TSTP Solution File: SET974+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 00:23:32 EDT 2022
% Result : Theorem 3.60s 1.61s
% Output : Proof 5.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 15:16:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.59 ____ _
% 0.20/0.59 ___ / __ \_____(_)___ ________ __________
% 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic
% 0.62/0.59 (ePrincess v.1.0)
% 0.62/0.59
% 0.62/0.59 (c) Philipp Rümmer, 2009-2015
% 0.62/0.59 (c) Peter Backeman, 2014-2015
% 0.62/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.59 Bug reports to peter@backeman.se
% 0.62/0.59
% 0.62/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.59
% 0.62/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.43/0.92 Prover 0: Preprocessing ...
% 1.85/1.11 Prover 0: Warning: ignoring some quantifiers
% 1.85/1.13 Prover 0: Constructing countermodel ...
% 2.52/1.32 Prover 0: gave up
% 2.52/1.32 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.52/1.35 Prover 1: Preprocessing ...
% 2.77/1.43 Prover 1: Constructing countermodel ...
% 3.33/1.61 Prover 1: proved (286ms)
% 3.60/1.61
% 3.60/1.61 No countermodel exists, formula is valid
% 3.60/1.61 % SZS status Theorem for theBenchmark
% 3.60/1.61
% 3.60/1.61 Generating proof ... found it (size 64)
% 4.90/1.92
% 4.90/1.92 % SZS output start Proof for theBenchmark
% 4.90/1.92 Assumed formulas after preprocessing and simplification:
% 4.90/1.92 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v10 = 0) & ~ (v8 = 0) & cartesian_product2(v1, v3) = v7 & cartesian_product2(v0, v2) = v6 & disjoint(v6, v7) = v8 & disjoint(v2, v3) = v5 & disjoint(v0, v1) = v4 & empty(v11) = 0 & empty(v9) = v10 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v15, v16) = v18) | ~ (cartesian_product2(v13, v14) = v17) | ~ (set_intersection2(v17, v18) = v19) | ~ (in(v12, v19) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (ordered_pair(v22, v23) = v12 & set_intersection2(v14, v16) = v21 & set_intersection2(v13, v15) = v20 & in(v23, v21) = 0 & in(v22, v20) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (singleton(v12) = v15) | ~ (unordered_pair(v14, v15) = v16) | ~ (unordered_pair(v12, v13) = v14) | ordered_pair(v12, v13) = v16) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (cartesian_product2(v15, v14) = v13) | ~ (cartesian_product2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (disjoint(v15, v14) = v13) | ~ (disjoint(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (ordered_pair(v15, v14) = v13) | ~ (ordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (set_intersection2(v15, v14) = v13) | ~ (set_intersection2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (unordered_pair(v15, v14) = v13) | ~ (unordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (in(v15, v14) = v13) | ~ (in(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (disjoint(v12, v13) = v14) | ? [v15] : ? [v16] : (set_intersection2(v12, v13) = v15 & in(v16, v15) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (empty(v14) = v13) | ~ (empty(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v14) = v13) | ~ (singleton(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | set_intersection2(v13, v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | unordered_pair(v13, v12) = v14) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_intersection2(v12, v12) = v13)) & ! [v12] : ! [v13] : ( ~ (disjoint(v12, v13) = 0) | disjoint(v13, v12) = 0) & ! [v12] : ! [v13] : ( ~ (disjoint(v12, v13) = 0) | ? [v14] : (set_intersection2(v12, v13) = v14 & ! [v15] : ~ (in(v15, v14) = 0))) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & (v5 = 0 | v4 = 0))
