TSTP Solution File: KLE029+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE029+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 01:51:01 EDT 2022
% Result : Theorem 4.84s 1.82s
% Output : Proof 7.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE029+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 12:02:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.49/0.58 ____ _
% 0.49/0.58 ___ / __ \_____(_)___ ________ __________
% 0.49/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.58
% 0.49/0.58 A Theorem Prover for First-Order Logic
% 0.49/0.59 (ePrincess v.1.0)
% 0.49/0.59
% 0.49/0.59 (c) Philipp Rümmer, 2009-2015
% 0.49/0.59 (c) Peter Backeman, 2014-2015
% 0.49/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.59 Bug reports to peter@backeman.se
% 0.49/0.59
% 0.49/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.59
% 0.49/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.36/0.93 Prover 0: Preprocessing ...
% 2.12/1.14 Prover 0: Warning: ignoring some quantifiers
% 2.22/1.16 Prover 0: Constructing countermodel ...
% 2.48/1.25 Prover 0: gave up
% 2.48/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.48/1.28 Prover 1: Preprocessing ...
% 3.08/1.37 Prover 1: Constructing countermodel ...
% 3.47/1.51 Prover 1: gave up
% 3.47/1.51 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.47/1.53 Prover 2: Preprocessing ...
% 4.06/1.61 Prover 2: Warning: ignoring some quantifiers
% 4.06/1.62 Prover 2: Constructing countermodel ...
% 4.84/1.82 Prover 2: proved (307ms)
% 4.84/1.82
% 4.84/1.82 No countermodel exists, formula is valid
% 4.84/1.82 % SZS status Theorem for theBenchmark
% 4.84/1.82
% 4.84/1.82 Generating proof ... Warning: ignoring some quantifiers
% 7.18/2.27 found it (size 156)
% 7.18/2.27
% 7.18/2.27 % SZS output start Proof for theBenchmark
% 7.18/2.27 Assumed formulas after preprocessing and simplification:
% 7.18/2.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ismeetu(v0, v1, v2) = v4 & ismeet(v0, v1, v2) = v3 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v6, v7) = v9) | ~ (multiplication(v5, v7) = v8) | ~ (addition(v8, v9) = v10) | ? [v11] : (multiplication(v11, v7) = v10 & addition(v5, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v5, v7) = v9) | ~ (multiplication(v5, v6) = v8) | ~ (addition(v8, v9) = v10) | ? [v11] : (multiplication(v5, v11) = v10 & addition(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (ismeetu(v7, v5, v6) = 0) | ~ (leq(v8, v7) = v9) | ? [v10] : (( ~ (v10 = 0) & leq(v8, v6) = v10) | ( ~ (v10 = 0) & leq(v8, v5) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (ismeet(v7, v5, v6) = 0) | ~ (leq(v8, v7) = v9) | ? [v10] : (( ~ (v10 = 0) & leq(v8, v6) = v10) | ( ~ (v10 = 0) & leq(v8, v5) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (ismeetu(v9, v8, v7) = v6) | ~ (ismeetu(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (ismeet(v9, v8, v7) = v6) | ~ (ismeet(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (ismeetu(v7, v5, v6) = 0) | ~ (leq(v8, v6) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & leq(v8, v5) = 0) | ( ~ (v10 = 0) & leq(v8, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (ismeetu(v7, v5, v6) = 0) | ~ (leq(v8, v5) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & leq(v8, v6) = 0) | ( ~ (v10 = 0) & leq(v8, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v8, v7) = v9) | ~ (multiplication(v5, v6) = v8) | ? [v10] : (multiplication(v6, v7) = v10 & multiplication(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v8, v7) = v9) | ~ (addition(v5, v6) = v8) | ? [v10] : ? [v11] : (multiplication(v6, v7) = v11 & multiplication(v5, v7) = v10 & addition(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v6, v7) = v8) | ~ (multiplication(v5, v8) = v9) | ? [v10] : (multiplication(v10, v7) = v9 & multiplication(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v5, v8) = v9) | ~ (addition(v6, v7) = v8) | ? [v10] : ? [v11] : (multiplication(v5, v7) = v11 & multiplication(v5, v6) = v10 & addition(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (addition(v8, v5) = v9) | ~ (addition(v7, v6) = v8) | ? [v10] : (addition(v7, v10) = v9 & addition(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (addition(v7, v8) = v9) | ~ (addition(v6, v5) = v8) | ? [v10] : (addition(v10, v5) = v9 & addition(v7, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (ismeetu(v7, v5, v6) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (((v12 = 0 & leq(v9, v7) = 0) | (v11 = 0 & v10 = 0 & leq(v9, v6) = 0 & leq(v9, v5) = 0)) & (( ~ (v12 = 0) & leq(v9, v7) = v12) | ( ~ (v11 = 0) & leq(v9, v6) = v11) | ( ~ (v10 = 0) & leq(v9, v5) = v10)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (ismeet(v7, v5, v6) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & ~ (v12 = 0) & leq(v9, v7) = v12 & leq(v9, v6) = 0 & leq(v9, v5) = 0) | ( ~ (v9 = 0) & leq(v7, v6) = v9) | ( ~ (v9 = 0) & leq(v7, v5) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (leq(v8, v7) = v6) | ~ (leq(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (multiplication(v8, v7) = v6) | ~ (multiplication(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (addition(v8, v7) = v6) | ~ (addition(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (ismeetu(v7, v5, v6) = 0) | ~ (leq(v8, v7) = 0) | (leq(v8, v6) = 0 & leq(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (ismeetu(v7, v5, v6) = 0) | ~ (leq(v8, v6) = 0) | ? [v9] : ((v9 = 0 & leq(v8, v7) = 0) | ( ~ (v9 = 0) & leq(v8, v5) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (ismeetu(v7, v5, v6) = 0) | ~ (leq(v8, v5) = 0) | ? [v9] : ((v9 = 0 & leq(v8, v7) = 0) | ( ~ (v9 = 0) & leq(v8, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (ismeet(v7, v5, v6) = 0) | ~ (leq(v8, v6) = 0) | ? [v9] : ((v9 = 0 & leq(v8, v7) = 0) | ( ~ (v9 = 0) & leq(v8, v5) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (ismeet(v7, v5, v6) = 0) | ~ (leq(v8, v5) = 0) | ? [v9] : ((v9 = 0 & leq(v8, v7) = 0) | ( ~ (v9 = 0) & leq(v8, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (addition(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & leq(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (leq(v5, v6) = v7) | ? [v8] : ( ~ (v8 = v6) & addition(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (ismeet(v7, v5, v6) = 0) | (leq(v7, v6) = 0 & leq(v7, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v6, v5) = v7) | addition(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v5, v6) = v7) | addition(v6, v5) = v7) & ! [v5] : ! [v6] : (v6 = v5 | ~ (multiplication(v5, one) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (multiplication(one, v5) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (addition(v5, v5) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (addition(v5, zero) = v6)) & ! [v5] : ! [v6] : (v6 = zero | ~ (multiplication(v5, zero) = v6)) & ! [v5] : ! [v6] : (v6 = zero | ~ (multiplication(zero, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (leq(v5, v6) = 0) | addition(v5, v6) = v6) & ! [v5] : ! [v6] : ( ~ (addition(v5, v6) = v6) | leq(v5, v6) = 0) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ismeetu(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ismeet(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : leq(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : multiplication(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : addition(v6, v5) = v7 & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))
