TSTP Solution File: SEU224+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU224+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 08:47:51 EDT 2022
% Result : Theorem 3.31s 1.44s
% Output : Proof 5.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU224+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n020.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 07:58:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.45/0.60 ____ _
% 0.45/0.60 ___ / __ \_____(_)___ ________ __________
% 0.45/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.45/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.45/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.45/0.60
% 0.45/0.60 A Theorem Prover for First-Order Logic
% 0.45/0.60 (ePrincess v.1.0)
% 0.45/0.60
% 0.45/0.60 (c) Philipp Rümmer, 2009-2015
% 0.45/0.60 (c) Peter Backeman, 2014-2015
% 0.45/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.45/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.45/0.60 Bug reports to peter@backeman.se
% 0.45/0.60
% 0.45/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.45/0.60
% 0.45/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.67/0.94 Prover 0: Preprocessing ...
% 2.29/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.29/1.20 Prover 0: Constructing countermodel ...
% 3.31/1.43 Prover 0: proved (784ms)
% 3.31/1.44
% 3.31/1.44 No countermodel exists, formula is valid
% 3.31/1.44 % SZS status Theorem for theBenchmark
% 3.31/1.44
% 3.31/1.44 Generating proof ... Warning: ignoring some quantifiers
% 4.89/1.80 found it (size 37)
% 4.89/1.80
% 4.89/1.80 % SZS output start Proof for theBenchmark
% 4.89/1.80 Assumed formulas after preprocessing and simplification:
% 4.89/1.80 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & relation_dom_restriction(v2, v0) = v3 & relation_empty_yielding(v6) & relation_empty_yielding(empty_set) & one_to_one(v7) & relation(v13) & relation(v12) & relation(v10) & relation(v9) & relation(v7) & relation(v6) & relation(v2) & relation(empty_set) & function(v13) & function(v10) & function(v7) & function(v2) & empty(v12) & empty(v11) & empty(v10) & empty(empty_set) & ~ empty(v9) & ~ empty(v8) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v18) | ~ (relation_dom(v15) = v16) | ~ (set_intersection2(v18, v14) = v19) | ~ relation(v17) | ~ relation(v15) | ~ function(v17) | ~ function(v15) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_dom_restriction(v17, v14) = v20 & ( ~ (v20 = v15) | (v19 = v16 & ! [v24] : ! [v25] : ( ~ (apply(v17, v24) = v25) | ~ in(v24, v16) | apply(v15, v24) = v25) & ! [v24] : ! [v25] : ( ~ (apply(v15, v24) = v25) | ~ in(v24, v16) | apply(v17, v24) = v25))) & ( ~ (v19 = v16) | v20 = v15 | ( ~ (v23 = v22) & apply(v17, v21) = v23 & apply(v15, v21) = v22 & in(v21, v16))))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v15) = v16) | ~ (relation_dom_restriction(v17, v14) = v18) | ~ relation(v17) | ~ relation(v15) | ~ function(v17) | ~ function(v15) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_dom(v17) = v19 & set_intersection2(v19, v14) = v20 & ( ~ (v20 = v16) | v18 = v15 | ( ~ (v23 = v22) & apply(v17, v21) = v23 & apply(v15, v21) = v22 & in(v21, v16))) & ( ~ (v18 = v15) | (v20 = v16 & ! [v24] : ! [v25] : ( ~ (apply(v17, v24) = v25) | ~ in(v24, v16) | apply(v15, v24) = v25) & ! [v24] : ! [v25] : ( ~ (apply(v15, v24) = v25) | ~ in(v24, v16) | apply(v17, v24) = v25))))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (apply(v17, v16) = v15) | ~ (apply(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (relation_dom_restriction(v17, v16) = v15) | ~ (relation_dom_restriction(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (set_intersection2(v17, v16) = v15) | ~ (set_intersection2(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v14, v15) = v16) | ~ in(v17, v16) | in(v17, v15)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v14, v15) = v16) | ~ in(v17, v16) | in(v17, v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v14, v15) = v16) | ~ in(v17, v15) | ~ in(v17, v14) | in(v17, v16)) & ? [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v14 | ~ (set_intersection2(v15, v16) = v17) | ? [v18] : (( ~ in(v18, v16) | ~ in(v18, v15) | ~ in(v18, v14)) & (in(v18, v14) | (in(v18, v16) & in(v18, v15))))) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_dom(v16) = v15) | ~ (relation_dom(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom_restriction(v14, v15) = v16) | ~ relation_empty_yielding(v14) | ~ relation(v14) | relation_empty_yielding(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom_restriction(v14, v15) = v16) | ~ relation_empty_yielding(v14) | ~ relation(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom_restriction(v14, v15) = v16) | ~ relation(v14) | ~ function(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom_restriction(v14, v15) = v16) | ~ relation(v14) | ~ function(v14) | function(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom_restriction(v14, v15) = v16) | ~ relation(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (set_intersection2(v15, v14) = v16) | set_intersection2(v14, v15) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (set_intersection2(v14, v15) = v16) | ~ relation(v15) | ~ relation(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (set_intersection2(v14, v15) = v16) | set_intersection2(v15, v14) = v16) & ! [v14] : ! [v15] : (v15 = v14 | ~ (set_intersection2(v14, v14) = v15)) & ! [v14] : ! [v15] : (v15 = v14 | ~ empty(v15) | ~ empty(v14)) & ! [v14] : ! [v15] : (v15 = empty_set | ~ (set_intersection2(v14, empty_set) = v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ relation(v14) | ~ empty(v15) | empty(v14)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ empty(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ empty(v14) | empty(v15)) & ! [v14] : ! [v15] : ( ~ element(v14, v15) | empty(v15) | in(v14, v15)) & ! [v14] : ! [v15] : ( ~ empty(v15) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ( ~ in(v15, v14) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ( ~ in(v14, v15) | element(v14, v15)) & ! [v14] : (v14 = empty_set | ~ empty(v14)) & ! [v14] : ( ~ relation(v14) | ~ function(v14) | ~ empty(v14) | one_to_one(v14)) & ! [v14] : ( ~ empty(v14) | relation(v14)) & ! [v14] : ( ~ empty(v14) | function(v14)) & ? [v14] : ? [v15] : element(v15, v14) & ((in(v1, v5) & in(v1, v0) & ~ in(v1, v4)) | (in(v1, v4) & ( ~ in(v1, v5) | ~ in(v1, v0)))))
% 5.17/1.85 | 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, all_0_13_13 yields:
% 5.17/1.85 | (1) relation_dom(all_0_10_10) = all_0_9_9 & relation_dom(all_0_11_11) = all_0_8_8 & relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10 & relation_empty_yielding(all_0_7_7) & 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_11_11) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_11_11) & 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] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v4, v0) = v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom_restriction(v3, v0) = v6 & ( ~ (v6 = v1) | (v5 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))) & ( ~ (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & ( ~ (v6 = v2) | v4 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(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] : ( ~ 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) & ((in(all_0_12_12, all_0_8_8) & in(all_0_12_12, all_0_13_13) & ~ in(all_0_12_12, all_0_9_9)) | (in(all_0_12_12, all_0_9_9) & ( ~ in(all_0_12_12, all_0_8_8) | ~ in(all_0_12_12, all_0_13_13))))
% 5.17/1.86 |
% 5.17/1.86 | Applying alpha-rule on (1) yields:
% 5.17/1.86 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 5.17/1.86 | (3) relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10
% 5.17/1.86 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 5.17/1.86 | (5) relation(all_0_11_11)
% 5.17/1.86 | (6) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1)))))
% 5.17/1.86 | (7) empty(all_0_2_2)
% 5.17/1.86 | (8) function(all_0_3_3)
% 5.17/1.86 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 5.17/1.86 | (10) empty(all_0_3_3)
% 5.17/1.86 | (11) relation(empty_set)
% 5.17/1.86 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2))
% 5.17/1.86 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | relation(v2))
% 5.17/1.86 | (14) relation(all_0_6_6)
% 5.35/1.86 | (15) function(all_0_6_6)
% 5.35/1.86 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 5.35/1.86 | (17) ? [v0] : ? [v1] : element(v1, v0)
% 5.35/1.86 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2))
% 5.35/1.86 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1))
% 5.35/1.86 | (20) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 5.35/1.86 | (21) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 5.35/1.86 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 5.35/1.86 | (23) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 5.35/1.86 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2))
% 5.35/1.86 | (25) relation_empty_yielding(all_0_7_7)
% 5.35/1.86 | (26) ! [v0] : ( ~ empty(v0) | function(v0))
% 5.35/1.86 | (27) relation(all_0_7_7)
% 5.35/1.86 | (28) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 5.35/1.87 | (29) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 5.35/1.87 | (30) function(all_0_11_11)
% 5.35/1.87 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | function(v2))
% 5.35/1.87 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0))
% 5.35/1.87 | (33) empty(all_0_1_1)
% 5.35/1.87 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2))
% 5.35/1.87 | (35) one_to_one(all_0_6_6)
% 5.35/1.87 | (36) ! [v0] : ( ~ empty(v0) | relation(v0))
% 5.35/1.87 | (37) ~ empty(all_0_4_4)
% 5.35/1.87 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & ( ~ (v6 = v2) | v4 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11)))))
% 5.35/1.87 | (39) relation(all_0_0_0)
% 5.35/1.87 | (40) function(all_0_0_0)