% 4.90/1.95 | 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, all_0_10_10, all_0_11_11 yields:
% 4.90/1.95 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & cartesian_product2(all_0_10_10, all_0_8_8) = all_0_4_4 & cartesian_product2(all_0_11_11, all_0_9_9) = all_0_5_5 & disjoint(all_0_5_5, all_0_4_4) = all_0_3_3 & disjoint(all_0_9_9, all_0_8_8) = all_0_6_6 & disjoint(all_0_11_11, all_0_10_10) = all_0_7_7 & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (cartesian_product2(v3, v4) = v6) | ~ (cartesian_product2(v1, v2) = v5) | ~ (set_intersection2(v5, v6) = v7) | ~ (in(v0, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (ordered_pair(v10, v11) = v0 & set_intersection2(v2, v4) = v9 & set_intersection2(v1, v3) = v8 & in(v11, v9) = 0 & in(v10, v8) = 0)) & ! [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] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(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] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & (all_0_6_6 = 0 | all_0_7_7 = 0)
% 4.90/1.96 |
% 4.90/1.96 | Applying alpha-rule on (1) yields:
% 4.90/1.96 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 4.90/1.96 | (3) empty(all_0_0_0) = 0
% 4.90/1.96 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 4.90/1.96 | (5) ~ (all_0_1_1 = 0)
% 4.90/1.96 | (6) ~ (all_0_3_3 = 0)
% 4.90/1.96 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 4.90/1.96 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 4.90/1.96 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 4.90/1.96 | (10) disjoint(all_0_9_9, all_0_8_8) = all_0_6_6
% 4.90/1.96 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 4.90/1.97 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 4.90/1.97 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.90/1.97 | (14) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 4.90/1.97 | (15) disjoint(all_0_5_5, all_0_4_4) = all_0_3_3
% 4.90/1.97 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 4.90/1.97 | (17) cartesian_product2(all_0_10_10, all_0_8_8) = all_0_4_4
% 4.90/1.97 | (18) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 4.90/1.97 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (cartesian_product2(v3, v4) = v6) | ~ (cartesian_product2(v1, v2) = v5) | ~ (set_intersection2(v5, v6) = v7) | ~ (in(v0, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (ordered_pair(v10, v11) = v0 & set_intersection2(v2, v4) = v9 & set_intersection2(v1, v3) = v8 & in(v11, v9) = 0 & in(v10, v8) = 0))
% 4.90/1.97 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 4.90/1.97 | (21) empty(all_0_2_2) = all_0_1_1
% 4.90/1.97 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 4.90/1.97 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 4.90/1.97 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 4.90/1.97 | (25) cartesian_product2(all_0_11_11, all_0_9_9) = all_0_5_5
% 4.90/1.97 | (26) all_0_6_6 = 0 | all_0_7_7 = 0
% 4.90/1.97 | (27) disjoint(all_0_11_11, all_0_10_10) = all_0_7_7
% 4.90/1.97 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 4.90/1.97 | (29) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (20) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms disjoint(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 4.90/1.97 | (30) all_0_3_3 = 0 | ? [v0] : ? [v1] : (set_intersection2(all_0_5_5, all_0_4_4) = v0 & in(v1, v0) = 0)
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (29) with all_0_8_8, all_0_9_9 yields:
% 4.90/1.97 | (31) ~ (disjoint(all_0_9_9, all_0_8_8) = 0) | disjoint(all_0_8_8, all_0_9_9) = 0
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (18) with all_0_8_8, all_0_9_9 yields:
% 4.90/1.97 | (32) ~ (disjoint(all_0_9_9, all_0_8_8) = 0) | ? [v0] : (set_intersection2(all_0_9_9, all_0_8_8) = v0 & ! [v1] : ~ (in(v1, v0) = 0))
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (29) with all_0_10_10, all_0_11_11 yields:
% 4.90/1.97 | (33) ~ (disjoint(all_0_11_11, all_0_10_10) = 0) | disjoint(all_0_10_10, all_0_11_11) = 0
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (18) with all_0_10_10, all_0_11_11 yields:
% 4.90/1.97 | (34) ~ (disjoint(all_0_11_11, all_0_10_10) = 0) | ? [v0] : (set_intersection2(all_0_11_11, all_0_10_10) = v0 & ! [v1] : ~ (in(v1, v0) = 0))
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (33), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (35) ~ (disjoint(all_0_11_11, all_0_10_10) = 0)
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (30), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (36) all_0_3_3 = 0
% 4.90/1.98 |
% 4.90/1.98 | Equations (36) can reduce 6 to:
% 4.90/1.98 | (37) $false
% 4.90/1.98 |
% 4.90/1.98 |-The branch is then unsatisfiable
% 4.90/1.98 |-Branch two:
% 4.90/1.98 | (6) ~ (all_0_3_3 = 0)
% 4.90/1.98 | (39) ? [v0] : ? [v1] : (set_intersection2(all_0_5_5, all_0_4_4) = v0 & in(v1, v0) = 0)
% 4.90/1.98 |
% 4.90/1.98 | Instantiating (39) with all_14_0_12, all_14_1_13 yields:
% 4.90/1.98 | (40) set_intersection2(all_0_5_5, all_0_4_4) = all_14_1_13 & in(all_14_0_12, all_14_1_13) = 0
% 4.90/1.98 |
% 4.90/1.98 | Applying alpha-rule on (40) yields:
% 4.90/1.98 | (41) set_intersection2(all_0_5_5, all_0_4_4) = all_14_1_13
% 4.90/1.98 | (42) in(all_14_0_12, all_14_1_13) = 0
% 4.90/1.98 |
% 4.90/1.98 | Using (27) and (35) yields:
% 4.90/1.98 | (43) ~ (all_0_7_7 = 0)
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (26), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (44) all_0_6_6 = 0
% 4.90/1.98 |
% 4.90/1.98 | From (44) and (10) follows:
% 4.90/1.98 | (45) disjoint(all_0_9_9, all_0_8_8) = 0
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (31), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (46) ~ (disjoint(all_0_9_9, all_0_8_8) = 0)
% 4.90/1.98 |
% 4.90/1.98 | Using (45) and (46) yields:
% 4.90/1.98 | (47) $false
% 4.90/1.98 |
% 4.90/1.98 |-The branch is then unsatisfiable
% 4.90/1.98 |-Branch two:
% 4.90/1.98 | (45) disjoint(all_0_9_9, all_0_8_8) = 0
% 4.90/1.98 | (49) disjoint(all_0_8_8, all_0_9_9) = 0
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (32), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (46) ~ (disjoint(all_0_9_9, all_0_8_8) = 0)
% 4.90/1.98 |
% 4.90/1.98 | Using (45) and (46) yields:
% 4.90/1.98 | (47) $false
% 4.90/1.98 |
% 4.90/1.98 |-The branch is then unsatisfiable
% 4.90/1.98 |-Branch two:
% 4.90/1.98 | (45) disjoint(all_0_9_9, all_0_8_8) = 0
% 4.90/1.98 | (53) ? [v0] : (set_intersection2(all_0_9_9, all_0_8_8) = v0 & ! [v1] : ~ (in(v1, v0) = 0))
% 4.90/1.98 |
% 4.90/1.98 | Instantiating (53) with all_37_0_16 yields:
% 4.90/1.98 | (54) set_intersection2(all_0_9_9, all_0_8_8) = all_37_0_16 & ! [v0] : ~ (in(v0, all_37_0_16) = 0)
% 4.90/1.98 |
% 4.90/1.98 | Applying alpha-rule on (54) yields:
% 4.90/1.98 | (55) set_intersection2(all_0_9_9, all_0_8_8) = all_37_0_16
% 4.90/1.98 | (56) ! [v0] : ~ (in(v0, all_37_0_16) = 0)
% 4.90/1.98 |
% 4.90/1.98 | Instantiating formula (18) with all_0_9_9, all_0_8_8 and discharging atoms disjoint(all_0_8_8, all_0_9_9) = 0, yields:
% 4.90/1.98 | (57) ? [v0] : (set_intersection2(all_0_8_8, all_0_9_9) = v0 & ! [v1] : ~ (in(v1, v0) = 0))
