TSTP Solution File: SET928+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 00:23:15 EDT 2022
% Result : Theorem 2.69s 1.48s
% Output : Proof 3.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 18:31:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.51/0.58 ____ _
% 0.51/0.58 ___ / __ \_____(_)___ ________ __________
% 0.51/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.58
% 0.51/0.58 A Theorem Prover for First-Order Logic
% 0.51/0.58 (ePrincess v.1.0)
% 0.51/0.58
% 0.51/0.58 (c) Philipp Rümmer, 2009-2015
% 0.51/0.58 (c) Peter Backeman, 2014-2015
% 0.51/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.58 Bug reports to peter@backeman.se
% 0.51/0.58
% 0.51/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.58
% 0.51/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.95 Prover 0: Preprocessing ...
% 1.59/1.10 Prover 0: Warning: ignoring some quantifiers
% 1.59/1.12 Prover 0: Constructing countermodel ...
% 2.07/1.32 Prover 0: gave up
% 2.26/1.32 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.26/1.34 Prover 1: Preprocessing ...
% 2.41/1.41 Prover 1: Constructing countermodel ...
% 2.69/1.48 Prover 1: proved (156ms)
% 2.69/1.48
% 2.69/1.48 No countermodel exists, formula is valid
% 2.69/1.48 % SZS status Theorem for theBenchmark
% 2.69/1.48
% 2.69/1.48 Generating proof ... found it (size 59)
% 3.21/1.69
% 3.21/1.69 % SZS output start Proof for theBenchmark
% 3.21/1.69 Assumed formulas after preprocessing and simplification:
% 3.21/1.69 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v8 = 0) & set_difference(v3, v2) = v4 & empty(v9) = 0 & empty(v7) = v8 & unordered_pair(v0, v1) = v3 & in(v1, v2) = v6 & in(v0, v2) = v5 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (disjoint(v13, v11) = v14) | ~ (unordered_pair(v10, v12) = v13) | ? [v15] : ? [v16] : (in(v12, v11) = v16 & in(v10, v11) = v15 & (v16 = 0 | v15 = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_difference(v13, v12) = v11) | ~ (set_difference(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (disjoint(v13, v12) = v11) | ~ (disjoint(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] : ( ~ (disjoint(v13, v12) = 0) | ~ (unordered_pair(v10, v11) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v10, v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (set_difference(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & disjoint(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : ( ~ (set_difference(v10, v11) = v10) | disjoint(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (disjoint(v10, v11) = 0) | disjoint(v11, v10) = 0) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ((v4 = v3 & (v6 = 0 | v5 = 0)) | ( ~ (v6 = 0) & ~ (v5 = 0) & ~ (v4 = v3))))
% 3.21/1.72 | 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:
% 3.21/1.72 | (1) ~ (all_0_1_1 = 0) & set_difference(all_0_6_6, all_0_7_7) = all_0_5_5 & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & unordered_pair(all_0_9_9, all_0_8_8) = all_0_6_6 & in(all_0_8_8, all_0_7_7) = all_0_3_3 & in(all_0_9_9, all_0_7_7) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (disjoint(v3, v1) = v4) | ~ (unordered_pair(v0, v2) = v3) | ? [v5] : ? [v6] : (in(v2, v1) = v6 & in(v0, v1) = v5 & (v6 = 0 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(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] : ( ~ (disjoint(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ((all_0_5_5 = all_0_6_6 & (all_0_3_3 = 0 | all_0_4_4 = 0)) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_5_5 = all_0_6_6)))
% 3.21/1.73 |
% 3.21/1.73 | Applying alpha-rule on (1) yields:
% 3.21/1.73 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (disjoint(v3, v1) = v4) | ~ (unordered_pair(v0, v2) = v3) | ? [v5] : ? [v6] : (in(v2, v1) = v6 & in(v0, v1) = v5 & (v6 = 0 | v5 = 0)))
% 3.21/1.73 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (disjoint(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v2) = v4))
% 3.21/1.73 | (4) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 3.21/1.73 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 3.21/1.73 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 3.21/1.73 | (7) empty(all_0_0_0) = 0
% 3.21/1.73 | (8) empty(all_0_2_2) = all_0_1_1
% 3.21/1.73 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 3.21/1.73 | (10) set_difference(all_0_6_6, all_0_7_7) = all_0_5_5
% 3.21/1.73 | (11) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 3.21/1.73 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 3.21/1.73 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 3.21/1.73 | (14) (all_0_5_5 = all_0_6_6 & (all_0_3_3 = 0 | all_0_4_4 = 0)) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_5_5 = all_0_6_6))
% 3.21/1.73 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 3.21/1.73 | (16) ~ (all_0_1_1 = 0)
% 3.21/1.73 | (17) in(all_0_9_9, all_0_7_7) = all_0_4_4
% 3.21/1.73 | (18) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1) = 0)
% 3.21/1.73 | (19) unordered_pair(all_0_9_9, all_0_8_8) = all_0_6_6
% 3.21/1.73 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 3.21/1.73 | (21) in(all_0_8_8, all_0_7_7) = all_0_3_3
% 3.21/1.73 |
% 3.21/1.73 | Instantiating formula (18) with all_0_7_7, all_0_6_6 yields:
% 3.21/1.73 | (22) ~ (set_difference(all_0_6_6, all_0_7_7) = all_0_6_6) | disjoint(all_0_6_6, all_0_7_7) = 0
% 3.21/1.73 |
% 3.21/1.73 | Instantiating formula (5) with all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_7_7) = all_0_5_5, yields:
% 3.21/1.73 | (23) all_0_5_5 = all_0_6_6 | ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_6_6, all_0_7_7) = v0)
% 3.21/1.74 |
% 3.21/1.74 | Instantiating formula (20) with 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, yields:
% 3.21/1.74 | (24) unordered_pair(all_0_8_8, all_0_9_9) = all_0_6_6
% 3.21/1.74 |
% 3.21/1.74 +-Applying beta-rule and splitting (22), into two cases.
% 3.21/1.74 |-Branch one:
% 3.21/1.74 | (25) disjoint(all_0_6_6, all_0_7_7) = 0
% 3.21/1.74 |
% 3.21/1.74 +-Applying beta-rule and splitting (23), into two cases.
% 3.21/1.74 |-Branch one:
% 3.21/1.74 | (26) all_0_5_5 = all_0_6_6
% 3.21/1.74 |
% 3.21/1.74 | Instantiating formula (3) with all_0_6_6, all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms disjoint(all_0_6_6, all_0_7_7) = 0, unordered_pair(all_0_8_8, all_0_9_9) = all_0_6_6, yields:
% 3.21/1.74 | (27) ? [v0] : ( ~ (v0 = 0) & in(all_0_8_8, all_0_7_7) = v0)
% 3.21/1.74 |
% 3.21/1.74 | Instantiating formula (3) with all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms disjoint(all_0_6_6, all_0_7_7) = 0, unordered_pair(all_0_9_9, all_0_8_8) = all_0_6_6, yields:
% 3.21/1.74 | (28) ? [v0] : ( ~ (v0 = 0) & in(all_0_9_9, all_0_7_7) = v0)
% 3.21/1.74 |
% 3.21/1.74 | Instantiating (28) with all_37_0_10 yields:
% 3.21/1.74 | (29) ~ (all_37_0_10 = 0) & in(all_0_9_9, all_0_7_7) = all_37_0_10
% 3.21/1.74 |
% 3.21/1.74 | Applying alpha-rule on (29) yields:
% 3.21/1.74 | (30) ~ (all_37_0_10 = 0)
% 3.21/1.74 | (31) in(all_0_9_9, all_0_7_7) = all_37_0_10
% 3.21/1.74 |
% 3.21/1.74 | Instantiating (27) with all_39_0_11 yields:
% 3.21/1.74 | (32) ~ (all_39_0_11 = 0) & in(all_0_8_8, all_0_7_7) = all_39_0_11
% 3.21/1.74 |
% 3.21/1.74 | Applying alpha-rule on (32) yields:
% 3.21/1.74 | (33) ~ (all_39_0_11 = 0)
% 3.21/1.74 | (34) in(all_0_8_8, all_0_7_7) = all_39_0_11
% 3.21/1.74 |
% 3.21/1.74 | Instantiating formula (6) with all_0_8_8, all_0_7_7, all_39_0_11, all_0_3_3 and discharging atoms in(all_0_8_8, all_0_7_7) = all_39_0_11, in(all_0_8_8, all_0_7_7) = all_0_3_3, yields:
% 3.21/1.74 | (35) all_39_0_11 = all_0_3_3
% 3.21/1.74 |
% 3.21/1.74 | Instantiating formula (6) with all_0_9_9, all_0_7_7, all_37_0_10, all_0_4_4 and discharging atoms in(all_0_9_9, all_0_7_7) = all_37_0_10, in(all_0_9_9, all_0_7_7) = all_0_4_4, yields:
% 3.21/1.74 | (36) all_37_0_10 = all_0_4_4
% 3.21/1.74 |
% 3.21/1.74 | Equations (35) can reduce 33 to:
% 3.21/1.74 | (37) ~ (all_0_3_3 = 0)
% 3.21/1.74 |
% 3.21/1.74 | Equations (36) can reduce 30 to:
% 3.21/1.74 | (38) ~ (all_0_4_4 = 0)
% 3.21/1.74 |
% 3.21/1.74 +-Applying beta-rule and splitting (14), into two cases.
% 3.21/1.74 |-Branch one:
% 3.21/1.74 | (39) all_0_5_5 = all_0_6_6 & (all_0_3_3 = 0 | all_0_4_4 = 0)
% 3.21/1.74 |
% 3.21/1.74 | Applying alpha-rule on (39) yields:
% 3.21/1.74 | (26) all_0_5_5 = all_0_6_6
% 3.21/1.74 | (41) all_0_3_3 = 0 | all_0_4_4 = 0
% 3.21/1.74 |
% 3.21/1.74 +-Applying beta-rule and splitting (41), into two cases.
% 3.21/1.74 |-Branch one:
% 3.21/1.74 | (42) all_0_3_3 = 0
% 3.21/1.74 |
% 3.21/1.74 | Equations (42) can reduce 37 to:
% 3.21/1.74 | (43) $false
% 3.21/1.74 |
% 3.21/1.74 |-The branch is then unsatisfiable
% 3.21/1.74 |-Branch two:
% 3.21/1.74 | (37) ~ (all_0_3_3 = 0)
% 3.21/1.74 | (45) all_0_4_4 = 0
% 3.21/1.74 |
% 3.21/1.74 | Equations (45) can reduce 38 to:
% 3.21/1.74 | (43) $false
% 3.21/1.74 |
% 3.21/1.74 |-The branch is then unsatisfiable
% 3.21/1.74 |-Branch two:
% 3.21/1.74 | (47) ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_5_5 = all_0_6_6)
% 3.21/1.75 |
% 3.21/1.75 | Applying alpha-rule on (47) yields:
% 3.21/1.75 | (37) ~ (all_0_3_3 = 0)
% 3.21/1.75 | (38) ~ (all_0_4_4 = 0)
% 3.46/1.75 | (50) ~ (all_0_5_5 = all_0_6_6)
% 3.46/1.75 |
% 3.46/1.75 | Equations (26) can reduce 50 to:
% 3.46/1.75 | (43) $false
% 3.46/1.75 |
% 3.46/1.75 |-The branch is then unsatisfiable
% 3.46/1.75 |-Branch two:
% 3.46/1.75 | (50) ~ (all_0_5_5 = all_0_6_6)