% 5.35/1.87 | (41) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 5.35/1.87 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 5.35/1.87 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 5.35/1.87 | (44) relation(all_0_1_1)
% 5.35/1.87 | (45) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 5.35/1.87 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 5.35/1.87 | (47) ~ empty(all_0_5_5)
% 5.35/1.87 | (48) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 5.35/1.87 | (49) relation(all_0_4_4)
% 5.35/1.87 | (50) relation_empty_yielding(empty_set)
% 5.35/1.87 | (51) empty(empty_set)
% 5.35/1.87 | (52) relation(all_0_3_3)
% 5.35/1.87 | (53) (in(all_0_12_12, all_0_8_8) & in(all_0_12_12, all_0_13_13) & ~ in(all_0_12_12, all_0_9_9)) | (in(all_0_12_12, all_0_9_9) & ( ~ in(all_0_12_12, all_0_8_8) | ~ in(all_0_12_12, all_0_13_13)))
% 5.35/1.87 | (54) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 5.35/1.87 | (55) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 5.35/1.87 | (56) relation_dom(all_0_10_10) = all_0_9_9
% 5.35/1.87 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 5.35/1.87 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v4, v0) = v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom_restriction(v3, v0) = v6 & ( ~ (v6 = v1) | (v5 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))) & ( ~ (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2)))))
% 5.35/1.87 | (59) relation_dom(all_0_11_11) = all_0_8_8
% 5.35/1.87 |
% 5.35/1.88 | Instantiating formula (38) with all_0_10_10, all_0_11_11, all_0_8_8, all_0_11_11, all_0_13_13 and discharging atoms relation_dom(all_0_11_11) = all_0_8_8, relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation(all_0_11_11), function(all_0_11_11), yields:
% 5.35/1.88 | (60) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_dom(all_0_11_11) = v0 & set_intersection2(v0, all_0_13_13) = v1 & ( ~ (v1 = all_0_8_8) | all_0_10_10 = all_0_11_11 | ( ~ (v4 = v3) & apply(all_0_11_11, v2) = v4 & apply(all_0_11_11, v2) = v3 & in(v2, all_0_8_8))) & ( ~ (all_0_10_10 = all_0_11_11) | v1 = all_0_8_8))
% 5.35/1.88 |
% 5.35/1.88 | Instantiating formula (13) with all_0_10_10, all_0_13_13, all_0_11_11 and discharging atoms relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation(all_0_11_11), function(all_0_11_11), yields:
% 5.35/1.88 | (61) relation(all_0_10_10)
% 5.35/1.88 |
% 5.35/1.88 | Instantiating formula (31) with all_0_10_10, all_0_13_13, all_0_11_11 and discharging atoms relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation(all_0_11_11), function(all_0_11_11), yields:
% 5.35/1.88 | (62) function(all_0_10_10)
% 5.35/1.88 |
% 5.35/1.88 | Instantiating (60) with all_17_0_17, all_17_1_18, all_17_2_19, all_17_3_20, all_17_4_21 yields:
% 5.35/1.88 | (63) relation_dom(all_0_11_11) = all_17_4_21 & set_intersection2(all_17_4_21, all_0_13_13) = all_17_3_20 & ( ~ (all_17_3_20 = all_0_8_8) | all_0_10_10 = all_0_11_11 | ( ~ (all_17_0_17 = all_17_1_18) & apply(all_0_11_11, all_17_2_19) = all_17_0_17 & apply(all_0_11_11, all_17_2_19) = all_17_1_18 & in(all_17_2_19, all_0_8_8))) & ( ~ (all_0_10_10 = all_0_11_11) | all_17_3_20 = all_0_8_8)
% 5.35/1.88 |
% 5.35/1.88 | Applying alpha-rule on (63) yields:
% 5.35/1.88 | (64) relation_dom(all_0_11_11) = all_17_4_21
% 5.35/1.88 | (65) set_intersection2(all_17_4_21, all_0_13_13) = all_17_3_20
