TSTP Solution File: KLE037+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE037+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 01:51:03 EDT 2022
% Result : Theorem 21.66s 6.46s
% Output : Proof 26.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE037+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 09:27:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ____ _
% 0.19/0.59 ___ / __ \_____(_)___ ________ __________
% 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic
% 0.19/0.60 (ePrincess v.1.0)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2015
% 0.19/0.60 (c) Peter Backeman, 2014-2015
% 0.19/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.60 Bug reports to peter@backeman.se
% 0.19/0.60
% 0.19/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.60
% 0.62/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.58/0.94 Prover 0: Preprocessing ...
% 1.97/1.16 Prover 0: Constructing countermodel ...
% 19.46/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.46/5.96 Prover 1: Preprocessing ...
% 19.96/6.04 Prover 1: Constructing countermodel ...
% 19.96/6.09 Prover 1: gave up
% 19.96/6.10 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 20.38/6.11 Prover 2: Preprocessing ...
% 20.38/6.19 Prover 2: Warning: ignoring some quantifiers
% 20.77/6.19 Prover 2: Constructing countermodel ...
% 21.66/6.45 Prover 2: proved (359ms)
% 21.66/6.46 Prover 0: stopped
% 21.66/6.46
% 21.66/6.46 No countermodel exists, formula is valid
% 21.66/6.46 % SZS status Theorem for theBenchmark
% 21.66/6.46
% 21.66/6.46 Generating proof ... Warning: ignoring some quantifiers
% 26.32/7.50 found it (size 147)
% 26.32/7.50
% 26.32/7.50 % SZS output start Proof for theBenchmark
% 26.32/7.50 Assumed formulas after preprocessing and simplification:
% 26.32/7.50 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & star(v0) = v1 & leq(one, 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)
% 26.39/7.54 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 26.39/7.54 | (1) ~ (all_0_0_0 = 0) & star(all_0_2_2) = all_0_1_1 & leq(one, 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
% 26.39/7.55 |
% 26.39/7.55 | Applying alpha-rule on (1) yields:
% 26.39/7.55 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 26.39/7.55 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 26.39/7.55 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 26.39/7.55 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 26.39/7.55 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 26.39/7.55 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 26.39/7.55 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 26.39/7.55 | (9) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2
% 26.39/7.55 | (10) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (leq(v3, v1) = 0 & multiplication(v1, v0) = v2 & addition(one, v2) = v3))
% 26.39/7.55 | (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))
% 26.39/7.55 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 26.39/7.55 | (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)))
% 26.39/7.55 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 26.39/7.55 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 26.39/7.55 | (16) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (leq(v3, v1) = 0 & multiplication(v0, v1) = v2 & addition(one, v2) = v3))
% 26.39/7.55 | (17) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 26.39/7.55 | (18) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 26.39/7.55 | (19) ? [v0] : ? [v1] : star(v0) = v1
% 26.39/7.55 | (20) ~ (all_0_0_0 = 0)
% 26.39/7.55 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 26.39/7.55 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 26.39/7.55 | (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))
% 26.39/7.55 | (24) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 26.39/7.55 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 26.39/7.55 | (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))
% 26.39/7.55 | (27) star(all_0_2_2) = all_0_1_1
% 26.39/7.55 | (28) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2
% 26.39/7.55 | (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))
% 26.39/7.55 | (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))
% 26.39/7.55 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 26.39/7.55 | (32) leq(one, all_0_1_1) = all_0_0_0
% 26.39/7.55 | (33) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2
% 26.39/7.55 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 26.39/7.55 | (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))
% 26.39/7.55 | (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)))
% 26.39/7.55 | (37) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 26.39/7.55 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0))
% 26.39/7.55 |
% 26.39/7.55 | 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:
% 26.39/7.55 | (39) ? [v0] : ? [v1] : (leq(v1, all_0_1_1) = 0 & multiplication(all_0_1_1, all_0_2_2) = v0 & addition(one, v0) = v1)
% 26.39/7.56 |
% 26.39/7.56 | 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:
% 26.39/7.56 | (40) ? [v0] : ? [v1] : (leq(v1, all_0_1_1) = 0 & multiplication(all_0_2_2, all_0_1_1) = v0 & addition(one, v0) = v1)
% 26.39/7.56 |
% 26.39/7.56 | Instantiating formula (6) with all_0_0_0, all_0_1_1, one and discharging atoms leq(one, all_0_1_1) = all_0_0_0, yields:
% 26.39/7.56 | (41) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = all_0_1_1) & addition(one, all_0_1_1) = v0)
% 26.39/7.56 |
% 26.39/7.56 | Instantiating (40) with all_16_0_14, all_16_1_15 yields:
% 26.39/7.56 | (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
% 26.39/7.56 |
% 26.39/7.56 | Applying alpha-rule on (42) yields:
% 26.39/7.56 | (43) leq(all_16_0_14, all_0_1_1) = 0
% 26.39/7.56 | (44) multiplication(all_0_2_2, all_0_1_1) = all_16_1_15
% 26.39/7.56 | (45) addition(one, all_16_1_15) = all_16_0_14
% 26.39/7.56 |
% 26.39/7.56 | Instantiating (39) with all_18_0_16, all_18_1_17 yields:
% 26.39/7.56 | (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
% 26.39/7.56 |
% 26.39/7.56 | Applying alpha-rule on (46) yields:
% 26.39/7.56 | (47) leq(all_18_0_16, all_0_1_1) = 0
% 26.39/7.56 | (48) multiplication(all_0_1_1, all_0_2_2) = all_18_1_17
% 26.39/7.56 | (49) addition(one, all_18_1_17) = all_18_0_16
% 26.39/7.56 |
% 26.39/7.56 +-Applying beta-rule and splitting (41), into two cases.
