TSTP Solution File: LCL656+1.005 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL656+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 09:37:51 EDT 2022
% Result : Theorem 21.77s 5.72s
% Output : Proof 34.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL656+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n005.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 : Mon Jul 4 18:54:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.68/0.96 Prover 0: Preprocessing ...
% 2.07/1.16 Prover 0: Warning: ignoring some quantifiers
% 2.41/1.19 Prover 0: Constructing countermodel ...
% 3.23/1.42 Prover 0: gave up
% 3.23/1.42 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.59/1.47 Prover 1: Preprocessing ...
% 4.35/1.63 Prover 1: Constructing countermodel ...
% 4.35/1.65 Prover 1: gave up
% 4.35/1.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.60/1.69 Prover 2: Preprocessing ...
% 8.52/2.62 Prover 2: Warning: ignoring some quantifiers
% 8.52/2.66 Prover 2: Constructing countermodel ...
% 9.15/2.74 Prover 2: gave up
% 9.15/2.74 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 9.15/2.77 Prover 3: Preprocessing ...
% 9.15/2.79 Prover 3: Warning: ignoring some quantifiers
% 9.15/2.79 Prover 3: Constructing countermodel ...
% 9.58/2.86 Prover 3: gave up
% 9.58/2.86 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 9.58/2.89 Prover 4: Preprocessing ...
% 11.61/3.41 Prover 4: Warning: ignoring some quantifiers
% 12.09/3.44 Prover 4: Constructing countermodel ...
% 14.17/3.97 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 14.53/4.03 Prover 5: Preprocessing ...
% 16.89/4.61 Prover 5: Constructing countermodel ...
% 16.89/4.63 Prover 5: gave up
% 16.89/4.63 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 16.89/4.67 Prover 6: Preprocessing ...
% 18.75/5.09 Prover 6: Warning: ignoring some quantifiers
% 18.75/5.12 Prover 6: Constructing countermodel ...
% 19.13/5.16 Prover 6: gave up
% 19.13/5.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 19.13/5.18 Prover 7: Preprocessing ...
% 19.40/5.19 Prover 7: Proving ...
% 21.77/5.71 Prover 7: proved (555ms)
% 21.77/5.72 Prover 4: stopped
% 21.77/5.72
% 21.77/5.72 % SZS status Theorem for theBenchmark
% 21.77/5.72
% 21.77/5.72 Generating proof ... found it (size 62)
% 34.12/10.73
% 34.12/10.73 % SZS output start Proof for theBenchmark
% 34.12/10.73 Assumed formulas after preprocessing and simplification:
% 34.12/10.73 | (0) ! [v0] : r1(v0, v0) & ? [v0] : (p100(v0) & ~ p101(v0) & ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | ! [v4] : ( ~ r1(v3, v4) | ! [v5] : ( ~ r1(v4, v5) | p3(v5)))))) & ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | ! [v4] : ( ~ r1(v3, v4) | ! [v5] : ( ~ r1(v4, v5) | (( ~ p100(v5) | p101(v5) | ( ? [v6] : (p2(v6) & p101(v6) & r1(v5, v6) & ~ p102(v6)) & ? [v6] : (p101(v6) & r1(v5, v6) & ~ p2(v6) & ~ p102(v6)))) & ( ~ p100(v5) | (( ~ p1(v5) | ! [v6] : ( ~ p100(v6) | ~ r1(v5, v6) | p1(v6))) & (p1(v5) | ! [v6] : ( ~ p1(v6) | ~ p100(v6) | ~ r1(v5, v6))))) & ( ~ p101(v5) | p100(v5)) & ( ~ p101(v5) | p102(v5) | ( ? [v6] : (p102(v6) & p3(v6) & r1(v5, v6) & ~ p103(v6)) & ? [v6] : (p102(v6) & r1(v5, v6) & ~ p103(v6) & ~ p3(v6)))) & ( ~ p101(v5) | (( ~ p2(v5) | ! [v6] : ( ~ p101(v6) | ~ r1(v5, v6) | p2(v6))) & (p2(v5) | ! [v6] : ( ~ p2(v6) | ~ p101(v6) | ~ r1(v5, v6))))) & ( ~ p102(v5) | p101(v5)) & ( ~ p102(v5) | p103(v5) | ( ? [v6] : (p4(v6) & p103(v6) & r1(v5, v6) & ~ p104(v6)) & ? [v6] : (p103(v6) & r1(v5, v6) & ~ p4(v6) & ~ p104(v6)))) & ( ~ p102(v5) | (( ~ p3(v5) | ! [v6] : ( ~ p102(v6) | ~ r1(v5, v6) | p3(v6))) & (p3(v5) | ! [v6] : ( ~ p102(v6) | ~ p3(v6) | ~ r1(v5, v6))))) & ( ~ p103(v5) | p102(v5)) & ( ~ p103(v5) | p104(v5) | ( ? [v6] : (p5(v6) & p104(v6) & r1(v5, v6) & ~ p105(v6)) & ? [v6] : (p104(v6) & r1(v5, v6) & ~ p5(v6) & ~ p105(v6)))) & ( ~ p103(v5) | (( ~ p4(v5) | ! [v6] : ( ~ p103(v6) | ~ r1(v5, v6) | p4(v6))) & (p4(v5) | ! [v6] : ( ~ p4(v6) | ~ p103(v6) | ~ r1(v5, v6))))) & ( ~ p104(v5) | p103(v5)) & ( ~ p104(v5) | p105(v5) | ( ? [v6] : (p105(v6) & p6(v6) & r1(v5, v6) & ~ p106(v6)) & ? [v6] : (p105(v6) & r1(v5, v6) & ~ p106(v6) & ~ p6(v6)))) & ( ~ p104(v5) | (( ~ p5(v5) | ! [v6] : ( ~ p104(v6) | ~ r1(v5, v6) | p5(v6))) & (p5(v5) | ! [v6] : ( ~ p5(v6) | ~ p104(v6) | ~ r1(v5, v6))))) & ( ~ p105(v5) | p104(v5)) & ( ~ p105(v5) | (( ~ p6(v5) | ! [v6] : ( ~ p105(v6) | ~ r1(v5, v6) | p6(v6))) & (p6(v5) | ! [v6] : ( ~ p105(v6) | ~ p6(v6) | ~ r1(v5, v6))))) & ( ~ p106(v5) | p105(v5)))))))))
% 34.12/10.74 | Applying alpha-rule on (0) yields:
% 34.12/10.74 | (1) ! [v0] : r1(v0, v0)
% 34.12/10.74 | (2) ? [v0] : (p100(v0) & ~ p101(v0) & ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | ! [v4] : ( ~ r1(v3, v4) | ! [v5] : ( ~ r1(v4, v5) | p3(v5)))))) & ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | ! [v4] : ( ~ r1(v3, v4) | ! [v5] : ( ~ r1(v4, v5) | (( ~ p100(v5) | p101(v5) | ( ? [v6] : (p2(v6) & p101(v6) & r1(v5, v6) & ~ p102(v6)) & ? [v6] : (p101(v6) & r1(v5, v6) & ~ p2(v6) & ~ p102(v6)))) & ( ~ p100(v5) | (( ~ p1(v5) | ! [v6] : ( ~ p100(v6) | ~ r1(v5, v6) | p1(v6))) & (p1(v5) | ! [v6] : ( ~ p1(v6) | ~ p100(v6) | ~ r1(v5, v6))))) & ( ~ p101(v5) | p100(v5)) & ( ~ p101(v5) | p102(v5) | ( ? [v6] : (p102(v6) & p3(v6) & r1(v5, v6) & ~ p103(v6)) & ? [v6] : (p102(v6) & r1(v5, v6) & ~ p103(v6) & ~ p3(v6)))) & ( ~ p101(v5) | (( ~ p2(v5) | ! [v6] : ( ~ p101(v6) | ~ r1(v5, v6) | p2(v6))) & (p2(v5) | ! [v6] : ( ~ p2(v6) | ~ p101(v6) | ~ r1(v5, v6))))) & ( ~ p102(v5) | p101(v5)) & ( ~ p102(v5) | p103(v5) | ( ? [v6] : (p4(v6) & p103(v6) & r1(v5, v6) & ~ p104(v6)) & ? [v6] : (p103(v6) & r1(v5, v6) & ~ p4(v6) & ~ p104(v6)))) & ( ~ p102(v5) | (( ~ p3(v5) | ! [v6] : ( ~ p102(v6) | ~ r1(v5, v6) | p3(v6))) & (p3(v5) | ! [v6] : ( ~ p102(v6) | ~ p3(v6) | ~ r1(v5, v6))))) & ( ~ p103(v5) | p102(v5)) & ( ~ p103(v5) | p104(v5) | ( ? [v6] : (p5(v6) & p104(v6) & r1(v5, v6) & ~ p105(v6)) & ? [v6] : (p104(v6) & r1(v5, v6) & ~ p5(v6) & ~ p105(v6)))) & ( ~ p103(v5) | (( ~ p4(v5) | ! [v6] : ( ~ p103(v6) | ~ r1(v5, v6) | p4(v6))) & (p4(v5) | ! [v6] : ( ~ p4(v6) | ~ p103(v6) | ~ r1(v5, v6))))) & ( ~ p104(v5) | p103(v5)) & ( ~ p104(v5) | p105(v5) | ( ? [v6] : (p105(v6) & p6(v6) & r1(v5, v6) & ~ p106(v6)) & ? [v6] : (p105(v6) & r1(v5, v6) & ~ p106(v6) & ~ p6(v6)))) & ( ~ p104(v5) | (( ~ p5(v5) | ! [v6] : ( ~ p104(v6) | ~ r1(v5, v6) | p5(v6))) & (p5(v5) | ! [v6] : ( ~ p5(v6) | ~ p104(v6) | ~ r1(v5, v6))))) & ( ~ p105(v5) | p104(v5)) & ( ~ p105(v5) | (( ~ p6(v5) | ! [v6] : ( ~ p105(v6) | ~ r1(v5, v6) | p6(v6))) & (p6(v5) | ! [v6] : ( ~ p105(v6) | ~ p6(v6) | ~ r1(v5, v6))))) & ( ~ p106(v5) | p105(v5)))))))))
% 34.12/10.75 |
