27) yields:
% 5.20/1.92 | (28) ~ (all_0_6_6 = all_0_9_9)
% 5.20/1.92 | (29) ~ (all_0_3_3 = all_0_9_9)
% 5.20/1.92 | (30) singleton(all_0_7_7) = all_0_3_3
% 5.20/1.92 | (31) ~ (all_0_9_9 = empty_set)
% 5.20/1.92 | (32) singleton(all_0_8_8) = all_0_4_4
% 5.20/1.92 | (33) ~ (all_0_4_4 = all_0_9_9)
% 5.20/1.92 | (34) all_0_5_5 = 0
% 5.20/1.92 |
% 5.20/1.92 | From (34) and (18) follows:
% 5.20/1.92 | (35) subset(all_0_9_9, all_0_6_6) = 0
% 5.20/1.92 |
% 5.20/1.92 | Instantiating formula (8) with all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_6_6) = 0, unordered_pair(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 5.20/1.92 | (36) all_0_6_6 = all_0_9_9 | all_0_9_9 = empty_set | ? [v0] : ((v0 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9) | (v0 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9))
% 5.20/1.92 |
% 5.20/1.92 +-Applying beta-rule and splitting (36), into two cases.
% 5.20/1.92 |-Branch one:
% 5.20/1.92 | (37) all_0_9_9 = empty_set
% 5.20/1.92 |
% 5.20/1.92 | Equations (37) can reduce 31 to:
% 5.20/1.92 | (38) $false
% 5.20/1.92 |
% 5.20/1.92 |-The branch is then unsatisfiable
% 5.20/1.92 |-Branch two:
% 5.20/1.92 | (31) ~ (all_0_9_9 = empty_set)
% 5.20/1.92 | (40) all_0_6_6 = all_0_9_9 | ? [v0] : ((v0 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9) | (v0 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9))
% 5.20/1.92 |
% 5.20/1.92 +-Applying beta-rule and splitting (40), into two cases.
% 5.20/1.92 |-Branch one:
% 5.20/1.92 | (41) all_0_6_6 = all_0_9_9
% 5.20/1.92 |
% 5.20/1.92 | Equations (41) can reduce 28 to:
% 5.20/1.92 | (38) $false
% 5.20/1.92 |
% 5.20/1.92 |-The branch is then unsatisfiable
% 5.20/1.92 |-Branch two:
% 5.20/1.92 | (28) ~ (all_0_6_6 = all_0_9_9)
% 5.20/1.92 | (44) ? [v0] : ((v0 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9) | (v0 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9))
% 5.20/1.92 |
% 5.20/1.92 | Instantiating (44) with all_35_0_20 yields:
% 5.20/1.92 | (45) (all_35_0_20 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9) | (all_35_0_20 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9)
% 5.20/1.92 |
% 5.20/1.92 +-Applying beta-rule and splitting (45), into two cases.
% 5.20/1.92 |-Branch one:
% 5.20/1.92 | (46) all_35_0_20 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9
% 5.20/1.92 |
% 5.20/1.92 | Applying alpha-rule on (46) yields:
% 5.20/1.92 | (47) all_35_0_20 = all_0_9_9
% 5.20/1.92 | (48) singleton(all_0_7_7) = all_0_9_9
% 5.20/1.92 |
% 5.20/1.92 | Instantiating formula (21) with all_0_7_7, all_0_9_9, all_0_3_3 and discharging atoms singleton(all_0_7_7) = all_0_3_3, singleton(all_0_7_7) = all_0_9_9, yields:
% 5.20/1.92 | (49) all_0_3_3 = all_0_9_9
% 5.20/1.92 |
% 5.20/1.92 | Equations (49) can reduce 29 to:
% 5.20/1.92 | (38) $false
% 5.20/1.92 |
% 5.20/1.92 |-The branch is then unsatisfiable
% 5.20/1.92 |-Branch two:
% 5.20/1.92 | (51) all_35_0_20 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9
% 5.20/1.92 |
% 5.20/1.92 | Applying alpha-rule on (51) yields:
% 5.20/1.92 | (47) all_35_0_20 = all_0_9_9
% 5.20/1.92 | (53) singleton(all_0_8_8) = all_0_9_9
% 5.20/1.92 |
% 5.20/1.92 | Instantiating formula (21) with all_0_8_8, all_0_9_9, all_0_4_4 and discharging atoms singleton(all_0_8_8) = all_0_4_4, singleton(all_0_8_8) = all_0_9_9, yields:
% 5.20/1.92 | (54) all_0_4_4 = all_0_9_9
% 5.20/1.92 |
% 5.20/1.92 | Equations (54) can reduce 33 to:
% 5.20/1.92 | (38) $false
% 5.20/1.92 |
% 5.20/1.92 |-The branch is then unsatisfiable
% 5.20/1.92 |-Branch two:
% 5.20/1.92 | (56) ~ (all_0_5_5 = 0) & (all_0_6_6 = all_0_9_9 | all_0_9_9 = empty_set | (all_0_3_3 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9) | (all_0_4_4 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9))
% 5.20/1.92 |
% 5.20/1.92 | Applying alpha-rule on (56) yields:
% 5.20/1.92 | (57) ~ (all_0_5_5 = 0)
% 5.20/1.93 | (58) all_0_6_6 = all_0_9_9 | all_0_9_9 = empty_set | (all_0_3_3 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9) | (all_0_4_4 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9)
% 5.20/1.93 |
% 5.20/1.93 +-Applying beta-rule and splitting (24), into two cases.
