TSTP Solution File: MSC017+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MSC017+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 22:40:08 EDT 2022
% Result : Theorem 3.37s 1.49s
% Output : Proof 4.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : MSC017+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 16:15:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.58 (ePrincess v.1.0)
% 0.55/0.58
% 0.59/0.58 (c) Philipp Rümmer, 2009-2015
% 0.59/0.58 (c) Peter Backeman, 2014-2015
% 0.59/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58 Bug reports to peter@backeman.se
% 0.59/0.58
% 0.59/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58
% 0.59/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.40/0.91 Prover 0: Preprocessing ...
% 1.72/1.08 Prover 0: Constructing countermodel ...
% 2.16/1.19 Prover 0: gave up
% 2.16/1.19 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.25/1.21 Prover 1: Preprocessing ...
% 2.40/1.27 Prover 1: Constructing countermodel ...
% 2.61/1.32 Prover 1: gave up
% 2.61/1.32 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.61/1.33 Prover 2: Preprocessing ...
% 2.90/1.43 Prover 2: Warning: ignoring some quantifiers
% 2.90/1.43 Prover 2: Constructing countermodel ...
% 3.37/1.48 Prover 2: proved (163ms)
% 3.37/1.48
% 3.37/1.48 No countermodel exists, formula is valid
% 3.37/1.49 % SZS status Theorem for theBenchmark
% 3.37/1.49
% 3.37/1.49 Generating proof ... Warning: ignoring some quantifiers
% 4.65/1.78 found it (size 54)
% 4.65/1.78
% 4.65/1.78 % SZS output start Proof for theBenchmark
% 4.65/1.78 Assumed formulas after preprocessing and simplification:
% 4.65/1.78 | (0) ? [v0] : ? [v1] : (bad(v1) = 0 & bad(dci) = 0 & outcome(v0, v1) = 0 & dive(v0) = 0 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (outcome(v5, v4) = v3) | ~ (outcome(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (greater(v5, v4) = v3) | ~ (greater(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (padi(v5, v4) = v3) | ~ (padi(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (bad(v4) = v3) | ~ (bad(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (nitrogen(v4) = v3) | ~ (nitrogen(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (dive(v4) = v3) | ~ (dive(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (depth(v4) = v3) | ~ (depth(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (time(v4) = v3) | ~ (time(v4) = v2)) & ! [v2] : ! [v3] : (v3 = dci | ~ (bad(v3) = 0) | ~ (dive(v2) = 0) | ? [v4] : ( ~ (v4 = 0) & outcome(v2, v3) = v4)) & ! [v2] : ! [v3] : (v3 = dci | ~ (outcome(v2, v3) = 0) | ~ (dive(v2) = 0) | ? [v4] : ( ~ (v4 = 0) & bad(v3) = v4)) & ! [v2] : ! [v3] : ( ~ (outcome(v2, dci) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & dive(v2) = v4) | (( ~ (v3 = 0) | (v5 = 0 & greater(v4, nitrogen_limit) = 0 & nitrogen(v2) = v4)) & (v3 = 0 | ( ~ (v5 = 0) & greater(v4, nitrogen_limit) = v5 & nitrogen(v2) = v4))))) & ! [v2] : ! [v3] : ( ~ (nitrogen(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v4 = 0) & dive(v2) = v4) | (((v8 = 0 & greater(v3, nitrogen_limit) = 0) | ( ~ (v7 = 0) & ~ (v5 = 0) & greater(v6, time_limit) = v7 & greater(v4, depth_limit) = v5 & depth(v2) = v4 & time(v2) = v6)) & ((v7 = 0 & greater(v6, time_limit) = 0 & time(v2) = v6) | (v5 = 0 & greater(v4, depth_limit) = 0 & depth(v2) = v4) | ( ~ (v8 = 0) & greater(v3, nitrogen_limit) = v8))))) & ! [v2] : ! [v3] : ( ~ (nitrogen(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = v3 & depth(v2) = v4 & time(v2) = v5 & padi(v4, v5) = v3) | ( ~ (v4 = 0) & dive(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (nitrogen(v2) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & dive(v2) = v4) | (((v5 = 0 & outcome(v2, dci) = 0) | ( ~ (v4 = 0) & greater(v3, nitrogen_limit) = v4)) & ((v4 = 0 & greater(v3, nitrogen_limit) = 0) | ( ~ (v5 = 0) & outcome(v2, dci) = v5))))) & ! [v2] : ! [v3] : ( ~ (depth(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v4 = 0) & dive(v2) = v4) | (((v8 = 0 & greater(v7, nitrogen_limit) = 0 & nitrogen(v2) = v7) | ( ~ (v6 = 0) & ~ (v4 = 0) & greater(v5, time_limit) = v6 & greater(v3, depth_limit) = v4 & time(v2) = v5)) & ((v6 = 0 & greater(v5, time_limit) = 0 & time(v2) = v5) | (v4 = 0 & greater(v3, depth_limit) = 0) | ( ~ (v8 = 0) & greater(v7, nitrogen_limit) = v8 & nitrogen(v2) = v7))))) & ! [v2] : ! [v3] : ( ~ (depth(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = v4 & nitrogen(v2) = v4 & time(v2) = v5 & padi(v3, v5) = v4) | ( ~ (v4 = 0) & dive(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (depth(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v4 = 0) & greater(v5, time_limit) = v6 & greater(v3, depth_limit) = v4 & time(v2) = v5) | ( ~ (v4 = 0) & dive(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (time(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v4 = 0) & dive(v2) = v4) | (((v8 = 0 & greater(v7, nitrogen_limit) = 0 & nitrogen(v2) = v7) | ( ~ (v6 = 0) & ~ (v5 = 0) & greater(v4, depth_limit) = v5 & greater(v3, time_limit) = v6 & depth(v2) = v4)) & ((v6 = 0 & greater(v3, time_limit) = 0) | (v5 = 0 & greater(v4, depth_limit) = 0 & depth(v2) = v4) | ( ~ (v8 = 0) & greater(v7, nitrogen_limit) = v8 & nitrogen(v2) = v7))))) & ! [v2] : ! [v3] : ( ~ (time(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = v4 & nitrogen(v2) = v4 & depth(v2) = v5 & padi(v5, v3) = v4) | ( ~ (v4 = 0) & dive(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (time(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v5 = 0) & greater(v4, depth_limit) = v5 & greater(v3, time_limit) = v6 & depth(v2) = v4) | ( ~ (v4 = 0) & dive(v2) = v4))) & ! [v2] : ( ~ (dive(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (((v8 = 0 & greater(v7, nitrogen_limit) = 0 & nitrogen(v2) = v7) | ( ~ (v6 = 0) & ~ (v4 = 0) & greater(v5, time_limit) = v6 & greater(v3, depth_limit) = v4 & depth(v2) = v3 & time(v2) = v5)) & ((v6 = 0 & greater(v5, time_limit) = 0 & time(v2) = v5) | (v4 = 0 & greater(v3, depth_limit) = 0 & depth(v2) = v3) | ( ~ (v8 = 0) & greater(v7, nitrogen_limit) = v8 & nitrogen(v2) = v7)))) & ! [v2] : ( ~ (dive(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v4 = 0) & greater(v5, time_limit) = v6 & greater(v3, depth_limit) = v4 & depth(v2) = v3 & time(v2) = v5)) & ! [v2] : ( ~ (dive(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : (nitrogen(v2) = v3 & depth(v2) = v4 & time(v2) = v5 & padi(v4, v5) = v3)) & ! [v2] : ( ~ (dive(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & outcome(v2, dci) = 0) | ( ~ (v4 = 0) & greater(v3, nitrogen_limit) = v4 & nitrogen(v2) = v3)) & ((v4 = 0 & greater(v3, nitrogen_limit) = 0 & nitrogen(v2) = v3) | ( ~ (v5 = 0) & outcome(v2, dci) = v5)))) & ? [v2] : ? [v3] : ? [v4] : outcome(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : greater(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : padi(v3, v2) = v4 & ? [v2] : ? [v3] : bad(v2) = v3 & ? [v2] : ? [v3] : nitrogen(v2) = v3 & ? [v2] : ? [v3] : dive(v2) = v3 & ? [v2] : ? [v3] : depth(v2) = v3 & ? [v2] : ? [v3] : time(v2) = v3)
% 4.79/1.83 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 4.79/1.83 | (1) bad(all_0_0_0) = 0 & bad(dci) = 0 & outcome(all_0_1_1, all_0_0_0) = 0 & dive(all_0_1_1) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (outcome(v3, v2) = v1) | ~ (outcome(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (padi(v3, v2) = v1) | ~ (padi(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bad(v2) = v1) | ~ (bad(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (nitrogen(v2) = v1) | ~ (nitrogen(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (dive(v2) = v1) | ~ (dive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (depth(v2) = v1) | ~ (depth(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (time(v2) = v1) | ~ (time(v2) = v0)) & ! [v0] : ! [v1] : (v1 = dci | ~ (bad(v1) = 0) | ~ (dive(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & outcome(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = dci | ~ (outcome(v0, v1) = 0) | ~ (dive(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & bad(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (outcome(v0, dci) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & dive(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & greater(v2, nitrogen_limit) = 0 & nitrogen(v0) = v2)) & (v1 = 0 | ( ~ (v3 = 0) & greater(v2, nitrogen_limit) = v3 & nitrogen(v0) = v2))))) & ! [v0] : ! [v1] : ( ~ (nitrogen(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v2 = 0) & dive(v0) = v2) | (((v6 = 0 & greater(v1, nitrogen_limit) = 0) | ( ~ (v5 = 0) & ~ (v3 = 0) & greater(v4, time_limit) = v5 & greater(v2, depth_limit) = v3 & depth(v0) = v2 & time(v0) = v4)) & ((v5 = 0 & greater(v4, time_limit) = 0 & time(v0) = v4) | (v3 = 0 & greater(v2, depth_limit) = 0 & depth(v0) = v2) | ( ~ (v6 = 0) & greater(v1, nitrogen_limit) = v6))))) & ! [v0] : ! [v1] : ( ~ (nitrogen(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & depth(v0) = v2 & time(v0) = v3 & padi(v2, v3) = v1) | ( ~ (v2 = 0) & dive(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (nitrogen(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & dive(v0) = v2) | (((v3 = 0 & outcome(v0, dci) = 0) | ( ~ (v2 = 0) & greater(v1, nitrogen_limit) = v2)) & ((v2 = 0 & greater(v1, nitrogen_limit) = 0) | ( ~ (v3 = 0) & outcome(v0, dci) = v3))))) & ! [v0] : ! [v1] : ( ~ (depth(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v2 = 0) & dive(v0) = v2) | (((v6 = 0 & greater(v5, nitrogen_limit) = 0 & nitrogen(v0) = v5) | ( ~ (v4 = 0) & ~ (v2 = 0) & greater(v3, time_limit) = v4 & greater(v1, depth_limit) = v2 & time(v0) = v3)) & ((v4 = 0 & greater(v3, time_limit) = 0 & time(v0) = v3) | (v2 = 0 & greater(v1, depth_limit) = 0) | ( ~ (v6 = 0) & greater(v5, nitrogen_limit) = v6 & nitrogen(v0) = v5))))) & ! [v0] : ! [v1] : ( ~ (depth(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & nitrogen(v0) = v2 & time(v0) = v3 & padi(v1, v3) = v2) | ( ~ (v2 = 0) & dive(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (depth(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v2 = 0) & greater(v3, time_limit) = v4 & greater(v1, depth_limit) = v2 & time(v0) = v3) | ( ~ (v2 = 0) & dive(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (time(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v2 = 0) & dive(v0) = v2) | (((v6 = 0 & greater(v5, nitrogen_limit) = 0 & nitrogen(v0) = v5) | ( ~ (v4 = 0) & ~ (v3 = 0) & greater(v2, depth_limit) = v3 & greater(v1, time_limit) = v4 & depth(v0) = v2)) & ((v4 = 0 & greater(v1, time_limit) = 0) | (v3 = 0 & greater(v2, depth_limit) = 0 & depth(v0) = v2) | ( ~ (v6 = 0) & greater(v5, nitrogen_limit) = v6 & nitrogen(v0) = v5))))) & ! [v0] : ! [v1] : ( ~ (time(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & nitrogen(v0) = v2 & depth(v0) = v3 & padi(v3, v1) = v2) | ( ~ (v2 = 0) & dive(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (time(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & greater(v2, depth_limit) = v3 & greater(v1, time_limit) = v4 & depth(v0) = v2) | ( ~ (v2 = 0) & dive(v0) = v2))) & ! [v0] : ( ~ (dive(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (((v6 = 0 & greater(v5, nitrogen_limit) = 0 & nitrogen(v0) = v5) | ( ~ (v4 = 0) & ~ (v2 = 0) & greater(v3, time_limit) = v4 & greater(v1, depth_limit) = v2 & depth(v0) = v1 & time(v0) = v3)) & ((v4 = 0 & greater(v3, time_limit) = 0 & time(v0) = v3) | (v2 = 0 & greater(v1, depth_limit) = 0 & depth(v0) = v1) | ( ~ (v6 = 0) & greater(v5, nitrogen_limit) = v6 & nitrogen(v0) = v5)))) & ! [v0] : ( ~ (dive(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v2 = 0) & greater(v3, time_limit) = v4 & greater(v1, depth_limit) = v2 & depth(v0) = v1 & time(v0) = v3)) & ! [v0] : ( ~ (dive(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (nitrogen(v0) = v1 & depth(v0) = v2 & time(v0) = v3 & padi(v2, v3) = v1)) & ! [v0] : ( ~ (dive(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & outcome(v0, dci) = 0) | ( ~ (v2 = 0) & greater(v1, nitrogen_limit) = v2 & nitrogen(v0) = v1)) & ((v2 = 0 & greater(v1, nitrogen_limit) = 0 & nitrogen(v0) = v1) | ( ~ (v3 = 0) & outcome(v0, dci) = v3)))) & ? [v0] : ? [v1] : ? [v2] : outcome(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : greater(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : padi(v1, v0) = v2 & ? [v0] : ? [v1] : bad(v0) = v1 & ? [v0] : ? [v1] : nitrogen(v0) = v1 & ? [v0] : ? [v1] : dive(v0) = v1 & ? [v0] : ? [v1] : depth(v0) = v1 & ? [v0] : ? [v1] : time(v0) = v1
