TSTP Solution File: LCL658+1.010 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL658+1.010 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 08:12:10 EDT 2023
% Result : Theorem 135.57s 18.50s
% Output : Proof 136.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL658+1.010 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 02:37:37 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.63/1.23 Prover 4: Preprocessing ...
% 3.63/1.23 Prover 1: Preprocessing ...
% 3.63/1.27 Prover 2: Preprocessing ...
% 3.63/1.27 Prover 3: Preprocessing ...
% 3.63/1.27 Prover 5: Preprocessing ...
% 3.63/1.27 Prover 0: Preprocessing ...
% 4.19/1.29 Prover 6: Preprocessing ...
% 5.93/1.59 Prover 2: Proving ...
% 6.60/1.62 Prover 5: Proving ...
% 9.37/2.05 Prover 6: Proving ...
% 9.37/2.09 Prover 3: Constructing countermodel ...
% 9.37/2.10 Prover 1: Constructing countermodel ...
% 11.81/2.36 Prover 0: Proving ...
% 12.98/2.47 Prover 4: Constructing countermodel ...
% 72.98/10.35 Prover 2: stopped
% 73.45/10.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.14/10.45 Prover 7: Preprocessing ...
% 74.14/10.48 Prover 7: Warning: ignoring some quantifiers
% 74.14/10.49 Prover 7: Constructing countermodel ...
% 100.64/13.95 Prover 5: stopped
% 100.64/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 101.39/14.06 Prover 8: Preprocessing ...
% 102.01/14.18 Prover 8: Warning: ignoring some quantifiers
% 102.85/14.20 Prover 8: Constructing countermodel ...
% 116.35/15.97 Prover 1: stopped
% 116.35/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 117.18/16.08 Prover 9: Preprocessing ...
% 118.65/16.34 Prover 9: Constructing countermodel ...
% 129.93/17.87 Prover 6: stopped
% 129.93/17.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 131.05/17.92 Prover 10: Preprocessing ...
% 131.05/17.94 Prover 10: Warning: ignoring some quantifiers
% 131.05/17.94 Prover 10: Constructing countermodel ...
% 134.64/18.49 Prover 10: Found proof (size 49)
% 134.64/18.49 Prover 10: proved (618ms)
% 134.64/18.49 Prover 9: stopped
% 134.64/18.49 Prover 3: stopped
% 134.64/18.49 Prover 0: stopped
% 135.57/18.49 Prover 7: stopped
% 135.57/18.49 Prover 4: stopped
% 135.57/18.50 Prover 8: stopped
% 135.57/18.50
% 135.57/18.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 135.57/18.50
% 135.57/18.50 % SZS output start Proof for theBenchmark
% 135.57/18.50 Assumptions after simplification:
% 135.57/18.50 ---------------------------------
% 135.57/18.50
% 135.57/18.50 (main)
% 135.57/18.53 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 135.57/18.53 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v8) & $i(v7) & $i(v6) &
% 135.57/18.53 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & r1(v6, v8) & r1(v6,
% 135.57/18.53 v7) & r1(v5, v6) & r1(v4, v5) & r1(v3, v4) & r1(v2, v3) & r1(v1, v2) &
% 135.57/18.53 r1(v0, v1) & ~ p1(v8) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 135.57/18.53 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : !
% 135.57/18.53 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ( ~ $i(v19) | ~ $i(v18) | ~
% 135.57/18.53 $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) |
% 135.57/18.53 ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ r1(v18, v19) | ~ r1(v17, v18) |
% 135.57/18.53 ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~
% 135.57/18.53 r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~
% 135.57/18.53 r1(v0, v9) | p1(v19) | ? [v20: $i] : ($i(v20) & r1(v17, v20) & ~
% 135.57/18.53 p1(v20))) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] :
% 135.57/18.53 ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : !
% 135.57/18.53 [v18: $i] : ( ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14)
% 135.57/18.53 | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~
% 135.57/18.53 r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~
% 135.57/18.53 r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~
% 135.57/18.53 r1(v9, v10) | ~ r1(v0, v9) | p1(v18) | ? [v19: $i] : ($i(v19) & r1(v16,
% 135.57/18.53 v19) & ~ p1(v19))) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 135.57/18.53 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : !
% 135.57/18.53 [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13)
% 135.57/18.53 | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ r1(v16, v17) | ~
% 135.57/18.53 r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~
% 135.57/18.53 r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v17)
% 135.57/18.53 | ? [v18: $i] : ($i(v18) & r1(v15, v18) & ~ p1(v18))) & ! [v9: $i] : !
% 135.57/18.53 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : !
% 135.57/18.53 [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~
% 135.57/18.53 $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ p1(v14) |
% 135.57/18.53 ~ r1(v14, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~
% 135.57/18.53 r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v16)
% 135.57/18.53 | ? [v17: $i] : ? [v18: $i] : ($i(v18) & $i(v17) & ((p1(v17) & r1(v17,
% 135.57/18.53 v18) & r1(v15, v17) & ~ p1(v18)) | (p1(v17) & r1(v17, v18) &
% 135.57/18.53 r1(v14, v17) & ~ p1(v18) & ! [v19: $i] : ! [v20: $i] : ! [v21:
% 135.57/18.53 $i] : ( ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ p1(v20) | ~
% 135.57/18.53 r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v17, v19) | p1(v21) |
% 135.57/18.53 p1(v19)) & ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~
% 135.57/18.53 $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ p1(v20) | ~ r1(v20, v21) |
% 135.57/18.53 ~ r1(v19, v20) | ~ r1(v17, v19) | p1(v21) | ? [v22: $i] :
% 135.57/18.53 ($i(v22) & r1(v19, v22) & ~ p1(v22))))))) & ! [v9: $i] : !
% 135.57/18.53 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : !
% 135.57/18.53 [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~
% 135.57/18.53 $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ r1(v15,
% 135.57/18.53 v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11,
% 135.57/18.53 v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v16) | ?
% 135.57/18.53 [v17: $i] : ? [v18: $i] : ($i(v18) & $i(v17) & ((p1(v17) & r1(v17, v18) &
% 135.57/18.53 r1(v16, v17) & ~ p1(v18)) | (r1(v14, v17) & ~ p1(v17) & ! [v19:
% 135.57/18.53 $i] : ! [v20: $i] : ( ~ $i(v20) | ~ $i(v19) | ~ p1(v19) | ~
% 135.57/18.53 r1(v19, v20) | ~ r1(v17, v19) | p1(v20)))))) & ! [v9: $i] : !
% 135.57/18.53 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : !
% 135.57/18.53 [v15: $i] : ( ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11)
% 135.57/18.53 | ~ $i(v10) | ~ $i(v9) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12,
% 135.57/18.53 v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0,
% 135.57/18.53 v9) | p1(v15) | ? [v16: $i] : ($i(v16) & r1(v13, v16) & ~ p1(v16))) &
% 135.57/18.53 ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : !
% 135.57/18.53 [v14: $i] : ! [v15: $i] : ( ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~
% 135.57/18.53 $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ r1(v14, v15) | ~
% 135.57/18.53 r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~
% 135.57/18.53 r1(v9, v10) | ~ r1(v0, v9) | p1(v14) | ? [v16: $i] : ($i(v16) &
% 135.57/18.53 ((r1(v15, v16) & ~ p1(v16)) | (r1(v14, v16) & ~ p1(v16) & ! [v17: $i]
% 135.57/18.53 : ! [v18: $i] : ( ~ $i(v18) | ~ $i(v17) | ~ p1(v17) | ~ r1(v17,
% 135.57/18.53 v18) | ~ r1(v16, v17) | p1(v18)))))) & ! [v9: $i] : ! [v10:
% 135.57/18.54 $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 135.57/18.54 $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) |
% 135.57/18.54 ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~
% 135.57/18.54 r1(v9, v10) | ~ r1(v0, v9) | p1(v14) | ? [v15: $i] : ($i(v15) & r1(v12,
% 135.57/18.54 v15) & ~ p1(v15))) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 135.57/18.54 [v12: $i] : ! [v13: $i] : ( ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~
% 135.57/18.54 $i(v10) | ~ $i(v9) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11)
% 135.57/18.54 | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v13) | ? [v14: $i] : ($i(v14) &
% 135.57/18.54 r1(v11, v14) & ~ p1(v14))) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i]
% 135.57/18.54 : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~
% 135.57/18.54 r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v12)
% 135.57/18.54 | ? [v13: $i] : ($i(v13) & r1(v10, v13) & ~ p1(v13))) & ! [v9: $i] : !