% 34.12/10.75 | Instantiating (2) with all_0_0_0 yields:
% 34.12/10.75 | (3) p100(all_0_0_0) & ~ p101(all_0_0_0) & ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | ! [v4] : ( ~ r1(v3, v4) | p3(v4)))))) & ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | ! [v4] : ( ~ r1(v3, v4) | (( ~ p100(v4) | p101(v4) | ( ? [v5] : (p2(v5) & p101(v5) & r1(v4, v5) & ~ p102(v5)) & ? [v5] : (p101(v5) & r1(v4, v5) & ~ p2(v5) & ~ p102(v5)))) & ( ~ p100(v4) | (( ~ p1(v4) | ! [v5] : ( ~ p100(v5) | ~ r1(v4, v5) | p1(v5))) & (p1(v4) | ! [v5] : ( ~ p1(v5) | ~ p100(v5) | ~ r1(v4, v5))))) & ( ~ p101(v4) | p100(v4)) & ( ~ p101(v4) | p102(v4) | ( ? [v5] : (p102(v5) & p3(v5) & r1(v4, v5) & ~ p103(v5)) & ? [v5] : (p102(v5) & r1(v4, v5) & ~ p103(v5) & ~ p3(v5)))) & ( ~ p101(v4) | (( ~ p2(v4) | ! [v5] : ( ~ p101(v5) | ~ r1(v4, v5) | p2(v5))) & (p2(v4) | ! [v5] : ( ~ p2(v5) | ~ p101(v5) | ~ r1(v4, v5))))) & ( ~ p102(v4) | p101(v4)) & ( ~ p102(v4) | p103(v4) | ( ? [v5] : (p4(v5) & p103(v5) & r1(v4, v5) & ~ p104(v5)) & ? [v5] : (p103(v5) & r1(v4, v5) & ~ p4(v5) & ~ p104(v5)))) & ( ~ p102(v4) | (( ~ p3(v4) | ! [v5] : ( ~ p102(v5) | ~ r1(v4, v5) | p3(v5))) & (p3(v4) | ! [v5] : ( ~ p102(v5) | ~ p3(v5) | ~ r1(v4, v5))))) & ( ~ p103(v4) | p102(v4)) & ( ~ p103(v4) | p104(v4) | ( ? [v5] : (p5(v5) & p104(v5) & r1(v4, v5) & ~ p105(v5)) & ? [v5] : (p104(v5) & r1(v4, v5) & ~ p5(v5) & ~ p105(v5)))) & ( ~ p103(v4) | (( ~ p4(v4) | ! [v5] : ( ~ p103(v5) | ~ r1(v4, v5) | p4(v5))) & (p4(v4) | ! [v5] : ( ~ p4(v5) | ~ p103(v5) | ~ r1(v4, v5))))) & ( ~ p104(v4) | p103(v4)) & ( ~ p104(v4) | p105(v4) | ( ? [v5] : (p105(v5) & p6(v5) & r1(v4, v5) & ~ p106(v5)) & ? [v5] : (p105(v5) & r1(v4, v5) & ~ p106(v5) & ~ p6(v5)))) & ( ~ p104(v4) | (( ~ p5(v4) | ! [v5] : ( ~ p104(v5) | ~ r1(v4, v5) | p5(v5))) & (p5(v4) | ! [v5] : ( ~ p5(v5) | ~ p104(v5) | ~ r1(v4, v5))))) & ( ~ p105(v4) | p104(v4)) & ( ~ p105(v4) | (( ~ p6(v4) | ! [v5] : ( ~ p105(v5) | ~ r1(v4, v5) | p6(v5))) & (p6(v4) | ! [v5] : ( ~ p105(v5) | ~ p6(v5) | ~ r1(v4, v5))))) & ( ~ p106(v4) | p105(v4))))))))
% 34.12/10.76 |
% 34.12/10.76 | Applying alpha-rule on (3) yields:
% 34.12/10.76 | (4) p100(all_0_0_0)
% 34.12/10.76 | (5) ~ p101(all_0_0_0)
% 34.12/10.76 | (6) ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | ! [v4] : ( ~ r1(v3, v4) | p3(v4))))))
% 34.12/10.76 | (7) ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | ! [v4] : ( ~ r1(v3, v4) | (( ~ p100(v4) | p101(v4) | ( ? [v5] : (p2(v5) & p101(v5) & r1(v4, v5) & ~ p102(v5)) & ? [v5] : (p101(v5) & r1(v4, v5) & ~ p2(v5) & ~ p102(v5)))) & ( ~ p100(v4) | (( ~ p1(v4) | ! [v5] : ( ~ p100(v5) | ~ r1(v4, v5) | p1(v5))) & (p1(v4) | ! [v5] : ( ~ p1(v5) | ~ p100(v5) | ~ r1(v4, v5))))) & ( ~ p101(v4) | p100(v4)) & ( ~ p101(v4) | p102(v4) | ( ? [v5] : (p102(v5) & p3(v5) & r1(v4, v5) & ~ p103(v5)) & ? [v5] : (p102(v5) & r1(v4, v5) & ~ p103(v5) & ~ p3(v5)))) & ( ~ p101(v4) | (( ~ p2(v4) | ! [v5] : ( ~ p101(v5) | ~ r1(v4, v5) | p2(v5))) & (p2(v4) | ! [v5] : ( ~ p2(v5) | ~ p101(v5) | ~ r1(v4, v5))))) & ( ~ p102(v4) | p101(v4)) & ( ~ p102(v4) | p103(v4) | ( ? [v5] : (p4(v5) & p103(v5) & r1(v4, v5) & ~ p104(v5)) & ? [v5] : (p103(v5) & r1(v4, v5) & ~ p4(v5) & ~ p104(v5)))) & ( ~ p102(v4) | (( ~ p3(v4) | ! [v5] : ( ~ p102(v5) | ~ r1(v4, v5) | p3(v5))) & (p3(v4) | ! [v5] : ( ~ p102(v5) | ~ p3(v5) | ~ r1(v4, v5))))) & ( ~ p103(v4) | p102(v4)) & ( ~ p103(v4) | p104(v4) | ( ? [v5] : (p5(v5) & p104(v5) & r1(v4, v5) & ~ p105(v5)) & ? [v5] : (p104(v5) & r1(v4, v5) & ~ p5(v5) & ~ p105(v5)))) & ( ~ p103(v4) | (( ~ p4(v4) | ! [v5] : ( ~ p103(v5) | ~ r1(v4, v5) | p4(v5))) & (p4(v4) | ! [v5] : ( ~ p4(v5) | ~ p103(v5) | ~ r1(v4, v5))))) & ( ~ p104(v4) | p103(v4)) & ( ~ p104(v4) | p105(v4) | ( ? [v5] : (p105(v5) & p6(v5) & r1(v4, v5) & ~ p106(v5)) & ? [v5] : (p105(v5) & r1(v4, v5) & ~ p106(v5) & ~ p6(v5)))) & ( ~ p104(v4) | (( ~ p5(v4) | ! [v5] : ( ~ p104(v5) | ~ r1(v4, v5) | p5(v5))) & (p5(v4) | ! [v5] : ( ~ p5(v5) | ~ p104(v5) | ~ r1(v4, v5))))) & ( ~ p105(v4) | p104(v4)) & ( ~ p105(v4) | (( ~ p6(v4) | ! [v5] : ( ~ p105(v5) | ~ r1(v4, v5) | p6(v5))) & (p6(v4) | ! [v5] : ( ~ p105(v5) | ~ p6(v5) | ~ r1(v4, v5))))) & ( ~ p106(v4) | p105(v4))))))))
% 34.12/10.76 |
% 34.12/10.76 | Introducing new symbol ex_9_0_1 defined by:
% 34.12/10.76 | (8) ex_9_0_1 = all_0_0_0
% 34.12/10.76 |
% 34.12/10.76 | Instantiating formula (1) with ex_9_0_1 yields:
% 34.12/10.76 | (9) r1(ex_9_0_1, ex_9_0_1)
% 34.12/10.76 |
% 34.12/10.76 | Instantiating formula (6) with all_0_0_0 yields:
% 34.12/10.76 | (10) ~ r1(all_0_0_0, all_0_0_0) | ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | p3(v3)))))
% 34.12/10.76 |
% 34.12/10.76 | Instantiating formula (7) with all_0_0_0 yields:
% 34.12/10.76 | (11) ~ r1(all_0_0_0, all_0_0_0) | ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | (( ~ p100(v3) | p101(v3) | ( ? [v4] : (p2(v4) & p101(v4) & r1(v3, v4) & ~ p102(v4)) & ? [v4] : (p101(v4) & r1(v3, v4) & ~ p2(v4) & ~ p102(v4)))) & ( ~ p100(v3) | (( ~ p1(v3) | ! [v4] : ( ~ p100(v4) | ~ r1(v3, v4) | p1(v4))) & (p1(v3) | ! [v4] : ( ~ p1(v4) | ~ p100(v4) | ~ r1(v3, v4))))) & ( ~ p101(v3) | p100(v3)) & ( ~ p101(v3) | p102(v3) | ( ? [v4] : (p102(v4) & p3(v4) & r1(v3, v4) & ~ p103(v4)) & ? [v4] : (p102(v4) & r1(v3, v4) & ~ p103(v4) & ~ p3(v4)))) & ( ~ p101(v3) | (( ~ p2(v3) | ! [v4] : ( ~ p101(v4) | ~ r1(v3, v4) | p2(v4))) & (p2(v3) | ! [v4] : ( ~ p2(v4) | ~ p101(v4) | ~ r1(v3, v4))))) & ( ~ p102(v3) | p101(v3)) & ( ~ p102(v3) | p103(v3) | ( ? [v4] : (p4(v4) & p103(v4) & r1(v3, v4) & ~ p104(v4)) & ? [v4] : (p103(v4) & r1(v3, v4) & ~ p4(v4) & ~ p104(v4)))) & ( ~ p102(v3) | (( ~ p3(v3) | ! [v4] : ( ~ p102(v4) | ~ r1(v3, v4) | p3(v4))) & (p3(v3) | ! [v4] : ( ~ p102(v4) | ~ p3(v4) | ~ r1(v3, v4))))) & ( ~ p103(v3) | p102(v3)) & ( ~ p103(v3) | p104(v3) | ( ? [v4] : (p5(v4) & p104(v4) & r1(v3, v4) & ~ p105(v4)) & ? [v4] : (p104(v4) & r1(v3, v4) & ~ p5(v4) & ~ p105(v4)))) & ( ~ p103(v3) | (( ~ p4(v3) | ! [v4] : ( ~ p103(v4) | ~ r1(v3, v4) | p4(v4))) & (p4(v3) | ! [v4] : ( ~ p4(v4) | ~ p103(v4) | ~ r1(v3, v4))))) & ( ~ p104(v3) | p103(v3)) & ( ~ p104(v3) | p105(v3) | ( ? [v4] : (p105(v4) & p6(v4) & r1(v3, v4) & ~ p106(v4)) & ? [v4] : (p105(v4) & r1(v3, v4) & ~ p106(v4) & ~ p6(v4)))) & ( ~ p104(v3) | (( ~ p5(v3) | ! [v4] : ( ~ p104(v4) | ~ r1(v3, v4) | p5(v4))) & (p5(v3) | ! [v4] : ( ~ p5(v4) | ~ p104(v4) | ~ r1(v3, v4))))) & ( ~ p105(v3) | p104(v3)) & ( ~ p105(v3) | (( ~ p6(v3) | ! [v4] : ( ~ p105(v4) | ~ r1(v3, v4) | p6(v4))) & (p6(v3) | ! [v4] : ( ~ p105(v4) | ~ p6(v4) | ~ r1(v3, v4))))) & ( ~ p106(v3) | p105(v3)))))))
% 34.12/10.77 |
% 34.12/10.77 +-Applying beta-rule and splitting (11), into two cases.
