TSTP Solution File: NUM842+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM842+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 19.93s 6.43s
% Output : Proof 22.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM842+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n015.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 : Tue Jul 5 03:54:17 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.61/0.67 ____ _
% 0.61/0.67 ___ / __ \_____(_)___ ________ __________
% 0.61/0.67 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.67 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.67 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.67
% 0.61/0.67 A Theorem Prover for First-Order Logic
% 0.61/0.67 (ePrincess v.1.0)
% 0.61/0.67
% 0.61/0.67 (c) Philipp Rümmer, 2009-2015
% 0.61/0.67 (c) Peter Backeman, 2014-2015
% 0.61/0.67 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.67 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.67 Bug reports to peter@backeman.se
% 0.61/0.67
% 0.61/0.67 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.67
% 0.61/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.77/0.72 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.82/1.04 Prover 0: Preprocessing ...
% 2.73/1.33 Prover 0: Warning: ignoring some quantifiers
% 2.99/1.35 Prover 0: Constructing countermodel ...
% 18.11/6.01 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.22/6.07 Prover 1: Preprocessing ...
% 18.97/6.20 Prover 1: Warning: ignoring some quantifiers
% 18.97/6.20 Prover 1: Constructing countermodel ...
% 19.93/6.43 Prover 1: proved (417ms)
% 19.93/6.43 Prover 0: stopped
% 19.93/6.43
% 19.93/6.43 No countermodel exists, formula is valid
% 19.93/6.43 % SZS status Theorem for theBenchmark
% 19.93/6.43
% 19.93/6.43 Generating proof ... Warning: ignoring some quantifiers
% 22.13/6.95 found it (size 124)
% 22.13/6.95
% 22.13/6.95 % SZS output start Proof for theBenchmark
% 22.13/6.95 Assumed formulas after preprocessing and simplification:
% 22.13/6.95 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & geq(vd355, vd356) = v2 & geq(vd353, vd354) = v1 & vplus(vd354, vd356) = v5 & vplus(vd353, vd355) = v4 & greater(v4, v5) = v6 & greater(vd355, vd356) = v0 & greater(vd353, vd354) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (vplus(v8, v10) = v12) | ~ (vplus(v7, v9) = v11) | ~ (greater(v11, v12) = v13) | ? [v14] : ? [v15] : (greater(v9, v10) = v14 & greater(v7, v8) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (less(v10, v11) = v12) | ~ (vplus(v8, v9) = v11) | ~ (vplus(v7, v9) = v10) | ? [v13] : ( ~ (v13 = 0) & less(v7, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (vplus(v8, v9) = v11) | ~ (vplus(v7, v9) = v10) | ~ (greater(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & greater(v7, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (leq(v8, v9) = v11) | ~ (leq(v7, v8) = v10) | ? [v12] : ? [v13] : ? [v14] : (less(v8, v9) = v12 & less(v7, v9) = v14 & less(v7, v8) = v13 & (v14 = 0 | (( ~ (v13 = 0) | ~ (v11 = 0)) & ( ~ (v12 = 0) | ~ (v10 = 0)))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (less(v10, v11) = 0) | ~ (vplus(v8, v9) = v11) | ~ (vplus(v7, v9) = v10) | less(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (vplus(v10, v9) = v11) | ~ (vplus(v7, v8) = v10) | ? [v12] : (vplus(v8, v9) = v12 & vplus(v7, v12) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (vplus(v8, v9) = v11) | ~ (vplus(v7, v9) = v10) | ~ (greater(v10, v11) = 0) | greater(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (vplus(v7, v8) = v10) | ~ (vplus(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (leq(v7, v9) = v10) | ~ (leq(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & leq(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (less(v7, v9) = v10) | ~ (less(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & less(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (vplus(v7, v8) = v9) | ~ (greater(v9, v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (less(v8, v7) = v9) | ~ (vplus(v8, v10) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (vplus(v7, v10) = v8) | ~ (greater(v8, v7) = v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (geq(v10, v9) = v8) | ~ (geq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (leq(v10, v9) = v8) | ~ (leq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (less(v10, v9) = v8) | ~ (less(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (vplus(v10, v9) = v8) | ~ (vplus(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (vplus(v8, v9) = v10) | ~ (vplus(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (greater(v10, v9) = v8) | ~ (greater(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (vsucc(v8) = v9) | ~ (vplus(v7, v9) = v10) | ? [v11] : (vsucc(v11) = v10 & vplus(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (vsucc(v7) = v9) | ~ (vplus(v9, v8) = v10) | ? [v11] : (vsucc(v11) = v10 & vplus(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (vplus(v8, v10) = v7) | ~ (vplus(v7, v9) = v8)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (vplus(v9, v8) = v10) | ? [v11] : ( ~ (v11 = v10) & vplus(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (less(v7, v8) = v9) | greater(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (geq(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & leq(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (geq(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & greater(v8, v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (leq(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & less(v8, v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (less(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & greater(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (vskolem2(v9) = v8) | ~ (vskolem2(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (vsucc(v9) = v8) | ~ (vsucc(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (vsucc(v8) = v9) | ~ (vsucc(v7) = v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (vplus(v7, v8) = v9) | vplus(v8, v7) = v9) & ! [v7] : ! [v8] : (v8 = v7 | ~ (geq(v8, v7) = 0) | greater(v8, v7) = 0) & ! [v7] : ! [v8] : (v8 = v7 | ~ (leq(v8, v7) = 0) | less(v8, v7) = 0) & ! [v7] : ! [v8] : (v8 = 0 | ~ (geq(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (leq(v7, v7) = v8)) & ! [v7] : ! [v8] : (v7 = v1 | ~ (vskolem2(v7) = v8) | vsucc(v8) = v7) & ! [v7] : ! [v8] : ( ~ (geq(v7, v8) = 0) | leq(v8, v7) = 0) & ! [v7] : ! [v8] : ( ~ (less(v8, v7) = 0) | ? [v9] : vplus(v8, v9) = v7) & ! [v7] : ! [v8] : ( ~ (less(v7, v8) = 0) | greater(v8, v7) = 0) & ! [v7] : ! [v8] : ( ~ (less(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & greater(v7, v8) = v9)) & ! [v7] : ! [v8] : ~ (vplus(v7, v8) = v8) & ! [v7] : ! [v8] : ~ (vplus(v7, v8) = v7) & ! [v7] : ! [v8] : ( ~ (vplus(v7, v1) = v8) | vsucc(v7) = v8) & ! [v7] : ! [v8] : ( ~ (vplus(v1, v7) = v8) | vsucc(v7) = v8) & ! [v7] : ! [v8] : ( ~ (greater(v8, v7) = 0) | ? [v9] : vplus(v7, v9) = v8) & ! [v7] : ~ (vsucc(v7) = v7) & ! [v7] : ~ (vsucc(v7) = v1) & ! [v7] : ~ (less(v7, v7) = 0) & ! [v7] : ~ (greater(v7, v7) = 0) & ? [v7] : ? [v8] : (v8 = v7 | ? [v9] : ? [v10] : ((v10 = v8 & vplus(v7, v9) = v8) | (v10 = v7 & vplus(v8, v9) = v7))) & ((v3 = 0 & v2 = 0) | (v1 = 0 & v0 = 0)))
% 22.63/7.00 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 22.63/7.00 | (1) ~ (all_0_0_0 = 0) & geq(vd355, vd356) = all_0_4_4 & geq(vd353, vd354) = all_0_5_5 & vplus(vd354, vd356) = all_0_1_1 & vplus(vd353, vd355) = all_0_2_2 & greater(all_0_2_2, all_0_1_1) = all_0_0_0 & greater(vd355, vd356) = all_0_6_6 & greater(vd353, vd354) = all_0_3_3 & ! [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(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 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [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 | ~ (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 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = 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 | ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v1, v0) = 0) | less(v1, v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0) & ! [v0] : ! [v1] : ( ~ (geq(v0, v1) = 0) | leq(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))) & ((all_0_3_3 = 0 & all_0_4_4 = 0) | (all_0_5_5 = 0 & all_0_6_6 = 0))
% 22.75/7.02 |
% 22.75/7.02 | Applying alpha-rule on (1) yields:
% 22.75/7.02 | (2) ! [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))
% 22.75/7.02 | (3) (all_0_3_3 = 0 & all_0_4_4 = 0) | (all_0_5_5 = 0 & all_0_6_6 = 0)
% 22.75/7.02 | (4) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0)))
% 22.75/7.02 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | less(v0, v1) = 0)
% 22.75/7.02 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1))
% 22.75/7.02 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (greater(v3, v4) = 0) | greater(v0, v1) = 0)
% 22.75/7.02 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v1, v0) = 0) | less(v1, v0) = 0)
% 22.75/7.02 | (9) ! [v0] : ! [v1] : ( ~ (geq(v0, v1) = 0) | leq(v1, v0) = 0)
% 22.75/7.02 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 22.75/7.02 | (11) ! [v0] : ! [v1] : ( ~ (greater(v1, v0) = 0) | ? [v2] : vplus(v0, v2) = v1)
% 22.75/7.02 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v0) = v2) | ~ (vplus(v2, v1) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4))
% 22.75/7.02 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 22.75/7.02 | (14) geq(vd353, vd354) = all_0_5_5
% 22.75/7.02 | (15) vplus(vd353, vd355) = all_0_2_2
% 22.75/7.02 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0))
% 22.75/7.02 | (17) ! [v0] : ~ (vsucc(v0) = v0)
% 22.75/7.02 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (less(v1, v0) = v2) | ~ (vplus(v1, v3) = v0))
% 22.75/7.02 | (19) greater(vd353, vd354) = all_0_3_3
% 22.75/7.02 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vplus(v0, v1) = v3) | ~ (vplus(v0, v1) = v2))
% 22.75/7.03 | (21) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v2, v1) = v3) | ? [v4] : ( ~ (v4 = v3) & vplus(v2, v0) = v4))
% 22.75/7.03 | (22) ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0)
% 22.75/7.03 | (23) ! [v0] : ~ (less(v0, v0) = 0)
% 22.75/7.03 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~ (vsucc(v0) = v2))
% 22.75/7.03 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v1, v3) = v0) | ~ (vplus(v0, v2) = v1))
% 22.75/7.03 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v0, v1) = v2) | ~ (greater(v2, v0) = v3))
% 22.75/7.03 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0))
% 22.75/7.03 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 22.75/7.03 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vplus(v0, v2) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4))
% 22.75/7.03 | (30) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v1)
% 22.75/7.03 | (31) vplus(vd354, vd356) = all_0_1_1
% 22.75/7.03 | (32) ! [v0] : ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1)
% 22.75/7.03 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 22.75/7.03 | (34) ! [v0] : ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1)
% 22.75/7.03 | (35) geq(vd355, vd356) = all_0_4_4
