TSTP Solution File: SEU156+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU156+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 08:47:04 EDT 2022
% Result : Theorem 2.59s 1.37s
% Output : Proof 3.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU156+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n027.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 : Mon Jun 20 01:45:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.61 ____ _
% 0.55/0.61 ___ / __ \_____(_)___ ________ __________
% 0.55/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.61
% 0.55/0.61 A Theorem Prover for First-Order Logic
% 0.55/0.61 (ePrincess v.1.0)
% 0.55/0.61
% 0.55/0.61 (c) Philipp Rümmer, 2009-2015
% 0.55/0.61 (c) Peter Backeman, 2014-2015
% 0.55/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.61 Bug reports to peter@backeman.se
% 0.55/0.61
% 0.55/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.61
% 0.55/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.94 Prover 0: Preprocessing ...
% 1.78/1.13 Prover 0: Warning: ignoring some quantifiers
% 1.78/1.14 Prover 0: Constructing countermodel ...
% 2.59/1.36 Prover 0: proved (693ms)
% 2.59/1.37
% 2.59/1.37 No countermodel exists, formula is valid
% 2.59/1.37 % SZS status Theorem for theBenchmark
% 2.59/1.37
% 2.59/1.37 Generating proof ... Warning: ignoring some quantifiers
% 3.66/1.66 found it (size 84)
% 3.66/1.66
% 3.66/1.66 % SZS output start Proof for theBenchmark
% 3.66/1.66 Assumed formulas after preprocessing and simplification:
% 3.66/1.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v2, v3) = v4 & ordered_pair(v0, v1) = v4 & empty(v6) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v7 | v9 = v7 | ~ (unordered_pair(v9, v10) = v11) | ~ (unordered_pair(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (singleton(v7) = v10) | ~ (unordered_pair(v9, v10) = v11) | ~ (unordered_pair(v7, v8) = v9) | ordered_pair(v7, v8) = v11) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v7) = v10) | ~ (unordered_pair(v8, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (singleton(v8) = v10) | ~ (singleton(v7) = v9) | ~ subset(v9, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (singleton(v7) = v10) | ~ (unordered_pair(v8, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (ordered_pair(v10, v9) = v8) | ~ (ordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ empty(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ? [v10] : ? [v11] : (singleton(v7) = v11 & unordered_pair(v10, v11) = v9 & unordered_pair(v7, v8) = v10)) & ! [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] : ( ~ (singleton(v7) = v8) | unordered_pair(v7, v7) = v8) & ! [v7] : ! [v8] : ( ~ (unordered_pair(v7, v7) = v8) | singleton(v7) = v8) & ? [v7] : subset(v7, v7) & ( ~ (v3 = v1) | ~ (v2 = v0)))
% 3.83/1.70 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 3.83/1.70 | (1) ordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2 & ordered_pair(all_0_6_6, all_0_5_5) = all_0_2_2 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(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] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [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] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ? [v0] : subset(v0, v0) & ( ~ (all_0_3_3 = all_0_5_5) | ~ (all_0_4_4 = all_0_6_6))
% 3.83/1.71 |
% 3.83/1.71 | Applying alpha-rule on (1) yields:
% 3.83/1.71 | (2) ~ empty(all_0_1_1)
% 3.83/1.71 | (3) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 3.83/1.71 | (4) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 3.83/1.71 | (5) empty(all_0_0_0)
