TSTP Solution File: LCL642+1.001 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL642+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n024.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 : 300s
% DateTime : Thu Aug 31 08:11:54 EDT 2023
% Result : Theorem 133.43s 18.10s
% Output : Proof 134.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL642+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n024.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 : 300
% 0.12/0.33 % DateTime : Thu Aug 24 17:51:24 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.63/1.14 Prover 4: Preprocessing ...
% 2.63/1.14 Prover 1: Preprocessing ...
% 3.24/1.18 Prover 3: Preprocessing ...
% 3.24/1.18 Prover 5: Preprocessing ...
% 3.24/1.19 Prover 0: Preprocessing ...
% 3.24/1.19 Prover 2: Preprocessing ...
% 3.49/1.20 Prover 6: Preprocessing ...
% 5.12/1.51 Prover 5: Constructing countermodel ...
% 5.85/1.53 Prover 2: Constructing countermodel ...
% 6.55/1.68 Prover 1: Constructing countermodel ...
% 7.15/1.72 Prover 3: Constructing countermodel ...
% 7.15/1.72 Prover 6: Proving ...
% 30.93/4.82 Prover 0: Proving ...
% 31.89/4.96 Prover 4: Constructing countermodel ...
% 74.23/10.51 Prover 2: stopped
% 74.84/10.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.84/10.58 Prover 7: Preprocessing ...
% 75.36/10.61 Prover 7: Constructing countermodel ...
% 101.29/13.95 Prover 5: stopped
% 101.29/13.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 101.29/14.05 Prover 8: Preprocessing ...
% 101.93/14.12 Prover 8: Warning: ignoring some quantifiers
% 101.93/14.12 Prover 8: Constructing countermodel ...
% 117.13/16.00 Prover 1: stopped
% 117.52/16.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 117.52/16.07 Prover 9: Preprocessing ...
% 119.14/16.28 Prover 9: Constructing countermodel ...
% 131.19/17.87 Prover 6: stopped
% 131.19/17.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 132.04/17.93 Prover 10: Preprocessing ...
% 132.04/17.95 Prover 10: Constructing countermodel ...
% 132.73/18.08 Prover 10: Found proof (size 50)
% 132.73/18.08 Prover 10: proved (212ms)
% 132.73/18.08 Prover 9: stopped
% 132.73/18.08 Prover 8: stopped
% 132.73/18.08 Prover 3: stopped
% 133.43/18.09 Prover 0: stopped
% 133.43/18.09 Prover 4: stopped
% 133.43/18.10 Prover 7: stopped
% 133.43/18.10
% 133.43/18.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 133.43/18.10
% 133.43/18.10 % SZS output start Proof for theBenchmark
% 133.43/18.10 Assumptions after simplification:
% 133.43/18.10 ---------------------------------
% 133.43/18.10
% 133.43/18.10 (main)
% 133.43/18.13 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 133.43/18.13 $i] : ? [v6: $i] : ($i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 133.43/18.13 $i(v0) & r1(v0, v6) & r1(v0, v5) & r1(v0, v4) & ~ p1(v4) & ~ p2(v5) & ~
% 133.43/18.13 p3(v6) & ! [v7: $i] : ( ~ $i(v7) | ~ r1(v0, v7) | p1(v7) | ? [v8: $i] :
% 133.43/18.13 ? [v9: $i] : ($i(v9) & $i(v8) & p1(v8) & r1(v8, v9) & r1(v7, v8) & ~
% 133.43/18.13 p1(v9))) & ! [v7: $i] : ( ~ $i(v7) | ~ r1(v0, v7) | p2(v7) | ? [v8:
% 133.43/18.13 $i] : ? [v9: $i] : ($i(v9) & $i(v8) & p2(v8) & r1(v8, v9) & r1(v7, v8)
% 133.43/18.13 & ~ p2(v9))) & ! [v7: $i] : ( ~ $i(v7) | ~ r1(v0, v7) | p2(v7) | ?
% 133.43/18.13 [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p2(v8) & ! [v9: $i] : ! [v10: $i] :
% 133.43/18.13 ( ~ $i(v10) | ~ $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v8, v9) |
% 133.43/18.13 p2(v10)))) & ! [v7: $i] : ( ~ $i(v7) | ~ r1(v0, v7) | p3(v7) | ?
% 133.43/18.13 [v8: $i] : ? [v9: $i] : ($i(v9) & $i(v8) & p3(v8) & r1(v8, v9) & r1(v7,
% 133.43/18.13 v8) & ~ p3(v9))) & ((r1(v0, v1) & ! [v7: $i] : ! [v8: $i] : ! [v9:
% 133.43/18.13 $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~
% 133.43/18.13 $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8)
% 133.43/18.13 | ~ $i(v7) | ~ p2(v8) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~
% 133.43/18.13 r1(v8, v9) | ~ r1(v7, v11) | ~ r1(v7, v10) | ~ r1(v7, v8) | ~
% 133.43/18.13 r1(v1, v7) | p2(v13) | p2(v10) | p2(v9) | ? [v14: $i] : ? [v15: $i]
% 133.43/18.13 : ($i(v15) & $i(v14) & ((p2(v14) & r1(v14, v15) & r1(v13, v14) & ~
% 133.43/18.13 p2(v15)) | (p2(v14) & r1(v14, v15) & r1(v10, v14) & ~ p2(v15))
% 133.43/18.13 | (r1(v11, v14) & ~ p2(v14) & ! [v16: $i] : ! [v17: $i] : ( ~
% 133.43/18.13 $i(v17) | ~ $i(v16) | ~ p2(v16) | ~ r1(v16, v17) | ~
% 133.43/18.13 r1(v14, v16) | p2(v17)))))) & ! [v7: $i] : ! [v8: $i] : !
% 133.43/18.13 [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ $i(v12) | ~
% 133.43/18.13 $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ p2(v8) |
% 133.43/18.13 ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8, v9) | ~ r1(v7, v10) |
% 133.43/18.13 ~ r1(v7, v8) | ~ r1(v1, v7) | p2(v12) | p2(v9) | ? [v13: $i] : ?