% 22.75/7.03 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 22.75/7.03 | (37) ! [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))))))
% 22.75/7.03 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v1, v2) = v3) | ~ (vplus(v0, v2) = v3))
% 22.75/7.03 | (39) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & greater(v0, v1) = v2))
% 22.75/7.03 | (40) ! [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))
% 22.75/7.03 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | greater(v0, v1) = 0)
% 22.75/7.03 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4))
% 22.75/7.03 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3))
% 22.75/7.03 | (44) ~ (all_0_0_0 = 0)
% 22.75/7.03 | (45) ! [v0] : ~ (vsucc(v0) = v1)
% 22.75/7.03 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2)
% 22.75/7.03 | (47) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3))
% 22.75/7.03 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4))
% 22.75/7.03 | (49) greater(all_0_2_2, all_0_1_1) = all_0_0_0
% 22.75/7.03 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0))
% 22.75/7.03 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3))
% 22.75/7.04 | (52) greater(vd355, vd356) = all_0_6_6
% 22.75/7.04 | (53) ! [v0] : ! [v1] : ( ~ (less(v1, v0) = 0) | ? [v2] : vplus(v1, v2) = v0)
% 22.75/7.04 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v0, v3) = v1) | ~ (greater(v1, v0) = v2))
% 22.75/7.04 | (55) ! [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))))
% 22.75/7.04 | (56) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1))
% 22.75/7.04 | (57) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v0)
% 22.75/7.04 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less(v0, v2) = v3) | ~ (less(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less(v1, v2) = v4))
% 22.75/7.04 | (59) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | greater(v1, v0) = 0)
% 22.75/7.04 | (60) ! [v0] : ~ (greater(v0, v0) = 0)
% 22.75/7.04 | (61) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0)
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (61) with vd355, vd356 yields:
% 22.75/7.04 | (62) vd356 = vd355 | ~ (geq(vd355, vd356) = 0) | greater(vd355, vd356) = 0
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (9) with vd356, vd355 yields:
% 22.75/7.04 | (63) ~ (geq(vd355, vd356) = 0) | leq(vd356, vd355) = 0
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (61) with vd353, vd354 yields:
% 22.75/7.04 | (64) vd354 = vd353 | ~ (geq(vd353, vd354) = 0) | greater(vd353, vd354) = 0
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (9) with vd354, vd353 yields:
% 22.75/7.04 | (65) ~ (geq(vd353, vd354) = 0) | leq(vd354, vd353) = 0
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (46) with all_0_1_1, vd356, vd354 and discharging atoms vplus(vd354, vd356) = all_0_1_1, yields:
% 22.75/7.04 | (66) vplus(vd356, vd354) = all_0_1_1
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (46) with all_0_2_2, vd355, vd353 and discharging atoms vplus(vd353, vd355) = all_0_2_2, yields:
% 22.75/7.04 | (67) vplus(vd355, vd353) = all_0_2_2
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (40) with all_0_0_0, all_0_1_1, all_0_2_2, vd355, vd354, vd353 and discharging atoms vplus(vd353, vd355) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.75/7.04 | (68) all_0_0_0 = 0 | ~ (vplus(vd354, vd355) = all_0_1_1) | ? [v0] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0)
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (55) with all_0_0_0, all_0_1_1, all_0_2_2, vd356, vd355, vd354, vd353 and discharging atoms vplus(vd354, vd356) = all_0_1_1, vplus(vd353, vd355) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.75/7.04 | (69) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd355, vd356) = v0 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (11) with vd355, vd356 yields:
% 22.75/7.04 | (70) ~ (greater(vd355, vd356) = 0) | ? [v0] : vplus(vd356, v0) = vd355
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (11) with vd353, vd354 yields:
% 22.75/7.04 | (71) ~ (greater(vd353, vd354) = 0) | ? [v0] : vplus(vd354, v0) = vd353
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (55) with all_0_0_0, all_0_1_1, all_0_2_2, vd354, vd355, vd356, vd353 and discharging atoms vplus(vd356, vd354) = all_0_1_1, vplus(vd353, vd355) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.75/7.04 | (72) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd355, vd354) = v0 & greater(vd353, vd356) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (55) with all_0_0_0, all_0_1_1, all_0_2_2, vd356, vd353, vd354, vd355 and discharging atoms vplus(vd354, vd356) = all_0_1_1, vplus(vd355, vd353) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.75/7.04 | (73) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd355, vd354) = v1 & greater(vd353, vd356) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.75/7.04 |
% 22.75/7.04 | Instantiating formula (55) with all_0_0_0, all_0_1_1, all_0_2_2, vd354, vd353, vd356, vd355 and discharging atoms vplus(vd356, vd354) = all_0_1_1, vplus(vd355, vd353) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.75/7.04 | (74) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd355, vd356) = v1 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.75/7.05 |
% 22.75/7.05 | Instantiating formula (40) with all_0_0_0, all_0_1_1, all_0_2_2, vd353, vd356, vd355 and discharging atoms vplus(vd355, vd353) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.75/7.05 | (75) all_0_0_0 = 0 | ~ (vplus(vd356, vd353) = all_0_1_1) | ? [v0] : ( ~ (v0 = 0) & greater(vd355, vd356) = v0)
% 22.75/7.05 |
% 22.75/7.05 +-Applying beta-rule and splitting (73), into two cases.