% 3.83/1.71 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 3.83/1.71 | (7) ordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2
% 3.83/1.71 | (8) ordered_pair(all_0_6_6, all_0_5_5) = all_0_2_2
% 3.83/1.71 | (9) ~ (all_0_3_3 = all_0_5_5) | ~ (all_0_4_4 = all_0_6_6)
% 3.83/1.71 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 3.83/1.71 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 3.83/1.71 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 3.83/1.71 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 3.83/1.71 | (14) ? [v0] : subset(v0, v0)
% 3.83/1.71 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 3.83/1.71 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 3.83/1.71 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 3.83/1.71 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 3.83/1.71 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 3.83/1.71 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 3.83/1.71 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3))
% 3.83/1.71 |
% 3.83/1.71 | Instantiating formula (18) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms ordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 3.83/1.71 | (22) ? [v0] : ? [v1] : (singleton(all_0_4_4) = v1 & unordered_pair(v0, v1) = all_0_2_2 & unordered_pair(all_0_4_4, all_0_3_3) = v0)
% 3.83/1.72 |
% 3.83/1.72 | Instantiating formula (18) with all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms ordered_pair(all_0_6_6, all_0_5_5) = all_0_2_2, yields:
% 3.83/1.72 | (23) ? [v0] : ? [v1] : (singleton(all_0_6_6) = v1 & unordered_pair(v0, v1) = all_0_2_2 & unordered_pair(all_0_6_6, all_0_5_5) = v0)
% 3.83/1.72 |
% 3.83/1.72 | Instantiating (23) with all_10_0_8, all_10_1_9 yields:
% 3.83/1.72 | (24) singleton(all_0_6_6) = all_10_0_8 & unordered_pair(all_10_1_9, all_10_0_8) = all_0_2_2 & unordered_pair(all_0_6_6, all_0_5_5) = all_10_1_9
% 3.83/1.72 |
% 3.83/1.72 | Applying alpha-rule on (24) yields:
% 3.83/1.72 | (25) singleton(all_0_6_6) = all_10_0_8
% 3.83/1.72 | (26) unordered_pair(all_10_1_9, all_10_0_8) = all_0_2_2
% 3.83/1.72 | (27) unordered_pair(all_0_6_6, all_0_5_5) = all_10_1_9
% 3.83/1.72 |
% 3.83/1.72 | Instantiating (22) with all_12_0_10, all_12_1_11 yields:
% 3.83/1.72 | (28) singleton(all_0_4_4) = all_12_0_10 & unordered_pair(all_12_1_11, all_12_0_10) = all_0_2_2 & unordered_pair(all_0_4_4, all_0_3_3) = all_12_1_11
% 3.83/1.72 |
% 3.83/1.72 | Applying alpha-rule on (28) yields:
% 3.83/1.72 | (29) singleton(all_0_4_4) = all_12_0_10
% 3.83/1.72 | (30) unordered_pair(all_12_1_11, all_12_0_10) = all_0_2_2
% 3.83/1.72 | (31) unordered_pair(all_0_4_4, all_0_3_3) = all_12_1_11
% 3.83/1.72 |
% 3.83/1.72 | Instantiating formula (4) with all_12_0_10, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_12_0_10, yields:
% 3.83/1.72 | (32) unordered_pair(all_0_4_4, all_0_4_4) = all_12_0_10
% 3.83/1.72 |
% 3.83/1.72 | Instantiating formula (12) with all_0_2_2, all_12_1_11, all_12_0_10 and discharging atoms unordered_pair(all_12_1_11, all_12_0_10) = all_0_2_2, yields:
% 3.83/1.72 | (33) unordered_pair(all_12_0_10, all_12_1_11) = all_0_2_2
% 3.83/1.72 |
% 3.83/1.72 | Instantiating formula (12) with all_0_2_2, all_10_1_9, all_10_0_8 and discharging atoms unordered_pair(all_10_1_9, all_10_0_8) = all_0_2_2, yields:
% 3.83/1.72 | (34) unordered_pair(all_10_0_8, all_10_1_9) = all_0_2_2
% 3.83/1.72 |
% 3.83/1.72 | Instantiating formula (12) with all_12_1_11, all_0_4_4, all_0_3_3 and discharging atoms unordered_pair(all_0_4_4, all_0_3_3) = all_12_1_11, yields:
% 3.83/1.72 | (35) unordered_pair(all_0_3_3, all_0_4_4) = all_12_1_11
% 3.83/1.72 |
% 3.83/1.72 | Instantiating formula (12) with all_10_1_9, all_0_6_6, all_0_5_5 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_10_1_9, yields:
% 3.83/1.72 | (36) unordered_pair(all_0_5_5, all_0_6_6) = all_10_1_9
% 3.83/1.72 |
% 3.83/1.72 | Instantiating formula (17) with all_0_2_2, all_12_1_11, all_12_0_10, all_10_0_8, all_10_1_9 and discharging atoms unordered_pair(all_12_0_10, all_12_1_11) = all_0_2_2, unordered_pair(all_10_1_9, all_10_0_8) = all_0_2_2, yields:
% 3.83/1.72 | (37) all_12_0_10 = all_10_1_9 | all_12_1_11 = all_10_1_9
% 3.83/1.72 |
% 3.83/1.72 | Instantiating formula (17) with all_0_2_2, all_10_1_9, all_10_0_8, all_12_0_10, all_12_1_11 and discharging atoms unordered_pair(all_12_1_11, all_12_0_10) = all_0_2_2, unordered_pair(all_10_0_8, all_10_1_9) = all_0_2_2, yields:
% 3.83/1.72 | (38) all_12_1_11 = all_10_0_8 | all_12_1_11 = all_10_1_9
% 3.83/1.72 |
% 3.83/1.72 | Instantiating formula (17) with all_0_2_2, all_12_1_11, all_12_0_10, all_10_1_9, all_10_0_8 and discharging atoms unordered_pair(all_12_0_10, all_12_1_11) = all_0_2_2, unordered_pair(all_10_0_8, all_10_1_9) = all_0_2_2, yields:
% 3.83/1.72 | (39) all_12_0_10 = all_10_0_8 | all_12_1_11 = all_10_0_8
% 3.83/1.72 |
% 3.83/1.72 +-Applying beta-rule and splitting (9), into two cases.
% 3.83/1.72 |-Branch one:
% 3.83/1.72 | (40) ~ (all_0_3_3 = all_0_5_5)
% 3.83/1.72 |
% 3.83/1.72 +-Applying beta-rule and splitting (38), into two cases.
% 3.83/1.72 |-Branch one:
% 3.83/1.72 | (41) all_12_1_11 = all_10_0_8
% 3.83/1.72 |
% 3.83/1.72 | From (41) and (35) follows:
% 3.83/1.72 | (42) unordered_pair(all_0_3_3, all_0_4_4) = all_10_0_8
% 3.83/1.72 |
% 3.83/1.72 | From (41) and (31) follows:
% 3.83/1.72 | (43) unordered_pair(all_0_4_4, all_0_3_3) = all_10_0_8
% 3.83/1.72 |
% 3.83/1.72 | Instantiating formula (19) with all_10_0_8, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_10_0_8, unordered_pair(all_0_3_3, all_0_4_4) = all_10_0_8, yields:
% 3.83/1.72 | (44) all_0_3_3 = all_0_6_6
% 3.83/1.72 |
% 3.83/1.72 | Instantiating formula (10) with all_10_0_8, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_10_0_8, unordered_pair(all_0_4_4, all_0_3_3) = all_10_0_8, yields:
% 3.83/1.72 | (45) all_0_3_3 = all_0_4_4
% 3.83/1.72 |
% 3.83/1.72 | Combining equations (45,44) yields a new equation:
% 3.83/1.72 | (46) all_0_4_4 = all_0_6_6
% 3.83/1.72 |
% 3.83/1.72 | Simplifying 46 yields:
% 3.83/1.72 | (47) all_0_4_4 = all_0_6_6
% 3.83/1.72 |
% 3.83/1.73 | Equations (44) can reduce 40 to:
% 3.83/1.73 | (48) ~ (all_0_5_5 = all_0_6_6)
% 3.83/1.73 |
% 3.83/1.73 | Simplifying 48 yields:
% 3.83/1.73 | (49) ~ (all_0_5_5 = all_0_6_6)
% 3.83/1.73 |
% 3.83/1.73 | From (47)(44) and (43) follows:
% 3.83/1.73 | (50) unordered_pair(all_0_6_6, all_0_6_6) = all_10_0_8
% 3.83/1.73 |
% 3.83/1.73 | From (47)(47) and (32) follows:
% 3.83/1.73 | (51) unordered_pair(all_0_6_6, all_0_6_6) = all_12_0_10
% 3.83/1.73 |
% 3.83/1.73 | Instantiating formula (20) with all_0_6_6, all_0_6_6, all_12_0_10, all_10_0_8 and discharging atoms unordered_pair(all_0_6_6, all_0_6_6) = all_12_0_10, unordered_pair(all_0_6_6, all_0_6_6) = all_10_0_8, yields:
% 3.83/1.73 | (52) all_12_0_10 = all_10_0_8
% 3.83/1.73 |
% 3.83/1.73 | From (52) and (51) follows:
% 3.83/1.73 | (50) unordered_pair(all_0_6_6, all_0_6_6) = all_10_0_8
% 3.83/1.73 |
% 3.83/1.73 +-Applying beta-rule and splitting (37), into two cases.
