TSTP Solution File: NUM843+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM843+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 08:49:04 EDT 2022
% Result : Theorem 19.91s 6.16s
% Output : Proof 21.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM843+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 10:17:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.47/0.58 ____ _
% 0.47/0.58 ___ / __ \_____(_)___ ________ __________
% 0.47/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.58
% 0.47/0.58 A Theorem Prover for First-Order Logic
% 0.47/0.58 (ePrincess v.1.0)
% 0.47/0.58
% 0.47/0.58 (c) Philipp Rümmer, 2009-2015
% 0.47/0.58 (c) Peter Backeman, 2014-2015
% 0.47/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.58 Bug reports to peter@backeman.se
% 0.47/0.58
% 0.47/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.58
% 0.47/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/0.94 Prover 0: Preprocessing ...
% 2.80/1.23 Prover 0: Warning: ignoring some quantifiers
% 2.80/1.26 Prover 0: Constructing countermodel ...
% 18.78/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.04/5.99 Prover 1: Preprocessing ...
% 19.42/6.10 Prover 1: Warning: ignoring some quantifiers
% 19.42/6.11 Prover 1: Constructing countermodel ...
% 19.91/6.16 Prover 1: proved (233ms)
% 19.91/6.16 Prover 0: stopped
% 19.91/6.16
% 19.91/6.16 No countermodel exists, formula is valid
% 19.91/6.16 % SZS status Theorem for theBenchmark
% 19.91/6.16
% 19.91/6.16 Generating proof ... Warning: ignoring some quantifiers
% 21.28/6.44 found it (size 35)
% 21.28/6.44
% 21.28/6.44 % SZS output start Proof for theBenchmark
% 21.28/6.44 Assumed formulas after preprocessing and simplification:
% 21.28/6.44 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v0 = 0) & leq(vd390, vd391) = v0 & less(vd390, v1) = 0 & vplus(vd391, v1) = v1 & greater(vd390, vd391) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (vplus(v4, v6) = v8) | ~ (vplus(v3, v5) = v7) | ~ (geq(v7, v8) = v9) | ? [v10] : ? [v11] : (geq(v5, v6) = v10 & geq(v3, v4) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (vplus(v4, v6) = v8) | ~ (vplus(v3, v5) = v7) | ~ (greater(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (geq(v5, v6) = v12 & geq(v3, v4) = v11 & greater(v5, v6) = v10 & greater(v3, v4) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)) & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (vplus(v4, v6) = v8) | ~ (vplus(v3, v5) = v7) | ~ (greater(v7, v8) = v9) | ? [v10] : ? [v11] : (greater(v5, v6) = v10 & greater(v3, v4) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (less(v6, v7) = v8) | ~ (vplus(v4, v5) = v7) | ~ (vplus(v3, v5) = v6) | ? [v9] : ( ~ (v9 = 0) & less(v3, v4) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (vplus(v4, v5) = v7) | ~ (vplus(v3, v5) = v6) | ~ (greater(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & greater(v3, v4) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (leq(v4, v5) = v7) | ~ (leq(v3, v4) = v6) | ? [v8] : ? [v9] : ? [v10] : (less(v4, v5) = v8 & less(v3, v5) = v10 & less(v3, v4) = v9 & (v10 = 0 | (( ~ (v9 = 0) | ~ (v7 = 0)) & ( ~ (v8 = 0) | ~ (v6 = 0)))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (less(v6, v7) = 0) | ~ (vplus(v4, v5) = v7) | ~ (vplus(v3, v5) = v6) | less(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vplus(v6, v5) = v7) | ~ (vplus(v3, v4) = v6) | ? [v8] : (vplus(v4, v5) = v8 & vplus(v3, v8) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vplus(v4, v5) = v7) | ~ (vplus(v3, v5) = v6) | ~ (greater(v6, v7) = 0) | greater(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (vplus(v3, v4) = v6) | ~ (vplus(v3, v4) = v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (leq(v3, v5) = v6) | ~ (leq(v3, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & leq(v4, v5) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (less(v3, v5) = v6) | ~ (less(v3, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & less(v4, v5) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v4, v1) = v5) | ~ (geq(v3, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & greater(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v3, v4) = v5) | ~ (greater(v5, v3) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (less(v4, v3) = v5) | ~ (vplus(v4, v6) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (vplus(v3, v6) = v4) | ~ (greater(v4, v3) = v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (leq(v6, v5) = v4) | ~ (leq(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (less(v6, v5) = v4) | ~ (less(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (vplus(v6, v5) = v4) | ~ (vplus(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (vplus(v4, v5) = v6) | ~ (vplus(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (geq(v6, v5) = v4) | ~ (geq(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (greater(v6, v5) = v4) | ~ (greater(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vsucc(v4) = v5) | ~ (vplus(v3, v5) = v6) | ? [v7] : (vsucc(v7) = v6 & vplus(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vsucc(v3) = v5) | ~ (vplus(v5, v4) = v6) | ? [v7] : (vsucc(v7) = v6 & vplus(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vplus(v4, v6) = v3) | ~ (vplus(v3, v5) = v4)) & ? [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (vplus(v5, v4) = v6) | ? [v7] : ( ~ (v7 = v6) & vplus(v5, v3) = v7)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = v3 | ~ (less(v3, v4) = v5) | greater(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & less(v4, v3) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & geq(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (less(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & greater(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (geq(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & greater(v4, v3) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (vskolem2(v5) = v4) | ~ (vskolem2(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (vsucc(v5) = v4) | ~ (vsucc(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (vsucc(v4) = v5) | ~ (vsucc(v3) = v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (vplus(v3, v4) = v5) | vplus(v4, v3) = v5) & ! [v3] : ! [v4] : (v4 = v3 | ~ (leq(v4, v3) = 0) | less(v4, v3) = 0) & ! [v3] : ! [v4] : (v4 = v3 | ~ (geq(v4, v3) = 0) | greater(v4, v3) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (leq(v3, v3) = v4)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (geq(v3, v3) = v4)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (geq(v3, v1) = v4)) & ! [v3] : ! [v4] : (v3 = v1 | ~ (vskolem2(v3) = v4) | vsucc(v4) = v3) & ! [v3] : ! [v4] : ( ~ (leq(v3, v4) = 0) | geq(v4, v3) = 0) & ! [v3] : ! [v4] : ( ~ (less(v4, v3) = 0) | ? [v5] : vplus(v4, v5) = v3) & ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | greater(v4, v3) = 0) & ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & greater(v3, v4) = v5)) & ! [v3] : ! [v4] : ~ (vplus(v3, v4) = v4) & ! [v3] : ! [v4] : ~ (vplus(v3, v4) = v3) & ! [v3] : ! [v4] : ( ~ (vplus(v3, v1) = v4) | vsucc(v3) = v4) & ! [v3] : ! [v4] : ( ~ (vplus(v1, v3) = v4) | vsucc(v3) = v4) & ! [v3] : ! [v4] : ( ~ (greater(v4, v3) = 0) | ? [v5] : vplus(v3, v5) = v4) & ! [v3] : ~ (vsucc(v3) = v3) & ! [v3] : ~ (vsucc(v3) = v1) & ! [v3] : ~ (less(v3, v3) = 0) & ! [v3] : ~ (greater(v3, v3) = 0) & ? [v3] : ? [v4] : (v4 = v3 | ? [v5] : ? [v6] : ((v6 = v4 & vplus(v3, v5) = v4) | (v6 = v3 & vplus(v4, v5) = v3))))
% 21.28/6.49 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 21.28/6.49 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_2_2 = 0) & leq(vd390, vd391) = all_0_2_2 & less(vd390, all_0_1_1) = 0 & vplus(vd391, v1) = all_0_1_1 & greater(vd390, vd391) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (geq(v4, v5) = v6) | ? [v7] : ? [v8] : (geq(v2, v3) = v7 & geq(v0, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (greater(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (geq(v2, v3) = v9 & geq(v0, v1) = v8 & greater(v2, v3) = v7 & greater(v0, v1) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0)) & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (greater(v4, v5) = v6) | ? [v7] : ? [v8] : (greater(v2, v3) = v7 & greater(v0, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (less(v3, v4) = v5) | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & less(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (greater(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & greater(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (leq(v1, v2) = v4) | ~ (leq(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (less(v1, v2) = v5 & less(v0, v2) = v7 & less(v0, v1) = v6 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v4 = 0)) & ( ~ (v5 = 0) | ~ (v3 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | less(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (greater(v3, v4) = 0) | greater(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vplus(v0, v1) = v3) | ~ (vplus(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less(v0, v2) = v3) | ~ (less(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v1, v1) = v2) | ~ (geq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & greater(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v0, v1) = v2) | ~ (greater(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (less(v1, v0) = v2) | ~ (vplus(v1, v3) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v0, v3) = v1) | ~ (greater(v1, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v1, v2) = v3) | ~ (vplus(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vplus(v0, v2) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v0) = v2) | ~ (vplus(v2, v1) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v1, v3) = v0) | ~ (vplus(v0, v2) = v1)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v2, v1) = v3) | ? [v4] : ( ~ (v4 = v3) & vplus(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | greater(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & geq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~ (vsucc(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v1, v0) = 0) | less(v1, v0) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v1) = v1)) & ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | geq(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (less(v1, v0) = 0) | ? [v2] : vplus(v1, v2) = v0) & ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | greater(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & greater(v0, v1) = v2)) & ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v1) & ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1) & ! [v0] : ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1) & ! [v0] : ! [v1] : ( ~ (greater(v1, v0) = 0) | ? [v2] : vplus(v0, v2) = v1) & ! [v0] : ~ (vsucc(v0) = v0) & ! [v0] : ~ (vsucc(v0) = v1) & ! [v0] : ~ (less(v0, v0) = 0) & ! [v0] : ~ (greater(v0, v0) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0)))
% 21.28/6.50 |
% 21.28/6.50 | Applying alpha-rule on (1) yields:
% 21.28/6.50 | (2) ! [v0] : ! [v1] : ( ~ (greater(v1, v0) = 0) | ? [v2] : vplus(v0, v2) = v1)
% 21.28/6.50 | (3) leq(vd390, vd391) = all_0_2_2
% 21.28/6.50 | (4) ! [v0] : ~ (less(v0, v0) = 0)
% 21.28/6.50 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vplus(v0, v1) = v3) | ~ (vplus(v0, v1) = v2))
% 21.28/6.50 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v1, v1) = v2) | ~ (geq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & greater(v0, v1) = v4))
% 21.28/6.50 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | less(v0, v1) = 0)
% 21.28/6.51 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0)
% 21.28/6.51 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v1, v0) = 0) | less(v1, v0) = 0)
% 21.28/6.51 | (10) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & greater(v0, v1) = v2))
% 21.28/6.51 | (11) ~ (all_0_0_0 = 0)
% 21.28/6.51 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vplus(v0, v2) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4))
% 21.28/6.51 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | greater(v0, v1) = 0)
% 21.28/6.51 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v1, v3) = v0) | ~ (vplus(v0, v2) = v1))
% 21.28/6.51 | (15) greater(vd390, vd391) = all_0_0_0
% 21.28/6.51 | (16) ! [v0] : ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1)
% 21.28/6.51 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 21.28/6.51 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3))
% 21.28/6.51 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (leq(v1, v2) = v4) | ~ (leq(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (less(v1, v2) = v5 & less(v0, v2) = v7 & less(v0, v1) = v6 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v4 = 0)) & ( ~ (v5 = 0) | ~ (v3 = 0))))))
