TSTP Solution File: SEU208+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU208+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 08:47:38 EDT 2022
% Result : Theorem 2.89s 1.43s
% Output : Proof 4.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU208+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n024.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 Jun 19 23:25:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.59/0.61 ____ _
% 0.59/0.61 ___ / __ \_____(_)___ ________ __________
% 0.59/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.61
% 0.59/0.61 A Theorem Prover for First-Order Logic
% 0.59/0.61 (ePrincess v.1.0)
% 0.59/0.61
% 0.59/0.61 (c) Philipp Rümmer, 2009-2015
% 0.59/0.61 (c) Peter Backeman, 2014-2015
% 0.59/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.61 Bug reports to peter@backeman.se
% 0.59/0.61
% 0.59/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.61
% 0.59/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/1.00 Prover 0: Preprocessing ...
% 2.18/1.22 Prover 0: Warning: ignoring some quantifiers
% 2.25/1.25 Prover 0: Constructing countermodel ...
% 2.89/1.43 Prover 0: proved (739ms)
% 2.89/1.43
% 2.89/1.43 No countermodel exists, formula is valid
% 2.89/1.43 % SZS status Theorem for theBenchmark
% 2.89/1.43
% 2.89/1.43 Generating proof ... Warning: ignoring some quantifiers
% 4.15/1.72 found it (size 18)
% 4.15/1.72
% 4.15/1.72 % SZS output start Proof for theBenchmark
% 4.15/1.72 Assumed formulas after preprocessing and simplification:
% 4.15/1.72 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_rng(v2) = v4 & relation_inverse_image(v2, v1) = v3 & relation(v10) & relation(v8) & relation(v2) & relation(empty_set) & empty(v10) & empty(v9) & empty(empty_set) & ~ empty(v8) & ~ empty(v7) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_inverse_image(v11, v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v11) | ~ in(v16, v11) | ~ in(v15, v12) | in(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (singleton(v11) = v14) | ~ (unordered_pair(v13, v14) = v15) | ~ (unordered_pair(v11, v12) = v13) | ordered_pair(v11, v12) = v15) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng(v11) = v12) | ~ (ordered_pair(v14, v13) = v15) | ~ relation(v11) | ~ in(v15, v11) | in(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (relation_inverse_image(v14, v13) = v12) | ~ (relation_inverse_image(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (ordered_pair(v14, v13) = v12) | ~ (ordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (unordered_pair(v14, v13) = v12) | ~ (unordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_inverse_image(v11, v12) = v13) | ~ relation(v11) | ~ in(v14, v13) | ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & in(v16, v11) & in(v15, v12))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (relation_inverse_image(v12, v13) = v14) | ~ relation(v12) | ? [v15] : ? [v16] : ? [v17] : (( ~ in(v15, v11) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v15, v18) = v19) | ~ in(v19, v12) | ~ in(v18, v13))) & (in(v15, v11) | (ordered_pair(v15, v16) = v17 & in(v17, v12) & in(v16, v13))))) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v13) = v12) | ~ (singleton(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_rng(v13) = v12) | ~ (relation_rng(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ~ in(v13, v12) | ? [v14] : ? [v15] : (ordered_pair(v14, v13) = v15 & in(v15, v11))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ~ empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : (singleton(v11) = v15 & unordered_pair(v14, v15) = v13 & unordered_pair(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v12, v11) = v13) | unordered_pair(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | ~ empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | unordered_pair(v12, v11) = v13) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (relation_rng(v12) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : ? [v16] : (( ~ in(v14, v11) | ! [v17] : ! [v18] : ( ~ (ordered_pair(v17, v14) = v18) | ~ in(v18, v12))) & (in(v14, v11) | (ordered_pair(v15, v14) = v16 & in(v16, v12))))) & ! [v11] : ! [v12] : (v12 = v11 | ~ empty(v12) | ~ empty(v11)) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ~ empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ element(v11, v12) | empty(v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ empty(v12) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v12, v11) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v11, v12) | element(v11, v12)) & ! [v11] : (v11 = empty_set | ~ empty(v11)) & ! [v11] : ( ~ empty(v11) | relation(v11)) & ? [v11] : ? [v12] : element(v12, v11) & ((ordered_pair(v0, v5) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1) & ~ in(v0, v3)) | (in(v0, v3) & ! [v11] : ( ~ in(v11, v4) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v0, v11) = v12 & ~ in(v12, v2))))))