% 3.83/1.73 |-Branch one:
% 3.83/1.73 | (54) all_12_0_10 = all_10_1_9
% 3.83/1.73 |
% 3.83/1.73 | Combining equations (54,52) yields a new equation:
% 3.83/1.73 | (55) all_10_0_8 = all_10_1_9
% 3.83/1.73 |
% 3.83/1.73 | From (55) and (50) follows:
% 3.83/1.73 | (56) unordered_pair(all_0_6_6, all_0_6_6) = all_10_1_9
% 3.83/1.73 |
% 3.83/1.73 | Instantiating formula (17) with all_10_1_9, all_0_6_6, all_0_6_6, all_0_6_6, all_0_5_5 and discharging atoms unordered_pair(all_0_5_5, all_0_6_6) = all_10_1_9, unordered_pair(all_0_6_6, all_0_6_6) = all_10_1_9, yields:
% 3.83/1.73 | (57) all_0_5_5 = all_0_6_6
% 3.83/1.73 |
% 3.83/1.73 | Equations (57) can reduce 49 to:
% 3.83/1.73 | (58) $false
% 3.83/1.73 |
% 3.83/1.73 |-The branch is then unsatisfiable
% 3.83/1.73 |-Branch two:
% 3.83/1.73 | (59) ~ (all_12_0_10 = all_10_1_9)
% 3.83/1.73 | (60) all_12_1_11 = all_10_1_9
% 3.83/1.73 |
% 3.83/1.73 | Combining equations (41,60) yields a new equation:
% 3.83/1.73 | (61) all_10_0_8 = all_10_1_9
% 3.83/1.73 |
% 3.83/1.73 | Simplifying 61 yields:
% 3.83/1.73 | (55) all_10_0_8 = all_10_1_9
% 3.83/1.73 |
% 3.83/1.73 | Combining equations (55,52) yields a new equation:
% 3.83/1.73 | (54) all_12_0_10 = all_10_1_9
% 3.83/1.73 |
% 3.83/1.73 | Equations (54) can reduce 59 to:
% 3.83/1.73 | (58) $false
% 3.83/1.73 |
% 3.83/1.73 |-The branch is then unsatisfiable
% 3.83/1.73 |-Branch two:
% 3.83/1.73 | (65) ~ (all_12_1_11 = all_10_0_8)
% 3.83/1.73 | (60) all_12_1_11 = all_10_1_9
% 3.83/1.73 |
% 3.83/1.73 | Equations (60) can reduce 65 to:
% 3.83/1.73 | (67) ~ (all_10_0_8 = all_10_1_9)
% 3.83/1.73 |
% 3.83/1.73 | Simplifying 67 yields:
% 3.83/1.73 | (68) ~ (all_10_0_8 = all_10_1_9)
% 3.83/1.73 |
% 3.83/1.73 | From (60) and (35) follows:
% 3.83/1.73 | (69) unordered_pair(all_0_3_3, all_0_4_4) = all_10_1_9
% 3.83/1.73 |
% 3.83/1.73 | From (60) and (31) follows:
% 3.83/1.73 | (70) unordered_pair(all_0_4_4, all_0_3_3) = all_10_1_9
% 3.83/1.73 |
% 3.83/1.73 +-Applying beta-rule and splitting (39), into two cases.