% 4.79/1.84 |
% 4.79/1.84 | Applying alpha-rule on (1) yields:
% 4.79/1.84 | (2) ! [v0] : ! [v1] : ( ~ (outcome(v0, dci) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & dive(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & greater(v2, nitrogen_limit) = 0 & nitrogen(v0) = v2)) & (v1 = 0 | ( ~ (v3 = 0) & greater(v2, nitrogen_limit) = v3 & nitrogen(v0) = v2)))))
% 4.79/1.84 | (3) ? [v0] : ? [v1] : dive(v0) = v1
% 4.79/1.84 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0))
% 4.79/1.84 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (nitrogen(v2) = v1) | ~ (nitrogen(v2) = v0))
% 4.79/1.84 | (6) ? [v0] : ? [v1] : nitrogen(v0) = v1
% 4.79/1.84 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (time(v2) = v1) | ~ (time(v2) = v0))
% 4.79/1.84 | (8) ! [v0] : ( ~ (dive(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (((v6 = 0 & greater(v5, nitrogen_limit) = 0 & nitrogen(v0) = v5) | ( ~ (v4 = 0) & ~ (v2 = 0) & greater(v3, time_limit) = v4 & greater(v1, depth_limit) = v2 & depth(v0) = v1 & time(v0) = v3)) & ((v4 = 0 & greater(v3, time_limit) = 0 & time(v0) = v3) | (v2 = 0 & greater(v1, depth_limit) = 0 & depth(v0) = v1) | ( ~ (v6 = 0) & greater(v5, nitrogen_limit) = v6 & nitrogen(v0) = v5))))
% 4.79/1.84 | (9) ? [v0] : ? [v1] : ? [v2] : outcome(v1, v0) = v2
% 4.79/1.84 | (10) ! [v0] : ! [v1] : ( ~ (nitrogen(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & depth(v0) = v2 & time(v0) = v3 & padi(v2, v3) = v1) | ( ~ (v2 = 0) & dive(v0) = v2)))
% 4.79/1.84 | (11) ? [v0] : ? [v1] : depth(v0) = v1
% 4.79/1.84 | (12) ? [v0] : ? [v1] : time(v0) = v1
% 4.79/1.84 | (13) bad(dci) = 0
% 4.79/1.85 | (14) ! [v0] : ! [v1] : ( ~ (time(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & nitrogen(v0) = v2 & depth(v0) = v3 & padi(v3, v1) = v2) | ( ~ (v2 = 0) & dive(v0) = v2)))
% 4.79/1.85 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (outcome(v3, v2) = v1) | ~ (outcome(v3, v2) = v0))
% 4.79/1.85 | (16) bad(all_0_0_0) = 0
% 4.79/1.85 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (dive(v2) = v1) | ~ (dive(v2) = v0))
% 4.79/1.85 | (18) ! [v0] : ( ~ (dive(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v2 = 0) & greater(v3, time_limit) = v4 & greater(v1, depth_limit) = v2 & depth(v0) = v1 & time(v0) = v3))
% 4.79/1.85 | (19) ? [v0] : ? [v1] : bad(v0) = v1
% 4.79/1.85 | (20) ! [v0] : ! [v1] : ( ~ (nitrogen(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & dive(v0) = v2) | (((v3 = 0 & outcome(v0, dci) = 0) | ( ~ (v2 = 0) & greater(v1, nitrogen_limit) = v2)) & ((v2 = 0 & greater(v1, nitrogen_limit) = 0) | ( ~ (v3 = 0) & outcome(v0, dci) = v3)))))
% 4.79/1.85 | (21) ! [v0] : ! [v1] : ( ~ (time(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & greater(v2, depth_limit) = v3 & greater(v1, time_limit) = v4 & depth(v0) = v2) | ( ~ (v2 = 0) & dive(v0) = v2)))
% 4.79/1.85 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (padi(v3, v2) = v1) | ~ (padi(v3, v2) = v0))
% 4.79/1.85 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bad(v2) = v1) | ~ (bad(v2) = v0))
% 4.79/1.85 | (24) ! [v0] : ! [v1] : (v1 = dci | ~ (bad(v1) = 0) | ~ (dive(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & outcome(v0, v1) = v2))
% 4.79/1.85 | (25) dive(all_0_1_1) = 0
% 4.79/1.85 | (26) ? [v0] : ? [v1] : ? [v2] : padi(v1, v0) = v2
% 4.79/1.85 | (27) ! [v0] : ! [v1] : ( ~ (depth(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & nitrogen(v0) = v2 & time(v0) = v3 & padi(v1, v3) = v2) | ( ~ (v2 = 0) & dive(v0) = v2)))
% 4.79/1.85 | (28) ! [v0] : ! [v1] : (v1 = dci | ~ (outcome(v0, v1) = 0) | ~ (dive(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & bad(v1) = v2))
% 4.79/1.85 | (29) outcome(all_0_1_1, all_0_0_0) = 0
