TSTP Solution File: SEU166+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU166+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 08:47:14 EDT 2022
% Result : Theorem 3.41s 1.55s
% Output : Proof 5.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU166+3 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n005.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 Jun 19 23:41:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.65/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.36/0.93 Prover 0: Preprocessing ...
% 1.82/1.10 Prover 0: Warning: ignoring some quantifiers
% 1.82/1.12 Prover 0: Constructing countermodel ...
% 2.59/1.33 Prover 0: gave up
% 2.59/1.33 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.59/1.35 Prover 1: Preprocessing ...
% 2.85/1.42 Prover 1: Warning: ignoring some quantifiers
% 2.85/1.42 Prover 1: Constructing countermodel ...
% 3.41/1.55 Prover 1: proved (216ms)
% 3.41/1.55
% 3.41/1.55 No countermodel exists, formula is valid
% 3.41/1.55 % SZS status Theorem for theBenchmark
% 3.41/1.55
% 3.41/1.55 Generating proof ... Warning: ignoring some quantifiers
% 4.71/1.88 found it (size 49)
% 4.71/1.88
% 4.71/1.88 % SZS output start Proof for theBenchmark
% 4.71/1.88 Assumed formulas after preprocessing and simplification:
% 4.71/1.88 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v10 = 0) & empty(v11) = 0 & empty(v9) = v10 & subset(v6, v7) = v8 & subset(v3, v4) = v5 & subset(v0, v1) = 0 & cartesian_product2(v2, v1) = v7 & cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v4 & cartesian_product2(v0, v2) = v3 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = 0 | ~ (cartesian_product2(v12, v13) = v14) | ~ (ordered_pair(v17, v18) = v15) | ~ (in(v15, v14) = v16) | ? [v19] : ? [v20] : (in(v18, v13) = v20 & in(v17, v12) = v19 & ( ~ (v20 = 0) | ~ (v19 = 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 | ~ (subset(v15, v14) = v13) | ~ (subset(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (cartesian_product2(v15, v14) = v13) | ~ (cartesian_product2(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 | ~ (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] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v14) | ~ (in(v15, v14) = 0) | ? [v16] : ? [v17] : (ordered_pair(v16, v17) = v15 & in(v17, v13) = 0 & in(v16, v12) = 0)) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (cartesian_product2(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (in(v16, v12) = v17 & ( ~ (v17 = 0) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v23, v24) = v16) | ? [v25] : ? [v26] : (in(v24, v14) = v26 & in(v23, v13) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0))))) & (v17 = 0 | (v22 = v16 & v21 = 0 & v20 = 0 & ordered_pair(v18, v19) = v16 & in(v19, v14) = 0 & in(v18, v13) = 0)))) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & in(v15, v13) = v16 & in(v15, v12) = 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] : ( ~ (subset(v12, v13) = 0) | ~ (in(v14, v12) = 0) | in(v14, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | unordered_pair(v13, v12) = v14) & ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v12) = v13)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & ( ~ (v8 = 0) | ~ (v5 = 0)))
% 4.71/1.92 | 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:
% 4.71/1.92 | (1) ~ (all_0_1_1 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & subset(all_0_5_5, all_0_4_4) = all_0_3_3 & subset(all_0_8_8, all_0_7_7) = all_0_6_6 & subset(all_0_11_11, all_0_10_10) = 0 & cartesian_product2(all_0_9_9, all_0_10_10) = all_0_4_4 & cartesian_product2(all_0_9_9, all_0_11_11) = all_0_5_5 & cartesian_product2(all_0_10_10, all_0_9_9) = all_0_7_7 & cartesian_product2(all_0_11_11, all_0_9_9) = all_0_8_8 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 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 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(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 | ~ (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] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0)))) & ! [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] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | ~ (all_0_6_6 = 0))
% 5.12/1.93 |
% 5.12/1.93 | Applying alpha-rule on (1) yields:
% 5.12/1.93 | (2) empty(all_0_2_2) = all_0_1_1
% 5.12/1.93 | (3) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0))))
% 5.12/1.93 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 5.12/1.93 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0))
% 5.12/1.93 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 5.12/1.93 | (7) cartesian_product2(all_0_11_11, all_0_9_9) = all_0_8_8
% 5.12/1.93 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 5.12/1.93 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 5.12/1.93 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 5.12/1.93 | (11) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 5.12/1.93 | (12) subset(all_0_11_11, all_0_10_10) = 0
% 5.12/1.93 | (13) subset(all_0_5_5, all_0_4_4) = all_0_3_3
% 5.12/1.93 | (14) ~ (all_0_3_3 = 0) | ~ (all_0_6_6 = 0)
% 5.12/1.93 | (15) cartesian_product2(all_0_9_9, all_0_11_11) = all_0_5_5
% 5.12/1.93 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 5.12/1.93 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 5.12/1.93 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 5.12/1.93 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 5.12/1.93 | (20) subset(all_0_8_8, all_0_7_7) = all_0_6_6
% 5.12/1.93 | (21) empty(all_0_0_0) = 0
% 5.12/1.93 | (22) cartesian_product2(all_0_9_9, all_0_10_10) = all_0_4_4
% 5.12/1.93 | (23) ~ (all_0_1_1 = 0)
% 5.12/1.94 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 5.12/1.94 | (25) cartesian_product2(all_0_10_10, all_0_9_9) = all_0_7_7
% 5.12/1.94 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 5.12/1.94 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 5.12/1.94 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 5.12/1.94 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 5.12/1.94 |
% 5.12/1.94 | Instantiating formula (9) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 5.12/1.94 | (30) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 5.12/1.94 |
% 5.12/1.94 | Instantiating formula (9) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 5.12/1.94 | (31) all_0_6_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 5.12/1.94 |
% 5.12/1.94 +-Applying beta-rule and splitting (14), into two cases.
% 5.12/1.94 |-Branch one:
% 5.12/1.94 | (32) ~ (all_0_3_3 = 0)
% 5.12/1.94 |
% 5.12/1.94 +-Applying beta-rule and splitting (30), into two cases.
% 5.12/1.94 |-Branch one:
% 5.12/1.94 | (33) all_0_3_3 = 0
% 5.12/1.94 |
% 5.12/1.94 | Equations (33) can reduce 32 to:
% 5.12/1.94 | (34) $false
% 5.12/1.94 |
% 5.12/1.94 |-The branch is then unsatisfiable
% 5.12/1.94 |-Branch two:
% 5.12/1.94 | (32) ~ (all_0_3_3 = 0)
% 5.12/1.94 | (36) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 5.12/1.94 |