% 7.29/2.31 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 7.29/2.31 | (1) ismeetu(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_0_0 & ismeet(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & leq(v3, v1) = v5) | ( ~ (v5 = 0) & leq(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (ismeet(v2, v0, v1) = 0) | ~ (leq(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & leq(v3, v1) = v5) | ( ~ (v5 = 0) & leq(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ismeetu(v4, v3, v2) = v1) | ~ (ismeetu(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ismeet(v4, v3, v2) = v1) | ~ (ismeet(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & leq(v3, v0) = 0) | ( ~ (v5 = 0) & leq(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & leq(v3, v1) = 0) | ( ~ (v5 = 0) & leq(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (ismeetu(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & leq(v4, v2) = 0) | (v6 = 0 & v5 = 0 & leq(v4, v1) = 0 & leq(v4, v0) = 0)) & (( ~ (v7 = 0) & leq(v4, v2) = v7) | ( ~ (v6 = 0) & leq(v4, v1) = v6) | ( ~ (v5 = 0) & leq(v4, v0) = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (ismeet(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & ~ (v7 = 0) & leq(v4, v2) = v7 & leq(v4, v1) = 0 & leq(v4, v0) = 0) | ( ~ (v4 = 0) & leq(v2, v1) = v4) | ( ~ (v4 = 0) & leq(v2, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v2) = 0) | (leq(v3, v1) = 0 & leq(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v1) = 0) | ? [v4] : ((v4 = 0 & leq(v3, v2) = 0) | ( ~ (v4 = 0) & leq(v3, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v0) = 0) | ? [v4] : ((v4 = 0 & leq(v3, v2) = 0) | ( ~ (v4 = 0) & leq(v3, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ismeet(v2, v0, v1) = 0) | ~ (leq(v3, v1) = 0) | ? [v4] : ((v4 = 0 & leq(v3, v2) = 0) | ( ~ (v4 = 0) & leq(v3, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ismeet(v2, v0, v1) = 0) | ~ (leq(v3, v0) = 0) | ? [v4] : ((v4 = 0 & leq(v3, v2) = 0) | ( ~ (v4 = 0) & leq(v3, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ismeet(v2, v0, v1) = 0) | (leq(v2, v1) = 0 & leq(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ismeetu(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ismeet(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))
% 7.47/2.32 |
% 7.47/2.32 | Applying alpha-rule on (1) yields:
% 7.47/2.32 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (ismeet(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & ~ (v7 = 0) & leq(v4, v2) = v7 & leq(v4, v1) = 0 & leq(v4, v0) = 0) | ( ~ (v4 = 0) & leq(v2, v1) = v4) | ( ~ (v4 = 0) & leq(v2, v0) = v4)))
% 7.47/2.33 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v0) = 0) | ? [v4] : ((v4 = 0 & leq(v3, v2) = 0) | ( ~ (v4 = 0) & leq(v3, v1) = v4)))
% 7.47/2.33 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 7.47/2.33 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 7.47/2.33 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4))
% 7.47/2.33 | (7) ismeetu(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_0_0
% 7.47/2.33 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (ismeetu(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & leq(v4, v2) = 0) | (v6 = 0 & v5 = 0 & leq(v4, v1) = 0 & leq(v4, v0) = 0)) & (( ~ (v7 = 0) & leq(v4, v2) = v7) | ( ~ (v6 = 0) & leq(v4, v1) = v6) | ( ~ (v5 = 0) & leq(v4, v0) = v5))))
% 7.47/2.33 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 7.47/2.33 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 7.47/2.33 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & leq(v3, v1) = 0) | ( ~ (v5 = 0) & leq(v3, v2) = v5)))
% 7.47/2.33 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 7.47/2.33 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v2) = 0) | (leq(v3, v1) = 0 & leq(v3, v0) = 0))
% 7.47/2.33 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (ismeet(v2, v0, v1) = 0) | ~ (leq(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & leq(v3, v1) = v5) | ( ~ (v5 = 0) & leq(v3, v0) = v5)))
% 7.47/2.33 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v1) = 0) | ? [v4] : ((v4 = 0 & leq(v3, v2) = 0) | ( ~ (v4 = 0) & leq(v3, v0) = v4)))
% 7.47/2.33 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ismeet(v2, v0, v1) = 0) | ~ (leq(v3, v1) = 0) | ? [v4] : ((v4 = 0 & leq(v3, v2) = 0) | ( ~ (v4 = 0) & leq(v3, v0) = v4)))
% 7.47/2.33 | (17) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 7.47/2.33 | (18) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 7.47/2.33 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4))
% 7.53/2.33 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 7.53/2.33 | (21) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ismeet(v2, v1, v0) = v3
% 7.53/2.33 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ismeetu(v4, v3, v2) = v1) | ~ (ismeetu(v4, v3, v2) = v0))
% 7.53/2.33 | (23) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2
% 7.53/2.33 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6))
% 7.53/2.34 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 7.53/2.34 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 7.53/2.34 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ismeet(v2, v0, v1) = 0) | ~ (leq(v3, v0) = 0) | ? [v4] : ((v4 = 0 & leq(v3, v2) = 0) | ( ~ (v4 = 0) & leq(v3, v1) = v4)))
% 7.53/2.34 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6))
% 7.53/2.34 | (29) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ismeetu(v2, v1, v0) = v3
% 7.53/2.34 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 7.53/2.34 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (ismeet(v2, v0, v1) = 0) | (leq(v2, v1) = 0 & leq(v2, v0) = 0))
% 7.53/2.34 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ismeet(v4, v3, v2) = v1) | ~ (ismeet(v4, v3, v2) = v0))
% 7.53/2.34 | (33) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2
% 7.53/2.34 | (34) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 7.53/2.34 | (35) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))
% 7.53/2.34 | (36) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2
% 7.53/2.34 | (37) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 7.53/2.34 | (38) ismeet(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1
% 7.53/2.34 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & leq(v3, v1) = v5) | ( ~ (v5 = 0) & leq(v3, v0) = v5)))
% 7.53/2.34 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 7.53/2.34 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & leq(v3, v0) = 0) | ( ~ (v5 = 0) & leq(v3, v2) = v5)))
% 7.53/2.34 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 7.53/2.34 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 7.53/2.34 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 7.53/2.34 | (45) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 7.53/2.34 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 7.53/2.34 |
% 7.53/2.34 | Instantiating formula (8) with all_0_0_0, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms ismeetu(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 7.53/2.34 | (47) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & leq(v0, all_0_4_4) = 0) | (v2 = 0 & v1 = 0 & leq(v0, all_0_2_2) = 0 & leq(v0, all_0_3_3) = 0)) & (( ~ (v3 = 0) & leq(v0, all_0_4_4) = v3) | ( ~ (v2 = 0) & leq(v0, all_0_2_2) = v2) | ( ~ (v1 = 0) & leq(v0, all_0_3_3) = v1)))
% 7.53/2.34 |
% 7.53/2.34 | Instantiating formula (2) with all_0_1_1, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms ismeet(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 7.53/2.35 | (48) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & v1 = 0 & ~ (v3 = 0) & leq(v0, all_0_2_2) = 0 & leq(v0, all_0_3_3) = 0 & leq(v0, all_0_4_4) = v3) | ( ~ (v0 = 0) & leq(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & leq(all_0_4_4, all_0_3_3) = v0))
% 7.53/2.35 |
% 7.53/2.35 +-Applying beta-rule and splitting (35), into two cases.
