TSTP Solution File: NUN062+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUN062+1 : TPTP v8.1.0. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 16:25:07 EDT 2022
% Result : Theorem 273.42s 199.09s
% Output : Proof 273.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN062+1 : TPTP v8.1.0. Bugfixed v7.4.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n020.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 04:18:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.47/0.58 ____ _
% 0.47/0.58 ___ / __ \_____(_)___ ________ __________
% 0.47/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.58
% 0.47/0.58 A Theorem Prover for First-Order Logic
% 0.47/0.58 (ePrincess v.1.0)
% 0.47/0.58
% 0.47/0.58 (c) Philipp Rümmer, 2009-2015
% 0.47/0.58 (c) Peter Backeman, 2014-2015
% 0.47/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.58 Bug reports to peter@backeman.se
% 0.47/0.58
% 0.47/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.58
% 0.47/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.67/0.95 Prover 0: Preprocessing ...
% 2.02/1.12 Prover 0: Warning: ignoring some quantifiers
% 2.16/1.14 Prover 0: Constructing countermodel ...
% 16.32/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 16.53/5.99 Prover 1: Preprocessing ...
% 17.32/6.14 Prover 1: Warning: ignoring some quantifiers
% 17.32/6.15 Prover 1: Constructing countermodel ...
% 27.08/8.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 27.42/8.57 Prover 2: Preprocessing ...
% 28.02/8.67 Prover 2: Warning: ignoring some quantifiers
% 28.02/8.67 Prover 2: Constructing countermodel ...
% 39.50/11.57 Prover 0: stopped
% 40.28/11.77 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 40.28/11.81 Prover 3: Preprocessing ...
% 40.28/11.83 Prover 3: Warning: ignoring some quantifiers
% 40.28/11.83 Prover 3: Constructing countermodel ...
% 87.19/53.09 Prover 3: stopped
% 87.69/53.29 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 87.69/53.32 Prover 4: Preprocessing ...
% 87.91/53.39 Prover 4: Warning: ignoring some quantifiers
% 87.91/53.39 Prover 4: Constructing countermodel ...
% 147.28/100.93 Prover 1: stopped
% 147.48/101.13 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 147.51/101.16 Prover 5: Preprocessing ...
% 147.51/101.20 Prover 5: Warning: ignoring some quantifiers
% 147.51/101.21 Prover 5: Constructing countermodel ...
% 157.75/110.10 Prover 5: stopped
% 157.91/110.30 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 157.91/110.33 Prover 6: Preprocessing ...
% 158.15/110.39 Prover 6: Warning: ignoring some quantifiers
% 158.15/110.39 Prover 6: Constructing countermodel ...
% 177.95/126.80 Prover 2: stopped
% 178.11/127.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 178.11/127.03 Prover 7: Preprocessing ...
% 178.25/127.05 Prover 7: Proving ...
% 231.95/166.14 Prover 4: stopped
% 232.22/166.34 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 232.22/166.38 Prover 8: Preprocessing ...
% 232.44/166.42 Prover 8: Proving ...
% 272.84/198.75 Prover 6: stopped
% 273.08/198.97 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal
% 273.08/199.00 Prover 9: Preprocessing ...
% 273.08/199.02 Prover 9: Proving ...
% 273.23/199.08 Prover 9: proved (114ms)
% 273.42/199.08 Prover 8: stopped
% 273.42/199.08 Prover 7: stopped
% 273.42/199.09
% 273.42/199.09 % SZS status Theorem for theBenchmark
% 273.42/199.09
% 273.42/199.09 Generating proof ... found it (size 18)
% 273.99/199.27
% 273.99/199.27 % SZS output start Proof for theBenchmark
% 273.99/199.27 Assumed formulas after preprocessing and simplification:
% 273.99/199.27 | (0) ? [v0] : ? [v1] : ( ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ r4(v5, v6, v7) | ~ id(v4, v7) | ~ id(v3, v6) | ~ id(v2, v5) | r4(v2, v3, v4)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ r4(v2, v3, v4) | ~ id(v4, v7) | ~ id(v3, v6) | ~ id(v2, v5) | r4(v5, v6, v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ r3(v5, v6, v7) | ~ id(v4, v7) | ~ id(v3, v6) | ~ id(v2, v5) | r3(v2, v3, v4)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ r3(v2, v3, v4) | ~ id(v4, v7) | ~ id(v3, v6) | ~ id(v2, v5) | r3(v5, v6, v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r2(v4, v5) | ~ id(v3, v5) | ~ id(v2, v4) | r2(v2, v3)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r2(v3, v4) | ~ r2(v2, v5) | ~ id(v5, v4) | id(v2, v3)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r2(v2, v3) | ~ id(v3, v5) | ~ id(v2, v4) | r2(v4, v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ r3(v0, v3, v4) | ~ id(v4, v2) | ? [v5] : (r1(v5) & id(v3, v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ r2(v2, v3) | ~ r1(v4) | ~ id(v4, v3)) & ! [v2] : ! [v3] : ! [v4] : ( ~ id(v3, v4) | ~ id(v2, v3) | id(v2, v4)) & ! [v2] : ! [v3] : ( ~ r1(v3) | ~ id(v2, v3) | r1(v2)) & ! [v2] : ! [v3] : ( ~ r1(v2) | ~ id(v2, v3) | r1(v3)) & ! [v2] : ! [v3] : ( ~ id(v2, v3) | id(v3, v2)) & ! [v2] : ( ~ r1(v2) | id(v2, v1)) & ! [v2] : ( ~ id(v2, v1) | r1(v2)) & ! [v2] : id(v2, v2) & ! [v2] : ! [v3] : ? [v4] : ( ! [v5] : ( ~ r4(v2, v3, v5) | id(v5, v4)) & ! [v5] : ( ~ id(v5, v4) | r4(v2, v3, v5))) & ! [v2] : ! [v3] : ? [v4] : ( ! [v5] : ( ~ r3(v2, v3, v5) | id(v5, v4)) & ! [v5] : ( ~ id(v5, v4) | r3(v2, v3, v5))) & ! [v2] : ? [v3] : ( ! [v4] : ( ~ r2(v2, v4) | id(v4, v3)) & ! [v4] : ( ~ id(v4, v3) | r2(v2, v4))) & ! [v2] : ? [v3] : ? [v4] : (r3(v2, v4, v3) & r1(v4) & id(v3, v2)) & ! [v2] : ? [v3] : ? [v4] : ((r2(v3, v4) & id(v2, v4)) | (r1(v3) & id(v2, v3))) & ! [v2] : ? [v3] : ? [v4] : ? [v5] : (r4(v2, v5, v3) & r1(v5) & r1(v4) & id(v3, v4)) & ! [v2] : ! [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (r4(v2, v7, v6) & r4(v2, v3, v5) & r3(v5, v2, v4) & r2(v3, v7) & id(v6, v4)) & ! [v2] : ! [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (r3(v2, v7, v6) & r3(v2, v3, v5) & r2(v5, v4) & r2(v3, v7) & id(v6, v4)))
% 273.99/199.28 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 273.99/199.28 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r4(v3, v4, v5) | ~ id(v2, v5) | ~ id(v1, v4) | ~ id(v0, v3) | r4(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r4(v0, v1, v2) | ~ id(v2, v5) | ~ id(v1, v4) | ~ id(v0, v3) | r4(v3, v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r3(v3, v4, v5) | ~ id(v2, v5) | ~ id(v1, v4) | ~ id(v0, v3) | r3(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r3(v0, v1, v2) | ~ id(v2, v5) | ~ id(v1, v4) | ~ id(v0, v3) | r3(v3, v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r2(v2, v3) | ~ id(v1, v3) | ~ id(v0, v2) | r2(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r2(v1, v2) | ~ r2(v0, v3) | ~ id(v3, v2) | id(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r2(v0, v1) | ~ id(v1, v3) | ~ id(v0, v2) | r2(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ r3(all_0_1_1, v1, v2) | ~ id(v2, v0) | ? [v3] : (r1(v3) & id(v1, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ r2(v0, v1) | ~ r1(v2) | ~ id(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ id(v1, v2) | ~ id(v0, v1) | id(v0, v2)) & ! [v0] : ! [v1] : ( ~ r1(v1) | ~ id(v0, v1) | r1(v0)) & ! [v0] : ! [v1] : ( ~ r1(v0) | ~ id(v0, v1) | r1(v1)) & ! [v0] : ! [v1] : ( ~ id(v0, v1) | id(v1, v0)) & ! [v0] : ( ~ r1(v0) | id(v0, all_0_0_0)) & ! [v0] : ( ~ id(v0, all_0_0_0) | r1(v0)) & ! [v0] : id(v0, v0) & ! [v0] : ! [v1] : ? [v2] : ( ! [v3] : ( ~ r4(v0, v1, v3) | id(v3, v2)) & ! [v3] : ( ~ id(v3, v2) | r4(v0, v1, v3))) & ! [v0] : ! [v1] : ? [v2] : ( ! [v3] : ( ~ r3(v0, v1, v3) | id(v3, v2)) & ! [v3] : ( ~ id(v3, v2) | r3(v0, v1, v3))) & ! [v0] : ? [v1] : ( ! [v2] : ( ~ r2(v0, v2) | id(v2, v1)) & ! [v2] : ( ~ id(v2, v1) | r2(v0, v2))) & ! [v0] : ? [v1] : ? [v2] : (r3(v0, v2, v1) & r1(v2) & id(v1, v0)) & ! [v0] : ? [v1] : ? [v2] : ((r2(v1, v2) & id(v0, v2)) | (r1(v1) & id(v0, v1))) & ! [v0] : ? [v1] : ? [v2] : ? [v3] : (r4(v0, v3, v1) & r1(v3) & r1(v2) & id(v1, v2)) & ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (r4(v0, v5, v4) & r4(v0, v1, v3) & r3(v3, v0, v2) & r2(v1, v5) & id(v4, v2)) & ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (r3(v0, v5, v4) & r3(v0, v1, v3) & r2(v3, v2) & r2(v1, v5) & id(v4, v2))
% 273.99/199.29 |
% 273.99/199.29 | Applying alpha-rule on (1) yields:
% 273.99/199.29 | (2) ! [v0] : ? [v1] : ? [v2] : (r3(v0, v2, v1) & r1(v2) & id(v1, v0))
% 273.99/199.29 | (3) ! [v0] : ? [v1] : ( ! [v2] : ( ~ r2(v0, v2) | id(v2, v1)) & ! [v2] : ( ~ id(v2, v1) | r2(v0, v2)))
% 273.99/199.29 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r2(v1, v2) | ~ r2(v0, v3) | ~ id(v3, v2) | id(v0, v1))
% 273.99/199.29 | (5) ! [v0] : ! [v1] : ? [v2] : ( ! [v3] : ( ~ r4(v0, v1, v3) | id(v3, v2)) & ! [v3] : ( ~ id(v3, v2) | r4(v0, v1, v3)))
% 273.99/199.29 | (6) ! [v0] : ! [v1] : ( ~ r1(v1) | ~ id(v0, v1) | r1(v0))
% 273.99/199.29 | (7) ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (r3(v0, v5, v4) & r3(v0, v1, v3) & r2(v3, v2) & r2(v1, v5) & id(v4, v2))
% 273.99/199.29 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r4(v0, v1, v2) | ~ id(v2, v5) | ~ id(v1, v4) | ~ id(v0, v3) | r4(v3, v4, v5))
% 273.99/199.29 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r4(v3, v4, v5) | ~ id(v2, v5) | ~ id(v1, v4) | ~ id(v0, v3) | r4(v0, v1, v2))
% 273.99/199.29 | (10) ! [v0] : ? [v1] : ? [v2] : ? [v3] : (r4(v0, v3, v1) & r1(v3) & r1(v2) & id(v1, v2))
% 273.99/199.29 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r3(v3, v4, v5) | ~ id(v2, v5) | ~ id(v1, v4) | ~ id(v0, v3) | r3(v0, v1, v2))
% 273.99/199.29 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ r3(all_0_1_1, v1, v2) | ~ id(v2, v0) | ? [v3] : (r1(v3) & id(v1, v3)))
% 273.99/199.29 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ r3(v0, v1, v2) | ~ id(v2, v5) | ~ id(v1, v4) | ~ id(v0, v3) | r3(v3, v4, v5))
% 273.99/199.29 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r2(v2, v3) | ~ id(v1, v3) | ~ id(v0, v2) | r2(v0, v1))
% 273.99/199.29 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r2(v0, v1) | ~ id(v1, v3) | ~ id(v0, v2) | r2(v2, v3))
% 273.99/199.29 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ id(v1, v2) | ~ id(v0, v1) | id(v0, v2))
% 273.99/199.29 | (17) ! [v0] : ! [v1] : ? [v2] : ( ! [v3] : ( ~ r3(v0, v1, v3) | id(v3, v2)) & ! [v3] : ( ~ id(v3, v2) | r3(v0, v1, v3)))
% 273.99/199.29 | (18) ! [v0] : ! [v1] : ( ~ r1(v0) | ~ id(v0, v1) | r1(v1))
% 273.99/199.29 | (19) ! [v0] : ? [v1] : ? [v2] : ((r2(v1, v2) & id(v0, v2)) | (r1(v1) & id(v0, v1)))
% 273.99/199.29 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ r2(v0, v1) | ~ r1(v2) | ~ id(v2, v1))
% 273.99/199.29 | (21) ! [v0] : ( ~ id(v0, all_0_0_0) | r1(v0))
% 273.99/199.29 | (22) ! [v0] : ( ~ r1(v0) | id(v0, all_0_0_0))