% 5.12/1.94 | Instantiating (36) with all_19_0_13, all_19_1_14 yields:
% 5.12/1.94 | (37) ~ (all_19_0_13 = 0) & in(all_19_1_14, all_0_4_4) = all_19_0_13 & in(all_19_1_14, all_0_5_5) = 0
% 5.12/1.94 |
% 5.12/1.94 | Applying alpha-rule on (37) yields:
% 5.12/1.94 | (38) ~ (all_19_0_13 = 0)
% 5.12/1.94 | (39) in(all_19_1_14, all_0_4_4) = all_19_0_13
% 5.12/1.94 | (40) in(all_19_1_14, all_0_5_5) = 0
% 5.12/1.94 |
% 5.12/1.94 | Instantiating formula (5) with all_19_1_14, all_0_5_5, all_0_11_11, all_0_9_9 and discharging atoms cartesian_product2(all_0_9_9, all_0_11_11) = all_0_5_5, in(all_19_1_14, all_0_5_5) = 0, yields:
% 5.12/1.94 | (41) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_19_1_14 & in(v1, all_0_11_11) = 0 & in(v0, all_0_9_9) = 0)
% 5.12/1.94 |
% 5.12/1.94 | Instantiating (41) with all_32_0_16, all_32_1_17 yields:
% 5.12/1.94 | (42) ordered_pair(all_32_1_17, all_32_0_16) = all_19_1_14 & in(all_32_0_16, all_0_11_11) = 0 & in(all_32_1_17, all_0_9_9) = 0
% 5.12/1.94 |
% 5.12/1.94 | Applying alpha-rule on (42) yields:
% 5.12/1.94 | (43) ordered_pair(all_32_1_17, all_32_0_16) = all_19_1_14
% 5.12/1.94 | (44) in(all_32_0_16, all_0_11_11) = 0
% 5.12/1.94 | (45) in(all_32_1_17, all_0_9_9) = 0
% 5.12/1.94 |
% 5.12/1.94 | Instantiating formula (28) with all_32_0_16, all_32_1_17, all_19_0_13, all_19_1_14, all_0_4_4, all_0_10_10, all_0_9_9 and discharging atoms cartesian_product2(all_0_9_9, all_0_10_10) = all_0_4_4, ordered_pair(all_32_1_17, all_32_0_16) = all_19_1_14, in(all_19_1_14, all_0_4_4) = all_19_0_13, yields:
% 5.12/1.94 | (46) all_19_0_13 = 0 | ? [v0] : ? [v1] : (in(all_32_0_16, all_0_10_10) = v1 & in(all_32_1_17, all_0_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 5.12/1.95 |
% 5.12/1.95 | Instantiating formula (6) with all_32_0_16, all_0_10_10, all_0_11_11 and discharging atoms subset(all_0_11_11, all_0_10_10) = 0, in(all_32_0_16, all_0_11_11) = 0, yields:
% 5.12/1.95 | (47) in(all_32_0_16, all_0_10_10) = 0
% 5.12/1.95 |
% 5.12/1.95 +-Applying beta-rule and splitting (46), into two cases.
% 5.12/1.95 |-Branch one:
% 5.12/1.95 | (48) all_19_0_13 = 0
% 5.12/1.95 |
% 5.12/1.95 | Equations (48) can reduce 38 to:
% 5.12/1.95 | (34) $false
% 5.12/1.95 |
% 5.12/1.95 |-The branch is then unsatisfiable
% 5.12/1.95 |-Branch two:
% 5.12/1.95 | (38) ~ (all_19_0_13 = 0)
% 5.12/1.95 | (51) ? [v0] : ? [v1] : (in(all_32_0_16, all_0_10_10) = v1 & in(all_32_1_17, all_0_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 5.12/1.95 |
% 5.12/1.95 | Instantiating (51) with all_50_0_21, all_50_1_22 yields:
% 5.12/1.95 | (52) in(all_32_0_16, all_0_10_10) = all_50_0_21 & in(all_32_1_17, all_0_9_9) = all_50_1_22 & ( ~ (all_50_0_21 = 0) | ~ (all_50_1_22 = 0))
% 5.12/1.95 |
% 5.12/1.95 | Applying alpha-rule on (52) yields:
% 5.12/1.95 | (53) in(all_32_0_16, all_0_10_10) = all_50_0_21
% 5.12/1.95 | (54) in(all_32_1_17, all_0_9_9) = all_50_1_22
% 5.12/1.95 | (55) ~ (all_50_0_21 = 0) | ~ (all_50_1_22 = 0)
% 5.12/1.95 |
% 5.12/1.95 | Instantiating formula (26) with all_32_0_16, all_0_10_10, 0, all_50_0_21 and discharging atoms in(all_32_0_16, all_0_10_10) = all_50_0_21, in(all_32_0_16, all_0_10_10) = 0, yields:
% 5.12/1.95 | (56) all_50_0_21 = 0
% 5.12/1.95 |
% 5.12/1.95 | Instantiating formula (26) with all_32_1_17, all_0_9_9, all_50_1_22, 0 and discharging atoms in(all_32_1_17, all_0_9_9) = all_50_1_22, in(all_32_1_17, all_0_9_9) = 0, yields:
% 5.12/1.95 | (57) all_50_1_22 = 0
% 5.12/1.95 |
% 5.12/1.95 +-Applying beta-rule and splitting (55), into two cases.