% 3.83/1.73 |-Branch one:
% 3.83/1.73 | (52) all_12_0_10 = all_10_0_8
% 3.83/1.73 |
% 3.83/1.73 | From (52) and (32) follows:
% 3.83/1.73 | (72) unordered_pair(all_0_4_4, all_0_4_4) = all_10_0_8
% 3.83/1.73 |
% 3.83/1.73 | Instantiating formula (17) with all_10_1_9, all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3 and discharging atoms unordered_pair(all_0_3_3, all_0_4_4) = all_10_1_9, unordered_pair(all_0_6_6, all_0_5_5) = all_10_1_9, yields:
% 3.83/1.73 | (73) all_0_3_3 = all_0_5_5 | all_0_3_3 = all_0_6_6
% 3.83/1.73 |
% 3.83/1.73 | Instantiating formula (17) with all_10_1_9, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms unordered_pair(all_0_4_4, all_0_3_3) = all_10_1_9, unordered_pair(all_0_5_5, all_0_6_6) = all_10_1_9, yields:
% 3.83/1.73 | (74) all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5
% 3.83/1.73 |
% 3.83/1.73 | Instantiating formula (19) with all_10_0_8, all_0_4_4, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_10_0_8, unordered_pair(all_0_4_4, all_0_4_4) = all_10_0_8, yields:
% 3.83/1.73 | (47) all_0_4_4 = all_0_6_6
% 3.83/1.73 |
% 3.83/1.73 +-Applying beta-rule and splitting (73), into two cases.
% 3.83/1.73 |-Branch one:
% 3.83/1.73 | (76) all_0_3_3 = all_0_5_5
% 3.83/1.73 |
% 3.83/1.73 | Equations (76) can reduce 40 to:
% 3.83/1.73 | (58) $false
% 3.83/1.73 |
% 3.83/1.73 |-The branch is then unsatisfiable
% 3.83/1.73 |-Branch two:
% 3.83/1.73 | (40) ~ (all_0_3_3 = all_0_5_5)
% 3.83/1.73 | (44) all_0_3_3 = all_0_6_6
% 3.83/1.73 |
% 3.83/1.73 | Equations (44) can reduce 40 to:
% 3.83/1.73 | (48) ~ (all_0_5_5 = all_0_6_6)
% 3.83/1.74 |
% 3.83/1.74 | Simplifying 48 yields:
% 3.83/1.74 | (49) ~ (all_0_5_5 = all_0_6_6)
% 3.83/1.74 |
% 3.83/1.74 +-Applying beta-rule and splitting (74), into two cases.
% 3.83/1.74 |-Branch one:
% 3.83/1.74 | (76) all_0_3_3 = all_0_5_5
% 3.83/1.74 |
% 3.83/1.74 | Combining equations (44,76) yields a new equation:
% 3.83/1.74 | (57) all_0_5_5 = all_0_6_6
% 3.83/1.74 |
% 3.83/1.74 | Equations (57) can reduce 49 to:
% 3.83/1.74 | (58) $false
% 3.83/1.74 |
% 3.83/1.74 |-The branch is then unsatisfiable
% 3.83/1.74 |-Branch two:
% 3.83/1.74 | (40) ~ (all_0_3_3 = all_0_5_5)
% 3.83/1.74 | (86) all_0_4_4 = all_0_5_5
% 3.83/1.74 |
% 3.83/1.74 | Combining equations (86,47) yields a new equation:
% 3.83/1.74 | (87) all_0_5_5 = all_0_6_6
% 3.83/1.74 |
% 3.83/1.74 | Simplifying 87 yields:
% 3.83/1.74 | (57) all_0_5_5 = all_0_6_6
% 3.83/1.74 |
% 3.83/1.74 | Equations (57) can reduce 49 to:
% 3.83/1.74 | (58) $false
% 3.83/1.74 |
% 3.83/1.74 |-The branch is then unsatisfiable
% 3.83/1.74 |-Branch two:
% 3.83/1.74 | (90) ~ (all_12_0_10 = all_10_0_8)
% 3.83/1.74 | (41) all_12_1_11 = all_10_0_8
% 3.83/1.74 |
% 3.83/1.74 | Combining equations (41,60) yields a new equation:
% 3.83/1.74 | (61) all_10_0_8 = all_10_1_9
% 3.83/1.74 |
% 3.83/1.74 | Simplifying 61 yields:
% 3.83/1.74 | (55) all_10_0_8 = all_10_1_9
% 3.83/1.74 |
% 3.83/1.74 | Equations (55) can reduce 68 to:
% 3.83/1.74 | (58) $false
% 3.83/1.74 |
% 3.83/1.74 |-The branch is then unsatisfiable
% 3.83/1.74 |-Branch two:
% 3.83/1.74 | (76) all_0_3_3 = all_0_5_5
% 3.83/1.74 | (96) ~ (all_0_4_4 = all_0_6_6)
% 3.83/1.74 |
% 3.83/1.74 | From (76) and (31) follows:
% 3.83/1.74 | (97) unordered_pair(all_0_4_4, all_0_5_5) = all_12_1_11
% 3.83/1.74 |
% 3.83/1.74 +-Applying beta-rule and splitting (38), into two cases.