% 21.28/6.51 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (greater(v4, v5) = v6) | ? [v7] : ? [v8] : (greater(v2, v3) = v7 & greater(v0, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 21.28/6.51 | (21) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v2, v1) = v3) | ? [v4] : ( ~ (v4 = v3) & vplus(v2, v0) = v4))
% 21.28/6.51 | (22) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v0)
% 21.28/6.51 | (23) ! [v0] : ! [v1] : ( ~ (less(v1, v0) = 0) | ? [v2] : vplus(v1, v2) = v0)
% 21.28/6.51 | (24) ! [v0] : ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1)
% 21.28/6.51 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3))
% 21.28/6.51 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4))
% 21.28/6.51 | (27) ! [v0] : ~ (vsucc(v0) = v0)
% 21.28/6.51 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (less(v1, v0) = v2) | ~ (vplus(v1, v3) = v0))
% 21.28/6.51 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~ (vsucc(v0) = v2))
% 21.28/6.51 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & geq(v0, v1) = v3))
% 21.28/6.51 | (31) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | greater(v1, v0) = 0)
% 21.28/6.51 | (32) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | geq(v1, v0) = 0)
% 21.28/6.51 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 21.28/6.51 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3))
% 21.28/6.51 | (35) ! [v0] : ~ (vsucc(v0) = v1)
% 21.28/6.51 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less(v0, v2) = v3) | ~ (less(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less(v1, v2) = v4))
% 21.28/6.51 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v0, v1) = v2) | ~ (greater(v2, v0) = v3))
% 21.28/6.51 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (greater(v3, v4) = 0) | greater(v0, v1) = 0)
% 21.28/6.51 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0))
% 21.28/6.51 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (greater(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (geq(v2, v3) = v9 & geq(v0, v1) = v8 & greater(v2, v3) = v7 & greater(v0, v1) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0)) & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 21.28/6.52 | (41) ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0)
% 21.28/6.52 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (geq(v4, v5) = v6) | ? [v7] : ? [v8] : (geq(v2, v3) = v7 & geq(v0, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 21.28/6.52 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v1, v2) = v3) | ~ (vplus(v0, v2) = v3))
% 21.28/6.52 | (44) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1))
% 21.28/6.52 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0))
% 21.28/6.52 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (less(v3, v4) = v5) | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & less(v0, v1) = v6))
% 21.28/6.52 | (47) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v1)
% 21.28/6.52 | (48) vplus(vd391, v1) = all_0_1_1
% 21.28/6.52 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v0, v3) = v1) | ~ (greater(v1, v0) = v2))
% 21.28/6.52 | (50) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1))
% 21.28/6.52 | (51) ! [v0] : ~ (greater(v0, v0) = 0)
% 21.28/6.52 | (52) less(vd390, all_0_1_1) = 0
% 21.28/6.52 | (53) ~ (all_0_2_2 = 0)
% 21.28/6.52 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 21.28/6.52 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0))
% 21.28/6.52 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 21.28/6.52 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v0) = v2) | ~ (vplus(v2, v1) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4))
% 21.28/6.52 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4))
% 21.28/6.52 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2)
% 21.28/6.52 | (60) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v1) = v1))
% 21.28/6.52 | (61) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0)))
% 21.28/6.52 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (greater(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & greater(v0, v1) = v6))
% 21.28/6.52 |
% 21.28/6.52 | Instantiating formula (44) with all_0_2_2, vd390 yields:
% 21.28/6.52 | (63) all_0_2_2 = 0 | ~ (leq(vd390, vd390) = all_0_2_2)
% 21.28/6.52 |
% 21.28/6.52 +-Applying beta-rule and splitting (63), into two cases.