% 135.57/18.54 [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ r1(v10,
% 135.57/18.54 v11) | ~ r1(v9, v10) | ~ r1(v0, v9) | p1(v11) | ? [v12: $i] :
% 135.57/18.54 ($i(v12) & r1(v9, v12) & ~ p1(v12))) & ! [v9: $i] : ( ~ $i(v9) | ~
% 135.57/18.54 r1(v7, v9) | p1(v9)) & ! [v9: $i] : ( ~ $i(v9) | ~ r1(v6, v9) | p1(v9) |
% 135.57/18.54 ? [v10: $i] : ? [v11: $i] : ($i(v11) & $i(v10) & p1(v10) & r1(v10, v11)
% 135.57/18.54 & r1(v9, v10) & ~ p1(v11))))
% 135.57/18.54
% 135.57/18.54 Further assumptions not needed in the proof:
% 135.57/18.54 --------------------------------------------
% 135.57/18.54 reflexivity
% 135.57/18.54
% 135.57/18.54 Those formulas are unsatisfiable:
% 135.57/18.54 ---------------------------------
% 135.57/18.54
% 135.57/18.54 Begin of proof
% 135.57/18.54 |
% 135.57/18.54 | DELTA: instantiating (main) with fresh symbols all_3_0, all_3_1, all_3_2,
% 135.57/18.54 | all_3_3, all_3_4, all_3_5, all_3_6, all_3_7, all_3_8 gives:
% 135.57/18.55 | (1) $i(all_3_0) & $i(all_3_1) & $i(all_3_2) & $i(all_3_3) & $i(all_3_4) &
% 135.57/18.55 | $i(all_3_5) & $i(all_3_6) & $i(all_3_7) & $i(all_3_8) & r1(all_3_2,
% 135.57/18.55 | all_3_0) & r1(all_3_2, all_3_1) & r1(all_3_3, all_3_2) & r1(all_3_4,
% 135.57/18.55 | all_3_3) & r1(all_3_5, all_3_4) & r1(all_3_6, all_3_5) & r1(all_3_7,
% 135.57/18.55 | all_3_6) & r1(all_3_8, all_3_7) & ~ p1(all_3_0) & ! [v0: $i] : !
% 135.57/18.55 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 135.57/18.55 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 135.57/18.55 | $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) |
% 135.57/18.55 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v9,
% 135.57/18.55 | v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5,
% 135.57/18.55 | v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2)
% 135.57/18.55 | | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v10) | ? [v11: $i] :
% 135.57/18.55 | ($i(v11) & r1(v8, v11) & ~ p1(v11))) & ! [v0: $i] : ! [v1: $i] :
% 135.57/18.56 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 135.57/18.56 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~
% 135.57/18.56 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 135.57/18.56 | ~ $i(v1) | ~ $i(v0) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7)
% 135.57/18.56 | | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~
% 135.57/18.56 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v9) | ? [v10:
% 135.57/18.56 | $i] : ($i(v10) & r1(v7, v10) & ~ p1(v10))) & ! [v0: $i] : ! [v1:
% 135.57/18.56 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 135.57/18.56 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6)
% 135.57/18.56 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 135.57/18.56 | $i(v0) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4,
% 135.57/18.56 | v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1)
% 135.57/18.56 | | ~ r1(all_3_8, v0) | p1(v8) | ? [v9: $i] : ($i(v9) & r1(v6, v9) &
% 135.57/18.56 | ~ p1(v9))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 135.57/18.56 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) |
% 135.57/18.56 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 135.57/18.56 | | ~ $i(v0) | ~ p1(v5) | ~ r1(v5, v7) | ~ r1(v5, v6) | ~ r1(v4,
% 135.57/18.56 | v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1)
% 135.57/18.56 | | ~ r1(all_3_8, v0) | p1(v7) | ? [v8: $i] : ? [v9: $i] : ($i(v9) &
% 135.57/18.56 | $i(v8) & ((p1(v8) & r1(v8, v9) & r1(v6, v8) & ~ p1(v9)) | (p1(v8)
% 135.57/18.56 | & r1(v8, v9) & r1(v5, v8) & ~ p1(v9) & ! [v10: $i] : ! [v11:
% 135.57/18.56 | $i] : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~ $i(v10) |
% 135.57/18.56 | ~ p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8,
% 135.57/18.56 | v10) | p1(v12) | p1(v10)) & ! [v10: $i] : ! [v11: $i] :
% 135.57/18.56 | ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~
% 135.57/18.56 | p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8, v10)
% 135.57/18.56 | | p1(v12) | ? [v13: $i] : ($i(v13) & r1(v10, v13) & ~
% 135.57/18.56 | p1(v13))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 135.57/18.56 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (
% 135.57/18.56 | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 135.57/18.56 | | ~ $i(v1) | ~ $i(v0) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4,
% 135.57/18.56 | v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1)
% 135.57/18.56 | | ~ r1(all_3_8, v0) | p1(v7) | ? [v8: $i] : ? [v9: $i] : ($i(v9) &
% 135.57/18.56 | $i(v8) & ((p1(v8) & r1(v8, v9) & r1(v7, v8) & ~ p1(v9)) | (r1(v5,
% 135.57/18.56 | v8) & ~ p1(v8) & ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) |
% 135.57/18.56 | ~ $i(v10) | ~ p1(v10) | ~ r1(v10, v11) | ~ r1(v8, v10) |
% 135.57/18.56 | p1(v11)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 135.57/18.56 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~