% 5.35/1.88 | (66) ~ (all_17_3_20 = all_0_8_8) | all_0_10_10 = all_0_11_11 | ( ~ (all_17_0_17 = all_17_1_18) & apply(all_0_11_11, all_17_2_19) = all_17_0_17 & apply(all_0_11_11, all_17_2_19) = all_17_1_18 & in(all_17_2_19, all_0_8_8))
% 5.35/1.88 | (67) ~ (all_0_10_10 = all_0_11_11) | all_17_3_20 = all_0_8_8
% 5.35/1.88 |
% 5.35/1.88 | Instantiating formula (46) with all_0_11_11, all_17_4_21, all_0_8_8 and discharging atoms relation_dom(all_0_11_11) = all_17_4_21, relation_dom(all_0_11_11) = all_0_8_8, yields:
% 5.35/1.88 | (68) all_17_4_21 = all_0_8_8
% 5.35/1.88 |
% 5.35/1.88 | From (68) and (64) follows:
% 5.35/1.88 | (59) relation_dom(all_0_11_11) = all_0_8_8
% 5.35/1.88 |
% 5.35/1.88 | From (68) and (65) follows:
% 5.35/1.88 | (70) set_intersection2(all_0_8_8, all_0_13_13) = all_17_3_20
% 5.35/1.88 |
% 5.35/1.88 | Instantiating formula (58) with all_17_3_20, all_0_8_8, all_0_11_11, all_0_8_8, all_0_11_11, all_0_13_13 and discharging atoms relation_dom(all_0_11_11) = all_0_8_8, set_intersection2(all_0_8_8, all_0_13_13) = all_17_3_20, relation(all_0_11_11), function(all_0_11_11), yields:
% 5.35/1.88 | (71) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom_restriction(all_0_11_11, all_0_13_13) = v0 & ( ~ (v0 = all_0_11_11) | all_17_3_20 = all_0_8_8) & ( ~ (all_17_3_20 = all_0_8_8) | v0 = all_0_11_11 | ( ~ (v3 = v2) & apply(all_0_11_11, v1) = v3 & apply(all_0_11_11, v1) = v2 & in(v1, all_0_8_8))))
% 5.35/1.88 |
% 5.35/1.88 | Instantiating formula (43) with all_17_3_20, all_0_8_8, all_0_13_13 and discharging atoms set_intersection2(all_0_8_8, all_0_13_13) = all_17_3_20, yields:
% 5.35/1.88 | (72) set_intersection2(all_0_13_13, all_0_8_8) = all_17_3_20
% 5.35/1.88 |
% 5.35/1.88 | Instantiating formula (58) with all_17_3_20, all_0_8_8, all_0_11_11, all_0_9_9, all_0_10_10, all_0_13_13 and discharging atoms relation_dom(all_0_10_10) = all_0_9_9, relation_dom(all_0_11_11) = all_0_8_8, set_intersection2(all_0_8_8, all_0_13_13) = all_17_3_20, relation(all_0_10_10), relation(all_0_11_11), function(all_0_10_10), function(all_0_11_11), yields:
% 5.35/1.88 | (73) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom_restriction(all_0_11_11, all_0_13_13) = v0 & ( ~ (v0 = all_0_10_10) | (all_17_3_20 = all_0_9_9 & ! [v4] : ! [v5] : ( ~ (apply(all_0_10_10, v4) = v5) | ~ in(v4, all_0_9_9) | apply(all_0_11_11, v4) = v5) & ! [v4] : ! [v5] : ( ~ (apply(all_0_11_11, v4) = v5) | ~ in(v4, all_0_9_9) | apply(all_0_10_10, v4) = v5))) & ( ~ (all_17_3_20 = all_0_9_9) | v0 = all_0_10_10 | ( ~ (v3 = v2) & apply(all_0_10_10, v1) = v2 & apply(all_0_11_11, v1) = v3 & in(v1, all_0_9_9))))
% 5.35/1.88 |
% 5.35/1.89 | Instantiating (73) with all_29_0_22, all_29_1_23, all_29_2_24, all_29_3_25 yields:
% 5.35/1.89 | (74) relation_dom_restriction(all_0_11_11, all_0_13_13) = all_29_3_25 & ( ~ (all_29_3_25 = all_0_10_10) | (all_17_3_20 = all_0_9_9 & ! [v0] : ! [v1] : ( ~ (apply(all_0_10_10, v0) = v1) | ~ in(v0, all_0_9_9) | apply(all_0_11_11, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, all_0_9_9) | apply(all_0_10_10, v0) = v1))) & ( ~ (all_17_3_20 = all_0_9_9) | all_29_3_25 = all_0_10_10 | ( ~ (all_29_0_22 = all_29_1_23) & apply(all_0_10_10, all_29_2_24) = all_29_1_23 & apply(all_0_11_11, all_29_2_24) = all_29_0_22 & in(all_29_2_24, all_0_9_9)))
% 5.35/1.89 |
% 5.35/1.89 | Applying alpha-rule on (74) yields:
% 5.35/1.89 | (75) relation_dom_restriction(all_0_11_11, all_0_13_13) = all_29_3_25