% 22.75/7.05 |-Branch one:
% 22.75/7.05 | (76) all_0_0_0 = 0
% 22.75/7.05 |
% 22.75/7.05 | Equations (76) can reduce 44 to:
% 22.75/7.05 | (77) $false
% 22.75/7.05 |
% 22.75/7.05 |-The branch is then unsatisfiable
% 22.75/7.05 |-Branch two:
% 22.75/7.05 | (44) ~ (all_0_0_0 = 0)
% 22.75/7.05 | (79) ? [v0] : ? [v1] : (greater(vd355, vd354) = v1 & greater(vd353, vd356) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.75/7.05 |
% 22.75/7.05 +-Applying beta-rule and splitting (72), into two cases.
% 22.75/7.05 |-Branch one:
% 22.75/7.05 | (76) all_0_0_0 = 0
% 22.75/7.05 |
% 22.75/7.05 | Equations (76) can reduce 44 to:
% 22.75/7.05 | (77) $false
% 22.75/7.05 |
% 22.75/7.05 |-The branch is then unsatisfiable
% 22.75/7.05 |-Branch two:
% 22.75/7.05 | (44) ~ (all_0_0_0 = 0)
% 22.75/7.05 | (83) ? [v0] : ? [v1] : (greater(vd355, vd354) = v0 & greater(vd353, vd356) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.75/7.05 |
% 22.75/7.05 +-Applying beta-rule and splitting (3), into two cases.
% 22.75/7.05 |-Branch one:
% 22.75/7.05 | (84) all_0_3_3 = 0 & all_0_4_4 = 0
% 22.75/7.05 |
% 22.75/7.05 | Applying alpha-rule on (84) yields:
% 22.75/7.05 | (85) all_0_3_3 = 0
% 22.75/7.05 | (86) all_0_4_4 = 0
% 22.75/7.05 |
% 22.75/7.05 | From (86) and (35) follows:
% 22.75/7.05 | (87) geq(vd355, vd356) = 0
% 22.75/7.05 |
% 22.75/7.05 | From (85) and (19) follows:
% 22.75/7.05 | (88) greater(vd353, vd354) = 0
% 22.75/7.05 |
% 22.75/7.05 +-Applying beta-rule and splitting (69), into two cases.
% 22.75/7.05 |-Branch one:
% 22.75/7.05 | (76) all_0_0_0 = 0
% 22.75/7.05 |
% 22.75/7.05 | Equations (76) can reduce 44 to:
% 22.75/7.05 | (77) $false
% 22.75/7.05 |
% 22.75/7.05 |-The branch is then unsatisfiable
% 22.75/7.05 |-Branch two:
% 22.75/7.05 | (44) ~ (all_0_0_0 = 0)
% 22.75/7.05 | (92) ? [v0] : ? [v1] : (greater(vd355, vd356) = v0 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.75/7.05 |
% 22.75/7.05 | Instantiating (92) with all_68_0_14, all_68_1_15 yields:
% 22.75/7.05 | (93) greater(vd355, vd356) = all_68_1_15 & greater(vd353, vd354) = all_68_0_14 & ( ~ (all_68_0_14 = 0) | ~ (all_68_1_15 = 0))
% 22.75/7.05 |
% 22.75/7.05 | Applying alpha-rule on (93) yields:
% 22.75/7.05 | (94) greater(vd355, vd356) = all_68_1_15
% 22.75/7.05 | (95) greater(vd353, vd354) = all_68_0_14
% 22.75/7.05 | (96) ~ (all_68_0_14 = 0) | ~ (all_68_1_15 = 0)
% 22.75/7.05 |
% 22.75/7.05 +-Applying beta-rule and splitting (63), into two cases.
% 22.75/7.05 |-Branch one:
% 22.75/7.05 | (97) ~ (geq(vd355, vd356) = 0)
% 22.75/7.05 |
% 22.75/7.05 | Using (87) and (97) yields:
% 22.75/7.05 | (98) $false
% 22.75/7.05 |
% 22.75/7.05 |-The branch is then unsatisfiable
% 22.75/7.05 |-Branch two:
% 22.75/7.05 | (87) geq(vd355, vd356) = 0
% 22.75/7.05 | (100) leq(vd356, vd355) = 0
% 22.75/7.05 |
% 22.75/7.05 +-Applying beta-rule and splitting (71), into two cases.