% 4.79/1.85 | (30) ! [v0] : ( ~ (dive(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & outcome(v0, dci) = 0) | ( ~ (v2 = 0) & greater(v1, nitrogen_limit) = v2 & nitrogen(v0) = v1)) & ((v2 = 0 & greater(v1, nitrogen_limit) = 0 & nitrogen(v0) = v1) | ( ~ (v3 = 0) & outcome(v0, dci) = v3))))
% 4.79/1.85 | (31) ? [v0] : ? [v1] : ? [v2] : greater(v1, v0) = v2
% 4.79/1.85 | (32) ! [v0] : ( ~ (dive(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (nitrogen(v0) = v1 & depth(v0) = v2 & time(v0) = v3 & padi(v2, v3) = v1))
% 4.79/1.85 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (depth(v2) = v1) | ~ (depth(v2) = v0))
% 4.79/1.85 | (34) ! [v0] : ! [v1] : ( ~ (time(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v2 = 0) & dive(v0) = v2) | (((v6 = 0 & greater(v5, nitrogen_limit) = 0 & nitrogen(v0) = v5) | ( ~ (v4 = 0) & ~ (v3 = 0) & greater(v2, depth_limit) = v3 & greater(v1, time_limit) = v4 & depth(v0) = v2)) & ((v4 = 0 & greater(v1, time_limit) = 0) | (v3 = 0 & greater(v2, depth_limit) = 0 & depth(v0) = v2) | ( ~ (v6 = 0) & greater(v5, nitrogen_limit) = v6 & nitrogen(v0) = v5)))))
% 4.79/1.85 | (35) ! [v0] : ! [v1] : ( ~ (nitrogen(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v2 = 0) & dive(v0) = v2) | (((v6 = 0 & greater(v1, nitrogen_limit) = 0) | ( ~ (v5 = 0) & ~ (v3 = 0) & greater(v4, time_limit) = v5 & greater(v2, depth_limit) = v3 & depth(v0) = v2 & time(v0) = v4)) & ((v5 = 0 & greater(v4, time_limit) = 0 & time(v0) = v4) | (v3 = 0 & greater(v2, depth_limit) = 0 & depth(v0) = v2) | ( ~ (v6 = 0) & greater(v1, nitrogen_limit) = v6)))))
% 4.79/1.86 | (36) ! [v0] : ! [v1] : ( ~ (depth(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v2 = 0) & dive(v0) = v2) | (((v6 = 0 & greater(v5, nitrogen_limit) = 0 & nitrogen(v0) = v5) | ( ~ (v4 = 0) & ~ (v2 = 0) & greater(v3, time_limit) = v4 & greater(v1, depth_limit) = v2 & time(v0) = v3)) & ((v4 = 0 & greater(v3, time_limit) = 0 & time(v0) = v3) | (v2 = 0 & greater(v1, depth_limit) = 0) | ( ~ (v6 = 0) & greater(v5, nitrogen_limit) = v6 & nitrogen(v0) = v5)))))
% 4.79/1.86 | (37) ! [v0] : ! [v1] : ( ~ (depth(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v2 = 0) & greater(v3, time_limit) = v4 & greater(v1, depth_limit) = v2 & time(v0) = v3) | ( ~ (v2 = 0) & dive(v0) = v2)))
% 4.79/1.86 |
% 4.79/1.86 | Instantiating formula (28) with all_0_0_0, all_0_1_1 and discharging atoms outcome(all_0_1_1, all_0_0_0) = 0, dive(all_0_1_1) = 0, yields:
% 4.79/1.86 | (38) all_0_0_0 = dci | ? [v0] : ( ~ (v0 = 0) & bad(all_0_0_0) = v0)
% 4.79/1.86 |
% 4.79/1.86 | Instantiating formula (8) with all_0_1_1 and discharging atoms dive(all_0_1_1) = 0, yields:
% 4.79/1.86 | (39) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & greater(v4, nitrogen_limit) = 0 & nitrogen(all_0_1_1) = v4) | ( ~ (v3 = 0) & ~ (v1 = 0) & greater(v2, time_limit) = v3 & greater(v0, depth_limit) = v1 & depth(all_0_1_1) = v0 & time(all_0_1_1) = v2)) & ((v3 = 0 & greater(v2, time_limit) = 0 & time(all_0_1_1) = v2) | (v1 = 0 & greater(v0, depth_limit) = 0 & depth(all_0_1_1) = v0) | ( ~ (v5 = 0) & greater(v4, nitrogen_limit) = v5 & nitrogen(all_0_1_1) = v4)))
% 4.79/1.86 |
% 4.79/1.86 | Instantiating formula (18) with all_0_1_1 and discharging atoms dive(all_0_1_1) = 0, yields:
% 4.79/1.86 | (40) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v1 = 0) & greater(v2, time_limit) = v3 & greater(v0, depth_limit) = v1 & depth(all_0_1_1) = v0 & time(all_0_1_1) = v2)
% 4.79/1.86 |
% 4.79/1.86 | Instantiating formula (32) with all_0_1_1 and discharging atoms dive(all_0_1_1) = 0, yields:
% 4.79/1.86 | (41) ? [v0] : ? [v1] : ? [v2] : (nitrogen(all_0_1_1) = v0 & depth(all_0_1_1) = v1 & time(all_0_1_1) = v2 & padi(v1, v2) = v0)
% 4.79/1.86 |
% 4.79/1.86 | Instantiating formula (30) with all_0_1_1 and discharging atoms dive(all_0_1_1) = 0, yields:
% 4.79/1.86 | (42) ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & outcome(all_0_1_1, dci) = 0) | ( ~ (v1 = 0) & greater(v0, nitrogen_limit) = v1 & nitrogen(all_0_1_1) = v0)) & ((v1 = 0 & greater(v0, nitrogen_limit) = 0 & nitrogen(all_0_1_1) = v0) | ( ~ (v2 = 0) & outcome(all_0_1_1, dci) = v2)))