% 5.35/1.89 | (76) ~ (all_29_3_25 = all_0_10_10) | (all_17_3_20 = all_0_9_9 & ! [v0] : ! [v1] : ( ~ (apply(all_0_10_10, v0) = v1) | ~ in(v0, all_0_9_9) | apply(all_0_11_11, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, all_0_9_9) | apply(all_0_10_10, v0) = v1))
% 5.35/1.89 | (77) ~ (all_17_3_20 = all_0_9_9) | all_29_3_25 = all_0_10_10 | ( ~ (all_29_0_22 = all_29_1_23) & apply(all_0_10_10, all_29_2_24) = all_29_1_23 & apply(all_0_11_11, all_29_2_24) = all_29_0_22 & in(all_29_2_24, all_0_9_9))
% 5.35/1.89 |
% 5.35/1.89 | Instantiating (71) with all_31_0_26, all_31_1_27, all_31_2_28, all_31_3_29 yields:
% 5.35/1.89 | (78) relation_dom_restriction(all_0_11_11, all_0_13_13) = all_31_3_29 & ( ~ (all_31_3_29 = all_0_11_11) | all_17_3_20 = all_0_8_8) & ( ~ (all_17_3_20 = all_0_8_8) | all_31_3_29 = all_0_11_11 | ( ~ (all_31_0_26 = all_31_1_27) & apply(all_0_11_11, all_31_2_28) = all_31_0_26 & apply(all_0_11_11, all_31_2_28) = all_31_1_27 & in(all_31_2_28, all_0_8_8)))
% 5.35/1.89 |
% 5.35/1.89 | Applying alpha-rule on (78) yields:
% 5.35/1.89 | (79) relation_dom_restriction(all_0_11_11, all_0_13_13) = all_31_3_29
% 5.35/1.89 | (80) ~ (all_31_3_29 = all_0_11_11) | all_17_3_20 = all_0_8_8
% 5.35/1.89 | (81) ~ (all_17_3_20 = all_0_8_8) | all_31_3_29 = all_0_11_11 | ( ~ (all_31_0_26 = all_31_1_27) & apply(all_0_11_11, all_31_2_28) = all_31_0_26 & apply(all_0_11_11, all_31_2_28) = all_31_1_27 & in(all_31_2_28, all_0_8_8))
% 5.35/1.89 |
% 5.35/1.89 | Instantiating formula (32) with all_0_11_11, all_0_13_13, all_31_3_29, all_0_10_10 and discharging atoms relation_dom_restriction(all_0_11_11, all_0_13_13) = all_31_3_29, relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, yields:
% 5.35/1.89 | (82) all_31_3_29 = all_0_10_10
% 5.35/1.89 |
% 5.35/1.89 | Instantiating formula (32) with all_0_11_11, all_0_13_13, all_29_3_25, all_31_3_29 and discharging atoms relation_dom_restriction(all_0_11_11, all_0_13_13) = all_31_3_29, relation_dom_restriction(all_0_11_11, all_0_13_13) = all_29_3_25, yields:
% 5.35/1.89 | (83) all_31_3_29 = all_29_3_25
% 5.35/1.89 |
% 5.35/1.89 | Combining equations (82,83) yields a new equation:
% 5.35/1.89 | (84) all_29_3_25 = all_0_10_10
% 5.35/1.89 |
% 5.35/1.89 +-Applying beta-rule and splitting (76), into two cases.
% 5.35/1.89 |-Branch one:
% 5.35/1.89 | (85) ~ (all_29_3_25 = all_0_10_10)
% 5.35/1.89 |
% 5.35/1.89 | Equations (84) can reduce 85 to:
% 5.35/1.89 | (86) $false
% 5.35/1.89 |
% 5.35/1.89 |-The branch is then unsatisfiable
% 5.35/1.89 |-Branch two:
% 5.35/1.89 | (84) all_29_3_25 = all_0_10_10
% 5.35/1.89 | (88) all_17_3_20 = all_0_9_9 & ! [v0] : ! [v1] : ( ~ (apply(all_0_10_10, v0) = v1) | ~ in(v0, all_0_9_9) | apply(all_0_11_11, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, all_0_9_9) | apply(all_0_10_10, v0) = v1)
% 5.35/1.89 |
% 5.35/1.89 | Applying alpha-rule on (88) yields:
% 5.35/1.89 | (89) all_17_3_20 = all_0_9_9
% 5.35/1.89 | (90) ! [v0] : ! [v1] : ( ~ (apply(all_0_10_10, v0) = v1) | ~ in(v0, all_0_9_9) | apply(all_0_11_11, v0) = v1)
% 5.35/1.89 | (91) ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, all_0_9_9) | apply(all_0_10_10, v0) = v1)
% 5.35/1.89 |
% 5.35/1.89 | From (89) and (72) follows:
% 5.35/1.89 | (92) set_intersection2(all_0_13_13, all_0_8_8) = all_0_9_9
% 5.35/1.89 |
% 5.35/1.89 +-Applying beta-rule and splitting (53), into two cases.