% 4.90/1.98 |
% 4.90/1.98 | Instantiating formula (8) with all_37_0_16, all_0_8_8, all_0_9_9 and discharging atoms set_intersection2(all_0_9_9, all_0_8_8) = all_37_0_16, yields:
% 4.90/1.98 | (58) set_intersection2(all_0_8_8, all_0_9_9) = all_37_0_16
% 4.90/1.98 |
% 4.90/1.98 | Instantiating formula (19) with all_14_1_13, all_0_4_4, all_0_5_5, all_0_8_8, all_0_10_10, all_0_9_9, all_0_11_11, all_14_0_12 and discharging atoms cartesian_product2(all_0_10_10, all_0_8_8) = all_0_4_4, cartesian_product2(all_0_11_11, all_0_9_9) = all_0_5_5, set_intersection2(all_0_5_5, all_0_4_4) = all_14_1_13, in(all_14_0_12, all_14_1_13) = 0, yields:
% 4.90/1.98 | (59) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v2, v3) = all_14_0_12 & set_intersection2(all_0_9_9, all_0_8_8) = v1 & set_intersection2(all_0_11_11, all_0_10_10) = v0 & in(v3, v1) = 0 & in(v2, v0) = 0)
% 4.90/1.98 |
% 4.90/1.98 | Instantiating (57) with all_55_0_17 yields:
% 4.90/1.98 | (60) set_intersection2(all_0_8_8, all_0_9_9) = all_55_0_17 & ! [v0] : ~ (in(v0, all_55_0_17) = 0)
% 4.90/1.98 |
% 4.90/1.98 | Applying alpha-rule on (60) yields:
% 4.90/1.98 | (61) set_intersection2(all_0_8_8, all_0_9_9) = all_55_0_17
% 4.90/1.99 | (62) ! [v0] : ~ (in(v0, all_55_0_17) = 0)
% 4.90/1.99 |
% 4.90/1.99 | Instantiating (59) with all_61_0_19, all_61_1_20, all_61_2_21, all_61_3_22 yields:
% 4.90/1.99 | (63) ordered_pair(all_61_1_20, all_61_0_19) = all_14_0_12 & set_intersection2(all_0_9_9, all_0_8_8) = all_61_2_21 & set_intersection2(all_0_11_11, all_0_10_10) = all_61_3_22 & in(all_61_0_19, all_61_2_21) = 0 & in(all_61_1_20, all_61_3_22) = 0
% 4.90/1.99 |
% 4.90/1.99 | Applying alpha-rule on (63) yields:
% 4.90/1.99 | (64) ordered_pair(all_61_1_20, all_61_0_19) = all_14_0_12
% 4.90/1.99 | (65) set_intersection2(all_0_11_11, all_0_10_10) = all_61_3_22
% 4.90/1.99 | (66) in(all_61_1_20, all_61_3_22) = 0
% 5.23/1.99 | (67) set_intersection2(all_0_9_9, all_0_8_8) = all_61_2_21
% 5.23/1.99 | (68) in(all_61_0_19, all_61_2_21) = 0
% 5.23/1.99 |
% 5.23/1.99 | Instantiating formula (24) with all_0_8_8, all_0_9_9, all_37_0_16, all_55_0_17 and discharging atoms set_intersection2(all_0_8_8, all_0_9_9) = all_55_0_17, set_intersection2(all_0_8_8, all_0_9_9) = all_37_0_16, yields:
% 5.23/1.99 | (69) all_55_0_17 = all_37_0_16
% 5.23/1.99 |
% 5.23/1.99 | Instantiating formula (24) with all_0_9_9, all_0_8_8, all_61_2_21, all_37_0_16 and discharging atoms set_intersection2(all_0_9_9, all_0_8_8) = all_61_2_21, set_intersection2(all_0_9_9, all_0_8_8) = all_37_0_16, yields:
% 5.23/1.99 | (70) all_61_2_21 = all_37_0_16
% 5.23/1.99 |
% 5.23/1.99 | Instantiating formula (62) with all_61_0_19 yields:
% 5.23/1.99 | (71) ~ (in(all_61_0_19, all_55_0_17) = 0)
% 5.23/1.99 |
% 5.23/1.99 | From (70) and (68) follows:
% 5.23/1.99 | (72) in(all_61_0_19, all_37_0_16) = 0
% 5.23/1.99 |
% 5.23/1.99 | From (69) and (71) follows:
% 5.23/1.99 | (73) ~ (in(all_61_0_19, all_37_0_16) = 0)
% 5.23/1.99 |
% 5.23/1.99 | Using (72) and (73) yields:
% 5.23/1.99 | (47) $false
% 5.23/1.99 |
% 5.23/1.99 |-The branch is then unsatisfiable
% 5.23/1.99 |-Branch two:
% 5.23/1.99 | (75) ~ (all_0_6_6 = 0)
% 5.23/1.99 | (76) all_0_7_7 = 0
% 5.23/1.99 |
% 5.23/1.99 | Equations (76) can reduce 43 to:
% 5.23/1.99 | (37) $false
% 5.23/1.99 |
% 5.23/1.99 |-The branch is then unsatisfiable
% 5.23/1.99 |-Branch two:
% 5.23/1.99 | (78) disjoint(all_0_11_11, all_0_10_10) = 0
% 5.23/1.99 | (79) disjoint(all_0_10_10, all_0_11_11) = 0
% 5.23/1.99 |
% 5.23/1.99 +-Applying beta-rule and splitting (34), into two cases.