% 7.53/2.35 |-Branch one:
% 7.53/2.35 | (49) all_0_0_0 = 0 & ~ (all_0_1_1 = 0)
% 7.53/2.35 |
% 7.53/2.35 | Applying alpha-rule on (49) yields:
% 7.53/2.35 | (50) all_0_0_0 = 0
% 7.53/2.35 | (51) ~ (all_0_1_1 = 0)
% 7.53/2.35 |
% 7.53/2.35 | From (50) and (7) follows:
% 7.53/2.35 | (52) ismeetu(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 7.53/2.35 |
% 7.53/2.35 +-Applying beta-rule and splitting (48), into two cases.
% 7.53/2.35 |-Branch one:
% 7.53/2.35 | (53) all_0_1_1 = 0
% 7.53/2.35 |
% 7.53/2.35 | Equations (53) can reduce 51 to:
% 7.53/2.35 | (54) $false
% 7.53/2.35 |
% 7.53/2.35 |-The branch is then unsatisfiable
% 7.53/2.35 |-Branch two:
% 7.53/2.35 | (51) ~ (all_0_1_1 = 0)
% 7.53/2.35 | (56) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & v1 = 0 & ~ (v3 = 0) & leq(v0, all_0_2_2) = 0 & leq(v0, all_0_3_3) = 0 & leq(v0, all_0_4_4) = v3) | ( ~ (v0 = 0) & leq(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & leq(all_0_4_4, all_0_3_3) = v0))
% 7.53/2.35 |
% 7.53/2.35 | Instantiating (56) with all_24_0_22, all_24_1_23, all_24_2_24, all_24_3_25 yields:
% 7.53/2.35 | (57) (all_24_1_23 = 0 & all_24_2_24 = 0 & ~ (all_24_0_22 = 0) & leq(all_24_3_25, all_0_2_2) = 0 & leq(all_24_3_25, all_0_3_3) = 0 & leq(all_24_3_25, all_0_4_4) = all_24_0_22) | ( ~ (all_24_3_25 = 0) & leq(all_0_4_4, all_0_2_2) = all_24_3_25) | ( ~ (all_24_3_25 = 0) & leq(all_0_4_4, all_0_3_3) = all_24_3_25)
% 7.53/2.35 |
% 7.53/2.35 +-Applying beta-rule and splitting (57), into two cases.
% 7.53/2.35 |-Branch one:
% 7.53/2.35 | (58) (all_24_1_23 = 0 & all_24_2_24 = 0 & ~ (all_24_0_22 = 0) & leq(all_24_3_25, all_0_2_2) = 0 & leq(all_24_3_25, all_0_3_3) = 0 & leq(all_24_3_25, all_0_4_4) = all_24_0_22) | ( ~ (all_24_3_25 = 0) & leq(all_0_4_4, all_0_2_2) = all_24_3_25)
% 7.53/2.35 |
% 7.53/2.35 +-Applying beta-rule and splitting (58), into two cases.
% 7.53/2.35 |-Branch one:
% 7.53/2.35 | (59) all_24_1_23 = 0 & all_24_2_24 = 0 & ~ (all_24_0_22 = 0) & leq(all_24_3_25, all_0_2_2) = 0 & leq(all_24_3_25, all_0_3_3) = 0 & leq(all_24_3_25, all_0_4_4) = all_24_0_22
% 7.53/2.35 |
% 7.53/2.35 | Applying alpha-rule on (59) yields:
% 7.53/2.35 | (60) leq(all_24_3_25, all_0_2_2) = 0
% 7.53/2.35 | (61) ~ (all_24_0_22 = 0)
% 7.53/2.35 | (62) all_24_1_23 = 0
% 7.53/2.35 | (63) leq(all_24_3_25, all_0_3_3) = 0
% 7.53/2.35 | (64) all_24_2_24 = 0
% 7.53/2.35 | (65) leq(all_24_3_25, all_0_4_4) = all_24_0_22
% 7.53/2.35 |
% 7.53/2.35 | Instantiating formula (15) with all_24_3_25, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms ismeetu(all_0_4_4, all_0_3_3, all_0_2_2) = 0, leq(all_24_3_25, all_0_2_2) = 0, yields:
% 7.53/2.35 | (66) ? [v0] : ((v0 = 0 & leq(all_24_3_25, all_0_4_4) = 0) | ( ~ (v0 = 0) & leq(all_24_3_25, all_0_3_3) = v0))
% 7.53/2.35 |
% 7.53/2.35 | Instantiating formula (40) with all_24_0_22, all_0_4_4, all_24_3_25 and discharging atoms leq(all_24_3_25, all_0_4_4) = all_24_0_22, yields:
% 7.53/2.35 | (67) all_24_0_22 = 0 | ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_24_3_25, all_0_4_4) = v0)
% 7.53/2.35 |
% 7.53/2.35 | Instantiating (66) with all_38_0_26 yields:
% 7.53/2.35 | (68) (all_38_0_26 = 0 & leq(all_24_3_25, all_0_4_4) = 0) | ( ~ (all_38_0_26 = 0) & leq(all_24_3_25, all_0_3_3) = all_38_0_26)
% 7.53/2.35 |
% 7.53/2.35 +-Applying beta-rule and splitting (68), into two cases.
% 7.53/2.35 |-Branch one:
% 7.53/2.35 | (69) all_38_0_26 = 0 & leq(all_24_3_25, all_0_4_4) = 0
% 7.53/2.35 |
% 7.53/2.35 | Applying alpha-rule on (69) yields:
% 7.53/2.35 | (70) all_38_0_26 = 0
% 7.53/2.35 | (71) leq(all_24_3_25, all_0_4_4) = 0
% 7.53/2.35 |
% 7.53/2.35 +-Applying beta-rule and splitting (67), into two cases.
% 7.53/2.35 |-Branch one:
% 7.53/2.35 | (72) all_24_0_22 = 0
% 7.53/2.35 |
% 7.53/2.35 | Equations (72) can reduce 61 to:
% 7.53/2.35 | (54) $false
% 7.53/2.35 |
% 7.53/2.35 |-The branch is then unsatisfiable
% 7.53/2.35 |-Branch two:
% 7.53/2.35 | (61) ~ (all_24_0_22 = 0)
% 7.53/2.35 | (75) ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_24_3_25, all_0_4_4) = v0)
% 7.53/2.35 |
% 7.53/2.35 | Instantiating formula (4) with all_24_3_25, all_0_4_4, 0, all_24_0_22 and discharging atoms leq(all_24_3_25, all_0_4_4) = all_24_0_22, leq(all_24_3_25, all_0_4_4) = 0, yields:
% 7.53/2.35 | (72) all_24_0_22 = 0
% 7.53/2.35 |
% 7.53/2.35 | Equations (72) can reduce 61 to:
% 7.53/2.35 | (54) $false
% 7.53/2.35 |
% 7.53/2.35 |-The branch is then unsatisfiable
% 7.53/2.35 |-Branch two:
% 7.53/2.35 | (78) ~ (all_38_0_26 = 0) & leq(all_24_3_25, all_0_3_3) = all_38_0_26
% 7.53/2.35 |
% 7.53/2.35 | Applying alpha-rule on (78) yields:
% 7.53/2.35 | (79) ~ (all_38_0_26 = 0)
% 7.53/2.35 | (80) leq(all_24_3_25, all_0_3_3) = all_38_0_26
% 7.53/2.35 |
% 7.53/2.35 | Instantiating formula (4) with all_24_3_25, all_0_3_3, all_38_0_26, 0 and discharging atoms leq(all_24_3_25, all_0_3_3) = all_38_0_26, leq(all_24_3_25, all_0_3_3) = 0, yields:
% 7.53/2.36 | (70) all_38_0_26 = 0
% 7.53/2.36 |
% 7.53/2.36 | Equations (70) can reduce 79 to:
% 7.53/2.36 | (54) $false
% 7.53/2.36 |
% 7.53/2.36 |-The branch is then unsatisfiable
% 7.53/2.36 |-Branch two:
% 7.53/2.36 | (83) ~ (all_24_3_25 = 0) & leq(all_0_4_4, all_0_2_2) = all_24_3_25
% 7.53/2.36 |
% 7.53/2.36 | Applying alpha-rule on (83) yields:
% 7.53/2.36 | (84) ~ (all_24_3_25 = 0)
% 7.53/2.36 | (85) leq(all_0_4_4, all_0_2_2) = all_24_3_25
% 7.53/2.36 |
% 7.53/2.36 | Instantiating formula (41) with all_24_3_25, all_0_4_4, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms ismeetu(all_0_4_4, all_0_3_3, all_0_2_2) = 0, leq(all_0_4_4, all_0_2_2) = all_24_3_25, yields:
% 7.53/2.36 | (86) ? [v0] : ((v0 = 0 & all_24_3_25 = 0 & leq(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & leq(all_0_4_4, all_0_4_4) = v0))
% 7.53/2.36 |
% 7.53/2.36 | Instantiating (86) with all_37_0_35 yields:
% 7.53/2.36 | (87) (all_37_0_35 = 0 & all_24_3_25 = 0 & leq(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_37_0_35 = 0) & leq(all_0_4_4, all_0_4_4) = all_37_0_35)
% 7.53/2.36 |
% 7.53/2.36 +-Applying beta-rule and splitting (87), into two cases.