% 133.43/18.13 [v14: $i] : ($i(v14) & $i(v13) & ((p2(v13) & r1(v13, v14) & r1(v12,
% 133.43/18.13 v13) & ~ p2(v14)) | (r1(v13, v14) & r1(v7, v13) & ~ p2(v14)
% 133.43/18.13 & ! [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~ $i(v15) | ~
% 133.43/18.13 p2(v15) | ~ r1(v15, v16) | ~ r1(v14, v15) | p2(v16))) |
% 133.43/18.13 (r1(v10, v13) & ~ p2(v13) & ! [v15: $i] : ! [v16: $i] : ( ~
% 133.43/18.13 $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v15, v16) | ~
% 133.43/18.13 r1(v13, v15) | p2(v16)))))) & ! [v7: $i] : ! [v8: $i] : !
% 133.43/18.13 [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~
% 133.43/18.13 $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ p2(v8) | ~ r1(v8, v9) | ~ r1(v7,
% 133.43/18.13 v11) | ~ r1(v7, v10) | ~ r1(v7, v8) | ~ r1(v1, v7) | p2(v11) |
% 133.43/18.13 p2(v10) | p2(v9) | ? [v12: $i] : ? [v13: $i] : ($i(v13) & $i(v12) &
% 133.43/18.13 ((p2(v12) & r1(v12, v13) & r1(v11, v12) & ~ p2(v13)) | (p2(v12) &
% 133.43/18.13 r1(v12, v13) & r1(v10, v12) & ~ p2(v13))))) & ! [v7: $i] : !
% 133.43/18.13 [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~
% 133.43/18.13 $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~ r1(v10,
% 133.43/18.13 v11) | ~ r1(v9, v10) | ~ r1(v7, v9) | ~ r1(v7, v8) | ~ r1(v1,
% 133.43/18.13 v7) | p2(v11) | p2(v8) | ? [v12: $i] : ? [v13: $i] : ($i(v13) &
% 133.43/18.13 $i(v12) & ((p2(v12) & r1(v12, v13) & r1(v11, v12) & ~ p2(v13)) |
% 133.43/18.13 (p2(v12) & r1(v12, v13) & r1(v8, v12) & ~ p2(v13)) | (r1(v9, v12)
% 133.43/18.13 & ~ p2(v12) & ! [v14: $i] : ! [v15: $i] : ( ~ $i(v15) | ~
% 133.43/18.13 $i(v14) | ~ p2(v14) | ~ r1(v14, v15) | ~ r1(v12, v14) |
% 133.43/18.13 p2(v15)))))) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 133.43/18.13 [v10: $i] : ( ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ p2(v8)
% 133.43/18.13 | ~ r1(v8, v9) | ~ r1(v7, v10) | ~ r1(v7, v8) | ~ r1(v1, v7) |
% 133.43/18.13 p2(v10) | p2(v9) | ? [v11: $i] : ? [v12: $i] : ($i(v12) & $i(v11) &
% 133.43/18.13 ((p2(v11) & r1(v11, v12) & r1(v10, v11) & ~ p2(v12)) | (r1(v11,
% 133.43/18.13 v12) & r1(v7, v11) & ~ p2(v12) & ! [v13: $i] : ! [v14: $i]
% 133.43/18.13 : ( ~ $i(v14) | ~ $i(v13) | ~ p2(v13) | ~ r1(v13, v14) | ~
% 133.43/18.13 r1(v12, v13) | p2(v14)))))) & ! [v7: $i] : ! [v8: $i] : !
% 133.43/18.13 [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~
% 133.43/18.13 $i(v7) | ~ p2(v7) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) |
% 133.43/18.13 ~ r1(v1, v7) | p2(v10) | ? [v11: $i] : ? [v12: $i] : ($i(v12) &
% 133.43/18.13 $i(v11) & ((p2(v11) & r1(v11, v12) & r1(v10, v11) & ~ p2(v12)) |
% 133.43/18.13 (r1(v11, v12) & r1(v7, v11) & ~ p2(v12) & ! [v13: $i] : ! [v14:
% 133.43/18.13 $i] : ( ~ $i(v14) | ~ $i(v13) | ~ p2(v13) | ~ r1(v13, v14)
% 133.43/18.13 | ~ r1(v12, v13) | p2(v14))) | (r1(v8, v11) & ~ p2(v11) & !
% 133.43/18.13 [v13: $i] : ! [v14: $i] : ( ~ $i(v14) | ~ $i(v13) | ~ p2(v13)
% 133.43/18.13 | ~ r1(v13, v14) | ~ r1(v11, v13) | p2(v14)))))) & ! [v7:
% 133.43/18.13 $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ $i(v7) |
% 133.43/18.13 ~ p2(v7) | ~ r1(v7, v9) | ~ r1(v7, v8) | ~ r1(v1, v7) | p2(v9) |
% 133.43/18.13 p2(v8) | ? [v10: $i] : ? [v11: $i] : ($i(v11) & $i(v10) & ((p2(v10)
% 133.43/18.13 & r1(v10, v11) & r1(v9, v10) & ~ p2(v11)) | (p2(v10) & r1(v10,
% 133.43/18.13 v11) & r1(v8, v10) & ~ p2(v11))))) & ! [v7: $i] : ! [v8:
% 133.43/18.13 $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~ r1(v7, v8) | ~ r1(v1,
% 133.43/18.13 v7) | p2(v8) | ? [v9: $i] : ? [v10: $i] : ($i(v10) & $i(v9) &
% 133.43/18.13 ((p2(v9) & r1(v9, v10) & r1(v8, v9) & ~ p2(v10)) | (r1(v9, v10) &
% 133.43/18.13 r1(v7, v9) & ~ p2(v10) & ! [v11: $i] : ! [v12: $i] : ( ~
% 133.43/18.13 $i(v12) | ~ $i(v11) | ~ p2(v11) | ~ r1(v11, v12) | ~
% 133.43/18.13 r1(v10, v11) | p2(v12)))))) & ((r1(v2, v3) & r1(v1, v2) & ~
% 133.43/18.14 p2(v3) & ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~
% 133.43/18.14 p2(v7) | ~ r1(v7, v8) | ~ r1(v3, v7) | p2(v8)) & ! [v7: $i] : (
% 133.43/18.14 ~ $i(v7) | ~ r1(v1, v7) | p2(v7) | ? [v8: $i] : ? [v9: $i] :
% 133.43/18.14 ($i(v9) & $i(v8) & p2(v8) & r1(v8, v9) & r1(v7, v8) & ~ p2(v9))))
% 133.43/18.14 | ( ~ p2(v1) & ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~
% 133.43/18.14 p2(v7) | ~ r1(v7, v8) | ~ r1(v1, v7) | p2(v8))))) | ((p2(v0) |
% 133.43/18.14 (p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2))) & ( ! [v7: $i] : !