% 22.75/7.05 |-Branch one:
% 22.75/7.05 | (101) ~ (greater(vd353, vd354) = 0)
% 22.75/7.05 |
% 22.75/7.05 | Using (88) and (101) yields:
% 22.75/7.05 | (98) $false
% 22.75/7.05 |
% 22.75/7.05 |-The branch is then unsatisfiable
% 22.75/7.05 |-Branch two:
% 22.75/7.05 | (88) greater(vd353, vd354) = 0
% 22.75/7.05 | (104) ? [v0] : vplus(vd354, v0) = vd353
% 22.75/7.05 |
% 22.75/7.05 | Instantiating formula (16) with vd355, vd356, all_68_1_15, all_0_6_6 and discharging atoms greater(vd355, vd356) = all_68_1_15, greater(vd355, vd356) = all_0_6_6, yields:
% 22.75/7.05 | (105) all_68_1_15 = all_0_6_6
% 22.75/7.05 |
% 22.75/7.05 | Instantiating formula (16) with vd353, vd354, 0, all_68_0_14 and discharging atoms greater(vd353, vd354) = all_68_0_14, greater(vd353, vd354) = 0, yields:
% 22.75/7.05 | (106) all_68_0_14 = 0
% 22.75/7.05 |
% 22.75/7.05 | From (105) and (94) follows:
% 22.75/7.05 | (52) greater(vd355, vd356) = all_0_6_6
% 22.75/7.05 |
% 22.75/7.05 | From (106) and (95) follows:
% 22.75/7.05 | (88) greater(vd353, vd354) = 0
% 22.75/7.05 |
% 22.75/7.06 +-Applying beta-rule and splitting (74), into two cases.
% 22.75/7.06 |-Branch one:
% 22.75/7.06 | (76) all_0_0_0 = 0
% 22.75/7.06 |
% 22.75/7.06 | Equations (76) can reduce 44 to:
% 22.75/7.06 | (77) $false
% 22.75/7.06 |
% 22.75/7.06 |-The branch is then unsatisfiable
% 22.75/7.06 |-Branch two:
% 22.75/7.06 | (44) ~ (all_0_0_0 = 0)
% 22.75/7.06 | (112) ? [v0] : ? [v1] : (greater(vd355, vd356) = v1 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.75/7.06 |
% 22.75/7.06 | Instantiating (112) with all_88_0_17, all_88_1_18 yields:
% 22.75/7.06 | (113) greater(vd355, vd356) = all_88_0_17 & greater(vd353, vd354) = all_88_1_18 & ( ~ (all_88_0_17 = 0) | ~ (all_88_1_18 = 0))
% 22.75/7.06 |
% 22.75/7.06 | Applying alpha-rule on (113) yields:
% 22.75/7.06 | (114) greater(vd355, vd356) = all_88_0_17
% 22.75/7.06 | (115) greater(vd353, vd354) = all_88_1_18
% 22.75/7.06 | (116) ~ (all_88_0_17 = 0) | ~ (all_88_1_18 = 0)
% 22.75/7.06 |
% 22.75/7.06 +-Applying beta-rule and splitting (96), into two cases.
% 22.75/7.06 |-Branch one:
% 22.75/7.06 | (117) ~ (all_68_0_14 = 0)
% 22.75/7.06 |
% 22.75/7.06 | Equations (106) can reduce 117 to:
% 22.75/7.06 | (77) $false
% 22.75/7.06 |
% 22.75/7.06 |-The branch is then unsatisfiable
% 22.75/7.06 |-Branch two:
% 22.75/7.06 | (106) all_68_0_14 = 0
% 22.75/7.06 | (120) ~ (all_68_1_15 = 0)
% 22.75/7.06 |
% 22.75/7.06 | Equations (105) can reduce 120 to:
% 22.75/7.06 | (121) ~ (all_0_6_6 = 0)
% 22.75/7.06 |
% 22.75/7.06 +-Applying beta-rule and splitting (62), into two cases.
% 22.75/7.06 |-Branch one:
% 22.75/7.06 | (97) ~ (geq(vd355, vd356) = 0)
% 22.75/7.06 |
% 22.75/7.06 | Using (87) and (97) yields:
% 22.75/7.06 | (98) $false
% 22.75/7.06 |
% 22.75/7.06 |-The branch is then unsatisfiable
% 22.75/7.06 |-Branch two:
% 22.75/7.06 | (87) geq(vd355, vd356) = 0
% 22.75/7.06 | (125) vd356 = vd355 | greater(vd355, vd356) = 0
% 22.75/7.06 |
% 22.75/7.06 +-Applying beta-rule and splitting (125), into two cases.