% 7.53/2.36 |-Branch one:
% 7.53/2.36 | (88) all_37_0_35 = 0 & all_24_3_25 = 0 & leq(all_0_4_4, all_0_3_3) = 0
% 7.53/2.36 |
% 7.53/2.36 | Applying alpha-rule on (88) yields:
% 7.53/2.36 | (89) all_37_0_35 = 0
% 7.53/2.36 | (90) all_24_3_25 = 0
% 7.53/2.36 | (91) leq(all_0_4_4, all_0_3_3) = 0
% 7.53/2.36 |
% 7.53/2.36 | Equations (90) can reduce 84 to:
% 7.53/2.36 | (54) $false
% 7.53/2.36 |
% 7.53/2.36 |-The branch is then unsatisfiable
% 7.53/2.36 |-Branch two:
% 7.53/2.36 | (93) ~ (all_37_0_35 = 0) & leq(all_0_4_4, all_0_4_4) = all_37_0_35
% 7.53/2.36 |
% 7.53/2.36 | Applying alpha-rule on (93) yields:
% 7.53/2.36 | (94) ~ (all_37_0_35 = 0)
% 7.53/2.36 | (95) leq(all_0_4_4, all_0_4_4) = all_37_0_35
% 7.53/2.36 |
% 7.53/2.36 | Instantiating formula (39) with all_37_0_35, all_0_4_4, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms ismeetu(all_0_4_4, all_0_3_3, all_0_2_2) = 0, leq(all_0_4_4, all_0_4_4) = all_37_0_35, yields:
% 7.53/2.36 | (96) all_37_0_35 = 0 | ? [v0] : (( ~ (v0 = 0) & leq(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & leq(all_0_4_4, all_0_3_3) = v0))
% 7.53/2.36 |
% 7.53/2.36 | Instantiating formula (40) with all_37_0_35, all_0_4_4, all_0_4_4 and discharging atoms leq(all_0_4_4, all_0_4_4) = all_37_0_35, yields:
% 7.53/2.36 | (97) all_37_0_35 = 0 | ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_0_4_4, all_0_4_4) = v0)
% 7.53/2.36 |
% 7.53/2.36 +-Applying beta-rule and splitting (96), into two cases.
% 7.53/2.36 |-Branch one:
% 7.53/2.36 | (89) all_37_0_35 = 0
% 7.53/2.36 |
% 7.53/2.36 | Equations (89) can reduce 94 to:
% 7.53/2.36 | (54) $false
% 7.53/2.36 |
% 7.53/2.36 |-The branch is then unsatisfiable
% 7.53/2.36 |-Branch two:
% 7.53/2.36 | (94) ~ (all_37_0_35 = 0)
% 7.53/2.36 | (101) ? [v0] : (( ~ (v0 = 0) & leq(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & leq(all_0_4_4, all_0_3_3) = v0))
% 7.53/2.36 |
% 7.53/2.36 +-Applying beta-rule and splitting (97), into two cases.
% 7.53/2.36 |-Branch one:
% 7.53/2.36 | (89) all_37_0_35 = 0
% 7.53/2.36 |
% 7.53/2.36 | Equations (89) can reduce 94 to:
% 7.53/2.36 | (54) $false
% 7.53/2.36 |
% 7.53/2.36 |-The branch is then unsatisfiable
% 7.53/2.36 |-Branch two:
% 7.53/2.36 | (94) ~ (all_37_0_35 = 0)
% 7.53/2.36 | (105) ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_0_4_4, all_0_4_4) = v0)
% 7.53/2.36 |
% 7.53/2.36 | Instantiating (105) with all_60_0_38 yields:
% 7.53/2.36 | (106) ~ (all_60_0_38 = all_0_4_4) & addition(all_0_4_4, all_0_4_4) = all_60_0_38
% 7.53/2.36 |
% 7.53/2.36 | Applying alpha-rule on (106) yields:
% 7.53/2.36 | (107) ~ (all_60_0_38 = all_0_4_4)
% 7.53/2.36 | (108) addition(all_0_4_4, all_0_4_4) = all_60_0_38
% 7.53/2.36 |
% 7.53/2.36 | Instantiating formula (10) with all_60_0_38, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_4_4) = all_60_0_38, yields:
% 7.53/2.36 | (109) all_60_0_38 = all_0_4_4
% 7.53/2.36 |
% 7.53/2.36 | Equations (109) can reduce 107 to:
% 7.53/2.36 | (54) $false
% 7.53/2.36 |
% 7.53/2.36 |-The branch is then unsatisfiable
% 7.53/2.36 |-Branch two:
% 7.53/2.36 | (111) ~ (all_24_3_25 = 0) & leq(all_0_4_4, all_0_3_3) = all_24_3_25
% 7.53/2.36 |
% 7.53/2.36 | Applying alpha-rule on (111) yields:
% 7.53/2.36 | (84) ~ (all_24_3_25 = 0)
% 7.53/2.36 | (113) leq(all_0_4_4, all_0_3_3) = all_24_3_25
% 7.53/2.36 |
% 7.53/2.36 | Instantiating formula (11) with all_24_3_25, all_0_4_4, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms ismeetu(all_0_4_4, all_0_3_3, all_0_2_2) = 0, leq(all_0_4_4, all_0_3_3) = all_24_3_25, yields:
% 7.53/2.36 | (114) ? [v0] : ((v0 = 0 & all_24_3_25 = 0 & leq(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & leq(all_0_4_4, all_0_4_4) = v0))
% 7.53/2.36 |
% 7.53/2.36 | Instantiating (114) with all_37_0_39 yields:
% 7.53/2.36 | (115) (all_37_0_39 = 0 & all_24_3_25 = 0 & leq(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_37_0_39 = 0) & leq(all_0_4_4, all_0_4_4) = all_37_0_39)
% 7.53/2.36 |
% 7.53/2.36 +-Applying beta-rule and splitting (115), into two cases.
