TSTP Solution File: KRS162+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS162+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 : Sun Jul 17 02:56:45 EDT 2022
% Result : Theorem 5.55s 1.92s
% Output : Proof 8.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS162+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n019.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 : Tue Jun 7 20:08:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.56/0.58 ____ _
% 0.56/0.58 ___ / __ \_____(_)___ ________ __________
% 0.56/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.58
% 0.56/0.58 A Theorem Prover for First-Order Logic
% 0.56/0.58 (ePrincess v.1.0)
% 0.56/0.58
% 0.56/0.58 (c) Philipp Rümmer, 2009-2015
% 0.56/0.58 (c) Peter Backeman, 2014-2015
% 0.56/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.59 Bug reports to peter@backeman.se
% 0.56/0.59
% 0.56/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.59
% 0.56/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/0.93 Prover 0: Preprocessing ...
% 1.87/1.06 Prover 0: Warning: ignoring some quantifiers
% 1.87/1.08 Prover 0: Constructing countermodel ...
% 2.08/1.16 Prover 0: gave up
% 2.08/1.16 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.35/1.20 Prover 1: Preprocessing ...
% 3.01/1.36 Prover 1: Constructing countermodel ...
% 5.55/1.92 Prover 1: proved (760ms)
% 5.55/1.92
% 5.55/1.92 No countermodel exists, formula is valid
% 5.55/1.92 % SZS status Theorem for theBenchmark
% 5.55/1.92
% 5.55/1.92 Generating proof ... found it (size 103)
% 8.18/2.59
% 8.18/2.59 % SZS output start Proof for theBenchmark
% 8.18/2.59 Assumed formulas after preprocessing and simplification:
% 8.18/2.59 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (rr(v14, v13) = v12) | ~ (rr(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (rq(v14, v13) = v12) | ~ (rq(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (rp(v14, v13) = v12) | ~ (rp(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (rr(v12, v11) = v13) | ~ (rr(v12, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (rr(v11, v12) = v13) | ~ (rr(v11, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (rq(v12, v11) = v13) | ~ (rq(v12, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (rq(v11, v12) = v13) | ~ (rq(v11, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (rp(v12, v11) = v13) | ~ (rp(v12, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (rp(v11, v12) = v13) | ~ (rp(v11, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (xsd_string(v13) = v12) | ~ (xsd_string(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (xsd_integer(v13) = v12) | ~ (xsd_integer(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (cowlThing(v13) = v12) | ~ (cowlThing(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (cowlNothing(v13) = v12) | ~ (cowlNothing(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (cB(v13) = v12) | ~ (cB(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (cA(v13) = v12) | ~ (cA(v13) = v11)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (xsd_string(v11) = v12) | ~ (xsd_string(v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (xsd_string(v11) = v12) | xsd_integer(v11) = 0) & ! [v11] : ! [v12] : (v12 = 0 | ~ (xsd_integer(v11) = v12) | ~ (xsd_integer(v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (cowlThing(v11) = v12) | ~ (cowlThing(v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (cowlThing(v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (cowlNothing(v11) = v12) | ~ (cowlNothing(v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (cB(v11) = v12) | ~ (cB(v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (cA(v11) = v12) | ~ (cA(v11) = 0)) & ! [v11] : ! [v12] : ( ~ (rq(v11, v12) = 0) | rr(v11, v12) = 0) & ! [v11] : ! [v12] : ( ~ (rq(v11, v12) = 0) | cB(v12) = 0) & ! [v11] : ! [v12] : ( ~ (rp(v11, v12) = 0) | rr(v11, v12) = 0) & ! [v11] : ! [v12] : ( ~ (rp(v11, v12) = 0) | cA(v12) = 0) & ! [v11] : ( ~ (xsd_string(v11) = 0) | ? [v12] : ( ~ (v12 = 0) & xsd_integer(v11) = v12)) & ! [v11] : ~ (cowlNothing(v11) = 0) & ! [v11] : ( ~ (cB(v11) = 0) | ? [v12] : ( ~ (v12 = 0) & cA(v11) = v12)) & ((v10 = 0 & v9 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & ~ (v8 = v7) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v2 = v1) & rq(v0, v3) = 0 & rq(v0, v2) = 0 & rq(v0, v1) = 0 & rp(v0, v8) = 0 & rp(v0, v7) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | v15 = v13 | v15 = v12 | v15 = v11 | v14 = v13 | v14 = v12 | v14 = v11 | v13 = v12 | v13 = v11 | v12 = v11 | ~ (rr(v0, v15) = 0) | ~ (rr(v0, v14) = 0) | ~ (rr(v0, v13) = 0) | ~ (rr(v0, v12) = 0) | ~ (rr(v0, v11) = 0))) | (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) | (cowlThing(v0) = v1 & cowlNothing(v0) = v2 & ( ~ (v1 = 0) | v2 = 0))))
% 8.66/2.62 | 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:
% 8.66/2.62 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rr(v3, v2) = v1) | ~ (rr(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rq(v3, v2) = v1) | ~ (rq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rr(v1, v0) = v2) | ~ (rr(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rr(v0, v1) = v2) | ~ (rr(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rq(v1, v0) = v2) | ~ (rq(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rq(v0, v1) = v2) | ~ (rq(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ (rp(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v0, v1) = v2) | ~ (rp(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cB(v2) = v1) | ~ (cB(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cB(v0) = v1) | ~ (cB(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (cA(v0) = 0)) & ! [v0] : ! [v1] : ( ~ (rq(v0, v1) = 0) | rr(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (rq(v0, v1) = 0) | cB(v1) = 0) & ! [v0] : ! [v1] : ( ~ (rp(v0, v1) = 0) | rr(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (rp(v0, v1) = 0) | cA(v1) = 0) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ! [v0] : ( ~ (cB(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cA(v0) = v1)) & ((all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_4_4 = 0 & all_0_5_5 = 0 & all_0_6_6 = 0 & ~ (all_0_2_2 = all_0_3_3) & ~ (all_0_7_7 = all_0_8_8) & ~ (all_0_7_7 = all_0_9_9) & ~ (all_0_8_8 = all_0_9_9) & rq(all_0_10_10, all_0_7_7) = 0 & rq(all_0_10_10, all_0_8_8) = 0 & rq(all_0_10_10, all_0_9_9) = 0 & rp(all_0_10_10, all_0_2_2) = 0 & rp(all_0_10_10, all_0_3_3) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | v4 = v2 | v4 = v1 | v4 = v0 | v3 = v2 | v3 = v1 | v3 = v0 | v2 = v1 | v2 = v0 | v1 = v0 | ~ (rr(all_0_10_10, v4) = 0) | ~ (rr(all_0_10_10, v3) = 0) | ~ (rr(all_0_10_10, v2) = 0) | ~ (rr(all_0_10_10, v1) = 0) | ~ (rr(all_0_10_10, v0) = 0))) | (xsd_string(all_0_10_10) = all_0_9_9 & xsd_integer(all_0_10_10) = all_0_8_8 & ((all_0_8_8 = 0 & all_0_9_9 = 0) | ( ~ (all_0_8_8 = 0) & ~ (all_0_9_9 = 0)))) | (cowlThing(all_0_10_10) = all_0_9_9 & cowlNothing(all_0_10_10) = all_0_8_8 & ( ~ (all_0_9_9 = 0) | all_0_8_8 = 0)))
% 8.66/2.63 |
% 8.66/2.63 | Applying alpha-rule on (1) yields:
% 8.66/2.63 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0))
% 8.66/2.63 | (3) ! [v0] : ! [v1] : ( ~ (rp(v0, v1) = 0) | cA(v1) = 0)
% 8.66/2.63 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0))
% 8.66/2.63 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0))
% 8.66/2.63 | (6) ! [v0] : ~ (cowlNothing(v0) = 0)
% 8.66/2.63 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0))
% 8.66/2.63 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ (rp(v1, v0) = 0))
% 8.66/2.63 | (9) ! [v0] : ! [v1] : ( ~ (rp(v0, v1) = 0) | rr(v0, v1) = 0)
% 8.66/2.63 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rr(v3, v2) = v1) | ~ (rr(v3, v2) = v0))
% 8.66/2.63 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v0, v1) = v2) | ~ (rp(v0, v1) = 0))
% 8.66/2.63 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rq(v3, v2) = v1) | ~ (rq(v3, v2) = v0))
% 8.66/2.63 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cB(v2) = v1) | ~ (cB(v2) = v0))
% 8.66/2.63 | (14) ! [v0] : ! [v1] : ( ~ (rq(v0, v1) = 0) | cB(v1) = 0)
% 8.66/2.63 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 8.66/2.63 | (16) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 8.66/2.63 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 8.66/2.64 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rr(v1, v0) = v2) | ~ (rr(v1, v0) = 0))
% 8.66/2.64 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rq(v0, v1) = v2) | ~ (rq(v0, v1) = 0))
% 8.66/2.64 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (cA(v0) = 0))
% 8.66/2.64 | (21) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0))
% 8.66/2.64 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rr(v0, v1) = v2) | ~ (rr(v0, v1) = 0))
% 8.66/2.64 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rq(v1, v0) = v2) | ~ (rq(v1, v0) = 0))
% 8.66/2.64 | (24) ! [v0] : ( ~ (cB(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cA(v0) = v1))
% 8.66/2.64 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 8.66/2.64 | (26) (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_4_4 = 0 & all_0_5_5 = 0 & all_0_6_6 = 0 & ~ (all_0_2_2 = all_0_3_3) & ~ (all_0_7_7 = all_0_8_8) & ~ (all_0_7_7 = all_0_9_9) & ~ (all_0_8_8 = all_0_9_9) & rq(all_0_10_10, all_0_7_7) = 0 & rq(all_0_10_10, all_0_8_8) = 0 & rq(all_0_10_10, all_0_9_9) = 0 & rp(all_0_10_10, all_0_2_2) = 0 & rp(all_0_10_10, all_0_3_3) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | v4 = v2 | v4 = v1 | v4 = v0 | v3 = v2 | v3 = v1 | v3 = v0 | v2 = v1 | v2 = v0 | v1 = v0 | ~ (rr(all_0_10_10, v4) = 0) | ~ (rr(all_0_10_10, v3) = 0) | ~ (rr(all_0_10_10, v2) = 0) | ~ (rr(all_0_10_10, v1) = 0) | ~ (rr(all_0_10_10, v0) = 0))) | (xsd_string(all_0_10_10) = all_0_9_9 & xsd_integer(all_0_10_10) = all_0_8_8 & ((all_0_8_8 = 0 & all_0_9_9 = 0) | ( ~ (all_0_8_8 = 0) & ~ (all_0_9_9 = 0)))) | (cowlThing(all_0_10_10) = all_0_9_9 & cowlNothing(all_0_10_10) = all_0_8_8 & ( ~ (all_0_9_9 = 0) | all_0_8_8 = 0))
% 8.66/2.64 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 8.66/2.64 | (28) ! [v0] : ! [v1] : ( ~ (rq(v0, v1) = 0) | rr(v0, v1) = 0)
% 8.66/2.64 | (29) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 8.66/2.64 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 8.66/2.64 | (31) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0))
% 8.66/2.64 | (32) ! [v0] : ! [v1] : (v1 = 0 | ~ (cB(v0) = v1) | ~ (cB(v0) = 0))
% 8.66/2.64 |
% 8.66/2.64 +-Applying beta-rule and splitting (26), into two cases.
