TSTP Solution File: SEU159+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU159+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 08:47:07 EDT 2022
% Result : Theorem 3.86s 1.68s
% Output : Proof 4.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU159+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 19 00:50:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.50/0.62 ____ _
% 0.50/0.62 ___ / __ \_____(_)___ ________ __________
% 0.50/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.62
% 0.50/0.62 A Theorem Prover for First-Order Logic
% 0.50/0.62 (ePrincess v.1.0)
% 0.50/0.62
% 0.50/0.62 (c) Philipp Rümmer, 2009-2015
% 0.50/0.62 (c) Peter Backeman, 2014-2015
% 0.50/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.62 Bug reports to peter@backeman.se
% 0.50/0.62
% 0.50/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.62
% 0.50/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.77/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.44/0.94 Prover 0: Preprocessing ...
% 1.74/1.09 Prover 0: Warning: ignoring some quantifiers
% 1.74/1.11 Prover 0: Constructing countermodel ...
% 2.54/1.35 Prover 0: gave up
% 2.54/1.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.72/1.37 Prover 1: Preprocessing ...
% 2.72/1.43 Prover 1: Warning: ignoring some quantifiers
% 2.72/1.43 Prover 1: Constructing countermodel ...
% 3.22/1.53 Prover 1: gave up
% 3.22/1.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.38/1.54 Prover 2: Preprocessing ...
% 3.42/1.59 Prover 2: Warning: ignoring some quantifiers
% 3.42/1.59 Prover 2: Constructing countermodel ...
% 3.69/1.68 Prover 2: proved (149ms)
% 3.69/1.68
% 3.69/1.68 No countermodel exists, formula is valid
% 3.86/1.68 % SZS status Theorem for theBenchmark
% 3.86/1.68
% 3.86/1.68 Generating proof ... Warning: ignoring some quantifiers
% 4.48/1.89 found it (size 43)
% 4.48/1.89
% 4.48/1.89 % SZS output start Proof for theBenchmark
% 4.48/1.89 Assumed formulas after preprocessing and simplification:
% 4.48/1.89 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v8 = 0) & empty(v9) = 0 & empty(v7) = v8 & subset(v3, v2) = v4 & unordered_pair(v0, v1) = v3 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | v13 = v10 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v13, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v10, v11) = 0) | ~ (in(v12, v11) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v12, v10) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v10, v12) = v13)) & ! [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] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (unordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : ((v14 = v12 | v14 = v11 | (v15 = 0 & in(v14, v10) = 0)) & (( ~ (v15 = 0) & in(v14, v10) = v15) | ( ~ (v14 = v12) & ~ (v14 = v11))))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & in(v13, v11) = v14 & in(v13, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (subset(v10, v11) = 0) | ~ (in(v12, v10) = 0) | in(v12, v11) = 0) & ! [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] : ( ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ? [v10] : ? [v11] : ? [v12] : subset(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : unordered_pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : in(v11, v10) = v12 & ? [v10] : ? [v11] : empty(v10) = v11 & ((v6 = 0 & v5 = 0 & ~ (v4 = 0) & in(v1, v2) = 0 & in(v0, v2) = 0) | (v4 = 0 & (( ~ (v6 = 0) & in(v1, v2) = v6) | ( ~ (v5 = 0) & in(v0, v2) = v5)))))
% 4.82/1.93 | 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:
% 4.82/1.93 | (1) ~ (all_0_1_1 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & subset(all_0_6_6, all_0_7_7) = all_0_5_5 & unordered_pair(all_0_9_9, all_0_8_8) = all_0_6_6 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) & ! [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] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = v2 | v4 = v1 | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [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] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ((all_0_3_3 = 0 & all_0_4_4 = 0 & ~ (all_0_5_5 = 0) & in(all_0_8_8, all_0_7_7) = 0 & in(all_0_9_9, all_0_7_7) = 0) | (all_0_5_5 = 0 & (( ~ (all_0_3_3 = 0) & in(all_0_8_8, all_0_7_7) = all_0_3_3) | ( ~ (all_0_4_4 = 0) & in(all_0_9_9, all_0_7_7) = all_0_4_4))))