% 133.43/18.14 [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ r1(v7, v8) | ~ r1(v0, v7) |
% 133.43/18.14 p2(v8) | ? [v9: $i] : ? [v10: $i] : ($i(v10) & $i(v9) & p2(v9) &
% 133.43/18.14 r1(v9, v10) & r1(v8, v9) & ~ p2(v10))) | (r1(v0, v3) & ~ p2(v3)
% 133.43/18.14 & ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) |
% 133.43/18.14 ~ r1(v7, v8) | ~ r1(v3, v7) | p2(v8)))))))
% 133.43/18.14
% 133.43/18.14 Those formulas are unsatisfiable:
% 133.43/18.14 ---------------------------------
% 133.43/18.14
% 133.43/18.14 Begin of proof
% 133.43/18.14 |
% 133.43/18.14 | DELTA: instantiating (main) with fresh symbols all_2_0, all_2_1, all_2_2,
% 133.43/18.14 | all_2_3, all_2_4, all_2_5, all_2_6 gives:
% 133.43/18.16 | (1) $i(all_2_0) & $i(all_2_1) & $i(all_2_2) & $i(all_2_3) & $i(all_2_4) &
% 133.43/18.16 | $i(all_2_5) & $i(all_2_6) & r1(all_2_6, all_2_0) & r1(all_2_6, all_2_1)
% 133.43/18.16 | & r1(all_2_6, all_2_2) & ~ p1(all_2_2) & ~ p2(all_2_1) & ~
% 133.43/18.16 | p3(all_2_0) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_6, v0) | p1(v0) |
% 133.43/18.16 | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) &
% 133.43/18.16 | r1(v0, v1) & ~ p1(v2))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 133.43/18.16 | r1(all_2_6, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) &
% 133.43/18.16 | $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2))) & ! [v0:
% 133.43/18.16 | $i] : ( ~ $i(v0) | ~ r1(all_2_6, v0) | p2(v0) | ? [v1: $i] :
% 133.43/18.16 | ($i(v1) & r1(v0, v1) & ~ p2(v1) & ! [v2: $i] : ! [v3: $i] : ( ~
% 133.43/18.16 | $i(v3) | ~ $i(v2) | ~ p2(v2) | ~ r1(v2, v3) | ~ r1(v1, v2) |
% 133.43/18.16 | p2(v3)))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_6, v0) |
% 133.43/18.16 | p3(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p3(v1) &
% 133.43/18.16 | r1(v1, v2) & r1(v0, v1) & ~ p3(v2))) & ((r1(all_2_6, all_2_5) & !
% 133.43/18.16 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 133.43/18.16 | ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 133.43/18.16 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~
% 133.43/18.16 | r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~
% 133.43/18.16 | r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v6) | p2(v3)
% 133.43/18.16 | | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) & $i(v7) &
% 133.43/18.16 | ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) | (p2(v7) &
% 133.43/18.16 | r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7) & ~
% 133.43/18.16 | p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~
% 133.43/18.16 | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) |
% 133.43/18.16 | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 133.43/18.16 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) |
% 133.43/18.16 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~
% 133.43/18.16 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~
% 133.43/18.16 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] :
% 133.43/18.16 | ? [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5,
% 133.43/18.16 | v6) & ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) &
% 133.43/18.16 | ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~
% 133.43/18.16 | p2(v8) | ~ r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) |
% 133.43/18.16 | (r1(v3, v6) & ~ p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~
% 133.43/18.16 | $i(v9) | ~ $i(v8) | ~ p2(v8) | ~ r1(v8, v9) | ~
% 133.43/18.16 | r1(v6, v8) | p2(v9)))))) & ! [v0: $i] : ! [v1: $i] : !
% 133.43/18.16 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~
% 133.43/18.16 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~
% 133.43/18.16 | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.43/18.16 | p2(v4) | p2(v3) | p2(v2) | ? [v5: $i] : ? [v6: $i] : ($i(v6) &
% 133.43/18.16 | $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4, v5) & ~ p2(v6)) |
% 133.43/18.16 | (p2(v5) & r1(v5, v6) & r1(v3, v5) & ~ p2(v6))))) & ! [v0:
% 133.43/18.16 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 133.43/18.16 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 133.43/18.16 | p2(v0) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | ~
% 133.43/18.16 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v1) | ? [v5: $i] :
% 133.43/18.16 | ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4,
% 133.43/18.16 | v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v1, v5) & ~
% 133.43/18.16 | p2(v6)) | (r1(v2, v5) & ~ p2(v5) & ! [v7: $i] : ! [v8:
% 133.43/18.16 | $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~ r1(v7, v8)
% 133.43/18.16 | | ~ r1(v5, v7) | p2(v8)))))) & ! [v0: $i] : ! [v1: $i]
% 133.43/18.16 | : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 133.43/18.16 | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0,
% 133.43/18.16 | v1) | ~ r1(all_2_5, v0) | p2(v3) | p2(v2) | ? [v4: $i] : ?
% 133.43/18.16 | [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4)
% 133.43/18.16 | & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & !
% 133.43/18.16 | [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6)
% 133.43/18.16 | | ~ r1(v6, v7) | ~ r1(v5, v6) | p2(v7)))))) & ! [v0:
% 133.43/18.16 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 133.43/18.16 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v2, v3) | ~
% 133.43/18.16 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | ?