% 5.12/1.95 |-Branch one:
% 5.12/1.95 | (58) ~ (all_50_0_21 = 0)
% 5.12/1.95 |
% 5.12/1.95 | Equations (56) can reduce 58 to:
% 5.12/1.95 | (34) $false
% 5.12/1.95 |
% 5.12/1.95 |-The branch is then unsatisfiable
% 5.12/1.95 |-Branch two:
% 5.12/1.95 | (56) all_50_0_21 = 0
% 5.12/1.95 | (61) ~ (all_50_1_22 = 0)
% 5.12/1.95 |
% 5.12/1.95 | Equations (57) can reduce 61 to:
% 5.12/1.95 | (34) $false
% 5.12/1.95 |
% 5.12/1.95 |-The branch is then unsatisfiable
% 5.12/1.95 |-Branch two:
% 5.12/1.95 | (33) all_0_3_3 = 0
% 5.12/1.95 | (64) ~ (all_0_6_6 = 0)
% 5.12/1.95 |
% 5.12/1.95 +-Applying beta-rule and splitting (31), into two cases.
% 5.12/1.95 |-Branch one:
% 5.12/1.95 | (65) all_0_6_6 = 0
% 5.12/1.95 |
% 5.12/1.95 | Equations (65) can reduce 64 to:
% 5.12/1.95 | (34) $false
% 5.12/1.95 |
% 5.12/1.95 |-The branch is then unsatisfiable
% 5.12/1.95 |-Branch two:
% 5.12/1.95 | (64) ~ (all_0_6_6 = 0)
% 5.12/1.95 | (68) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 5.12/1.95 |
% 5.12/1.95 | Instantiating (68) with all_19_0_23, all_19_1_24 yields:
% 5.12/1.95 | (69) ~ (all_19_0_23 = 0) & in(all_19_1_24, all_0_7_7) = all_19_0_23 & in(all_19_1_24, all_0_8_8) = 0
% 5.12/1.95 |
% 5.12/1.95 | Applying alpha-rule on (69) yields:
% 5.12/1.95 | (70) ~ (all_19_0_23 = 0)
% 5.12/1.95 | (71) in(all_19_1_24, all_0_7_7) = all_19_0_23
% 5.12/1.95 | (72) in(all_19_1_24, all_0_8_8) = 0
% 5.12/1.95 |
% 5.12/1.95 | Instantiating formula (5) with all_19_1_24, all_0_8_8, all_0_9_9, all_0_11_11 and discharging atoms cartesian_product2(all_0_11_11, all_0_9_9) = all_0_8_8, in(all_19_1_24, all_0_8_8) = 0, yields:
% 5.12/1.95 | (73) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_19_1_24 & in(v1, all_0_9_9) = 0 & in(v0, all_0_11_11) = 0)
% 5.12/1.95 |
% 5.12/1.95 | Instantiating (73) with all_32_0_26, all_32_1_27 yields:
% 5.12/1.95 | (74) ordered_pair(all_32_1_27, all_32_0_26) = all_19_1_24 & in(all_32_0_26, all_0_9_9) = 0 & in(all_32_1_27, all_0_11_11) = 0
% 5.12/1.95 |
% 5.12/1.95 | Applying alpha-rule on (74) yields:
% 5.12/1.95 | (75) ordered_pair(all_32_1_27, all_32_0_26) = all_19_1_24
% 5.12/1.95 | (76) in(all_32_0_26, all_0_9_9) = 0
% 5.12/1.95 | (77) in(all_32_1_27, all_0_11_11) = 0
% 5.12/1.95 |
% 5.12/1.95 | Instantiating formula (28) with all_32_0_26, all_32_1_27, all_19_0_23, all_19_1_24, all_0_7_7, all_0_9_9, all_0_10_10 and discharging atoms cartesian_product2(all_0_10_10, all_0_9_9) = all_0_7_7, ordered_pair(all_32_1_27, all_32_0_26) = all_19_1_24, in(all_19_1_24, all_0_7_7) = all_19_0_23, yields:
% 5.12/1.96 | (78) all_19_0_23 = 0 | ? [v0] : ? [v1] : (in(all_32_0_26, all_0_9_9) = v1 & in(all_32_1_27, all_0_10_10) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 5.12/1.96 |
% 5.12/1.96 | Instantiating formula (6) with all_32_1_27, all_0_10_10, all_0_11_11 and discharging atoms subset(all_0_11_11, all_0_10_10) = 0, in(all_32_1_27, all_0_11_11) = 0, yields:
% 5.12/1.96 | (79) in(all_32_1_27, all_0_10_10) = 0
% 5.12/1.96 |
% 5.12/1.96 +-Applying beta-rule and splitting (78), into two cases.