% 3.83/1.74 |-Branch one:
% 3.83/1.74 | (41) all_12_1_11 = all_10_0_8
% 3.83/1.74 |
% 3.83/1.74 | From (41) and (97) follows:
% 3.83/1.74 | (99) unordered_pair(all_0_4_4, all_0_5_5) = all_10_0_8
% 3.83/1.74 |
% 3.83/1.74 | Instantiating formula (19) with all_10_0_8, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_10_0_8, unordered_pair(all_0_4_4, all_0_5_5) = all_10_0_8, yields:
% 3.83/1.74 | (47) all_0_4_4 = all_0_6_6
% 3.83/1.74 |
% 3.83/1.74 | Equations (47) can reduce 96 to:
% 3.83/1.74 | (58) $false
% 3.83/1.74 |
% 3.83/1.74 |-The branch is then unsatisfiable
% 3.83/1.74 |-Branch two:
% 3.83/1.74 | (65) ~ (all_12_1_11 = all_10_0_8)
% 3.83/1.74 | (60) all_12_1_11 = all_10_1_9
% 3.83/1.74 |
% 3.83/1.74 | Equations (60) can reduce 65 to:
% 3.83/1.74 | (67) ~ (all_10_0_8 = all_10_1_9)
% 3.83/1.74 |
% 3.83/1.74 | Simplifying 67 yields:
% 3.83/1.74 | (68) ~ (all_10_0_8 = all_10_1_9)
% 3.83/1.74 |
% 3.83/1.74 +-Applying beta-rule and splitting (39), into two cases.
% 3.83/1.74 |-Branch one:
% 3.83/1.74 | (52) all_12_0_10 = all_10_0_8
% 3.83/1.74 |
% 3.83/1.74 | From (52) and (32) follows:
% 3.83/1.74 | (72) unordered_pair(all_0_4_4, all_0_4_4) = all_10_0_8
% 3.83/1.74 |
% 3.83/1.74 | Instantiating formula (19) with all_10_0_8, all_0_4_4, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_10_0_8, unordered_pair(all_0_4_4, all_0_4_4) = all_10_0_8, yields:
% 3.83/1.74 | (47) all_0_4_4 = all_0_6_6
% 3.83/1.74 |
% 3.83/1.74 | Equations (47) can reduce 96 to:
% 3.83/1.74 | (58) $false
% 3.83/1.74 |
% 3.83/1.74 |-The branch is then unsatisfiable
% 3.83/1.74 |-Branch two:
% 3.83/1.74 | (90) ~ (all_12_0_10 = all_10_0_8)
% 3.83/1.74 | (41) all_12_1_11 = all_10_0_8
% 3.83/1.74 |
% 3.83/1.74 | Combining equations (41,60) yields a new equation:
% 3.83/1.74 | (61) all_10_0_8 = all_10_1_9
% 3.83/1.74 |
% 3.83/1.74 | Simplifying 61 yields:
% 3.83/1.74 | (55) all_10_0_8 = all_10_1_9
% 3.83/1.74 |
% 3.83/1.74 | Equations (55) can reduce 68 to:
% 3.83/1.74 | (58) $false
% 3.83/1.74 |
% 3.83/1.74 |-The branch is then unsatisfiable
% 3.83/1.74 % SZS output end Proof for theBenchmark
% 3.83/1.74
% 3.83/1.74 1118ms
%------------------------------------------------------------------------------