% 8.66/2.64 |-Branch one:
% 8.66/2.64 | (33) (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_4_4 = 0 & all_0_5_5 = 0 & all_0_6_6 = 0 & ~ (all_0_2_2 = all_0_3_3) & ~ (all_0_7_7 = all_0_8_8) & ~ (all_0_7_7 = all_0_9_9) & ~ (all_0_8_8 = all_0_9_9) & rq(all_0_10_10, all_0_7_7) = 0 & rq(all_0_10_10, all_0_8_8) = 0 & rq(all_0_10_10, all_0_9_9) = 0 & rp(all_0_10_10, all_0_2_2) = 0 & rp(all_0_10_10, all_0_3_3) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | v4 = v2 | v4 = v1 | v4 = v0 | v3 = v2 | v3 = v1 | v3 = v0 | v2 = v1 | v2 = v0 | v1 = v0 | ~ (rr(all_0_10_10, v4) = 0) | ~ (rr(all_0_10_10, v3) = 0) | ~ (rr(all_0_10_10, v2) = 0) | ~ (rr(all_0_10_10, v1) = 0) | ~ (rr(all_0_10_10, v0) = 0))) | (xsd_string(all_0_10_10) = all_0_9_9 & xsd_integer(all_0_10_10) = all_0_8_8 & ((all_0_8_8 = 0 & all_0_9_9 = 0) | ( ~ (all_0_8_8 = 0) & ~ (all_0_9_9 = 0))))
% 8.66/2.64 |
% 8.66/2.64 +-Applying beta-rule and splitting (33), into two cases.
% 8.66/2.64 |-Branch one:
% 8.66/2.64 | (34) all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_4_4 = 0 & all_0_5_5 = 0 & all_0_6_6 = 0 & ~ (all_0_2_2 = all_0_3_3) & ~ (all_0_7_7 = all_0_8_8) & ~ (all_0_7_7 = all_0_9_9) & ~ (all_0_8_8 = all_0_9_9) & rq(all_0_10_10, all_0_7_7) = 0 & rq(all_0_10_10, all_0_8_8) = 0 & rq(all_0_10_10, all_0_9_9) = 0 & rp(all_0_10_10, all_0_2_2) = 0 & rp(all_0_10_10, all_0_3_3) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | v4 = v2 | v4 = v1 | v4 = v0 | v3 = v2 | v3 = v1 | v3 = v0 | v2 = v1 | v2 = v0 | v1 = v0 | ~ (rr(all_0_10_10, v4) = 0) | ~ (rr(all_0_10_10, v3) = 0) | ~ (rr(all_0_10_10, v2) = 0) | ~ (rr(all_0_10_10, v1) = 0) | ~ (rr(all_0_10_10, v0) = 0))
% 8.66/2.64 |
% 8.66/2.64 | Applying alpha-rule on (34) yields:
% 8.66/2.64 | (35) all_0_4_4 = 0
% 8.66/2.64 | (36) all_0_6_6 = 0
% 8.66/2.64 | (37) rq(all_0_10_10, all_0_7_7) = 0
% 8.66/2.64 | (38) all_0_1_1 = 0
% 8.66/2.64 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | v4 = v2 | v4 = v1 | v4 = v0 | v3 = v2 | v3 = v1 | v3 = v0 | v2 = v1 | v2 = v0 | v1 = v0 | ~ (rr(all_0_10_10, v4) = 0) | ~ (rr(all_0_10_10, v3) = 0) | ~ (rr(all_0_10_10, v2) = 0) | ~ (rr(all_0_10_10, v1) = 0) | ~ (rr(all_0_10_10, v0) = 0))
% 8.66/2.65 | (40) rp(all_0_10_10, all_0_3_3) = 0
% 8.66/2.65 | (41) ~ (all_0_8_8 = all_0_9_9)
% 8.66/2.65 | (42) rq(all_0_10_10, all_0_8_8) = 0
% 8.66/2.65 | (43) ~ (all_0_2_2 = all_0_3_3)
% 8.66/2.65 | (44) all_0_5_5 = 0
% 8.66/2.65 | (45) ~ (all_0_7_7 = all_0_8_8)
% 8.66/2.65 | (46) all_0_0_0 = 0
% 8.66/2.65 | (47) ~ (all_0_7_7 = all_0_9_9)
% 8.66/2.65 | (48) rp(all_0_10_10, all_0_2_2) = 0
% 8.66/2.65 | (49) rq(all_0_10_10, all_0_9_9) = 0
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (28) with all_0_7_7, all_0_10_10 and discharging atoms rq(all_0_10_10, all_0_7_7) = 0, yields:
% 8.66/2.65 | (50) rr(all_0_10_10, all_0_7_7) = 0
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (14) with all_0_7_7, all_0_10_10 and discharging atoms rq(all_0_10_10, all_0_7_7) = 0, yields:
% 8.66/2.65 | (51) cB(all_0_7_7) = 0
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (28) with all_0_8_8, all_0_10_10 and discharging atoms rq(all_0_10_10, all_0_8_8) = 0, yields:
% 8.66/2.65 | (52) rr(all_0_10_10, all_0_8_8) = 0
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (14) with all_0_8_8, all_0_10_10 and discharging atoms rq(all_0_10_10, all_0_8_8) = 0, yields:
% 8.66/2.65 | (53) cB(all_0_8_8) = 0
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (28) with all_0_9_9, all_0_10_10 and discharging atoms rq(all_0_10_10, all_0_9_9) = 0, yields:
% 8.66/2.65 | (54) rr(all_0_10_10, all_0_9_9) = 0
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (14) with all_0_9_9, all_0_10_10 and discharging atoms rq(all_0_10_10, all_0_9_9) = 0, yields:
% 8.66/2.65 | (55) cB(all_0_9_9) = 0
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (9) with all_0_2_2, all_0_10_10 and discharging atoms rp(all_0_10_10, all_0_2_2) = 0, yields:
% 8.66/2.65 | (56) rr(all_0_10_10, all_0_2_2) = 0
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (3) with all_0_2_2, all_0_10_10 and discharging atoms rp(all_0_10_10, all_0_2_2) = 0, yields:
% 8.66/2.65 | (57) cA(all_0_2_2) = 0
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (9) with all_0_3_3, all_0_10_10 and discharging atoms rp(all_0_10_10, all_0_3_3) = 0, yields:
% 8.66/2.65 | (58) rr(all_0_10_10, all_0_3_3) = 0
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (3) with all_0_3_3, all_0_10_10 and discharging atoms rp(all_0_10_10, all_0_3_3) = 0, yields:
% 8.66/2.65 | (59) cA(all_0_3_3) = 0
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (39) with all_0_9_9, all_0_2_2, all_0_3_3, all_0_7_7, all_0_8_8 and discharging atoms rr(all_0_10_10, all_0_2_2) = 0, rr(all_0_10_10, all_0_3_3) = 0, rr(all_0_10_10, all_0_7_7) = 0, rr(all_0_10_10, all_0_8_8) = 0, rr(all_0_10_10, all_0_9_9) = 0, yields:
% 8.66/2.65 | (60) all_0_2_2 = all_0_3_3 | all_0_2_2 = all_0_7_7 | all_0_2_2 = all_0_8_8 | all_0_2_2 = all_0_9_9 | all_0_3_3 = all_0_7_7 | all_0_3_3 = all_0_8_8 | all_0_3_3 = all_0_9_9 | all_0_7_7 = all_0_8_8 | all_0_7_7 = all_0_9_9 | all_0_8_8 = all_0_9_9
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (24) with all_0_7_7 and discharging atoms cB(all_0_7_7) = 0, yields:
% 8.66/2.65 | (61) ? [v0] : ( ~ (v0 = 0) & cA(all_0_7_7) = v0)
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (24) with all_0_8_8 and discharging atoms cB(all_0_8_8) = 0, yields:
% 8.66/2.65 | (62) ? [v0] : ( ~ (v0 = 0) & cA(all_0_8_8) = v0)
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (24) with all_0_9_9 and discharging atoms cB(all_0_9_9) = 0, yields:
% 8.66/2.65 | (63) ? [v0] : ( ~ (v0 = 0) & cA(all_0_9_9) = v0)
% 8.66/2.65 |
% 8.66/2.65 | Instantiating (63) with all_18_0_11 yields:
% 8.66/2.65 | (64) ~ (all_18_0_11 = 0) & cA(all_0_9_9) = all_18_0_11
% 8.66/2.65 |
% 8.66/2.65 | Applying alpha-rule on (64) yields:
% 8.66/2.65 | (65) ~ (all_18_0_11 = 0)
% 8.66/2.65 | (66) cA(all_0_9_9) = all_18_0_11
% 8.66/2.65 |
% 8.66/2.65 | Instantiating (61) with all_20_0_12 yields:
% 8.66/2.65 | (67) ~ (all_20_0_12 = 0) & cA(all_0_7_7) = all_20_0_12
% 8.66/2.65 |
% 8.66/2.65 | Applying alpha-rule on (67) yields:
% 8.66/2.65 | (68) ~ (all_20_0_12 = 0)
% 8.66/2.65 | (69) cA(all_0_7_7) = all_20_0_12
% 8.66/2.65 |
% 8.66/2.65 | Instantiating (62) with all_22_0_13 yields:
% 8.66/2.65 | (70) ~ (all_22_0_13 = 0) & cA(all_0_8_8) = all_22_0_13
% 8.66/2.65 |
% 8.66/2.65 | Applying alpha-rule on (70) yields:
% 8.66/2.65 | (71) ~ (all_22_0_13 = 0)
% 8.66/2.65 | (72) cA(all_0_8_8) = all_22_0_13
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (20) with all_20_0_12, all_0_7_7 and discharging atoms cA(all_0_7_7) = all_20_0_12, yields:
% 8.66/2.65 | (73) all_20_0_12 = 0 | ~ (cA(all_0_7_7) = 0)
% 8.66/2.65 |
% 8.66/2.65 | Instantiating formula (20) with all_22_0_13, all_0_8_8 and discharging atoms cA(all_0_8_8) = all_22_0_13, yields:
% 8.66/2.65 | (74) all_22_0_13 = 0 | ~ (cA(all_0_8_8) = 0)
% 8.66/2.66 |
% 8.66/2.66 | Instantiating formula (20) with all_18_0_11, all_0_9_9 and discharging atoms cA(all_0_9_9) = all_18_0_11, yields:
% 8.66/2.66 | (75) all_18_0_11 = 0 | ~ (cA(all_0_9_9) = 0)
% 8.66/2.66 |
% 8.66/2.66 +-Applying beta-rule and splitting (75), into two cases.
% 8.66/2.66 |-Branch one:
% 8.66/2.66 | (76) ~ (cA(all_0_9_9) = 0)
% 8.66/2.66 |
% 8.66/2.66 | Using (57) and (76) yields:
% 8.66/2.66 | (77) ~ (all_0_2_2 = all_0_9_9)
% 8.66/2.66 |
% 8.66/2.66 | Using (59) and (76) yields:
% 8.66/2.66 | (78) ~ (all_0_3_3 = all_0_9_9)
% 8.66/2.66 |
% 8.66/2.66 +-Applying beta-rule and splitting (73), into two cases.
% 8.66/2.66 |-Branch one:
% 8.66/2.66 | (79) ~ (cA(all_0_7_7) = 0)
% 8.66/2.66 |
% 8.66/2.66 | Using (57) and (79) yields:
% 8.66/2.66 | (80) ~ (all_0_2_2 = all_0_7_7)
% 8.66/2.66 |
% 8.66/2.66 | Using (59) and (79) yields:
% 8.66/2.66 | (81) ~ (all_0_3_3 = all_0_7_7)
% 8.66/2.66 |
% 8.66/2.66 +-Applying beta-rule and splitting (74), into two cases.
% 8.66/2.66 |-Branch one:
% 8.66/2.66 | (82) ~ (cA(all_0_8_8) = 0)
% 8.66/2.66 |
% 8.66/2.66 | Using (57) and (82) yields:
% 8.66/2.66 | (83) ~ (all_0_2_2 = all_0_8_8)
% 8.66/2.66 |
% 8.66/2.66 | Using (59) and (82) yields:
% 8.66/2.66 | (84) ~ (all_0_3_3 = all_0_8_8)
% 8.66/2.66 |
% 8.66/2.66 +-Applying beta-rule and splitting (60), into two cases.
% 8.66/2.66 |-Branch one:
% 8.66/2.66 | (85) all_0_2_2 = all_0_3_3
% 8.66/2.66 |
% 8.66/2.66 | Equations (85) can reduce 43 to:
% 8.66/2.66 | (86) $false
% 8.66/2.66 |
% 8.66/2.66 |-The branch is then unsatisfiable
% 8.66/2.66 |-Branch two:
% 8.66/2.66 | (43) ~ (all_0_2_2 = all_0_3_3)
% 8.66/2.66 | (88) all_0_2_2 = all_0_7_7 | all_0_2_2 = all_0_8_8 | all_0_2_2 = all_0_9_9 | all_0_3_3 = all_0_7_7 | all_0_3_3 = all_0_8_8 | all_0_3_3 = all_0_9_9 | all_0_7_7 = all_0_8_8 | all_0_7_7 = all_0_9_9 | all_0_8_8 = all_0_9_9
% 8.66/2.66 |
% 8.66/2.66 +-Applying beta-rule and splitting (88), into two cases.
% 8.66/2.66 |-Branch one:
% 8.66/2.66 | (89) all_0_2_2 = all_0_7_7
% 8.66/2.66 |
% 8.66/2.66 | Equations (89) can reduce 80 to:
% 8.66/2.66 | (86) $false
% 8.66/2.66 |
% 8.66/2.66 |-The branch is then unsatisfiable
% 8.66/2.66 |-Branch two:
% 8.66/2.66 | (80) ~ (all_0_2_2 = all_0_7_7)
% 8.66/2.66 | (92) all_0_2_2 = all_0_8_8 | all_0_2_2 = all_0_9_9 | all_0_3_3 = all_0_7_7 | all_0_3_3 = all_0_8_8 | all_0_3_3 = all_0_9_9 | all_0_7_7 = all_0_8_8 | all_0_7_7 = all_0_9_9 | all_0_8_8 = all_0_9_9
% 8.66/2.66 |
% 8.66/2.66 +-Applying beta-rule and splitting (92), into two cases.
