TSTP Solution File: KLE038+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE038+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.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 01:51:04 EDT 2022
% Result : Theorem 21.59s 6.34s
% Output : Proof 27.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE038+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 16 08:37:10 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.58/0.57 ____ _
% 0.58/0.57 ___ / __ \_____(_)___ ________ __________
% 0.58/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.57
% 0.58/0.57 A Theorem Prover for First-Order Logic
% 0.58/0.57 (ePrincess v.1.0)
% 0.58/0.57
% 0.58/0.57 (c) Philipp Rümmer, 2009-2015
% 0.58/0.57 (c) Peter Backeman, 2014-2015
% 0.58/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.57 Bug reports to peter@backeman.se
% 0.58/0.57
% 0.58/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.57
% 0.58/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.62/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.50/0.92 Prover 0: Preprocessing ...
% 1.98/1.14 Prover 0: Constructing countermodel ...
% 19.85/5.91 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.85/5.94 Prover 1: Preprocessing ...
% 19.85/5.99 Prover 1: Constructing countermodel ...
% 20.23/6.04 Prover 1: gave up
% 20.23/6.04 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 20.23/6.05 Prover 2: Preprocessing ...
% 20.70/6.09 Prover 2: Warning: ignoring some quantifiers
% 20.70/6.10 Prover 2: Constructing countermodel ...
% 21.59/6.34 Prover 2: proved (297ms)
% 21.59/6.34 Prover 0: stopped
% 21.59/6.34
% 21.59/6.34 No countermodel exists, formula is valid
% 21.59/6.34 % SZS status Theorem for theBenchmark
% 21.59/6.34
% 21.59/6.34 Generating proof ... Warning: ignoring some quantifiers
% 26.86/7.60 found it (size 265)
% 26.86/7.60
% 26.86/7.60 % SZS output start Proof for theBenchmark
% 26.86/7.60 Assumed formulas after preprocessing and simplification:
% 26.86/7.60 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & star(v0) = v1 & leq(v0, v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (star(v4) = v6) | ~ (leq(v7, v3) = v8) | ~ (multiplication(v5, v6) = v7) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = 0) & leq(v10, v3) = v11 & multiplication(v3, v4) = v9 & addition(v9, v5) = v10)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (star(v3) = v6) | ~ (leq(v7, v4) = v8) | ~ (multiplication(v6, v5) = v7) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = 0) & leq(v10, v4) = v11 & multiplication(v3, v4) = v9 & addition(v9, v5) = v10)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v4, v5) = v7) | ~ (multiplication(v3, v5) = v6) | ~ (addition(v6, v7) = v8) | ? [v9] : (multiplication(v9, v5) = v8 & addition(v3, v4) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v3, v5) = v7) | ~ (multiplication(v3, v4) = v6) | ~ (addition(v6, v7) = v8) | ? [v9] : (multiplication(v3, v9) = v8 & addition(v4, v5) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v6, v5) = v7) | ~ (multiplication(v3, v4) = v6) | ? [v8] : (multiplication(v4, v5) = v8 & multiplication(v3, v8) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v6, v5) = v7) | ~ (addition(v3, v4) = v6) | ? [v8] : ? [v9] : (multiplication(v4, v5) = v9 & multiplication(v3, v5) = v8 & addition(v8, v9) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v4, v5) = v6) | ~ (multiplication(v3, v6) = v7) | ? [v8] : (multiplication(v8, v5) = v7 & multiplication(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v3, v6) = v7) | ~ (addition(v4, v5) = v6) | ? [v8] : ? [v9] : (multiplication(v3, v5) = v9 & multiplication(v3, v4) = v8 & addition(v8, v9) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v3, v4) = v6) | ~ (addition(v6, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & star(v4) = v8 & leq(v9, v3) = 0 & multiplication(v5, v8) = v9) | ( ~ (v8 = 0) & leq(v7, v3) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v3, v4) = v6) | ~ (addition(v6, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & star(v3) = v8 & leq(v9, v4) = 0 & multiplication(v8, v5) = v9) | ( ~ (v8 = 0) & leq(v7, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v6, v3) = v7) | ~ (addition(v5, v4) = v6) | ? [v8] : (addition(v5, v8) = v7 & addition(v4, v3) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v5, v6) = v7) | ~ (addition(v4, v3) = v6) | ? [v8] : (addition(v8, v3) = v7 & addition(v5, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (leq(v6, v5) = v4) | ~ (leq(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (multiplication(v6, v5) = v4) | ~ (multiplication(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (addition(v6, v5) = v4) | ~ (addition(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (addition(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & leq(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v3, v4) = v5) | ? [v6] : ( ~ (v6 = v4) & addition(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (star(v5) = v4) | ~ (star(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (addition(v4, v3) = v5) | addition(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (addition(v3, v4) = v5) | addition(v4, v3) = v5) & ! [v3] : ! [v4] : (v4 = v3 | ~ (multiplication(v3, one) = v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (multiplication(one, v3) = v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (addition(v3, v3) = v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (addition(v3, zero) = v4)) & ! [v3] : ! [v4] : (v4 = zero | ~ (multiplication(v3, zero) = v4)) & ! [v3] : ! [v4] : (v4 = zero | ~ (multiplication(zero, v3) = v4)) & ! [v3] : ! [v4] : ( ~ (star(v3) = v4) | ? [v5] : ? [v6] : (leq(v6, v4) = 0 & multiplication(v4, v3) = v5 & addition(one, v5) = v6)) & ! [v3] : ! [v4] : ( ~ (star(v3) = v4) | ? [v5] : ? [v6] : (leq(v6, v4) = 0 & multiplication(v3, v4) = v5 & addition(one, v5) = v6)) & ! [v3] : ! [v4] : ( ~ (leq(v3, v4) = 0) | addition(v3, v4) = v4) & ! [v3] : ! [v4] : ( ~ (addition(v3, v4) = v4) | leq(v3, v4) = 0) & ? [v3] : ? [v4] : ? [v5] : leq(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : multiplication(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : addition(v4, v3) = v5 & ? [v3] : ? [v4] : star(v3) = v4)
% 26.86/7.64 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 26.86/7.64 | (1) ~ (all_0_0_0 = 0) & star(all_0_2_2) = all_0_1_1 & leq(all_0_2_2, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (star(v1) = v3) | ~ (leq(v4, v0) = v5) | ~ (multiplication(v2, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v0) = v8 & multiplication(v0, v1) = v6 & addition(v6, v2) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (star(v0) = v3) | ~ (leq(v4, v1) = v5) | ~ (multiplication(v3, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v1) = v8 & multiplication(v0, v1) = v6 & addition(v6, v2) = v7)) & ! [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] : ( ~ (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] : ( ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & star(v1) = v5 & leq(v6, v0) = 0 & multiplication(v2, v5) = v6) | ( ~ (v5 = 0) & leq(v4, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & star(v0) = v5 & leq(v6, v1) = 0 & multiplication(v5, v2) = v6) | ( ~ (v5 = 0) & leq(v4, v1) = v5))) & ! [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] : (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] : (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] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) & ! [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] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (leq(v3, v1) = 0 & multiplication(v1, v0) = v2 & addition(one, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (leq(v3, v1) = 0 & multiplication(v0, v1) = v2 & addition(one, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) & ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 & ? [v0] : ? [v1] : star(v0) = v1
% 26.86/7.65 |
% 26.86/7.65 | Applying alpha-rule on (1) yields:
% 26.86/7.65 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 26.86/7.65 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 26.86/7.65 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 26.86/7.65 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 26.86/7.66 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 26.86/7.66 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 26.86/7.66 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 26.86/7.66 | (9) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2
% 26.86/7.66 | (10) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (leq(v3, v1) = 0 & multiplication(v1, v0) = v2 & addition(one, v2) = v3))
% 26.86/7.66 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (star(v0) = v3) | ~ (leq(v4, v1) = v5) | ~ (multiplication(v3, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v1) = v8 & multiplication(v0, v1) = v6 & addition(v6, v2) = v7))
% 26.86/7.66 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 26.86/7.66 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & star(v0) = v5 & leq(v6, v1) = 0 & multiplication(v5, v2) = v6) | ( ~ (v5 = 0) & leq(v4, v1) = v5)))
% 26.86/7.66 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 26.86/7.66 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 26.86/7.66 | (16) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (leq(v3, v1) = 0 & multiplication(v0, v1) = v2 & addition(one, v2) = v3))
% 26.86/7.66 | (17) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 26.86/7.66 | (18) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 26.86/7.66 | (19) ? [v0] : ? [v1] : star(v0) = v1
% 26.86/7.66 | (20) ~ (all_0_0_0 = 0)
% 26.86/7.66 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 26.86/7.66 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 26.86/7.66 | (23) ! [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))
% 26.86/7.66 | (24) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 26.86/7.66 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 26.86/7.66 | (26) ! [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))
% 26.86/7.66 | (27) star(all_0_2_2) = all_0_1_1
% 26.86/7.66 | (28) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2
% 26.86/7.66 | (29) ! [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))
% 27.28/7.66 | (30) ! [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))
% 27.28/7.66 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 27.28/7.66 | (32) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2
% 27.28/7.66 | (33) leq(all_0_2_2, all_0_1_1) = all_0_0_0
% 27.28/7.66 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 27.28/7.66 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (star(v1) = v3) | ~ (leq(v4, v0) = v5) | ~ (multiplication(v2, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v0) = v8 & multiplication(v0, v1) = v6 & addition(v6, v2) = v7))
% 27.28/7.67 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & star(v1) = v5 & leq(v6, v0) = 0 & multiplication(v2, v5) = v6) | ( ~ (v5 = 0) & leq(v4, v0) = v5)))
% 27.28/7.67 | (37) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 27.28/7.67 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0))
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (10) with all_0_1_1, all_0_2_2 and discharging atoms star(all_0_2_2) = all_0_1_1, yields:
% 27.28/7.67 | (39) ? [v0] : ? [v1] : (leq(v1, all_0_1_1) = 0 & multiplication(all_0_1_1, all_0_2_2) = v0 & addition(one, v0) = v1)
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (16) with all_0_1_1, all_0_2_2 and discharging atoms star(all_0_2_2) = all_0_1_1, yields:
% 27.28/7.67 | (40) ? [v0] : ? [v1] : (leq(v1, all_0_1_1) = 0 & multiplication(all_0_2_2, all_0_1_1) = v0 & addition(one, v0) = v1)
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (6) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms leq(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 27.28/7.67 | (41) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_2_2, all_0_1_1) = v0)
% 27.28/7.67 |
% 27.28/7.67 | Instantiating (40) with all_16_0_14, all_16_1_15 yields:
% 27.28/7.67 | (42) leq(all_16_0_14, all_0_1_1) = 0 & multiplication(all_0_2_2, all_0_1_1) = all_16_1_15 & addition(one, all_16_1_15) = all_16_0_14
% 27.28/7.67 |
% 27.28/7.67 | Applying alpha-rule on (42) yields:
% 27.28/7.67 | (43) leq(all_16_0_14, all_0_1_1) = 0
% 27.28/7.67 | (44) multiplication(all_0_2_2, all_0_1_1) = all_16_1_15
% 27.28/7.67 | (45) addition(one, all_16_1_15) = all_16_0_14
% 27.28/7.67 |
% 27.28/7.67 | Instantiating (39) with all_18_0_16, all_18_1_17 yields:
% 27.28/7.67 | (46) leq(all_18_0_16, all_0_1_1) = 0 & multiplication(all_0_1_1, all_0_2_2) = all_18_1_17 & addition(one, all_18_1_17) = all_18_0_16
% 27.28/7.67 |
% 27.28/7.67 | Applying alpha-rule on (46) yields:
% 27.28/7.67 | (47) leq(all_18_0_16, all_0_1_1) = 0
% 27.28/7.67 | (48) multiplication(all_0_1_1, all_0_2_2) = all_18_1_17
% 27.28/7.67 | (49) addition(one, all_18_1_17) = all_18_0_16
% 27.28/7.67 |
% 27.28/7.67 +-Applying beta-rule and splitting (41), into two cases.