% 22.75/7.06 |-Branch one:
% 22.75/7.06 | (126) greater(vd355, vd356) = 0
% 22.75/7.06 |
% 22.75/7.06 | Instantiating formula (16) with vd355, vd356, all_88_0_17, all_0_6_6 and discharging atoms greater(vd355, vd356) = all_88_0_17, greater(vd355, vd356) = all_0_6_6, yields:
% 22.75/7.06 | (127) all_88_0_17 = all_0_6_6
% 22.75/7.06 |
% 22.75/7.06 | Instantiating formula (16) with vd355, vd356, 0, all_88_0_17 and discharging atoms greater(vd355, vd356) = all_88_0_17, greater(vd355, vd356) = 0, yields:
% 22.75/7.06 | (128) all_88_0_17 = 0
% 22.75/7.06 |
% 22.75/7.06 | Combining equations (127,128) yields a new equation:
% 22.75/7.06 | (129) all_0_6_6 = 0
% 22.75/7.06 |
% 22.75/7.06 | Simplifying 129 yields:
% 22.75/7.06 | (130) all_0_6_6 = 0
% 22.75/7.06 |
% 22.75/7.06 | Equations (130) can reduce 121 to:
% 22.75/7.06 | (77) $false
% 22.75/7.06 |
% 22.75/7.06 |-The branch is then unsatisfiable
% 22.75/7.06 |-Branch two:
% 22.75/7.06 | (132) ~ (greater(vd355, vd356) = 0)
% 22.75/7.06 | (133) vd356 = vd355
% 22.75/7.06 |
% 22.75/7.06 | From (133) and (31) follows:
% 22.75/7.06 | (134) vplus(vd354, vd355) = all_0_1_1
% 22.75/7.06 |
% 22.75/7.06 +-Applying beta-rule and splitting (68), into two cases.
% 22.75/7.06 |-Branch one:
% 22.75/7.06 | (135) ~ (vplus(vd354, vd355) = all_0_1_1)
% 22.75/7.06 |
% 22.75/7.06 | Using (134) and (135) yields:
% 22.75/7.06 | (98) $false
% 22.75/7.06 |
% 22.75/7.06 |-The branch is then unsatisfiable
% 22.75/7.06 |-Branch two:
% 22.75/7.06 | (134) vplus(vd354, vd355) = all_0_1_1
% 22.75/7.06 | (138) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0)
% 22.75/7.06 |
% 22.75/7.06 +-Applying beta-rule and splitting (138), into two cases.
% 22.75/7.06 |-Branch one:
% 22.75/7.06 | (76) all_0_0_0 = 0
% 22.75/7.06 |
% 22.75/7.06 | Equations (76) can reduce 44 to:
% 22.75/7.06 | (77) $false
% 22.75/7.06 |
% 22.75/7.06 |-The branch is then unsatisfiable
% 22.75/7.06 |-Branch two:
% 22.75/7.06 | (44) ~ (all_0_0_0 = 0)
% 22.75/7.06 | (142) ? [v0] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0)
% 22.75/7.06 |
% 22.75/7.06 | Instantiating (142) with all_110_0_19 yields:
% 22.75/7.06 | (143) ~ (all_110_0_19 = 0) & greater(vd353, vd354) = all_110_0_19
% 22.75/7.06 |
% 22.75/7.06 | Applying alpha-rule on (143) yields:
% 22.75/7.06 | (144) ~ (all_110_0_19 = 0)
% 22.75/7.06 | (145) greater(vd353, vd354) = all_110_0_19
% 22.75/7.06 |
% 22.75/7.06 | Instantiating formula (16) with vd353, vd354, all_110_0_19, 0 and discharging atoms greater(vd353, vd354) = all_110_0_19, greater(vd353, vd354) = 0, yields:
% 22.75/7.06 | (146) all_110_0_19 = 0
% 22.75/7.06 |
% 22.75/7.06 | Instantiating formula (16) with vd353, vd354, all_88_1_18, all_110_0_19 and discharging atoms greater(vd353, vd354) = all_110_0_19, greater(vd353, vd354) = all_88_1_18, yields:
% 22.75/7.07 | (147) all_110_0_19 = all_88_1_18
% 22.75/7.07 |
% 22.75/7.07 | Combining equations (146,147) yields a new equation:
% 22.75/7.07 | (148) all_88_1_18 = 0
% 22.75/7.07 |
% 22.75/7.07 | Combining equations (148,147) yields a new equation:
% 22.75/7.07 | (146) all_110_0_19 = 0
% 22.75/7.07 |
% 22.75/7.07 | Equations (146) can reduce 144 to:
% 22.75/7.07 | (77) $false
% 22.75/7.07 |
% 22.75/7.07 |-The branch is then unsatisfiable
% 22.75/7.07 |-Branch two:
% 22.75/7.07 | (151) all_0_5_5 = 0 & all_0_6_6 = 0
% 22.75/7.07 |
% 22.75/7.07 | Applying alpha-rule on (151) yields:
% 22.75/7.07 | (152) all_0_5_5 = 0
% 22.75/7.07 | (130) all_0_6_6 = 0
% 22.75/7.07 |
% 22.75/7.07 | From (152) and (14) follows:
% 22.75/7.07 | (154) geq(vd353, vd354) = 0
% 22.75/7.07 |
% 22.75/7.07 | From (130) and (52) follows:
% 22.75/7.07 | (126) greater(vd355, vd356) = 0
% 22.75/7.07 |
% 22.75/7.07 +-Applying beta-rule and splitting (69), into two cases.
