TSTP Solution File: KLE138+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 01:51:31 EDT 2022
% Result : Theorem 2.90s 1.38s
% Output : Proof 4.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 12:45:36 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.58/0.60 ____ _
% 0.58/0.60 ___ / __ \_____(_)___ ________ __________
% 0.58/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.60
% 0.58/0.60 A Theorem Prover for First-Order Logic
% 0.58/0.61 (ePrincess v.1.0)
% 0.58/0.61
% 0.58/0.61 (c) Philipp Rümmer, 2009-2015
% 0.58/0.61 (c) Peter Backeman, 2014-2015
% 0.58/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.61 Bug reports to peter@backeman.se
% 0.58/0.61
% 0.58/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.61
% 0.58/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.95 Prover 0: Preprocessing ...
% 2.24/1.20 Prover 0: Constructing countermodel ...
% 2.90/1.38 Prover 0: proved (725ms)
% 2.90/1.38
% 2.90/1.38 No countermodel exists, formula is valid
% 2.90/1.38 % SZS status Theorem for theBenchmark
% 2.90/1.38
% 2.90/1.38 Generating proof ... found it (size 11)
% 4.26/1.68
% 4.26/1.68 % SZS output start Proof for theBenchmark
% 4.26/1.68 Assumed formulas after preprocessing and simplification:
% 4.26/1.68 | (0) ? [v0] : ( ~ (v0 = one) & strong_iteration(zero) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v2, v3) = v5) | ~ (multiplication(v1, v3) = v4) | ~ (addition(v4, v5) = v6) | ? [v7] : (multiplication(v7, v3) = v6 & addition(v1, v2) = v7)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v1, v3) = v5) | ~ (multiplication(v1, v2) = v4) | ~ (addition(v4, v5) = v6) | ? [v7] : (multiplication(v1, v7) = v6 & addition(v2, v3) = v7)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v2 | ~ (strong_iteration(v1) = v2) | ~ (star(v1) = v3) | ~ (multiplication(v2, zero) = v4) | ~ (addition(v3, v4) = v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v4, v3) = v5) | ~ (multiplication(v1, v2) = v4) | ? [v6] : (multiplication(v2, v3) = v6 & multiplication(v1, v6) = v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v4, v3) = v5) | ~ (addition(v1, v2) = v4) | ? [v6] : ? [v7] : (multiplication(v2, v3) = v7 & multiplication(v1, v3) = v6 & addition(v6, v7) = v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v3, v1) = v4) | ~ (addition(v4, v2) = v5) | ~ leq(v5, v3) | ? [v6] : ? [v7] : (star(v1) = v6 & multiplication(v2, v6) = v7 & leq(v7, v3))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v2, v3) = v4) | ~ (multiplication(v1, v4) = v5) | ? [v6] : (multiplication(v6, v3) = v5 & multiplication(v1, v2) = v6)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v4) = v5) | ~ (addition(v2, v3) = v4) | ? [v6] : ? [v7] : (multiplication(v1, v3) = v7 & multiplication(v1, v2) = v6 & addition(v6, v7) = v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v3) = v4) | ~ (addition(v4, v2) = v5) | ~ leq(v5, v3) | ? [v6] : ? [v7] : (star(v1) = v6 & multiplication(v6, v2) = v7 & leq(v7, v3))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v3) = v4) | ~ (addition(v4, v2) = v5) | ~ leq(v3, v5) | ? [v6] : ? [v7] : (strong_iteration(v1) = v6 & multiplication(v6, v2) = v7 & leq(v3, v7))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (addition(v4, v1) = v5) | ~ (addition(v3, v2) = v4) | ? [v6] : (addition(v3, v6) = v5 & addition(v2, v1) = v6)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (addition(v3, v4) = v5) | ~ (addition(v2, v1) = v4) | ? [v6] : (addition(v6, v1) = v5 & addition(v3, v2) = v6)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (multiplication(v4, v3) = v2) | ~ (multiplication(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (addition(v4, v3) = v2) | ~ (addition(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (addition(v1, v2) = v3) | ~ leq(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (strong_iteration(v3) = v2) | ~ (strong_iteration(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (star(v3) = v2) | ~ (star(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (strong_iteration(v1) = v2) | ~ (multiplication(v1, v2) = v3) | addition(v3, one) = v2) & ! [v1] : ! [v2] : ! [v3] : ( ~ (star(v1) = v2) | ~ (multiplication(v2, v1) = v3) | addition(one, v3) = v2) & ! [v1] : ! [v2] : ! [v3] : ( ~ (star(v1) = v2) | ~ (multiplication(v1, v2) = v3) | addition(one, v3) = v2) & ! [v1] : ! [v2] : ! [v3] : ( ~ (addition(v2, v1) = v3) | addition(v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (addition(v1, v2) = v3) | addition(v2, v1) = v3) & ! [v1] : ! [v2] : (v2 = v1 | ~ (multiplication(v1, one) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (multiplication(one, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v1, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v1, zero) = v2)) & ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(zero, v1) = v2)) & ! [v1] : ! [v2] : ( ~ (strong_iteration(v1) = v2) | ? [v3] : ? [v4] : (star(v1) = v3 & multiplication(v2, zero) = v4 & addition(v3, v4) = v2)) & ! [v1] : ! [v2] : ( ~ (strong_iteration(v1) = v2) | ? [v3] : (multiplication(v1, v2) = v3 & addition(v3, one) = v2)) & ! [v1] : ! [v2] : ( ~ (star(v1) = v2) | ? [v3] : (multiplication(v2, v1) = v3 & addition(one, v3) = v2)) & ! [v1] : ! [v2] : ( ~ (star(v1) = v2) | ? [v3] : (multiplication(v1, v2) = v3 & addition(one, v3) = v2)) & ! [v1] : ! [v2] : ( ~ (addition(v1, v2) = v2) | leq(v1, v2)))
% 4.26/1.73 | Instantiating (0) with all_0_0_0 yields:
% 4.26/1.73 | (1) ~ (all_0_0_0 = one) & strong_iteration(zero) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | ~ (strong_iteration(v0) = v1) | ~ (star(v0) = v2) | ~ (multiplication(v1, zero) = v3) | ~ (addition(v2, v3) = v4)) & ! [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(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v4, v2) | ? [v5] : ? [v6] : (star(v0) = v5 & multiplication(v1, v5) = v6 & leq(v6, v2))) & ! [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, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v4, v2) | ? [v5] : ? [v6] : (star(v0) = v5 & multiplication(v5, v1) = v6 & leq(v6, v2))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v2, v4) | ? [v5] : ? [v6] : (strong_iteration(v0) = v5 & multiplication(v5, v1) = v6 & leq(v2, v6))) & ! [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 | ~ (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) | ~ leq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (strong_iteration(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1) & ! [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(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 4.26/1.74 |
% 4.26/1.74 | Applying alpha-rule on (1) yields:
% 4.26/1.74 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 4.26/1.74 | (3) ! [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))
% 4.26/1.74 | (4) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 4.26/1.74 | (5) ! [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))
% 4.26/1.74 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1)
% 4.26/1.74 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 4.26/1.74 | (8) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1))
% 4.26/1.75 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 4.26/1.75 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1))
% 4.26/1.75 | (11) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 4.26/1.75 | (12) strong_iteration(zero) = all_0_0_0
% 4.26/1.75 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 4.26/1.75 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0))
% 4.26/1.75 | (15) ! [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))
% 4.26/1.75 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (strong_iteration(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1)
% 4.26/1.75 | (17) ~ (all_0_0_0 = one)
% 4.26/1.75 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0))
% 4.26/1.75 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v4, v2) | ? [v5] : ? [v6] : (star(v0) = v5 & multiplication(v5, v1) = v6 & leq(v6, v2)))
% 4.26/1.75 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 4.26/1.75 | (21) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1))
% 4.26/1.75 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 4.26/1.75 | (23) ! [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))
% 4.26/1.75 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | ~ (strong_iteration(v0) = v1) | ~ (star(v0) = v2) | ~ (multiplication(v1, zero) = v3) | ~ (addition(v2, v3) = v4))
% 4.26/1.75 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 4.26/1.75 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v2, v4) | ? [v5] : ? [v6] : (strong_iteration(v0) = v5 & multiplication(v5, v1) = v6 & leq(v2, v6)))
% 4.26/1.75 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1)
% 4.26/1.75 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 4.26/1.75 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 4.26/1.75 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 4.26/1.76 | (31) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1))
% 4.26/1.76 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 4.26/1.76 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v4, v2) | ? [v5] : ? [v6] : (star(v0) = v5 & multiplication(v1, v5) = v6 & leq(v6, v2)))
% 4.26/1.76 | (34) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 4.26/1.76 | (35) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1))
% 4.26/1.76 |
% 4.26/1.76 | Instantiating formula (35) with all_0_0_0, zero and discharging atoms strong_iteration(zero) = all_0_0_0, yields:
% 4.26/1.76 | (36) ? [v0] : (multiplication(zero, all_0_0_0) = v0 & addition(v0, one) = all_0_0_0)
% 4.26/1.76 |
% 4.26/1.76 | Instantiating (36) with all_8_0_1 yields:
% 4.26/1.76 | (37) multiplication(zero, all_0_0_0) = all_8_0_1 & addition(all_8_0_1, one) = all_0_0_0
% 4.26/1.76 |
% 4.26/1.76 | Applying alpha-rule on (37) yields:
% 4.26/1.76 | (38) multiplication(zero, all_0_0_0) = all_8_0_1
% 4.26/1.76 | (39) addition(all_8_0_1, one) = all_0_0_0
% 4.26/1.76 |
% 4.26/1.76 | Instantiating formula (11) with all_8_0_1, all_0_0_0 and discharging atoms multiplication(zero, all_0_0_0) = all_8_0_1, yields:
% 4.26/1.76 | (40) all_8_0_1 = zero
% 4.26/1.76 |
% 4.26/1.76 | From (40) and (39) follows:
% 4.26/1.76 | (41) addition(zero, one) = all_0_0_0
% 4.26/1.76 |
% 4.26/1.76 | Instantiating formula (30) with all_0_0_0, zero, one and discharging atoms addition(zero, one) = all_0_0_0, yields:
% 4.26/1.76 | (42) addition(one, zero) = all_0_0_0
% 4.26/1.76 |
% 4.26/1.76 | Instantiating formula (13) with all_0_0_0, one and discharging atoms addition(one, zero) = all_0_0_0, yields:
% 4.26/1.76 | (43) all_0_0_0 = one
% 4.26/1.76 |
% 4.26/1.76 | Equations (43) can reduce 17 to:
% 4.26/1.76 | (44) $false
% 4.26/1.76 |
% 4.26/1.76 |-The branch is then unsatisfiable
% 4.26/1.76 % SZS output end Proof for theBenchmark
% 4.26/1.76
% 4.26/1.76 1147ms
%------------------------------------------------------------------------------