% 4.79/1.86 |
% 4.79/1.86 | Instantiating (42) with all_24_0_21, all_24_1_22, all_24_2_23 yields:
% 4.79/1.86 | (43) ((all_24_0_21 = 0 & outcome(all_0_1_1, dci) = 0) | ( ~ (all_24_1_22 = 0) & greater(all_24_2_23, nitrogen_limit) = all_24_1_22 & nitrogen(all_0_1_1) = all_24_2_23)) & ((all_24_1_22 = 0 & greater(all_24_2_23, nitrogen_limit) = 0 & nitrogen(all_0_1_1) = all_24_2_23) | ( ~ (all_24_0_21 = 0) & outcome(all_0_1_1, dci) = all_24_0_21))
% 4.79/1.86 |
% 4.79/1.86 | Applying alpha-rule on (43) yields:
% 4.79/1.86 | (44) (all_24_0_21 = 0 & outcome(all_0_1_1, dci) = 0) | ( ~ (all_24_1_22 = 0) & greater(all_24_2_23, nitrogen_limit) = all_24_1_22 & nitrogen(all_0_1_1) = all_24_2_23)
% 4.79/1.86 | (45) (all_24_1_22 = 0 & greater(all_24_2_23, nitrogen_limit) = 0 & nitrogen(all_0_1_1) = all_24_2_23) | ( ~ (all_24_0_21 = 0) & outcome(all_0_1_1, dci) = all_24_0_21)
% 4.79/1.86 |
% 4.79/1.86 | Instantiating (40) with all_25_0_24, all_25_1_25, all_25_2_26, all_25_3_27 yields:
% 4.79/1.86 | (46) ~ (all_25_0_24 = 0) & ~ (all_25_2_26 = 0) & greater(all_25_1_25, time_limit) = all_25_0_24 & greater(all_25_3_27, depth_limit) = all_25_2_26 & depth(all_0_1_1) = all_25_3_27 & time(all_0_1_1) = all_25_1_25
% 4.79/1.86 |
% 4.79/1.86 | Applying alpha-rule on (46) yields:
% 4.79/1.86 | (47) depth(all_0_1_1) = all_25_3_27
% 4.79/1.86 | (48) greater(all_25_3_27, depth_limit) = all_25_2_26
% 4.79/1.86 | (49) ~ (all_25_2_26 = 0)
% 4.79/1.86 | (50) ~ (all_25_0_24 = 0)
% 4.79/1.86 | (51) time(all_0_1_1) = all_25_1_25
% 4.79/1.86 | (52) greater(all_25_1_25, time_limit) = all_25_0_24
% 4.79/1.86 |
% 4.79/1.86 | Instantiating (39) with all_27_0_28, all_27_1_29, all_27_2_30, all_27_3_31, all_27_4_32, all_27_5_33 yields:
% 4.79/1.86 | (53) ((all_27_0_28 = 0 & greater(all_27_1_29, nitrogen_limit) = 0 & nitrogen(all_0_1_1) = all_27_1_29) | ( ~ (all_27_2_30 = 0) & ~ (all_27_4_32 = 0) & greater(all_27_3_31, time_limit) = all_27_2_30 & greater(all_27_5_33, depth_limit) = all_27_4_32 & depth(all_0_1_1) = all_27_5_33 & time(all_0_1_1) = all_27_3_31)) & ((all_27_2_30 = 0 & greater(all_27_3_31, time_limit) = 0 & time(all_0_1_1) = all_27_3_31) | (all_27_4_32 = 0 & greater(all_27_5_33, depth_limit) = 0 & depth(all_0_1_1) = all_27_5_33) | ( ~ (all_27_0_28 = 0) & greater(all_27_1_29, nitrogen_limit) = all_27_0_28 & nitrogen(all_0_1_1) = all_27_1_29))
% 4.79/1.87 |
% 4.79/1.87 | Applying alpha-rule on (53) yields:
% 4.79/1.87 | (54) (all_27_0_28 = 0 & greater(all_27_1_29, nitrogen_limit) = 0 & nitrogen(all_0_1_1) = all_27_1_29) | ( ~ (all_27_2_30 = 0) & ~ (all_27_4_32 = 0) & greater(all_27_3_31, time_limit) = all_27_2_30 & greater(all_27_5_33, depth_limit) = all_27_4_32 & depth(all_0_1_1) = all_27_5_33 & time(all_0_1_1) = all_27_3_31)
% 4.79/1.87 | (55) (all_27_2_30 = 0 & greater(all_27_3_31, time_limit) = 0 & time(all_0_1_1) = all_27_3_31) | (all_27_4_32 = 0 & greater(all_27_5_33, depth_limit) = 0 & depth(all_0_1_1) = all_27_5_33) | ( ~ (all_27_0_28 = 0) & greater(all_27_1_29, nitrogen_limit) = all_27_0_28 & nitrogen(all_0_1_1) = all_27_1_29)
% 4.79/1.87 |
% 4.79/1.87 | Instantiating (41) with all_28_0_34, all_28_1_35, all_28_2_36 yields:
% 4.79/1.87 | (56) nitrogen(all_0_1_1) = all_28_2_36 & depth(all_0_1_1) = all_28_1_35 & time(all_0_1_1) = all_28_0_34 & padi(all_28_1_35, all_28_0_34) = all_28_2_36
% 4.79/1.87 |
% 4.79/1.87 | Applying alpha-rule on (56) yields:
% 4.79/1.87 | (57) nitrogen(all_0_1_1) = all_28_2_36
% 4.79/1.87 | (58) depth(all_0_1_1) = all_28_1_35
% 4.79/1.87 | (59) time(all_0_1_1) = all_28_0_34
% 4.79/1.87 | (60) padi(all_28_1_35, all_28_0_34) = all_28_2_36
% 4.79/1.87 |
% 4.79/1.87 +-Applying beta-rule and splitting (38), into two cases.
% 4.79/1.87 |-Branch one:
% 4.79/1.87 | (61) all_0_0_0 = dci
% 4.79/1.87 |
% 4.79/1.87 | From (61) and (29) follows:
% 4.79/1.87 | (62) outcome(all_0_1_1, dci) = 0
% 4.79/1.87 |
% 4.79/1.87 +-Applying beta-rule and splitting (45), into two cases.