% 22.75/7.07 |-Branch one:
% 22.75/7.07 | (76) all_0_0_0 = 0
% 22.75/7.07 |
% 22.75/7.07 | Equations (76) can reduce 44 to:
% 22.75/7.07 | (77) $false
% 22.75/7.07 |
% 22.75/7.07 |-The branch is then unsatisfiable
% 22.75/7.07 |-Branch two:
% 22.75/7.07 | (44) ~ (all_0_0_0 = 0)
% 22.75/7.07 | (92) ? [v0] : ? [v1] : (greater(vd355, vd356) = v0 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.75/7.07 |
% 22.75/7.07 | Instantiating (92) with all_68_0_20, all_68_1_21 yields:
% 22.75/7.07 | (160) greater(vd355, vd356) = all_68_1_21 & greater(vd353, vd354) = all_68_0_20 & ( ~ (all_68_0_20 = 0) | ~ (all_68_1_21 = 0))
% 22.75/7.07 |
% 22.75/7.07 | Applying alpha-rule on (160) yields:
% 22.75/7.07 | (161) greater(vd355, vd356) = all_68_1_21
% 22.75/7.07 | (162) greater(vd353, vd354) = all_68_0_20
% 22.75/7.07 | (163) ~ (all_68_0_20 = 0) | ~ (all_68_1_21 = 0)
% 22.75/7.07 |
% 22.75/7.07 +-Applying beta-rule and splitting (65), into two cases.
% 22.75/7.07 |-Branch one:
% 22.75/7.07 | (164) ~ (geq(vd353, vd354) = 0)
% 22.75/7.07 |
% 22.75/7.07 | Using (154) and (164) yields:
% 22.75/7.07 | (98) $false
% 22.75/7.07 |
% 22.75/7.07 |-The branch is then unsatisfiable
% 22.75/7.07 |-Branch two:
% 22.75/7.07 | (154) geq(vd353, vd354) = 0
% 22.75/7.07 | (167) leq(vd354, vd353) = 0
% 22.75/7.07 |
% 22.75/7.07 +-Applying beta-rule and splitting (70), into two cases.
% 22.75/7.07 |-Branch one:
% 22.75/7.07 | (132) ~ (greater(vd355, vd356) = 0)
% 22.75/7.07 |
% 22.75/7.07 | Using (126) and (132) yields:
% 22.75/7.07 | (98) $false
% 22.75/7.07 |
% 22.75/7.07 |-The branch is then unsatisfiable
% 22.75/7.07 |-Branch two:
% 22.75/7.07 | (126) greater(vd355, vd356) = 0
% 22.75/7.07 | (171) ? [v0] : vplus(vd356, v0) = vd355
% 22.75/7.07 |
% 22.75/7.07 | Instantiating formula (16) with vd355, vd356, 0, all_68_1_21 and discharging atoms greater(vd355, vd356) = all_68_1_21, greater(vd355, vd356) = 0, yields:
% 22.75/7.07 | (172) all_68_1_21 = 0
% 22.75/7.07 |
% 22.75/7.07 | Instantiating formula (16) with vd353, vd354, all_68_0_20, all_0_3_3 and discharging atoms greater(vd353, vd354) = all_68_0_20, greater(vd353, vd354) = all_0_3_3, yields:
% 22.75/7.07 | (173) all_68_0_20 = all_0_3_3
% 22.75/7.07 |
% 22.75/7.07 | From (172) and (161) follows:
% 22.75/7.07 | (126) greater(vd355, vd356) = 0
% 22.75/7.07 |
% 22.75/7.07 | From (173) and (162) follows:
% 22.75/7.07 | (19) greater(vd353, vd354) = all_0_3_3
% 22.75/7.07 |
% 22.75/7.07 +-Applying beta-rule and splitting (75), into two cases.
% 22.75/7.07 |-Branch one:
% 22.75/7.07 | (176) ~ (vplus(vd356, vd353) = all_0_1_1)
% 22.75/7.07 |
% 22.75/7.07 +-Applying beta-rule and splitting (163), into two cases.
% 22.75/7.07 |-Branch one:
% 22.75/7.07 | (177) ~ (all_68_0_20 = 0)
% 22.75/7.07 |
% 22.75/7.08 | Equations (173) can reduce 177 to:
% 22.75/7.08 | (178) ~ (all_0_3_3 = 0)
% 22.75/7.08 |
% 22.75/7.08 +-Applying beta-rule and splitting (64), into two cases.
% 22.75/7.08 |-Branch one:
% 22.75/7.08 | (164) ~ (geq(vd353, vd354) = 0)
% 22.75/7.08 |
% 22.75/7.08 | Using (154) and (164) yields:
% 22.75/7.08 | (98) $false
% 22.75/7.08 |
% 22.75/7.08 |-The branch is then unsatisfiable
% 22.75/7.08 |-Branch two:
% 22.75/7.08 | (154) geq(vd353, vd354) = 0
% 22.75/7.08 | (182) vd354 = vd353 | greater(vd353, vd354) = 0
% 22.75/7.08 |
% 22.75/7.08 +-Applying beta-rule and splitting (182), into two cases.
