TSTP Solution File: LCL672+1.001 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL672+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 09:38:12 EDT 2022
% Result : Theorem 215.25s 166.46s
% Output : Proof 216.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL672+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n029.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 : Tue Jul 5 01:20:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.57/0.61 ____ _
% 0.57/0.61 ___ / __ \_____(_)___ ________ __________
% 0.57/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.61
% 0.57/0.61 A Theorem Prover for First-Order Logic
% 0.57/0.62 (ePrincess v.1.0)
% 0.57/0.62
% 0.57/0.62 (c) Philipp Rümmer, 2009-2015
% 0.57/0.62 (c) Peter Backeman, 2014-2015
% 0.57/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.62 Bug reports to peter@backeman.se
% 0.57/0.62
% 0.57/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.62
% 0.57/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.52/1.00 Prover 0: Preprocessing ...
% 1.85/1.10 Prover 0: Warning: ignoring some quantifiers
% 1.85/1.12 Prover 0: Constructing countermodel ...
% 17.00/5.98 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.22/6.02 Prover 1: Preprocessing ...
% 17.68/6.15 Prover 1: Constructing countermodel ...
% 27.74/8.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 28.02/8.61 Prover 2: Preprocessing ...
% 28.02/8.68 Prover 2: Warning: ignoring some quantifiers
% 28.02/8.68 Prover 2: Constructing countermodel ...
% 38.00/11.59 Prover 0: stopped
% 38.62/11.79 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 38.62/11.81 Prover 3: Preprocessing ...
% 38.62/11.81 Prover 3: Warning: ignoring some quantifiers
% 38.62/11.82 Prover 3: Constructing countermodel ...
% 83.41/53.12 Prover 3: stopped
% 83.67/53.33 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 83.67/53.36 Prover 4: Preprocessing ...
% 84.08/53.43 Prover 4: Warning: ignoring some quantifiers
% 84.08/53.43 Prover 4: Constructing countermodel ...
% 135.96/100.86 Prover 1: stopped
% 136.10/101.06 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 136.21/101.09 Prover 5: Preprocessing ...
% 136.44/101.13 Prover 5: Constructing countermodel ...
% 147.30/110.24 Prover 5: stopped
% 147.56/110.44 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 147.56/110.47 Prover 6: Preprocessing ...
% 147.56/110.51 Prover 6: Warning: ignoring some quantifiers
% 147.56/110.51 Prover 6: Constructing countermodel ...
% 165.31/126.94 Prover 2: stopped
% 165.54/127.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 165.54/127.16 Prover 7: Preprocessing ...
% 165.54/127.18 Prover 7: Proving ...
% 214.50/166.05 Prover 4: stopped
% 214.77/166.25 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 214.85/166.28 Prover 8: Preprocessing ...
% 214.85/166.31 Prover 8: Constructing countermodel ...
% 215.25/166.45 Prover 8: proved (200ms)
% 215.25/166.45 Prover 6: stopped
% 215.25/166.46 Prover 7: stopped
% 215.25/166.46
% 215.25/166.46 No countermodel exists, formula is valid
% 215.25/166.46 % SZS status Theorem for theBenchmark
% 215.25/166.46
% 215.25/166.46 Generating proof ... found it (size 103)
% 216.27/166.76
% 216.27/166.76 % SZS output start Proof for theBenchmark
% 216.27/166.76 Assumed formulas after preprocessing and simplification:
% 216.27/166.76 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (r1(v0, v2) = v3) | ~ (r1(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & r1(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p1(v2) = v1) | ~ (p1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p2(v2) = v1) | ~ (p2(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (r1(v0, v0) = v1)) & ? [v0] : ( ? [v1] : ? [v2] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0) & ? [v1] : ? [v2] : ( ~ (v2 = 0) & p2(v1) = v2 & r1(v0, v1) = 0) & ? [v1] : (r1(v0, v1) = 0 & ? [v2] : ? [v3] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0) & ? [v2] : (r1(v1, v2) = 0 & ! [v3] : ! [v4] : (v4 = 0 | ~ (p1(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & r1(v2, v3) = v5)))) & ( ! [v1] : ! [v2] : (v2 = 0 | ~ (p1(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) | ! [v1] : ! [v2] : (v2 = 0 | ~ (p2(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) | ( ! [v1] : ( ~ (p1(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & r1(v0, v1) = v2) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ? [v3] : (p1(v3) = 0 & r1(v2, v3) = 0))) & ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : r1(v1, v2) = 0) & ! [v1] : ( ~ (r1(v0, v1) = 0) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & p1(v3) = v4 & r1(v2, v3) = 0)) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ? [v3] : (r1(v2, v3) = 0 & ! [v4] : ! [v5] : (v5 = 0 | ~ (p1(v4) = v5) | ? [v6] : ( ~ (v6 = 0) & r1(v3, v4) = v6))))) & ! [v1] : ( ~ (r1(v0, v1) = 0) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ! [v3] : ! [v4] : (v4 = 0 | ~ (p1(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & r1(v2, v3) = v5)) | ! [v3] : ( ~ (r1(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & p1(v4) = v5 & r1(v3, v4) = 0)))))))