% 34.12/10.77 |-Branch one:
% 34.12/10.77 | (12) ~ r1(all_0_0_0, all_0_0_0)
% 34.12/10.77 |
% 34.12/10.77 | From (8)(8) and (9) follows:
% 34.12/10.77 | (13) r1(all_0_0_0, all_0_0_0)
% 34.12/10.77 |
% 34.12/10.77 | Using (13) and (12) yields:
% 34.12/10.77 | (14) $false
% 34.12/10.77 |
% 34.12/10.77 |-The branch is then unsatisfiable
% 34.12/10.77 |-Branch two:
% 34.12/10.77 | (13) r1(all_0_0_0, all_0_0_0)
% 34.12/10.77 | (16) ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | (( ~ p100(v3) | p101(v3) | ( ? [v4] : (p2(v4) & p101(v4) & r1(v3, v4) & ~ p102(v4)) & ? [v4] : (p101(v4) & r1(v3, v4) & ~ p2(v4) & ~ p102(v4)))) & ( ~ p100(v3) | (( ~ p1(v3) | ! [v4] : ( ~ p100(v4) | ~ r1(v3, v4) | p1(v4))) & (p1(v3) | ! [v4] : ( ~ p1(v4) | ~ p100(v4) | ~ r1(v3, v4))))) & ( ~ p101(v3) | p100(v3)) & ( ~ p101(v3) | p102(v3) | ( ? [v4] : (p102(v4) & p3(v4) & r1(v3, v4) & ~ p103(v4)) & ? [v4] : (p102(v4) & r1(v3, v4) & ~ p103(v4) & ~ p3(v4)))) & ( ~ p101(v3) | (( ~ p2(v3) | ! [v4] : ( ~ p101(v4) | ~ r1(v3, v4) | p2(v4))) & (p2(v3) | ! [v4] : ( ~ p2(v4) | ~ p101(v4) | ~ r1(v3, v4))))) & ( ~ p102(v3) | p101(v3)) & ( ~ p102(v3) | p103(v3) | ( ? [v4] : (p4(v4) & p103(v4) & r1(v3, v4) & ~ p104(v4)) & ? [v4] : (p103(v4) & r1(v3, v4) & ~ p4(v4) & ~ p104(v4)))) & ( ~ p102(v3) | (( ~ p3(v3) | ! [v4] : ( ~ p102(v4) | ~ r1(v3, v4) | p3(v4))) & (p3(v3) | ! [v4] : ( ~ p102(v4) | ~ p3(v4) | ~ r1(v3, v4))))) & ( ~ p103(v3) | p102(v3)) & ( ~ p103(v3) | p104(v3) | ( ? [v4] : (p5(v4) & p104(v4) & r1(v3, v4) & ~ p105(v4)) & ? [v4] : (p104(v4) & r1(v3, v4) & ~ p5(v4) & ~ p105(v4)))) & ( ~ p103(v3) | (( ~ p4(v3) | ! [v4] : ( ~ p103(v4) | ~ r1(v3, v4) | p4(v4))) & (p4(v3) | ! [v4] : ( ~ p4(v4) | ~ p103(v4) | ~ r1(v3, v4))))) & ( ~ p104(v3) | p103(v3)) & ( ~ p104(v3) | p105(v3) | ( ? [v4] : (p105(v4) & p6(v4) & r1(v3, v4) & ~ p106(v4)) & ? [v4] : (p105(v4) & r1(v3, v4) & ~ p106(v4) & ~ p6(v4)))) & ( ~ p104(v3) | (( ~ p5(v3) | ! [v4] : ( ~ p104(v4) | ~ r1(v3, v4) | p5(v4))) & (p5(v3) | ! [v4] : ( ~ p5(v4) | ~ p104(v4) | ~ r1(v3, v4))))) & ( ~ p105(v3) | p104(v3)) & ( ~ p105(v3) | (( ~ p6(v3) | ! [v4] : ( ~ p105(v4) | ~ r1(v3, v4) | p6(v4))) & (p6(v3) | ! [v4] : ( ~ p105(v4) | ~ p6(v4) | ~ r1(v3, v4))))) & ( ~ p106(v3) | p105(v3)))))))
% 34.12/10.78 |
% 34.12/10.78 | Instantiating formula (16) with all_0_0_0 yields:
% 34.12/10.78 | (17) ~ r1(all_0_0_0, all_0_0_0) | ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | (( ~ p100(v2) | p101(v2) | ( ? [v3] : (p2(v3) & p101(v3) & r1(v2, v3) & ~ p102(v3)) & ? [v3] : (p101(v3) & r1(v2, v3) & ~ p2(v3) & ~ p102(v3)))) & ( ~ p100(v2) | (( ~ p1(v2) | ! [v3] : ( ~ p100(v3) | ~ r1(v2, v3) | p1(v3))) & (p1(v2) | ! [v3] : ( ~ p1(v3) | ~ p100(v3) | ~ r1(v2, v3))))) & ( ~ p101(v2) | p100(v2)) & ( ~ p101(v2) | p102(v2) | ( ? [v3] : (p102(v3) & p3(v3) & r1(v2, v3) & ~ p103(v3)) & ? [v3] : (p102(v3) & r1(v2, v3) & ~ p103(v3) & ~ p3(v3)))) & ( ~ p101(v2) | (( ~ p2(v2) | ! [v3] : ( ~ p101(v3) | ~ r1(v2, v3) | p2(v3))) & (p2(v2) | ! [v3] : ( ~ p2(v3) | ~ p101(v3) | ~ r1(v2, v3))))) & ( ~ p102(v2) | p101(v2)) & ( ~ p102(v2) | p103(v2) | ( ? [v3] : (p4(v3) & p103(v3) & r1(v2, v3) & ~ p104(v3)) & ? [v3] : (p103(v3) & r1(v2, v3) & ~ p4(v3) & ~ p104(v3)))) & ( ~ p102(v2) | (( ~ p3(v2) | ! [v3] : ( ~ p102(v3) | ~ r1(v2, v3) | p3(v3))) & (p3(v2) | ! [v3] : ( ~ p102(v3) | ~ p3(v3) | ~ r1(v2, v3))))) & ( ~ p103(v2) | p102(v2)) & ( ~ p103(v2) | p104(v2) | ( ? [v3] : (p5(v3) & p104(v3) & r1(v2, v3) & ~ p105(v3)) & ? [v3] : (p104(v3) & r1(v2, v3) & ~ p5(v3) & ~ p105(v3)))) & ( ~ p103(v2) | (( ~ p4(v2) | ! [v3] : ( ~ p103(v3) | ~ r1(v2, v3) | p4(v3))) & (p4(v2) | ! [v3] : ( ~ p4(v3) | ~ p103(v3) | ~ r1(v2, v3))))) & ( ~ p104(v2) | p103(v2)) & ( ~ p104(v2) | p105(v2) | ( ? [v3] : (p105(v3) & p6(v3) & r1(v2, v3) & ~ p106(v3)) & ? [v3] : (p105(v3) & r1(v2, v3) & ~ p106(v3) & ~ p6(v3)))) & ( ~ p104(v2) | (( ~ p5(v2) | ! [v3] : ( ~ p104(v3) | ~ r1(v2, v3) | p5(v3))) & (p5(v2) | ! [v3] : ( ~ p5(v3) | ~ p104(v3) | ~ r1(v2, v3))))) & ( ~ p105(v2) | p104(v2)) & ( ~ p105(v2) | (( ~ p6(v2) | ! [v3] : ( ~ p105(v3) | ~ r1(v2, v3) | p6(v3))) & (p6(v2) | ! [v3] : ( ~ p105(v3) | ~ p6(v3) | ~ r1(v2, v3))))) & ( ~ p106(v2) | p105(v2))))))
% 34.12/10.78 |
% 34.12/10.78 +-Applying beta-rule and splitting (10), into two cases.