% 27.28/7.67 |-Branch one:
% 27.28/7.67 | (50) all_0_0_0 = 0
% 27.28/7.67 |
% 27.28/7.67 | Equations (50) can reduce 20 to:
% 27.28/7.67 | (51) $false
% 27.28/7.67 |
% 27.28/7.67 |-The branch is then unsatisfiable
% 27.28/7.67 |-Branch two:
% 27.28/7.67 | (20) ~ (all_0_0_0 = 0)
% 27.28/7.67 | (53) ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_2_2, all_0_1_1) = v0)
% 27.28/7.67 |
% 27.28/7.67 | Instantiating (53) with all_24_0_18 yields:
% 27.28/7.67 | (54) ~ (all_24_0_18 = all_0_1_1) & addition(all_0_2_2, all_0_1_1) = all_24_0_18
% 27.28/7.67 |
% 27.28/7.67 | Applying alpha-rule on (54) yields:
% 27.28/7.67 | (55) ~ (all_24_0_18 = all_0_1_1)
% 27.28/7.67 | (56) addition(all_0_2_2, all_0_1_1) = all_24_0_18
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (18) with all_0_1_1, all_18_0_16 and discharging atoms leq(all_18_0_16, all_0_1_1) = 0, yields:
% 27.28/7.67 | (57) addition(all_18_0_16, all_0_1_1) = all_0_1_1
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (18) with all_0_1_1, all_16_0_14 and discharging atoms leq(all_16_0_14, all_0_1_1) = 0, yields:
% 27.28/7.67 | (58) addition(all_16_0_14, all_0_1_1) = all_0_1_1
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (8) with all_18_0_16, one, all_18_1_17 and discharging atoms addition(one, all_18_1_17) = all_18_0_16, yields:
% 27.28/7.67 | (59) addition(all_18_1_17, one) = all_18_0_16
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (8) with all_16_0_14, one, all_16_1_15 and discharging atoms addition(one, all_16_1_15) = all_16_0_14, yields:
% 27.28/7.67 | (60) addition(all_16_1_15, one) = all_16_0_14
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (30) with all_18_1_17, all_0_1_1, all_0_2_2, all_0_1_1, all_18_0_16 and discharging atoms multiplication(all_0_1_1, all_0_2_2) = all_18_1_17, addition(all_18_0_16, all_0_1_1) = all_0_1_1, yields:
% 27.28/7.67 | (61) ? [v0] : ? [v1] : (multiplication(all_18_0_16, all_0_2_2) = v0 & multiplication(all_0_1_1, all_0_2_2) = v1 & addition(v0, v1) = all_18_1_17)
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (29) with all_16_1_15, all_0_1_1, all_0_1_1, all_18_0_16, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, addition(all_18_0_16, all_0_1_1) = all_0_1_1, yields:
% 27.28/7.67 | (62) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_18_0_16) = v0 & multiplication(all_0_2_2, all_0_1_1) = v1 & addition(v0, v1) = all_16_1_15)
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (25) with all_24_0_18, all_0_1_1, all_0_2_2, all_18_0_16, all_0_1_1 and discharging atoms addition(all_18_0_16, all_0_1_1) = all_0_1_1, addition(all_0_2_2, all_0_1_1) = all_24_0_18, yields:
% 27.28/7.67 | (63) ? [v0] : (addition(v0, all_0_1_1) = all_24_0_18 & addition(all_0_2_2, all_18_0_16) = v0)
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (34) with all_0_1_1, all_18_0_16, one, all_18_1_17, all_0_1_1 and discharging atoms addition(all_18_0_16, all_0_1_1) = all_0_1_1, addition(one, all_18_1_17) = all_18_0_16, yields:
% 27.28/7.67 | (64) ? [v0] : (addition(all_18_1_17, all_0_1_1) = v0 & addition(one, v0) = all_0_1_1)
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (8) with all_0_1_1, all_18_0_16, all_0_1_1 and discharging atoms addition(all_18_0_16, all_0_1_1) = all_0_1_1, yields:
% 27.28/7.67 | (65) addition(all_0_1_1, all_18_0_16) = all_0_1_1
% 27.28/7.67 |
% 27.28/7.67 | Instantiating formula (36) with all_18_0_16, all_18_1_17, one, all_0_2_2, all_0_1_1 and discharging atoms multiplication(all_0_1_1, all_0_2_2) = all_18_1_17, addition(all_18_1_17, one) = all_18_0_16, yields:
% 27.28/7.67 | (66) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & star(all_0_2_2) = v0 & leq(v1, all_0_1_1) = 0 & multiplication(one, v0) = v1) | ( ~ (v0 = 0) & leq(all_18_0_16, all_0_1_1) = v0))
% 27.28/7.68 |
% 27.28/7.68 | Instantiating formula (34) with all_0_1_1, all_18_0_16, all_18_1_17, one, all_0_1_1 and discharging atoms addition(all_18_0_16, all_0_1_1) = all_0_1_1, addition(all_18_1_17, one) = all_18_0_16, yields:
% 27.28/7.68 | (67) ? [v0] : (addition(all_18_1_17, v0) = all_0_1_1 & addition(one, all_0_1_1) = v0)
% 27.28/7.68 |
% 27.28/7.68 | Instantiating formula (30) with all_18_1_17, all_0_1_1, all_0_2_2, all_0_1_1, all_16_0_14 and discharging atoms multiplication(all_0_1_1, all_0_2_2) = all_18_1_17, addition(all_16_0_14, all_0_1_1) = all_0_1_1, yields:
% 27.28/7.68 | (68) ? [v0] : ? [v1] : (multiplication(all_16_0_14, all_0_2_2) = v0 & multiplication(all_0_1_1, all_0_2_2) = v1 & addition(v0, v1) = all_18_1_17)
% 27.28/7.68 |
% 27.28/7.68 | Instantiating formula (29) with all_16_1_15, all_0_1_1, all_0_1_1, all_16_0_14, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, addition(all_16_0_14, all_0_1_1) = all_0_1_1, yields:
% 27.28/7.68 | (69) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_16_0_14) = v0 & multiplication(all_0_2_2, all_0_1_1) = v1 & addition(v0, v1) = all_16_1_15)
% 27.28/7.68 |
% 27.28/7.68 | Instantiating formula (25) with all_24_0_18, all_0_1_1, all_0_2_2, all_16_0_14, all_0_1_1 and discharging atoms addition(all_16_0_14, all_0_1_1) = all_0_1_1, addition(all_0_2_2, all_0_1_1) = all_24_0_18, yields:
% 27.28/7.68 | (70) ? [v0] : (addition(v0, all_0_1_1) = all_24_0_18 & addition(all_0_2_2, all_16_0_14) = v0)
% 27.28/7.68 |
% 27.28/7.68 | Instantiating formula (34) with all_0_1_1, all_16_0_14, one, all_16_1_15, all_0_1_1 and discharging atoms addition(all_16_0_14, all_0_1_1) = all_0_1_1, addition(one, all_16_1_15) = all_16_0_14, yields:
% 27.28/7.68 | (71) ? [v0] : (addition(all_16_1_15, all_0_1_1) = v0 & addition(one, v0) = all_0_1_1)
% 27.28/7.68 |
% 27.28/7.68 | Instantiating formula (25) with all_0_1_1, all_0_1_1, all_16_0_14, all_18_0_16, all_0_1_1 and discharging atoms addition(all_18_0_16, all_0_1_1) = all_0_1_1, addition(all_16_0_14, all_0_1_1) = all_0_1_1, yields:
% 27.28/7.68 | (72) ? [v0] : (addition(v0, all_0_1_1) = all_0_1_1 & addition(all_16_0_14, all_18_0_16) = v0)
% 27.28/7.68 |
% 27.28/7.68 | Instantiating formula (25) with all_0_1_1, all_0_1_1, all_18_0_16, all_16_0_14, all_0_1_1 and discharging atoms addition(all_18_0_16, all_0_1_1) = all_0_1_1, addition(all_16_0_14, all_0_1_1) = all_0_1_1, yields:
% 27.28/7.68 | (73) ? [v0] : (addition(v0, all_0_1_1) = all_0_1_1 & addition(all_18_0_16, all_16_0_14) = v0)
% 27.28/7.68 |
% 27.28/7.68 | Instantiating formula (8) with all_0_1_1, all_16_0_14, all_0_1_1 and discharging atoms addition(all_16_0_14, all_0_1_1) = all_0_1_1, yields:
% 27.28/7.68 | (74) addition(all_0_1_1, all_16_0_14) = all_0_1_1
% 27.28/7.68 |
% 27.28/7.68 | Instantiating formula (13) with all_16_0_14, all_16_1_15, one, all_0_1_1, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, addition(all_16_1_15, one) = all_16_0_14, yields:
% 27.28/7.68 | (75) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & star(all_0_2_2) = v0 & leq(v1, all_0_1_1) = 0 & multiplication(v0, one) = v1) | ( ~ (v0 = 0) & leq(all_16_0_14, all_0_1_1) = v0))