% 5.23/1.99 |-Branch one:
% 5.23/1.99 | (35) ~ (disjoint(all_0_11_11, all_0_10_10) = 0)
% 5.23/1.99 |
% 5.23/1.99 | Using (78) and (35) yields:
% 5.23/1.99 | (47) $false
% 5.23/1.99 |
% 5.23/1.99 |-The branch is then unsatisfiable
% 5.23/1.99 |-Branch two:
% 5.23/1.99 | (78) disjoint(all_0_11_11, all_0_10_10) = 0
% 5.23/1.99 | (83) ? [v0] : (set_intersection2(all_0_11_11, all_0_10_10) = v0 & ! [v1] : ~ (in(v1, v0) = 0))
% 5.23/1.99 |
% 5.23/1.99 | Instantiating (83) with all_14_0_24 yields:
% 5.23/1.99 | (84) set_intersection2(all_0_11_11, all_0_10_10) = all_14_0_24 & ! [v0] : ~ (in(v0, all_14_0_24) = 0)
% 5.23/1.99 |
% 5.23/1.99 | Applying alpha-rule on (84) yields:
% 5.23/1.99 | (85) set_intersection2(all_0_11_11, all_0_10_10) = all_14_0_24
% 5.23/1.99 | (86) ! [v0] : ~ (in(v0, all_14_0_24) = 0)
% 5.23/1.99 |
% 5.23/1.99 +-Applying beta-rule and splitting (30), into two cases.
% 5.23/1.99 |-Branch one:
% 5.23/1.99 | (36) all_0_3_3 = 0
% 5.23/1.99 |
% 5.23/1.99 | Equations (36) can reduce 6 to:
% 5.23/1.99 | (37) $false
% 5.23/1.99 |
% 5.23/1.99 |-The branch is then unsatisfiable
% 5.23/1.99 |-Branch two:
% 5.23/1.99 | (6) ~ (all_0_3_3 = 0)
% 5.23/1.99 | (39) ? [v0] : ? [v1] : (set_intersection2(all_0_5_5, all_0_4_4) = v0 & in(v1, v0) = 0)
% 5.23/1.99 |
% 5.23/1.99 | Instantiating (39) with all_20_0_25, all_20_1_26 yields:
% 5.23/1.99 | (91) set_intersection2(all_0_5_5, all_0_4_4) = all_20_1_26 & in(all_20_0_25, all_20_1_26) = 0
% 5.23/1.99 |
% 5.23/1.99 | Applying alpha-rule on (91) yields:
% 5.23/1.99 | (92) set_intersection2(all_0_5_5, all_0_4_4) = all_20_1_26
% 5.23/1.99 | (93) in(all_20_0_25, all_20_1_26) = 0
% 5.23/1.99 |
% 5.23/1.99 | Instantiating formula (18) with all_0_11_11, all_0_10_10 and discharging atoms disjoint(all_0_10_10, all_0_11_11) = 0, yields:
% 5.23/1.99 | (94) ? [v0] : (set_intersection2(all_0_10_10, all_0_11_11) = v0 & ! [v1] : ~ (in(v1, v0) = 0))
% 5.23/2.00 |
% 5.23/2.00 | Instantiating formula (8) with all_14_0_24, all_0_10_10, all_0_11_11 and discharging atoms set_intersection2(all_0_11_11, all_0_10_10) = all_14_0_24, yields:
% 5.23/2.00 | (95) set_intersection2(all_0_10_10, all_0_11_11) = all_14_0_24
% 5.23/2.00 |
% 5.23/2.00 | Instantiating formula (19) with all_20_1_26, all_0_4_4, all_0_5_5, all_0_8_8, all_0_10_10, all_0_9_9, all_0_11_11, all_20_0_25 and discharging atoms cartesian_product2(all_0_10_10, all_0_8_8) = all_0_4_4, cartesian_product2(all_0_11_11, all_0_9_9) = all_0_5_5, set_intersection2(all_0_5_5, all_0_4_4) = all_20_1_26, in(all_20_0_25, all_20_1_26) = 0, yields:
% 5.23/2.00 | (96) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v2, v3) = all_20_0_25 & set_intersection2(all_0_9_9, all_0_8_8) = v1 & set_intersection2(all_0_11_11, all_0_10_10) = v0 & in(v3, v1) = 0 & in(v2, v0) = 0)
% 5.23/2.00 |
% 5.23/2.00 | Instantiating (94) with all_36_0_27 yields:
% 5.23/2.00 | (97) set_intersection2(all_0_10_10, all_0_11_11) = all_36_0_27 & ! [v0] : ~ (in(v0, all_36_0_27) = 0)
% 5.23/2.00 |
% 5.23/2.00 | Applying alpha-rule on (97) yields:
% 5.23/2.00 | (98) set_intersection2(all_0_10_10, all_0_11_11) = all_36_0_27
% 5.23/2.00 | (99) ! [v0] : ~ (in(v0, all_36_0_27) = 0)
% 5.23/2.00 |
% 5.23/2.00 | Instantiating (96) with all_42_0_29, all_42_1_30, all_42_2_31, all_42_3_32 yields:
% 5.23/2.00 | (100) ordered_pair(all_42_1_30, all_42_0_29) = all_20_0_25 & set_intersection2(all_0_9_9, all_0_8_8) = all_42_2_31 & set_intersection2(all_0_11_11, all_0_10_10) = all_42_3_32 & in(all_42_0_29, all_42_2_31) = 0 & in(all_42_1_30, all_42_3_32) = 0
% 5.23/2.00 |
% 5.23/2.00 | Applying alpha-rule on (100) yields:
% 5.23/2.00 | (101) set_intersection2(all_0_9_9, all_0_8_8) = all_42_2_31
% 5.23/2.00 | (102) in(all_42_0_29, all_42_2_31) = 0
% 5.23/2.00 | (103) set_intersection2(all_0_11_11, all_0_10_10) = all_42_3_32
% 5.23/2.00 | (104) ordered_pair(all_42_1_30, all_42_0_29) = all_20_0_25
% 5.23/2.00 | (105) in(all_42_1_30, all_42_3_32) = 0
% 5.23/2.00 |
% 5.23/2.00 | Instantiating formula (24) with all_0_10_10, all_0_11_11, all_14_0_24, all_36_0_27 and discharging atoms set_intersection2(all_0_10_10, all_0_11_11) = all_36_0_27, set_intersection2(all_0_10_10, all_0_11_11) = all_14_0_24, yields:
% 5.23/2.00 | (106) all_36_0_27 = all_14_0_24
% 5.23/2.00 |
% 5.23/2.00 | Instantiating formula (24) with all_0_11_11, all_0_10_10, all_42_3_32, all_14_0_24 and discharging atoms set_intersection2(all_0_11_11, all_0_10_10) = all_42_3_32, set_intersection2(all_0_11_11, all_0_10_10) = all_14_0_24, yields:
% 5.23/2.00 | (107) all_42_3_32 = all_14_0_24
% 5.23/2.00 |
% 5.23/2.00 | Instantiating formula (99) with all_42_1_30 yields:
% 5.23/2.00 | (108) ~ (in(all_42_1_30, all_36_0_27) = 0)
% 5.23/2.00 |
% 5.23/2.00 | From (107) and (105) follows:
% 5.23/2.00 | (109) in(all_42_1_30, all_14_0_24) = 0
% 5.23/2.00 |
% 5.23/2.00 | From (106) and (108) follows:
% 5.23/2.00 | (110) ~ (in(all_42_1_30, all_14_0_24) = 0)
% 5.23/2.00 |
% 5.23/2.00 | Using (109) and (110) yields:
% 5.23/2.00 | (47) $false
% 5.23/2.00 |
% 5.23/2.00 |-The branch is then unsatisfiable
% 5.23/2.00 % SZS output end Proof for theBenchmark
% 5.23/2.00
% 5.23/2.00 1398ms
%------------------------------------------------------------------------------