% 3.46/1.75 | (53) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_6_6, all_0_7_7) = v0)
% 3.46/1.75 |
% 3.46/1.75 | Instantiating (53) with all_31_0_12 yields:
% 3.46/1.75 | (54) ~ (all_31_0_12 = 0) & disjoint(all_0_6_6, all_0_7_7) = all_31_0_12
% 3.46/1.75 |
% 3.46/1.75 | Applying alpha-rule on (54) yields:
% 3.46/1.75 | (55) ~ (all_31_0_12 = 0)
% 3.46/1.75 | (56) disjoint(all_0_6_6, all_0_7_7) = all_31_0_12
% 3.46/1.75 |
% 3.46/1.75 | Instantiating formula (13) with all_0_6_6, all_0_7_7, 0, all_31_0_12 and discharging atoms disjoint(all_0_6_6, all_0_7_7) = all_31_0_12, disjoint(all_0_6_6, all_0_7_7) = 0, yields:
% 3.46/1.75 | (57) all_31_0_12 = 0
% 3.46/1.75 |
% 3.46/1.75 | Equations (57) can reduce 55 to:
% 3.46/1.75 | (43) $false
% 3.46/1.75 |
% 3.46/1.75 |-The branch is then unsatisfiable
% 3.46/1.75 |-Branch two:
% 3.46/1.75 | (59) ~ (disjoint(all_0_6_6, all_0_7_7) = 0)
% 3.46/1.75 | (60) ~ (set_difference(all_0_6_6, all_0_7_7) = all_0_6_6)
% 3.46/1.75 |
% 3.46/1.75 | Using (10) and (60) yields:
% 3.46/1.75 | (50) ~ (all_0_5_5 = all_0_6_6)
% 3.46/1.75 |
% 3.46/1.75 +-Applying beta-rule and splitting (14), into two cases.
% 3.46/1.75 |-Branch one:
% 3.46/1.75 | (39) all_0_5_5 = all_0_6_6 & (all_0_3_3 = 0 | all_0_4_4 = 0)
% 3.46/1.75 |
% 3.46/1.75 | Applying alpha-rule on (39) yields:
% 3.46/1.75 | (26) all_0_5_5 = all_0_6_6
% 3.46/1.75 | (41) all_0_3_3 = 0 | all_0_4_4 = 0
% 3.46/1.75 |
% 3.46/1.75 | Equations (26) can reduce 50 to:
% 3.46/1.75 | (43) $false
% 3.46/1.75 |
% 3.46/1.75 |-The branch is then unsatisfiable
% 3.46/1.75 |-Branch two:
% 3.46/1.75 | (47) ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_5_5 = all_0_6_6)
% 3.46/1.75 |
% 3.46/1.75 | Applying alpha-rule on (47) yields:
% 3.46/1.75 | (37) ~ (all_0_3_3 = 0)
% 3.46/1.75 | (38) ~ (all_0_4_4 = 0)
% 3.46/1.75 | (50) ~ (all_0_5_5 = all_0_6_6)
% 3.46/1.75 |
% 3.46/1.75 +-Applying beta-rule and splitting (23), into two cases.
% 3.46/1.75 |-Branch one:
% 3.46/1.75 | (26) all_0_5_5 = all_0_6_6
% 3.46/1.75 |
% 3.46/1.75 | Equations (26) can reduce 50 to:
% 3.46/1.75 | (43) $false
% 3.46/1.75 |
% 3.46/1.75 |-The branch is then unsatisfiable
% 3.46/1.75 |-Branch two:
% 3.46/1.75 | (50) ~ (all_0_5_5 = all_0_6_6)
% 3.46/1.75 | (53) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_6_6, all_0_7_7) = v0)
% 3.46/1.75 |
% 3.46/1.75 | Instantiating (53) with all_39_0_13 yields:
% 3.46/1.75 | (74) ~ (all_39_0_13 = 0) & disjoint(all_0_6_6, all_0_7_7) = all_39_0_13
% 3.46/1.75 |
% 3.46/1.75 | Applying alpha-rule on (74) yields:
% 3.46/1.75 | (75) ~ (all_39_0_13 = 0)
% 3.46/1.75 | (76) disjoint(all_0_6_6, all_0_7_7) = all_39_0_13
% 3.46/1.75 |
% 3.46/1.75 | Instantiating formula (2) with all_39_0_13, all_0_6_6, all_0_8_8, all_0_7_7, all_0_9_9 and discharging atoms disjoint(all_0_6_6, all_0_7_7) = all_39_0_13, unordered_pair(all_0_9_9, all_0_8_8) = all_0_6_6, yields:
% 3.46/1.75 | (77) all_39_0_13 = 0 | ? [v0] : ? [v1] : (in(all_0_8_8, all_0_7_7) = v1 & in(all_0_9_9, all_0_7_7) = v0 & (v1 = 0 | v0 = 0))
% 3.46/1.75 |
% 3.46/1.75 +-Applying beta-rule and splitting (77), into two cases.