% 26.39/7.56 |-Branch one:
% 26.39/7.56 | (50) all_0_0_0 = 0
% 26.39/7.56 |
% 26.39/7.56 | Equations (50) can reduce 20 to:
% 26.39/7.56 | (51) $false
% 26.39/7.56 |
% 26.39/7.56 |-The branch is then unsatisfiable
% 26.39/7.56 |-Branch two:
% 26.39/7.56 | (20) ~ (all_0_0_0 = 0)
% 26.39/7.56 | (53) ? [v0] : ( ~ (v0 = all_0_1_1) & addition(one, all_0_1_1) = v0)
% 26.39/7.56 |
% 26.39/7.56 | Instantiating (53) with all_24_0_18 yields:
% 26.39/7.56 | (54) ~ (all_24_0_18 = all_0_1_1) & addition(one, all_0_1_1) = all_24_0_18
% 26.39/7.56 |
% 26.39/7.56 | Applying alpha-rule on (54) yields:
% 26.39/7.56 | (55) ~ (all_24_0_18 = all_0_1_1)
% 26.39/7.56 | (56) addition(one, all_0_1_1) = all_24_0_18
% 26.39/7.56 |
% 26.39/7.56 | 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:
% 26.39/7.56 | (57) addition(all_18_0_16, all_0_1_1) = all_0_1_1
% 26.39/7.56 |
% 26.39/7.56 | 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:
% 26.39/7.56 | (58) addition(all_16_0_14, all_0_1_1) = all_0_1_1
% 26.39/7.56 |
% 26.39/7.56 | 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:
% 26.39/7.56 | (59) addition(all_18_1_17, one) = all_18_0_16
% 26.39/7.56 |
% 26.39/7.56 | 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:
% 26.39/7.56 | (60) addition(all_16_1_15, one) = all_16_0_14
% 26.39/7.56 |
% 26.39/7.56 | 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:
% 26.39/7.56 | (61) ? [v0] : (addition(all_18_1_17, all_0_1_1) = v0 & addition(one, v0) = all_0_1_1)
% 26.39/7.56 |
% 26.39/7.56 | Instantiating formula (25) with all_24_0_18, all_0_1_1, one, 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(one, all_0_1_1) = all_24_0_18, yields:
% 26.39/7.56 | (62) ? [v0] : (addition(v0, all_0_1_1) = all_24_0_18 & addition(one, all_18_0_16) = v0)
% 26.39/7.56 |
% 26.39/7.56 | 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:
% 26.39/7.56 | (63) ? [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))
% 26.39/7.56 |
% 26.39/7.56 | 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:
% 26.39/7.56 | (64) ? [v0] : (addition(all_18_1_17, v0) = all_0_1_1 & addition(one, all_0_1_1) = v0)
% 26.39/7.56 |
% 26.39/7.56 | 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:
% 26.39/7.56 | (65) ? [v0] : (addition(all_16_1_15, all_0_1_1) = v0 & addition(one, v0) = all_0_1_1)
% 26.39/7.56 |
% 26.39/7.56 | Instantiating formula (25) with all_24_0_18, all_0_1_1, one, 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(one, all_0_1_1) = all_24_0_18, yields:
% 26.39/7.56 | (66) ? [v0] : (addition(v0, all_0_1_1) = all_24_0_18 & addition(one, all_16_0_14) = v0)
% 26.39/7.56 |
% 26.39/7.56 | 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:
% 26.39/7.56 | (67) ? [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))
% 26.39/7.56 |
% 26.39/7.56 | 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:
% 26.39/7.56 | (68) ? [v0] : (addition(all_16_1_15, v0) = all_0_1_1 & addition(one, all_0_1_1) = v0)
% 26.39/7.56 |
% 26.39/7.56 | Instantiating (66) with all_38_0_19 yields:
% 26.39/7.56 | (69) addition(all_38_0_19, all_0_1_1) = all_24_0_18 & addition(one, all_16_0_14) = all_38_0_19
% 26.39/7.56 |
% 26.39/7.56 | Applying alpha-rule on (69) yields:
% 26.39/7.56 | (70) addition(all_38_0_19, all_0_1_1) = all_24_0_18
% 26.39/7.56 | (71) addition(one, all_16_0_14) = all_38_0_19
% 26.39/7.56 |
% 26.39/7.56 | Instantiating (65) with all_40_0_20 yields:
% 26.39/7.56 | (72) addition(all_16_1_15, all_0_1_1) = all_40_0_20 & addition(one, all_40_0_20) = all_0_1_1
% 26.39/7.56 |
% 26.39/7.56 | Applying alpha-rule on (72) yields:
% 26.39/7.56 | (73) addition(all_16_1_15, all_0_1_1) = all_40_0_20
% 26.39/7.56 | (74) addition(one, all_40_0_20) = all_0_1_1
% 26.39/7.56 |
% 26.39/7.56 | Instantiating (64) with all_42_0_21 yields:
% 26.39/7.56 | (75) addition(all_18_1_17, all_42_0_21) = all_0_1_1 & addition(one, all_0_1_1) = all_42_0_21
% 26.39/7.56 |
% 26.39/7.56 | Applying alpha-rule on (75) yields:
% 26.39/7.56 | (76) addition(all_18_1_17, all_42_0_21) = all_0_1_1
% 26.39/7.56 | (77) addition(one, all_0_1_1) = all_42_0_21
% 26.39/7.56 |
% 26.39/7.56 | Instantiating (62) with all_46_0_24 yields:
% 26.39/7.56 | (78) addition(all_46_0_24, all_0_1_1) = all_24_0_18 & addition(one, all_18_0_16) = all_46_0_24
% 26.39/7.56 |
% 26.39/7.56 | Applying alpha-rule on (78) yields:
% 26.39/7.56 | (79) addition(all_46_0_24, all_0_1_1) = all_24_0_18
% 26.39/7.56 | (80) addition(one, all_18_0_16) = all_46_0_24
% 26.39/7.56 |
% 26.39/7.56 | Instantiating (61) with all_50_0_27 yields:
% 26.39/7.56 | (81) addition(all_18_1_17, all_0_1_1) = all_50_0_27 & addition(one, all_50_0_27) = all_0_1_1
% 26.39/7.56 |
% 26.39/7.56 | Applying alpha-rule on (81) yields:
% 26.39/7.56 | (82) addition(all_18_1_17, all_0_1_1) = all_50_0_27
% 26.39/7.56 | (83) addition(one, all_50_0_27) = all_0_1_1
% 26.39/7.56 |
% 26.39/7.56 | Instantiating (68) with all_52_0_28 yields:
% 26.39/7.56 | (84) addition(all_16_1_15, all_52_0_28) = all_0_1_1 & addition(one, all_0_1_1) = all_52_0_28
% 26.39/7.56 |
% 26.39/7.56 | Applying alpha-rule on (84) yields:
% 26.39/7.56 | (85) addition(all_16_1_15, all_52_0_28) = all_0_1_1
% 26.39/7.56 | (86) addition(one, all_0_1_1) = all_52_0_28
% 26.39/7.56 |
% 26.39/7.56 | Instantiating (67) with all_54_0_29, all_54_1_30, all_54_2_31 yields:
% 26.39/7.56 | (87) (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)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating (63) with all_73_0_48, all_73_1_49, all_73_2_50 yields:
% 26.39/7.57 | (88) (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)
% 26.39/7.57 |
% 26.39/7.57 +-Applying beta-rule and splitting (87), into two cases.
% 26.39/7.57 |-Branch one:
% 26.39/7.57 | (89) 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
% 26.39/7.57 |
% 26.39/7.57 | Applying alpha-rule on (89) yields:
% 26.39/7.57 | (90) all_54_0_29 = 0
% 26.39/7.57 | (91) star(all_0_2_2) = all_54_2_31
% 26.39/7.57 | (92) leq(all_54_1_30, all_0_1_1) = 0
% 26.39/7.57 | (93) multiplication(all_54_2_31, one) = all_54_1_30
% 26.39/7.57 |
% 26.39/7.57 +-Applying beta-rule and splitting (88), into two cases.