% 7.53/2.36 |-Branch one:
% 7.53/2.36 | (116) all_37_0_39 = 0 & all_24_3_25 = 0 & leq(all_0_4_4, all_0_2_2) = 0
% 7.53/2.36 |
% 7.53/2.36 | Applying alpha-rule on (116) yields:
% 7.53/2.36 | (117) all_37_0_39 = 0
% 7.53/2.36 | (90) all_24_3_25 = 0
% 7.53/2.36 | (119) leq(all_0_4_4, all_0_2_2) = 0
% 7.53/2.36 |
% 7.53/2.36 | Equations (90) can reduce 84 to:
% 7.53/2.36 | (54) $false
% 7.53/2.36 |
% 7.53/2.36 |-The branch is then unsatisfiable
% 7.53/2.36 |-Branch two:
% 7.53/2.36 | (121) ~ (all_37_0_39 = 0) & leq(all_0_4_4, all_0_4_4) = all_37_0_39
% 7.53/2.36 |
% 7.53/2.36 | Applying alpha-rule on (121) yields:
% 7.53/2.36 | (122) ~ (all_37_0_39 = 0)
% 7.53/2.37 | (123) leq(all_0_4_4, all_0_4_4) = all_37_0_39
% 7.53/2.37 |
% 7.53/2.37 | Instantiating formula (39) with all_37_0_39, all_0_4_4, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms ismeetu(all_0_4_4, all_0_3_3, all_0_2_2) = 0, leq(all_0_4_4, all_0_4_4) = all_37_0_39, yields:
% 7.53/2.37 | (124) all_37_0_39 = 0 | ? [v0] : (( ~ (v0 = 0) & leq(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & leq(all_0_4_4, all_0_3_3) = v0))
% 7.53/2.37 |
% 7.53/2.37 | Instantiating formula (40) with all_37_0_39, all_0_4_4, all_0_4_4 and discharging atoms leq(all_0_4_4, all_0_4_4) = all_37_0_39, yields:
% 7.53/2.37 | (125) all_37_0_39 = 0 | ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_0_4_4, all_0_4_4) = v0)
% 7.53/2.37 |
% 7.53/2.37 +-Applying beta-rule and splitting (124), into two cases.
% 7.53/2.37 |-Branch one:
% 7.53/2.37 | (117) all_37_0_39 = 0
% 7.53/2.37 |
% 7.53/2.37 | Equations (117) can reduce 122 to:
% 7.53/2.37 | (54) $false
% 7.53/2.37 |
% 7.53/2.37 |-The branch is then unsatisfiable
% 7.53/2.37 |-Branch two:
% 7.53/2.37 | (122) ~ (all_37_0_39 = 0)
% 7.53/2.37 | (101) ? [v0] : (( ~ (v0 = 0) & leq(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & leq(all_0_4_4, all_0_3_3) = v0))
% 7.53/2.37 |
% 7.53/2.37 +-Applying beta-rule and splitting (125), into two cases.
% 7.53/2.37 |-Branch one:
% 7.53/2.37 | (117) all_37_0_39 = 0
% 7.53/2.37 |
% 7.53/2.37 | Equations (117) can reduce 122 to:
% 7.53/2.37 | (54) $false
% 7.53/2.37 |
% 7.53/2.37 |-The branch is then unsatisfiable
% 7.53/2.37 |-Branch two:
% 7.53/2.37 | (122) ~ (all_37_0_39 = 0)
% 7.53/2.37 | (105) ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_0_4_4, all_0_4_4) = v0)
% 7.53/2.37 |
% 7.53/2.37 | Instantiating (105) with all_60_0_42 yields:
% 7.53/2.37 | (134) ~ (all_60_0_42 = all_0_4_4) & addition(all_0_4_4, all_0_4_4) = all_60_0_42
% 7.53/2.37 |
% 7.53/2.37 | Applying alpha-rule on (134) yields:
% 7.53/2.37 | (135) ~ (all_60_0_42 = all_0_4_4)
% 7.53/2.37 | (136) addition(all_0_4_4, all_0_4_4) = all_60_0_42
% 7.53/2.37 |
% 7.53/2.37 | Instantiating formula (10) with all_60_0_42, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_4_4) = all_60_0_42, yields:
% 7.53/2.37 | (137) all_60_0_42 = all_0_4_4
% 7.53/2.37 |
% 7.53/2.37 | Equations (137) can reduce 135 to:
% 7.53/2.37 | (54) $false
% 7.53/2.37 |
% 7.53/2.37 |-The branch is then unsatisfiable
% 7.53/2.37 |-Branch two:
% 7.53/2.37 | (139) all_0_1_1 = 0 & ~ (all_0_0_0 = 0)
% 7.53/2.37 |
% 7.53/2.37 | Applying alpha-rule on (139) yields:
% 7.53/2.37 | (53) all_0_1_1 = 0
% 7.53/2.37 | (141) ~ (all_0_0_0 = 0)
% 7.53/2.37 |
% 7.53/2.37 | From (53) and (38) follows:
% 7.53/2.37 | (142) ismeet(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 7.53/2.37 |
% 7.53/2.37 +-Applying beta-rule and splitting (47), into two cases.