% 273.99/199.29 | (23) ! [v0] : ! [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (r4(v0, v5, v4) & r4(v0, v1, v3) & r3(v3, v0, v2) & r2(v1, v5) & id(v4, v2))
% 273.99/199.29 | (24) ! [v0] : ! [v1] : ( ~ id(v0, v1) | id(v1, v0))
% 273.99/199.29 | (25) ! [v0] : id(v0, v0)
% 273.99/199.29 |
% 273.99/199.29 | Introducing new symbol ex_25_1_9 defined by:
% 273.99/199.29 | (26) ex_25_1_9 = all_0_1_1
% 273.99/199.29 |
% 273.99/199.29 | Instantiating formula (7) with ex_25_0_8, ex_25_1_9 yields:
% 273.99/199.29 | (27) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (r3(ex_25_1_9, v3, v2) & r3(ex_25_1_9, ex_25_0_8, v1) & r2(v1, v0) & r2(ex_25_0_8, v3) & id(v2, v0))
% 273.99/199.29 |
% 273.99/199.29 | Instantiating (27) with all_26_0_10, all_26_1_11, all_26_2_12, all_26_3_13 yields:
% 273.99/199.29 | (28) r3(ex_25_1_9, all_26_0_10, all_26_1_11) & r3(ex_25_1_9, ex_25_0_8, all_26_2_12) & r2(all_26_2_12, all_26_3_13) & r2(ex_25_0_8, all_26_0_10) & id(all_26_1_11, all_26_3_13)
% 273.99/199.29 |
% 273.99/199.29 | Applying alpha-rule on (28) yields:
% 273.99/199.29 | (29) r3(ex_25_1_9, ex_25_0_8, all_26_2_12)
% 273.99/199.30 | (30) r2(ex_25_0_8, all_26_0_10)
% 273.99/199.30 | (31) r2(all_26_2_12, all_26_3_13)
% 273.99/199.30 | (32) r3(ex_25_1_9, all_26_0_10, all_26_1_11)
% 273.99/199.30 | (33) id(all_26_1_11, all_26_3_13)
% 273.99/199.30 |
% 273.99/199.30 | Instantiating formula (24) with all_26_3_13, all_26_1_11 and discharging atoms id(all_26_1_11, all_26_3_13), yields:
% 273.99/199.30 | (34) id(all_26_3_13, all_26_1_11)
% 273.99/199.30 |
% 273.99/199.30 | Instantiating formula (16) with all_26_1_11, all_26_3_13, all_26_1_11 and discharging atoms id(all_26_1_11, all_26_3_13), id(all_26_3_13, all_26_1_11), yields:
% 273.99/199.30 | (35) id(all_26_1_11, all_26_1_11)
% 273.99/199.30 |
% 273.99/199.30 | Instantiating formula (12) with all_26_1_11, all_26_0_10, all_26_1_11 and discharging atoms id(all_26_1_11, all_26_1_11), yields:
% 273.99/199.30 | (36) ~ r3(all_0_1_1, all_26_0_10, all_26_1_11) | ? [v0] : (r1(v0) & id(all_26_0_10, v0))
% 273.99/199.30 |
% 273.99/199.30 +-Applying beta-rule and splitting (36), into two cases.
% 273.99/199.30 |-Branch one:
% 273.99/199.30 | (37) ~ r3(all_0_1_1, all_26_0_10, all_26_1_11)
% 273.99/199.30 |
% 273.99/199.30 | From (26) and (32) follows:
% 273.99/199.30 | (38) r3(all_0_1_1, all_26_0_10, all_26_1_11)
% 273.99/199.30 |
% 273.99/199.30 | Using (38) and (37) yields:
% 273.99/199.30 | (39) $false
% 273.99/199.30 |
% 273.99/199.30 |-The branch is then unsatisfiable
% 273.99/199.30 |-Branch two:
% 273.99/199.30 | (40) ? [v0] : (r1(v0) & id(all_26_0_10, v0))
% 273.99/199.30 |
% 273.99/199.30 | Instantiating (40) with all_58_0_14 yields:
% 273.99/199.30 | (41) r1(all_58_0_14) & id(all_26_0_10, all_58_0_14)
% 273.99/199.30 |
% 273.99/199.30 | Applying alpha-rule on (41) yields:
% 273.99/199.30 | (42) r1(all_58_0_14)
% 273.99/199.30 | (43) id(all_26_0_10, all_58_0_14)
% 273.99/199.30 |
% 273.99/199.30 | Instantiating formula (24) with all_58_0_14, all_26_0_10 and discharging atoms id(all_26_0_10, all_58_0_14), yields:
% 273.99/199.30 | (44) id(all_58_0_14, all_26_0_10)
% 273.99/199.30 |
% 273.99/199.30 | Instantiating formula (20) with all_58_0_14, all_26_0_10, ex_25_0_8 and discharging atoms r2(ex_25_0_8, all_26_0_10), r1(all_58_0_14), id(all_58_0_14, all_26_0_10), yields:
% 273.99/199.30 | (39) $false
% 273.99/199.30 |
% 273.99/199.30 |-The branch is then unsatisfiable
% 273.99/199.30 % SZS output end Proof for theBenchmark
% 273.99/199.30
% 273.99/199.30 198707ms
%------------------------------------------------------------------------------