% 21.28/6.52 |-Branch one:
% 21.28/6.52 | (64) ~ (leq(vd390, vd390) = all_0_2_2)
% 21.28/6.52 |
% 21.28/6.52 | Using (3) and (64) yields:
% 21.28/6.52 | (65) ~ (vd391 = vd390)
% 21.28/6.52 |
% 21.28/6.52 | Instantiating formula (18) with all_0_2_2, vd390, vd391 and discharging atoms leq(vd390, vd391) = all_0_2_2, yields:
% 21.28/6.52 | (66) all_0_2_2 = 0 | ? [v0] : ( ~ (v0 = 0) & less(vd390, vd391) = v0)
% 21.28/6.53 |
% 21.28/6.53 | Instantiating formula (30) with all_0_2_2, vd390, vd391 and discharging atoms leq(vd390, vd391) = all_0_2_2, yields:
% 21.28/6.53 | (67) all_0_2_2 = 0 | ? [v0] : ( ~ (v0 = 0) & geq(vd391, vd390) = v0)
% 21.28/6.53 |
% 21.28/6.53 +-Applying beta-rule and splitting (67), into two cases.
% 21.28/6.53 |-Branch one:
% 21.28/6.53 | (68) all_0_2_2 = 0
% 21.28/6.53 |
% 21.28/6.53 | Equations (68) can reduce 53 to:
% 21.28/6.53 | (69) $false
% 21.28/6.53 |
% 21.28/6.53 |-The branch is then unsatisfiable
% 21.28/6.53 |-Branch two:
% 21.28/6.53 | (53) ~ (all_0_2_2 = 0)
% 21.28/6.53 | (71) ? [v0] : ( ~ (v0 = 0) & geq(vd391, vd390) = v0)
% 21.28/6.53 |
% 21.28/6.53 +-Applying beta-rule and splitting (66), into two cases.
% 21.28/6.53 |-Branch one:
% 21.28/6.53 | (68) all_0_2_2 = 0
% 21.28/6.53 |
% 21.28/6.53 | Equations (68) can reduce 53 to:
% 21.28/6.53 | (69) $false
% 21.28/6.53 |
% 21.28/6.53 |-The branch is then unsatisfiable
% 21.28/6.53 |-Branch two:
% 21.28/6.53 | (53) ~ (all_0_2_2 = 0)
% 21.28/6.53 | (75) ? [v0] : ( ~ (v0 = 0) & less(vd390, vd391) = v0)
% 21.28/6.53 |
% 21.28/6.53 | Instantiating (75) with all_41_0_9 yields:
% 21.28/6.53 | (76) ~ (all_41_0_9 = 0) & less(vd390, vd391) = all_41_0_9
% 21.28/6.53 |
% 21.28/6.53 | Applying alpha-rule on (76) yields:
% 21.28/6.53 | (77) ~ (all_41_0_9 = 0)
% 21.28/6.53 | (78) less(vd390, vd391) = all_41_0_9
% 21.28/6.53 |
% 21.28/6.53 | Instantiating formula (36) with all_41_0_9, vd391, all_0_1_1, vd390 and discharging atoms less(vd390, all_0_1_1) = 0, less(vd390, vd391) = all_41_0_9, yields:
% 21.28/6.53 | (79) all_41_0_9 = 0 | ? [v0] : ( ~ (v0 = 0) & less(all_0_1_1, vd391) = v0)
% 21.28/6.53 |
% 21.28/6.53 | Instantiating formula (13) with all_41_0_9, vd391, vd390 and discharging atoms less(vd390, vd391) = all_41_0_9, yields:
% 21.28/6.53 | (80) all_41_0_9 = 0 | vd391 = vd390 | greater(vd390, vd391) = 0
% 21.28/6.53 |
% 21.28/6.53 | Instantiating formula (34) with all_41_0_9, vd390, vd391 and discharging atoms less(vd390, vd391) = all_41_0_9, yields:
% 21.28/6.53 | (81) all_41_0_9 = 0 | ? [v0] : ( ~ (v0 = 0) & greater(vd391, vd390) = v0)
% 21.28/6.53 |
% 21.28/6.53 +-Applying beta-rule and splitting (80), into two cases.