% 34.12/10.78 |-Branch one:
% 34.12/10.78 | (12) ~ r1(all_0_0_0, all_0_0_0)
% 34.12/10.78 |
% 34.12/10.78 | Using (13) and (12) yields:
% 34.12/10.78 | (14) $false
% 34.12/10.78 |
% 34.12/10.78 |-The branch is then unsatisfiable
% 34.12/10.78 |-Branch two:
% 34.12/10.78 | (20) ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | ! [v3] : ( ~ r1(v2, v3) | p3(v3)))))
% 34.12/10.78 |
% 34.12/10.78 | Instantiating formula (20) with all_0_0_0 yields:
% 34.12/10.78 | (21) ~ r1(all_0_0_0, all_0_0_0) | ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | p3(v2))))
% 34.12/10.78 |
% 34.12/10.78 +-Applying beta-rule and splitting (17), into two cases.
% 34.12/10.78 |-Branch one:
% 34.12/10.78 | (12) ~ r1(all_0_0_0, all_0_0_0)
% 34.12/10.78 |
% 34.12/10.78 | Using (13) and (12) yields:
% 34.12/10.78 | (14) $false
% 34.12/10.78 |
% 34.12/10.78 |-The branch is then unsatisfiable
% 34.12/10.78 |-Branch two:
% 34.12/10.78 | (24) ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | (( ~ p100(v2) | p101(v2) | ( ? [v3] : (p2(v3) & p101(v3) & r1(v2, v3) & ~ p102(v3)) & ? [v3] : (p101(v3) & r1(v2, v3) & ~ p2(v3) & ~ p102(v3)))) & ( ~ p100(v2) | (( ~ p1(v2) | ! [v3] : ( ~ p100(v3) | ~ r1(v2, v3) | p1(v3))) & (p1(v2) | ! [v3] : ( ~ p1(v3) | ~ p100(v3) | ~ r1(v2, v3))))) & ( ~ p101(v2) | p100(v2)) & ( ~ p101(v2) | p102(v2) | ( ? [v3] : (p102(v3) & p3(v3) & r1(v2, v3) & ~ p103(v3)) & ? [v3] : (p102(v3) & r1(v2, v3) & ~ p103(v3) & ~ p3(v3)))) & ( ~ p101(v2) | (( ~ p2(v2) | ! [v3] : ( ~ p101(v3) | ~ r1(v2, v3) | p2(v3))) & (p2(v2) | ! [v3] : ( ~ p2(v3) | ~ p101(v3) | ~ r1(v2, v3))))) & ( ~ p102(v2) | p101(v2)) & ( ~ p102(v2) | p103(v2) | ( ? [v3] : (p4(v3) & p103(v3) & r1(v2, v3) & ~ p104(v3)) & ? [v3] : (p103(v3) & r1(v2, v3) & ~ p4(v3) & ~ p104(v3)))) & ( ~ p102(v2) | (( ~ p3(v2) | ! [v3] : ( ~ p102(v3) | ~ r1(v2, v3) | p3(v3))) & (p3(v2) | ! [v3] : ( ~ p102(v3) | ~ p3(v3) | ~ r1(v2, v3))))) & ( ~ p103(v2) | p102(v2)) & ( ~ p103(v2) | p104(v2) | ( ? [v3] : (p5(v3) & p104(v3) & r1(v2, v3) & ~ p105(v3)) & ? [v3] : (p104(v3) & r1(v2, v3) & ~ p5(v3) & ~ p105(v3)))) & ( ~ p103(v2) | (( ~ p4(v2) | ! [v3] : ( ~ p103(v3) | ~ r1(v2, v3) | p4(v3))) & (p4(v2) | ! [v3] : ( ~ p4(v3) | ~ p103(v3) | ~ r1(v2, v3))))) & ( ~ p104(v2) | p103(v2)) & ( ~ p104(v2) | p105(v2) | ( ? [v3] : (p105(v3) & p6(v3) & r1(v2, v3) & ~ p106(v3)) & ? [v3] : (p105(v3) & r1(v2, v3) & ~ p106(v3) & ~ p6(v3)))) & ( ~ p104(v2) | (( ~ p5(v2) | ! [v3] : ( ~ p104(v3) | ~ r1(v2, v3) | p5(v3))) & (p5(v2) | ! [v3] : ( ~ p5(v3) | ~ p104(v3) | ~ r1(v2, v3))))) & ( ~ p105(v2) | p104(v2)) & ( ~ p105(v2) | (( ~ p6(v2) | ! [v3] : ( ~ p105(v3) | ~ r1(v2, v3) | p6(v3))) & (p6(v2) | ! [v3] : ( ~ p105(v3) | ~ p6(v3) | ~ r1(v2, v3))))) & ( ~ p106(v2) | p105(v2))))))
% 34.58/10.79 |
% 34.58/10.79 | Instantiating formula (24) with all_0_0_0 yields:
% 34.58/10.79 | (25) ~ r1(all_0_0_0, all_0_0_0) | ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | (( ~ p100(v1) | p101(v1) | ( ? [v2] : (p2(v2) & p101(v2) & r1(v1, v2) & ~ p102(v2)) & ? [v2] : (p101(v2) & r1(v1, v2) & ~ p2(v2) & ~ p102(v2)))) & ( ~ p100(v1) | (( ~ p1(v1) | ! [v2] : ( ~ p100(v2) | ~ r1(v1, v2) | p1(v2))) & (p1(v1) | ! [v2] : ( ~ p1(v2) | ~ p100(v2) | ~ r1(v1, v2))))) & ( ~ p101(v1) | p100(v1)) & ( ~ p101(v1) | p102(v1) | ( ? [v2] : (p102(v2) & p3(v2) & r1(v1, v2) & ~ p103(v2)) & ? [v2] : (p102(v2) & r1(v1, v2) & ~ p103(v2) & ~ p3(v2)))) & ( ~ p101(v1) | (( ~ p2(v1) | ! [v2] : ( ~ p101(v2) | ~ r1(v1, v2) | p2(v2))) & (p2(v1) | ! [v2] : ( ~ p2(v2) | ~ p101(v2) | ~ r1(v1, v2))))) & ( ~ p102(v1) | p101(v1)) & ( ~ p102(v1) | p103(v1) | ( ? [v2] : (p4(v2) & p103(v2) & r1(v1, v2) & ~ p104(v2)) & ? [v2] : (p103(v2) & r1(v1, v2) & ~ p4(v2) & ~ p104(v2)))) & ( ~ p102(v1) | (( ~ p3(v1) | ! [v2] : ( ~ p102(v2) | ~ r1(v1, v2) | p3(v2))) & (p3(v1) | ! [v2] : ( ~ p102(v2) | ~ p3(v2) | ~ r1(v1, v2))))) & ( ~ p103(v1) | p102(v1)) & ( ~ p103(v1) | p104(v1) | ( ? [v2] : (p5(v2) & p104(v2) & r1(v1, v2) & ~ p105(v2)) & ? [v2] : (p104(v2) & r1(v1, v2) & ~ p5(v2) & ~ p105(v2)))) & ( ~ p103(v1) | (( ~ p4(v1) | ! [v2] : ( ~ p103(v2) | ~ r1(v1, v2) | p4(v2))) & (p4(v1) | ! [v2] : ( ~ p4(v2) | ~ p103(v2) | ~ r1(v1, v2))))) & ( ~ p104(v1) | p103(v1)) & ( ~ p104(v1) | p105(v1) | ( ? [v2] : (p105(v2) & p6(v2) & r1(v1, v2) & ~ p106(v2)) & ? [v2] : (p105(v2) & r1(v1, v2) & ~ p106(v2) & ~ p6(v2)))) & ( ~ p104(v1) | (( ~ p5(v1) | ! [v2] : ( ~ p104(v2) | ~ r1(v1, v2) | p5(v2))) & (p5(v1) | ! [v2] : ( ~ p5(v2) | ~ p104(v2) | ~ r1(v1, v2))))) & ( ~ p105(v1) | p104(v1)) & ( ~ p105(v1) | (( ~ p6(v1) | ! [v2] : ( ~ p105(v2) | ~ r1(v1, v2) | p6(v2))) & (p6(v1) | ! [v2] : ( ~ p105(v2) | ~ p6(v2) | ~ r1(v1, v2))))) & ( ~ p106(v1) | p105(v1)))))
% 34.61/10.79 |
% 34.61/10.79 +-Applying beta-rule and splitting (21), into two cases.
% 34.61/10.79 |-Branch one:
% 34.61/10.79 | (12) ~ r1(all_0_0_0, all_0_0_0)
% 34.61/10.79 |
% 34.61/10.79 | Using (13) and (12) yields:
% 34.61/10.79 | (14) $false
% 34.61/10.79 |
% 34.61/10.79 |-The branch is then unsatisfiable
% 34.61/10.79 |-Branch two:
% 34.61/10.79 | (28) ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | ! [v2] : ( ~ r1(v1, v2) | p3(v2))))
% 34.61/10.79 |
% 34.61/10.79 | Instantiating formula (28) with all_0_0_0 yields:
% 34.61/10.79 | (29) ~ r1(all_0_0_0, all_0_0_0) | ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | p3(v1)))
% 34.61/10.80 |
% 34.61/10.80 +-Applying beta-rule and splitting (25), into two cases.