% 22.75/7.08 |-Branch one:
% 22.75/7.08 | (88) greater(vd353, vd354) = 0
% 22.75/7.08 |
% 22.75/7.08 | Instantiating formula (16) with vd353, vd354, 0, all_0_3_3 and discharging atoms greater(vd353, vd354) = all_0_3_3, greater(vd353, vd354) = 0, yields:
% 22.75/7.08 | (85) all_0_3_3 = 0
% 22.75/7.08 |
% 22.75/7.08 | Equations (85) can reduce 178 to:
% 22.75/7.08 | (77) $false
% 22.75/7.08 |
% 22.75/7.08 |-The branch is then unsatisfiable
% 22.75/7.08 |-Branch two:
% 22.75/7.08 | (101) ~ (greater(vd353, vd354) = 0)
% 22.75/7.08 | (187) vd354 = vd353
% 22.75/7.08 |
% 22.75/7.08 | From (187) and (66) follows:
% 22.75/7.08 | (188) vplus(vd356, vd353) = all_0_1_1
% 22.75/7.08 |
% 22.75/7.08 | Using (188) and (176) yields:
% 22.75/7.08 | (98) $false
% 22.75/7.08 |
% 22.75/7.08 |-The branch is then unsatisfiable
% 22.75/7.08 |-Branch two:
% 22.75/7.08 | (190) all_68_0_20 = 0
% 22.75/7.08 | (191) ~ (all_68_1_21 = 0)
% 22.75/7.08 |
% 22.75/7.08 | Equations (172) can reduce 191 to:
% 22.75/7.08 | (77) $false
% 22.75/7.08 |
% 22.75/7.08 |-The branch is then unsatisfiable
% 22.75/7.08 |-Branch two:
% 22.75/7.08 | (188) vplus(vd356, vd353) = all_0_1_1
% 22.75/7.08 | (194) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & greater(vd355, vd356) = v0)
% 22.75/7.08 |
% 22.75/7.08 +-Applying beta-rule and splitting (74), into two cases.
% 22.75/7.08 |-Branch one:
% 22.75/7.08 | (76) all_0_0_0 = 0
% 22.75/7.08 |
% 22.75/7.08 | Equations (76) can reduce 44 to:
% 22.75/7.08 | (77) $false
% 22.75/7.08 |
% 22.75/7.08 |-The branch is then unsatisfiable
% 22.75/7.08 |-Branch two:
% 22.75/7.08 | (44) ~ (all_0_0_0 = 0)
% 22.75/7.08 | (112) ? [v0] : ? [v1] : (greater(vd355, vd356) = v1 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.75/7.08 |
% 22.75/7.08 | Instantiating (112) with all_91_0_23, all_91_1_24 yields:
% 22.75/7.08 | (199) greater(vd355, vd356) = all_91_0_23 & greater(vd353, vd354) = all_91_1_24 & ( ~ (all_91_0_23 = 0) | ~ (all_91_1_24 = 0))
% 22.75/7.08 |
% 22.75/7.08 | Applying alpha-rule on (199) yields:
% 22.75/7.08 | (200) greater(vd355, vd356) = all_91_0_23
% 22.75/7.08 | (201) greater(vd353, vd354) = all_91_1_24
% 22.75/7.08 | (202) ~ (all_91_0_23 = 0) | ~ (all_91_1_24 = 0)
% 22.75/7.08 |
% 22.75/7.08 +-Applying beta-rule and splitting (194), into two cases.
% 22.75/7.08 |-Branch one:
% 22.75/7.08 | (76) all_0_0_0 = 0
% 22.75/7.08 |
% 22.75/7.08 | Equations (76) can reduce 44 to:
% 22.75/7.08 | (77) $false
% 22.75/7.08 |
% 22.75/7.08 |-The branch is then unsatisfiable
% 22.75/7.08 |-Branch two:
% 22.75/7.08 | (44) ~ (all_0_0_0 = 0)
% 22.75/7.08 | (206) ? [v0] : ( ~ (v0 = 0) & greater(vd355, vd356) = v0)
% 22.75/7.08 |
% 22.75/7.08 | Instantiating (206) with all_109_0_26 yields:
% 22.75/7.08 | (207) ~ (all_109_0_26 = 0) & greater(vd355, vd356) = all_109_0_26
% 22.75/7.08 |
% 22.75/7.08 | Applying alpha-rule on (207) yields:
% 22.75/7.08 | (208) ~ (all_109_0_26 = 0)
% 22.75/7.08 | (209) greater(vd355, vd356) = all_109_0_26
% 22.75/7.08 |
% 22.75/7.08 | Instantiating formula (16) with vd355, vd356, all_109_0_26, 0 and discharging atoms greater(vd355, vd356) = all_109_0_26, greater(vd355, vd356) = 0, yields:
% 22.75/7.08 | (210) all_109_0_26 = 0
% 22.75/7.08 |
% 22.75/7.08 | Instantiating formula (16) with vd355, vd356, all_91_0_23, all_109_0_26 and discharging atoms greater(vd355, vd356) = all_109_0_26, greater(vd355, vd356) = all_91_0_23, yields:
% 22.75/7.08 | (211) all_109_0_26 = all_91_0_23
% 22.75/7.08 |
% 22.75/7.09 | Combining equations (210,211) yields a new equation:
% 22.75/7.09 | (212) all_91_0_23 = 0
% 22.75/7.09 |
% 22.75/7.09 | Combining equations (212,211) yields a new equation:
% 22.75/7.09 | (210) all_109_0_26 = 0
% 22.75/7.09 |
% 22.75/7.09 | Equations (210) can reduce 208 to:
% 22.75/7.09 | (77) $false
% 22.75/7.09 |
% 22.75/7.09 |-The branch is then unsatisfiable
% 22.75/7.09 % SZS output end Proof for theBenchmark
% 22.75/7.09
% 22.75/7.09 6405ms
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