% 133.43/18.16 | [v4: $i] : ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5)
% 133.43/18.16 | & r1(v3, v4) & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~
% 133.43/18.16 | p2(v5) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6)
% 133.43/18.16 | | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | p2(v7))) |
% 133.43/18.16 | (r1(v1, v4) & ~ p2(v4) & ! [v6: $i] : ! [v7: $i] : ( ~
% 133.43/18.16 | $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) | ~
% 133.43/18.16 | r1(v4, v6) | p2(v7)))))) & ! [v0: $i] : ! [v1: $i] : !
% 133.43/18.16 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~
% 133.43/18.16 | r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v2) | p2(v1)
% 133.43/18.16 | | ? [v3: $i] : ? [v4: $i] : ($i(v4) & $i(v3) & ((p2(v3) &
% 133.43/18.16 | r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) | (p2(v3) & r1(v3, v4)
% 133.43/18.16 | & r1(v1, v3) & ~ p2(v4))))) & ! [v0: $i] : ! [v1: $i] :
% 133.43/18.16 | ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5,
% 133.43/18.16 | v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) &
% 133.43/18.16 | ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3)) | (r1(v2, v3) &
% 133.43/18.16 | r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5: $i] : ( ~
% 133.43/18.16 | $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) | ~
% 133.43/18.16 | r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) &
% 133.43/18.16 | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1:
% 133.43/18.16 | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.43/18.16 | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 133.43/18.16 | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] :
% 133.43/18.16 | ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~
% 133.43/18.16 | p2(v2)))) | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : (
% 133.43/18.16 | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.43/18.16 | r1(all_2_5, v0) | p2(v1))))) | ((p2(all_2_6) | (p2(all_2_5) &
% 133.43/18.16 | r1(all_2_5, all_2_4) & r1(all_2_6, all_2_5) & ~ p2(all_2_4)))
% 133.43/18.16 | & ( ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0,
% 133.43/18.16 | v1) | ~ r1(all_2_6, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i]
% 133.43/18.16 | : ($i(v3) & $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~
% 133.43/18.16 | p2(v3))) | (r1(all_2_6, all_2_3) & ~ p2(all_2_3) & ! [v0:
% 133.43/18.16 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~
% 133.43/18.16 | r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1))))))
% 133.43/18.16 |
% 133.43/18.16 | ALPHA: (1) implies:
% 133.43/18.17 | (2) ~ p2(all_2_1)
% 133.43/18.17 | (3) r1(all_2_6, all_2_1)
% 133.43/18.17 | (4) $i(all_2_5)
% 133.43/18.17 | (5) $i(all_2_4)
% 133.43/18.17 | (6) $i(all_2_3)
% 133.43/18.17 | (7) $i(all_2_1)
% 133.43/18.18 | (8) (r1(all_2_6, all_2_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 133.43/18.18 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~
% 133.43/18.18 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 133.43/18.18 | | ~ p2(v1) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~
% 133.43/18.18 | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.43/18.18 | p2(v6) | p2(v3) | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) &
% 133.43/18.18 | $i(v7) & ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) |
% 133.43/18.18 | (p2(v7) & r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7) &
% 133.43/18.18 | ~ p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~
% 133.43/18.18 | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) |
% 133.43/18.18 | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 133.43/18.18 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~
% 133.43/18.18 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v4,
% 133.43/18.18 | v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0,
% 133.43/18.18 | v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] : ?
% 133.43/18.18 | [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5, v6) &
% 133.43/18.18 | ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) & ! [v8:
% 133.43/18.18 | $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ p2(v8) | ~
% 133.43/18.18 | r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) | (r1(v3, v6) & ~
% 133.43/18.18 | p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) |
% 133.43/18.18 | ~ p2(v8) | ~ r1(v8, v9) | ~ r1(v6, v8) | p2(v9)))))) &
% 133.43/18.18 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 133.43/18.18 | ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 133.43/18.18 | p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0,
% 133.43/18.18 | v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ? [v5: $i]
% 133.43/18.18 | : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4,
% 133.43/18.18 | v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3, v5) & ~
% 133.43/18.18 | p2(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 133.43/18.18 | [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 133.43/18.18 | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~
% 133.43/18.18 | r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v1) |
% 133.43/18.18 | ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5,
% 133.43/18.18 | v6) & r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) &
% 133.43/18.18 | r1(v1, v5) & ~ p2(v6)) | (r1(v2, v5) & ~ p2(v5) & ! [v7:
% 133.43/18.18 | $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~
% 133.43/18.18 | r1(v7, v8) | ~ r1(v5, v7) | p2(v8)))))) & ! [v0: $i] : !
% 133.43/18.18 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 133.43/18.18 | $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~
% 133.43/18.18 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | p2(v2) | ? [v4: $i] :
% 133.43/18.18 | ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4)
% 133.43/18.18 | & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6:
% 133.43/18.18 | $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~
% 133.43/18.18 | r1(v6, v7) | ~ r1(v5, v6) | p2(v7)))))) & ! [v0: $i] : !
