TSTP Solution File: NUN068+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUN068+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 16:25:08 EDT 2022
% Result : Theorem 171.27s 135.95s
% Output : Proof 176.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN068+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 2 08:25:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.53/0.59 ____ _
% 0.53/0.59 ___ / __ \_____(_)___ ________ __________
% 0.53/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.59
% 0.53/0.59 A Theorem Prover for First-Order Logic
% 0.53/0.59 (ePrincess v.1.0)
% 0.53/0.59
% 0.53/0.59 (c) Philipp Rümmer, 2009-2015
% 0.53/0.59 (c) Peter Backeman, 2014-2015
% 0.53/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.59 Bug reports to peter@backeman.se
% 0.53/0.59
% 0.53/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.59
% 0.53/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.77/0.96 Prover 0: Preprocessing ...
% 2.15/1.10 Prover 0: Warning: ignoring some quantifiers
% 2.15/1.11 Prover 0: Constructing countermodel ...
% 3.09/1.37 Prover 0: gave up
% 3.09/1.37 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.09/1.40 Prover 1: Preprocessing ...
% 3.46/1.47 Prover 1: Warning: ignoring some quantifiers
% 3.46/1.48 Prover 1: Constructing countermodel ...
% 4.10/1.64 Prover 1: gave up
% 4.10/1.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.10/1.66 Prover 2: Preprocessing ...
% 4.34/1.70 Prover 2: Warning: ignoring some quantifiers
% 4.34/1.71 Prover 2: Constructing countermodel ...
% 4.87/1.80 Prover 2: gave up
% 4.87/1.80 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.87/1.82 Prover 3: Preprocessing ...
% 5.10/1.84 Prover 3: Warning: ignoring some quantifiers
% 5.10/1.84 Prover 3: Constructing countermodel ...
% 5.43/1.92 Prover 3: gave up
% 5.43/1.92 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.43/1.93 Prover 4: Preprocessing ...
% 5.72/1.97 Prover 4: Warning: ignoring some quantifiers
% 5.72/1.98 Prover 4: Constructing countermodel ...
% 6.41/2.13 Prover 4: gave up
% 6.41/2.13 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.41/2.15 Prover 5: Preprocessing ...
% 6.54/2.17 Prover 5: Warning: ignoring some quantifiers
% 6.54/2.18 Prover 5: Constructing countermodel ...
% 6.87/2.23 Prover 5: gave up
% 6.87/2.23 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.87/2.25 Prover 6: Preprocessing ...
% 6.87/2.27 Prover 6: Warning: ignoring some quantifiers
% 6.87/2.27 Prover 6: Constructing countermodel ...
% 7.14/2.34 Prover 6: gave up
% 7.14/2.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 7.14/2.36 Prover 7: Preprocessing ...
% 7.49/2.37 Prover 7: Proving ...
% 27.22/12.98 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 27.31/13.01 Prover 8: Preprocessing ...
% 27.31/13.05 Prover 8: Proving ...
% 50.56/31.46 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal
% 50.62/31.49 Prover 9: Preprocessing ...
% 50.62/31.51 Prover 9: Proving ...
% 76.14/52.28 Prover 9: stopped
% 76.36/52.50 Prover 10: Options: -triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 76.43/52.52 Prover 10: Preprocessing ...
% 76.43/52.54 Prover 10: Warning: ignoring some quantifiers
% 76.43/52.54 Prover 10: Constructing countermodel ...
% 76.83/52.61 Prover 10: gave up
% 76.83/52.61 Prover 11: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 76.92/52.63 Prover 11: Preprocessing ...
% 76.92/52.64 Prover 11: Warning: ignoring some quantifiers
% 76.92/52.64 Prover 11: Constructing countermodel ...
% 76.92/52.68 Prover 11: gave up
% 76.92/52.68 Prover 12: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 76.92/52.69 Prover 12: Preprocessing ...
% 76.92/52.71 Prover 12: Proving ...
% 80.61/55.40 Prover 12: stopped
% 80.87/55.60 Prover 13: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 80.87/55.62 Prover 13: Preprocessing ...
% 80.87/55.64 Prover 13: Warning: ignoring some quantifiers
% 80.87/55.64 Prover 13: Constructing countermodel ...
