TSTP Solution File: SEU159+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 3.79s 1.61s
% Output : Proof 4.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jun 18 22:47:08 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.33/0.90 Prover 0: Preprocessing ...
% 1.65/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.65/1.06 Prover 0: Constructing countermodel ...
% 2.63/1.30 Prover 0: gave up
% 2.63/1.30 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.63/1.32 Prover 1: Preprocessing ...
% 2.63/1.36 Prover 1: Warning: ignoring some quantifiers
% 2.92/1.37 Prover 1: Constructing countermodel ...
% 2.92/1.46 Prover 1: gave up
% 2.92/1.46 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.26/1.47 Prover 2: Preprocessing ...
% 3.37/1.51 Prover 2: Warning: ignoring some quantifiers
% 3.37/1.52 Prover 2: Constructing countermodel ...
% 3.79/1.60 Prover 2: proved (146ms)
% 3.79/1.61
% 3.79/1.61 No countermodel exists, formula is valid
% 3.79/1.61 % SZS status Theorem for theBenchmark
% 3.79/1.61
% 3.79/1.61 Generating proof ... Warning: ignoring some quantifiers
% 4.53/1.81 found it (size 43)
% 4.53/1.81
% 4.53/1.81 % SZS output start Proof for theBenchmark
% 4.53/1.81 Assumed formulas after preprocessing and simplification:
% 4.53/1.81 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v3, v2) = v4 & unordered_pair(v0, v1) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v10 = v7 | ~ (unordered_pair(v7, v8) = v9) | ~ (in(v10, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v8) = 0) | ~ (in(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (in(v8, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (in(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (unordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : ((v11 = v9 | v11 = v8 | (v12 = 0 & in(v11, v7) = 0)) & (( ~ (v12 = 0) & in(v11, v7) = v12) | ( ~ (v11 = v9) & ~ (v11 = v8))))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (in(v9, v7) = 0) | in(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (in(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ? [v7] : ? [v8] : ? [v9] : subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : unordered_pair(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : in(v8, v7) = v9 & ((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)))))
% 4.71/1.84 | 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 yields:
% 4.71/1.84 | (1) subset(all_0_3_3, all_0_4_4) = all_0_2_2 & unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3 & ! [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] : ( ~ (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 & ((all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = 0) & in(all_0_5_5, all_0_4_4) = 0 & in(all_0_6_6, all_0_4_4) = 0) | (all_0_2_2 = 0 & (( ~ (all_0_0_0 = 0) & in(all_0_5_5, all_0_4_4) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & in(all_0_6_6, all_0_4_4) = all_0_1_1))))
% 4.71/1.84 |
% 4.71/1.84 | Applying alpha-rule on (1) yields:
% 4.71/1.84 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 4.71/1.84 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 4.71/1.85 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 4.71/1.85 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 4.71/1.85 | (6) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 4.71/1.85 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 4.71/1.85 | (8) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 4.71/1.85 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 4.71/1.85 | (10) (all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = 0) & in(all_0_5_5, all_0_4_4) = 0 & in(all_0_6_6, all_0_4_4) = 0) | (all_0_2_2 = 0 & (( ~ (all_0_0_0 = 0) & in(all_0_5_5, all_0_4_4) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & in(all_0_6_6, all_0_4_4) = all_0_1_1)))
% 4.71/1.85 | (11) unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3
% 4.71/1.85 | (12) subset(all_0_3_3, all_0_4_4) = all_0_2_2
% 4.71/1.85 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 4.71/1.85 | (14) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 4.71/1.85 | (15) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 4.71/1.85 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 4.71/1.85 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.71/1.85 | (18) ? [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)))))
% 4.71/1.85 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 4.71/1.85 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 4.71/1.85 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 4.71/1.85 | (22) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 4.71/1.85 |
% 4.71/1.85 | Instantiating formula (4) with all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_4_4) = all_0_2_2, yields:
% 4.71/1.85 | (23) all_0_2_2 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_3_3) = 0 & in(v0, all_0_4_4) = v1)
% 4.71/1.85 |
% 4.71/1.85 +-Applying beta-rule and splitting (10), into two cases.
% 4.71/1.85 |-Branch one:
% 4.71/1.85 | (24) all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = 0) & in(all_0_5_5, all_0_4_4) = 0 & in(all_0_6_6, all_0_4_4) = 0
% 4.71/1.85 |
% 4.71/1.85 | Applying alpha-rule on (24) yields:
% 4.71/1.85 | (25) all_0_0_0 = 0
% 4.71/1.85 | (26) all_0_1_1 = 0
% 4.71/1.85 | (27) ~ (all_0_2_2 = 0)
% 4.71/1.85 | (28) in(all_0_5_5, all_0_4_4) = 0
% 4.71/1.85 | (29) in(all_0_6_6, all_0_4_4) = 0
% 4.71/1.85 |
% 4.71/1.85 +-Applying beta-rule and splitting (23), into two cases.