% 8.66/2.66 |-Branch one:
% 8.66/2.66 | (93) all_0_2_2 = all_0_8_8
% 8.66/2.66 |
% 8.66/2.66 | Equations (93) can reduce 83 to:
% 8.66/2.66 | (86) $false
% 8.66/2.66 |
% 8.66/2.66 |-The branch is then unsatisfiable
% 8.66/2.66 |-Branch two:
% 8.66/2.66 | (83) ~ (all_0_2_2 = all_0_8_8)
% 8.66/2.66 | (96) all_0_2_2 = all_0_9_9 | all_0_3_3 = all_0_7_7 | all_0_3_3 = all_0_8_8 | all_0_3_3 = all_0_9_9 | all_0_7_7 = all_0_8_8 | all_0_7_7 = all_0_9_9 | all_0_8_8 = all_0_9_9
% 8.66/2.66 |
% 8.66/2.66 +-Applying beta-rule and splitting (96), into two cases.
% 8.66/2.66 |-Branch one:
% 8.66/2.66 | (97) all_0_2_2 = all_0_9_9
% 8.66/2.66 |
% 8.66/2.66 | Equations (97) can reduce 77 to:
% 8.66/2.66 | (86) $false
% 8.66/2.66 |
% 8.66/2.66 |-The branch is then unsatisfiable
% 8.66/2.66 |-Branch two:
% 8.66/2.66 | (77) ~ (all_0_2_2 = all_0_9_9)
% 8.66/2.66 | (100) all_0_3_3 = all_0_7_7 | all_0_3_3 = all_0_8_8 | all_0_3_3 = all_0_9_9 | all_0_7_7 = all_0_8_8 | all_0_7_7 = all_0_9_9 | all_0_8_8 = all_0_9_9
% 8.66/2.66 |
% 8.66/2.66 +-Applying beta-rule and splitting (100), into two cases.
% 8.66/2.66 |-Branch one:
% 8.66/2.66 | (101) all_0_3_3 = all_0_7_7
% 8.66/2.66 |
% 8.66/2.66 | Equations (101) can reduce 81 to:
% 8.66/2.66 | (86) $false
% 8.66/2.66 |
% 8.66/2.66 |-The branch is then unsatisfiable
% 8.66/2.66 |-Branch two:
% 8.66/2.66 | (81) ~ (all_0_3_3 = all_0_7_7)
% 8.66/2.66 | (104) all_0_3_3 = all_0_8_8 | all_0_3_3 = all_0_9_9 | all_0_7_7 = all_0_8_8 | all_0_7_7 = all_0_9_9 | all_0_8_8 = all_0_9_9
% 8.66/2.66 |
% 8.66/2.66 +-Applying beta-rule and splitting (104), into two cases.
% 8.66/2.66 |-Branch one:
% 8.66/2.66 | (105) all_0_3_3 = all_0_8_8
% 8.66/2.66 |
% 8.66/2.66 | Equations (105) can reduce 84 to:
% 8.66/2.66 | (86) $false
% 8.66/2.66 |
% 8.66/2.66 |-The branch is then unsatisfiable
% 8.66/2.66 |-Branch two:
% 8.66/2.66 | (84) ~ (all_0_3_3 = all_0_8_8)
% 8.66/2.66 | (108) all_0_3_3 = all_0_9_9 | all_0_7_7 = all_0_8_8 | all_0_7_7 = all_0_9_9 | all_0_8_8 = all_0_9_9
% 8.66/2.66 |
% 8.66/2.66 +-Applying beta-rule and splitting (108), into two cases.
% 8.66/2.66 |-Branch one:
% 8.66/2.66 | (109) all_0_3_3 = all_0_9_9
% 8.66/2.67 |
% 8.66/2.67 | Equations (109) can reduce 78 to:
% 8.66/2.67 | (86) $false
% 8.66/2.67 |
% 8.66/2.67 |-The branch is then unsatisfiable
% 8.66/2.67 |-Branch two:
% 8.66/2.67 | (78) ~ (all_0_3_3 = all_0_9_9)
% 8.66/2.67 | (112) all_0_7_7 = all_0_8_8 | all_0_7_7 = all_0_9_9 | all_0_8_8 = all_0_9_9
% 8.66/2.67 |
% 8.66/2.67 +-Applying beta-rule and splitting (112), into two cases.
% 8.66/2.67 |-Branch one:
% 8.66/2.67 | (113) all_0_7_7 = all_0_8_8
% 8.66/2.67 |
% 8.66/2.67 | Equations (113) can reduce 45 to:
% 8.66/2.67 | (86) $false
% 8.66/2.67 |
% 8.66/2.67 |-The branch is then unsatisfiable
% 8.66/2.67 |-Branch two:
% 8.66/2.67 | (45) ~ (all_0_7_7 = all_0_8_8)
% 8.66/2.67 | (116) all_0_7_7 = all_0_9_9 | all_0_8_8 = all_0_9_9
% 8.66/2.67 |
% 8.66/2.67 +-Applying beta-rule and splitting (116), into two cases.