% 4.15/1.76 | 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 yields:
% 4.15/1.76 | (1) relation_rng(all_0_8_8) = all_0_6_6 & relation_inverse_image(all_0_8_8, all_0_9_9) = all_0_7_7 & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_8_8) & relation(empty_set) & empty(all_0_0_0) & empty(all_0_1_1) & empty(empty_set) & ~ empty(all_0_2_2) & ~ empty(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [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] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(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] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) & in(v4, v1))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v4, v5) = v6 & in(v6, v1) & in(v5, v2))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, 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) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ((ordered_pair(all_0_10_10, all_0_5_5) = all_0_4_4 & in(all_0_4_4, all_0_8_8) & in(all_0_5_5, all_0_6_6) & in(all_0_5_5, all_0_9_9) & ~ in(all_0_10_10, all_0_7_7)) | (in(all_0_10_10, all_0_7_7) & ! [v0] : ( ~ in(v0, all_0_6_6) | ~ in(v0, all_0_9_9) | ? [v1] : (ordered_pair(all_0_10_10, v0) = v1 & ~ in(v1, all_0_8_8)))))
% 4.15/1.77 |
% 4.15/1.77 | Applying alpha-rule on (1) yields:
% 4.15/1.77 | (2) empty(empty_set)
% 4.15/1.77 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 4.15/1.77 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 4.15/1.77 | (5) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 4.15/1.77 | (6) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1))
% 4.15/1.77 | (7) ! [v0] : ( ~ empty(v0) | relation(v0))
% 4.15/1.77 | (8) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 4.15/1.77 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 4.15/1.77 | (10) empty(all_0_1_1)
% 4.15/1.77 | (11) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 4.15/1.77 | (12) empty(all_0_0_0)
% 4.15/1.77 | (13) relation(all_0_0_0)
% 4.15/1.77 | (14) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 4.15/1.77 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 4.15/1.77 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 4.15/1.77 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 4.15/1.77 | (18) ~ empty(all_0_2_2)
% 4.15/1.77 | (19) relation(empty_set)
% 4.15/1.77 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 4.15/1.77 | (21) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.15/1.77 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 4.15/1.78 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 4.15/1.78 | (24) ? [v0] : ? [v1] : element(v1, v0)
% 4.15/1.78 | (25) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v4, v5) = v6 & in(v6, v1) & in(v5, v2)))))
% 4.15/1.78 | (26) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 4.15/1.78 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 4.15/1.78 | (28) relation(all_0_8_8)
% 4.15/1.78 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0)))
% 4.47/1.78 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) & in(v4, v1)))
% 4.47/1.78 | (31) relation_rng(all_0_8_8) = all_0_6_6
% 4.47/1.78 | (32) relation(all_0_2_2)
% 4.47/1.78 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 4.47/1.78 | (34) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 4.47/1.78 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2))
% 4.47/1.78 | (36) (ordered_pair(all_0_10_10, all_0_5_5) = all_0_4_4 & in(all_0_4_4, all_0_8_8) & in(all_0_5_5, all_0_6_6) & in(all_0_5_5, all_0_9_9) & ~ in(all_0_10_10, all_0_7_7)) | (in(all_0_10_10, all_0_7_7) & ! [v0] : ( ~ in(v0, all_0_6_6) | ~ in(v0, all_0_9_9) | ? [v1] : (ordered_pair(all_0_10_10, v0) = v1 & ~ in(v1, all_0_8_8))))
% 4.47/1.78 | (37) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.47/1.78 | (38) relation_inverse_image(all_0_8_8, all_0_9_9) = all_0_7_7
% 4.47/1.78 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 4.47/1.78 | (40) ~ empty(all_0_3_3)
% 4.47/1.78 | (41) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1)))))
% 4.47/1.78 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2))
% 4.47/1.78 |
% 4.47/1.78 +-Applying beta-rule and splitting (36), into two cases.