% 81.11/55.68 Prover 13: gave up
% 81.11/55.68 Prover 14: Options: -triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 81.11/55.69 Prover 14: Preprocessing ...
% 81.11/55.70 Prover 14: Warning: ignoring some quantifiers
% 81.11/55.70 Prover 14: Constructing countermodel ...
% 81.32/55.73 Prover 14: gave up
% 81.32/55.73 Prover 15: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 81.32/55.74 Prover 15: Preprocessing ...
% 81.46/55.75 Prover 15: Proving ...
% 149.88/117.50 Prover 15: stopped
% 150.14/117.70 Prover 16: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 150.14/117.72 Prover 16: Preprocessing ...
% 150.14/117.74 Prover 16: Proving ...
% 171.27/135.94 Prover 16: proved (9505ms)
% 171.27/135.94 Prover 7: stopped
% 171.27/135.94 Prover 8: stopped
% 171.27/135.94
% 171.27/135.95 % SZS status Theorem for theBenchmark
% 171.27/135.95
% 171.27/135.95 Generating proof ... found it (size 61)
% 176.46/138.04
% 176.46/138.04 % SZS output start Proof for theBenchmark
% 176.46/138.04 Assumed formulas after preprocessing and simplification:
% 176.46/138.04 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (r4(v5, v4, v3) = v2) | ~ (r4(v5, v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (r3(v5, v4, v3) = v2) | ~ (r3(v5, v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (r2(v4, v3) = v2) | ~ (r2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (r2(v2, v3) = 0) | ~ (r2(v1, v3) = 0)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (r1(v3) = v2) | ~ (r1(v3) = v1)) & ! [v1] : ! [v2] : ( ~ (r2(v1, v2) = 0) | ~ (r1(v2) = 0)) & ! [v1] : (v1 = v0 | ~ (r1(v1) = 0)) & ! [v1] : (v1 = 0 | ~ (r1(v0) = v1)) & ! [v1] : ! [v2] : ? [v3] : ( ! [v4] : (v4 = v3 | ~ (r4(v1, v2, v4) = 0)) & ! [v4] : (v4 = 0 | ~ (r4(v1, v2, v3) = v4))) & ! [v1] : ! [v2] : ? [v3] : ( ! [v4] : (v4 = v3 | ~ (r3(v1, v2, v4) = 0)) & ! [v4] : (v4 = 0 | ~ (r3(v1, v2, v3) = v4))) & ! [v1] : ? [v2] : (r3(v1, v2, v1) = 0 & r1(v2) = 0) & ! [v1] : ? [v2] : ( ! [v3] : (v3 = v2 | ~ (r2(v1, v3) = 0)) & ! [v3] : (v3 = 0 | ~ (r2(v1, v2) = v3))) & ! [v1] : ? [v2] : ? [v3] : (r4(v1, v3, v2) = 0 & r1(v3) = 0 & r1(v2) = 0) & ! [v1] : ! [v2] : ? [v3] : ? [v4] : ? [v5] : (r4(v1, v5, v3) = 0 & r4(v1, v2, v4) = 0 & r3(v4, v1, v3) = 0 & r2(v2, v5) = 0) & ! [v1] : ! [v2] : ? [v3] : ? [v4] : ? [v5] : (r3(v1, v5, v3) = 0 & r3(v1, v2, v4) = 0 & r2(v4, v3) = 0 & r2(v2, v5) = 0) & ! [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = v1 & r2(v2, v1) = 0) | (v3 = 0 & v2 = v1 & r1(v1) = 0)) & ! [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v2 = v1 & r2(v3, v1) = 0 & r1(v3) = 0) | (v3 = 0 & v2 = v1 & r1(v1) = 0)))
% 176.46/138.06 | Instantiating (0) with all_0_0_0 yields:
% 176.46/138.06 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (r4(v4, v3, v2) = v1) | ~ (r4(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (r3(v4, v3, v2) = v1) | ~ (r3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r2(v3, v2) = v1) | ~ (r2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r2(v1, v2) = 0) | ~ (r2(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r1(v2) = v1) | ~ (r1(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (r2(v0, v1) = 0) | ~ (r1(v1) = 0)) & ! [v0] : (v0 = all_0_0_0 | ~ (r1(v0) = 0)) & ! [v0] : (v0 = 0 | ~ (r1(all_0_0_0) = v0)) & ! [v0] : ! [v1] : ? [v2] : ( ! [v3] : (v3 = v2 | ~ (r4(v0, v1, v3) = 0)) & ! [v3] : (v3 = 0 | ~ (r4(v0, v1, v2) = v3))) & ! [v0] : ! [v1] : ? [v2] : ( ! [v3] : (v3 = v2 | ~ (r3(v0, v1, v3) = 0)) & ! [v3] : (v3 = 0 | ~ (r3(v0, v1, v2) = v3))) & ! [v0] : ? [v1] : (r3(v0, v1, v0) = 0 & r1(v1) = 0) & ! [v0] : ? [v1] : ( ! [v2] : (v2 = v1 | ~ (r2(v0, v2) = 0)) & ! [v2] : (v2 = 0 | ~ (r2(v0, v1) = v2))) & ! [v0] : ? [v1] : ? [v2] : (r4(v0, v2, v1) = 0 & r1(v2) = 0 & r1(v1) = 0) & ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : (r4(v0, v4, v2) = 0 & r4(v0, v1, v3) = 0 & r3(v3, v0, v2) = 0 & r2(v1, v4) = 0) & ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : (r3(v0, v4, v2) = 0 & r3(v0, v1, v3) = 0 & r2(v3, v2) = 0 & r2(v1, v4) = 0) & ! [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = v0 & r2(v1, v0) = 0) | (v2 = 0 & v1 = v0 & r1(v0) = 0)) & ! [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v1 = v0 & r2(v2, v0) = 0 & r1(v2) = 0) | (v2 = 0 & v1 = v0 & r1(v0) = 0))
% 176.46/138.07 |
% 176.46/138.07 | Applying alpha-rule on (1) yields:
% 176.46/138.07 | (2) ! [v0] : (v0 = all_0_0_0 | ~ (r1(v0) = 0))
% 176.46/138.07 | (3) ! [v0] : ! [v1] : ? [v2] : ( ! [v3] : (v3 = v2 | ~ (r3(v0, v1, v3) = 0)) & ! [v3] : (v3 = 0 | ~ (r3(v0, v1, v2) = v3)))
% 176.46/138.07 | (4) ! [v0] : ? [v1] : ? [v2] : (r4(v0, v2, v1) = 0 & r1(v2) = 0 & r1(v1) = 0)
% 176.46/138.07 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (r4(v4, v3, v2) = v1) | ~ (r4(v4, v3, v2) = v0))
% 176.46/138.07 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (r3(v4, v3, v2) = v1) | ~ (r3(v4, v3, v2) = v0))
% 176.46/138.07 | (7) ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : (r4(v0, v4, v2) = 0 & r4(v0, v1, v3) = 0 & r3(v3, v0, v2) = 0 & r2(v1, v4) = 0)
% 176.46/138.07 | (8) ! [v0] : ! [v1] : ? [v2] : ( ! [v3] : (v3 = v2 | ~ (r4(v0, v1, v3) = 0)) & ! [v3] : (v3 = 0 | ~ (r4(v0, v1, v2) = v3)))
% 176.46/138.07 | (9) ! [v0] : ! [v1] : ( ~ (r2(v0, v1) = 0) | ~ (r1(v1) = 0))
% 176.46/138.07 | (10) ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : (r3(v0, v4, v2) = 0 & r3(v0, v1, v3) = 0 & r2(v3, v2) = 0 & r2(v1, v4) = 0)
% 176.46/138.07 | (11) ! [v0] : ? [v1] : (r3(v0, v1, v0) = 0 & r1(v1) = 0)
% 176.46/138.07 | (12) ! [v0] : (v0 = 0 | ~ (r1(all_0_0_0) = v0))
% 176.46/138.07 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r2(v3, v2) = v1) | ~ (r2(v3, v2) = v0))