% 8.66/2.67 |-Branch one:
% 8.66/2.67 | (117) all_0_7_7 = all_0_9_9
% 8.66/2.67 |
% 8.66/2.67 | Equations (117) can reduce 47 to:
% 8.66/2.67 | (86) $false
% 8.66/2.67 |
% 8.66/2.67 |-The branch is then unsatisfiable
% 8.66/2.67 |-Branch two:
% 8.66/2.67 | (47) ~ (all_0_7_7 = all_0_9_9)
% 8.66/2.67 | (120) all_0_8_8 = all_0_9_9
% 8.66/2.67 |
% 8.66/2.67 | Equations (120) can reduce 41 to:
% 8.66/2.67 | (86) $false
% 8.66/2.67 |
% 8.66/2.67 |-The branch is then unsatisfiable
% 8.66/2.67 |-Branch two:
% 8.66/2.67 | (122) cA(all_0_8_8) = 0
% 8.66/2.67 | (123) all_22_0_13 = 0
% 8.66/2.67 |
% 8.66/2.67 | Equations (123) can reduce 71 to:
% 8.66/2.67 | (86) $false
% 8.66/2.67 |
% 8.66/2.67 |-The branch is then unsatisfiable
% 8.66/2.67 |-Branch two:
% 8.66/2.67 | (125) cA(all_0_7_7) = 0
% 8.66/2.67 | (126) all_20_0_12 = 0
% 8.66/2.67 |
% 8.66/2.67 | Equations (126) can reduce 68 to:
% 8.66/2.67 | (86) $false
% 8.66/2.67 |
% 8.66/2.67 |-The branch is then unsatisfiable
% 8.66/2.67 |-Branch two:
% 8.66/2.67 | (128) cA(all_0_9_9) = 0
% 8.66/2.67 | (129) all_18_0_11 = 0
% 8.66/2.67 |
% 8.66/2.67 | Equations (129) can reduce 65 to:
% 8.66/2.67 | (86) $false
% 8.66/2.67 |
% 8.66/2.67 |-The branch is then unsatisfiable
% 8.66/2.67 |-Branch two:
% 8.66/2.67 | (131) xsd_string(all_0_10_10) = all_0_9_9 & xsd_integer(all_0_10_10) = all_0_8_8 & ((all_0_8_8 = 0 & all_0_9_9 = 0) | ( ~ (all_0_8_8 = 0) & ~ (all_0_9_9 = 0)))
% 8.66/2.67 |
% 8.66/2.67 | Applying alpha-rule on (131) yields:
% 8.66/2.67 | (132) xsd_string(all_0_10_10) = all_0_9_9
% 8.66/2.67 | (133) xsd_integer(all_0_10_10) = all_0_8_8
% 8.66/2.67 | (134) (all_0_8_8 = 0 & all_0_9_9 = 0) | ( ~ (all_0_8_8 = 0) & ~ (all_0_9_9 = 0))
% 8.66/2.67 |
% 8.66/2.67 | Instantiating formula (16) with all_0_10_10 yields:
% 8.66/2.67 | (135) ~ (xsd_string(all_0_10_10) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_10_10) = v0)
% 8.66/2.67 |
% 8.66/2.67 | Instantiating formula (17) with all_0_9_9, all_0_10_10 and discharging atoms xsd_string(all_0_10_10) = all_0_9_9, yields:
% 8.66/2.67 | (136) all_0_9_9 = 0 | xsd_integer(all_0_10_10) = 0
% 8.66/2.67 |
% 8.66/2.67 +-Applying beta-rule and splitting (134), into two cases.
% 8.66/2.67 |-Branch one:
% 8.66/2.67 | (137) all_0_8_8 = 0 & all_0_9_9 = 0
% 8.66/2.67 |
% 8.66/2.67 | Applying alpha-rule on (137) yields:
% 8.66/2.67 | (138) all_0_8_8 = 0
% 8.66/2.67 | (139) all_0_9_9 = 0
% 8.66/2.67 |
% 8.66/2.67 | From (139) and (132) follows:
% 8.66/2.67 | (140) xsd_string(all_0_10_10) = 0
% 8.66/2.67 |
% 8.66/2.67 | From (138) and (133) follows:
% 8.66/2.67 | (141) xsd_integer(all_0_10_10) = 0
% 8.66/2.67 |
% 8.66/2.67 +-Applying beta-rule and splitting (135), into two cases.