% 26.39/7.57 |-Branch one:
% 26.39/7.57 | (94) 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
% 26.39/7.57 |
% 26.39/7.57 | Applying alpha-rule on (94) yields:
% 26.39/7.57 | (95) all_73_0_48 = 0
% 26.39/7.57 | (96) star(all_0_2_2) = all_73_2_50
% 26.39/7.57 | (97) leq(all_73_1_49, all_0_1_1) = 0
% 26.39/7.57 | (98) multiplication(one, all_73_2_50) = all_73_1_49
% 26.39/7.57 |
% 26.39/7.57 | 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:
% 26.39/7.57 | (99) all_73_2_50 = all_0_1_1
% 26.39/7.57 |
% 26.39/7.57 | 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:
% 26.39/7.57 | (100) all_73_2_50 = all_54_2_31
% 26.39/7.57 |
% 26.39/7.57 | 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:
% 26.39/7.57 | (101) all_54_1_30 = all_54_2_31
% 26.39/7.57 |
% 26.39/7.57 | 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:
% 26.39/7.57 | (102) all_73_1_49 = all_73_2_50
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (2) with one, all_0_1_1, all_52_0_28, all_24_0_18 and discharging atoms addition(one, all_0_1_1) = all_52_0_28, addition(one, all_0_1_1) = all_24_0_18, yields:
% 26.39/7.57 | (103) all_52_0_28 = all_24_0_18
% 26.39/7.57 |
% 26.39/7.57 | 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:
% 26.39/7.57 | (104) all_52_0_28 = all_42_0_21
% 26.39/7.57 |
% 26.39/7.57 | Combining equations (99,100) yields a new equation:
% 26.39/7.57 | (105) all_54_2_31 = all_0_1_1
% 26.39/7.57 |
% 26.39/7.57 | Combining equations (103,104) yields a new equation:
% 26.39/7.57 | (106) all_42_0_21 = all_24_0_18
% 26.39/7.57 |
% 26.39/7.57 | Combining equations (106,104) yields a new equation:
% 26.39/7.57 | (103) all_52_0_28 = all_24_0_18
% 26.39/7.57 |
% 26.39/7.57 | Combining equations (105,101) yields a new equation:
% 26.39/7.57 | (108) all_54_1_30 = all_0_1_1
% 26.39/7.57 |
% 26.39/7.57 | Combining equations (105,100) yields a new equation:
% 26.39/7.57 | (99) all_73_2_50 = all_0_1_1
% 26.39/7.57 |
% 26.39/7.57 | Combining equations (99,102) yields a new equation:
% 26.39/7.57 | (110) all_73_1_49 = all_0_1_1
% 26.39/7.57 |
% 26.39/7.57 | From (105)(108) and (93) follows:
% 26.39/7.57 | (111) multiplication(all_0_1_1, one) = all_0_1_1
% 26.39/7.57 |
% 26.39/7.57 | From (99)(110) and (98) follows:
% 26.39/7.57 | (112) multiplication(one, all_0_1_1) = all_0_1_1
% 26.39/7.57 |
% 26.39/7.57 | From (106) and (76) follows:
% 26.39/7.57 | (113) addition(all_18_1_17, all_24_0_18) = all_0_1_1
% 26.39/7.57 |
% 26.39/7.57 | From (103) and (85) follows:
% 26.39/7.57 | (114) addition(all_16_1_15, all_24_0_18) = all_0_1_1
% 26.39/7.57 |
% 26.39/7.57 | From (106) and (77) follows:
% 26.39/7.57 | (56) addition(one, all_0_1_1) = all_24_0_18
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (4) with all_0_1_1, all_0_1_1, one, one, all_0_1_1 and discharging atoms multiplication(all_0_1_1, one) = all_0_1_1, yields:
% 26.39/7.57 | (116) ? [v0] : (multiplication(all_0_1_1, v0) = all_0_1_1 & multiplication(one, one) = v0)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (5) with all_0_1_1, all_0_1_1, all_0_1_1, one, one and discharging atoms multiplication(one, all_0_1_1) = all_0_1_1, yields:
% 26.39/7.57 | (117) ? [v0] : (multiplication(v0, all_0_1_1) = all_0_1_1 & multiplication(one, one) = v0)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (21) with all_24_0_18, all_0_1_1, all_46_0_24 and discharging atoms addition(all_46_0_24, all_0_1_1) = all_24_0_18, yields:
% 26.39/7.57 | (118) all_24_0_18 = all_0_1_1 | ? [v0] : ( ~ (v0 = 0) & leq(all_46_0_24, all_0_1_1) = v0)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (21) with all_24_0_18, all_0_1_1, all_38_0_19 and discharging atoms addition(all_38_0_19, all_0_1_1) = all_24_0_18, yields:
% 26.39/7.57 | (119) all_24_0_18 = all_0_1_1 | ? [v0] : ( ~ (v0 = 0) & leq(all_38_0_19, all_0_1_1) = v0)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (21) with all_0_1_1, all_24_0_18, all_18_1_17 and discharging atoms addition(all_18_1_17, all_24_0_18) = all_0_1_1, yields:
% 26.39/7.57 | (120) all_24_0_18 = all_0_1_1 | ? [v0] : ( ~ (v0 = 0) & leq(all_18_1_17, all_24_0_18) = v0)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (21) with all_0_1_1, all_24_0_18, all_16_1_15 and discharging atoms addition(all_16_1_15, all_24_0_18) = all_0_1_1, yields:
% 26.39/7.57 | (121) all_24_0_18 = all_0_1_1 | ? [v0] : ( ~ (v0 = 0) & leq(all_16_1_15, all_24_0_18) = v0)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (30) with all_0_1_1, all_0_1_1, one, all_50_0_27, one and discharging atoms multiplication(all_0_1_1, one) = all_0_1_1, addition(one, all_50_0_27) = all_0_1_1, yields:
% 26.39/7.57 | (122) ? [v0] : ? [v1] : (multiplication(all_50_0_27, one) = v1 & multiplication(one, one) = v0 & addition(v0, v1) = all_0_1_1)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (29) with all_0_1_1, all_0_1_1, all_50_0_27, one, one and discharging atoms multiplication(one, all_0_1_1) = all_0_1_1, addition(one, all_50_0_27) = all_0_1_1, yields:
% 26.39/7.57 | (123) ? [v0] : ? [v1] : (multiplication(one, all_50_0_27) = v1 & multiplication(one, one) = v0 & addition(v0, v1) = all_0_1_1)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (25) with all_24_0_18, all_0_1_1, one, one, all_50_0_27 and discharging atoms addition(one, all_50_0_27) = all_0_1_1, addition(one, all_0_1_1) = all_24_0_18, yields:
% 26.39/7.57 | (124) ? [v0] : (addition(v0, all_50_0_27) = all_24_0_18 & addition(one, one) = v0)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (30) with all_0_1_1, all_0_1_1, one, all_40_0_20, one and discharging atoms multiplication(all_0_1_1, one) = all_0_1_1, addition(one, all_40_0_20) = all_0_1_1, yields:
% 26.39/7.57 | (125) ? [v0] : ? [v1] : (multiplication(all_40_0_20, one) = v1 & multiplication(one, one) = v0 & addition(v0, v1) = all_0_1_1)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (29) with all_0_1_1, all_0_1_1, all_40_0_20, one, one and discharging atoms multiplication(one, all_0_1_1) = all_0_1_1, addition(one, all_40_0_20) = all_0_1_1, yields:
% 26.39/7.57 | (126) ? [v0] : ? [v1] : (multiplication(one, all_40_0_20) = v1 & multiplication(one, one) = v0 & addition(v0, v1) = all_0_1_1)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (25) with all_24_0_18, all_0_1_1, one, one, all_40_0_20 and discharging atoms addition(one, all_40_0_20) = all_0_1_1, addition(one, all_0_1_1) = all_24_0_18, yields:
% 26.39/7.57 | (127) ? [v0] : (addition(v0, all_40_0_20) = all_24_0_18 & addition(one, one) = v0)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (25) with all_46_0_24, all_18_0_16, one, one, all_18_1_17 and discharging atoms addition(one, all_18_0_16) = all_46_0_24, addition(one, all_18_1_17) = all_18_0_16, yields:
% 26.39/7.57 | (128) ? [v0] : (addition(v0, all_18_1_17) = all_46_0_24 & addition(one, one) = v0)
% 26.39/7.57 |
% 26.39/7.57 | Instantiating formula (25) with all_38_0_19, all_16_0_14, one, one, all_16_1_15 and discharging atoms addition(one, all_16_0_14) = all_38_0_19, addition(one, all_16_1_15) = all_16_0_14, yields:
% 26.39/7.58 | (129) ? [v0] : (addition(v0, all_16_1_15) = all_38_0_19 & addition(one, one) = v0)
% 26.39/7.58 |
% 26.39/7.58 | Instantiating (116) with all_191_0_130 yields:
% 26.39/7.58 | (130) multiplication(all_0_1_1, all_191_0_130) = all_0_1_1 & multiplication(one, one) = all_191_0_130
% 26.39/7.58 |
% 26.39/7.58 | Applying alpha-rule on (130) yields:
% 26.39/7.58 | (131) multiplication(all_0_1_1, all_191_0_130) = all_0_1_1
% 26.39/7.58 | (132) multiplication(one, one) = all_191_0_130
% 26.39/7.58 |
% 26.39/7.58 | Instantiating (127) with all_241_0_164 yields:
% 26.39/7.58 | (133) addition(all_241_0_164, all_40_0_20) = all_24_0_18 & addition(one, one) = all_241_0_164
% 26.39/7.58 |
% 26.39/7.58 | Applying alpha-rule on (133) yields:
% 26.39/7.58 | (134) addition(all_241_0_164, all_40_0_20) = all_24_0_18
% 26.39/7.58 | (135) addition(one, one) = all_241_0_164
% 26.39/7.58 |
% 26.39/7.58 | Instantiating (126) with all_303_0_216, all_303_1_217 yields:
% 26.39/7.58 | (136) multiplication(one, all_40_0_20) = all_303_0_216 & multiplication(one, one) = all_303_1_217 & addition(all_303_1_217, all_303_0_216) = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Applying alpha-rule on (136) yields:
% 26.39/7.58 | (137) multiplication(one, all_40_0_20) = all_303_0_216
% 26.39/7.58 | (138) multiplication(one, one) = all_303_1_217
% 26.39/7.58 | (139) addition(all_303_1_217, all_303_0_216) = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Instantiating (125) with all_307_0_219, all_307_1_220 yields:
% 26.39/7.58 | (140) multiplication(all_40_0_20, one) = all_307_0_219 & multiplication(one, one) = all_307_1_220 & addition(all_307_1_220, all_307_0_219) = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Applying alpha-rule on (140) yields:
% 26.39/7.58 | (141) multiplication(all_40_0_20, one) = all_307_0_219
% 26.39/7.58 | (142) multiplication(one, one) = all_307_1_220
% 26.39/7.58 | (143) addition(all_307_1_220, all_307_0_219) = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Instantiating (124) with all_331_0_234 yields:
% 26.39/7.58 | (144) addition(all_331_0_234, all_50_0_27) = all_24_0_18 & addition(one, one) = all_331_0_234
% 26.39/7.58 |
% 26.39/7.58 | Applying alpha-rule on (144) yields:
% 26.39/7.58 | (145) addition(all_331_0_234, all_50_0_27) = all_24_0_18
% 26.39/7.58 | (146) addition(one, one) = all_331_0_234
% 26.39/7.58 |
% 26.39/7.58 | Instantiating (123) with all_386_0_272, all_386_1_273 yields:
% 26.39/7.58 | (147) multiplication(one, all_50_0_27) = all_386_0_272 & multiplication(one, one) = all_386_1_273 & addition(all_386_1_273, all_386_0_272) = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Applying alpha-rule on (147) yields:
% 26.39/7.58 | (148) multiplication(one, all_50_0_27) = all_386_0_272
% 26.39/7.58 | (149) multiplication(one, one) = all_386_1_273
% 26.39/7.58 | (150) addition(all_386_1_273, all_386_0_272) = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Instantiating (129) with all_417_0_296 yields:
% 26.39/7.58 | (151) addition(all_417_0_296, all_16_1_15) = all_38_0_19 & addition(one, one) = all_417_0_296
% 26.39/7.58 |
% 26.39/7.58 | Applying alpha-rule on (151) yields:
% 26.39/7.58 | (152) addition(all_417_0_296, all_16_1_15) = all_38_0_19
% 26.39/7.58 | (153) addition(one, one) = all_417_0_296
% 26.39/7.58 |
% 26.39/7.58 | Instantiating (128) with all_421_0_298 yields:
% 26.39/7.58 | (154) addition(all_421_0_298, all_18_1_17) = all_46_0_24 & addition(one, one) = all_421_0_298
% 26.39/7.58 |
% 26.39/7.58 | Applying alpha-rule on (154) yields:
% 26.39/7.58 | (155) addition(all_421_0_298, all_18_1_17) = all_46_0_24
% 26.39/7.58 | (156) addition(one, one) = all_421_0_298
% 26.39/7.58 |
% 26.39/7.58 | Instantiating (122) with all_495_0_342, all_495_1_343 yields:
% 26.39/7.58 | (157) multiplication(all_50_0_27, one) = all_495_0_342 & multiplication(one, one) = all_495_1_343 & addition(all_495_1_343, all_495_0_342) = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Applying alpha-rule on (157) yields:
% 26.39/7.58 | (158) multiplication(all_50_0_27, one) = all_495_0_342
% 26.39/7.58 | (159) multiplication(one, one) = all_495_1_343
% 26.39/7.58 | (160) addition(all_495_1_343, all_495_0_342) = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Instantiating (117) with all_544_0_385 yields:
% 26.39/7.58 | (161) multiplication(all_544_0_385, all_0_1_1) = all_0_1_1 & multiplication(one, one) = all_544_0_385
% 26.39/7.58 |
% 26.39/7.58 | Applying alpha-rule on (161) yields:
% 26.39/7.58 | (162) multiplication(all_544_0_385, all_0_1_1) = all_0_1_1
% 26.39/7.58 | (163) multiplication(one, one) = all_544_0_385
% 26.39/7.58 |
% 26.39/7.58 +-Applying beta-rule and splitting (121), into two cases.
% 26.39/7.58 |-Branch one:
% 26.39/7.58 | (164) all_24_0_18 = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Equations (164) can reduce 55 to:
% 26.39/7.58 | (51) $false
% 26.39/7.58 |
% 26.39/7.58 |-The branch is then unsatisfiable
% 26.39/7.58 |-Branch two:
% 26.39/7.58 | (55) ~ (all_24_0_18 = all_0_1_1)
% 26.39/7.58 | (167) ? [v0] : ( ~ (v0 = 0) & leq(all_16_1_15, all_24_0_18) = v0)
% 26.39/7.58 |
% 26.39/7.58 +-Applying beta-rule and splitting (119), into two cases.