% 176.46/138.07 | (14) ! [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v1 = v0 & r2(v2, v0) = 0 & r1(v2) = 0) | (v2 = 0 & v1 = v0 & r1(v0) = 0))
% 176.46/138.07 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r1(v2) = v1) | ~ (r1(v2) = v0))
% 176.46/138.07 | (16) ! [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = v0 & r2(v1, v0) = 0) | (v2 = 0 & v1 = v0 & r1(v0) = 0))
% 176.46/138.07 | (17) ! [v0] : ? [v1] : ( ! [v2] : (v2 = v1 | ~ (r2(v0, v2) = 0)) & ! [v2] : (v2 = 0 | ~ (r2(v0, v1) = v2)))
% 176.46/138.08 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r2(v1, v2) = 0) | ~ (r2(v0, v2) = 0))
% 176.46/138.08 |
% 176.46/138.08 | Introducing new symbol ex_4_0_1 defined by:
% 176.46/138.08 | (19) ex_4_0_1 = all_0_0_0
% 176.46/138.08 |
% 176.46/138.08 | Instantiating formula (16) with ex_4_0_1 yields:
% 176.46/138.08 | (20) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = ex_4_0_1 & r2(v0, ex_4_0_1) = 0) | (v1 = 0 & v0 = ex_4_0_1 & r1(ex_4_0_1) = 0))
% 176.46/138.08 |
% 176.46/138.08 | Instantiating (20) with all_5_0_2, all_5_1_3, all_5_2_4 yields:
% 176.46/138.08 | (21) (all_5_0_2 = 0 & all_5_1_3 = ex_4_0_1 & r2(all_5_2_4, ex_4_0_1) = 0) | (all_5_1_3 = 0 & all_5_2_4 = ex_4_0_1 & r1(ex_4_0_1) = 0)
% 176.46/138.08 |
% 176.46/138.08 +-Applying beta-rule and splitting (21), into two cases.
% 176.46/138.08 |-Branch one:
% 176.46/138.08 | (22) all_5_0_2 = 0 & all_5_1_3 = ex_4_0_1 & r2(all_5_2_4, ex_4_0_1) = 0
% 176.46/138.08 |
% 176.46/138.08 | Applying alpha-rule on (22) yields:
% 176.46/138.08 | (23) all_5_0_2 = 0
% 176.46/138.08 | (24) all_5_1_3 = ex_4_0_1
% 176.46/138.08 | (25) r2(all_5_2_4, ex_4_0_1) = 0
% 176.46/138.08 |
% 176.46/138.08 | Instantiating formula (11) with ex_19_0_8 yields:
% 176.46/138.08 | (26) ? [v0] : (r3(ex_19_0_8, v0, ex_19_0_8) = 0 & r1(v0) = 0)
% 176.46/138.08 |
% 176.46/138.08 | Instantiating (26) with all_20_0_9 yields:
% 176.46/138.08 | (27) r3(ex_19_0_8, all_20_0_9, ex_19_0_8) = 0 & r1(all_20_0_9) = 0
% 176.46/138.08 |
% 176.46/138.08 | Applying alpha-rule on (27) yields:
% 176.46/138.08 | (28) r3(ex_19_0_8, all_20_0_9, ex_19_0_8) = 0
% 176.46/138.08 | (29) r1(all_20_0_9) = 0
% 176.46/138.08 |
% 176.46/138.08 | Instantiating formula (2) with all_20_0_9 and discharging atoms r1(all_20_0_9) = 0, yields:
% 176.46/138.08 | (30) all_20_0_9 = all_0_0_0
% 176.46/138.08 |
% 176.46/138.08 | From (30) and (29) follows:
% 176.46/138.08 | (31) r1(all_0_0_0) = 0
% 176.46/138.08 |
% 176.46/138.08 | Instantiating formula (9) with all_0_0_0, all_5_2_4 and discharging atoms r1(all_0_0_0) = 0, yields:
% 176.46/138.08 | (32) ~ (r2(all_5_2_4, all_0_0_0) = 0)
% 176.46/138.08 |
% 176.46/138.08 | From (19) and (25) follows:
% 176.46/138.08 | (33) r2(all_5_2_4, all_0_0_0) = 0
% 176.46/138.08 |