% 5.20/1.93 |-Branch one:
% 5.20/1.93 | (34) all_0_5_5 = 0
% 5.20/1.93 |
% 5.20/1.93 | Equations (34) can reduce 57 to:
% 5.20/1.93 | (38) $false
% 5.20/1.93 |
% 5.20/1.93 |-The branch is then unsatisfiable
% 5.20/1.93 |-Branch two:
% 5.20/1.93 | (57) ~ (all_0_5_5 = 0)
% 5.20/1.93 | (62) ? [v0] : ? [v1] : ( ~ (v1 = all_0_9_9) & ~ (v0 = all_0_9_9) & singleton(all_0_7_7) = v1 & singleton(all_0_8_8) = v0)
% 5.20/1.93 |
% 5.20/1.93 | Instantiating (62) with all_28_0_21, all_28_1_22 yields:
% 5.20/1.93 | (63) ~ (all_28_0_21 = all_0_9_9) & ~ (all_28_1_22 = all_0_9_9) & singleton(all_0_7_7) = all_28_0_21 & singleton(all_0_8_8) = all_28_1_22
% 5.20/1.93 |
% 5.20/1.93 | Applying alpha-rule on (63) yields:
% 5.20/1.93 | (64) ~ (all_28_0_21 = all_0_9_9)
% 5.20/1.93 | (65) ~ (all_28_1_22 = all_0_9_9)
% 5.20/1.93 | (66) singleton(all_0_7_7) = all_28_0_21
% 5.20/1.93 | (67) singleton(all_0_8_8) = all_28_1_22
% 5.20/1.93 |
% 5.20/1.93 +-Applying beta-rule and splitting (26), into two cases.
% 5.20/1.93 |-Branch one:
% 5.20/1.93 | (34) all_0_5_5 = 0
% 5.20/1.93 |
% 5.20/1.93 | Equations (34) can reduce 57 to:
% 5.20/1.93 | (38) $false
% 5.20/1.93 |
% 5.20/1.93 |-The branch is then unsatisfiable
% 5.20/1.93 |-Branch two:
% 5.20/1.93 | (57) ~ (all_0_5_5 = 0)
% 5.20/1.93 | (71) ? [v0] : ? [v1] : ( ~ (v1 = all_0_9_9) & ~ (v0 = all_0_9_9) & singleton(all_0_7_7) = v0 & singleton(all_0_8_8) = v1)
% 5.20/1.93 |
% 5.20/1.93 | Instantiating (71) with all_33_0_23, all_33_1_24 yields:
% 5.20/1.93 | (72) ~ (all_33_0_23 = all_0_9_9) & ~ (all_33_1_24 = all_0_9_9) & singleton(all_0_7_7) = all_33_1_24 & singleton(all_0_8_8) = all_33_0_23
% 5.20/1.93 |
% 5.20/1.93 | Applying alpha-rule on (72) yields:
% 5.20/1.93 | (73) ~ (all_33_0_23 = all_0_9_9)
% 5.20/1.93 | (74) ~ (all_33_1_24 = all_0_9_9)
% 5.20/1.93 | (75) singleton(all_0_7_7) = all_33_1_24
% 5.20/1.93 | (76) singleton(all_0_8_8) = all_33_0_23
% 5.20/1.93 |
% 5.20/1.93 | Instantiating formula (21) with all_0_7_7, all_28_0_21, all_33_1_24 and discharging atoms singleton(all_0_7_7) = all_33_1_24, singleton(all_0_7_7) = all_28_0_21, yields:
% 5.20/1.93 | (77) all_33_1_24 = all_28_0_21
% 5.20/1.93 |
% 5.20/1.93 | Instantiating formula (21) with all_0_8_8, all_28_1_22, all_33_0_23 and discharging atoms singleton(all_0_8_8) = all_33_0_23, singleton(all_0_8_8) = all_28_1_22, yields:
% 5.20/1.93 | (78) all_33_0_23 = all_28_1_22
% 5.20/1.93 |
% 5.20/1.93 | Equations (78) can reduce 73 to:
% 5.20/1.93 | (65) ~ (all_28_1_22 = all_0_9_9)
% 5.20/1.93 |
% 5.20/1.93 | Equations (77) can reduce 74 to:
% 5.20/1.93 | (64) ~ (all_28_0_21 = all_0_9_9)
% 5.20/1.93 |
% 5.20/1.93 | From (77) and (75) follows:
% 5.20/1.93 | (66) singleton(all_0_7_7) = all_28_0_21
% 5.20/1.93 |
% 5.20/1.93 | From (78) and (76) follows:
% 5.20/1.93 | (67) singleton(all_0_8_8) = all_28_1_22
% 5.20/1.93 |
% 5.20/1.93 +-Applying beta-rule and splitting (58), into two cases.
