TSTP Solution File: SET804+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET804+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.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 00:22:11 EDT 2022
% Result : Theorem 2.62s 1.31s
% Output : Proof 3.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET804+4 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n006.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 Jul 10 12:53:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.66/0.64 ____ _
% 0.66/0.64 ___ / __ \_____(_)___ ________ __________
% 0.66/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.66/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.66/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.66/0.64
% 0.66/0.64 A Theorem Prover for First-Order Logic
% 0.66/0.64 (ePrincess v.1.0)
% 0.66/0.64
% 0.66/0.64 (c) Philipp Rümmer, 2009-2015
% 0.66/0.64 (c) Peter Backeman, 2014-2015
% 0.66/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.66/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.66/0.64 Bug reports to peter@backeman.se
% 0.66/0.64
% 0.66/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.66/0.64
% 0.66/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.80/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.68/0.98 Prover 0: Preprocessing ...
% 2.20/1.15 Prover 0: Warning: ignoring some quantifiers
% 2.28/1.18 Prover 0: Constructing countermodel ...
% 2.62/1.31 Prover 0: proved (617ms)
% 2.62/1.31
% 2.62/1.31 No countermodel exists, formula is valid
% 2.62/1.31 % SZS status Theorem for theBenchmark
% 2.62/1.31
% 2.62/1.31 Generating proof ... Warning: ignoring some quantifiers
% 3.73/1.55 found it (size 13)
% 3.73/1.55
% 3.73/1.55 % SZS output start Proof for theBenchmark
% 3.73/1.55 Assumed formulas after preprocessing and simplification:
% 3.73/1.55 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v3 = v2) & min(v3, v0, v1) & min(v2, v0, v1) & least(v4, v0, v1) & order(v0, v1) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ greatest_lower_bound(v5, v6, v7, v8) | ~ lower_bound(v9, v7, v6) | ~ member(v9, v8) | apply(v7, v9, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ least_upper_bound(v5, v6, v7, v8) | ~ upper_bound(v9, v7, v6) | ~ member(v9, v8) | apply(v7, v5, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ apply(v5, v8, v9) | ~ apply(v5, v7, v8) | ~ member(v9, v6) | ~ member(v8, v6) | ~ member(v7, v6) | ~ order(v5, v6) | apply(v5, v7, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ min(v7, v5, v6) | ~ apply(v5, v8, v7) | ~ member(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ max(v7, v5, v6) | ~ apply(v5, v7, v8) | ~ member(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ apply(v5, v8, v7) | ~ apply(v5, v7, v8) | ~ member(v8, v6) | ~ member(v7, v6) | ~ order(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ greatest_lower_bound(v5, v6, v7, v8) | lower_bound(v5, v7, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ greatest_lower_bound(v5, v6, v7, v8) | member(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ least_upper_bound(v5, v6, v7, v8) | upper_bound(v5, v7, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ least_upper_bound(v5, v6, v7, v8) | member(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ least(v7, v5, v6) | ~ member(v8, v6) | apply(v5, v7, v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ greatest(v7, v5, v6) | ~ member(v8, v6) | apply(v5, v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ lower_bound(v7, v5, v6) | ~ member(v8, v6) | apply(v5, v7, v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ upper_bound(v7, v5, v6) | ~ member(v8, v6) | apply(v5, v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ total_order(v5, v6) | ~ member(v8, v6) | ~ member(v7, v6) | apply(v5, v8, v7) | apply(v5, v7, v8)) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ lower_bound(v6, v8, v7) | ~ member(v6, v7) | greatest_lower_bound(v6, v7, v8, v5) | ? [v9] : (lower_bound(v9, v8, v7) & member(v9, v5) & ~ apply(v8, v9, v6))) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ upper_bound(v6, v8, v7) | ~ member(v6, v7) | least_upper_bound(v6, v7, v8, v5) | ? [v9] : (upper_bound(v9, v8, v7) & member(v9, v5) & ~ apply(v8, v6, v9))) & ! [v5] : ! [v6] : ! [v7] : ( ~ min(v7, v5, v6) | member(v7, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ max(v7, v5, v6) | member(v7, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ least(v7, v5, v6) | member(v7, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ greatest(v7, v5, v6) | member(v7, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ member(v7, v6) | ~ order(v5, v6) | apply(v5, v7, v7)) & ? [v5] : ! [v6] : ! [v7] : ( ~ member(v7, v6) | min(v7, v5, v6) | ? [v8] : ( ~ (v8 = v7) & apply(v5, v8, v7) & member(v8, v6))) & ? [v5] : ! [v6] : ! [v7] : ( ~ member(v7, v6) | max(v7, v5, v6) | ? [v8] : ( ~ (v8 = v7) & apply(v5, v7, v8) & member(v8, v6))) & ? [v5] : ! [v6] : ! [v7] : ( ~ member(v7, v6) | least(v7, v5, v6) | ? [v8] : (member(v8, v6) & ~ apply(v5, v7, v8))) & ? [v5] : ! [v6] : ! [v7] : ( ~ member(v7, v6) | greatest(v7, v5, v6) | ? [v8] : (member(v8, v6) & ~ apply(v5, v8, v7))) & ! [v5] : ! [v6] : ( ~ total_order(v5, v6) | order(v5, v6)) & ! [v5] : ! [v6] : ( ~ order(v5, v6) | total_order(v5, v6) | ? [v7] : ? [v8] : (member(v8, v6) & member(v7, v6) & ~ apply(v5, v8, v7) & ~ apply(v5, v7, v8))) & ? [v5] : ? [v6] : ? [v7] : (lower_bound(v7, v5, v6) | ? [v8] : (member(v8, v6) & ~ apply(v5, v7, v8))) & ? [v5] : ? [v6] : ? [v7] : (upper_bound(v7, v5, v6) | ? [v8] : (member(v8, v6) & ~ apply(v5, v8, v7))) & ? [v5] : ? [v6] : (order(v5, v6) | ? [v7] : ? [v8] : ? [v9] : (( ~ (v8 = v7) & apply(v5, v8, v7) & apply(v5, v7, v8) & member(v8, v6) & member(v7, v6)) | (apply(v5, v8, v9) & apply(v5, v7, v8) & member(v9, v6) & member(v8, v6) & member(v7, v6) & ~ apply(v5, v7, v9)) | (member(v7, v6) & ~ apply(v5, v7, v7)))))
% 3.87/1.58 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.87/1.58 | (1) ~ (all_0_1_1 = all_0_2_2) & min(all_0_1_1, all_0_4_4, all_0_3_3) & min(all_0_2_2, all_0_4_4, all_0_3_3) & least(all_0_0_0, all_0_4_4, all_0_3_3) & order(all_0_4_4, all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ greatest_lower_bound(v0, v1, v2, v3) | ~ lower_bound(v4, v2, v1) | ~ member(v4, v3) | apply(v2, v4, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ least_upper_bound(v0, v1, v2, v3) | ~ upper_bound(v4, v2, v1) | ~ member(v4, v3) | apply(v2, v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ apply(v0, v3, v4) | ~ apply(v0, v2, v3) | ~ member(v4, v1) | ~ member(v3, v1) | ~ member(v2, v1) | ~ order(v0, v1) | apply(v0, v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ min(v2, v0, v1) | ~ apply(v0, v3, v2) | ~ member(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ max(v2, v0, v1) | ~ apply(v0, v2, v3) | ~ member(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ apply(v0, v3, v2) | ~ apply(v0, v2, v3) | ~ member(v3, v1) | ~ member(v2, v1) | ~ order(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ greatest_lower_bound(v0, v1, v2, v3) | lower_bound(v0, v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ greatest_lower_bound(v0, v1, v2, v3) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ least_upper_bound(v0, v1, v2, v3) | upper_bound(v0, v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ least_upper_bound(v0, v1, v2, v3) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ least(v2, v0, v1) | ~ member(v3, v1) | apply(v0, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ greatest(v2, v0, v1) | ~ member(v3, v1) | apply(v0, v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ lower_bound(v2, v0, v1) | ~ member(v3, v1) | apply(v0, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ upper_bound(v2, v0, v1) | ~ member(v3, v1) | apply(v0, v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ total_order(v0, v1) | ~ member(v3, v1) | ~ member(v2, v1) | apply(v0, v3, v2) | apply(v0, v2, v3)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ lower_bound(v1, v3, v2) | ~ member(v1, v2) | greatest_lower_bound(v1, v2, v3, v0) | ? [v4] : (lower_bound(v4, v3, v2) & member(v4, v0) & ~ apply(v3, v4, v1))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ upper_bound(v1, v3, v2) | ~ member(v1, v2) | least_upper_bound(v1, v2, v3, v0) | ? [v4] : (upper_bound(v4, v3, v2) & member(v4, v0) & ~ apply(v3, v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ min(v2, v0, v1) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ max(v2, v0, v1) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ least(v2, v0, v1) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ greatest(v2, v0, v1) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | ~ order(v0, v1) | apply(v0, v2, v2)) & ? [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | min(v2, v0, v1) | ? [v3] : ( ~ (v3 = v2) & apply(v0, v3, v2) & member(v3, v1))) & ? [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | max(v2, v0, v1) | ? [v3] : ( ~ (v3 = v2) & apply(v0, v2, v3) & member(v3, v1))) & ? [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | least(v2, v0, v1) | ? [v3] : (member(v3, v1) & ~ apply(v0, v2, v3))) & ? [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | greatest(v2, v0, v1) | ? [v3] : (member(v3, v1) & ~ apply(v0, v3, v2))) & ! [v0] : ! [v1] : ( ~ total_order(v0, v1) | order(v0, v1)) & ! [v0] : ! [v1] : ( ~ order(v0, v1) | total_order(v0, v1) | ? [v2] : ? [v3] : (member(v3, v1) & member(v2, v1) & ~ apply(v0, v3, v2) & ~ apply(v0, v2, v3))) & ? [v0] : ? [v1] : ? [v2] : (lower_bound(v2, v0, v1) | ? [v3] : (member(v3, v1) & ~ apply(v0, v2, v3))) & ? [v0] : ? [v1] : ? [v2] : (upper_bound(v2, v0, v1) | ? [v3] : (member(v3, v1) & ~ apply(v0, v3, v2))) & ? [v0] : ? [v1] : (order(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v3 = v2) & apply(v0, v3, v2) & apply(v0, v2, v3) & member(v3, v1) & member(v2, v1)) | (apply(v0, v3, v4) & apply(v0, v2, v3) & member(v4, v1) & member(v3, v1) & member(v2, v1) & ~ apply(v0, v2, v4)) | (member(v2, v1) & ~ apply(v0, v2, v2))))
% 3.87/1.59 |
% 3.87/1.59 | Applying alpha-rule on (1) yields:
% 3.87/1.59 | (2) ! [v0] : ! [v1] : ( ~ total_order(v0, v1) | order(v0, v1))
% 3.87/1.59 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ least_upper_bound(v0, v1, v2, v3) | member(v0, v1))
