TSTP Solution File: NUM386+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM386+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n016.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 : Mon Jul 18 08:44:05 EDT 2022
% Result : Theorem 3.15s 1.45s
% Output : Proof 4.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM386+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n016.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 : Thu Jul 7 07:01:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.59/0.59 ____ _
% 0.59/0.59 ___ / __ \_____(_)___ ________ __________
% 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.59
% 0.59/0.59 A Theorem Prover for First-Order Logic
% 0.59/0.59 (ePrincess v.1.0)
% 0.59/0.59
% 0.59/0.59 (c) Philipp Rümmer, 2009-2015
% 0.59/0.59 (c) Peter Backeman, 2014-2015
% 0.59/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.59 Bug reports to peter@backeman.se
% 0.59/0.59
% 0.59/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.59
% 0.59/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/0.93 Prover 0: Preprocessing ...
% 2.08/1.13 Prover 0: Warning: ignoring some quantifiers
% 2.08/1.14 Prover 0: Constructing countermodel ...
% 3.15/1.45 Prover 0: proved (809ms)
% 3.15/1.45
% 3.15/1.45 No countermodel exists, formula is valid
% 3.15/1.45 % SZS status Theorem for theBenchmark
% 3.15/1.45
% 3.15/1.45 Generating proof ... Warning: ignoring some quantifiers
% 4.45/1.73 found it (size 21)
% 4.45/1.73
% 4.45/1.73 % SZS output start Proof for theBenchmark
% 4.45/1.73 Assumed formulas after preprocessing and simplification:
% 4.45/1.73 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (succ(v1) = v2 & relation_non_empty(v3) & relation_empty_yielding(v5) & relation_empty_yielding(v4) & relation_empty_yielding(empty_set) & one_to_one(v6) & relation(v12) & relation(v11) & relation(v9) & relation(v8) & relation(v6) & relation(v5) & relation(v4) & relation(v3) & relation(empty_set) & function(v12) & function(v9) & function(v6) & function(v4) & function(v3) & empty(v11) & empty(v10) & empty(v9) & empty(empty_set) & ~ empty(v8) & ~ empty(v7) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (set_union2(v16, v15) = v14) | ~ (set_union2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v13, v14) = v15) | ~ in(v16, v15) | in(v16, v14) | in(v16, v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v13, v14) = v15) | ~ in(v16, v14) | in(v16, v15)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v13, v14) = v15) | ~ in(v16, v13) | in(v16, v15)) & ? [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v13 | ~ (set_union2(v14, v15) = v16) | ? [v17] : (( ~ in(v17, v13) | ( ~ in(v17, v15) & ~ in(v17, v14))) & (in(v17, v15) | in(v17, v14) | in(v17, v13)))) & ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (singleton(v13) = v14) | ~ in(v15, v14)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (singleton(v15) = v14) | ~ (singleton(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (succ(v15) = v14) | ~ (succ(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (singleton(v13) = v14) | ~ (set_union2(v13, v14) = v15) | succ(v13) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v14, v13) = v15) | ~ empty(v15) | empty(v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v14, v13) = v15) | set_union2(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v13, v14) = v15) | ~ relation(v14) | ~ relation(v13) | relation(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v13, v14) = v15) | ~ empty(v15) | empty(v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v13, v14) = v15) | set_union2(v14, v13) = v15) & ? [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (singleton(v14) = v15) | ? [v16] : (( ~ (v16 = v14) | ~ in(v14, v13)) & (v16 = v14 | in(v16, v13)))) & ! [v13] : ! [v14] : (v14 = v13 | ~ (set_union2(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (set_union2(v13, empty_set) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ empty(v14) | ~ empty(v13)) & ! [v13] : ! [v14] : ( ~ (singleton(v13) = v14) | in(v13, v14)) & ! [v13] : ! [v14] : ( ~ (succ(v13) = v14) | ~ empty(v14)) & ! [v13] : ! [v14] : ( ~ (succ(v13) = v14) | ? [v15] : (singleton(v13) = v15 & set_union2(v13, v15) = v14)) & ! [v13] : ! [v14] : ( ~ element(v13, v14) | empty(v14) | in(v13, v14)) & ! [v13] : ! [v14] : ( ~ empty(v14) | ~ in(v13, v14)) & ! [v13] : ! [v14] : ( ~ in(v14, v13) | ~ in(v13, v14)) & ! [v13] : ! [v14] : ( ~ in(v13, v14) | element(v13, v14)) & ! [v13] : (v13 = empty_set | ~ empty(v13)) & ! [v13] : ( ~ relation(v13) | ~ function(v13) | ~ empty(v13) | one_to_one(v13)) & ! [v13] : ( ~ empty(v13) | relation(v13)) & ! [v13] : ( ~ empty(v13) | function(v13)) & ? [v13] : ? [v14] : element(v14, v13) & (( ~ (v1 = v0) & in(v0, v2) & ~ in(v0, v1)) | ( ~ in(v0, v2) & (v1 = v0 | in(v0, v1)))))
% 4.45/1.77 | 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, all_0_12_12 yields:
% 4.45/1.77 | (1) succ(all_0_11_11) = all_0_10_10 & relation_non_empty(all_0_9_9) & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(all_0_8_8) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_8_8) & relation(all_0_9_9) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_8_8) & function(all_0_9_9) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = 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] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & (( ~ (all_0_11_11 = all_0_12_12) & in(all_0_12_12, all_0_10_10) & ~ in(all_0_12_12, all_0_11_11)) | ( ~ in(all_0_12_12, all_0_10_10) & (all_0_11_11 = all_0_12_12 | in(all_0_12_12, all_0_11_11))))
% 4.45/1.78 |
% 4.45/1.78 | Applying alpha-rule on (1) yields:
% 4.45/1.78 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 4.45/1.78 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 4.45/1.78 | (4) relation(all_0_6_6)
% 4.45/1.78 | (5) relation(all_0_3_3)
% 4.45/1.78 | (6) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 4.45/1.78 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 4.45/1.78 | (8) ~ empty(all_0_4_4)
% 4.84/1.78 | (9) one_to_one(all_0_6_6)
% 4.84/1.78 | (10) relation_empty_yielding(all_0_7_7)
% 4.84/1.78 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 4.84/1.78 | (12) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1))
% 4.84/1.78 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 4.84/1.78 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 4.84/1.78 | (15) relation_empty_yielding(all_0_8_8)
% 4.84/1.78 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 4.84/1.78 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 4.84/1.78 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2)
% 4.84/1.78 | (19) function(all_0_8_8)
% 4.84/1.78 | (20) function(all_0_9_9)
% 4.84/1.78 | (21) ( ~ (all_0_11_11 = all_0_12_12) & in(all_0_12_12, all_0_10_10) & ~ in(all_0_12_12, all_0_11_11)) | ( ~ in(all_0_12_12, all_0_10_10) & (all_0_11_11 = all_0_12_12 | in(all_0_12_12, all_0_11_11)))
% 4.84/1.78 | (22) relation(all_0_9_9)
% 4.84/1.78 | (23) ! [v0] : ( ~ empty(v0) | function(v0))
% 4.84/1.78 | (24) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 4.84/1.78 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 4.84/1.78 | (26) relation_non_empty(all_0_9_9)
% 4.84/1.78 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 4.84/1.79 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 4.84/1.79 | (29) function(all_0_6_6)
% 4.84/1.79 | (30) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0))))
% 4.84/1.79 | (31) ~ empty(all_0_5_5)
% 4.84/1.79 | (32) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 4.84/1.79 | (33) function(all_0_0_0)
% 4.84/1.79 | (34) ! [v0] : ( ~ empty(v0) | relation(v0))
% 4.84/1.79 | (35) relation(all_0_0_0)
% 4.84/1.79 | (36) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 4.84/1.79 | (37) empty(all_0_1_1)
% 4.84/1.79 | (38) relation(all_0_8_8)
% 4.84/1.79 | (39) empty(all_0_3_3)
% 4.84/1.79 | (40) relation(all_0_4_4)
% 4.84/1.79 | (41) empty(all_0_2_2)
% 4.84/1.79 | (42) relation_empty_yielding(empty_set)
% 4.84/1.79 | (43) function(all_0_3_3)
% 4.84/1.79 | (44) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 4.84/1.79 | (45) relation(all_0_1_1)
% 4.84/1.79 | (46) relation(all_0_7_7)
% 4.84/1.79 | (47) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 4.84/1.79 | (48) ? [v0] : ? [v1] : element(v1, v0)
% 4.84/1.79 | (49) relation(empty_set)
% 4.84/1.79 | (50) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.84/1.79 | (51) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 4.84/1.79 | (52) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.84/1.79 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 4.84/1.79 | (54) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 4.84/1.79 | (55) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1))
% 4.84/1.79 | (56) succ(all_0_11_11) = all_0_10_10
% 4.84/1.79 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 4.84/1.79 | (58) empty(empty_set)
% 4.84/1.79 |
% 4.84/1.79 | Instantiating formula (12) with all_0_10_10, all_0_11_11 and discharging atoms succ(all_0_11_11) = all_0_10_10, yields:
% 4.84/1.79 | (59) ? [v0] : (singleton(all_0_11_11) = v0 & set_union2(all_0_11_11, v0) = all_0_10_10)
% 4.84/1.79 |
% 4.84/1.79 | Instantiating (59) with all_19_0_17 yields:
% 4.84/1.79 | (60) singleton(all_0_11_11) = all_19_0_17 & set_union2(all_0_11_11, all_19_0_17) = all_0_10_10
% 4.84/1.79 |
% 4.84/1.79 | Applying alpha-rule on (60) yields:
% 4.84/1.79 | (61) singleton(all_0_11_11) = all_19_0_17
% 4.84/1.79 | (62) set_union2(all_0_11_11, all_19_0_17) = all_0_10_10
% 4.84/1.79 |
% 4.84/1.79 | Instantiating formula (32) with all_19_0_17, all_0_11_11 and discharging atoms singleton(all_0_11_11) = all_19_0_17, yields:
% 4.84/1.79 | (63) in(all_0_11_11, all_19_0_17)
% 4.84/1.79 |
% 4.84/1.79 | Instantiating formula (3) with all_0_10_10, all_0_11_11, all_19_0_17 and discharging atoms set_union2(all_0_11_11, all_19_0_17) = all_0_10_10, yields:
% 4.84/1.79 | (64) set_union2(all_19_0_17, all_0_11_11) = all_0_10_10
% 4.84/1.79 |
% 4.84/1.80 | Instantiating formula (28) with all_0_11_11, all_0_10_10, all_0_11_11, all_19_0_17 and discharging atoms set_union2(all_19_0_17, all_0_11_11) = all_0_10_10, in(all_0_11_11, all_19_0_17), yields:
% 4.84/1.80 | (65) in(all_0_11_11, all_0_10_10)
% 4.84/1.80 |
% 4.84/1.80 +-Applying beta-rule and splitting (21), into two cases.