% 216.27/166.79 | Applying alpha-rule on (0) yields:
% 216.27/166.79 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0))
% 216.27/166.79 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p1(v2) = v1) | ~ (p1(v2) = v0))
% 216.27/166.79 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (r1(v0, v2) = v3) | ~ (r1(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & r1(v1, v2) = v4))
% 216.27/166.79 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p2(v2) = v1) | ~ (p2(v2) = v0))
% 216.27/166.79 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (r1(v0, v0) = v1))
% 216.27/166.79 | (6) ? [v0] : ( ? [v1] : ? [v2] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0) & ? [v1] : ? [v2] : ( ~ (v2 = 0) & p2(v1) = v2 & r1(v0, v1) = 0) & ? [v1] : (r1(v0, v1) = 0 & ? [v2] : ? [v3] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0) & ? [v2] : (r1(v1, v2) = 0 & ! [v3] : ! [v4] : (v4 = 0 | ~ (p1(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & r1(v2, v3) = v5)))) & ( ! [v1] : ! [v2] : (v2 = 0 | ~ (p1(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) | ! [v1] : ! [v2] : (v2 = 0 | ~ (p2(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) | ( ! [v1] : ( ~ (p1(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & r1(v0, v1) = v2) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ? [v3] : (p1(v3) = 0 & r1(v2, v3) = 0))) & ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : r1(v1, v2) = 0) & ! [v1] : ( ~ (r1(v0, v1) = 0) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & p1(v3) = v4 & r1(v2, v3) = 0)) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ? [v3] : (r1(v2, v3) = 0 & ! [v4] : ! [v5] : (v5 = 0 | ~ (p1(v4) = v5) | ? [v6] : ( ~ (v6 = 0) & r1(v3, v4) = v6))))) & ! [v1] : ( ~ (r1(v0, v1) = 0) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ! [v3] : ! [v4] : (v4 = 0 | ~ (p1(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & r1(v2, v3) = v5)) | ! [v3] : ( ~ (r1(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & p1(v4) = v5 & r1(v3, v4) = 0)))))))
% 216.27/166.80 |
% 216.27/166.80 | Instantiating (6) with all_1_0_0 yields:
% 216.27/166.80 | (7) ? [v0] : ? [v1] : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_1_0_0, v0) = 0) & ? [v0] : ? [v1] : ( ~ (v1 = 0) & p2(v0) = v1 & r1(all_1_0_0, v0) = 0) & ? [v0] : (r1(all_1_0_0, v0) = 0 & ? [v1] : ? [v2] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0) & ? [v1] : (r1(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (p1(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & r1(v1, v2) = v4)))) & ( ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_1_0_0, v0) = v2)) | ! [v0] : ! [v1] : (v1 = 0 | ~ (p2(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_1_0_0, v0) = v2)) | ( ! [v0] : ( ~ (p1(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & r1(all_1_0_0, v0) = v1) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : (p1(v2) = 0 & r1(v1, v2) = 0))) & ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ? [v1] : r1(v0, v1) = 0) & ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0)) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : (r1(v1, v2) = 0 & ! [v3] : ! [v4] : (v4 = 0 | ~ (p1(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & r1(v2, v3) = v5))))) & ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ! [v2] : ! [v3] : (v3 = 0 | ~ (p1(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & r1(v1, v2) = v4)) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & p1(v3) = v4 & r1(v2, v3) = 0))))))
% 216.57/166.81 |
% 216.57/166.81 | Applying alpha-rule on (7) yields:
% 216.57/166.81 | (8) ? [v0] : ? [v1] : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_1_0_0, v0) = 0)
% 216.57/166.81 | (9) ? [v0] : ? [v1] : ( ~ (v1 = 0) & p2(v0) = v1 & r1(all_1_0_0, v0) = 0)
% 216.57/166.81 | (10) ? [v0] : (r1(all_1_0_0, v0) = 0 & ? [v1] : ? [v2] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0) & ? [v1] : (r1(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (p1(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & r1(v1, v2) = v4))))