% 5.35/1.89 |-Branch one:
% 5.35/1.89 | (93) in(all_0_12_12, all_0_8_8) & in(all_0_12_12, all_0_13_13) & ~ in(all_0_12_12, all_0_9_9)
% 5.35/1.89 |
% 5.35/1.89 | Applying alpha-rule on (93) yields:
% 5.35/1.89 | (94) in(all_0_12_12, all_0_8_8)
% 5.35/1.89 | (95) in(all_0_12_12, all_0_13_13)
% 5.35/1.89 | (96) ~ in(all_0_12_12, all_0_9_9)
% 5.35/1.89 |
% 5.35/1.89 | Instantiating formula (18) with all_0_12_12, all_0_9_9, all_0_8_8, all_0_13_13 and discharging atoms set_intersection2(all_0_13_13, all_0_8_8) = all_0_9_9, in(all_0_12_12, all_0_8_8), in(all_0_12_12, all_0_13_13), ~ in(all_0_12_12, all_0_9_9), yields:
% 5.35/1.90 | (97) $false
% 5.35/1.90 |
% 5.35/1.90 |-The branch is then unsatisfiable
% 5.35/1.90 |-Branch two:
% 5.35/1.90 | (98) in(all_0_12_12, all_0_9_9) & ( ~ in(all_0_12_12, all_0_8_8) | ~ in(all_0_12_12, all_0_13_13))
% 5.35/1.90 |
% 5.35/1.90 | Applying alpha-rule on (98) yields:
% 5.35/1.90 | (99) in(all_0_12_12, all_0_9_9)
% 5.35/1.90 | (100) ~ in(all_0_12_12, all_0_8_8) | ~ in(all_0_12_12, all_0_13_13)
% 5.35/1.90 |
% 5.35/1.90 | Instantiating formula (19) with all_0_12_12, all_0_9_9, all_0_8_8, all_0_13_13 and discharging atoms set_intersection2(all_0_13_13, all_0_8_8) = all_0_9_9, in(all_0_12_12, all_0_9_9), yields:
% 5.35/1.90 | (94) in(all_0_12_12, all_0_8_8)
% 5.35/1.90 |
% 5.35/1.90 | Instantiating formula (57) with all_0_12_12, all_0_9_9, all_0_8_8, all_0_13_13 and discharging atoms set_intersection2(all_0_13_13, all_0_8_8) = all_0_9_9, in(all_0_12_12, all_0_9_9), yields:
% 5.35/1.90 | (95) in(all_0_12_12, all_0_13_13)
% 5.35/1.90 |
% 5.35/1.90 +-Applying beta-rule and splitting (100), into two cases.
% 5.35/1.90 |-Branch one:
% 5.35/1.90 | (103) ~ in(all_0_12_12, all_0_8_8)
% 5.35/1.90 |
% 5.35/1.90 | Using (94) and (103) yields:
% 5.35/1.90 | (97) $false
% 5.35/1.90 |
% 5.35/1.90 |-The branch is then unsatisfiable
% 5.35/1.90 |-Branch two:
% 5.35/1.90 | (94) in(all_0_12_12, all_0_8_8)
% 5.35/1.90 | (106) ~ in(all_0_12_12, all_0_13_13)
% 5.35/1.90 |
% 5.35/1.90 | Using (95) and (106) yields:
% 5.35/1.90 | (97) $false
% 5.35/1.90 |
% 5.35/1.90 |-The branch is then unsatisfiable
% 5.35/1.90 % SZS output end Proof for theBenchmark
% 5.35/1.90
% 5.35/1.90 1286ms
%------------------------------------------------------------------------------