% 3.87/1.59 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ greatest_lower_bound(v0, v1, v2, v3) | lower_bound(v0, v2, v1))
% 3.87/1.59 | (5) ! [v0] : ! [v1] : ( ~ order(v0, v1) | total_order(v0, v1) | ? [v2] : ? [v3] : (member(v3, v1) & member(v2, v1) & ~ apply(v0, v3, v2) & ~ apply(v0, v2, v3)))
% 3.87/1.59 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ least_upper_bound(v0, v1, v2, v3) | upper_bound(v0, v2, v1))
% 3.87/1.59 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ min(v2, v0, v1) | ~ apply(v0, v3, v2) | ~ member(v3, v1))
% 3.87/1.59 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | ~ order(v0, v1) | apply(v0, v2, v2))
% 3.87/1.59 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ greatest(v2, v0, v1) | ~ member(v3, v1) | apply(v0, v3, v2))
% 3.87/1.59 | (10) least(all_0_0_0, all_0_4_4, all_0_3_3)
% 3.87/1.59 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ total_order(v0, v1) | ~ member(v3, v1) | ~ member(v2, v1) | apply(v0, v3, v2) | apply(v0, v2, v3))
% 3.87/1.59 | (12) min(all_0_1_1, all_0_4_4, all_0_3_3)
% 3.87/1.59 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ apply(v0, v3, v4) | ~ apply(v0, v2, v3) | ~ member(v4, v1) | ~ member(v3, v1) | ~ member(v2, v1) | ~ order(v0, v1) | apply(v0, v2, v4))
% 3.87/1.59 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ greatest_lower_bound(v0, v1, v2, v3) | ~ lower_bound(v4, v2, v1) | ~ member(v4, v3) | apply(v2, v4, v0))
% 3.87/1.59 | (15) min(all_0_2_2, all_0_4_4, all_0_3_3)
% 3.87/1.59 | (16) order(all_0_4_4, all_0_3_3)
% 3.87/1.60 | (17) ? [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | least(v2, v0, v1) | ? [v3] : (member(v3, v1) & ~ apply(v0, v2, v3)))
% 3.87/1.60 | (18) ? [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | max(v2, v0, v1) | ? [v3] : ( ~ (v3 = v2) & apply(v0, v2, v3) & member(v3, v1)))
% 3.87/1.60 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ least(v2, v0, v1) | member(v2, v1))
% 3.87/1.60 | (20) ? [v0] : ? [v1] : (order(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v3 = v2) & apply(v0, v3, v2) & apply(v0, v2, v3) & member(v3, v1) & member(v2, v1)) | (apply(v0, v3, v4) & apply(v0, v2, v3) & member(v4, v1) & member(v3, v1) & member(v2, v1) & ~ apply(v0, v2, v4)) | (member(v2, v1) & ~ apply(v0, v2, v2))))
% 3.87/1.60 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ greatest_lower_bound(v0, v1, v2, v3) | member(v0, v1))
% 3.87/1.60 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ least(v2, v0, v1) | ~ member(v3, v1) | apply(v0, v2, v3))
% 3.87/1.60 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ apply(v0, v3, v2) | ~ apply(v0, v2, v3) | ~ member(v3, v1) | ~ member(v2, v1) | ~ order(v0, v1))
% 3.87/1.60 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ upper_bound(v2, v0, v1) | ~ member(v3, v1) | apply(v0, v3, v2))
% 3.87/1.60 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ greatest(v2, v0, v1) | member(v2, v1))
% 3.87/1.60 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ lower_bound(v2, v0, v1) | ~ member(v3, v1) | apply(v0, v2, v3))
% 3.87/1.60 | (27) ? [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | min(v2, v0, v1) | ? [v3] : ( ~ (v3 = v2) & apply(v0, v3, v2) & member(v3, v1)))
% 3.87/1.60 | (28) ? [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | greatest(v2, v0, v1) | ? [v3] : (member(v3, v1) & ~ apply(v0, v3, v2)))