% 216.57/166.81 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_1_0_0, v0) = v2)) | ! [v0] : ! [v1] : (v1 = 0 | ~ (p2(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_1_0_0, v0) = v2)) | ( ! [v0] : ( ~ (p1(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & r1(all_1_0_0, v0) = v1) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : (p1(v2) = 0 & r1(v1, v2) = 0))) & ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ? [v1] : r1(v0, v1) = 0) & ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0)) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : (r1(v1, v2) = 0 & ! [v3] : ! [v4] : (v4 = 0 | ~ (p1(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & r1(v2, v3) = v5))))) & ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ! [v2] : ! [v3] : (v3 = 0 | ~ (p1(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & r1(v1, v2) = v4)) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & p1(v3) = v4 & r1(v2, v3) = 0)))))
% 216.57/166.81 |
% 216.57/166.81 | Instantiating (10) with all_2_0_1 yields:
% 216.57/166.81 | (12) r1(all_1_0_0, all_2_0_1) = 0 & ? [v0] : ? [v1] : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_2_0_1, v0) = 0) & ? [v0] : (r1(all_2_0_1, v0) = 0 & ! [v1] : ! [v2] : (v2 = 0 | ~ (p1(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r1(v0, v1) = v3)))
% 216.57/166.82 |
% 216.57/166.82 | Applying alpha-rule on (12) yields:
% 216.57/166.82 | (13) r1(all_1_0_0, all_2_0_1) = 0
% 216.57/166.82 | (14) ? [v0] : ? [v1] : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_2_0_1, v0) = 0)
% 216.57/166.82 | (15) ? [v0] : (r1(all_2_0_1, v0) = 0 & ! [v1] : ! [v2] : (v2 = 0 | ~ (p1(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r1(v0, v1) = v3)))
% 216.57/166.82 |
% 216.57/166.82 | Instantiating (9) with all_4_0_2, all_4_1_3 yields:
% 216.57/166.82 | (16) ~ (all_4_0_2 = 0) & p2(all_4_1_3) = all_4_0_2 & r1(all_1_0_0, all_4_1_3) = 0
% 216.57/166.82 |
% 216.57/166.82 | Applying alpha-rule on (16) yields:
% 216.57/166.82 | (17) ~ (all_4_0_2 = 0)
% 216.57/166.82 | (18) p2(all_4_1_3) = all_4_0_2
% 216.57/166.82 | (19) r1(all_1_0_0, all_4_1_3) = 0
% 216.57/166.82 |
% 216.57/166.82 | Instantiating (8) with all_6_0_4, all_6_1_5 yields:
% 216.57/166.82 | (20) ~ (all_6_0_4 = 0) & p1(all_6_1_5) = all_6_0_4 & r1(all_1_0_0, all_6_1_5) = 0
% 216.57/166.82 |
% 216.57/166.82 | Applying alpha-rule on (20) yields:
% 216.57/166.82 | (21) ~ (all_6_0_4 = 0)
% 216.57/166.82 | (22) p1(all_6_1_5) = all_6_0_4
% 216.57/166.82 | (23) r1(all_1_0_0, all_6_1_5) = 0
% 216.57/166.82 |
% 216.57/166.82 | Instantiating (15) with all_8_0_6 yields:
% 216.57/166.82 | (24) r1(all_2_0_1, all_8_0_6) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_8_0_6, v0) = v2))
% 216.57/166.82 |
% 216.57/166.82 | Applying alpha-rule on (24) yields:
% 216.57/166.82 | (25) r1(all_2_0_1, all_8_0_6) = 0
% 216.57/166.82 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_8_0_6, v0) = v2))
% 216.57/166.82 |
% 216.57/166.82 | Instantiating (14) with all_11_0_7, all_11_1_8 yields:
% 216.57/166.82 | (27) ~ (all_11_0_7 = 0) & p1(all_11_1_8) = all_11_0_7 & r1(all_2_0_1, all_11_1_8) = 0
% 216.57/166.82 |
% 216.57/166.82 | Applying alpha-rule on (27) yields:
% 216.57/166.82 | (28) ~ (all_11_0_7 = 0)
% 216.57/166.82 | (29) p1(all_11_1_8) = all_11_0_7
% 216.57/166.82 | (30) r1(all_2_0_1, all_11_1_8) = 0
% 216.57/166.82 |
% 216.57/166.82 | Instantiating formula (26) with all_11_0_7, all_11_1_8 and discharging atoms p1(all_11_1_8) = all_11_0_7, yields:
% 216.57/166.82 | (31) all_11_0_7 = 0 | ? [v0] : ( ~ (v0 = 0) & r1(all_8_0_6, all_11_1_8) = v0)
% 216.57/166.82 |
% 216.57/166.82 | Instantiating formula (26) with all_6_0_4, all_6_1_5 and discharging atoms p1(all_6_1_5) = all_6_0_4, yields:
% 216.57/166.82 | (32) all_6_0_4 = 0 | ? [v0] : ( ~ (v0 = 0) & r1(all_8_0_6, all_6_1_5) = v0)
% 216.57/166.82 |
% 216.57/166.82 +-Applying beta-rule and splitting (11), into two cases.
% 216.57/166.82 |-Branch one:
% 216.57/166.82 | (33) ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_1_0_0, v0) = v2)) | ! [v0] : ! [v1] : (v1 = 0 | ~ (p2(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_1_0_0, v0) = v2))
% 216.57/166.82 |
% 216.57/166.82 +-Applying beta-rule and splitting (33), into two cases.
% 216.57/166.82 |-Branch one:
% 216.57/166.82 | (34) ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_1_0_0, v0) = v2))
% 216.57/166.82 |
% 216.57/166.82 | Instantiating formula (34) with all_6_0_4, all_6_1_5 and discharging atoms p1(all_6_1_5) = all_6_0_4, yields:
% 216.57/166.82 | (35) all_6_0_4 = 0 | ? [v0] : ( ~ (v0 = 0) & r1(all_1_0_0, all_6_1_5) = v0)
% 216.57/166.82 |
% 216.57/166.82 +-Applying beta-rule and splitting (32), into two cases.