% 27.28/7.68 |
% 27.28/7.68 | Instantiating formula (34) with all_0_1_1, all_16_0_14, all_16_1_15, one, all_0_1_1 and discharging atoms addition(all_16_0_14, all_0_1_1) = all_0_1_1, addition(all_16_1_15, one) = all_16_0_14, yields:
% 27.28/7.68 | (76) ? [v0] : (addition(all_16_1_15, v0) = all_0_1_1 & addition(one, all_0_1_1) = v0)
% 27.28/7.68 |
% 27.28/7.68 | Instantiating (71) with all_38_0_19 yields:
% 27.28/7.68 | (77) addition(all_16_1_15, all_0_1_1) = all_38_0_19 & addition(one, all_38_0_19) = all_0_1_1
% 27.28/7.68 |
% 27.28/7.68 | Applying alpha-rule on (77) yields:
% 27.28/7.68 | (78) addition(all_16_1_15, all_0_1_1) = all_38_0_19
% 27.28/7.68 | (79) addition(one, all_38_0_19) = all_0_1_1
% 27.28/7.68 |
% 27.28/7.68 | Instantiating (70) with all_40_0_20 yields:
% 27.28/7.68 | (80) addition(all_40_0_20, all_0_1_1) = all_24_0_18 & addition(all_0_2_2, all_16_0_14) = all_40_0_20
% 27.28/7.68 |
% 27.28/7.68 | Applying alpha-rule on (80) yields:
% 27.28/7.68 | (81) addition(all_40_0_20, all_0_1_1) = all_24_0_18
% 27.28/7.68 | (82) addition(all_0_2_2, all_16_0_14) = all_40_0_20
% 27.28/7.68 |
% 27.28/7.68 | Instantiating (67) with all_42_0_21 yields:
% 27.28/7.68 | (83) addition(all_18_1_17, all_42_0_21) = all_0_1_1 & addition(one, all_0_1_1) = all_42_0_21
% 27.28/7.68 |
% 27.28/7.68 | Applying alpha-rule on (83) yields:
% 27.28/7.68 | (84) addition(all_18_1_17, all_42_0_21) = all_0_1_1
% 27.28/7.68 | (85) addition(one, all_0_1_1) = all_42_0_21
% 27.28/7.68 |
% 27.28/7.68 | Instantiating (69) with all_44_0_22, all_44_1_23 yields:
% 27.28/7.68 | (86) multiplication(all_0_2_2, all_16_0_14) = all_44_1_23 & multiplication(all_0_2_2, all_0_1_1) = all_44_0_22 & addition(all_44_1_23, all_44_0_22) = all_16_1_15
% 27.28/7.68 |
% 27.28/7.68 | Applying alpha-rule on (86) yields:
% 27.28/7.68 | (87) multiplication(all_0_2_2, all_16_0_14) = all_44_1_23
% 27.28/7.68 | (88) multiplication(all_0_2_2, all_0_1_1) = all_44_0_22
% 27.28/7.68 | (89) addition(all_44_1_23, all_44_0_22) = all_16_1_15
% 27.28/7.68 |
% 27.28/7.68 | Instantiating (64) with all_46_0_24 yields:
% 27.28/7.68 | (90) addition(all_18_1_17, all_0_1_1) = all_46_0_24 & addition(one, all_46_0_24) = all_0_1_1
% 27.28/7.68 |
% 27.28/7.68 | Applying alpha-rule on (90) yields:
% 27.28/7.68 | (91) addition(all_18_1_17, all_0_1_1) = all_46_0_24
% 27.28/7.68 | (92) addition(one, all_46_0_24) = all_0_1_1
% 27.28/7.68 |
% 27.28/7.68 | Instantiating (68) with all_48_0_25, all_48_1_26 yields:
% 27.28/7.68 | (93) multiplication(all_16_0_14, all_0_2_2) = all_48_1_26 & multiplication(all_0_1_1, all_0_2_2) = all_48_0_25 & addition(all_48_1_26, all_48_0_25) = all_18_1_17
% 27.28/7.68 |
% 27.28/7.68 | Applying alpha-rule on (93) yields:
% 27.28/7.68 | (94) multiplication(all_16_0_14, all_0_2_2) = all_48_1_26
% 27.28/7.68 | (95) multiplication(all_0_1_1, all_0_2_2) = all_48_0_25
% 27.28/7.68 | (96) addition(all_48_1_26, all_48_0_25) = all_18_1_17
% 27.28/7.68 |
% 27.28/7.68 | Instantiating (63) with all_50_0_27 yields:
% 27.28/7.68 | (97) addition(all_50_0_27, all_0_1_1) = all_24_0_18 & addition(all_0_2_2, all_18_0_16) = all_50_0_27
% 27.28/7.68 |
% 27.28/7.68 | Applying alpha-rule on (97) yields:
% 27.28/7.68 | (98) addition(all_50_0_27, all_0_1_1) = all_24_0_18
% 27.28/7.68 | (99) addition(all_0_2_2, all_18_0_16) = all_50_0_27
% 27.28/7.68 |
% 27.28/7.68 | Instantiating (76) with all_52_0_28 yields:
% 27.28/7.68 | (100) addition(all_16_1_15, all_52_0_28) = all_0_1_1 & addition(one, all_0_1_1) = all_52_0_28
% 27.28/7.68 |
% 27.28/7.68 | Applying alpha-rule on (100) yields:
% 27.28/7.68 | (101) addition(all_16_1_15, all_52_0_28) = all_0_1_1
% 27.28/7.68 | (102) addition(one, all_0_1_1) = all_52_0_28
% 27.28/7.68 |
% 27.28/7.69 | Instantiating (75) with all_54_0_29, all_54_1_30, all_54_2_31 yields:
% 27.28/7.69 | (103) (all_54_0_29 = 0 & star(all_0_2_2) = all_54_2_31 & leq(all_54_1_30, all_0_1_1) = 0 & multiplication(all_54_2_31, one) = all_54_1_30) | ( ~ (all_54_2_31 = 0) & leq(all_16_0_14, all_0_1_1) = all_54_2_31)
% 27.28/7.69 |
% 27.28/7.69 | Instantiating (62) with all_59_0_34, all_59_1_35 yields:
% 27.28/7.69 | (104) multiplication(all_0_2_2, all_18_0_16) = all_59_1_35 & multiplication(all_0_2_2, all_0_1_1) = all_59_0_34 & addition(all_59_1_35, all_59_0_34) = all_16_1_15
% 27.28/7.69 |
% 27.28/7.69 | Applying alpha-rule on (104) yields:
% 27.28/7.69 | (105) multiplication(all_0_2_2, all_18_0_16) = all_59_1_35
% 27.28/7.69 | (106) multiplication(all_0_2_2, all_0_1_1) = all_59_0_34
% 27.28/7.69 | (107) addition(all_59_1_35, all_59_0_34) = all_16_1_15
% 27.28/7.69 |
% 27.28/7.69 | Instantiating (61) with all_61_0_36, all_61_1_37 yields:
% 27.28/7.69 | (108) multiplication(all_18_0_16, all_0_2_2) = all_61_1_37 & multiplication(all_0_1_1, all_0_2_2) = all_61_0_36 & addition(all_61_1_37, all_61_0_36) = all_18_1_17
% 27.28/7.69 |
% 27.28/7.69 | Applying alpha-rule on (108) yields:
% 27.28/7.69 | (109) multiplication(all_18_0_16, all_0_2_2) = all_61_1_37
% 27.28/7.69 | (110) multiplication(all_0_1_1, all_0_2_2) = all_61_0_36
% 27.28/7.69 | (111) addition(all_61_1_37, all_61_0_36) = all_18_1_17
% 27.28/7.69 |
% 27.28/7.69 | Instantiating (73) with all_69_0_46 yields:
% 27.28/7.69 | (112) addition(all_69_0_46, all_0_1_1) = all_0_1_1 & addition(all_18_0_16, all_16_0_14) = all_69_0_46
% 27.28/7.69 |
% 27.28/7.69 | Applying alpha-rule on (112) yields:
% 27.28/7.69 | (113) addition(all_69_0_46, all_0_1_1) = all_0_1_1
% 27.28/7.69 | (114) addition(all_18_0_16, all_16_0_14) = all_69_0_46
% 27.41/7.69 |
% 27.41/7.69 | Instantiating (72) with all_71_0_47 yields:
% 27.41/7.69 | (115) addition(all_71_0_47, all_0_1_1) = all_0_1_1 & addition(all_16_0_14, all_18_0_16) = all_71_0_47
% 27.41/7.69 |
% 27.41/7.69 | Applying alpha-rule on (115) yields:
% 27.41/7.69 | (116) addition(all_71_0_47, all_0_1_1) = all_0_1_1
% 27.41/7.69 | (117) addition(all_16_0_14, all_18_0_16) = all_71_0_47
% 27.41/7.69 |
% 27.41/7.69 | Instantiating (66) with all_73_0_48, all_73_1_49, all_73_2_50 yields:
% 27.41/7.69 | (118) (all_73_0_48 = 0 & star(all_0_2_2) = all_73_2_50 & leq(all_73_1_49, all_0_1_1) = 0 & multiplication(one, all_73_2_50) = all_73_1_49) | ( ~ (all_73_2_50 = 0) & leq(all_18_0_16, all_0_1_1) = all_73_2_50)
% 27.41/7.69 |
% 27.41/7.69 +-Applying beta-rule and splitting (103), into two cases.
% 27.41/7.69 |-Branch one:
% 27.41/7.69 | (119) all_54_0_29 = 0 & star(all_0_2_2) = all_54_2_31 & leq(all_54_1_30, all_0_1_1) = 0 & multiplication(all_54_2_31, one) = all_54_1_30
% 27.41/7.69 |
% 27.41/7.69 | Applying alpha-rule on (119) yields:
% 27.41/7.69 | (120) all_54_0_29 = 0
% 27.41/7.69 | (121) star(all_0_2_2) = all_54_2_31
% 27.41/7.69 | (122) leq(all_54_1_30, all_0_1_1) = 0
% 27.41/7.69 | (123) multiplication(all_54_2_31, one) = all_54_1_30
% 27.41/7.69 |
% 27.41/7.69 +-Applying beta-rule and splitting (118), into two cases.