% 176.46/138.08 | Using (33) and (32) yields:
% 176.46/138.08 | (34) $false
% 176.46/138.08 |
% 176.46/138.08 |-The branch is then unsatisfiable
% 176.46/138.08 |-Branch two:
% 176.46/138.08 | (35) all_5_1_3 = 0 & all_5_2_4 = ex_4_0_1 & r1(ex_4_0_1) = 0
% 176.46/138.08 |
% 176.46/138.08 | Applying alpha-rule on (35) yields:
% 176.46/138.08 | (36) all_5_1_3 = 0
% 176.46/138.08 | (37) all_5_2_4 = ex_4_0_1
% 176.46/138.08 | (38) r1(ex_4_0_1) = 0
% 176.46/138.08 |
% 176.46/138.08 | Combining equations (19,37) yields a new equation:
% 176.46/138.08 | (39) all_5_2_4 = all_0_0_0
% 176.46/138.08 |
% 176.46/138.08 | Introducing new symbol ex_18_0_10 defined by:
% 176.46/138.08 | (40) ex_18_0_10 = all_5_2_4
% 176.46/138.08 |
% 176.46/138.08 | Instantiating formula (10) with ex_18_0_10, ex_18_1_11 yields:
% 176.46/138.08 | (41) ? [v0] : ? [v1] : ? [v2] : (r3(ex_18_1_11, v2, v0) = 0 & r3(ex_18_1_11, ex_18_0_10, v1) = 0 & r2(v1, v0) = 0 & r2(ex_18_0_10, v2) = 0)
% 176.46/138.08 |
% 176.46/138.08 | Instantiating (41) with all_19_0_12, all_19_1_13, all_19_2_14 yields:
% 176.46/138.08 | (42) r3(ex_18_1_11, all_19_0_12, all_19_2_14) = 0 & r3(ex_18_1_11, ex_18_0_10, all_19_1_13) = 0 & r2(all_19_1_13, all_19_2_14) = 0 & r2(ex_18_0_10, all_19_0_12) = 0
% 176.46/138.08 |
% 176.46/138.08 | Applying alpha-rule on (42) yields:
% 176.46/138.08 | (43) r3(ex_18_1_11, all_19_0_12, all_19_2_14) = 0
% 176.46/138.08 | (44) r3(ex_18_1_11, ex_18_0_10, all_19_1_13) = 0
% 176.46/138.08 | (45) r2(all_19_1_13, all_19_2_14) = 0
% 176.46/138.08 | (46) r2(ex_18_0_10, all_19_0_12) = 0
% 176.46/138.08 |
% 176.46/138.08 | Introducing new symbol ex_50_0_23 defined by:
% 176.46/138.08 | (47) ex_50_0_23 = all_19_0_12
% 176.46/138.08 |
% 176.46/138.08 | Instantiating formula (7) with ex_50_0_23, ex_50_1_24 yields:
% 176.46/138.08 | (48) ? [v0] : ? [v1] : ? [v2] : (r4(ex_50_1_24, v2, v0) = 0 & r4(ex_50_1_24, ex_50_0_23, v1) = 0 & r3(v1, ex_50_1_24, v0) = 0 & r2(ex_50_0_23, v2) = 0)
% 176.46/138.08 |
% 176.46/138.08 | Instantiating (48) with all_51_0_25, all_51_1_26, all_51_2_27 yields:
% 176.46/138.08 | (49) r4(ex_50_1_24, all_51_0_25, all_51_2_27) = 0 & r4(ex_50_1_24, ex_50_0_23, all_51_1_26) = 0 & r3(all_51_1_26, ex_50_1_24, all_51_2_27) = 0 & r2(ex_50_0_23, all_51_0_25) = 0
% 176.46/138.08 |
% 176.46/138.08 | Applying alpha-rule on (49) yields:
% 176.46/138.08 | (50) r4(ex_50_1_24, all_51_0_25, all_51_2_27) = 0
% 176.46/138.08 | (51) r4(ex_50_1_24, ex_50_0_23, all_51_1_26) = 0
% 176.46/138.08 | (52) r3(all_51_1_26, ex_50_1_24, all_51_2_27) = 0
% 176.46/138.09 | (53) r2(ex_50_0_23, all_51_0_25) = 0
% 176.46/138.09 |
% 176.46/138.09 | Instantiating formula (11) with ex_59_0_28 yields:
% 176.46/138.09 | (54) ? [v0] : (r3(ex_59_0_28, v0, ex_59_0_28) = 0 & r1(v0) = 0)
% 176.46/138.09 |
% 176.46/138.09 | Instantiating (54) with all_60_0_29 yields:
% 176.46/138.09 | (55) r3(ex_59_0_28, all_60_0_29, ex_59_0_28) = 0 & r1(all_60_0_29) = 0
% 176.46/138.09 |
% 176.46/138.09 | Applying alpha-rule on (55) yields:
% 176.46/138.09 | (56) r3(ex_59_0_28, all_60_0_29, ex_59_0_28) = 0
% 176.46/138.09 | (57) r1(all_60_0_29) = 0
% 176.46/138.09 |
% 176.46/138.09 | Instantiating formula (2) with all_60_0_29 and discharging atoms r1(all_60_0_29) = 0, yields:
% 176.46/138.09 | (58) all_60_0_29 = all_0_0_0
% 176.46/138.09 |
% 176.46/138.09 | From (58) and (57) follows:
% 176.46/138.09 | (31) r1(all_0_0_0) = 0
% 176.46/138.09 |
% 176.46/138.09 | Introducing new symbol ex_77_0_33 defined by:
% 176.46/138.09 | (60) ex_77_0_33 = all_51_0_25
% 176.46/138.09 |
% 176.46/138.09 | Instantiating formula (14) with ex_77_0_33 yields:
% 176.46/138.09 | (61) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v0 = ex_77_0_33 & r2(v1, ex_77_0_33) = 0 & r1(v1) = 0) | (v1 = 0 & v0 = ex_77_0_33 & r1(ex_77_0_33) = 0))
% 176.46/138.09 |
% 176.46/138.09 | Instantiating (61) with all_78_0_34, all_78_1_35, all_78_2_36, all_78_3_37 yields:
% 176.46/138.09 | (62) (all_78_0_34 = 0 & all_78_1_35 = 0 & all_78_3_37 = ex_77_0_33 & r2(all_78_2_36, ex_77_0_33) = 0 & r1(all_78_2_36) = 0) | (all_78_2_36 = 0 & all_78_3_37 = ex_77_0_33 & r1(ex_77_0_33) = 0)
% 176.46/138.09 |
% 176.46/138.09 +-Applying beta-rule and splitting (62), into two cases.
% 176.46/138.09 |-Branch one:
% 176.46/138.09 | (63) all_78_0_34 = 0 & all_78_1_35 = 0 & all_78_3_37 = ex_77_0_33 & r2(all_78_2_36, ex_77_0_33) = 0 & r1(all_78_2_36) = 0
% 176.46/138.09 |
% 176.46/138.09 | Applying alpha-rule on (63) yields:
% 176.46/138.09 | (64) r2(all_78_2_36, ex_77_0_33) = 0
% 176.46/138.09 | (65) all_78_0_34 = 0
% 176.46/138.09 | (66) all_78_1_35 = 0
% 176.46/138.09 | (67) r1(all_78_2_36) = 0
% 176.46/138.09 | (68) all_78_3_37 = ex_77_0_33
% 176.46/138.09 |
% 176.46/138.09 | Instantiating formula (18) with all_51_0_25, all_78_2_36, ex_50_0_23 and discharging atoms r2(ex_50_0_23, all_51_0_25) = 0, yields:
% 176.46/138.09 | (69) all_78_2_36 = ex_50_0_23 | ~ (r2(all_78_2_36, all_51_0_25) = 0)
% 176.46/138.09 |
% 176.46/138.09 | Instantiating formula (9) with all_0_0_0, all_78_2_36 and discharging atoms r1(all_0_0_0) = 0, yields:
% 176.46/138.09 | (70) ~ (r2(all_78_2_36, all_0_0_0) = 0)
% 176.46/138.09 |
% 176.46/138.09 | Instantiating formula (2) with all_78_2_36 and discharging atoms r1(all_78_2_36) = 0, yields:
% 176.46/138.09 | (71) all_78_2_36 = all_0_0_0
% 176.46/138.09 |
% 176.46/138.09 | From (71) and (64) follows:
% 176.46/138.09 | (72) r2(all_0_0_0, ex_77_0_33) = 0
% 176.46/138.09 |
% 176.46/138.09 | From (71) and (70) follows:
% 176.46/138.09 | (73) ~ (r2(all_0_0_0, all_0_0_0) = 0)
% 176.46/138.09 |
% 176.46/138.09 +-Applying beta-rule and splitting (69), into two cases.