% 216.57/166.82 |-Branch one:
% 216.57/166.82 | (36) all_6_0_4 = 0
% 216.57/166.82 |
% 216.57/166.82 | Equations (36) can reduce 21 to:
% 216.57/166.82 | (37) $false
% 216.57/166.82 |
% 216.57/166.82 |-The branch is then unsatisfiable
% 216.57/166.82 |-Branch two:
% 216.57/166.82 | (21) ~ (all_6_0_4 = 0)
% 216.57/166.82 | (39) ? [v0] : ( ~ (v0 = 0) & r1(all_8_0_6, all_6_1_5) = v0)
% 216.57/166.82 |
% 216.57/166.82 +-Applying beta-rule and splitting (35), into two cases.
% 216.57/166.82 |-Branch one:
% 216.57/166.82 | (36) all_6_0_4 = 0
% 216.57/166.82 |
% 216.57/166.82 | Equations (36) can reduce 21 to:
% 216.57/166.82 | (37) $false
% 216.57/166.82 |
% 216.57/166.82 |-The branch is then unsatisfiable
% 216.57/166.82 |-Branch two:
% 216.57/166.82 | (21) ~ (all_6_0_4 = 0)
% 216.57/166.83 | (43) ? [v0] : ( ~ (v0 = 0) & r1(all_1_0_0, all_6_1_5) = v0)
% 216.57/166.83 |
% 216.57/166.83 | Instantiating (43) with all_30_0_10 yields:
% 216.57/166.83 | (44) ~ (all_30_0_10 = 0) & r1(all_1_0_0, all_6_1_5) = all_30_0_10
% 216.57/166.83 |
% 216.57/166.83 | Applying alpha-rule on (44) yields:
% 216.57/166.83 | (45) ~ (all_30_0_10 = 0)
% 216.57/166.83 | (46) r1(all_1_0_0, all_6_1_5) = all_30_0_10
% 216.57/166.83 |
% 216.57/166.83 | Instantiating formula (1) with all_1_0_0, all_6_1_5, all_30_0_10, 0 and discharging atoms r1(all_1_0_0, all_6_1_5) = all_30_0_10, r1(all_1_0_0, all_6_1_5) = 0, yields:
% 216.57/166.83 | (47) all_30_0_10 = 0
% 216.57/166.83 |
% 216.57/166.83 | Equations (47) can reduce 45 to:
% 216.57/166.83 | (37) $false
% 216.57/166.83 |
% 216.57/166.83 |-The branch is then unsatisfiable
% 216.57/166.83 |-Branch two:
% 216.57/166.83 | (49) ! [v0] : ! [v1] : (v1 = 0 | ~ (p2(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_1_0_0, v0) = v2))
% 216.57/166.83 |
% 216.57/166.83 | Instantiating formula (49) with all_4_0_2, all_4_1_3 and discharging atoms p2(all_4_1_3) = all_4_0_2, yields:
% 216.57/166.83 | (50) all_4_0_2 = 0 | ? [v0] : ( ~ (v0 = 0) & r1(all_1_0_0, all_4_1_3) = v0)
% 216.57/166.83 |
% 216.57/166.83 +-Applying beta-rule and splitting (50), into two cases.
% 216.57/166.83 |-Branch one:
% 216.57/166.83 | (51) all_4_0_2 = 0
% 216.57/166.83 |
% 216.57/166.83 | Equations (51) can reduce 17 to:
% 216.57/166.83 | (37) $false
% 216.57/166.83 |
% 216.57/166.83 |-The branch is then unsatisfiable
% 216.57/166.83 |-Branch two:
% 216.57/166.83 | (17) ~ (all_4_0_2 = 0)
% 216.57/166.83 | (54) ? [v0] : ( ~ (v0 = 0) & r1(all_1_0_0, all_4_1_3) = v0)
% 216.57/166.83 |
% 216.57/166.83 | Instantiating (54) with all_30_0_14 yields:
% 216.57/166.83 | (55) ~ (all_30_0_14 = 0) & r1(all_1_0_0, all_4_1_3) = all_30_0_14
% 216.57/166.83 |
% 216.57/166.83 | Applying alpha-rule on (55) yields:
% 216.57/166.83 | (56) ~ (all_30_0_14 = 0)
% 216.57/166.83 | (57) r1(all_1_0_0, all_4_1_3) = all_30_0_14
% 216.57/166.83 |
% 216.57/166.83 | Instantiating formula (1) with all_1_0_0, all_4_1_3, all_30_0_14, 0 and discharging atoms r1(all_1_0_0, all_4_1_3) = all_30_0_14, r1(all_1_0_0, all_4_1_3) = 0, yields:
% 216.57/166.83 | (58) all_30_0_14 = 0
% 216.57/166.83 |
% 216.57/166.83 | Equations (58) can reduce 56 to:
% 216.57/166.83 | (37) $false
% 216.57/166.83 |
% 216.57/166.83 |-The branch is then unsatisfiable
% 216.57/166.83 |-Branch two:
% 216.57/166.83 | (60) ! [v0] : ( ~ (p1(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & r1(all_1_0_0, v0) = v1) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : (p1(v2) = 0 & r1(v1, v2) = 0))) & ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ? [v1] : r1(v0, v1) = 0) & ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0)) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : (r1(v1, v2) = 0 & ! [v3] : ! [v4] : (v4 = 0 | ~ (p1(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & r1(v2, v3) = v5))))) & ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ! [v2] : ! [v3] : (v3 = 0 | ~ (p1(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & r1(v1, v2) = v4)) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & p1(v3) = v4 & r1(v2, v3) = 0))))
% 216.57/166.83 |
% 216.57/166.83 | Applying alpha-rule on (60) yields:
% 216.57/166.83 | (61) ! [v0] : ( ~ (p1(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & r1(all_1_0_0, v0) = v1) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : (p1(v2) = 0 & r1(v1, v2) = 0)))
% 216.57/166.83 | (62) ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ? [v1] : r1(v0, v1) = 0)
% 216.57/166.83 | (63) ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0)) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : (r1(v1, v2) = 0 & ! [v3] : ! [v4] : (v4 = 0 | ~ (p1(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & r1(v2, v3) = v5)))))
% 216.57/166.83 | (64) ! [v0] : ( ~ (r1(all_1_0_0, v0) = 0) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ! [v2] : ! [v3] : (v3 = 0 | ~ (p1(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & r1(v1, v2) = v4)) | ! [v2] : ( ~ (r1(v1, v2) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & p1(v3) = v4 & r1(v2, v3) = 0))))
% 216.57/166.83 |
% 216.57/166.84 | Instantiating formula (62) with all_2_0_1 and discharging atoms r1(all_1_0_0, all_2_0_1) = 0, yields:
% 216.57/166.84 | (65) ? [v0] : r1(all_2_0_1, v0) = 0
% 216.57/166.84 |
% 216.57/166.84 | Instantiating formula (63) with all_2_0_1 and discharging atoms r1(all_1_0_0, all_2_0_1) = 0, yields:
% 216.57/166.84 | (66) ! [v0] : ( ~ (r1(all_2_0_1, v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0)) | ! [v0] : ( ~ (r1(all_2_0_1, v0) = 0) | ? [v1] : (r1(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (p1(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & r1(v1, v2) = v4))))
% 216.57/166.84 |
% 216.57/166.84 | Instantiating formula (64) with all_2_0_1 and discharging atoms r1(all_1_0_0, all_2_0_1) = 0, yields:
% 216.57/166.84 | (67) ! [v0] : ( ~ (r1(all_2_0_1, v0) = 0) | ! [v1] : ! [v2] : (v2 = 0 | ~ (p1(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r1(v0, v1) = v3)) | ! [v1] : ( ~ (r1(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & p1(v2) = v3 & r1(v1, v2) = 0)))
% 216.57/166.84 |
% 216.57/166.84 | Instantiating formula (67) with all_11_1_8 and discharging atoms r1(all_2_0_1, all_11_1_8) = 0, yields:
% 216.57/166.84 | (68) ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_11_1_8, v0) = v2)) | ! [v0] : ( ~ (r1(all_11_1_8, v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0))
% 216.57/166.84 |
% 216.57/166.84 | Instantiating (65) with all_27_0_18 yields:
% 216.57/166.84 | (69) r1(all_2_0_1, all_27_0_18) = 0
% 216.57/166.84 |
% 216.57/166.84 +-Applying beta-rule and splitting (31), into two cases.
% 216.57/166.84 |-Branch one:
% 216.57/166.84 | (70) all_11_0_7 = 0
% 216.57/166.84 |
% 216.57/166.84 | Equations (70) can reduce 28 to:
% 216.57/166.84 | (37) $false
% 216.57/166.84 |
% 216.57/166.84 |-The branch is then unsatisfiable
% 216.57/166.84 |-Branch two:
% 216.57/166.84 | (28) ~ (all_11_0_7 = 0)
% 216.57/166.84 | (73) ? [v0] : ( ~ (v0 = 0) & r1(all_8_0_6, all_11_1_8) = v0)
% 216.57/166.84 |
% 216.57/166.84 +-Applying beta-rule and splitting (66), into two cases.