% 4.84/1.80 |-Branch one:
% 4.84/1.80 | (66) ~ (all_0_11_11 = all_0_12_12) & in(all_0_12_12, all_0_10_10) & ~ in(all_0_12_12, all_0_11_11)
% 4.84/1.80 |
% 4.84/1.80 | Applying alpha-rule on (66) yields:
% 4.84/1.80 | (67) ~ (all_0_11_11 = all_0_12_12)
% 4.84/1.80 | (68) in(all_0_12_12, all_0_10_10)
% 4.84/1.80 | (69) ~ in(all_0_12_12, all_0_11_11)
% 4.84/1.80 |
% 4.84/1.80 | Instantiating formula (57) with all_0_12_12, all_0_10_10, all_19_0_17, all_0_11_11 and discharging atoms set_union2(all_0_11_11, all_19_0_17) = all_0_10_10, in(all_0_12_12, all_0_10_10), ~ in(all_0_12_12, all_0_11_11), yields:
% 4.84/1.80 | (70) in(all_0_12_12, all_19_0_17)
% 4.84/1.80 |
% 4.84/1.80 | Instantiating formula (25) with all_0_12_12, all_19_0_17, all_0_11_11 and discharging atoms singleton(all_0_11_11) = all_19_0_17, in(all_0_12_12, all_19_0_17), yields:
% 4.84/1.80 | (71) all_0_11_11 = all_0_12_12
% 4.84/1.80 |
% 4.84/1.80 | Equations (71) can reduce 67 to:
% 4.84/1.80 | (72) $false
% 4.84/1.80 |
% 4.84/1.80 |-The branch is then unsatisfiable
% 4.84/1.80 |-Branch two:
% 4.84/1.80 | (73) ~ in(all_0_12_12, all_0_10_10) & (all_0_11_11 = all_0_12_12 | in(all_0_12_12, all_0_11_11))
% 4.84/1.80 |
% 4.84/1.80 | Applying alpha-rule on (73) yields:
% 4.84/1.80 | (74) ~ in(all_0_12_12, all_0_10_10)
% 4.84/1.80 | (75) all_0_11_11 = all_0_12_12 | in(all_0_12_12, all_0_11_11)
% 4.84/1.80 |
% 4.84/1.80 +-Applying beta-rule and splitting (75), into two cases.
% 4.84/1.80 |-Branch one:
% 4.84/1.80 | (76) in(all_0_12_12, all_0_11_11)
% 4.92/1.80 |
% 4.92/1.80 | Instantiating formula (28) with all_0_12_12, all_0_10_10, all_19_0_17, all_0_11_11 and discharging atoms set_union2(all_0_11_11, all_19_0_17) = all_0_10_10, in(all_0_12_12, all_0_11_11), ~ in(all_0_12_12, all_0_10_10), yields:
% 4.92/1.80 | (77) $false
% 4.92/1.80 |
% 4.92/1.80 |-The branch is then unsatisfiable
% 4.92/1.80 |-Branch two:
% 4.92/1.80 | (69) ~ in(all_0_12_12, all_0_11_11)
% 4.92/1.80 | (71) all_0_11_11 = all_0_12_12
% 4.92/1.80 |
% 4.92/1.80 | From (71) and (65) follows:
% 4.92/1.80 | (68) in(all_0_12_12, all_0_10_10)
% 4.92/1.80 |
% 4.92/1.80 | Using (68) and (74) yields:
% 4.92/1.80 | (77) $false
% 4.92/1.80 |
% 4.92/1.80 |-The branch is then unsatisfiable
% 4.92/1.80 % SZS output end Proof for theBenchmark
% 4.92/1.80
% 4.92/1.80 1201ms
%------------------------------------------------------------------------------