% 133.43/18.18 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 133.43/18.18 | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 133.43/18.18 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | ? [v4: $i] : ? [v5:
% 133.43/18.18 | $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) & ~
% 133.43/18.18 | p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6: $i]
% 133.43/18.18 | : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~
% 133.43/18.18 | r1(v6, v7) | ~ r1(v5, v6) | p2(v7))) | (r1(v1, v4) & ~
% 133.43/18.18 | p2(v4) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) |
% 133.91/18.18 | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v4, v6) | p2(v7)))))) &
% 133.91/18.18 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 133.91/18.18 | $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5,
% 133.91/18.18 | v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] : ($i(v4) &
% 133.91/18.18 | $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) |
% 133.91/18.18 | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4))))) & ! [v0: $i]
% 133.91/18.18 | : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) |
% 133.91/18.18 | ~ r1(all_2_5, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) &
% 133.91/18.18 | $i(v2) & ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3)) |
% 133.91/18.18 | (r1(v2, v3) & r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5:
% 133.91/18.18 | $i] : ( ~ $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) |
% 133.91/18.18 | ~ r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) &
% 133.91/18.18 | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i]
% 133.91/18.18 | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.91/18.18 | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 133.91/18.18 | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2)
% 133.91/18.18 | & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2)))) |
% 133.91/18.18 | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 133.91/18.18 | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.91/18.18 | p2(v1))))) | ((p2(all_2_6) | (p2(all_2_5) & r1(all_2_5,
% 133.91/18.18 | all_2_4) & r1(all_2_6, all_2_5) & ~ p2(all_2_4))) & ( ! [v0:
% 133.91/18.19 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~
% 133.91/18.19 | r1(all_2_6, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) &
% 133.91/18.19 | $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3))) |
% 133.91/18.19 | (r1(all_2_6, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i]
% 133.91/18.19 | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.91/18.19 | r1(all_2_3, v0) | p2(v1)))))
% 133.91/18.19 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_6, v0) | p2(v0) | ? [v1: $i] :
% 133.91/18.19 | ($i(v1) & r1(v0, v1) & ~ p2(v1) & ! [v2: $i] : ! [v3: $i] : ( ~
% 133.91/18.19 | $i(v3) | ~ $i(v2) | ~ p2(v2) | ~ r1(v2, v3) | ~ r1(v1, v2) |
% 133.91/18.19 | p2(v3))))
% 133.91/18.19 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_6, v0) | p2(v0) | ? [v1: $i] :
% 133.91/18.19 | ? [v2: $i] : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) &
% 133.91/18.19 | ~ p2(v2)))
% 133.91/18.19 |
% 133.91/18.19 | GROUND_INST: instantiating (9) with all_2_1, simplifying with (2), (3), (7)
% 133.91/18.19 | gives:
% 133.91/18.19 | (11) ? [v0: $i] : ($i(v0) & r1(all_2_1, v0) & ~ p2(v0) & ! [v1: $i] : !
% 133.91/18.19 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ p2(v1) | ~ r1(v1, v2) | ~
% 133.91/18.19 | r1(v0, v1) | p2(v2)))
% 133.91/18.19 |
% 133.91/18.19 | DELTA: instantiating (11) with fresh symbol all_16_0 gives:
% 133.91/18.19 | (12) $i(all_16_0) & r1(all_2_1, all_16_0) & ~ p2(all_16_0) & ! [v0: $i] :
% 133.91/18.19 | ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.91/18.19 | r1(all_16_0, v0) | p2(v1))
% 133.91/18.19 |
% 133.91/18.19 | ALPHA: (12) implies:
% 133.91/18.19 | (13) ~ p2(all_16_0)
% 133.91/18.19 | (14) r1(all_2_1, all_16_0)
% 133.91/18.19 | (15) $i(all_16_0)
% 133.91/18.19 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~
% 133.91/18.19 | r1(v0, v1) | ~ r1(all_16_0, v0) | p2(v1))
% 133.91/18.19 |
% 133.91/18.19 | BETA: splitting (8) gives:
% 133.91/18.19 |
% 133.91/18.19 | Case 1:
% 133.91/18.19 | |
% 133.96/18.20 | | (17) r1(all_2_6, all_2_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 133.96/18.20 | | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~
% 133.96/18.20 | | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 133.96/18.20 | | | ~ p2(v1) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~
% 133.96/18.20 | | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.96/18.20 | | p2(v6) | p2(v3) | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) &
% 133.96/18.20 | | $i(v7) & ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) |
% 133.96/18.20 | | (p2(v7) & r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7) &
% 133.96/18.20 | | ~ p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~
% 133.96/18.20 | | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) |
% 133.96/18.20 | | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 133.96/18.20 | | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~
% 133.96/18.20 | | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v4,
% 133.96/18.20 | | v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0,
% 133.96/18.20 | | v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] : ?
% 133.96/18.20 | | [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5, v6) &
% 133.96/18.20 | | ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) & ! [v8:
% 133.96/18.20 | | $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ p2(v8) |
% 133.96/18.20 | | ~ r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) | (r1(v3, v6) & ~
% 133.96/18.20 | | p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8)
% 133.96/18.20 | | | ~ p2(v8) | ~ r1(v8, v9) | ~ r1(v6, v8) | p2(v9))))))
% 133.96/18.20 | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 133.96/18.20 | | $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 133.96/18.20 | | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~
% 133.96/18.20 | | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ?
% 133.96/18.20 | | [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6)
% 133.96/18.20 | | & r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3,
% 133.96/18.20 | | v5) & ~ p2(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 133.96/18.20 | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~
% 133.96/18.20 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v3, v4) | ~
% 133.96/18.20 | | r1(v2, v3) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.96/18.20 | | p2(v4) | p2(v1) | ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) &
% 133.96/18.20 | | ((p2(v5) & r1(v5, v6) & r1(v4, v5) & ~ p2(v6)) | (p2(v5) &
% 133.96/18.20 | | r1(v5, v6) & r1(v1, v5) & ~ p2(v6)) | (r1(v2, v5) & ~
% 133.96/18.20 | | p2(v5) & ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7)
% 133.96/18.20 | | | ~ p2(v7) | ~ r1(v7, v8) | ~ r1(v5, v7) | p2(v8))))))
% 133.96/18.20 | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3)
% 133.96/18.20 | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) |
% 133.96/18.20 | | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) |
% 133.96/18.20 | | p2(v2) | ? [v4: $i] : ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) &
% 133.96/18.20 | | r1(v4, v5) & r1(v3, v4) & ~ p2(v5)) | (r1(v4, v5) & r1(v0,
% 133.96/18.20 | | v4) & ~ p2(v5) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) |
% 133.96/18.20 | | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) |
% 133.96/18.20 | | p2(v7)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 133.96/18.20 | | [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 133.96/18.20 | | p2(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 133.96/18.20 | | r1(all_2_5, v0) | p2(v3) | ? [v4: $i] : ? [v5: $i] : ($i(v5) &
% 133.96/18.20 | | $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) & ~ p2(v5)) |
% 133.96/18.20 | | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6: $i] : ! [v7:
% 133.96/18.20 | | $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) |
% 133.96/18.20 | | ~ r1(v5, v6) | p2(v7))) | (r1(v1, v4) & ~ p2(v4) & !