% 7.53/2.37 |-Branch one:
% 7.53/2.37 | (50) all_0_0_0 = 0
% 7.53/2.37 |
% 7.53/2.37 | Equations (50) can reduce 141 to:
% 7.53/2.37 | (54) $false
% 7.53/2.37 |
% 7.53/2.37 |-The branch is then unsatisfiable
% 7.53/2.37 |-Branch two:
% 7.53/2.37 | (141) ~ (all_0_0_0 = 0)
% 7.53/2.37 | (146) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & leq(v0, all_0_4_4) = 0) | (v2 = 0 & v1 = 0 & leq(v0, all_0_2_2) = 0 & leq(v0, all_0_3_3) = 0)) & (( ~ (v3 = 0) & leq(v0, all_0_4_4) = v3) | ( ~ (v2 = 0) & leq(v0, all_0_2_2) = v2) | ( ~ (v1 = 0) & leq(v0, all_0_3_3) = v1)))
% 7.53/2.37 |
% 7.53/2.37 | Instantiating (146) with all_24_0_43, all_24_1_44, all_24_2_45, all_24_3_46 yields:
% 7.53/2.37 | (147) ((all_24_0_43 = 0 & leq(all_24_3_46, all_0_4_4) = 0) | (all_24_1_44 = 0 & all_24_2_45 = 0 & leq(all_24_3_46, all_0_2_2) = 0 & leq(all_24_3_46, all_0_3_3) = 0)) & (( ~ (all_24_0_43 = 0) & leq(all_24_3_46, all_0_4_4) = all_24_0_43) | ( ~ (all_24_1_44 = 0) & leq(all_24_3_46, all_0_2_2) = all_24_1_44) | ( ~ (all_24_2_45 = 0) & leq(all_24_3_46, all_0_3_3) = all_24_2_45))
% 7.53/2.37 |
% 7.53/2.37 | Applying alpha-rule on (147) yields:
% 7.53/2.37 | (148) (all_24_0_43 = 0 & leq(all_24_3_46, all_0_4_4) = 0) | (all_24_1_44 = 0 & all_24_2_45 = 0 & leq(all_24_3_46, all_0_2_2) = 0 & leq(all_24_3_46, all_0_3_3) = 0)
% 7.53/2.37 | (149) ( ~ (all_24_0_43 = 0) & leq(all_24_3_46, all_0_4_4) = all_24_0_43) | ( ~ (all_24_1_44 = 0) & leq(all_24_3_46, all_0_2_2) = all_24_1_44) | ( ~ (all_24_2_45 = 0) & leq(all_24_3_46, all_0_3_3) = all_24_2_45)
% 7.53/2.37 |
% 7.53/2.37 | Instantiating formula (31) with all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms ismeet(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 7.53/2.37 | (150) leq(all_0_4_4, all_0_2_2) = 0 & leq(all_0_4_4, all_0_3_3) = 0
% 7.53/2.37 |
% 7.53/2.37 | Applying alpha-rule on (150) yields:
% 7.53/2.37 | (119) leq(all_0_4_4, all_0_2_2) = 0
% 7.53/2.37 | (91) leq(all_0_4_4, all_0_3_3) = 0
% 7.53/2.37 |
% 7.53/2.37 | Instantiating formula (18) with all_0_2_2, all_0_4_4 and discharging atoms leq(all_0_4_4, all_0_2_2) = 0, yields:
% 7.53/2.37 | (153) addition(all_0_4_4, all_0_2_2) = all_0_2_2
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (27) with all_0_4_4, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms ismeet(all_0_4_4, all_0_3_3, all_0_2_2) = 0, leq(all_0_4_4, all_0_3_3) = 0, yields:
% 7.53/2.38 | (154) ? [v0] : ((v0 = 0 & leq(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & leq(all_0_4_4, all_0_2_2) = v0))
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (18) with all_0_3_3, all_0_4_4 and discharging atoms leq(all_0_4_4, all_0_3_3) = 0, yields:
% 7.53/2.38 | (155) addition(all_0_4_4, all_0_3_3) = all_0_3_3
% 7.53/2.38 |
% 7.53/2.38 | Instantiating (154) with all_38_0_48 yields:
% 7.53/2.38 | (156) (all_38_0_48 = 0 & leq(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_38_0_48 = 0) & leq(all_0_4_4, all_0_2_2) = all_38_0_48)
% 7.53/2.38 |
% 7.53/2.38 +-Applying beta-rule and splitting (156), into two cases.
% 7.53/2.38 |-Branch one:
% 7.53/2.38 | (157) all_38_0_48 = 0 & leq(all_0_4_4, all_0_4_4) = 0
% 7.53/2.38 |
% 7.53/2.38 | Applying alpha-rule on (157) yields:
% 7.53/2.38 | (158) all_38_0_48 = 0
% 7.53/2.38 | (159) leq(all_0_4_4, all_0_4_4) = 0
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (18) with all_0_4_4, all_0_4_4 and discharging atoms leq(all_0_4_4, all_0_4_4) = 0, yields:
% 7.53/2.38 | (160) addition(all_0_4_4, all_0_4_4) = all_0_4_4
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (30) with all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_4_4, all_0_2_2) = all_0_2_2, yields:
% 7.53/2.38 | (161) ? [v0] : (addition(v0, all_0_2_2) = all_0_2_2 & addition(all_0_4_4, all_0_4_4) = v0)
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (30) with all_0_3_3, all_0_3_3, all_0_4_4, all_0_4_4, all_0_3_3 and discharging atoms addition(all_0_4_4, all_0_3_3) = all_0_3_3, yields:
% 7.53/2.38 | (162) ? [v0] : (addition(v0, all_0_3_3) = all_0_3_3 & addition(all_0_4_4, all_0_4_4) = v0)
% 7.53/2.38 |
% 7.53/2.38 | Instantiating (162) with all_53_0_49 yields:
% 7.53/2.38 | (163) addition(all_53_0_49, all_0_3_3) = all_0_3_3 & addition(all_0_4_4, all_0_4_4) = all_53_0_49
% 7.53/2.38 |
% 7.53/2.38 | Applying alpha-rule on (163) yields:
% 7.53/2.38 | (164) addition(all_53_0_49, all_0_3_3) = all_0_3_3
% 7.53/2.38 | (165) addition(all_0_4_4, all_0_4_4) = all_53_0_49
% 7.53/2.38 |
% 7.53/2.38 | Instantiating (161) with all_55_0_50 yields:
% 7.53/2.38 | (166) addition(all_55_0_50, all_0_2_2) = all_0_2_2 & addition(all_0_4_4, all_0_4_4) = all_55_0_50
% 7.53/2.38 |
% 7.53/2.38 | Applying alpha-rule on (166) yields:
% 7.53/2.38 | (167) addition(all_55_0_50, all_0_2_2) = all_0_2_2
% 7.53/2.38 | (168) addition(all_0_4_4, all_0_4_4) = all_55_0_50
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (20) with all_0_4_4, all_0_4_4, all_53_0_49, all_55_0_50 and discharging atoms addition(all_0_4_4, all_0_4_4) = all_55_0_50, addition(all_0_4_4, all_0_4_4) = all_53_0_49, yields:
% 7.53/2.38 | (169) all_55_0_50 = all_53_0_49
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (20) with all_0_4_4, all_0_4_4, all_0_4_4, all_55_0_50 and discharging atoms addition(all_0_4_4, all_0_4_4) = all_55_0_50, addition(all_0_4_4, all_0_4_4) = all_0_4_4, yields:
% 7.53/2.38 | (170) all_55_0_50 = all_0_4_4
% 7.53/2.38 |
% 7.53/2.38 | Combining equations (170,169) yields a new equation:
% 7.53/2.38 | (171) all_53_0_49 = all_0_4_4
% 7.53/2.38 |
% 7.53/2.38 | Combining equations (171,169) yields a new equation:
% 7.53/2.38 | (170) all_55_0_50 = all_0_4_4
% 7.53/2.38 |
% 7.53/2.38 | From (170) and (167) follows:
% 7.53/2.38 | (153) addition(all_0_4_4, all_0_2_2) = all_0_2_2
% 7.53/2.38 |
% 7.53/2.38 | From (171) and (164) follows:
% 7.53/2.38 | (155) addition(all_0_4_4, all_0_3_3) = all_0_3_3
% 7.53/2.38 |
% 7.53/2.38 +-Applying beta-rule and splitting (148), into two cases.