% 4.71/1.85 |-Branch one:
% 4.71/1.85 | (30) all_0_2_2 = 0
% 4.71/1.85 |
% 4.71/1.85 | Equations (30) can reduce 27 to:
% 4.71/1.85 | (31) $false
% 4.71/1.85 |
% 4.71/1.86 |-The branch is then unsatisfiable
% 4.71/1.86 |-Branch two:
% 4.71/1.86 | (27) ~ (all_0_2_2 = 0)
% 4.71/1.86 | (33) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_3_3) = 0 & in(v0, all_0_4_4) = v1)
% 4.71/1.86 |
% 4.71/1.86 | Instantiating (33) with all_28_0_17, all_28_1_18 yields:
% 4.71/1.86 | (34) ~ (all_28_0_17 = 0) & in(all_28_1_18, all_0_3_3) = 0 & in(all_28_1_18, all_0_4_4) = all_28_0_17
% 4.71/1.86 |
% 4.71/1.86 | Applying alpha-rule on (34) yields:
% 4.71/1.86 | (35) ~ (all_28_0_17 = 0)
% 4.71/1.86 | (36) in(all_28_1_18, all_0_3_3) = 0
% 4.71/1.86 | (37) in(all_28_1_18, all_0_4_4) = all_28_0_17
% 4.71/1.86 |
% 4.71/1.86 | Instantiating formula (9) with all_28_1_18, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, in(all_28_1_18, all_0_3_3) = 0, yields:
% 4.71/1.86 | (38) all_28_1_18 = all_0_5_5 | all_28_1_18 = all_0_6_6
% 4.71/1.86 |
% 4.71/1.86 +-Applying beta-rule and splitting (38), into two cases.
% 4.71/1.86 |-Branch one:
% 4.71/1.86 | (39) all_28_1_18 = all_0_5_5
% 4.71/1.86 |
% 4.71/1.86 | From (39) and (37) follows:
% 4.71/1.86 | (40) in(all_0_5_5, all_0_4_4) = all_28_0_17
% 4.71/1.86 |
% 4.71/1.86 | Instantiating formula (17) with all_0_5_5, all_0_4_4, all_28_0_17, 0 and discharging atoms in(all_0_5_5, all_0_4_4) = all_28_0_17, in(all_0_5_5, all_0_4_4) = 0, yields:
% 4.71/1.86 | (41) all_28_0_17 = 0
% 4.71/1.86 |
% 4.71/1.86 | Equations (41) can reduce 35 to:
% 4.71/1.86 | (31) $false
% 4.71/1.86 |
% 4.71/1.86 |-The branch is then unsatisfiable
% 4.71/1.86 |-Branch two:
% 4.71/1.86 | (43) ~ (all_28_1_18 = all_0_5_5)
% 4.71/1.86 | (44) all_28_1_18 = all_0_6_6
% 4.71/1.86 |
% 4.71/1.86 | From (44) and (37) follows:
% 4.71/1.86 | (45) in(all_0_6_6, all_0_4_4) = all_28_0_17
% 4.71/1.86 |
% 4.71/1.86 | Instantiating formula (17) with all_0_6_6, all_0_4_4, all_28_0_17, 0 and discharging atoms in(all_0_6_6, all_0_4_4) = all_28_0_17, in(all_0_6_6, all_0_4_4) = 0, yields:
% 4.71/1.86 | (41) all_28_0_17 = 0
% 4.71/1.86 |
% 4.71/1.86 | Equations (41) can reduce 35 to:
% 4.71/1.86 | (31) $false
% 4.71/1.86 |
% 4.71/1.86 |-The branch is then unsatisfiable
% 4.71/1.86 |-Branch two:
% 4.71/1.86 | (48) all_0_2_2 = 0 & (( ~ (all_0_0_0 = 0) & in(all_0_5_5, all_0_4_4) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & in(all_0_6_6, all_0_4_4) = all_0_1_1))
% 4.71/1.86 |
% 4.71/1.86 | Applying alpha-rule on (48) yields:
% 4.71/1.86 | (30) all_0_2_2 = 0
% 4.71/1.86 | (50) ( ~ (all_0_0_0 = 0) & in(all_0_5_5, all_0_4_4) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & in(all_0_6_6, all_0_4_4) = all_0_1_1)
% 4.71/1.86 |
% 4.71/1.86 | From (30) and (12) follows:
% 4.71/1.86 | (51) subset(all_0_3_3, all_0_4_4) = 0
% 4.71/1.86 |
% 4.71/1.86 +-Applying beta-rule and splitting (50), into two cases.