% 133.96/18.20 | | [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6)
% 133.96/18.20 | | | ~ r1(v6, v7) | ~ r1(v4, v6) | p2(v7)))))) & ! [v0:
% 133.96/18.20 | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 133.96/18.20 | | $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~
% 133.96/18.20 | | r1(all_2_5, v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] :
% 133.96/18.20 | | ($i(v4) & $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4))
% 133.96/18.20 | | | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4))))) & ! [v0:
% 133.96/18.20 | | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0,
% 133.96/18.20 | | v1) | ~ r1(all_2_5, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] :
% 133.96/18.20 | | ($i(v3) & $i(v2) & ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3))
% 133.96/18.20 | | | (r1(v2, v3) & r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5:
% 133.96/18.20 | | $i] : ( ~ $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) |
% 133.96/18.20 | | ~ r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) &
% 133.96/18.20 | | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1:
% 133.96/18.20 | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.96/18.20 | | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 133.96/18.20 | | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2)
% 133.96/18.20 | | & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2)))) |
% 133.96/18.20 | | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 133.96/18.20 | | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.96/18.20 | | p2(v1))))
% 133.96/18.20 | |
% 133.96/18.20 | | ALPHA: (17) implies:
% 133.96/18.20 | | (18) r1(all_2_6, all_2_5)
% 133.96/18.20 | | (19) (r1(all_2_4, all_2_3) & r1(all_2_5, all_2_4) & ~ p2(all_2_3) & !
% 133.96/18.20 | | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~
% 133.96/18.20 | | r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~
% 133.96/18.20 | | $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i]
% 133.96/18.20 | | : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~
% 133.96/18.20 | | p2(v2)))) | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~
% 133.96/18.20 | | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5,
% 133.96/18.20 | | v0) | p2(v1)))
% 133.96/18.21 | | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) |
% 133.96/18.21 | | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~
% 133.96/18.21 | | r1(all_2_5, v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] :
% 133.96/18.21 | | ($i(v4) & $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4))
% 133.96/18.21 | | | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4)))))
% 134.01/18.21 | | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 134.01/18.21 | | : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 134.01/18.21 | | p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0,
% 134.01/18.21 | | v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ? [v5:
% 134.01/18.21 | | $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) &
% 134.01/18.21 | | r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3, v5)
% 134.01/18.21 | | & ~ p2(v6)))))
% 134.01/18.21 | |
% 134.01/18.21 | | GROUND_INST: instantiating (10) with all_2_5, simplifying with (4), (18)
% 134.01/18.21 | | gives:
% 134.01/18.21 | | (22) p2(all_2_5) | ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0)
% 134.01/18.21 | | & r1(v0, v1) & r1(all_2_5, v0) & ~ p2(v1))
% 134.01/18.21 | |
% 134.01/18.21 | | BETA: splitting (19) gives:
% 134.01/18.21 | |
% 134.01/18.21 | | Case 1:
% 134.01/18.21 | | |
% 134.02/18.21 | | | (23) r1(all_2_4, all_2_3) & r1(all_2_5, all_2_4) & ~ p2(all_2_3) & !
% 134.02/18.21 | | | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~
% 134.02/18.21 | | | r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~
% 134.02/18.21 | | | $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i]
% 134.02/18.21 | | | : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~
% 134.02/18.21 | | | p2(v2)))
% 134.02/18.21 | | |
% 134.02/18.21 | | | ALPHA: (23) implies:
% 134.02/18.21 | | | (24) ~ p2(all_2_3)
% 134.02/18.21 | | | (25) r1(all_2_5, all_2_4)
% 134.02/18.21 | | | (26) r1(all_2_4, all_2_3)
% 134.02/18.21 | | | (27) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1:
% 134.02/18.21 | | | $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) &
% 134.02/18.21 | | | r1(v0, v1) & ~ p2(v2)))
% 134.02/18.21 | | | (28) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) |
% 134.02/18.21 | | | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1))
% 134.02/18.21 | | |
% 134.02/18.21 | | | GROUND_INST: instantiating (27) with all_2_4, simplifying with (5), (25)
% 134.02/18.21 | | | gives:
% 134.02/18.21 | | | (29) p2(all_2_4) | ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) &
% 134.02/18.21 | | | p2(v0) & r1(v0, v1) & r1(all_2_4, v0) & ~ p2(v1))
% 134.02/18.21 | | |
% 134.02/18.21 | | | BETA: splitting (29) gives:
% 134.02/18.21 | | |
% 134.02/18.21 | | | Case 1:
% 134.02/18.21 | | | |
% 134.02/18.21 | | | | (30) p2(all_2_4)
% 134.02/18.21 | | | |
% 134.02/18.21 | | | | GROUND_INST: instantiating (20) with all_2_4, all_2_3, all_2_3,
% 134.02/18.21 | | | | simplifying with (5), (6), (24), (25), (26), (30) gives:
% 134.02/18.21 | | | | (31) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0,
% 134.02/18.21 | | | | v1) & r1(all_2_3, v0) & ~ p2(v1))
% 134.02/18.21 | | | |
% 134.02/18.21 | | | | DELTA: instantiating (31) with fresh symbols all_123_0, all_123_1 gives:
% 134.02/18.21 | | | | (32) $i(all_123_0) & $i(all_123_1) & p2(all_123_1) & r1(all_123_1,
% 134.02/18.21 | | | | all_123_0) & r1(all_2_3, all_123_1) & ~ p2(all_123_0)
% 134.02/18.21 | | | |
% 134.02/18.21 | | | | ALPHA: (32) implies:
% 134.02/18.21 | | | | (33) ~ p2(all_123_0)
% 134.02/18.21 | | | | (34) r1(all_2_3, all_123_1)
% 134.02/18.21 | | | | (35) r1(all_123_1, all_123_0)
% 134.02/18.21 | | | | (36) p2(all_123_1)
% 134.02/18.21 | | | | (37) $i(all_123_1)
% 134.02/18.21 | | | | (38) $i(all_123_0)
% 134.02/18.21 | | | |
% 134.02/18.21 | | | | GROUND_INST: instantiating (28) with all_123_1, all_123_0, simplifying
% 134.02/18.21 | | | | with (33), (34), (35), (36), (37), (38) gives:
% 134.02/18.21 | | | | (39) $false
% 134.02/18.21 | | | |
% 134.02/18.21 | | | | CLOSE: (39) is inconsistent.