% 26.39/7.58 |-Branch one:
% 26.39/7.58 | (164) all_24_0_18 = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Equations (164) can reduce 55 to:
% 26.39/7.58 | (51) $false
% 26.39/7.58 |
% 26.39/7.58 |-The branch is then unsatisfiable
% 26.39/7.58 |-Branch two:
% 26.39/7.58 | (55) ~ (all_24_0_18 = all_0_1_1)
% 26.39/7.58 | (171) ? [v0] : ( ~ (v0 = 0) & leq(all_38_0_19, all_0_1_1) = v0)
% 26.39/7.58 |
% 26.39/7.58 +-Applying beta-rule and splitting (120), into two cases.
% 26.39/7.58 |-Branch one:
% 26.39/7.58 | (164) all_24_0_18 = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Equations (164) can reduce 55 to:
% 26.39/7.58 | (51) $false
% 26.39/7.58 |
% 26.39/7.58 |-The branch is then unsatisfiable
% 26.39/7.58 |-Branch two:
% 26.39/7.58 | (55) ~ (all_24_0_18 = all_0_1_1)
% 26.39/7.58 | (175) ? [v0] : ( ~ (v0 = 0) & leq(all_18_1_17, all_24_0_18) = v0)
% 26.39/7.58 |
% 26.39/7.58 +-Applying beta-rule and splitting (118), into two cases.
% 26.39/7.58 |-Branch one:
% 26.39/7.58 | (164) all_24_0_18 = all_0_1_1
% 26.39/7.58 |
% 26.39/7.58 | Equations (164) can reduce 55 to:
% 26.39/7.58 | (51) $false
% 26.39/7.58 |
% 26.39/7.58 |-The branch is then unsatisfiable
% 26.39/7.58 |-Branch two:
% 26.39/7.58 | (55) ~ (all_24_0_18 = all_0_1_1)
% 26.39/7.58 | (179) ? [v0] : ( ~ (v0 = 0) & leq(all_46_0_24, all_0_1_1) = v0)
% 26.39/7.58 |
% 26.39/7.58 | Instantiating formula (31) with all_303_0_216, all_40_0_20 and discharging atoms multiplication(one, all_40_0_20) = all_303_0_216, yields:
% 26.39/7.58 | (180) all_303_0_216 = all_40_0_20
% 26.39/7.58 |
% 26.39/7.58 | Instantiating formula (22) with one, one, all_495_1_343, all_544_0_385 and discharging atoms multiplication(one, one) = all_544_0_385, multiplication(one, one) = all_495_1_343, yields:
% 26.39/7.58 | (181) all_544_0_385 = all_495_1_343
% 26.39/7.58 |
% 26.39/7.58 | Instantiating formula (22) with one, one, all_386_1_273, all_544_0_385 and discharging atoms multiplication(one, one) = all_544_0_385, multiplication(one, one) = all_386_1_273, yields:
% 26.39/7.58 | (182) all_544_0_385 = all_386_1_273
% 26.39/7.58 |
% 26.39/7.58 | Instantiating formula (22) with one, one, all_307_1_220, all_544_0_385 and discharging atoms multiplication(one, one) = all_544_0_385, multiplication(one, one) = all_307_1_220, yields:
% 26.39/7.58 | (183) all_544_0_385 = all_307_1_220
% 26.39/7.58 |
% 26.39/7.58 | Instantiating formula (14) with all_307_1_220, one and discharging atoms multiplication(one, one) = all_307_1_220, yields:
% 26.39/7.58 | (184) all_307_1_220 = one
% 26.39/7.58 |
% 26.39/7.58 | Instantiating formula (22) with one, one, all_303_1_217, all_544_0_385 and discharging atoms multiplication(one, one) = all_544_0_385, multiplication(one, one) = all_303_1_217, yields:
% 26.39/7.58 | (185) all_544_0_385 = all_303_1_217
% 26.39/7.58 |
% 26.39/7.58 | Instantiating formula (22) with one, one, all_191_0_130, all_307_1_220 and discharging atoms multiplication(one, one) = all_307_1_220, multiplication(one, one) = all_191_0_130, yields:
% 26.39/7.58 | (186) all_307_1_220 = all_191_0_130
% 26.39/7.58 |
% 26.39/7.58 | Instantiating formula (15) with all_421_0_298, one and discharging atoms addition(one, one) = all_421_0_298, yields:
% 26.39/7.58 | (187) all_421_0_298 = one
% 26.39/7.58 |
% 26.39/7.58 | Instantiating formula (2) with one, one, all_417_0_296, all_421_0_298 and discharging atoms addition(one, one) = all_421_0_298, addition(one, one) = all_417_0_296, yields:
% 26.39/7.58 | (188) all_421_0_298 = all_417_0_296
% 26.39/7.59 |
% 26.39/7.59 | Instantiating formula (2) with one, one, all_331_0_234, all_417_0_296 and discharging atoms addition(one, one) = all_417_0_296, addition(one, one) = all_331_0_234, yields:
% 26.39/7.59 | (189) all_417_0_296 = all_331_0_234
% 26.39/7.59 |
% 26.39/7.59 | Instantiating formula (2) with one, one, all_241_0_164, all_331_0_234 and discharging atoms addition(one, one) = all_331_0_234, addition(one, one) = all_241_0_164, yields:
% 26.39/7.59 | (190) all_331_0_234 = all_241_0_164
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (185,181) yields a new equation:
% 26.39/7.59 | (191) all_495_1_343 = all_303_1_217
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (183,181) yields a new equation:
% 26.39/7.59 | (192) all_495_1_343 = all_307_1_220
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (182,181) yields a new equation:
% 26.39/7.59 | (193) all_495_1_343 = all_386_1_273
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (191,193) yields a new equation:
% 26.39/7.59 | (194) all_386_1_273 = all_303_1_217
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (192,193) yields a new equation:
% 26.39/7.59 | (195) all_386_1_273 = all_307_1_220
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (188,187) yields a new equation:
% 26.39/7.59 | (196) all_417_0_296 = one
% 26.39/7.59 |
% 26.39/7.59 | Simplifying 196 yields:
% 26.39/7.59 | (197) all_417_0_296 = one
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (189,197) yields a new equation:
% 26.39/7.59 | (198) all_331_0_234 = one
% 26.39/7.59 |
% 26.39/7.59 | Simplifying 198 yields:
% 26.39/7.59 | (199) all_331_0_234 = one
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (195,194) yields a new equation:
% 26.39/7.59 | (200) all_307_1_220 = all_303_1_217
% 26.39/7.59 |
% 26.39/7.59 | Simplifying 200 yields:
% 26.39/7.59 | (201) all_307_1_220 = all_303_1_217
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (199,190) yields a new equation:
% 26.39/7.59 | (202) all_241_0_164 = one
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (186,201) yields a new equation:
% 26.39/7.59 | (203) all_303_1_217 = all_191_0_130
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (184,201) yields a new equation:
% 26.39/7.59 | (204) all_303_1_217 = one
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (204,203) yields a new equation:
% 26.39/7.59 | (205) all_191_0_130 = one
% 26.39/7.59 |
% 26.39/7.59 | Combining equations (205,203) yields a new equation:
% 26.39/7.59 | (204) all_303_1_217 = one
% 26.39/7.59 |
% 26.39/7.59 | From (204)(180) and (139) follows:
% 26.39/7.59 | (74) addition(one, all_40_0_20) = all_0_1_1
% 26.39/7.59 |
% 26.39/7.59 | From (202) and (134) follows:
% 26.39/7.59 | (208) addition(one, all_40_0_20) = all_24_0_18
% 26.39/7.59 |
% 26.39/7.59 | Instantiating formula (2) with one, all_40_0_20, all_24_0_18, all_0_1_1 and discharging atoms addition(one, all_40_0_20) = all_24_0_18, addition(one, all_40_0_20) = all_0_1_1, yields:
% 26.39/7.59 | (164) all_24_0_18 = all_0_1_1
% 26.39/7.59 |
% 26.39/7.59 | Equations (164) can reduce 55 to:
% 26.39/7.59 | (51) $false
% 26.39/7.59 |
% 26.39/7.59 |-The branch is then unsatisfiable
% 26.39/7.59 |-Branch two:
% 26.39/7.59 | (211) ~ (all_73_2_50 = 0) & leq(all_18_0_16, all_0_1_1) = all_73_2_50
% 26.39/7.59 |
% 26.39/7.59 | Applying alpha-rule on (211) yields:
% 26.39/7.59 | (212) ~ (all_73_2_50 = 0)
% 26.39/7.59 | (213) leq(all_18_0_16, all_0_1_1) = all_73_2_50
% 26.39/7.59 |
% 26.39/7.59 | 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:
% 26.39/7.59 | (214) all_73_2_50 = 0
% 26.39/7.59 |
% 26.39/7.59 | Equations (214) can reduce 212 to:
% 26.39/7.59 | (51) $false
% 26.39/7.59 |
% 26.39/7.59 |-The branch is then unsatisfiable
% 26.39/7.59 |-Branch two:
% 26.39/7.59 | (216) ~ (all_54_2_31 = 0) & leq(all_16_0_14, all_0_1_1) = all_54_2_31
% 26.39/7.59 |
% 26.39/7.59 | Applying alpha-rule on (216) yields:
% 26.39/7.59 | (217) ~ (all_54_2_31 = 0)
% 26.39/7.59 | (218) leq(all_16_0_14, all_0_1_1) = all_54_2_31
% 26.39/7.59 |
% 26.39/7.59 | 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:
% 26.39/7.59 | (219) all_54_2_31 = 0
% 26.39/7.59 |
% 26.39/7.59 | Equations (219) can reduce 217 to:
% 26.39/7.59 | (51) $false
% 26.39/7.59 |
% 26.39/7.59 |-The branch is then unsatisfiable
% 26.39/7.59 % SZS output end Proof for theBenchmark
% 26.39/7.59
% 26.39/7.59 6986ms
%------------------------------------------------------------------------------