% 176.46/138.09 |-Branch one:
% 176.46/138.09 | (74) ~ (r2(all_78_2_36, all_51_0_25) = 0)
% 176.46/138.09 |
% 176.46/138.09 | From (71) and (74) follows:
% 176.46/138.09 | (75) ~ (r2(all_0_0_0, all_51_0_25) = 0)
% 176.46/138.09 |
% 176.46/138.09 | From (60) and (72) follows:
% 176.46/138.09 | (76) r2(all_0_0_0, all_51_0_25) = 0
% 176.46/138.09 |
% 176.46/138.09 | Using (76) and (75) yields:
% 176.46/138.09 | (34) $false
% 176.46/138.09 |
% 176.46/138.09 |-The branch is then unsatisfiable
% 176.46/138.09 |-Branch two:
% 176.46/138.09 | (78) all_78_2_36 = ex_50_0_23
% 176.46/138.09 |
% 176.46/138.09 | Combining equations (78,71) yields a new equation:
% 176.46/138.09 | (79) ex_50_0_23 = all_0_0_0
% 176.46/138.09 |
% 176.46/138.09 | Simplifying 79 yields:
% 176.46/138.09 | (80) ex_50_0_23 = all_0_0_0
% 176.46/138.09 |
% 176.46/138.09 | Combining equations (80,47) yields a new equation:
% 176.46/138.09 | (81) all_19_0_12 = all_0_0_0
% 176.46/138.09 |
% 176.46/138.09 | Combining equations (39,40) yields a new equation:
% 176.46/138.09 | (82) ex_18_0_10 = all_0_0_0
% 176.46/138.09 |
% 176.46/138.09 | From (82)(81) and (46) follows:
% 176.46/138.09 | (83) r2(all_0_0_0, all_0_0_0) = 0
% 176.46/138.09 |
% 176.46/138.09 | Using (83) and (73) yields:
% 176.46/138.09 | (34) $false
% 176.46/138.09 |
% 176.46/138.09 |-The branch is then unsatisfiable
% 176.46/138.09 |-Branch two:
% 176.46/138.09 | (85) all_78_2_36 = 0 & all_78_3_37 = ex_77_0_33 & r1(ex_77_0_33) = 0
% 176.46/138.09 |
% 176.46/138.09 | Applying alpha-rule on (85) yields:
% 176.46/138.09 | (86) all_78_2_36 = 0
% 176.46/138.09 | (68) all_78_3_37 = ex_77_0_33
% 176.46/138.09 | (88) r1(ex_77_0_33) = 0
% 176.46/138.09 |
% 176.46/138.09 | Instantiating formula (9) with all_51_0_25, ex_50_0_23 and discharging atoms r2(ex_50_0_23, all_51_0_25) = 0, yields:
% 176.46/138.09 | (89) ~ (r1(all_51_0_25) = 0)
% 176.46/138.09 |
% 176.46/138.09 | Instantiating formula (2) with ex_77_0_33 and discharging atoms r1(ex_77_0_33) = 0, yields:
% 176.46/138.09 | (90) ex_77_0_33 = all_0_0_0
% 176.46/138.09 |
% 176.46/138.09 | Combining equations (60,90) yields a new equation:
% 176.46/138.09 | (91) all_51_0_25 = all_0_0_0
% 176.46/138.09 |
% 176.46/138.09 | Simplifying 91 yields:
% 176.46/138.09 | (92) all_51_0_25 = all_0_0_0
% 176.46/138.09 |
% 176.46/138.09 | From (92) and (89) follows:
% 176.46/138.09 | (93) ~ (r1(all_0_0_0) = 0)
% 176.46/138.09 |
% 176.46/138.09 | Using (31) and (93) yields:
% 176.46/138.09 | (34) $false
% 176.46/138.09 |
% 176.46/138.09 |-The branch is then unsatisfiable
% 176.46/138.09 % SZS output end Proof for theBenchmark
% 176.46/138.09
% 176.46/138.09 137490ms
%------------------------------------------------------------------------------