% 134.02/18.21 | | | |
% 134.02/18.21 | | | Case 2:
% 134.02/18.21 | | | |
% 134.02/18.21 | | | | (40) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0,
% 134.02/18.21 | | | | v1) & r1(all_2_4, v0) & ~ p2(v1))
% 134.02/18.21 | | | |
% 134.02/18.21 | | | | DELTA: instantiating (40) with fresh symbols all_118_0, all_118_1 gives:
% 134.02/18.22 | | | | (41) $i(all_118_0) & $i(all_118_1) & p2(all_118_1) & r1(all_118_1,
% 134.02/18.22 | | | | all_118_0) & r1(all_2_4, all_118_1) & ~ p2(all_118_0)
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | ALPHA: (41) implies:
% 134.02/18.22 | | | | (42) ~ p2(all_118_0)
% 134.02/18.22 | | | | (43) r1(all_2_4, all_118_1)
% 134.02/18.22 | | | | (44) r1(all_118_1, all_118_0)
% 134.02/18.22 | | | | (45) p2(all_118_1)
% 134.02/18.22 | | | | (46) $i(all_118_1)
% 134.02/18.22 | | | | (47) $i(all_118_0)
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | GROUND_INST: instantiating (21) with all_2_4, all_118_1, all_118_0,
% 134.02/18.22 | | | | all_2_3, all_2_3, simplifying with (5), (6), (24), (25),
% 134.02/18.22 | | | | (26), (42), (43), (44), (45), (46), (47) gives:
% 134.02/18.22 | | | | (48) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0,
% 134.02/18.22 | | | | v1) & r1(all_2_3, v0) & ~ p2(v1))
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | DELTA: instantiating (48) with fresh symbols all_125_0, all_125_1 gives:
% 134.02/18.22 | | | | (49) $i(all_125_0) & $i(all_125_1) & p2(all_125_1) & r1(all_125_1,
% 134.02/18.22 | | | | all_125_0) & r1(all_2_3, all_125_1) & ~ p2(all_125_0)
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | ALPHA: (49) implies:
% 134.02/18.22 | | | | (50) ~ p2(all_125_0)
% 134.02/18.22 | | | | (51) r1(all_2_3, all_125_1)
% 134.02/18.22 | | | | (52) r1(all_125_1, all_125_0)
% 134.02/18.22 | | | | (53) p2(all_125_1)
% 134.02/18.22 | | | | (54) $i(all_125_1)
% 134.02/18.22 | | | | (55) $i(all_125_0)
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | GROUND_INST: instantiating (28) with all_125_1, all_125_0, simplifying
% 134.02/18.22 | | | | with (50), (51), (52), (53), (54), (55) gives:
% 134.02/18.22 | | | | (56) $false
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | CLOSE: (56) is inconsistent.
% 134.02/18.22 | | | |
% 134.02/18.22 | | | End of split
% 134.02/18.22 | | |
% 134.02/18.22 | | Case 2:
% 134.02/18.22 | | |
% 134.02/18.22 | | | (57) ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 134.02/18.22 | | | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 134.02/18.22 | | | p2(v1))
% 134.02/18.22 | | |
% 134.02/18.22 | | | ALPHA: (57) implies:
% 134.02/18.22 | | | (58) ~ p2(all_2_5)
% 134.02/18.22 | | | (59) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) |
% 134.02/18.22 | | | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v1))
% 134.02/18.22 | | |
% 134.02/18.22 | | | BETA: splitting (22) gives:
% 134.02/18.22 | | |
% 134.02/18.22 | | | Case 1:
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | (60) p2(all_2_5)
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | PRED_UNIFY: (58), (60) imply:
% 134.02/18.22 | | | | (61) $false
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | CLOSE: (61) is inconsistent.
% 134.02/18.22 | | | |
% 134.02/18.22 | | | Case 2:
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | (62) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0,
% 134.02/18.22 | | | | v1) & r1(all_2_5, v0) & ~ p2(v1))
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | DELTA: instantiating (62) with fresh symbols all_92_0, all_92_1 gives:
% 134.02/18.22 | | | | (63) $i(all_92_0) & $i(all_92_1) & p2(all_92_1) & r1(all_92_1,
% 134.02/18.22 | | | | all_92_0) & r1(all_2_5, all_92_1) & ~ p2(all_92_0)
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | ALPHA: (63) implies:
% 134.02/18.22 | | | | (64) ~ p2(all_92_0)
% 134.02/18.22 | | | | (65) r1(all_2_5, all_92_1)
% 134.02/18.22 | | | | (66) r1(all_92_1, all_92_0)
% 134.02/18.22 | | | | (67) p2(all_92_1)
% 134.02/18.22 | | | | (68) $i(all_92_1)
% 134.02/18.22 | | | | (69) $i(all_92_0)
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | GROUND_INST: instantiating (59) with all_92_1, all_92_0, simplifying
% 134.02/18.22 | | | | with (64), (65), (66), (67), (68), (69) gives:
% 134.02/18.22 | | | | (70) $false
% 134.02/18.22 | | | |
% 134.02/18.22 | | | | CLOSE: (70) is inconsistent.