% 5.12/1.96 |-Branch one:
% 5.12/1.96 | (80) all_19_0_23 = 0
% 5.12/1.96 |
% 5.12/1.96 | Equations (80) can reduce 70 to:
% 5.12/1.96 | (34) $false
% 5.12/1.96 |
% 5.12/1.96 |-The branch is then unsatisfiable
% 5.12/1.96 |-Branch two:
% 5.12/1.96 | (70) ~ (all_19_0_23 = 0)
% 5.12/1.96 | (83) ? [v0] : ? [v1] : (in(all_32_0_26, all_0_9_9) = v1 & in(all_32_1_27, all_0_10_10) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 5.12/1.96 |
% 5.12/1.96 | Instantiating (83) with all_50_0_31, all_50_1_32 yields:
% 5.12/1.96 | (84) in(all_32_0_26, all_0_9_9) = all_50_0_31 & in(all_32_1_27, all_0_10_10) = all_50_1_32 & ( ~ (all_50_0_31 = 0) | ~ (all_50_1_32 = 0))
% 5.12/1.96 |
% 5.12/1.96 | Applying alpha-rule on (84) yields:
% 5.12/1.96 | (85) in(all_32_0_26, all_0_9_9) = all_50_0_31
% 5.12/1.96 | (86) in(all_32_1_27, all_0_10_10) = all_50_1_32
% 5.12/1.96 | (87) ~ (all_50_0_31 = 0) | ~ (all_50_1_32 = 0)
% 5.12/1.96 |
% 5.12/1.96 | Instantiating formula (26) with all_32_0_26, all_0_9_9, all_50_0_31, 0 and discharging atoms in(all_32_0_26, all_0_9_9) = all_50_0_31, in(all_32_0_26, all_0_9_9) = 0, yields:
% 5.12/1.96 | (88) all_50_0_31 = 0
% 5.12/1.96 |
% 5.12/1.96 | Instantiating formula (26) with all_32_1_27, all_0_10_10, 0, all_50_1_32 and discharging atoms in(all_32_1_27, all_0_10_10) = all_50_1_32, in(all_32_1_27, all_0_10_10) = 0, yields:
% 5.12/1.96 | (89) all_50_1_32 = 0
% 5.12/1.96 |
% 5.12/1.96 +-Applying beta-rule and splitting (87), into two cases.
% 5.12/1.96 |-Branch one:
% 5.12/1.96 | (90) ~ (all_50_0_31 = 0)
% 5.12/1.96 |
% 5.12/1.96 | Equations (88) can reduce 90 to:
% 5.12/1.96 | (34) $false
% 5.12/1.96 |
% 5.12/1.96 |-The branch is then unsatisfiable
% 5.12/1.96 |-Branch two:
% 5.12/1.96 | (88) all_50_0_31 = 0
% 5.12/1.96 | (93) ~ (all_50_1_32 = 0)
% 5.12/1.96 |
% 5.12/1.96 | Equations (89) can reduce 93 to:
% 5.12/1.96 | (34) $false
% 5.12/1.96 |
% 5.12/1.96 |-The branch is then unsatisfiable
% 5.12/1.96 % SZS output end Proof for theBenchmark
% 5.12/1.96
% 5.12/1.96 1370ms
%------------------------------------------------------------------------------