% 4.71/1.86 |-Branch one:
% 4.71/1.86 | (52) ~ (all_0_0_0 = 0) & in(all_0_5_5, all_0_4_4) = all_0_0_0
% 4.71/1.86 |
% 4.71/1.86 | Applying alpha-rule on (52) yields:
% 4.71/1.86 | (53) ~ (all_0_0_0 = 0)
% 4.71/1.86 | (54) in(all_0_5_5, all_0_4_4) = all_0_0_0
% 4.71/1.86 |
% 4.71/1.86 | Instantiating formula (5) with all_0_0_0, all_0_5_5, all_0_4_4, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_4_4) = 0, in(all_0_5_5, all_0_4_4) = all_0_0_0, yields:
% 4.71/1.86 | (55) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_5_5, all_0_3_3) = v0)
% 4.71/1.86 |
% 4.71/1.86 +-Applying beta-rule and splitting (55), into two cases.
% 4.71/1.86 |-Branch one:
% 4.71/1.86 | (25) all_0_0_0 = 0
% 4.71/1.86 |
% 4.71/1.86 | Equations (25) can reduce 53 to:
% 4.71/1.86 | (31) $false
% 4.71/1.86 |
% 4.71/1.86 |-The branch is then unsatisfiable
% 4.71/1.86 |-Branch two:
% 4.71/1.86 | (53) ~ (all_0_0_0 = 0)
% 4.71/1.86 | (59) ? [v0] : ( ~ (v0 = 0) & in(all_0_5_5, all_0_3_3) = v0)
% 4.71/1.86 |
% 4.71/1.86 | Instantiating (59) with all_45_0_22 yields:
% 4.71/1.86 | (60) ~ (all_45_0_22 = 0) & in(all_0_5_5, all_0_3_3) = all_45_0_22
% 4.71/1.86 |
% 4.71/1.86 | Applying alpha-rule on (60) yields:
% 4.71/1.86 | (61) ~ (all_45_0_22 = 0)
% 4.71/1.86 | (62) in(all_0_5_5, all_0_3_3) = all_45_0_22
% 4.71/1.86 |
% 4.71/1.86 | Instantiating formula (13) with all_45_0_22, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, in(all_0_5_5, all_0_3_3) = all_45_0_22, yields:
% 4.71/1.86 | (63) all_45_0_22 = 0
% 4.71/1.86 |
% 4.71/1.86 | Equations (63) can reduce 61 to:
% 4.71/1.86 | (31) $false
% 4.71/1.86 |
% 4.71/1.86 |-The branch is then unsatisfiable
% 4.71/1.86 |-Branch two:
% 4.71/1.86 | (65) ~ (all_0_1_1 = 0) & in(all_0_6_6, all_0_4_4) = all_0_1_1
% 4.71/1.86 |
% 4.71/1.86 | Applying alpha-rule on (65) yields:
% 4.71/1.86 | (66) ~ (all_0_1_1 = 0)
% 4.71/1.86 | (67) in(all_0_6_6, all_0_4_4) = all_0_1_1
% 4.71/1.86 |
% 4.71/1.86 | Instantiating formula (5) with all_0_1_1, all_0_6_6, all_0_4_4, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_4_4) = 0, in(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 4.71/1.87 | (68) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_6_6, all_0_3_3) = v0)
% 4.71/1.87 |
% 4.71/1.87 +-Applying beta-rule and splitting (68), into two cases.
% 4.71/1.87 |-Branch one:
% 4.71/1.87 | (26) all_0_1_1 = 0
% 4.71/1.87 |
% 4.71/1.87 | Equations (26) can reduce 66 to:
% 4.71/1.87 | (31) $false
% 4.71/1.87 |
% 4.71/1.87 |-The branch is then unsatisfiable
% 4.71/1.87 |-Branch two:
% 4.71/1.87 | (66) ~ (all_0_1_1 = 0)
% 4.71/1.87 | (72) ? [v0] : ( ~ (v0 = 0) & in(all_0_6_6, all_0_3_3) = v0)
% 4.71/1.87 |
% 4.71/1.87 | Instantiating (72) with all_45_0_23 yields:
% 4.71/1.87 | (73) ~ (all_45_0_23 = 0) & in(all_0_6_6, all_0_3_3) = all_45_0_23
% 4.71/1.87 |
% 4.71/1.87 | Applying alpha-rule on (73) yields:
% 4.71/1.87 | (74) ~ (all_45_0_23 = 0)
% 4.71/1.87 | (75) in(all_0_6_6, all_0_3_3) = all_45_0_23
% 4.71/1.87 |
% 4.71/1.87 | Instantiating formula (7) with all_45_0_23, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, in(all_0_6_6, all_0_3_3) = all_45_0_23, yields:
% 4.71/1.87 | (76) all_45_0_23 = 0
% 4.71/1.87 |
% 4.71/1.87 | Equations (76) can reduce 74 to:
% 4.71/1.87 | (31) $false
% 4.71/1.87 |
% 4.71/1.87 |-The branch is then unsatisfiable
% 4.71/1.87 % SZS output end Proof for theBenchmark
% 4.71/1.87
% 4.71/1.87 1276ms
%------------------------------------------------------------------------------