% 3.46/1.75 |-Branch one:
% 3.46/1.75 | (78) all_39_0_13 = 0
% 3.46/1.75 |
% 3.46/1.75 | Equations (78) can reduce 75 to:
% 3.46/1.75 | (43) $false
% 3.46/1.75 |
% 3.46/1.75 |-The branch is then unsatisfiable
% 3.46/1.75 |-Branch two:
% 3.46/1.75 | (75) ~ (all_39_0_13 = 0)
% 3.46/1.75 | (81) ? [v0] : ? [v1] : (in(all_0_8_8, all_0_7_7) = v1 & in(all_0_9_9, all_0_7_7) = v0 & (v1 = 0 | v0 = 0))
% 3.46/1.76 |
% 3.46/1.76 | Instantiating (81) with all_52_0_14, all_52_1_15 yields:
% 3.46/1.76 | (82) in(all_0_8_8, all_0_7_7) = all_52_0_14 & in(all_0_9_9, all_0_7_7) = all_52_1_15 & (all_52_0_14 = 0 | all_52_1_15 = 0)
% 3.46/1.76 |
% 3.46/1.76 | Applying alpha-rule on (82) yields:
% 3.46/1.76 | (83) in(all_0_8_8, all_0_7_7) = all_52_0_14
% 3.46/1.76 | (84) in(all_0_9_9, all_0_7_7) = all_52_1_15
% 3.46/1.76 | (85) all_52_0_14 = 0 | all_52_1_15 = 0
% 3.46/1.76 |
% 3.46/1.76 | Instantiating formula (6) with all_0_8_8, all_0_7_7, all_52_0_14, all_0_3_3 and discharging atoms in(all_0_8_8, all_0_7_7) = all_52_0_14, in(all_0_8_8, all_0_7_7) = all_0_3_3, yields:
% 3.46/1.76 | (86) all_52_0_14 = all_0_3_3
% 3.46/1.76 |
% 3.46/1.76 | Instantiating formula (6) with all_0_9_9, all_0_7_7, all_52_1_15, all_0_4_4 and discharging atoms in(all_0_9_9, all_0_7_7) = all_52_1_15, in(all_0_9_9, all_0_7_7) = all_0_4_4, yields:
% 3.46/1.76 | (87) all_52_1_15 = all_0_4_4
% 3.46/1.76 |
% 3.46/1.76 +-Applying beta-rule and splitting (85), into two cases.
% 3.46/1.76 |-Branch one:
% 3.46/1.76 | (88) all_52_0_14 = 0
% 3.46/1.76 |
% 3.46/1.76 | Combining equations (88,86) yields a new equation:
% 3.46/1.76 | (42) all_0_3_3 = 0
% 3.46/1.76 |
% 3.46/1.76 | Equations (42) can reduce 37 to:
% 3.46/1.76 | (43) $false
% 3.46/1.76 |
% 3.46/1.76 |-The branch is then unsatisfiable
% 3.46/1.76 |-Branch two:
% 3.46/1.76 | (91) ~ (all_52_0_14 = 0)
% 3.46/1.76 | (92) all_52_1_15 = 0
% 3.46/1.76 |
% 3.46/1.76 | Combining equations (87,92) yields a new equation:
% 3.46/1.76 | (93) all_0_4_4 = 0
% 3.46/1.76 |
% 3.46/1.76 | Simplifying 93 yields:
% 3.46/1.76 | (45) all_0_4_4 = 0
% 3.46/1.76 |
% 3.46/1.76 | Equations (45) can reduce 38 to:
% 3.46/1.76 | (43) $false
% 3.46/1.76 |
% 3.46/1.76 |-The branch is then unsatisfiable
% 3.46/1.76 % SZS output end Proof for theBenchmark
% 3.46/1.76
% 3.46/1.76 1158ms
%------------------------------------------------------------------------------