% 3.87/1.60 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ max(v2, v0, v1) | member(v2, v1))
% 3.87/1.60 | (30) ? [v0] : ? [v1] : ? [v2] : (lower_bound(v2, v0, v1) | ? [v3] : (member(v3, v1) & ~ apply(v0, v2, v3)))
% 3.87/1.60 | (31) ~ (all_0_1_1 = all_0_2_2)
% 3.87/1.60 | (32) ? [v0] : ? [v1] : ? [v2] : (upper_bound(v2, v0, v1) | ? [v3] : (member(v3, v1) & ~ apply(v0, v3, v2)))
% 3.87/1.60 | (33) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ upper_bound(v1, v3, v2) | ~ member(v1, v2) | least_upper_bound(v1, v2, v3, v0) | ? [v4] : (upper_bound(v4, v3, v2) & member(v4, v0) & ~ apply(v3, v1, v4)))
% 3.87/1.60 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ max(v2, v0, v1) | ~ apply(v0, v2, v3) | ~ member(v3, v1))
% 3.87/1.60 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ min(v2, v0, v1) | member(v2, v1))
% 3.87/1.60 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ least_upper_bound(v0, v1, v2, v3) | ~ upper_bound(v4, v2, v1) | ~ member(v4, v3) | apply(v2, v0, v4))
% 3.87/1.60 | (37) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ lower_bound(v1, v3, v2) | ~ member(v1, v2) | greatest_lower_bound(v1, v2, v3, v0) | ? [v4] : (lower_bound(v4, v3, v2) & member(v4, v0) & ~ apply(v3, v4, v1)))
% 3.87/1.60 |
% 3.87/1.60 | Instantiating formula (35) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms min(all_0_1_1, all_0_4_4, all_0_3_3), yields:
% 3.87/1.60 | (38) member(all_0_1_1, all_0_3_3)
% 3.87/1.60 |
% 3.87/1.60 | Instantiating formula (35) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms min(all_0_2_2, all_0_4_4, all_0_3_3), yields:
% 3.87/1.60 | (39) member(all_0_2_2, all_0_3_3)
% 3.87/1.60 |
% 3.87/1.60 | Instantiating formula (19) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms least(all_0_0_0, all_0_4_4, all_0_3_3), yields:
% 3.87/1.61 | (40) member(all_0_0_0, all_0_3_3)
% 3.87/1.61 |
% 3.87/1.61 | Instantiating formula (22) with all_0_1_1, all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms least(all_0_0_0, all_0_4_4, all_0_3_3), member(all_0_1_1, all_0_3_3), yields:
% 3.87/1.61 | (41) apply(all_0_4_4, all_0_0_0, all_0_1_1)
% 3.87/1.61 |
% 3.87/1.61 | Instantiating formula (22) with all_0_2_2, all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms least(all_0_0_0, all_0_4_4, all_0_3_3), member(all_0_2_2, all_0_3_3), yields:
% 3.87/1.61 | (42) apply(all_0_4_4, all_0_0_0, all_0_2_2)
% 3.87/1.61 |
% 3.87/1.61 | Instantiating formula (7) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms min(all_0_1_1, all_0_4_4, all_0_3_3), apply(all_0_4_4, all_0_0_0, all_0_1_1), member(all_0_0_0, all_0_3_3), yields:
% 3.87/1.61 | (43) all_0_0_0 = all_0_1_1
% 3.87/1.61 |
% 3.87/1.61 | Instantiating formula (7) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms min(all_0_2_2, all_0_4_4, all_0_3_3), apply(all_0_4_4, all_0_0_0, all_0_2_2), member(all_0_0_0, all_0_3_3), yields:
% 3.87/1.61 | (44) all_0_0_0 = all_0_2_2
% 3.87/1.61 |
% 3.87/1.61 | Combining equations (43,44) yields a new equation:
% 3.87/1.61 | (45) all_0_1_1 = all_0_2_2
% 3.87/1.61 |
% 3.87/1.61 | Simplifying 45 yields:
% 3.87/1.61 | (46) all_0_1_1 = all_0_2_2
% 3.87/1.61 |
% 3.87/1.61 | Equations (46) can reduce 31 to:
% 3.87/1.61 | (47) $false
% 3.87/1.61 |
% 3.87/1.61 |-The branch is then unsatisfiable
% 3.87/1.61 % SZS output end Proof for theBenchmark
% 3.87/1.61
% 3.87/1.61 958ms
%------------------------------------------------------------------------------