% 27.41/7.69 |-Branch one:
% 27.41/7.69 | (124) all_73_0_48 = 0 & star(all_0_2_2) = all_73_2_50 & leq(all_73_1_49, all_0_1_1) = 0 & multiplication(one, all_73_2_50) = all_73_1_49
% 27.41/7.69 |
% 27.41/7.69 | Applying alpha-rule on (124) yields:
% 27.41/7.69 | (125) all_73_0_48 = 0
% 27.41/7.69 | (126) star(all_0_2_2) = all_73_2_50
% 27.41/7.69 | (127) leq(all_73_1_49, all_0_1_1) = 0
% 27.41/7.69 | (128) multiplication(one, all_73_2_50) = all_73_1_49
% 27.41/7.69 |
% 27.41/7.69 | Instantiating formula (38) with all_0_2_2, all_73_2_50, all_0_1_1 and discharging atoms star(all_0_2_2) = all_73_2_50, star(all_0_2_2) = all_0_1_1, yields:
% 27.41/7.69 | (129) all_73_2_50 = all_0_1_1
% 27.41/7.69 |
% 27.41/7.69 | Instantiating formula (38) with all_0_2_2, all_54_2_31, all_73_2_50 and discharging atoms star(all_0_2_2) = all_73_2_50, star(all_0_2_2) = all_54_2_31, yields:
% 27.41/7.69 | (130) all_73_2_50 = all_54_2_31
% 27.41/7.69 |
% 27.41/7.69 | Instantiating formula (14) with all_54_1_30, all_54_2_31 and discharging atoms multiplication(all_54_2_31, one) = all_54_1_30, yields:
% 27.41/7.69 | (131) all_54_1_30 = all_54_2_31
% 27.41/7.69 |
% 27.41/7.69 | Instantiating formula (22) with all_0_1_1, all_0_2_2, all_61_0_36, all_18_1_17 and discharging atoms multiplication(all_0_1_1, all_0_2_2) = all_61_0_36, multiplication(all_0_1_1, all_0_2_2) = all_18_1_17, yields:
% 27.41/7.69 | (132) all_61_0_36 = all_18_1_17
% 27.41/7.69 |
% 27.41/7.69 | Instantiating formula (22) with all_0_1_1, all_0_2_2, all_48_0_25, all_61_0_36 and discharging atoms multiplication(all_0_1_1, all_0_2_2) = all_61_0_36, multiplication(all_0_1_1, all_0_2_2) = all_48_0_25, yields:
% 27.41/7.69 | (133) all_61_0_36 = all_48_0_25
% 27.41/7.69 |
% 27.41/7.69 | Instantiating formula (22) with all_0_2_2, all_0_1_1, all_59_0_34, all_16_1_15 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_59_0_34, multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, yields:
% 27.41/7.69 | (134) all_59_0_34 = all_16_1_15
% 27.41/7.69 |
% 27.41/7.69 | Instantiating formula (22) with all_0_2_2, all_0_1_1, all_44_0_22, all_59_0_34 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_59_0_34, multiplication(all_0_2_2, all_0_1_1) = all_44_0_22, yields:
% 27.41/7.69 | (135) all_59_0_34 = all_44_0_22
% 27.41/7.69 |
% 27.41/7.69 | Instantiating formula (31) with all_73_1_49, all_73_2_50 and discharging atoms multiplication(one, all_73_2_50) = all_73_1_49, yields:
% 27.41/7.69 | (136) all_73_1_49 = all_73_2_50
% 27.41/7.69 |
% 27.41/7.69 | Instantiating formula (2) with one, all_0_1_1, all_42_0_21, all_52_0_28 and discharging atoms addition(one, all_0_1_1) = all_52_0_28, addition(one, all_0_1_1) = all_42_0_21, yields:
% 27.41/7.69 | (137) all_52_0_28 = all_42_0_21
% 27.41/7.69 |
% 27.41/7.69 | Combining equations (130,129) yields a new equation:
% 27.41/7.69 | (138) all_54_2_31 = all_0_1_1
% 27.41/7.69 |
% 27.41/7.69 | Simplifying 138 yields:
% 27.41/7.69 | (139) all_54_2_31 = all_0_1_1
% 27.41/7.69 |
% 27.41/7.69 | Combining equations (133,132) yields a new equation:
% 27.41/7.69 | (140) all_48_0_25 = all_18_1_17
% 27.41/7.69 |
% 27.41/7.69 | Simplifying 140 yields:
% 27.41/7.69 | (141) all_48_0_25 = all_18_1_17
% 27.41/7.69 |
% 27.41/7.69 | Combining equations (135,134) yields a new equation:
% 27.41/7.69 | (142) all_44_0_22 = all_16_1_15
% 27.41/7.69 |
% 27.41/7.69 | Simplifying 142 yields:
% 27.41/7.69 | (143) all_44_0_22 = all_16_1_15
% 27.41/7.69 |
% 27.41/7.69 | Combining equations (139,131) yields a new equation:
% 27.41/7.69 | (144) all_54_1_30 = all_0_1_1
% 27.41/7.69 |
% 27.41/7.69 | Combining equations (129,136) yields a new equation:
% 27.41/7.70 | (145) all_73_1_49 = all_0_1_1
% 27.41/7.70 |
% 27.41/7.70 | From (139)(144) and (123) follows:
% 27.41/7.70 | (146) multiplication(all_0_1_1, one) = all_0_1_1
% 27.41/7.70 |
% 27.41/7.70 | From (143) and (88) follows:
% 27.41/7.70 | (44) multiplication(all_0_2_2, all_0_1_1) = all_16_1_15
% 27.41/7.70 |
% 27.41/7.70 | From (129)(145) and (128) follows:
% 27.41/7.70 | (148) multiplication(one, all_0_1_1) = all_0_1_1
% 27.41/7.70 |
% 27.41/7.70 | From (132) and (111) follows:
% 27.41/7.70 | (149) addition(all_61_1_37, all_18_1_17) = all_18_1_17
% 27.41/7.70 |
% 27.41/7.70 | From (134) and (107) follows:
% 27.41/7.70 | (150) addition(all_59_1_35, all_16_1_15) = all_16_1_15
% 27.41/7.70 |
% 27.41/7.70 | From (141) and (96) follows:
% 27.41/7.70 | (151) addition(all_48_1_26, all_18_1_17) = all_18_1_17
% 27.41/7.70 |
% 27.41/7.70 | From (143) and (89) follows:
% 27.41/7.70 | (152) addition(all_44_1_23, all_16_1_15) = all_16_1_15
% 27.41/7.70 |
% 27.41/7.70 | From (137) and (101) follows:
% 27.41/7.70 | (153) addition(all_16_1_15, all_42_0_21) = all_0_1_1
% 27.41/7.70 |
% 27.41/7.70 | From (137) and (102) follows:
% 27.41/7.70 | (85) addition(one, all_0_1_1) = all_42_0_21
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (5) with all_16_1_15, all_0_1_1, one, all_0_1_1, all_0_2_2 and discharging atoms multiplication(all_0_1_1, one) = all_0_1_1, multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, yields:
% 27.41/7.70 | (155) ? [v0] : (multiplication(v0, one) = all_16_1_15 & multiplication(all_0_2_2, all_0_1_1) = v0)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (29) with all_59_1_35, all_18_0_16, all_18_1_17, one, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_18_0_16) = all_59_1_35, addition(one, all_18_1_17) = all_18_0_16, yields:
% 27.41/7.70 | (156) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_18_1_17) = v1 & multiplication(all_0_2_2, one) = v0 & addition(v0, v1) = all_59_1_35)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (5) with all_16_1_15, all_0_1_1, all_0_1_1, one, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, multiplication(one, all_0_1_1) = all_0_1_1, yields:
% 27.41/7.70 | (157) ? [v0] : (multiplication(v0, all_0_1_1) = all_16_1_15 & multiplication(all_0_2_2, one) = v0)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (29) with all_16_1_15, all_0_1_1, all_0_1_1, all_71_0_47, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, addition(all_71_0_47, all_0_1_1) = all_0_1_1, yields:
% 27.41/7.70 | (158) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_71_0_47) = v0 & multiplication(all_0_2_2, all_0_1_1) = v1 & addition(v0, v1) = all_16_1_15)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (29) with all_16_1_15, all_0_1_1, all_0_1_1, all_69_0_46, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, addition(all_69_0_46, all_0_1_1) = all_0_1_1, yields:
% 27.41/7.70 | (159) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_69_0_46) = v0 & multiplication(all_0_2_2, all_0_1_1) = v1 & addition(v0, v1) = all_16_1_15)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (21) with all_24_0_18, all_0_1_1, all_50_0_27 and discharging atoms addition(all_50_0_27, all_0_1_1) = all_24_0_18, yields:
% 27.41/7.70 | (160) all_24_0_18 = all_0_1_1 | ? [v0] : ( ~ (v0 = 0) & leq(all_50_0_27, all_0_1_1) = v0)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (21) with all_24_0_18, all_0_1_1, all_40_0_20 and discharging atoms addition(all_40_0_20, all_0_1_1) = all_24_0_18, yields:
% 27.41/7.70 | (161) all_24_0_18 = all_0_1_1 | ? [v0] : ( ~ (v0 = 0) & leq(all_40_0_20, all_0_1_1) = v0)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (29) with all_16_1_15, all_0_1_1, all_42_0_21, all_18_1_17, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, addition(all_18_1_17, all_42_0_21) = all_0_1_1, yields:
% 27.41/7.70 | (162) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_42_0_21) = v1 & multiplication(all_0_2_2, all_18_1_17) = v0 & addition(v0, v1) = all_16_1_15)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (34) with all_0_1_1, all_18_1_17, all_61_1_37, all_18_1_17, all_42_0_21 and discharging atoms addition(all_61_1_37, all_18_1_17) = all_18_1_17, addition(all_18_1_17, all_42_0_21) = all_0_1_1, yields:
% 27.41/7.70 | (163) ? [v0] : (addition(all_61_1_37, v0) = all_0_1_1 & addition(all_18_1_17, all_42_0_21) = v0)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (34) with all_0_1_1, all_18_1_17, all_48_1_26, all_18_1_17, all_42_0_21 and discharging atoms addition(all_48_1_26, all_18_1_17) = all_18_1_17, addition(all_18_1_17, all_42_0_21) = all_0_1_1, yields:
% 27.41/7.70 | (164) ? [v0] : (addition(all_48_1_26, v0) = all_0_1_1 & addition(all_18_1_17, all_42_0_21) = v0)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (25) with all_46_0_24, all_0_1_1, all_18_1_17, all_18_1_17, all_42_0_21 and discharging atoms addition(all_18_1_17, all_42_0_21) = all_0_1_1, addition(all_18_1_17, all_0_1_1) = all_46_0_24, yields:
% 27.41/7.70 | (165) ? [v0] : (addition(v0, all_42_0_21) = all_46_0_24 & addition(all_18_1_17, all_18_1_17) = v0)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (29) with all_16_1_15, all_0_1_1, all_42_0_21, all_16_1_15, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, addition(all_16_1_15, all_42_0_21) = all_0_1_1, yields:
% 27.41/7.70 | (166) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_42_0_21) = v1 & multiplication(all_0_2_2, all_16_1_15) = v0 & addition(v0, v1) = all_16_1_15)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (25) with all_24_0_18, all_0_1_1, all_0_2_2, all_16_1_15, all_42_0_21 and discharging atoms addition(all_16_1_15, all_42_0_21) = all_0_1_1, addition(all_0_2_2, all_0_1_1) = all_24_0_18, yields:
% 27.41/7.70 | (167) ? [v0] : (addition(v0, all_42_0_21) = all_24_0_18 & addition(all_0_2_2, all_16_1_15) = v0)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (34) with all_0_1_1, all_16_1_15, all_59_1_35, all_16_1_15, all_42_0_21 and discharging atoms addition(all_59_1_35, all_16_1_15) = all_16_1_15, addition(all_16_1_15, all_42_0_21) = all_0_1_1, yields:
% 27.41/7.70 | (168) ? [v0] : (addition(all_59_1_35, v0) = all_0_1_1 & addition(all_16_1_15, all_42_0_21) = v0)
% 27.41/7.70 |
% 27.41/7.70 | Instantiating formula (34) with all_0_1_1, all_16_1_15, all_44_1_23, all_16_1_15, all_42_0_21 and discharging atoms addition(all_44_1_23, all_16_1_15) = all_16_1_15, addition(all_16_1_15, all_42_0_21) = all_0_1_1, yields:
% 27.41/7.70 | (169) ? [v0] : (addition(all_44_1_23, v0) = all_0_1_1 & addition(all_16_1_15, all_42_0_21) = v0)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (34) with all_38_0_19, all_16_1_15, all_59_1_35, all_16_1_15, all_0_1_1 and discharging atoms addition(all_59_1_35, all_16_1_15) = all_16_1_15, addition(all_16_1_15, all_0_1_1) = all_38_0_19, yields:
% 27.41/7.71 | (170) ? [v0] : (addition(all_59_1_35, v0) = all_38_0_19 & addition(all_16_1_15, all_0_1_1) = v0)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (34) with all_38_0_19, all_16_1_15, all_44_1_23, all_16_1_15, all_0_1_1 and discharging atoms addition(all_44_1_23, all_16_1_15) = all_16_1_15, addition(all_16_1_15, all_0_1_1) = all_38_0_19, yields:
% 27.41/7.71 | (171) ? [v0] : (addition(all_44_1_23, v0) = all_38_0_19 & addition(all_16_1_15, all_0_1_1) = v0)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (25) with all_38_0_19, all_0_1_1, all_16_1_15, all_16_1_15, all_42_0_21 and discharging atoms addition(all_16_1_15, all_42_0_21) = all_0_1_1, addition(all_16_1_15, all_0_1_1) = all_38_0_19, yields:
% 27.41/7.71 | (172) ? [v0] : (addition(v0, all_42_0_21) = all_38_0_19 & addition(all_16_1_15, all_16_1_15) = v0)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (29) with all_16_1_15, all_0_1_1, all_18_0_16, all_0_1_1, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, addition(all_0_1_1, all_18_0_16) = all_0_1_1, yields:
% 27.41/7.71 | (173) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_18_0_16) = v1 & multiplication(all_0_2_2, all_0_1_1) = v0 & addition(v0, v1) = all_16_1_15)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (25) with all_38_0_19, all_0_1_1, all_16_1_15, all_0_1_1, all_18_0_16 and discharging atoms addition(all_16_1_15, all_0_1_1) = all_38_0_19, addition(all_0_1_1, all_18_0_16) = all_0_1_1, yields:
% 27.41/7.71 | (174) ? [v0] : (addition(v0, all_18_0_16) = all_38_0_19 & addition(all_16_1_15, all_0_1_1) = v0)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (29) with all_16_1_15, all_0_1_1, all_16_0_14, all_0_1_1, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, addition(all_0_1_1, all_16_0_14) = all_0_1_1, yields:
% 27.41/7.71 | (175) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_16_0_14) = v1 & multiplication(all_0_2_2, all_0_1_1) = v0 & addition(v0, v1) = all_16_1_15)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (25) with all_38_0_19, all_0_1_1, all_16_1_15, all_0_1_1, all_16_0_14 and discharging atoms addition(all_16_1_15, all_0_1_1) = all_38_0_19, addition(all_0_1_1, all_16_0_14) = all_0_1_1, yields:
% 27.41/7.71 | (176) ? [v0] : (addition(v0, all_16_0_14) = all_38_0_19 & addition(all_16_1_15, all_0_1_1) = v0)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (25) with all_40_0_20, all_16_0_14, all_0_2_2, all_16_1_15, one and discharging atoms addition(all_16_1_15, one) = all_16_0_14, addition(all_0_2_2, all_16_0_14) = all_40_0_20, yields:
% 27.41/7.71 | (177) ? [v0] : (addition(v0, one) = all_40_0_20 & addition(all_0_2_2, all_16_1_15) = v0)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (29) with all_16_1_15, all_0_1_1, all_46_0_24, one, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, addition(one, all_46_0_24) = all_0_1_1, yields:
% 27.41/7.71 | (178) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_46_0_24) = v1 & multiplication(all_0_2_2, one) = v0 & addition(v0, v1) = all_16_1_15)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (29) with all_16_1_15, all_0_1_1, all_38_0_19, one, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, addition(one, all_38_0_19) = all_0_1_1, yields:
% 27.41/7.71 | (179) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_38_0_19) = v1 & multiplication(all_0_2_2, one) = v0 & addition(v0, v1) = all_16_1_15)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (29) with all_0_1_1, all_0_1_1, all_38_0_19, one, one and discharging atoms multiplication(one, all_0_1_1) = all_0_1_1, addition(one, all_38_0_19) = all_0_1_1, yields:
% 27.41/7.71 | (180) ? [v0] : ? [v1] : (multiplication(one, all_38_0_19) = v1 & multiplication(one, one) = v0 & addition(v0, v1) = all_0_1_1)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (25) with all_42_0_21, all_0_1_1, one, one, all_46_0_24 and discharging atoms addition(one, all_46_0_24) = all_0_1_1, addition(one, all_0_1_1) = all_42_0_21, yields:
% 27.41/7.71 | (181) ? [v0] : (addition(v0, all_46_0_24) = all_42_0_21 & addition(one, one) = v0)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating formula (25) with all_42_0_21, all_0_1_1, one, one, all_38_0_19 and discharging atoms addition(one, all_38_0_19) = all_0_1_1, addition(one, all_0_1_1) = all_42_0_21, yields:
% 27.41/7.71 | (182) ? [v0] : (addition(v0, all_38_0_19) = all_42_0_21 & addition(one, one) = v0)
% 27.41/7.71 |
% 27.41/7.71 | Instantiating (155) with all_108_0_73 yields:
% 27.41/7.71 | (183) multiplication(all_108_0_73, one) = all_16_1_15 & multiplication(all_0_2_2, all_0_1_1) = all_108_0_73
% 27.41/7.71 |
% 27.41/7.71 | Applying alpha-rule on (183) yields:
% 27.41/7.71 | (184) multiplication(all_108_0_73, one) = all_16_1_15
% 27.41/7.71 | (185) multiplication(all_0_2_2, all_0_1_1) = all_108_0_73
% 27.41/7.71 |
% 27.41/7.71 | Instantiating (156) with all_141_0_96, all_141_1_97 yields:
% 27.41/7.71 | (186) multiplication(all_0_2_2, all_18_1_17) = all_141_0_96 & multiplication(all_0_2_2, one) = all_141_1_97 & addition(all_141_1_97, all_141_0_96) = all_59_1_35
% 27.41/7.71 |
% 27.41/7.71 | Applying alpha-rule on (186) yields:
% 27.41/7.71 | (187) multiplication(all_0_2_2, all_18_1_17) = all_141_0_96
% 27.41/7.71 | (188) multiplication(all_0_2_2, one) = all_141_1_97
% 27.41/7.71 | (189) addition(all_141_1_97, all_141_0_96) = all_59_1_35
% 27.41/7.71 |
% 27.41/7.71 | Instantiating (157) with all_143_0_98 yields:
% 27.41/7.71 | (190) multiplication(all_143_0_98, all_0_1_1) = all_16_1_15 & multiplication(all_0_2_2, one) = all_143_0_98
% 27.41/7.71 |
% 27.41/7.71 | Applying alpha-rule on (190) yields:
% 27.41/7.71 | (191) multiplication(all_143_0_98, all_0_1_1) = all_16_1_15
% 27.41/7.71 | (192) multiplication(all_0_2_2, one) = all_143_0_98
% 27.41/7.71 |
% 27.41/7.71 | Instantiating (162) with all_161_0_107, all_161_1_108 yields:
% 27.41/7.71 | (193) multiplication(all_0_2_2, all_42_0_21) = all_161_0_107 & multiplication(all_0_2_2, all_18_1_17) = all_161_1_108 & addition(all_161_1_108, all_161_0_107) = all_16_1_15
% 27.41/7.71 |
% 27.41/7.71 | Applying alpha-rule on (193) yields:
% 27.41/7.71 | (194) multiplication(all_0_2_2, all_42_0_21) = all_161_0_107
% 27.41/7.71 | (195) multiplication(all_0_2_2, all_18_1_17) = all_161_1_108
% 27.41/7.71 | (196) addition(all_161_1_108, all_161_0_107) = all_16_1_15
% 27.41/7.71 |
% 27.41/7.71 | Instantiating (173) with all_183_0_126, all_183_1_127 yields:
% 27.41/7.71 | (197) multiplication(all_0_2_2, all_18_0_16) = all_183_0_126 & multiplication(all_0_2_2, all_0_1_1) = all_183_1_127 & addition(all_183_1_127, all_183_0_126) = all_16_1_15
% 27.41/7.71 |
% 27.41/7.71 | Applying alpha-rule on (197) yields:
% 27.41/7.71 | (198) multiplication(all_0_2_2, all_18_0_16) = all_183_0_126
% 27.41/7.71 | (199) multiplication(all_0_2_2, all_0_1_1) = all_183_1_127
% 27.41/7.71 | (200) addition(all_183_1_127, all_183_0_126) = all_16_1_15
% 27.41/7.72 |
% 27.41/7.72 | Instantiating (170) with all_215_0_150 yields:
% 27.41/7.72 | (201) addition(all_59_1_35, all_215_0_150) = all_38_0_19 & addition(all_16_1_15, all_0_1_1) = all_215_0_150
% 27.41/7.72 |
% 27.41/7.72 | Applying alpha-rule on (201) yields:
% 27.41/7.72 | (202) addition(all_59_1_35, all_215_0_150) = all_38_0_19
% 27.41/7.72 | (203) addition(all_16_1_15, all_0_1_1) = all_215_0_150
% 27.41/7.72 |
% 27.41/7.72 | Instantiating (171) with all_218_0_154 yields:
% 27.41/7.72 | (204) addition(all_44_1_23, all_218_0_154) = all_38_0_19 & addition(all_16_1_15, all_0_1_1) = all_218_0_154
% 27.41/7.72 |
% 27.41/7.72 | Applying alpha-rule on (204) yields:
% 27.41/7.72 | (205) addition(all_44_1_23, all_218_0_154) = all_38_0_19
% 27.41/7.72 | (206) addition(all_16_1_15, all_0_1_1) = all_218_0_154
% 27.41/7.72 |
% 27.41/7.72 | Instantiating (168) with all_229_0_163 yields:
% 27.41/7.72 | (207) addition(all_59_1_35, all_229_0_163) = all_0_1_1 & addition(all_16_1_15, all_42_0_21) = all_229_0_163
% 27.41/7.72 |
% 27.41/7.72 | Applying alpha-rule on (207) yields:
% 27.41/7.72 | (208) addition(all_59_1_35, all_229_0_163) = all_0_1_1
% 27.41/7.72 | (209) addition(all_16_1_15, all_42_0_21) = all_229_0_163
% 27.41/7.72 |
% 27.41/7.72 | Instantiating (167) with all_233_0_165 yields:
% 27.41/7.72 | (210) addition(all_233_0_165, all_42_0_21) = all_24_0_18 & addition(all_0_2_2, all_16_1_15) = all_233_0_165
% 27.41/7.72 |
% 27.41/7.72 | Applying alpha-rule on (210) yields:
% 27.41/7.72 | (211) addition(all_233_0_165, all_42_0_21) = all_24_0_18
% 27.41/7.72 | (212) addition(all_0_2_2, all_16_1_15) = all_233_0_165
% 27.41/7.72 |
% 27.41/7.72 | Instantiating (169) with all_282_0_199 yields:
% 27.41/7.72 | (213) addition(all_44_1_23, all_282_0_199) = all_0_1_1 & addition(all_16_1_15, all_42_0_21) = all_282_0_199
% 27.41/7.72 |
% 27.41/7.72 | Applying alpha-rule on (213) yields:
% 27.41/7.72 | (214) addition(all_44_1_23, all_282_0_199) = all_0_1_1
% 27.41/7.72 | (215) addition(all_16_1_15, all_42_0_21) = all_282_0_199
% 27.41/7.72 |
% 27.41/7.72 | Instantiating (176) with all_295_0_208 yields:
% 27.41/7.72 | (216) addition(all_295_0_208, all_16_0_14) = all_38_0_19 & addition(all_16_1_15, all_0_1_1) = all_295_0_208
% 27.41/7.72 |
% 27.41/7.72 | Applying alpha-rule on (216) yields:
% 27.41/7.72 | (217) addition(all_295_0_208, all_16_0_14) = all_38_0_19
% 27.41/7.72 | (218) addition(all_16_1_15, all_0_1_1) = all_295_0_208
% 27.41/7.72 |
% 27.41/7.72 | Instantiating (182) with all_299_0_210 yields:
% 27.41/7.72 | (219) addition(all_299_0_210, all_38_0_19) = all_42_0_21 & addition(one, one) = all_299_0_210
% 27.41/7.72 |
% 27.41/7.72 | Applying alpha-rule on (219) yields:
% 27.41/7.72 | (220) addition(all_299_0_210, all_38_0_19) = all_42_0_21
% 27.41/7.72 | (221) addition(one, one) = all_299_0_210
% 27.41/7.72 |
% 27.41/7.72 | Instantiating (181) with all_311_0_216 yields:
% 27.41/7.72 | (222) addition(all_311_0_216, all_46_0_24) = all_42_0_21 & addition(one, one) = all_311_0_216
% 27.41/7.72 |
% 27.41/7.72 | Applying alpha-rule on (222) yields:
% 27.41/7.72 | (223) addition(all_311_0_216, all_46_0_24) = all_42_0_21
% 27.41/7.72 | (224) addition(one, one) = all_311_0_216
% 27.41/7.72 |
% 27.41/7.72 | Instantiating (172) with all_334_0_231 yields:
% 27.41/7.72 | (225) addition(all_334_0_231, all_42_0_21) = all_38_0_19 & addition(all_16_1_15, all_16_1_15) = all_334_0_231
% 27.57/7.72 |
% 27.57/7.72 | Applying alpha-rule on (225) yields:
% 27.57/7.72 | (226) addition(all_334_0_231, all_42_0_21) = all_38_0_19
% 27.57/7.72 | (227) addition(all_16_1_15, all_16_1_15) = all_334_0_231
% 27.57/7.72 |
% 27.57/7.72 | Instantiating (180) with all_340_0_234, all_340_1_235 yields:
% 27.57/7.72 | (228) multiplication(one, all_38_0_19) = all_340_0_234 & multiplication(one, one) = all_340_1_235 & addition(all_340_1_235, all_340_0_234) = all_0_1_1
% 27.57/7.72 |
% 27.57/7.72 | Applying alpha-rule on (228) yields:
% 27.57/7.72 | (229) multiplication(one, all_38_0_19) = all_340_0_234
% 27.57/7.72 | (230) multiplication(one, one) = all_340_1_235
% 27.57/7.72 | (231) addition(all_340_1_235, all_340_0_234) = all_0_1_1
% 27.57/7.72 |
% 27.57/7.72 | Instantiating (179) with all_344_0_238, all_344_1_239 yields:
% 27.57/7.72 | (232) multiplication(all_0_2_2, all_38_0_19) = all_344_0_238 & multiplication(all_0_2_2, one) = all_344_1_239 & addition(all_344_1_239, all_344_0_238) = all_16_1_15
% 27.57/7.72 |
% 27.57/7.72 | Applying alpha-rule on (232) yields:
% 27.57/7.72 | (233) multiplication(all_0_2_2, all_38_0_19) = all_344_0_238
% 27.57/7.72 | (234) multiplication(all_0_2_2, one) = all_344_1_239
% 27.57/7.72 | (235) addition(all_344_1_239, all_344_0_238) = all_16_1_15
% 27.57/7.72 |
% 27.57/7.72 | Instantiating (175) with all_364_0_262, all_364_1_263 yields:
% 27.57/7.72 | (236) multiplication(all_0_2_2, all_16_0_14) = all_364_0_262 & multiplication(all_0_2_2, all_0_1_1) = all_364_1_263 & addition(all_364_1_263, all_364_0_262) = all_16_1_15
% 27.57/7.72 |
% 27.57/7.72 | Applying alpha-rule on (236) yields:
% 27.57/7.72 | (237) multiplication(all_0_2_2, all_16_0_14) = all_364_0_262
% 27.57/7.72 | (238) multiplication(all_0_2_2, all_0_1_1) = all_364_1_263
% 27.57/7.72 | (239) addition(all_364_1_263, all_364_0_262) = all_16_1_15
% 27.57/7.72 |
% 27.57/7.72 | Instantiating (174) with all_366_0_264 yields:
% 27.57/7.72 | (240) addition(all_366_0_264, all_18_0_16) = all_38_0_19 & addition(all_16_1_15, all_0_1_1) = all_366_0_264
% 27.57/7.72 |
% 27.57/7.72 | Applying alpha-rule on (240) yields:
% 27.57/7.72 | (241) addition(all_366_0_264, all_18_0_16) = all_38_0_19
% 27.57/7.72 | (242) addition(all_16_1_15, all_0_1_1) = all_366_0_264
% 27.57/7.72 |
% 27.57/7.72 | Instantiating (178) with all_372_0_269, all_372_1_270 yields:
% 27.57/7.72 | (243) multiplication(all_0_2_2, all_46_0_24) = all_372_0_269 & multiplication(all_0_2_2, one) = all_372_1_270 & addition(all_372_1_270, all_372_0_269) = all_16_1_15
% 27.57/7.73 |
% 27.57/7.73 | Applying alpha-rule on (243) yields:
% 27.57/7.73 | (244) multiplication(all_0_2_2, all_46_0_24) = all_372_0_269
% 27.57/7.73 | (245) multiplication(all_0_2_2, one) = all_372_1_270
% 27.57/7.73 | (246) addition(all_372_1_270, all_372_0_269) = all_16_1_15
% 27.57/7.73 |
% 27.57/7.73 | Instantiating (166) with all_389_0_287, all_389_1_288 yields:
% 27.57/7.73 | (247) multiplication(all_0_2_2, all_42_0_21) = all_389_0_287 & multiplication(all_0_2_2, all_16_1_15) = all_389_1_288 & addition(all_389_1_288, all_389_0_287) = all_16_1_15
% 27.57/7.73 |
% 27.57/7.73 | Applying alpha-rule on (247) yields:
% 27.57/7.73 | (248) multiplication(all_0_2_2, all_42_0_21) = all_389_0_287
% 27.57/7.73 | (249) multiplication(all_0_2_2, all_16_1_15) = all_389_1_288
% 27.57/7.73 | (250) addition(all_389_1_288, all_389_0_287) = all_16_1_15
% 27.57/7.73 |
% 27.57/7.73 | Instantiating (177) with all_423_0_308 yields:
% 27.57/7.73 | (251) addition(all_423_0_308, one) = all_40_0_20 & addition(all_0_2_2, all_16_1_15) = all_423_0_308
% 27.57/7.73 |
% 27.57/7.73 | Applying alpha-rule on (251) yields:
% 27.57/7.73 | (252) addition(all_423_0_308, one) = all_40_0_20
% 27.57/7.73 | (253) addition(all_0_2_2, all_16_1_15) = all_423_0_308
% 27.57/7.73 |
% 27.57/7.73 | Instantiating (159) with all_449_0_329, all_449_1_330 yields:
% 27.57/7.73 | (254) multiplication(all_0_2_2, all_69_0_46) = all_449_1_330 & multiplication(all_0_2_2, all_0_1_1) = all_449_0_329 & addition(all_449_1_330, all_449_0_329) = all_16_1_15
% 27.57/7.73 |
% 27.57/7.73 | Applying alpha-rule on (254) yields:
% 27.57/7.73 | (255) multiplication(all_0_2_2, all_69_0_46) = all_449_1_330
% 27.57/7.73 | (256) multiplication(all_0_2_2, all_0_1_1) = all_449_0_329
% 27.57/7.73 | (257) addition(all_449_1_330, all_449_0_329) = all_16_1_15
% 27.57/7.73 |
% 27.57/7.73 | Instantiating (158) with all_499_0_362, all_499_1_363 yields:
% 27.57/7.73 | (258) multiplication(all_0_2_2, all_71_0_47) = all_499_1_363 & multiplication(all_0_2_2, all_0_1_1) = all_499_0_362 & addition(all_499_1_363, all_499_0_362) = all_16_1_15
% 27.57/7.73 |
% 27.57/7.73 | Applying alpha-rule on (258) yields:
% 27.57/7.73 | (259) multiplication(all_0_2_2, all_71_0_47) = all_499_1_363
% 27.57/7.73 | (260) multiplication(all_0_2_2, all_0_1_1) = all_499_0_362
% 27.57/7.73 | (261) addition(all_499_1_363, all_499_0_362) = all_16_1_15
% 27.57/7.73 |
% 27.57/7.73 | Instantiating (165) with all_515_0_373 yields:
% 27.57/7.73 | (262) addition(all_515_0_373, all_42_0_21) = all_46_0_24 & addition(all_18_1_17, all_18_1_17) = all_515_0_373
% 27.57/7.73 |
% 27.57/7.73 | Applying alpha-rule on (262) yields:
% 27.57/7.73 | (263) addition(all_515_0_373, all_42_0_21) = all_46_0_24
% 27.62/7.73 | (264) addition(all_18_1_17, all_18_1_17) = all_515_0_373
% 27.62/7.73 |
% 27.62/7.73 | Instantiating (163) with all_537_0_384 yields:
% 27.62/7.73 | (265) addition(all_61_1_37, all_537_0_384) = all_0_1_1 & addition(all_18_1_17, all_42_0_21) = all_537_0_384
% 27.62/7.73 |
% 27.62/7.73 | Applying alpha-rule on (265) yields:
% 27.62/7.73 | (266) addition(all_61_1_37, all_537_0_384) = all_0_1_1
% 27.62/7.73 | (267) addition(all_18_1_17, all_42_0_21) = all_537_0_384
% 27.62/7.73 |
% 27.62/7.73 | Instantiating (164) with all_539_0_385 yields:
% 27.62/7.73 | (268) addition(all_48_1_26, all_539_0_385) = all_0_1_1 & addition(all_18_1_17, all_42_0_21) = all_539_0_385
% 27.62/7.73 |
% 27.62/7.73 | Applying alpha-rule on (268) yields:
% 27.62/7.73 | (269) addition(all_48_1_26, all_539_0_385) = all_0_1_1
% 27.62/7.73 | (270) addition(all_18_1_17, all_42_0_21) = all_539_0_385
% 27.62/7.73 |
% 27.62/7.73 +-Applying beta-rule and splitting (161), into two cases.