% 34.61/10.80 |-Branch one:
% 34.61/10.80 | (12) ~ r1(all_0_0_0, all_0_0_0)
% 34.61/10.80 |
% 34.61/10.80 | Using (13) and (12) yields:
% 34.61/10.80 | (14) $false
% 34.61/10.80 |
% 34.61/10.80 |-The branch is then unsatisfiable
% 34.61/10.80 |-Branch two:
% 34.61/10.80 | (32) ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | (( ~ p100(v1) | p101(v1) | ( ? [v2] : (p2(v2) & p101(v2) & r1(v1, v2) & ~ p102(v2)) & ? [v2] : (p101(v2) & r1(v1, v2) & ~ p2(v2) & ~ p102(v2)))) & ( ~ p100(v1) | (( ~ p1(v1) | ! [v2] : ( ~ p100(v2) | ~ r1(v1, v2) | p1(v2))) & (p1(v1) | ! [v2] : ( ~ p1(v2) | ~ p100(v2) | ~ r1(v1, v2))))) & ( ~ p101(v1) | p100(v1)) & ( ~ p101(v1) | p102(v1) | ( ? [v2] : (p102(v2) & p3(v2) & r1(v1, v2) & ~ p103(v2)) & ? [v2] : (p102(v2) & r1(v1, v2) & ~ p103(v2) & ~ p3(v2)))) & ( ~ p101(v1) | (( ~ p2(v1) | ! [v2] : ( ~ p101(v2) | ~ r1(v1, v2) | p2(v2))) & (p2(v1) | ! [v2] : ( ~ p2(v2) | ~ p101(v2) | ~ r1(v1, v2))))) & ( ~ p102(v1) | p101(v1)) & ( ~ p102(v1) | p103(v1) | ( ? [v2] : (p4(v2) & p103(v2) & r1(v1, v2) & ~ p104(v2)) & ? [v2] : (p103(v2) & r1(v1, v2) & ~ p4(v2) & ~ p104(v2)))) & ( ~ p102(v1) | (( ~ p3(v1) | ! [v2] : ( ~ p102(v2) | ~ r1(v1, v2) | p3(v2))) & (p3(v1) | ! [v2] : ( ~ p102(v2) | ~ p3(v2) | ~ r1(v1, v2))))) & ( ~ p103(v1) | p102(v1)) & ( ~ p103(v1) | p104(v1) | ( ? [v2] : (p5(v2) & p104(v2) & r1(v1, v2) & ~ p105(v2)) & ? [v2] : (p104(v2) & r1(v1, v2) & ~ p5(v2) & ~ p105(v2)))) & ( ~ p103(v1) | (( ~ p4(v1) | ! [v2] : ( ~ p103(v2) | ~ r1(v1, v2) | p4(v2))) & (p4(v1) | ! [v2] : ( ~ p4(v2) | ~ p103(v2) | ~ r1(v1, v2))))) & ( ~ p104(v1) | p103(v1)) & ( ~ p104(v1) | p105(v1) | ( ? [v2] : (p105(v2) & p6(v2) & r1(v1, v2) & ~ p106(v2)) & ? [v2] : (p105(v2) & r1(v1, v2) & ~ p106(v2) & ~ p6(v2)))) & ( ~ p104(v1) | (( ~ p5(v1) | ! [v2] : ( ~ p104(v2) | ~ r1(v1, v2) | p5(v2))) & (p5(v1) | ! [v2] : ( ~ p5(v2) | ~ p104(v2) | ~ r1(v1, v2))))) & ( ~ p105(v1) | p104(v1)) & ( ~ p105(v1) | (( ~ p6(v1) | ! [v2] : ( ~ p105(v2) | ~ r1(v1, v2) | p6(v2))) & (p6(v1) | ! [v2] : ( ~ p105(v2) | ~ p6(v2) | ~ r1(v1, v2))))) & ( ~ p106(v1) | p105(v1)))))
% 34.61/10.80 |
% 34.61/10.80 | Instantiating formula (32) with all_0_0_0 yields:
% 34.61/10.80 | (33) ~ r1(all_0_0_0, all_0_0_0) | ! [v0] : ( ~ r1(all_0_0_0, v0) | (( ~ p100(v0) | p101(v0) | ( ? [v1] : (p2(v1) & p101(v1) & r1(v0, v1) & ~ p102(v1)) & ? [v1] : (p101(v1) & r1(v0, v1) & ~ p2(v1) & ~ p102(v1)))) & ( ~ p100(v0) | (( ~ p1(v0) | ! [v1] : ( ~ p100(v1) | ~ r1(v0, v1) | p1(v1))) & (p1(v0) | ! [v1] : ( ~ p1(v1) | ~ p100(v1) | ~ r1(v0, v1))))) & ( ~ p101(v0) | p100(v0)) & ( ~ p101(v0) | p102(v0) | ( ? [v1] : (p102(v1) & p3(v1) & r1(v0, v1) & ~ p103(v1)) & ? [v1] : (p102(v1) & r1(v0, v1) & ~ p103(v1) & ~ p3(v1)))) & ( ~ p101(v0) | (( ~ p2(v0) | ! [v1] : ( ~ p101(v1) | ~ r1(v0, v1) | p2(v1))) & (p2(v0) | ! [v1] : ( ~ p2(v1) | ~ p101(v1) | ~ r1(v0, v1))))) & ( ~ p102(v0) | p101(v0)) & ( ~ p102(v0) | p103(v0) | ( ? [v1] : (p4(v1) & p103(v1) & r1(v0, v1) & ~ p104(v1)) & ? [v1] : (p103(v1) & r1(v0, v1) & ~ p4(v1) & ~ p104(v1)))) & ( ~ p102(v0) | (( ~ p3(v0) | ! [v1] : ( ~ p102(v1) | ~ r1(v0, v1) | p3(v1))) & (p3(v0) | ! [v1] : ( ~ p102(v1) | ~ p3(v1) | ~ r1(v0, v1))))) & ( ~ p103(v0) | p102(v0)) & ( ~ p103(v0) | p104(v0) | ( ? [v1] : (p5(v1) & p104(v1) & r1(v0, v1) & ~ p105(v1)) & ? [v1] : (p104(v1) & r1(v0, v1) & ~ p5(v1) & ~ p105(v1)))) & ( ~ p103(v0) | (( ~ p4(v0) | ! [v1] : ( ~ p103(v1) | ~ r1(v0, v1) | p4(v1))) & (p4(v0) | ! [v1] : ( ~ p4(v1) | ~ p103(v1) | ~ r1(v0, v1))))) & ( ~ p104(v0) | p103(v0)) & ( ~ p104(v0) | p105(v0) | ( ? [v1] : (p105(v1) & p6(v1) & r1(v0, v1) & ~ p106(v1)) & ? [v1] : (p105(v1) & r1(v0, v1) & ~ p106(v1) & ~ p6(v1)))) & ( ~ p104(v0) | (( ~ p5(v0) | ! [v1] : ( ~ p104(v1) | ~ r1(v0, v1) | p5(v1))) & (p5(v0) | ! [v1] : ( ~ p5(v1) | ~ p104(v1) | ~ r1(v0, v1))))) & ( ~ p105(v0) | p104(v0)) & ( ~ p105(v0) | (( ~ p6(v0) | ! [v1] : ( ~ p105(v1) | ~ r1(v0, v1) | p6(v1))) & (p6(v0) | ! [v1] : ( ~ p105(v1) | ~ p6(v1) | ~ r1(v0, v1))))) & ( ~ p106(v0) | p105(v0))))
% 34.68/10.81 |
% 34.68/10.81 +-Applying beta-rule and splitting (29), into two cases.
% 34.68/10.81 |-Branch one:
% 34.68/10.81 | (12) ~ r1(all_0_0_0, all_0_0_0)
% 34.68/10.81 |
% 34.68/10.81 | Using (13) and (12) yields:
% 34.68/10.81 | (14) $false
% 34.68/10.81 |
% 34.68/10.81 |-The branch is then unsatisfiable
% 34.68/10.81 |-Branch two:
% 34.68/10.81 | (36) ! [v0] : ( ~ r1(all_0_0_0, v0) | ! [v1] : ( ~ r1(v0, v1) | p3(v1)))
% 34.68/10.81 |
% 34.68/10.81 +-Applying beta-rule and splitting (33), into two cases.