% 7.53/2.38 |-Branch one:
% 7.53/2.38 | (175) all_24_0_43 = 0 & leq(all_24_3_46, all_0_4_4) = 0
% 7.53/2.38 |
% 7.53/2.38 | Applying alpha-rule on (175) yields:
% 7.53/2.38 | (176) all_24_0_43 = 0
% 7.53/2.38 | (177) leq(all_24_3_46, all_0_4_4) = 0
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (18) with all_0_4_4, all_24_3_46 and discharging atoms leq(all_24_3_46, all_0_4_4) = 0, yields:
% 7.53/2.38 | (178) addition(all_24_3_46, all_0_4_4) = all_0_4_4
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (9) with all_0_2_2, all_0_4_4, all_24_3_46, all_0_4_4, all_0_2_2 and discharging atoms addition(all_24_3_46, all_0_4_4) = all_0_4_4, addition(all_0_4_4, all_0_2_2) = all_0_2_2, yields:
% 7.53/2.38 | (179) ? [v0] : (addition(all_24_3_46, v0) = all_0_2_2 & addition(all_0_4_4, all_0_2_2) = v0)
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (9) with all_0_3_3, all_0_4_4, all_24_3_46, all_0_4_4, all_0_3_3 and discharging atoms addition(all_24_3_46, all_0_4_4) = all_0_4_4, addition(all_0_4_4, all_0_3_3) = all_0_3_3, yields:
% 7.53/2.38 | (180) ? [v0] : (addition(all_24_3_46, v0) = all_0_3_3 & addition(all_0_4_4, all_0_3_3) = v0)
% 7.53/2.38 |
% 7.53/2.38 | Instantiating (180) with all_80_0_51 yields:
% 7.53/2.38 | (181) addition(all_24_3_46, all_80_0_51) = all_0_3_3 & addition(all_0_4_4, all_0_3_3) = all_80_0_51
% 7.53/2.38 |
% 7.53/2.38 | Applying alpha-rule on (181) yields:
% 7.53/2.38 | (182) addition(all_24_3_46, all_80_0_51) = all_0_3_3
% 7.53/2.38 | (183) addition(all_0_4_4, all_0_3_3) = all_80_0_51
% 7.53/2.38 |
% 7.53/2.38 | Instantiating (179) with all_82_0_52 yields:
% 7.53/2.38 | (184) addition(all_24_3_46, all_82_0_52) = all_0_2_2 & addition(all_0_4_4, all_0_2_2) = all_82_0_52
% 7.53/2.38 |
% 7.53/2.38 | Applying alpha-rule on (184) yields:
% 7.53/2.38 | (185) addition(all_24_3_46, all_82_0_52) = all_0_2_2
% 7.53/2.38 | (186) addition(all_0_4_4, all_0_2_2) = all_82_0_52
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (20) with all_0_4_4, all_0_2_2, all_82_0_52, all_0_2_2 and discharging atoms addition(all_0_4_4, all_0_2_2) = all_82_0_52, addition(all_0_4_4, all_0_2_2) = all_0_2_2, yields:
% 7.53/2.38 | (187) all_82_0_52 = all_0_2_2
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (20) with all_0_4_4, all_0_3_3, all_80_0_51, all_0_3_3 and discharging atoms addition(all_0_4_4, all_0_3_3) = all_80_0_51, addition(all_0_4_4, all_0_3_3) = all_0_3_3, yields:
% 7.53/2.38 | (188) all_80_0_51 = all_0_3_3
% 7.53/2.38 |
% 7.53/2.38 | From (187) and (185) follows:
% 7.53/2.38 | (189) addition(all_24_3_46, all_0_2_2) = all_0_2_2
% 7.53/2.38 |
% 7.53/2.38 | From (188) and (182) follows:
% 7.53/2.38 | (190) addition(all_24_3_46, all_0_3_3) = all_0_3_3
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (17) with all_0_2_2, all_24_3_46 and discharging atoms addition(all_24_3_46, all_0_2_2) = all_0_2_2, yields:
% 7.53/2.38 | (191) leq(all_24_3_46, all_0_2_2) = 0
% 7.53/2.38 |
% 7.53/2.38 | Instantiating formula (17) with all_0_3_3, all_24_3_46 and discharging atoms addition(all_24_3_46, all_0_3_3) = all_0_3_3, yields:
% 7.53/2.38 | (192) leq(all_24_3_46, all_0_3_3) = 0
% 7.53/2.38 |
% 7.53/2.38 +-Applying beta-rule and splitting (149), into two cases.
% 7.53/2.38 |-Branch one:
% 7.53/2.38 | (193) ( ~ (all_24_0_43 = 0) & leq(all_24_3_46, all_0_4_4) = all_24_0_43) | ( ~ (all_24_1_44 = 0) & leq(all_24_3_46, all_0_2_2) = all_24_1_44)
% 7.53/2.39 |
% 7.53/2.39 +-Applying beta-rule and splitting (193), into two cases.
% 7.53/2.39 |-Branch one:
% 7.53/2.39 | (194) ~ (all_24_0_43 = 0) & leq(all_24_3_46, all_0_4_4) = all_24_0_43
% 7.53/2.39 |
% 7.53/2.39 | Applying alpha-rule on (194) yields:
% 7.53/2.39 | (195) ~ (all_24_0_43 = 0)
% 7.53/2.39 | (196) leq(all_24_3_46, all_0_4_4) = all_24_0_43
% 7.53/2.39 |
% 7.53/2.39 | Equations (176) can reduce 195 to:
% 7.53/2.39 | (54) $false
% 7.53/2.39 |
% 7.53/2.39 |-The branch is then unsatisfiable
% 7.53/2.39 |-Branch two:
% 7.53/2.39 | (198) ~ (all_24_1_44 = 0) & leq(all_24_3_46, all_0_2_2) = all_24_1_44
% 7.53/2.39 |
% 7.53/2.39 | Applying alpha-rule on (198) yields:
% 7.53/2.39 | (199) ~ (all_24_1_44 = 0)
% 7.53/2.39 | (200) leq(all_24_3_46, all_0_2_2) = all_24_1_44
% 7.53/2.39 |
% 7.53/2.39 | Instantiating formula (4) with all_24_3_46, all_0_2_2, 0, all_24_1_44 and discharging atoms leq(all_24_3_46, all_0_2_2) = all_24_1_44, leq(all_24_3_46, all_0_2_2) = 0, yields:
% 7.53/2.39 | (201) all_24_1_44 = 0
% 7.53/2.39 |
% 7.53/2.39 | Equations (201) can reduce 199 to:
% 7.53/2.39 | (54) $false
% 7.53/2.39 |
% 7.53/2.39 |-The branch is then unsatisfiable
% 7.53/2.39 |-Branch two:
% 7.53/2.39 | (203) ~ (all_24_2_45 = 0) & leq(all_24_3_46, all_0_3_3) = all_24_2_45
% 7.53/2.39 |
% 7.53/2.39 | Applying alpha-rule on (203) yields:
% 7.53/2.39 | (204) ~ (all_24_2_45 = 0)
% 7.53/2.39 | (205) leq(all_24_3_46, all_0_3_3) = all_24_2_45
% 7.53/2.39 |
% 7.53/2.39 | Instantiating formula (4) with all_24_3_46, all_0_3_3, 0, all_24_2_45 and discharging atoms leq(all_24_3_46, all_0_3_3) = all_24_2_45, leq(all_24_3_46, all_0_3_3) = 0, yields:
% 7.53/2.39 | (206) all_24_2_45 = 0
% 7.53/2.39 |
% 7.53/2.39 | Equations (206) can reduce 204 to:
% 7.53/2.39 | (54) $false
% 7.53/2.39 |
% 7.53/2.39 |-The branch is then unsatisfiable
% 7.53/2.39 |-Branch two:
% 7.53/2.39 | (208) all_24_1_44 = 0 & all_24_2_45 = 0 & leq(all_24_3_46, all_0_2_2) = 0 & leq(all_24_3_46, all_0_3_3) = 0
% 7.53/2.39 |
% 7.53/2.39 | Applying alpha-rule on (208) yields:
% 7.53/2.39 | (201) all_24_1_44 = 0
% 7.53/2.39 | (206) all_24_2_45 = 0
% 7.53/2.39 | (191) leq(all_24_3_46, all_0_2_2) = 0
% 7.53/2.39 | (192) leq(all_24_3_46, all_0_3_3) = 0
% 7.53/2.39 |
% 7.53/2.39 +-Applying beta-rule and splitting (149), into two cases.