% 4.82/1.93 |
% 4.82/1.93 | Applying alpha-rule on (1) yields:
% 4.82/1.93 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 4.82/1.93 | (3) ~ (all_0_1_1 = 0)
% 4.82/1.93 | (4) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = v2 | v4 = v1 | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v4 = v2) & ~ (v4 = v1)))))
% 4.82/1.93 | (5) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 4.82/1.93 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 4.82/1.93 | (7) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 4.82/1.93 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.82/1.94 | (9) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 4.82/1.94 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 4.82/1.94 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 4.82/1.94 | (12) subset(all_0_6_6, all_0_7_7) = all_0_5_5
% 4.82/1.94 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 4.82/1.94 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 4.82/1.94 | (15) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 4.82/1.94 | (16) unordered_pair(all_0_9_9, all_0_8_8) = all_0_6_6
% 4.82/1.94 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 4.82/1.94 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 4.82/1.94 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 4.82/1.94 | (20) ? [v0] : ? [v1] : empty(v0) = v1
% 4.82/1.94 | (21) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 4.82/1.94 | (22) (all_0_3_3 = 0 & all_0_4_4 = 0 & ~ (all_0_5_5 = 0) & in(all_0_8_8, all_0_7_7) = 0 & in(all_0_9_9, all_0_7_7) = 0) | (all_0_5_5 = 0 & (( ~ (all_0_3_3 = 0) & in(all_0_8_8, all_0_7_7) = all_0_3_3) | ( ~ (all_0_4_4 = 0) & in(all_0_9_9, all_0_7_7) = all_0_4_4)))
% 4.82/1.94 | (23) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 4.82/1.94 | (24) empty(all_0_2_2) = all_0_1_1
% 4.82/1.94 | (25) empty(all_0_0_0) = 0
% 4.82/1.94 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 4.82/1.94 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 4.82/1.94 |
% 4.82/1.94 | Instantiating formula (10) with all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_7_7) = all_0_5_5, yields:
% 4.82/1.94 | (28) all_0_5_5 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_6_6) = 0 & in(v0, all_0_7_7) = v1)
% 4.82/1.94 |
% 4.82/1.94 +-Applying beta-rule and splitting (22), into two cases.
% 4.82/1.94 |-Branch one:
% 4.82/1.94 | (29) all_0_3_3 = 0 & all_0_4_4 = 0 & ~ (all_0_5_5 = 0) & in(all_0_8_8, all_0_7_7) = 0 & in(all_0_9_9, all_0_7_7) = 0
% 4.82/1.94 |
% 4.82/1.94 | Applying alpha-rule on (29) yields:
% 4.82/1.94 | (30) all_0_3_3 = 0
% 4.82/1.94 | (31) ~ (all_0_5_5 = 0)
% 4.82/1.94 | (32) in(all_0_8_8, all_0_7_7) = 0
% 4.82/1.94 | (33) all_0_4_4 = 0
% 4.82/1.94 | (34) in(all_0_9_9, all_0_7_7) = 0
% 4.82/1.94 |
% 4.82/1.94 +-Applying beta-rule and splitting (28), into two cases.
% 4.82/1.94 |-Branch one:
% 4.82/1.94 | (35) all_0_5_5 = 0
% 4.82/1.94 |
% 4.82/1.94 | Equations (35) can reduce 31 to:
% 4.82/1.94 | (36) $false
% 4.82/1.94 |
% 4.82/1.94 |-The branch is then unsatisfiable
% 4.82/1.94 |-Branch two:
% 4.82/1.94 | (31) ~ (all_0_5_5 = 0)
% 4.82/1.94 | (38) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_6_6) = 0 & in(v0, all_0_7_7) = v1)
% 4.82/1.95 |
% 4.82/1.95 | Instantiating (38) with all_30_0_22, all_30_1_23 yields:
% 4.82/1.95 | (39) ~ (all_30_0_22 = 0) & in(all_30_1_23, all_0_6_6) = 0 & in(all_30_1_23, all_0_7_7) = all_30_0_22
% 4.82/1.95 |
% 4.82/1.95 | Applying alpha-rule on (39) yields:
% 4.82/1.95 | (40) ~ (all_30_0_22 = 0)
% 4.82/1.95 | (41) in(all_30_1_23, all_0_6_6) = 0
% 4.82/1.95 | (42) in(all_30_1_23, all_0_7_7) = all_30_0_22
% 4.82/1.95 |
% 4.82/1.95 | Instantiating formula (14) with all_30_1_23, all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms unordered_pair(all_0_9_9, all_0_8_8) = all_0_6_6, in(all_30_1_23, all_0_6_6) = 0, yields:
% 4.82/1.95 | (43) all_30_1_23 = all_0_8_8 | all_30_1_23 = all_0_9_9
% 4.82/1.95 |
% 4.82/1.95 +-Applying beta-rule and splitting (43), into two cases.