% 27.62/7.73 |-Branch one:
% 27.62/7.73 | (271) all_24_0_18 = all_0_1_1
% 27.62/7.73 |
% 27.62/7.73 | Equations (271) can reduce 55 to:
% 27.62/7.73 | (51) $false
% 27.62/7.73 |
% 27.62/7.73 |-The branch is then unsatisfiable
% 27.62/7.73 |-Branch two:
% 27.62/7.73 | (55) ~ (all_24_0_18 = all_0_1_1)
% 27.62/7.73 | (274) ? [v0] : ( ~ (v0 = 0) & leq(all_40_0_20, all_0_1_1) = v0)
% 27.62/7.73 |
% 27.62/7.73 +-Applying beta-rule and splitting (160), into two cases.
% 27.62/7.73 |-Branch one:
% 27.62/7.73 | (271) all_24_0_18 = all_0_1_1
% 27.62/7.73 |
% 27.62/7.73 | Equations (271) can reduce 55 to:
% 27.62/7.73 | (51) $false
% 27.62/7.73 |
% 27.62/7.73 |-The branch is then unsatisfiable
% 27.62/7.73 |-Branch two:
% 27.62/7.73 | (55) ~ (all_24_0_18 = all_0_1_1)
% 27.62/7.73 | (278) ? [v0] : ( ~ (v0 = 0) & leq(all_50_0_27, all_0_1_1) = v0)
% 27.62/7.73 |
% 27.62/7.73 | Instantiating formula (22) with all_0_2_2, all_42_0_21, all_161_0_107, all_389_0_287 and discharging atoms multiplication(all_0_2_2, all_42_0_21) = all_389_0_287, multiplication(all_0_2_2, all_42_0_21) = all_161_0_107, yields:
% 27.62/7.73 | (279) all_389_0_287 = all_161_0_107
% 27.62/7.73 |
% 27.62/7.73 | Instantiating formula (22) with all_0_2_2, all_0_1_1, all_499_0_362, all_16_1_15 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_499_0_362, multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, yields:
% 27.62/7.73 | (280) all_499_0_362 = all_16_1_15
% 27.62/7.73 |
% 27.62/7.73 | Instantiating formula (22) with all_0_2_2, all_0_1_1, all_364_1_263, all_499_0_362 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_499_0_362, multiplication(all_0_2_2, all_0_1_1) = all_364_1_263, yields:
% 27.62/7.73 | (281) all_499_0_362 = all_364_1_263
% 27.62/7.73 |
% 27.62/7.73 | Instantiating formula (22) with all_0_2_2, all_0_1_1, all_364_1_263, all_449_0_329 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_449_0_329, multiplication(all_0_2_2, all_0_1_1) = all_364_1_263, yields:
% 27.62/7.73 | (282) all_449_0_329 = all_364_1_263
% 27.62/7.73 |
% 27.62/7.73 | Instantiating formula (22) with all_0_2_2, all_0_1_1, all_183_1_127, all_499_0_362 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_499_0_362, multiplication(all_0_2_2, all_0_1_1) = all_183_1_127, yields:
% 27.62/7.73 | (283) all_499_0_362 = all_183_1_127
% 27.62/7.73 |
% 27.62/7.73 | Instantiating formula (22) with all_0_2_2, all_0_1_1, all_108_0_73, all_449_0_329 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_449_0_329, multiplication(all_0_2_2, all_0_1_1) = all_108_0_73, yields:
% 27.62/7.74 | (284) all_449_0_329 = all_108_0_73
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (14) with all_372_1_270, all_0_2_2 and discharging atoms multiplication(all_0_2_2, one) = all_372_1_270, yields:
% 27.62/7.74 | (285) all_372_1_270 = all_0_2_2
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (22) with all_0_2_2, one, all_143_0_98, all_372_1_270 and discharging atoms multiplication(all_0_2_2, one) = all_372_1_270, multiplication(all_0_2_2, one) = all_143_0_98, yields:
% 27.62/7.74 | (286) all_372_1_270 = all_143_0_98
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (22) with all_0_2_2, one, all_143_0_98, all_344_1_239 and discharging atoms multiplication(all_0_2_2, one) = all_344_1_239, multiplication(all_0_2_2, one) = all_143_0_98, yields:
% 27.62/7.74 | (287) all_344_1_239 = all_143_0_98
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (22) with all_0_2_2, one, all_141_1_97, all_344_1_239 and discharging atoms multiplication(all_0_2_2, one) = all_344_1_239, multiplication(all_0_2_2, one) = all_141_1_97, yields:
% 27.62/7.74 | (288) all_344_1_239 = all_141_1_97
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (31) with all_340_0_234, all_38_0_19 and discharging atoms multiplication(one, all_38_0_19) = all_340_0_234, yields:
% 27.62/7.74 | (289) all_340_0_234 = all_38_0_19
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (14) with all_340_1_235, one and discharging atoms multiplication(one, one) = all_340_1_235, yields:
% 27.62/7.74 | (290) all_340_1_235 = one
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with all_18_1_17, all_42_0_21, all_539_0_385, all_0_1_1 and discharging atoms addition(all_18_1_17, all_42_0_21) = all_539_0_385, addition(all_18_1_17, all_42_0_21) = all_0_1_1, yields:
% 27.62/7.74 | (291) all_539_0_385 = all_0_1_1
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with all_18_1_17, all_42_0_21, all_537_0_384, all_539_0_385 and discharging atoms addition(all_18_1_17, all_42_0_21) = all_539_0_385, addition(all_18_1_17, all_42_0_21) = all_537_0_384, yields:
% 27.62/7.74 | (292) all_539_0_385 = all_537_0_384
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (15) with all_515_0_373, all_18_1_17 and discharging atoms addition(all_18_1_17, all_18_1_17) = all_515_0_373, yields:
% 27.62/7.74 | (293) all_515_0_373 = all_18_1_17
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with all_16_1_15, all_42_0_21, all_282_0_199, all_0_1_1 and discharging atoms addition(all_16_1_15, all_42_0_21) = all_282_0_199, addition(all_16_1_15, all_42_0_21) = all_0_1_1, yields:
% 27.62/7.74 | (294) all_282_0_199 = all_0_1_1
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with all_16_1_15, all_42_0_21, all_229_0_163, all_282_0_199 and discharging atoms addition(all_16_1_15, all_42_0_21) = all_282_0_199, addition(all_16_1_15, all_42_0_21) = all_229_0_163, yields:
% 27.62/7.74 | (295) all_282_0_199 = all_229_0_163
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (15) with all_334_0_231, all_16_1_15 and discharging atoms addition(all_16_1_15, all_16_1_15) = all_334_0_231, yields:
% 27.62/7.74 | (296) all_334_0_231 = all_16_1_15
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with all_16_1_15, all_0_1_1, all_295_0_208, all_38_0_19 and discharging atoms addition(all_16_1_15, all_0_1_1) = all_295_0_208, addition(all_16_1_15, all_0_1_1) = all_38_0_19, yields:
% 27.62/7.74 | (297) all_295_0_208 = all_38_0_19
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with all_16_1_15, all_0_1_1, all_295_0_208, all_366_0_264 and discharging atoms addition(all_16_1_15, all_0_1_1) = all_366_0_264, addition(all_16_1_15, all_0_1_1) = all_295_0_208, yields:
% 27.62/7.74 | (298) all_366_0_264 = all_295_0_208
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with all_16_1_15, all_0_1_1, all_218_0_154, all_366_0_264 and discharging atoms addition(all_16_1_15, all_0_1_1) = all_366_0_264, addition(all_16_1_15, all_0_1_1) = all_218_0_154, yields:
% 27.62/7.74 | (299) all_366_0_264 = all_218_0_154
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with all_16_1_15, all_0_1_1, all_215_0_150, all_295_0_208 and discharging atoms addition(all_16_1_15, all_0_1_1) = all_295_0_208, addition(all_16_1_15, all_0_1_1) = all_215_0_150, yields:
% 27.62/7.74 | (300) all_295_0_208 = all_215_0_150
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with all_0_2_2, all_16_1_15, all_233_0_165, all_423_0_308 and discharging atoms addition(all_0_2_2, all_16_1_15) = all_423_0_308, addition(all_0_2_2, all_16_1_15) = all_233_0_165, yields:
% 27.62/7.74 | (301) all_423_0_308 = all_233_0_165
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (15) with all_311_0_216, one and discharging atoms addition(one, one) = all_311_0_216, yields:
% 27.62/7.74 | (302) all_311_0_216 = one
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with one, one, all_299_0_210, all_311_0_216 and discharging atoms addition(one, one) = all_311_0_216, addition(one, one) = all_299_0_210, yields:
% 27.62/7.74 | (303) all_311_0_216 = all_299_0_210
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (292,291) yields a new equation:
% 27.62/7.74 | (304) all_537_0_384 = all_0_1_1
% 27.62/7.74 |
% 27.62/7.74 | Simplifying 304 yields:
% 27.62/7.74 | (305) all_537_0_384 = all_0_1_1
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (281,283) yields a new equation:
% 27.62/7.74 | (306) all_364_1_263 = all_183_1_127
% 27.62/7.74 |
% 27.62/7.74 | Simplifying 306 yields:
% 27.62/7.74 | (307) all_364_1_263 = all_183_1_127
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (280,283) yields a new equation:
% 27.62/7.74 | (308) all_183_1_127 = all_16_1_15
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (282,284) yields a new equation:
% 27.62/7.74 | (309) all_364_1_263 = all_108_0_73
% 27.62/7.74 |
% 27.62/7.74 | Simplifying 309 yields:
% 27.62/7.74 | (310) all_364_1_263 = all_108_0_73
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (286,285) yields a new equation:
% 27.62/7.74 | (311) all_143_0_98 = all_0_2_2
% 27.62/7.74 |
% 27.62/7.74 | Simplifying 311 yields:
% 27.62/7.74 | (312) all_143_0_98 = all_0_2_2