% 7.53/2.39 |-Branch one:
% 7.53/2.39 | (193) ( ~ (all_24_0_43 = 0) & leq(all_24_3_46, all_0_4_4) = all_24_0_43) | ( ~ (all_24_1_44 = 0) & leq(all_24_3_46, all_0_2_2) = all_24_1_44)
% 7.53/2.39 |
% 7.53/2.39 +-Applying beta-rule and splitting (193), into two cases.
% 7.53/2.39 |-Branch one:
% 7.53/2.39 | (194) ~ (all_24_0_43 = 0) & leq(all_24_3_46, all_0_4_4) = all_24_0_43
% 7.53/2.39 |
% 7.53/2.39 | Applying alpha-rule on (194) yields:
% 7.53/2.39 | (195) ~ (all_24_0_43 = 0)
% 7.53/2.39 | (196) leq(all_24_3_46, all_0_4_4) = all_24_0_43
% 7.53/2.39 |
% 7.53/2.39 | Instantiating formula (27) with all_24_3_46, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms ismeet(all_0_4_4, all_0_3_3, all_0_2_2) = 0, leq(all_24_3_46, all_0_3_3) = 0, yields:
% 7.53/2.39 | (217) ? [v0] : ((v0 = 0 & leq(all_24_3_46, all_0_4_4) = 0) | ( ~ (v0 = 0) & leq(all_24_3_46, all_0_2_2) = v0))
% 7.53/2.39 |
% 7.53/2.39 | Instantiating formula (40) with all_24_0_43, all_0_4_4, all_24_3_46 and discharging atoms leq(all_24_3_46, all_0_4_4) = all_24_0_43, yields:
% 7.53/2.39 | (218) all_24_0_43 = 0 | ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_24_3_46, all_0_4_4) = v0)
% 7.53/2.39 |
% 7.53/2.39 | Instantiating (217) with all_78_0_77 yields:
% 7.53/2.39 | (219) (all_78_0_77 = 0 & leq(all_24_3_46, all_0_4_4) = 0) | ( ~ (all_78_0_77 = 0) & leq(all_24_3_46, all_0_2_2) = all_78_0_77)
% 7.53/2.39 |
% 7.53/2.39 +-Applying beta-rule and splitting (219), into two cases.
% 7.53/2.39 |-Branch one:
% 7.53/2.39 | (220) all_78_0_77 = 0 & leq(all_24_3_46, all_0_4_4) = 0
% 7.53/2.39 |
% 7.53/2.39 | Applying alpha-rule on (220) yields:
% 7.53/2.39 | (221) all_78_0_77 = 0
% 7.53/2.39 | (177) leq(all_24_3_46, all_0_4_4) = 0
% 7.53/2.39 |
% 7.53/2.39 +-Applying beta-rule and splitting (218), into two cases.
% 7.53/2.39 |-Branch one:
% 7.53/2.39 | (176) all_24_0_43 = 0
% 7.53/2.39 |
% 7.53/2.39 | Equations (176) can reduce 195 to:
% 7.53/2.39 | (54) $false
% 7.53/2.39 |
% 7.53/2.39 |-The branch is then unsatisfiable
% 7.53/2.39 |-Branch two:
% 7.53/2.39 | (195) ~ (all_24_0_43 = 0)
% 7.53/2.39 | (226) ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_24_3_46, all_0_4_4) = v0)
% 7.53/2.39 |
% 7.53/2.39 | Instantiating formula (4) with all_24_3_46, all_0_4_4, 0, all_24_0_43 and discharging atoms leq(all_24_3_46, all_0_4_4) = all_24_0_43, leq(all_24_3_46, all_0_4_4) = 0, yields:
% 7.53/2.39 | (176) all_24_0_43 = 0
% 7.53/2.39 |
% 7.53/2.39 | Equations (176) can reduce 195 to:
% 7.53/2.39 | (54) $false
% 7.53/2.39 |
% 7.53/2.39 |-The branch is then unsatisfiable
% 7.53/2.39 |-Branch two:
% 7.53/2.39 | (229) ~ (all_78_0_77 = 0) & leq(all_24_3_46, all_0_2_2) = all_78_0_77
% 7.53/2.39 |
% 7.53/2.39 | Applying alpha-rule on (229) yields:
% 7.53/2.39 | (230) ~ (all_78_0_77 = 0)
% 7.53/2.39 | (231) leq(all_24_3_46, all_0_2_2) = all_78_0_77
% 7.53/2.39 |
% 7.53/2.39 | Instantiating formula (4) with all_24_3_46, all_0_2_2, all_78_0_77, 0 and discharging atoms leq(all_24_3_46, all_0_2_2) = all_78_0_77, leq(all_24_3_46, all_0_2_2) = 0, yields:
% 7.53/2.39 | (221) all_78_0_77 = 0
% 7.53/2.39 |
% 7.53/2.39 | Equations (221) can reduce 230 to:
% 7.53/2.39 | (54) $false
% 7.53/2.39 |
% 7.53/2.39 |-The branch is then unsatisfiable
% 7.53/2.39 |-Branch two:
% 7.53/2.39 | (198) ~ (all_24_1_44 = 0) & leq(all_24_3_46, all_0_2_2) = all_24_1_44
% 7.53/2.39 |
% 7.53/2.39 | Applying alpha-rule on (198) yields:
% 7.53/2.39 | (199) ~ (all_24_1_44 = 0)
% 7.53/2.39 | (200) leq(all_24_3_46, all_0_2_2) = all_24_1_44
% 7.53/2.39 |
% 7.53/2.39 | Equations (201) can reduce 199 to:
% 7.53/2.39 | (54) $false
% 7.53/2.39 |
% 7.53/2.39 |-The branch is then unsatisfiable
% 7.53/2.39 |-Branch two:
% 7.53/2.39 | (203) ~ (all_24_2_45 = 0) & leq(all_24_3_46, all_0_3_3) = all_24_2_45
% 7.53/2.39 |
% 7.53/2.39 | Applying alpha-rule on (203) yields:
% 7.53/2.39 | (204) ~ (all_24_2_45 = 0)
% 7.53/2.39 | (205) leq(all_24_3_46, all_0_3_3) = all_24_2_45
% 7.53/2.39 |
% 7.53/2.39 | Equations (206) can reduce 204 to:
% 7.53/2.39 | (54) $false
% 7.53/2.39 |
% 7.53/2.39 |-The branch is then unsatisfiable
% 7.53/2.39 |-Branch two:
% 7.53/2.39 | (242) ~ (all_38_0_48 = 0) & leq(all_0_4_4, all_0_2_2) = all_38_0_48
% 7.53/2.39 |
% 7.53/2.39 | Applying alpha-rule on (242) yields:
% 7.53/2.39 | (243) ~ (all_38_0_48 = 0)
% 7.53/2.39 | (244) leq(all_0_4_4, all_0_2_2) = all_38_0_48
% 7.53/2.39 |
% 7.53/2.39 | Instantiating formula (4) with all_0_4_4, all_0_2_2, all_38_0_48, 0 and discharging atoms leq(all_0_4_4, all_0_2_2) = all_38_0_48, leq(all_0_4_4, all_0_2_2) = 0, yields:
% 7.53/2.39 | (158) all_38_0_48 = 0
% 7.53/2.39 |
% 7.53/2.39 | Equations (158) can reduce 243 to:
% 7.53/2.39 | (54) $false
% 7.53/2.39 |
% 7.53/2.39 |-The branch is then unsatisfiable
% 7.53/2.39 % SZS output end Proof for theBenchmark
% 7.53/2.39
% 7.53/2.39 1797ms
%------------------------------------------------------------------------------