% 134.02/18.22 | | | |
% 134.02/18.22 | | | End of split
% 134.02/18.22 | | |
% 134.02/18.22 | | End of split
% 134.02/18.22 | |
% 134.02/18.22 | Case 2:
% 134.02/18.22 | |
% 134.02/18.22 | | (71) (p2(all_2_6) | (p2(all_2_5) & r1(all_2_5, all_2_4) & r1(all_2_6,
% 134.02/18.22 | | all_2_5) & ~ p2(all_2_4))) & ( ! [v0: $i] : ! [v1: $i] : ( ~
% 134.02/18.22 | | $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_6, v0) | p2(v1)
% 134.02/18.22 | | | ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & p2(v2) & r1(v2,
% 134.02/18.22 | | v3) & r1(v1, v2) & ~ p2(v3))) | (r1(all_2_6, all_2_3) & ~
% 134.02/18.22 | | p2(all_2_3) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0)
% 134.02/18.22 | | | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1))))
% 134.02/18.22 | |
% 134.02/18.22 | | ALPHA: (71) implies:
% 134.02/18.22 | | (72) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) |
% 134.02/18.22 | | ~ r1(all_2_6, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3)
% 134.02/18.22 | | & $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3))) |
% 134.02/18.22 | | (r1(all_2_6, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i] :
% 134.02/18.22 | | ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 134.02/18.22 | | r1(all_2_3, v0) | p2(v1)))
% 134.02/18.22 | |
% 134.02/18.22 | | BETA: splitting (72) gives:
% 134.02/18.22 | |
% 134.02/18.22 | | Case 1:
% 134.02/18.22 | | |
% 134.02/18.23 | | | (73) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1)
% 134.02/18.23 | | | | ~ r1(all_2_6, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] :
% 134.02/18.23 | | | ($i(v3) & $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~
% 134.02/18.23 | | | p2(v3)))
% 134.02/18.23 | | |
% 134.02/18.23 | | | GROUND_INST: instantiating (73) with all_2_1, all_16_0, simplifying with
% 134.02/18.23 | | | (3), (7), (13), (14), (15) gives:
% 134.02/18.23 | | | (74) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, v1)
% 134.02/18.23 | | | & r1(all_16_0, v0) & ~ p2(v1))
% 134.02/18.23 | | |
% 134.02/18.23 | | | DELTA: instantiating (74) with fresh symbols all_91_0, all_91_1 gives:
% 134.02/18.23 | | | (75) $i(all_91_0) & $i(all_91_1) & p2(all_91_1) & r1(all_91_1,
% 134.02/18.23 | | | all_91_0) & r1(all_16_0, all_91_1) & ~ p2(all_91_0)
% 134.02/18.23 | | |
% 134.02/18.23 | | | ALPHA: (75) implies:
% 134.02/18.23 | | | (76) ~ p2(all_91_0)
% 134.02/18.23 | | | (77) r1(all_16_0, all_91_1)
% 134.02/18.23 | | | (78) r1(all_91_1, all_91_0)
% 134.02/18.23 | | | (79) p2(all_91_1)
% 134.02/18.23 | | | (80) $i(all_91_1)
% 134.02/18.23 | | | (81) $i(all_91_0)
% 134.02/18.23 | | |
% 134.02/18.23 | | | GROUND_INST: instantiating (16) with all_91_1, all_91_0, simplifying with
% 134.02/18.23 | | | (76), (77), (78), (79), (80), (81) gives:
% 134.02/18.23 | | | (82) $false
% 134.02/18.23 | | |
% 134.02/18.23 | | | CLOSE: (82) is inconsistent.
% 134.02/18.23 | | |
% 134.02/18.23 | | Case 2:
% 134.02/18.23 | | |
% 134.02/18.23 | | | (83) r1(all_2_6, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i]
% 134.02/18.23 | | | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 134.02/18.23 | | | r1(all_2_3, v0) | p2(v1))
% 134.02/18.23 | | |
% 134.02/18.23 | | | ALPHA: (83) implies:
% 134.02/18.23 | | | (84) ~ p2(all_2_3)
% 134.02/18.23 | | | (85) r1(all_2_6, all_2_3)
% 134.02/18.23 | | | (86) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) |
% 134.02/18.23 | | | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1))
% 134.02/18.23 | | |
% 134.02/18.23 | | | GROUND_INST: instantiating (10) with all_2_3, simplifying with (6), (84),
% 134.02/18.23 | | | (85) gives:
% 134.02/18.23 | | | (87) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, v1)
% 134.02/18.23 | | | & r1(all_2_3, v0) & ~ p2(v1))
% 134.02/18.23 | | |
% 134.02/18.23 | | | DELTA: instantiating (87) with fresh symbols all_95_0, all_95_1 gives:
% 134.02/18.23 | | | (88) $i(all_95_0) & $i(all_95_1) & p2(all_95_1) & r1(all_95_1,
% 134.02/18.23 | | | all_95_0) & r1(all_2_3, all_95_1) & ~ p2(all_95_0)
% 134.02/18.23 | | |
% 134.02/18.23 | | | ALPHA: (88) implies:
% 134.02/18.23 | | | (89) ~ p2(all_95_0)
% 134.02/18.23 | | | (90) r1(all_2_3, all_95_1)
% 134.02/18.23 | | | (91) r1(all_95_1, all_95_0)
% 134.02/18.23 | | | (92) p2(all_95_1)
% 134.02/18.23 | | | (93) $i(all_95_1)
% 134.02/18.23 | | | (94) $i(all_95_0)
% 134.02/18.23 | | |
% 134.02/18.23 | | | GROUND_INST: instantiating (86) with all_95_1, all_95_0, simplifying with
% 134.02/18.23 | | | (89), (90), (91), (92), (93), (94) gives:
% 134.02/18.23 | | | (95) $false
% 134.02/18.23 | | |
% 134.02/18.23 | | | CLOSE: (95) is inconsistent.
% 134.02/18.23 | | |
% 134.02/18.23 | | End of split
% 134.02/18.23 | |
% 134.02/18.23 | End of split
% 134.02/18.23 |
% 134.02/18.23 End of proof
% 134.02/18.23 % SZS output end Proof for theBenchmark
% 134.02/18.23
% 134.02/18.23 17636ms
%------------------------------------------------------------------------------