% 5.20/1.93 |-Branch one:
% 5.20/1.93 | (37) all_0_9_9 = empty_set
% 5.20/1.93 |
% 5.20/1.93 | From (37) and (18) follows:
% 5.20/1.93 | (84) subset(empty_set, all_0_6_6) = all_0_5_5
% 5.20/1.93 |
% 5.20/1.93 | Instantiating formula (6) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms subset(empty_set, all_0_6_6) = all_0_5_5, unordered_pair(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 5.20/1.93 | (34) all_0_5_5 = 0
% 5.20/1.93 |
% 5.20/1.93 | Equations (34) can reduce 57 to:
% 5.20/1.93 | (38) $false
% 5.20/1.93 |
% 5.20/1.93 |-The branch is then unsatisfiable
% 5.20/1.93 |-Branch two:
% 5.20/1.93 | (31) ~ (all_0_9_9 = empty_set)
% 5.20/1.93 | (88) all_0_6_6 = all_0_9_9 | (all_0_3_3 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9) | (all_0_4_4 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9)
% 5.20/1.93 |
% 5.20/1.93 +-Applying beta-rule and splitting (88), into two cases.
% 5.20/1.93 |-Branch one:
% 5.20/1.93 | (41) all_0_6_6 = all_0_9_9
% 5.20/1.93 |
% 5.20/1.93 | From (41) and (18) follows:
% 5.20/1.93 | (90) subset(all_0_9_9, all_0_9_9) = all_0_5_5
% 5.20/1.93 |
% 5.20/1.93 | From (41) and (17) follows:
% 5.20/1.93 | (91) unordered_pair(all_0_8_8, all_0_7_7) = all_0_9_9
% 5.20/1.93 |
% 5.20/1.93 | Instantiating formula (14) with all_0_5_5, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_9_9) = all_0_5_5, unordered_pair(all_0_8_8, all_0_7_7) = all_0_9_9, yields:
% 5.20/1.93 | (34) all_0_5_5 = 0
% 5.20/1.93 |
% 5.20/1.93 | Equations (34) can reduce 57 to:
% 5.20/1.93 | (38) $false
% 5.20/1.93 |
% 5.20/1.93 |-The branch is then unsatisfiable
% 5.20/1.93 |-Branch two:
% 5.20/1.93 | (28) ~ (all_0_6_6 = all_0_9_9)
% 5.20/1.93 | (95) (all_0_3_3 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9) | (all_0_4_4 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9)
% 5.20/1.93 |
% 5.20/1.93 +-Applying beta-rule and splitting (95), into two cases.
% 5.20/1.93 |-Branch one:
% 5.20/1.93 | (96) all_0_3_3 = all_0_9_9 & singleton(all_0_7_7) = all_0_9_9
% 5.20/1.93 |
% 5.20/1.93 | Applying alpha-rule on (96) yields:
% 5.20/1.93 | (49) all_0_3_3 = all_0_9_9
% 5.20/1.93 | (48) singleton(all_0_7_7) = all_0_9_9
% 5.20/1.93 |
% 5.20/1.93 | Instantiating formula (21) with all_0_7_7, all_0_9_9, all_28_0_21 and discharging atoms singleton(all_0_7_7) = all_28_0_21, singleton(all_0_7_7) = all_0_9_9, yields:
% 5.20/1.93 | (99) all_28_0_21 = all_0_9_9
% 5.20/1.93 |
% 5.20/1.94 | Equations (99) can reduce 64 to:
% 5.20/1.94 | (38) $false
% 5.20/1.94 |
% 5.20/1.94 |-The branch is then unsatisfiable
% 5.20/1.94 |-Branch two:
% 5.20/1.94 | (101) all_0_4_4 = all_0_9_9 & singleton(all_0_8_8) = all_0_9_9
% 5.20/1.94 |
% 5.20/1.94 | Applying alpha-rule on (101) yields:
% 5.20/1.94 | (54) all_0_4_4 = all_0_9_9
% 5.20/1.94 | (53) singleton(all_0_8_8) = all_0_9_9
% 5.20/1.94 |
% 5.20/1.94 | Instantiating formula (21) with all_0_8_8, all_0_9_9, all_28_1_22 and discharging atoms singleton(all_0_8_8) = all_28_1_22, singleton(all_0_8_8) = all_0_9_9, yields:
% 5.20/1.94 | (104) all_28_1_22 = all_0_9_9
% 5.20/1.94 |
% 5.20/1.94 | Equations (104) can reduce 65 to:
% 5.20/1.94 | (38) $false
% 5.20/1.94 |
% 5.20/1.94 |-The branch is then unsatisfiable
% 5.20/1.94 % SZS output end Proof for theBenchmark
% 5.20/1.94
% 5.20/1.94 1312ms
%------------------------------------------------------------------------------