% 4.47/1.78 |-Branch one:
% 4.47/1.78 | (43) ordered_pair(all_0_10_10, all_0_5_5) = all_0_4_4 & in(all_0_4_4, all_0_8_8) & in(all_0_5_5, all_0_6_6) & in(all_0_5_5, all_0_9_9) & ~ in(all_0_10_10, all_0_7_7)
% 4.47/1.78 |
% 4.47/1.78 | Applying alpha-rule on (43) yields:
% 4.47/1.78 | (44) ~ in(all_0_10_10, all_0_7_7)
% 4.47/1.78 | (45) in(all_0_5_5, all_0_9_9)
% 4.47/1.78 | (46) ordered_pair(all_0_10_10, all_0_5_5) = all_0_4_4
% 4.47/1.78 | (47) in(all_0_4_4, all_0_8_8)
% 4.47/1.78 | (48) in(all_0_5_5, all_0_6_6)
% 4.47/1.78 |
% 4.47/1.79 | Instantiating formula (42) with all_0_4_4, all_0_5_5, all_0_10_10, all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms relation_inverse_image(all_0_8_8, all_0_9_9) = all_0_7_7, ordered_pair(all_0_10_10, all_0_5_5) = all_0_4_4, relation(all_0_8_8), in(all_0_4_4, all_0_8_8), in(all_0_5_5, all_0_9_9), ~ in(all_0_10_10, all_0_7_7), yields:
% 4.55/1.79 | (49) $false
% 4.55/1.79 |
% 4.55/1.79 |-The branch is then unsatisfiable
% 4.55/1.79 |-Branch two:
% 4.55/1.79 | (50) in(all_0_10_10, all_0_7_7) & ! [v0] : ( ~ in(v0, all_0_6_6) | ~ in(v0, all_0_9_9) | ? [v1] : (ordered_pair(all_0_10_10, v0) = v1 & ~ in(v1, all_0_8_8)))
% 4.55/1.79 |
% 4.55/1.79 | Applying alpha-rule on (50) yields:
% 4.55/1.79 | (51) in(all_0_10_10, all_0_7_7)
% 4.55/1.79 | (52) ! [v0] : ( ~ in(v0, all_0_6_6) | ~ in(v0, all_0_9_9) | ? [v1] : (ordered_pair(all_0_10_10, v0) = v1 & ~ in(v1, all_0_8_8)))
% 4.55/1.79 |
% 4.55/1.79 | Instantiating formula (30) with all_0_10_10, all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms relation_inverse_image(all_0_8_8, all_0_9_9) = all_0_7_7, relation(all_0_8_8), in(all_0_10_10, all_0_7_7), yields:
% 4.55/1.79 | (53) ? [v0] : ? [v1] : (ordered_pair(all_0_10_10, v0) = v1 & in(v1, all_0_8_8) & in(v0, all_0_9_9))
% 4.55/1.79 |
% 4.55/1.79 | Instantiating (53) with all_27_0_15, all_27_1_16 yields:
% 4.55/1.79 | (54) ordered_pair(all_0_10_10, all_27_1_16) = all_27_0_15 & in(all_27_0_15, all_0_8_8) & in(all_27_1_16, all_0_9_9)
% 4.55/1.79 |
% 4.55/1.79 | Applying alpha-rule on (54) yields:
% 4.55/1.79 | (55) ordered_pair(all_0_10_10, all_27_1_16) = all_27_0_15
% 4.55/1.79 | (56) in(all_27_0_15, all_0_8_8)
% 4.55/1.79 | (57) in(all_27_1_16, all_0_9_9)
% 4.55/1.79 |
% 4.55/1.79 | Instantiating formula (23) with all_27_0_15, all_0_10_10, all_27_1_16, all_0_6_6, all_0_8_8 and discharging atoms relation_rng(all_0_8_8) = all_0_6_6, ordered_pair(all_0_10_10, all_27_1_16) = all_27_0_15, relation(all_0_8_8), in(all_27_0_15, all_0_8_8), yields:
% 4.55/1.79 | (58) in(all_27_1_16, all_0_6_6)
% 4.55/1.79 |
% 4.55/1.79 | Instantiating formula (52) with all_27_1_16 and discharging atoms in(all_27_1_16, all_0_6_6), in(all_27_1_16, all_0_9_9), yields:
% 4.55/1.79 | (59) ? [v0] : (ordered_pair(all_0_10_10, all_27_1_16) = v0 & ~ in(v0, all_0_8_8))
% 4.55/1.79 |
% 4.55/1.79 | Instantiating (59) with all_43_0_19 yields:
% 4.55/1.79 | (60) ordered_pair(all_0_10_10, all_27_1_16) = all_43_0_19 & ~ in(all_43_0_19, all_0_8_8)
% 4.55/1.79 |
% 4.55/1.79 | Applying alpha-rule on (60) yields:
% 4.55/1.79 | (61) ordered_pair(all_0_10_10, all_27_1_16) = all_43_0_19
% 4.55/1.79 | (62) ~ in(all_43_0_19, all_0_8_8)
% 4.55/1.79 |
% 4.55/1.79 | Instantiating formula (4) with all_0_10_10, all_27_1_16, all_43_0_19, all_27_0_15 and discharging atoms ordered_pair(all_0_10_10, all_27_1_16) = all_43_0_19, ordered_pair(all_0_10_10, all_27_1_16) = all_27_0_15, yields:
% 4.55/1.79 | (63) all_43_0_19 = all_27_0_15
% 4.55/1.79 |
% 4.55/1.79 | From (63) and (62) follows:
% 4.55/1.79 | (64) ~ in(all_27_0_15, all_0_8_8)
% 4.55/1.79 |
% 4.55/1.79 | Using (56) and (64) yields:
% 4.55/1.79 | (49) $false
% 4.55/1.79 |
% 4.55/1.79 |-The branch is then unsatisfiable
% 4.55/1.79 % SZS output end Proof for theBenchmark
% 4.55/1.79
% 4.55/1.79 1165ms
%------------------------------------------------------------------------------