% 21.28/6.53 |-Branch one:
% 21.28/6.53 | (82) greater(vd390, vd391) = 0
% 21.28/6.53 |
% 21.28/6.53 | Instantiating formula (45) with vd390, vd391, 0, all_0_0_0 and discharging atoms greater(vd390, vd391) = all_0_0_0, greater(vd390, vd391) = 0, yields:
% 21.28/6.53 | (83) all_0_0_0 = 0
% 21.28/6.53 |
% 21.28/6.53 | Equations (83) can reduce 11 to:
% 21.28/6.53 | (69) $false
% 21.28/6.53 |
% 21.28/6.53 |-The branch is then unsatisfiable
% 21.28/6.53 |-Branch two:
% 21.28/6.53 | (85) ~ (greater(vd390, vd391) = 0)
% 21.28/6.53 | (86) all_41_0_9 = 0 | vd391 = vd390
% 21.28/6.53 |
% 21.28/6.53 +-Applying beta-rule and splitting (79), into two cases.
% 21.28/6.53 |-Branch one:
% 21.28/6.53 | (87) all_41_0_9 = 0
% 21.28/6.53 |
% 21.28/6.53 | Equations (87) can reduce 77 to:
% 21.28/6.53 | (69) $false
% 21.28/6.53 |
% 21.28/6.53 |-The branch is then unsatisfiable
% 21.28/6.53 |-Branch two:
% 21.28/6.53 | (77) ~ (all_41_0_9 = 0)
% 21.28/6.53 | (90) ? [v0] : ( ~ (v0 = 0) & less(all_0_1_1, vd391) = v0)
% 21.28/6.53 |
% 21.28/6.53 +-Applying beta-rule and splitting (81), into two cases.
% 21.28/6.53 |-Branch one:
% 21.28/6.53 | (87) all_41_0_9 = 0
% 21.28/6.53 |
% 21.28/6.53 | Equations (87) can reduce 77 to:
% 21.28/6.53 | (69) $false
% 21.28/6.53 |
% 21.28/6.53 |-The branch is then unsatisfiable
% 21.28/6.53 |-Branch two:
% 21.28/6.53 | (77) ~ (all_41_0_9 = 0)
% 21.28/6.53 | (94) ? [v0] : ( ~ (v0 = 0) & greater(vd391, vd390) = v0)
% 21.28/6.53 |
% 21.28/6.53 +-Applying beta-rule and splitting (86), into two cases.
% 21.28/6.53 |-Branch one:
% 21.28/6.53 | (87) all_41_0_9 = 0
% 21.28/6.53 |
% 21.28/6.53 | Equations (87) can reduce 77 to:
% 21.28/6.53 | (69) $false
% 21.28/6.53 |
% 21.28/6.53 |-The branch is then unsatisfiable
% 21.28/6.53 |-Branch two:
% 21.28/6.53 | (77) ~ (all_41_0_9 = 0)
% 21.28/6.53 | (98) vd391 = vd390
% 21.28/6.53 |
% 21.28/6.53 | Equations (98) can reduce 65 to:
% 21.28/6.53 | (69) $false
% 21.28/6.53 |
% 21.28/6.53 |-The branch is then unsatisfiable
% 21.28/6.53 |-Branch two:
% 21.28/6.53 | (100) leq(vd390, vd390) = all_0_2_2
% 21.28/6.53 | (68) all_0_2_2 = 0
% 21.28/6.53 |
% 21.28/6.53 | Equations (68) can reduce 53 to:
% 21.28/6.53 | (69) $false
% 21.28/6.53 |
% 21.28/6.53 |-The branch is then unsatisfiable
% 21.28/6.53 % SZS output end Proof for theBenchmark
% 21.28/6.53
% 21.28/6.53 5937ms
%------------------------------------------------------------------------------