% 4.79/1.87 |-Branch one:
% 4.79/1.87 | (63) all_24_1_22 = 0 & greater(all_24_2_23, nitrogen_limit) = 0 & nitrogen(all_0_1_1) = all_24_2_23
% 4.79/1.87 |
% 4.79/1.87 | Applying alpha-rule on (63) yields:
% 4.79/1.87 | (64) all_24_1_22 = 0
% 4.79/1.87 | (65) greater(all_24_2_23, nitrogen_limit) = 0
% 4.79/1.87 | (66) nitrogen(all_0_1_1) = all_24_2_23
% 4.79/1.87 |
% 4.79/1.87 | Instantiating formula (5) with all_0_1_1, all_24_2_23, all_28_2_36 and discharging atoms nitrogen(all_0_1_1) = all_28_2_36, nitrogen(all_0_1_1) = all_24_2_23, yields:
% 4.79/1.87 | (67) all_28_2_36 = all_24_2_23
% 4.79/1.87 |
% 4.79/1.87 | Instantiating formula (33) with all_0_1_1, all_25_3_27, all_28_1_35 and discharging atoms depth(all_0_1_1) = all_28_1_35, depth(all_0_1_1) = all_25_3_27, yields:
% 4.79/1.87 | (68) all_28_1_35 = all_25_3_27
% 4.79/1.87 |
% 4.79/1.87 | Instantiating formula (7) with all_0_1_1, all_25_1_25, all_28_0_34 and discharging atoms time(all_0_1_1) = all_28_0_34, time(all_0_1_1) = all_25_1_25, yields:
% 4.79/1.87 | (69) all_28_0_34 = all_25_1_25
% 4.79/1.87 |
% 4.79/1.87 | From (67) and (57) follows:
% 4.79/1.87 | (66) nitrogen(all_0_1_1) = all_24_2_23
% 4.79/1.87 |
% 4.79/1.87 | From (68) and (58) follows:
% 4.79/1.87 | (47) depth(all_0_1_1) = all_25_3_27
% 4.79/1.87 |
% 4.79/1.87 | From (69) and (59) follows:
% 4.79/1.87 | (51) time(all_0_1_1) = all_25_1_25
% 4.79/1.87 |
% 4.79/1.87 +-Applying beta-rule and splitting (55), into two cases.
% 4.79/1.87 |-Branch one:
% 4.79/1.87 | (73) (all_27_2_30 = 0 & greater(all_27_3_31, time_limit) = 0 & time(all_0_1_1) = all_27_3_31) | (all_27_4_32 = 0 & greater(all_27_5_33, depth_limit) = 0 & depth(all_0_1_1) = all_27_5_33)
% 4.79/1.87 |
% 4.79/1.87 +-Applying beta-rule and splitting (73), into two cases.
% 4.79/1.87 |-Branch one:
% 4.79/1.87 | (74) all_27_2_30 = 0 & greater(all_27_3_31, time_limit) = 0 & time(all_0_1_1) = all_27_3_31
% 4.79/1.87 |
% 4.79/1.87 | Applying alpha-rule on (74) yields:
% 4.79/1.87 | (75) all_27_2_30 = 0
% 4.79/1.87 | (76) greater(all_27_3_31, time_limit) = 0
% 4.79/1.87 | (77) time(all_0_1_1) = all_27_3_31
% 4.79/1.87 |
% 4.79/1.87 | Instantiating formula (7) with all_0_1_1, all_27_3_31, all_25_1_25 and discharging atoms time(all_0_1_1) = all_27_3_31, time(all_0_1_1) = all_25_1_25, yields:
% 4.79/1.87 | (78) all_27_3_31 = all_25_1_25
% 4.79/1.87 |
% 4.79/1.87 | From (78) and (76) follows:
% 4.79/1.87 | (79) greater(all_25_1_25, time_limit) = 0
% 4.79/1.87 |
% 4.79/1.87 | Instantiating formula (4) with all_25_1_25, time_limit, 0, all_25_0_24 and discharging atoms greater(all_25_1_25, time_limit) = all_25_0_24, greater(all_25_1_25, time_limit) = 0, yields:
% 4.79/1.87 | (80) all_25_0_24 = 0
% 4.79/1.88 |
% 4.79/1.88 | Equations (80) can reduce 50 to:
% 4.79/1.88 | (81) $false
% 4.79/1.88 |
% 4.79/1.88 |-The branch is then unsatisfiable
% 4.79/1.88 |-Branch two:
% 4.79/1.88 | (82) all_27_4_32 = 0 & greater(all_27_5_33, depth_limit) = 0 & depth(all_0_1_1) = all_27_5_33
% 4.79/1.88 |
% 4.79/1.88 | Applying alpha-rule on (82) yields:
% 4.79/1.88 | (83) all_27_4_32 = 0
% 4.79/1.88 | (84) greater(all_27_5_33, depth_limit) = 0
% 4.79/1.88 | (85) depth(all_0_1_1) = all_27_5_33
% 4.79/1.88 |
% 4.79/1.88 | Instantiating formula (33) with all_0_1_1, all_27_5_33, all_25_3_27 and discharging atoms depth(all_0_1_1) = all_27_5_33, depth(all_0_1_1) = all_25_3_27, yields:
% 4.79/1.88 | (86) all_27_5_33 = all_25_3_27
% 4.79/1.88 |
% 4.79/1.88 | From (86) and (84) follows:
% 4.79/1.88 | (87) greater(all_25_3_27, depth_limit) = 0
% 4.79/1.88 |
% 4.79/1.88 | Instantiating formula (4) with all_25_3_27, depth_limit, 0, all_25_2_26 and discharging atoms greater(all_25_3_27, depth_limit) = all_25_2_26, greater(all_25_3_27, depth_limit) = 0, yields:
% 4.79/1.88 | (88) all_25_2_26 = 0
% 4.79/1.88 |
% 4.79/1.88 | Equations (88) can reduce 49 to:
% 4.79/1.88 | (81) $false
% 4.79/1.88 |
% 4.79/1.88 |-The branch is then unsatisfiable
% 4.79/1.88 |-Branch two:
% 4.79/1.88 | (90) ~ (all_27_0_28 = 0) & greater(all_27_1_29, nitrogen_limit) = all_27_0_28 & nitrogen(all_0_1_1) = all_27_1_29
% 4.79/1.88 |
% 4.79/1.88 | Applying alpha-rule on (90) yields:
% 4.79/1.88 | (91) ~ (all_27_0_28 = 0)
% 4.79/1.88 | (92) greater(all_27_1_29, nitrogen_limit) = all_27_0_28
% 4.79/1.88 | (93) nitrogen(all_0_1_1) = all_27_1_29
% 4.79/1.88 |
% 4.79/1.88 | Instantiating formula (5) with all_0_1_1, all_27_1_29, all_24_2_23 and discharging atoms nitrogen(all_0_1_1) = all_27_1_29, nitrogen(all_0_1_1) = all_24_2_23, yields:
% 4.79/1.88 | (94) all_27_1_29 = all_24_2_23
% 4.79/1.88 |
% 4.79/1.88 | From (94) and (92) follows:
% 4.79/1.88 | (95) greater(all_24_2_23, nitrogen_limit) = all_27_0_28
% 4.79/1.88 |
% 4.79/1.88 | Instantiating formula (4) with all_24_2_23, nitrogen_limit, all_27_0_28, 0 and discharging atoms greater(all_24_2_23, nitrogen_limit) = all_27_0_28, greater(all_24_2_23, nitrogen_limit) = 0, yields:
% 4.79/1.88 | (96) all_27_0_28 = 0
% 4.79/1.88 |
% 4.79/1.88 | Equations (96) can reduce 91 to:
% 4.79/1.88 | (81) $false
% 4.79/1.88 |
% 4.79/1.88 |-The branch is then unsatisfiable
% 4.79/1.88 |-Branch two:
% 4.79/1.88 | (98) ~ (all_24_0_21 = 0) & outcome(all_0_1_1, dci) = all_24_0_21
% 4.79/1.88 |
% 4.79/1.88 | Applying alpha-rule on (98) yields:
% 4.79/1.88 | (99) ~ (all_24_0_21 = 0)
% 4.79/1.88 | (100) outcome(all_0_1_1, dci) = all_24_0_21
% 4.79/1.88 |
% 4.79/1.88 | Instantiating formula (15) with all_0_1_1, dci, 0, all_24_0_21 and discharging atoms outcome(all_0_1_1, dci) = all_24_0_21, outcome(all_0_1_1, dci) = 0, yields:
% 4.79/1.88 | (101) all_24_0_21 = 0
% 4.79/1.88 |
% 4.79/1.88 | Equations (101) can reduce 99 to:
% 4.79/1.88 | (81) $false
% 4.79/1.88 |
% 4.79/1.88 |-The branch is then unsatisfiable
% 4.79/1.88 |-Branch two:
% 4.79/1.88 | (103) ~ (all_0_0_0 = dci)
% 4.79/1.88 | (104) ? [v0] : ( ~ (v0 = 0) & bad(all_0_0_0) = v0)
% 4.79/1.88 |
% 4.79/1.88 | Instantiating (104) with all_34_0_37 yields:
% 4.79/1.88 | (105) ~ (all_34_0_37 = 0) & bad(all_0_0_0) = all_34_0_37
% 4.79/1.88 |
% 4.79/1.88 | Applying alpha-rule on (105) yields:
% 4.79/1.88 | (106) ~ (all_34_0_37 = 0)
% 4.79/1.88 | (107) bad(all_0_0_0) = all_34_0_37
% 4.79/1.88 |
% 4.79/1.88 | Instantiating formula (23) with all_0_0_0, all_34_0_37, 0 and discharging atoms bad(all_0_0_0) = all_34_0_37, bad(all_0_0_0) = 0, yields:
% 4.79/1.88 | (108) all_34_0_37 = 0
% 4.79/1.88 |
% 4.79/1.89 | Equations (108) can reduce 106 to:
% 4.79/1.89 | (81) $false
% 4.79/1.89 |
% 4.79/1.89 |-The branch is then unsatisfiable
% 4.79/1.89 % SZS output end Proof for theBenchmark
% 4.79/1.89
% 4.79/1.89 1297ms
%------------------------------------------------------------------------------