% 216.57/166.84 |-Branch one:
% 216.57/166.84 | (74) ! [v0] : ( ~ (r1(all_2_0_1, v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0))
% 216.57/166.84 |
% 216.57/166.84 | Instantiating formula (74) with all_8_0_6 and discharging atoms r1(all_2_0_1, all_8_0_6) = 0, yields:
% 216.57/166.84 | (75) ? [v0] : ? [v1] : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_8_0_6, v0) = 0)
% 216.57/166.84 |
% 216.57/166.84 | Instantiating (75) with all_47_0_21, all_47_1_22 yields:
% 216.57/166.84 | (76) ~ (all_47_0_21 = 0) & p1(all_47_1_22) = all_47_0_21 & r1(all_8_0_6, all_47_1_22) = 0
% 216.57/166.84 |
% 216.57/166.84 | Applying alpha-rule on (76) yields:
% 216.57/166.84 | (77) ~ (all_47_0_21 = 0)
% 216.57/166.84 | (78) p1(all_47_1_22) = all_47_0_21
% 216.57/166.84 | (79) r1(all_8_0_6, all_47_1_22) = 0
% 216.57/166.84 |
% 216.57/166.84 | Instantiating formula (26) with all_47_0_21, all_47_1_22 and discharging atoms p1(all_47_1_22) = all_47_0_21, yields:
% 216.57/166.84 | (80) all_47_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & r1(all_8_0_6, all_47_1_22) = v0)
% 216.57/166.84 |
% 216.57/166.84 +-Applying beta-rule and splitting (80), into two cases.
% 216.57/166.84 |-Branch one:
% 216.57/166.84 | (81) all_47_0_21 = 0
% 216.57/166.84 |
% 216.57/166.84 | Equations (81) can reduce 77 to:
% 216.57/166.84 | (37) $false
% 216.57/166.84 |
% 216.57/166.84 |-The branch is then unsatisfiable
% 216.57/166.84 |-Branch two:
% 216.57/166.84 | (77) ~ (all_47_0_21 = 0)
% 216.57/166.84 | (84) ? [v0] : ( ~ (v0 = 0) & r1(all_8_0_6, all_47_1_22) = v0)
% 216.57/166.84 |
% 216.57/166.84 | Instantiating (84) with all_66_0_29 yields:
% 216.57/166.84 | (85) ~ (all_66_0_29 = 0) & r1(all_8_0_6, all_47_1_22) = all_66_0_29
% 216.57/166.84 |
% 216.57/166.84 | Applying alpha-rule on (85) yields:
% 216.57/166.84 | (86) ~ (all_66_0_29 = 0)
% 216.57/166.84 | (87) r1(all_8_0_6, all_47_1_22) = all_66_0_29
% 216.57/166.84 |
% 216.57/166.84 | Instantiating formula (1) with all_8_0_6, all_47_1_22, all_66_0_29, 0 and discharging atoms r1(all_8_0_6, all_47_1_22) = all_66_0_29, r1(all_8_0_6, all_47_1_22) = 0, yields:
% 216.57/166.84 | (88) all_66_0_29 = 0
% 216.57/166.84 |
% 216.57/166.84 | Equations (88) can reduce 86 to:
% 216.57/166.84 | (37) $false
% 216.57/166.84 |
% 216.57/166.84 |-The branch is then unsatisfiable
% 216.57/166.84 |-Branch two:
% 216.57/166.84 | (90) ! [v0] : ( ~ (r1(all_2_0_1, v0) = 0) | ? [v1] : (r1(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (p1(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & r1(v1, v2) = v4))))
% 216.57/166.84 |
% 216.57/166.84 | Instantiating formula (90) with all_27_0_18 and discharging atoms r1(all_2_0_1, all_27_0_18) = 0, yields:
% 216.57/166.84 | (91) ? [v0] : (r1(all_27_0_18, v0) = 0 & ! [v1] : ! [v2] : (v2 = 0 | ~ (p1(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r1(v0, v1) = v3)))
% 216.57/166.85 |
% 216.57/166.85 | Instantiating formula (90) with all_11_1_8 and discharging atoms r1(all_2_0_1, all_11_1_8) = 0, yields:
% 216.57/166.85 | (92) ? [v0] : (r1(all_11_1_8, v0) = 0 & ! [v1] : ! [v2] : (v2 = 0 | ~ (p1(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r1(v0, v1) = v3)))
% 216.57/166.85 |
% 216.57/166.85 | Instantiating formula (90) with all_8_0_6 and discharging atoms r1(all_2_0_1, all_8_0_6) = 0, yields:
% 216.57/166.85 | (93) ? [v0] : (r1(all_8_0_6, v0) = 0 & ! [v1] : ! [v2] : (v2 = 0 | ~ (p1(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & r1(v0, v1) = v3)))
% 216.57/166.85 |
% 216.57/166.85 | Instantiating (93) with all_47_0_34 yields:
% 216.57/166.85 | (94) r1(all_8_0_6, all_47_0_34) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_47_0_34, v0) = v2))
% 216.57/166.85 |
% 216.57/166.85 | Applying alpha-rule on (94) yields:
% 216.57/166.85 | (95) r1(all_8_0_6, all_47_0_34) = 0
% 216.57/166.85 | (96) ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_47_0_34, v0) = v2))
% 216.57/166.85 |
% 216.57/166.85 | Instantiating formula (96) with all_11_0_7, all_11_1_8 and discharging atoms p1(all_11_1_8) = all_11_0_7, yields:
% 216.57/166.85 | (97) all_11_0_7 = 0 | ? [v0] : ( ~ (v0 = 0) & r1(all_47_0_34, all_11_1_8) = v0)
% 216.57/166.85 |
% 216.57/166.85 | Instantiating (92) with all_50_0_35 yields:
% 216.57/166.85 | (98) r1(all_11_1_8, all_50_0_35) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_50_0_35, v0) = v2))
% 216.57/166.85 |
% 216.57/166.85 | Applying alpha-rule on (98) yields:
% 216.57/166.85 | (99) r1(all_11_1_8, all_50_0_35) = 0
% 216.57/166.85 | (100) ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_50_0_35, v0) = v2))
% 216.57/166.85 |
% 216.57/166.85 | Instantiating formula (100) with all_11_0_7, all_11_1_8 and discharging atoms p1(all_11_1_8) = all_11_0_7, yields:
% 216.57/166.85 | (101) all_11_0_7 = 0 | ? [v0] : ( ~ (v0 = 0) & r1(all_50_0_35, all_11_1_8) = v0)
% 216.57/166.85 |
% 216.57/166.85 | Instantiating (91) with all_53_0_36 yields:
% 216.57/166.85 | (102) r1(all_27_0_18, all_53_0_36) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_53_0_36, v0) = v2))
% 216.57/166.85 |
% 216.57/166.85 | Applying alpha-rule on (102) yields:
% 216.57/166.85 | (103) r1(all_27_0_18, all_53_0_36) = 0
% 216.57/166.85 | (104) ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_53_0_36, v0) = v2))
% 216.57/166.85 |
% 216.57/166.85 | Instantiating formula (104) with all_11_0_7, all_11_1_8 and discharging atoms p1(all_11_1_8) = all_11_0_7, yields:
% 216.57/166.85 | (105) all_11_0_7 = 0 | ? [v0] : ( ~ (v0 = 0) & r1(all_53_0_36, all_11_1_8) = v0)
% 216.57/166.85 |
% 216.57/166.85 +-Applying beta-rule and splitting (97), into two cases.
% 216.57/166.85 |-Branch one:
% 216.57/166.85 | (70) all_11_0_7 = 0
% 216.57/166.85 |
% 216.57/166.85 | Equations (70) can reduce 28 to:
% 216.57/166.85 | (37) $false
% 216.57/166.85 |
% 216.57/166.85 |-The branch is then unsatisfiable
% 216.57/166.85 |-Branch two:
% 216.57/166.85 | (28) ~ (all_11_0_7 = 0)
% 216.57/166.85 | (109) ? [v0] : ( ~ (v0 = 0) & r1(all_47_0_34, all_11_1_8) = v0)
% 216.57/166.85 |
% 216.57/166.85 +-Applying beta-rule and splitting (101), into two cases.
% 216.57/166.85 |-Branch one:
% 216.57/166.85 | (70) all_11_0_7 = 0
% 216.57/166.85 |
% 216.57/166.85 | Equations (70) can reduce 28 to:
% 216.57/166.85 | (37) $false
% 216.57/166.85 |
% 216.57/166.85 |-The branch is then unsatisfiable
% 216.57/166.85 |-Branch two:
% 216.57/166.85 | (28) ~ (all_11_0_7 = 0)
% 216.57/166.85 | (113) ? [v0] : ( ~ (v0 = 0) & r1(all_50_0_35, all_11_1_8) = v0)
% 216.57/166.85 |
% 216.57/166.85 +-Applying beta-rule and splitting (105), into two cases.
% 216.57/166.85 |-Branch one:
% 216.57/166.85 | (70) all_11_0_7 = 0
% 216.57/166.85 |
% 216.57/166.85 | Equations (70) can reduce 28 to:
% 216.57/166.85 | (37) $false
% 216.57/166.85 |
% 216.57/166.85 |-The branch is then unsatisfiable
% 216.57/166.85 |-Branch two:
% 216.57/166.85 | (28) ~ (all_11_0_7 = 0)
% 216.57/166.85 | (117) ? [v0] : ( ~ (v0 = 0) & r1(all_53_0_36, all_11_1_8) = v0)
% 216.57/166.85 |
% 216.57/166.85 +-Applying beta-rule and splitting (68), into two cases.
% 216.57/166.85 |-Branch one:
% 216.57/166.85 | (118) ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_11_1_8, v0) = v2))
% 216.57/166.85 |
% 216.57/166.85 | Instantiating formula (118) with all_11_0_7, all_11_1_8 and discharging atoms p1(all_11_1_8) = all_11_0_7, yields:
% 216.57/166.85 | (119) all_11_0_7 = 0 | ? [v0] : ( ~ (v0 = 0) & r1(all_11_1_8, all_11_1_8) = v0)
% 216.57/166.86 |
% 216.57/166.86 +-Applying beta-rule and splitting (119), into two cases.