% 4.82/1.95 |-Branch one:
% 4.82/1.95 | (44) all_30_1_23 = all_0_8_8
% 4.82/1.95 |
% 4.82/1.95 | From (44) and (42) follows:
% 4.82/1.95 | (45) in(all_0_8_8, all_0_7_7) = all_30_0_22
% 4.82/1.95 |
% 4.82/1.95 | Instantiating formula (8) with all_0_8_8, all_0_7_7, all_30_0_22, 0 and discharging atoms in(all_0_8_8, all_0_7_7) = all_30_0_22, in(all_0_8_8, all_0_7_7) = 0, yields:
% 4.82/1.95 | (46) all_30_0_22 = 0
% 4.82/1.95 |
% 4.82/1.95 | Equations (46) can reduce 40 to:
% 4.82/1.95 | (36) $false
% 4.82/1.95 |
% 4.82/1.95 |-The branch is then unsatisfiable
% 4.82/1.95 |-Branch two:
% 4.82/1.95 | (48) ~ (all_30_1_23 = all_0_8_8)
% 4.82/1.95 | (49) all_30_1_23 = all_0_9_9
% 4.82/1.95 |
% 4.82/1.95 | From (49) and (42) follows:
% 4.82/1.95 | (50) in(all_0_9_9, all_0_7_7) = all_30_0_22
% 4.82/1.95 |
% 4.82/1.95 | Instantiating formula (8) with all_0_9_9, all_0_7_7, all_30_0_22, 0 and discharging atoms in(all_0_9_9, all_0_7_7) = all_30_0_22, in(all_0_9_9, all_0_7_7) = 0, yields:
% 4.82/1.95 | (46) all_30_0_22 = 0
% 4.82/1.95 |
% 4.82/1.95 | Equations (46) can reduce 40 to:
% 4.82/1.95 | (36) $false
% 4.82/1.95 |
% 4.82/1.95 |-The branch is then unsatisfiable
% 4.82/1.95 |-Branch two:
% 4.82/1.95 | (53) all_0_5_5 = 0 & (( ~ (all_0_3_3 = 0) & in(all_0_8_8, all_0_7_7) = all_0_3_3) | ( ~ (all_0_4_4 = 0) & in(all_0_9_9, all_0_7_7) = all_0_4_4))
% 4.82/1.95 |
% 4.82/1.95 | Applying alpha-rule on (53) yields:
% 4.82/1.95 | (35) all_0_5_5 = 0
% 4.82/1.95 | (55) ( ~ (all_0_3_3 = 0) & in(all_0_8_8, all_0_7_7) = all_0_3_3) | ( ~ (all_0_4_4 = 0) & in(all_0_9_9, all_0_7_7) = all_0_4_4)
% 4.82/1.95 |
% 4.82/1.95 | From (35) and (12) follows:
% 4.82/1.95 | (56) subset(all_0_6_6, all_0_7_7) = 0
% 4.82/1.95 |
% 4.82/1.95 +-Applying beta-rule and splitting (55), into two cases.
% 4.82/1.95 |-Branch one:
% 4.82/1.95 | (57) ~ (all_0_3_3 = 0) & in(all_0_8_8, all_0_7_7) = all_0_3_3
% 4.82/1.95 |
% 4.82/1.95 | Applying alpha-rule on (57) yields:
% 4.82/1.95 | (58) ~ (all_0_3_3 = 0)
% 4.82/1.95 | (59) in(all_0_8_8, all_0_7_7) = all_0_3_3
% 4.82/1.95 |
% 4.82/1.95 | Instantiating formula (11) with all_0_3_3, all_0_8_8, all_0_7_7, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_7_7) = 0, in(all_0_8_8, all_0_7_7) = all_0_3_3, yields:
% 4.82/1.95 | (60) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_8_8, all_0_6_6) = v0)
% 4.82/1.95 |
% 4.82/1.95 +-Applying beta-rule and splitting (60), into two cases.