% 34.68/10.81 |-Branch one:
% 34.68/10.81 | (12) ~ r1(all_0_0_0, all_0_0_0)
% 34.68/10.81 |
% 34.68/10.81 | Using (13) and (12) yields:
% 34.68/10.81 | (14) $false
% 34.68/10.81 |
% 34.68/10.81 |-The branch is then unsatisfiable
% 34.68/10.81 |-Branch two:
% 34.68/10.81 | (39) ! [v0] : ( ~ r1(all_0_0_0, v0) | (( ~ p100(v0) | p101(v0) | ( ? [v1] : (p2(v1) & p101(v1) & r1(v0, v1) & ~ p102(v1)) & ? [v1] : (p101(v1) & r1(v0, v1) & ~ p2(v1) & ~ p102(v1)))) & ( ~ p100(v0) | (( ~ p1(v0) | ! [v1] : ( ~ p100(v1) | ~ r1(v0, v1) | p1(v1))) & (p1(v0) | ! [v1] : ( ~ p1(v1) | ~ p100(v1) | ~ r1(v0, v1))))) & ( ~ p101(v0) | p100(v0)) & ( ~ p101(v0) | p102(v0) | ( ? [v1] : (p102(v1) & p3(v1) & r1(v0, v1) & ~ p103(v1)) & ? [v1] : (p102(v1) & r1(v0, v1) & ~ p103(v1) & ~ p3(v1)))) & ( ~ p101(v0) | (( ~ p2(v0) | ! [v1] : ( ~ p101(v1) | ~ r1(v0, v1) | p2(v1))) & (p2(v0) | ! [v1] : ( ~ p2(v1) | ~ p101(v1) | ~ r1(v0, v1))))) & ( ~ p102(v0) | p101(v0)) & ( ~ p102(v0) | p103(v0) | ( ? [v1] : (p4(v1) & p103(v1) & r1(v0, v1) & ~ p104(v1)) & ? [v1] : (p103(v1) & r1(v0, v1) & ~ p4(v1) & ~ p104(v1)))) & ( ~ p102(v0) | (( ~ p3(v0) | ! [v1] : ( ~ p102(v1) | ~ r1(v0, v1) | p3(v1))) & (p3(v0) | ! [v1] : ( ~ p102(v1) | ~ p3(v1) | ~ r1(v0, v1))))) & ( ~ p103(v0) | p102(v0)) & ( ~ p103(v0) | p104(v0) | ( ? [v1] : (p5(v1) & p104(v1) & r1(v0, v1) & ~ p105(v1)) & ? [v1] : (p104(v1) & r1(v0, v1) & ~ p5(v1) & ~ p105(v1)))) & ( ~ p103(v0) | (( ~ p4(v0) | ! [v1] : ( ~ p103(v1) | ~ r1(v0, v1) | p4(v1))) & (p4(v0) | ! [v1] : ( ~ p4(v1) | ~ p103(v1) | ~ r1(v0, v1))))) & ( ~ p104(v0) | p103(v0)) & ( ~ p104(v0) | p105(v0) | ( ? [v1] : (p105(v1) & p6(v1) & r1(v0, v1) & ~ p106(v1)) & ? [v1] : (p105(v1) & r1(v0, v1) & ~ p106(v1) & ~ p6(v1)))) & ( ~ p104(v0) | (( ~ p5(v0) | ! [v1] : ( ~ p104(v1) | ~ r1(v0, v1) | p5(v1))) & (p5(v0) | ! [v1] : ( ~ p5(v1) | ~ p104(v1) | ~ r1(v0, v1))))) & ( ~ p105(v0) | p104(v0)) & ( ~ p105(v0) | (( ~ p6(v0) | ! [v1] : ( ~ p105(v1) | ~ r1(v0, v1) | p6(v1))) & (p6(v0) | ! [v1] : ( ~ p105(v1) | ~ p6(v1) | ~ r1(v0, v1))))) & ( ~ p106(v0) | p105(v0))))
% 34.71/10.81 |
% 34.71/10.81 | Instantiating formula (39) with all_0_0_0 yields:
% 34.71/10.81 | (40) ~ r1(all_0_0_0, all_0_0_0) | (( ~ p100(all_0_0_0) | p101(all_0_0_0) | ( ? [v0] : (p2(v0) & p101(v0) & r1(all_0_0_0, v0) & ~ p102(v0)) & ? [v0] : (p101(v0) & r1(all_0_0_0, v0) & ~ p2(v0) & ~ p102(v0)))) & ( ~ p100(all_0_0_0) | (( ~ p1(all_0_0_0) | ! [v0] : ( ~ p100(v0) | ~ r1(all_0_0_0, v0) | p1(v0))) & (p1(all_0_0_0) | ! [v0] : ( ~ p1(v0) | ~ p100(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p101(all_0_0_0) | p100(all_0_0_0)) & ( ~ p101(all_0_0_0) | p102(all_0_0_0) | ( ? [v0] : (p102(v0) & p3(v0) & r1(all_0_0_0, v0) & ~ p103(v0)) & ? [v0] : (p102(v0) & r1(all_0_0_0, v0) & ~ p103(v0) & ~ p3(v0)))) & ( ~ p101(all_0_0_0) | (( ~ p2(all_0_0_0) | ! [v0] : ( ~ p101(v0) | ~ r1(all_0_0_0, v0) | p2(v0))) & (p2(all_0_0_0) | ! [v0] : ( ~ p2(v0) | ~ p101(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p102(all_0_0_0) | p101(all_0_0_0)) & ( ~ p102(all_0_0_0) | p103(all_0_0_0) | ( ? [v0] : (p4(v0) & p103(v0) & r1(all_0_0_0, v0) & ~ p104(v0)) & ? [v0] : (p103(v0) & r1(all_0_0_0, v0) & ~ p4(v0) & ~ p104(v0)))) & ( ~ p102(all_0_0_0) | (( ~ p3(all_0_0_0) | ! [v0] : ( ~ p102(v0) | ~ r1(all_0_0_0, v0) | p3(v0))) & (p3(all_0_0_0) | ! [v0] : ( ~ p102(v0) | ~ p3(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p103(all_0_0_0) | p102(all_0_0_0)) & ( ~ p103(all_0_0_0) | p104(all_0_0_0) | ( ? [v0] : (p5(v0) & p104(v0) & r1(all_0_0_0, v0) & ~ p105(v0)) & ? [v0] : (p104(v0) & r1(all_0_0_0, v0) & ~ p5(v0) & ~ p105(v0)))) & ( ~ p103(all_0_0_0) | (( ~ p4(all_0_0_0) | ! [v0] : ( ~ p103(v0) | ~ r1(all_0_0_0, v0) | p4(v0))) & (p4(all_0_0_0) | ! [v0] : ( ~ p4(v0) | ~ p103(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p104(all_0_0_0) | p103(all_0_0_0)) & ( ~ p104(all_0_0_0) | p105(all_0_0_0) | ( ? [v0] : (p105(v0) & p6(v0) & r1(all_0_0_0, v0) & ~ p106(v0)) & ? [v0] : (p105(v0) & r1(all_0_0_0, v0) & ~ p106(v0) & ~ p6(v0)))) & ( ~ p104(all_0_0_0) | (( ~ p5(all_0_0_0) | ! [v0] : ( ~ p104(v0) | ~ r1(all_0_0_0, v0) | p5(v0))) & (p5(all_0_0_0) | ! [v0] : ( ~ p5(v0) | ~ p104(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p105(all_0_0_0) | p104(all_0_0_0)) & ( ~ p105(all_0_0_0) | (( ~ p6(all_0_0_0) | ! [v0] : ( ~ p105(v0) | ~ r1(all_0_0_0, v0) | p6(v0))) & (p6(all_0_0_0) | ! [v0] : ( ~ p105(v0) | ~ p6(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p106(all_0_0_0) | p105(all_0_0_0)))
% 34.71/10.82 |
% 34.71/10.82 +-Applying beta-rule and splitting (40), into two cases.
% 34.71/10.82 |-Branch one:
% 34.71/10.82 | (12) ~ r1(all_0_0_0, all_0_0_0)
% 34.71/10.82 |
% 34.71/10.82 | Using (13) and (12) yields:
% 34.71/10.82 | (14) $false
% 34.71/10.82 |
% 34.71/10.82 |-The branch is then unsatisfiable
% 34.71/10.82 |-Branch two:
% 34.71/10.82 | (43) ( ~ p100(all_0_0_0) | p101(all_0_0_0) | ( ? [v0] : (p2(v0) & p101(v0) & r1(all_0_0_0, v0) & ~ p102(v0)) & ? [v0] : (p101(v0) & r1(all_0_0_0, v0) & ~ p2(v0) & ~ p102(v0)))) & ( ~ p100(all_0_0_0) | (( ~ p1(all_0_0_0) | ! [v0] : ( ~ p100(v0) | ~ r1(all_0_0_0, v0) | p1(v0))) & (p1(all_0_0_0) | ! [v0] : ( ~ p1(v0) | ~ p100(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p101(all_0_0_0) | p100(all_0_0_0)) & ( ~ p101(all_0_0_0) | p102(all_0_0_0) | ( ? [v0] : (p102(v0) & p3(v0) & r1(all_0_0_0, v0) & ~ p103(v0)) & ? [v0] : (p102(v0) & r1(all_0_0_0, v0) & ~ p103(v0) & ~ p3(v0)))) & ( ~ p101(all_0_0_0) | (( ~ p2(all_0_0_0) | ! [v0] : ( ~ p101(v0) | ~ r1(all_0_0_0, v0) | p2(v0))) & (p2(all_0_0_0) | ! [v0] : ( ~ p2(v0) | ~ p101(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p102(all_0_0_0) | p101(all_0_0_0)) & ( ~ p102(all_0_0_0) | p103(all_0_0_0) | ( ? [v0] : (p4(v0) & p103(v0) & r1(all_0_0_0, v0) & ~ p104(v0)) & ? [v0] : (p103(v0) & r1(all_0_0_0, v0) & ~ p4(v0) & ~ p104(v0)))) & ( ~ p102(all_0_0_0) | (( ~ p3(all_0_0_0) | ! [v0] : ( ~ p102(v0) | ~ r1(all_0_0_0, v0) | p3(v0))) & (p3(all_0_0_0) | ! [v0] : ( ~ p102(v0) | ~ p3(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p103(all_0_0_0) | p102(all_0_0_0)) & ( ~ p103(all_0_0_0) | p104(all_0_0_0) | ( ? [v0] : (p5(v0) & p104(v0) & r1(all_0_0_0, v0) & ~ p105(v0)) & ? [v0] : (p104(v0) & r1(all_0_0_0, v0) & ~ p5(v0) & ~ p105(v0)))) & ( ~ p103(all_0_0_0) | (( ~ p4(all_0_0_0) | ! [v0] : ( ~ p103(v0) | ~ r1(all_0_0_0, v0) | p4(v0))) & (p4(all_0_0_0) | ! [v0] : ( ~ p4(v0) | ~ p103(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p104(all_0_0_0) | p103(all_0_0_0)) & ( ~ p104(all_0_0_0) | p105(all_0_0_0) | ( ? [v0] : (p105(v0) & p6(v0) & r1(all_0_0_0, v0) & ~ p106(v0)) & ? [v0] : (p105(v0) & r1(all_0_0_0, v0) & ~ p106(v0) & ~ p6(v0)))) & ( ~ p104(all_0_0_0) | (( ~ p5(all_0_0_0) | ! [v0] : ( ~ p104(v0) | ~ r1(all_0_0_0, v0) | p5(v0))) & (p5(all_0_0_0) | ! [v0] : ( ~ p5(v0) | ~ p104(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p105(all_0_0_0) | p104(all_0_0_0)) & ( ~ p105(all_0_0_0) | (( ~ p6(all_0_0_0) | ! [v0] : ( ~ p105(v0) | ~ r1(all_0_0_0, v0) | p6(v0))) & (p6(all_0_0_0) | ! [v0] : ( ~ p105(v0) | ~ p6(v0) | ~ r1(all_0_0_0, v0))))) & ( ~ p106(all_0_0_0) | p105(all_0_0_0))
% 34.71/10.82 |
% 34.71/10.82 | Applying alpha-rule on (43) yields:
% 34.71/10.82 | (44) ~ p105(all_0_0_0) | (( ~ p6(all_0_0_0) | ! [v0] : ( ~ p105(v0) | ~ r1(all_0_0_0, v0) | p6(v0))) & (p6(all_0_0_0) | ! [v0] : ( ~ p105(v0) | ~ p6(v0) | ~ r1(all_0_0_0, v0))))
% 34.71/10.82 | (45) ~ p103(all_0_0_0) | p104(all_0_0_0) | ( ? [v0] : (p5(v0) & p104(v0) & r1(all_0_0_0, v0) & ~ p105(v0)) & ? [v0] : (p104(v0) & r1(all_0_0_0, v0) & ~ p5(v0) & ~ p105(v0)))
% 34.71/10.82 | (46) ~ p102(all_0_0_0) | p101(all_0_0_0)
% 34.71/10.82 | (47) ~ p101(all_0_0_0) | (( ~ p2(all_0_0_0) | ! [v0] : ( ~ p101(v0) | ~ r1(all_0_0_0, v0) | p2(v0))) & (p2(all_0_0_0) | ! [v0] : ( ~ p2(v0) | ~ p101(v0) | ~ r1(all_0_0_0, v0))))
% 34.71/10.83 | (48) ~ p104(all_0_0_0) | p103(all_0_0_0)
% 34.71/10.83 | (49) ~ p103(all_0_0_0) | p102(all_0_0_0)
% 34.71/10.83 | (50) ~ p104(all_0_0_0) | p105(all_0_0_0) | ( ? [v0] : (p105(v0) & p6(v0) & r1(all_0_0_0, v0) & ~ p106(v0)) & ? [v0] : (p105(v0) & r1(all_0_0_0, v0) & ~ p106(v0) & ~ p6(v0)))
% 34.71/10.83 | (51) ~ p100(all_0_0_0) | (( ~ p1(all_0_0_0) | ! [v0] : ( ~ p100(v0) | ~ r1(all_0_0_0, v0) | p1(v0))) & (p1(all_0_0_0) | ! [v0] : ( ~ p1(v0) | ~ p100(v0) | ~ r1(all_0_0_0, v0))))
% 34.71/10.83 | (52) ~ p102(all_0_0_0) | (( ~ p3(all_0_0_0) | ! [v0] : ( ~ p102(v0) | ~ r1(all_0_0_0, v0) | p3(v0))) & (p3(all_0_0_0) | ! [v0] : ( ~ p102(v0) | ~ p3(v0) | ~ r1(all_0_0_0, v0))))
% 34.71/10.83 | (53) ~ p106(all_0_0_0) | p105(all_0_0_0)
% 34.71/10.83 | (54) ~ p102(all_0_0_0) | p103(all_0_0_0) | ( ? [v0] : (p4(v0) & p103(v0) & r1(all_0_0_0, v0) & ~ p104(v0)) & ? [v0] : (p103(v0) & r1(all_0_0_0, v0) & ~ p4(v0) & ~ p104(v0)))
% 34.71/10.83 | (55) ~ p105(all_0_0_0) | p104(all_0_0_0)
% 34.71/10.83 | (56) ~ p101(all_0_0_0) | p102(all_0_0_0) | ( ? [v0] : (p102(v0) & p3(v0) & r1(all_0_0_0, v0) & ~ p103(v0)) & ? [v0] : (p102(v0) & r1(all_0_0_0, v0) & ~ p103(v0) & ~ p3(v0)))
% 34.71/10.83 | (57) ~ p101(all_0_0_0) | p100(all_0_0_0)
% 34.71/10.83 | (58) ~ p100(all_0_0_0) | p101(all_0_0_0) | ( ? [v0] : (p2(v0) & p101(v0) & r1(all_0_0_0, v0) & ~ p102(v0)) & ? [v0] : (p101(v0) & r1(all_0_0_0, v0) & ~ p2(v0) & ~ p102(v0)))
% 34.71/10.83 | (59) ~ p104(all_0_0_0) | (( ~ p5(all_0_0_0) | ! [v0] : ( ~ p104(v0) | ~ r1(all_0_0_0, v0) | p5(v0))) & (p5(all_0_0_0) | ! [v0] : ( ~ p5(v0) | ~ p104(v0) | ~ r1(all_0_0_0, v0))))
% 34.71/10.83 | (60) ~ p103(all_0_0_0) | (( ~ p4(all_0_0_0) | ! [v0] : ( ~ p103(v0) | ~ r1(all_0_0_0, v0) | p4(v0))) & (p4(all_0_0_0) | ! [v0] : ( ~ p4(v0) | ~ p103(v0) | ~ r1(all_0_0_0, v0))))
% 34.71/10.83 |
% 34.71/10.83 +-Applying beta-rule and splitting (58), into two cases.
% 34.71/10.83 |-Branch one:
% 34.71/10.83 | (61) ~ p100(all_0_0_0)
% 34.71/10.83 |
% 34.71/10.83 | Using (4) and (61) yields:
% 34.71/10.83 | (14) $false
% 34.71/10.83 |
% 34.71/10.83 |-The branch is then unsatisfiable
% 34.71/10.83 |-Branch two:
% 34.71/10.83 | (63) p101(all_0_0_0) | ( ? [v0] : (p2(v0) & p101(v0) & r1(all_0_0_0, v0) & ~ p102(v0)) & ? [v0] : (p101(v0) & r1(all_0_0_0, v0) & ~ p2(v0) & ~ p102(v0)))
% 34.71/10.83 |
% 34.71/10.83 +-Applying beta-rule and splitting (63), into two cases.
% 34.71/10.83 |-Branch one:
% 34.71/10.83 | (64) p101(all_0_0_0)
% 34.71/10.83 |
% 34.71/10.83 | Using (64) and (5) yields:
% 34.71/10.83 | (14) $false
% 34.71/10.83 |
% 34.71/10.83 |-The branch is then unsatisfiable
% 34.71/10.83 |-Branch two:
% 34.71/10.83 | (66) ? [v0] : (p2(v0) & p101(v0) & r1(all_0_0_0, v0) & ~ p102(v0)) & ? [v0] : (p101(v0) & r1(all_0_0_0, v0) & ~ p2(v0) & ~ p102(v0))
% 34.71/10.83 |
% 34.71/10.83 | Applying alpha-rule on (66) yields:
% 34.71/10.83 | (67) ? [v0] : (p2(v0) & p101(v0) & r1(all_0_0_0, v0) & ~ p102(v0))
% 34.71/10.83 | (68) ? [v0] : (p101(v0) & r1(all_0_0_0, v0) & ~ p2(v0) & ~ p102(v0))
% 34.71/10.83 |
% 34.71/10.83 | Instantiating (68) with all_79_0_2 yields:
% 34.71/10.83 | (69) p101(all_79_0_2) & r1(all_0_0_0, all_79_0_2) & ~ p2(all_79_0_2) & ~ p102(all_79_0_2)
% 34.71/10.83 |
% 34.71/10.83 | Applying alpha-rule on (69) yields:
% 34.71/10.83 | (70) p101(all_79_0_2)
% 34.71/10.83 | (71) r1(all_0_0_0, all_79_0_2)
% 34.71/10.83 | (72) ~ p2(all_79_0_2)
% 34.71/10.83 | (73) ~ p102(all_79_0_2)
% 34.71/10.83 |
% 34.71/10.83 | Instantiating formula (36) with all_79_0_2 and discharging atoms r1(all_0_0_0, all_79_0_2), yields:
% 34.71/10.83 | (74) ! [v0] : ( ~ r1(all_79_0_2, v0) | p3(v0))
% 34.71/10.84 |
% 34.71/10.84 | Instantiating formula (39) with all_79_0_2 and discharging atoms r1(all_0_0_0, all_79_0_2), yields:
% 34.71/10.84 | (75) ( ~ p100(all_79_0_2) | p101(all_79_0_2) | ( ? [v0] : (p2(v0) & p101(v0) & r1(all_79_0_2, v0) & ~ p102(v0)) & ? [v0] : (p101(v0) & r1(all_79_0_2, v0) & ~ p2(v0) & ~ p102(v0)))) & ( ~ p100(all_79_0_2) | (( ~ p1(all_79_0_2) | ! [v0] : ( ~ p100(v0) | ~ r1(all_79_0_2, v0) | p1(v0))) & (p1(all_79_0_2) | ! [v0] : ( ~ p1(v0) | ~ p100(v0) | ~ r1(all_79_0_2, v0))))) & ( ~ p101(all_79_0_2) | p100(all_79_0_2)) & ( ~ p101(all_79_0_2) | p102(all_79_0_2) | ( ? [v0] : (p102(v0) & p3(v0) & r1(all_79_0_2, v0) & ~ p103(v0)) & ? [v0] : (p102(v0) & r1(all_79_0_2, v0) & ~ p103(v0) & ~ p3(v0)))) & ( ~ p101(all_79_0_2) | (( ~ p2(all_79_0_2) | ! [v0] : ( ~ p101(v0) | ~ r1(all_79_0_2, v0) | p2(v0))) & (p2(all_79_0_2) | ! [v0] : ( ~ p2(v0) | ~ p101(v0) | ~ r1(all_79_0_2, v0))))) & ( ~ p102(all_79_0_2) | p101(all_79_0_2)) & ( ~ p102(all_79_0_2) | p103(all_79_0_2) | ( ? [v0] : (p4(v0) & p103(v0) & r1(all_79_0_2, v0) & ~ p104(v0)) & ? [v0] : (p103(v0) & r1(all_79_0_2, v0) & ~ p4(v0) & ~ p104(v0)))) & ( ~ p102(all_79_0_2) | (( ~ p3(all_79_0_2) | ! [v0] : ( ~ p102(v0) | ~ r1(all_79_0_2, v0) | p3(v0))) & (p3(all_79_0_2) | ! [v0] : ( ~ p102(v0) | ~ p3(v0) | ~ r1(all_79_0_2, v0))))) & ( ~ p103(all_79_0_2) | p102(all_79_0_2)) & ( ~ p103(all_79_0_2) | p104(all_79_0_2) | ( ? [v0] : (p5(v0) & p104(v0) & r1(all_79_0_2, v0) & ~ p105(v0)) & ? [v0] : (p104(v0) & r1(all_79_0_2, v0) & ~ p5(v0) & ~ p105(v0)))) & ( ~ p103(all_79_0_2) | (( ~ p4(all_79_0_2) | ! [v0] : ( ~ p103(v0) | ~ r1(all_79_0_2, v0) | p4(v0))) & (p4(all_79_0_2) | ! [v0] : ( ~ p4(v0) | ~ p103(v0) | ~ r1(all_79_0_2, v0))))) & ( ~ p104(all_79_0_2) | p103(all_79_0_2)) & ( ~ p104(all_79_0_2) | p105(all_79_0_2) | ( ? [v0] : (p105(v0) & p6(v0) & r1(all_79_0_2, v0) & ~ p106(v0)) & ? [v0] : (p105(v0) & r1(all_79_0_2, v0) & ~ p106(v0) & ~ p6(v0)))) & ( ~ p104(all_79_0_2) | (( ~ p5(all_79_0_2) | ! [v0] : ( ~ p104(v0) | ~ r1(all_79_0_2, v0) | p5(v0))) & (p5(all_79_0_2) | ! [v0] : ( ~ p5(v0) | ~ p104(v0) | ~ r1(all_79_0_2, v0))))) & ( ~ p105(all_79_0_2) | p104(all_79_0_2)) & ( ~ p105(all_79_0_2) | (( ~ p6(all_79_0_2) | ! [v0] : ( ~ p105(v0) | ~ r1(all_79_0_2, v0) | p6(v0))) & (p6(all_79_0_2) | ! [v0] : ( ~ p105(v0) | ~ p6(v0) | ~ r1(all_79_0_2, v0))))) & ( ~ p106(all_79_0_2) | p105(all_79_0_2))
% 34.71/10.84 |
% 34.71/10.84 | Applying alpha-rule on (75) yields:
% 34.71/10.84 | (76) ~ p104(all_79_0_2) | p105(all_79_0_2) | ( ? [v0] : (p105(v0) & p6(v0) & r1(all_79_0_2, v0) & ~ p106(v0)) & ? [v0] : (p105(v0) & r1(all_79_0_2, v0) & ~ p106(v0) & ~ p6(v0)))
% 34.71/10.84 | (77) ~ p103(all_79_0_2) | (( ~ p4(all_79_0_2) | ! [v0] : ( ~ p103(v0) | ~ r1(all_79_0_2, v0) | p4(v0))) & (p4(all_79_0_2) | ! [v0] : ( ~ p4(v0) | ~ p103(v0) | ~ r1(all_79_0_2, v0))))
% 34.71/10.84 | (78) ~ p104(all_79_0_2) | (( ~ p5(all_79_0_2) | ! [v0] : ( ~ p104(v0) | ~ r1(all_79_0_2, v0) | p5(v0))) & (p5(all_79_0_2) | ! [v0] : ( ~ p5(v0) | ~ p104(v0) | ~ r1(all_79_0_2, v0))))
% 34.71/10.84 | (79) ~ p105(all_79_0_2) | (( ~ p6(all_79_0_2) | ! [v0] : ( ~ p105(v0) | ~ r1(all_79_0_2, v0) | p6(v0))) & (p6(all_79_0_2) | ! [v0] : ( ~ p105(v0) | ~ p6(v0) | ~ r1(all_79_0_2, v0))))
% 34.71/10.84 | (80) ~ p101(all_79_0_2) | p100(all_79_0_2)
% 34.71/10.84 | (81) ~ p103(all_79_0_2) | p102(all_79_0_2)
% 34.71/10.84 | (82) ~ p102(all_79_0_2) | p103(all_79_0_2) | ( ? [v0] : (p4(v0) & p103(v0) & r1(all_79_0_2, v0) & ~ p104(v0)) & ? [v0] : (p103(v0) & r1(all_79_0_2, v0) & ~ p4(v0) & ~ p104(v0)))
% 34.71/10.84 | (83) ~ p101(all_79_0_2) | p102(all_79_0_2) | ( ? [v0] : (p102(v0) & p3(v0) & r1(all_79_0_2, v0) & ~ p103(v0)) & ? [v0] : (p102(v0) & r1(all_79_0_2, v0) & ~ p103(v0) & ~ p3(v0)))
% 34.71/10.84 | (84) ~ p106(all_79_0_2) | p105(all_79_0_2)
% 34.71/10.84 | (85) ~ p102(all_79_0_2) | p101(all_79_0_2)
% 34.71/10.84 | (86) ~ p105(all_79_0_2) | p104(all_79_0_2)
% 34.71/10.84 | (87) ~ p100(all_79_0_2) | p101(all_79_0_2) | ( ? [v0] : (p2(v0) & p101(v0) & r1(all_79_0_2, v0) & ~ p102(v0)) & ? [v0] : (p101(v0) & r1(all_79_0_2, v0) & ~ p2(v0) & ~ p102(v0)))
% 34.71/10.84 | (88) ~ p104(all_79_0_2) | p103(all_79_0_2)
% 34.71/10.84 | (89) ~ p100(all_79_0_2) | (( ~ p1(all_79_0_2) | ! [v0] : ( ~ p100(v0) | ~ r1(all_79_0_2, v0) | p1(v0))) & (p1(all_79_0_2) | ! [v0] : ( ~ p1(v0) | ~ p100(v0) | ~ r1(all_79_0_2, v0))))
% 34.71/10.84 | (90) ~ p103(all_79_0_2) | p104(all_79_0_2) | ( ? [v0] : (p5(v0) & p104(v0) & r1(all_79_0_2, v0) & ~ p105(v0)) & ? [v0] : (p104(v0) & r1(all_79_0_2, v0) & ~ p5(v0) & ~ p105(v0)))
% 34.71/10.84 | (91) ~ p102(all_79_0_2) | (( ~ p3(all_79_0_2) | ! [v0] : ( ~ p102(v0) | ~ r1(all_79_0_2, v0) | p3(v0))) & (p3(all_79_0_2) | ! [v0] : ( ~ p102(v0) | ~ p3(v0) | ~ r1(all_79_0_2, v0))))
% 34.71/10.84 | (92) ~ p101(all_79_0_2) | (( ~ p2(all_79_0_2) | ! [v0] : ( ~ p101(v0) | ~ r1(all_79_0_2, v0) | p2(v0))) & (p2(all_79_0_2) | ! [v0] : ( ~ p2(v0) | ~ p101(v0) | ~ r1(all_79_0_2, v0))))
% 34.71/10.84 |
% 34.71/10.84 +-Applying beta-rule and splitting (83), into two cases.
% 34.71/10.84 |-Branch one:
% 34.71/10.84 | (93) ~ p101(all_79_0_2)
% 34.71/10.84 |
% 34.71/10.84 | Using (70) and (93) yields:
% 34.71/10.84 | (14) $false
% 34.71/10.84 |
% 34.71/10.84 |-The branch is then unsatisfiable
% 34.71/10.84 |-Branch two:
% 34.71/10.84 | (95) p102(all_79_0_2) | ( ? [v0] : (p102(v0) & p3(v0) & r1(all_79_0_2, v0) & ~ p103(v0)) & ? [v0] : (p102(v0) & r1(all_79_0_2, v0) & ~ p103(v0) & ~ p3(v0)))
% 34.71/10.84 |
% 34.71/10.84 +-Applying beta-rule and splitting (95), into two cases.
% 34.71/10.84 |-Branch one:
% 34.71/10.84 | (96) p102(all_79_0_2)
% 34.71/10.84 |
% 34.71/10.84 | Using (96) and (73) yields:
% 34.71/10.84 | (14) $false
% 34.71/10.84 |
% 34.71/10.84 |-The branch is then unsatisfiable
% 34.71/10.84 |-Branch two:
% 34.71/10.84 | (98) ? [v0] : (p102(v0) & p3(v0) & r1(all_79_0_2, v0) & ~ p103(v0)) & ? [v0] : (p102(v0) & r1(all_79_0_2, v0) & ~ p103(v0) & ~ p3(v0))
% 34.71/10.84 |
% 34.71/10.84 | Applying alpha-rule on (98) yields:
% 34.71/10.84 | (99) ? [v0] : (p102(v0) & p3(v0) & r1(all_79_0_2, v0) & ~ p103(v0))
% 34.71/10.84 | (100) ? [v0] : (p102(v0) & r1(all_79_0_2, v0) & ~ p103(v0) & ~ p3(v0))
% 34.71/10.85 |
% 34.71/10.85 | Instantiating (100) with all_149_0_4 yields:
% 34.71/10.85 | (101) p102(all_149_0_4) & r1(all_79_0_2, all_149_0_4) & ~ p103(all_149_0_4) & ~ p3(all_149_0_4)
% 34.71/10.85 |
% 34.71/10.85 | Applying alpha-rule on (101) yields:
% 34.71/10.85 | (102) p102(all_149_0_4)
% 34.71/10.85 | (103) r1(all_79_0_2, all_149_0_4)
% 34.71/10.85 | (104) ~ p103(all_149_0_4)
% 34.71/10.85 | (105) ~ p3(all_149_0_4)
% 34.71/10.85 |
% 34.71/10.85 | Instantiating formula (74) with all_149_0_4 and discharging atoms r1(all_79_0_2, all_149_0_4), ~ p3(all_149_0_4), yields:
% 34.71/10.85 | (14) $false
% 34.71/10.85 |
% 34.71/10.85 |-The branch is then unsatisfiable
% 34.71/10.85 % SZS output end Proof for theBenchmark
% 34.71/10.85
% 34.71/10.85 10242ms
%------------------------------------------------------------------------------