% 8.66/2.67 |-Branch one:
% 8.66/2.67 | (142) ~ (xsd_string(all_0_10_10) = 0)
% 8.66/2.67 |
% 8.66/2.67 | Using (140) and (142) yields:
% 8.66/2.67 | (143) $false
% 8.66/2.67 |
% 8.66/2.67 |-The branch is then unsatisfiable
% 8.66/2.67 |-Branch two:
% 8.66/2.67 | (140) xsd_string(all_0_10_10) = 0
% 8.66/2.67 | (145) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_10_10) = v0)
% 8.66/2.67 |
% 8.66/2.68 | Instantiating (145) with all_17_0_14 yields:
% 8.66/2.68 | (146) ~ (all_17_0_14 = 0) & xsd_integer(all_0_10_10) = all_17_0_14
% 8.66/2.68 |
% 8.66/2.68 | Applying alpha-rule on (146) yields:
% 8.66/2.68 | (147) ~ (all_17_0_14 = 0)
% 8.66/2.68 | (148) xsd_integer(all_0_10_10) = all_17_0_14
% 8.66/2.68 |
% 8.66/2.68 | Instantiating formula (27) with all_0_10_10, 0, all_17_0_14 and discharging atoms xsd_integer(all_0_10_10) = all_17_0_14, xsd_integer(all_0_10_10) = 0, yields:
% 8.66/2.68 | (149) all_17_0_14 = 0
% 8.66/2.68 |
% 8.66/2.68 | Equations (149) can reduce 147 to:
% 8.66/2.68 | (86) $false
% 8.66/2.68 |
% 8.66/2.68 |-The branch is then unsatisfiable
% 8.66/2.68 |-Branch two:
% 8.66/2.68 | (151) ~ (all_0_8_8 = 0) & ~ (all_0_9_9 = 0)
% 8.66/2.68 |
% 8.66/2.68 | Applying alpha-rule on (151) yields:
% 8.66/2.68 | (152) ~ (all_0_8_8 = 0)
% 8.66/2.68 | (153) ~ (all_0_9_9 = 0)
% 8.66/2.68 |
% 8.66/2.68 +-Applying beta-rule and splitting (136), into two cases.
% 8.66/2.68 |-Branch one:
% 8.66/2.68 | (141) xsd_integer(all_0_10_10) = 0
% 8.66/2.68 |
% 8.66/2.68 | Instantiating formula (27) with all_0_10_10, 0, all_0_8_8 and discharging atoms xsd_integer(all_0_10_10) = all_0_8_8, xsd_integer(all_0_10_10) = 0, yields:
% 8.66/2.68 | (138) all_0_8_8 = 0
% 8.66/2.68 |
% 8.66/2.68 | Equations (138) can reduce 152 to:
% 8.66/2.68 | (86) $false
% 8.66/2.68 |
% 8.66/2.68 |-The branch is then unsatisfiable
% 8.66/2.68 |-Branch two:
% 8.66/2.68 | (157) ~ (xsd_integer(all_0_10_10) = 0)
% 8.66/2.68 | (139) all_0_9_9 = 0
% 8.66/2.68 |
% 8.66/2.68 | Equations (139) can reduce 153 to:
% 8.66/2.68 | (86) $false
% 8.66/2.68 |
% 8.66/2.68 |-The branch is then unsatisfiable
% 8.66/2.68 |-Branch two:
% 8.66/2.68 | (160) cowlThing(all_0_10_10) = all_0_9_9 & cowlNothing(all_0_10_10) = all_0_8_8 & ( ~ (all_0_9_9 = 0) | all_0_8_8 = 0)
% 8.66/2.68 |
% 8.66/2.68 | Applying alpha-rule on (160) yields:
% 8.66/2.68 | (161) cowlThing(all_0_10_10) = all_0_9_9
% 8.66/2.68 | (162) cowlNothing(all_0_10_10) = all_0_8_8
% 8.66/2.68 | (163) ~ (all_0_9_9 = 0) | all_0_8_8 = 0
% 8.66/2.68 |
% 8.66/2.68 | Instantiating formula (29) with all_0_9_9, all_0_10_10 and discharging atoms cowlThing(all_0_10_10) = all_0_9_9, yields:
% 8.66/2.68 | (139) all_0_9_9 = 0
% 8.66/2.68 |
% 8.66/2.68 | Instantiating formula (6) with all_0_10_10 yields:
% 8.66/2.68 | (165) ~ (cowlNothing(all_0_10_10) = 0)
% 8.66/2.68 |
% 8.66/2.68 +-Applying beta-rule and splitting (163), into two cases.
% 8.66/2.68 |-Branch one:
% 8.66/2.68 | (153) ~ (all_0_9_9 = 0)
% 8.66/2.68 |
% 8.66/2.68 | Equations (139) can reduce 153 to:
% 8.66/2.68 | (86) $false
% 8.66/2.68 |
% 8.66/2.68 |-The branch is then unsatisfiable
% 8.66/2.68 |-Branch two:
% 8.66/2.68 | (139) all_0_9_9 = 0
% 8.66/2.68 | (138) all_0_8_8 = 0
% 8.66/2.68 |
% 8.66/2.68 | From (138) and (162) follows:
% 8.66/2.68 | (170) cowlNothing(all_0_10_10) = 0
% 8.66/2.68 |
% 8.66/2.68 | Using (170) and (165) yields:
% 8.66/2.68 | (143) $false
% 8.66/2.68 |
% 8.66/2.68 |-The branch is then unsatisfiable
% 8.66/2.68 % SZS output end Proof for theBenchmark
% 8.66/2.68
% 8.66/2.68 2084ms
%------------------------------------------------------------------------------