% 4.82/1.95 |-Branch one:
% 4.82/1.95 | (30) all_0_3_3 = 0
% 4.82/1.95 |
% 4.82/1.95 | Equations (30) can reduce 58 to:
% 4.82/1.95 | (36) $false
% 4.82/1.95 |
% 4.82/1.95 |-The branch is then unsatisfiable
% 4.82/1.95 |-Branch two:
% 4.82/1.95 | (58) ~ (all_0_3_3 = 0)
% 4.82/1.95 | (64) ? [v0] : ( ~ (v0 = 0) & in(all_0_8_8, all_0_6_6) = v0)
% 4.82/1.95 |
% 4.82/1.95 | Instantiating (64) with all_47_0_27 yields:
% 4.82/1.95 | (65) ~ (all_47_0_27 = 0) & in(all_0_8_8, all_0_6_6) = all_47_0_27
% 4.82/1.95 |
% 4.82/1.95 | Applying alpha-rule on (65) yields:
% 4.82/1.95 | (66) ~ (all_47_0_27 = 0)
% 4.82/1.95 | (67) in(all_0_8_8, all_0_6_6) = all_47_0_27
% 4.82/1.95 |
% 4.82/1.95 | Instantiating formula (13) with all_47_0_27, all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms unordered_pair(all_0_9_9, all_0_8_8) = all_0_6_6, in(all_0_8_8, all_0_6_6) = all_47_0_27, yields:
% 4.82/1.95 | (68) all_47_0_27 = 0
% 4.82/1.95 |
% 4.82/1.95 | Equations (68) can reduce 66 to:
% 4.82/1.95 | (36) $false
% 4.82/1.95 |
% 4.82/1.95 |-The branch is then unsatisfiable
% 4.82/1.95 |-Branch two:
% 4.82/1.95 | (70) ~ (all_0_4_4 = 0) & in(all_0_9_9, all_0_7_7) = all_0_4_4
% 4.82/1.95 |
% 4.82/1.95 | Applying alpha-rule on (70) yields:
% 4.82/1.95 | (71) ~ (all_0_4_4 = 0)
% 4.82/1.95 | (72) in(all_0_9_9, all_0_7_7) = all_0_4_4
% 4.82/1.95 |
% 4.82/1.95 | Instantiating formula (11) with all_0_4_4, all_0_9_9, all_0_7_7, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_7_7) = 0, in(all_0_9_9, all_0_7_7) = all_0_4_4, yields:
% 4.82/1.95 | (73) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_9_9, all_0_6_6) = v0)
% 4.82/1.96 |
% 4.82/1.96 +-Applying beta-rule and splitting (73), into two cases.
% 4.82/1.96 |-Branch one:
% 4.82/1.96 | (33) all_0_4_4 = 0
% 4.82/1.96 |
% 4.82/1.96 | Equations (33) can reduce 71 to:
% 4.82/1.96 | (36) $false
% 4.82/1.96 |
% 4.82/1.96 |-The branch is then unsatisfiable
% 4.82/1.96 |-Branch two:
% 4.82/1.96 | (71) ~ (all_0_4_4 = 0)
% 4.82/1.96 | (77) ? [v0] : ( ~ (v0 = 0) & in(all_0_9_9, all_0_6_6) = v0)
% 4.82/1.96 |
% 4.82/1.96 | Instantiating (77) with all_47_0_28 yields:
% 4.82/1.96 | (78) ~ (all_47_0_28 = 0) & in(all_0_9_9, all_0_6_6) = all_47_0_28
% 4.82/1.96 |
% 4.82/1.96 | Applying alpha-rule on (78) yields:
% 4.82/1.96 | (79) ~ (all_47_0_28 = 0)
% 4.82/1.96 | (80) in(all_0_9_9, all_0_6_6) = all_47_0_28
% 4.82/1.96 |
% 4.82/1.96 | Instantiating formula (17) with all_47_0_28, all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms unordered_pair(all_0_9_9, all_0_8_8) = all_0_6_6, in(all_0_9_9, all_0_6_6) = all_47_0_28, yields:
% 4.82/1.96 | (81) all_47_0_28 = 0
% 4.82/1.96 |
% 4.82/1.96 | Equations (81) can reduce 79 to:
% 4.82/1.96 | (36) $false
% 4.82/1.96 |
% 4.82/1.96 |-The branch is then unsatisfiable
% 4.82/1.96 % SZS output end Proof for theBenchmark
% 4.82/1.96
% 4.82/1.96 1326ms
%------------------------------------------------------------------------------