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (298,299) yields a new equation:
% 27.62/7.74 | (313) all_295_0_208 = all_218_0_154
% 27.62/7.74 |
% 27.62/7.74 | Simplifying 313 yields:
% 27.62/7.74 | (314) all_295_0_208 = all_218_0_154
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (307,310) yields a new equation:
% 27.62/7.74 | (315) all_183_1_127 = all_108_0_73
% 27.62/7.74 |
% 27.62/7.74 | Simplifying 315 yields:
% 27.62/7.74 | (316) all_183_1_127 = all_108_0_73
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (287,288) yields a new equation:
% 27.62/7.74 | (317) all_143_0_98 = all_141_1_97
% 27.62/7.74 |
% 27.62/7.74 | Simplifying 317 yields:
% 27.62/7.74 | (318) all_143_0_98 = all_141_1_97
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (302,303) yields a new equation:
% 27.62/7.74 | (319) all_299_0_210 = one
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (300,314) yields a new equation:
% 27.62/7.74 | (320) all_218_0_154 = all_215_0_150
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (297,314) yields a new equation:
% 27.62/7.74 | (321) all_218_0_154 = all_38_0_19
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (294,295) yields a new equation:
% 27.62/7.74 | (322) all_229_0_163 = all_0_1_1
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (321,320) yields a new equation:
% 27.62/7.74 | (323) all_215_0_150 = all_38_0_19
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (308,316) yields a new equation:
% 27.62/7.74 | (324) all_108_0_73 = all_16_1_15
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (318,312) yields a new equation:
% 27.62/7.74 | (325) all_141_1_97 = all_0_2_2
% 27.62/7.74 |
% 27.62/7.74 | Simplifying 325 yields:
% 27.62/7.74 | (326) all_141_1_97 = all_0_2_2
% 27.62/7.74 |
% 27.62/7.74 | Combining equations (326,288) yields a new equation:
% 27.62/7.74 | (327) all_344_1_239 = all_0_2_2
% 27.62/7.74 |
% 27.62/7.74 | From (279) and (248) follows:
% 27.62/7.74 | (194) multiplication(all_0_2_2, all_42_0_21) = all_161_0_107
% 27.62/7.74 |
% 27.62/7.74 | From (324) and (185) follows:
% 27.62/7.74 | (44) multiplication(all_0_2_2, all_0_1_1) = all_16_1_15
% 27.62/7.74 |
% 27.62/7.74 | From (293) and (263) follows:
% 27.62/7.74 | (330) addition(all_18_1_17, all_42_0_21) = all_46_0_24
% 27.62/7.74 |
% 27.62/7.74 | From (327) and (235) follows:
% 27.62/7.74 | (331) addition(all_0_2_2, all_344_0_238) = all_16_1_15
% 27.62/7.74 |
% 27.62/7.74 | From (290)(289) and (231) follows:
% 27.62/7.74 | (79) addition(one, all_38_0_19) = all_0_1_1
% 27.62/7.74 |
% 27.62/7.74 | From (296) and (226) follows:
% 27.62/7.74 | (333) addition(all_16_1_15, all_42_0_21) = all_38_0_19
% 27.62/7.74 |
% 27.62/7.74 | From (319) and (220) follows:
% 27.62/7.74 | (334) addition(one, all_38_0_19) = all_42_0_21
% 27.62/7.74 |
% 27.62/7.74 | From (305) and (267) follows:
% 27.62/7.74 | (84) addition(all_18_1_17, all_42_0_21) = all_0_1_1
% 27.62/7.74 |
% 27.62/7.74 | From (322) and (209) follows:
% 27.62/7.74 | (153) addition(all_16_1_15, all_42_0_21) = all_0_1_1
% 27.62/7.74 |
% 27.62/7.74 | From (323) and (203) follows:
% 27.62/7.74 | (78) addition(all_16_1_15, all_0_1_1) = all_38_0_19
% 27.62/7.74 |
% 27.62/7.74 | From (301) and (253) follows:
% 27.62/7.74 | (212) addition(all_0_2_2, all_16_1_15) = all_233_0_165
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with all_18_1_17, all_42_0_21, all_46_0_24, all_0_1_1 and discharging atoms addition(all_18_1_17, all_42_0_21) = all_46_0_24, addition(all_18_1_17, all_42_0_21) = all_0_1_1, yields:
% 27.62/7.74 | (339) all_46_0_24 = all_0_1_1
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with all_16_1_15, all_42_0_21, all_38_0_19, all_0_1_1 and discharging atoms addition(all_16_1_15, all_42_0_21) = all_38_0_19, addition(all_16_1_15, all_42_0_21) = all_0_1_1, yields:
% 27.62/7.74 | (340) all_38_0_19 = all_0_1_1
% 27.62/7.74 |
% 27.62/7.74 | Instantiating formula (2) with one, all_38_0_19, all_42_0_21, all_0_1_1 and discharging atoms addition(one, all_38_0_19) = all_42_0_21, addition(one, all_38_0_19) = all_0_1_1, yields:
% 27.62/7.74 | (341) all_42_0_21 = all_0_1_1
% 27.62/7.74 |
% 27.62/7.74 | From (339) and (244) follows:
% 27.62/7.74 | (342) multiplication(all_0_2_2, all_0_1_1) = all_372_0_269
% 27.62/7.74 |
% 27.62/7.74 | From (341) and (194) follows:
% 27.62/7.75 | (343) multiplication(all_0_2_2, all_0_1_1) = all_161_0_107
% 27.62/7.75 |
% 27.62/7.75 | From (340) and (233) follows:
% 27.62/7.75 | (344) multiplication(all_0_2_2, all_0_1_1) = all_344_0_238
% 27.62/7.75 |
% 27.62/7.75 | From (341) and (211) follows:
% 27.62/7.75 | (345) addition(all_233_0_165, all_0_1_1) = all_24_0_18
% 27.62/7.75 |
% 27.62/7.75 | From (340) and (78) follows:
% 27.62/7.75 | (346) addition(all_16_1_15, all_0_1_1) = all_0_1_1
% 27.62/7.75 |
% 27.62/7.75 | Instantiating formula (22) with all_0_2_2, all_0_1_1, all_372_0_269, all_16_1_15 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_372_0_269, multiplication(all_0_2_2, all_0_1_1) = all_16_1_15, yields:
% 27.62/7.75 | (347) all_372_0_269 = all_16_1_15
% 27.62/7.75 |
% 27.62/7.75 | Instantiating formula (22) with all_0_2_2, all_0_1_1, all_344_0_238, all_372_0_269 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_372_0_269, multiplication(all_0_2_2, all_0_1_1) = all_344_0_238, yields:
% 27.62/7.75 | (348) all_372_0_269 = all_344_0_238
% 27.62/7.75 |
% 27.62/7.75 | Instantiating formula (22) with all_0_2_2, all_0_1_1, all_161_0_107, all_372_0_269 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_372_0_269, multiplication(all_0_2_2, all_0_1_1) = all_161_0_107, yields:
% 27.62/7.75 | (349) all_372_0_269 = all_161_0_107
% 27.62/7.75 |
% 27.62/7.75 | Combining equations (349,348) yields a new equation:
% 27.62/7.75 | (350) all_344_0_238 = all_161_0_107
% 27.62/7.75 |
% 27.62/7.75 | Combining equations (347,348) yields a new equation:
% 27.62/7.75 | (351) all_344_0_238 = all_16_1_15
% 27.62/7.75 |
% 27.62/7.75 | Combining equations (351,350) yields a new equation:
% 27.62/7.75 | (352) all_161_0_107 = all_16_1_15
% 27.62/7.75 |
% 27.62/7.75 | Combining equations (352,350) yields a new equation:
% 27.62/7.75 | (351) all_344_0_238 = all_16_1_15
% 27.62/7.75 |
% 27.62/7.75 | From (351) and (331) follows:
% 27.62/7.75 | (354) addition(all_0_2_2, all_16_1_15) = all_16_1_15
% 27.62/7.75 |
% 27.62/7.75 | Instantiating formula (2) with all_0_2_2, all_16_1_15, all_16_1_15, all_233_0_165 and discharging atoms addition(all_0_2_2, all_16_1_15) = all_233_0_165, addition(all_0_2_2, all_16_1_15) = all_16_1_15, yields:
% 27.62/7.75 | (355) all_233_0_165 = all_16_1_15
% 27.62/7.75 |
% 27.62/7.75 | From (355) and (345) follows:
% 27.62/7.75 | (356) addition(all_16_1_15, all_0_1_1) = all_24_0_18
% 27.62/7.75 |
% 27.62/7.75 | Instantiating formula (2) with all_16_1_15, all_0_1_1, all_24_0_18, all_0_1_1 and discharging atoms addition(all_16_1_15, all_0_1_1) = all_24_0_18, addition(all_16_1_15, all_0_1_1) = all_0_1_1, yields:
% 27.62/7.75 | (271) all_24_0_18 = all_0_1_1
% 27.62/7.75 |
% 27.62/7.75 | Equations (271) can reduce 55 to:
% 27.62/7.75 | (51) $false
% 27.62/7.75 |
% 27.62/7.75 |-The branch is then unsatisfiable
% 27.62/7.75 |-Branch two:
% 27.62/7.75 | (359) ~ (all_73_2_50 = 0) & leq(all_18_0_16, all_0_1_1) = all_73_2_50
% 27.62/7.75 |
% 27.62/7.75 | Applying alpha-rule on (359) yields:
% 27.62/7.75 | (360) ~ (all_73_2_50 = 0)
% 27.62/7.75 | (361) leq(all_18_0_16, all_0_1_1) = all_73_2_50
% 27.62/7.75 |
% 27.62/7.75 | Instantiating formula (3) with all_18_0_16, all_0_1_1, all_73_2_50, 0 and discharging atoms leq(all_18_0_16, all_0_1_1) = all_73_2_50, leq(all_18_0_16, all_0_1_1) = 0, yields:
% 27.62/7.75 | (362) all_73_2_50 = 0
% 27.62/7.75 |
% 27.62/7.75 | Equations (362) can reduce 360 to:
% 27.62/7.75 | (51) $false
% 27.62/7.75 |
% 27.62/7.75 |-The branch is then unsatisfiable
% 27.62/7.75 |-Branch two:
% 27.62/7.75 | (364) ~ (all_54_2_31 = 0) & leq(all_16_0_14, all_0_1_1) = all_54_2_31
% 27.62/7.75 |
% 27.62/7.75 | Applying alpha-rule on (364) yields:
% 27.62/7.75 | (365) ~ (all_54_2_31 = 0)
% 27.62/7.75 | (366) leq(all_16_0_14, all_0_1_1) = all_54_2_31
% 27.62/7.75 |
% 27.62/7.75 | Instantiating formula (3) with all_16_0_14, all_0_1_1, all_54_2_31, 0 and discharging atoms leq(all_16_0_14, all_0_1_1) = all_54_2_31, leq(all_16_0_14, all_0_1_1) = 0, yields:
% 27.62/7.75 | (367) all_54_2_31 = 0
% 27.62/7.75 |
% 27.62/7.75 | Equations (367) can reduce 365 to:
% 27.62/7.75 | (51) $false
% 27.62/7.75 |
% 27.62/7.75 |-The branch is then unsatisfiable
% 27.62/7.75 % SZS output end Proof for theBenchmark
% 27.62/7.75
% 27.62/7.75 7169ms
%------------------------------------------------------------------------------