% 216.57/166.86 |-Branch one:
% 216.57/166.86 | (70) all_11_0_7 = 0
% 216.57/166.86 |
% 216.57/166.86 | Equations (70) can reduce 28 to:
% 216.57/166.86 | (37) $false
% 216.57/166.86 |
% 216.57/166.86 |-The branch is then unsatisfiable
% 216.57/166.86 |-Branch two:
% 216.57/166.86 | (28) ~ (all_11_0_7 = 0)
% 216.57/166.86 | (123) ? [v0] : ( ~ (v0 = 0) & r1(all_11_1_8, all_11_1_8) = v0)
% 216.57/166.86 |
% 216.57/166.86 | Instantiating (123) with all_167_0_77 yields:
% 216.57/166.86 | (124) ~ (all_167_0_77 = 0) & r1(all_11_1_8, all_11_1_8) = all_167_0_77
% 216.57/166.86 |
% 216.57/166.86 | Applying alpha-rule on (124) yields:
% 216.57/166.86 | (125) ~ (all_167_0_77 = 0)
% 216.57/166.86 | (126) r1(all_11_1_8, all_11_1_8) = all_167_0_77
% 216.57/166.86 |
% 216.57/166.86 | Instantiating formula (5) with all_167_0_77, all_11_1_8 and discharging atoms r1(all_11_1_8, all_11_1_8) = all_167_0_77, yields:
% 216.57/166.86 | (127) all_167_0_77 = 0
% 216.57/166.86 |
% 216.57/166.86 | Equations (127) can reduce 125 to:
% 216.57/166.86 | (37) $false
% 216.57/166.86 |
% 216.57/166.86 |-The branch is then unsatisfiable
% 216.57/166.86 |-Branch two:
% 216.57/166.86 | (129) ! [v0] : ( ~ (r1(all_11_1_8, v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & p1(v1) = v2 & r1(v0, v1) = 0))
% 216.57/166.86 |
% 216.57/166.86 | Instantiating formula (129) with all_50_0_35 and discharging atoms r1(all_11_1_8, all_50_0_35) = 0, yields:
% 216.57/166.86 | (130) ? [v0] : ? [v1] : ( ~ (v1 = 0) & p1(v0) = v1 & r1(all_50_0_35, v0) = 0)
% 216.57/166.86 |
% 216.57/166.86 | Instantiating (130) with all_133_0_81, all_133_1_82 yields:
% 216.57/166.86 | (131) ~ (all_133_0_81 = 0) & p1(all_133_1_82) = all_133_0_81 & r1(all_50_0_35, all_133_1_82) = 0
% 216.57/166.86 |
% 216.57/166.86 | Applying alpha-rule on (131) yields:
% 216.57/166.86 | (132) ~ (all_133_0_81 = 0)
% 216.57/166.86 | (133) p1(all_133_1_82) = all_133_0_81
% 216.57/166.86 | (134) r1(all_50_0_35, all_133_1_82) = 0
% 216.57/166.86 |
% 216.57/166.86 | Instantiating formula (100) with all_133_0_81, all_133_1_82 and discharging atoms p1(all_133_1_82) = all_133_0_81, yields:
% 216.57/166.86 | (135) all_133_0_81 = 0 | ? [v0] : ( ~ (v0 = 0) & r1(all_50_0_35, all_133_1_82) = v0)
% 216.57/166.86 |
% 216.57/166.86 +-Applying beta-rule and splitting (135), into two cases.
% 216.57/166.86 |-Branch one:
% 216.57/166.86 | (136) all_133_0_81 = 0
% 216.57/166.86 |
% 216.57/166.86 | Equations (136) can reduce 132 to:
% 216.57/166.86 | (37) $false
% 216.57/166.86 |
% 216.57/166.86 |-The branch is then unsatisfiable
% 216.57/166.86 |-Branch two:
% 216.57/166.86 | (132) ~ (all_133_0_81 = 0)
% 216.57/166.86 | (139) ? [v0] : ( ~ (v0 = 0) & r1(all_50_0_35, all_133_1_82) = v0)
% 216.57/166.86 |
% 216.57/166.86 | Instantiating (139) with all_181_0_112 yields:
% 216.57/166.86 | (140) ~ (all_181_0_112 = 0) & r1(all_50_0_35, all_133_1_82) = all_181_0_112
% 216.57/166.86 |
% 216.57/166.86 | Applying alpha-rule on (140) yields:
% 216.57/166.86 | (141) ~ (all_181_0_112 = 0)
% 216.57/166.86 | (142) r1(all_50_0_35, all_133_1_82) = all_181_0_112
% 216.57/166.86 |
% 216.57/166.86 | Instantiating formula (1) with all_50_0_35, all_133_1_82, all_181_0_112, 0 and discharging atoms r1(all_50_0_35, all_133_1_82) = all_181_0_112, r1(all_50_0_35, all_133_1_82) = 0, yields:
% 216.57/166.86 | (143) all_181_0_112 = 0
% 216.57/166.86 |
% 216.57/166.86 | Equations (143) can reduce 141 to:
% 216.57/166.86 | (37) $false
% 216.57/166.86 |
% 216.57/166.86 |-The branch is then unsatisfiable
% 216.57/166.86 % SZS output end Proof for theBenchmark
% 216.57/166.86
% 216.57/166.86 166231ms
%------------------------------------------------------------------------------