% 135.57/18.56 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 135.57/18.56 | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~
% 135.57/18.56 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v6) | ? [v7:
% 135.57/18.56 | $i] : ($i(v7) & r1(v4, v7) & ~ p1(v7))) & ! [v0: $i] : ! [v1:
% 135.57/18.56 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 135.57/18.56 | $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 135.57/18.56 | $i(v1) | ~ $i(v0) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) |
% 135.57/18.56 | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) |
% 135.57/18.56 | p1(v5) | ? [v7: $i] : ($i(v7) & ((r1(v6, v7) & ~ p1(v7)) | (r1(v5,
% 135.57/18.56 | v7) & ~ p1(v7) & ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~
% 135.57/18.56 | $i(v8) | ~ p1(v8) | ~ r1(v8, v9) | ~ r1(v7, v8) |
% 135.57/18.56 | p1(v9)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 135.57/18.56 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~
% 135.57/18.56 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v4, v5) | ~
% 135.57/18.56 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 135.57/18.56 | r1(all_3_8, v0) | p1(v5) | ? [v6: $i] : ($i(v6) & r1(v3, v6) & ~
% 135.57/18.56 | p1(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 135.57/18.56 | ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 135.57/18.56 | | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 135.57/18.56 | r1(all_3_8, v0) | p1(v4) | ? [v5: $i] : ($i(v5) & r1(v2, v5) & ~
% 135.57/18.56 | p1(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 135.57/18.56 | ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~
% 135.57/18.56 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v3) | ? [v4:
% 135.57/18.56 | $i] : ($i(v4) & r1(v1, v4) & ~ p1(v4))) & ! [v0: $i] : ! [v1:
% 135.57/18.56 | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1,
% 135.57/18.56 | v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v2) | ? [v3: $i] :
% 135.57/18.56 | ($i(v3) & r1(v0, v3) & ~ p1(v3))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 135.57/18.56 | r1(all_3_1, v0) | p1(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2,
% 135.57/18.56 | v0) | p1(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) &
% 135.57/18.56 | p1(v1) & r1(v1, v2) & r1(v0, v1) & ~ p1(v2)))
% 135.57/18.56 |
% 135.57/18.56 | ALPHA: (1) implies:
% 135.57/18.56 | (2) ~ p1(all_3_0)
% 135.57/18.56 | (3) r1(all_3_8, all_3_7)
% 135.57/18.56 | (4) r1(all_3_7, all_3_6)
% 135.57/18.56 | (5) r1(all_3_6, all_3_5)
% 135.57/18.56 | (6) r1(all_3_5, all_3_4)
% 135.57/18.56 | (7) r1(all_3_4, all_3_3)
% 135.57/18.56 | (8) r1(all_3_3, all_3_2)
% 135.57/18.56 | (9) r1(all_3_2, all_3_1)
% 135.57/18.56 | (10) r1(all_3_2, all_3_0)
% 135.57/18.56 | (11) $i(all_3_7)
% 135.57/18.56 | (12) $i(all_3_6)
% 135.57/18.56 | (13) $i(all_3_5)
% 135.57/18.56 | (14) $i(all_3_4)
% 135.57/18.56 | (15) $i(all_3_3)
% 135.57/18.56 | (16) $i(all_3_2)
% 135.57/18.57 | (17) $i(all_3_1)
% 135.57/18.57 | (18) $i(all_3_0)
% 135.57/18.57 | (19) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2, v0) | p1(v0) | ? [v1: $i] :
% 135.57/18.57 | ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) & r1(v0, v1) &
% 135.57/18.57 | ~ p1(v2)))
% 135.57/18.57 | (20) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_1, v0) | p1(v0))
% 135.57/18.57 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 135.57/18.57 | ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 135.57/18.57 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v5, v6) | ~
% 135.57/18.57 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 135.57/18.57 | r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v5) | ? [v7: $i] : ($i(v7) &
% 135.57/18.57 | ((r1(v6, v7) & ~ p1(v7)) | (r1(v5, v7) & ~ p1(v7) & ! [v8: $i]
% 135.57/18.57 | : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ p1(v8) | ~ r1(v8,
% 135.57/18.57 | v9) | ~ r1(v7, v8) | p1(v9))))))
% 135.57/18.57 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 135.57/18.57 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~
% 135.57/18.57 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 135.57/18.57 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 135.57/18.57 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) |
% 135.57/18.57 | p1(v7) | ? [v8: $i] : ? [v9: $i] : ($i(v9) & $i(v8) & ((p1(v8) &
% 135.57/18.57 | r1(v8, v9) & r1(v7, v8) & ~ p1(v9)) | (r1(v5, v8) & ~ p1(v8)
% 135.57/18.57 | & ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~
% 135.57/18.57 | p1(v10) | ~ r1(v10, v11) | ~ r1(v8, v10) | p1(v11))))))
% 135.57/18.57 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 135.57/18.57 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~
% 135.57/18.57 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 135.57/18.57 | ~ p1(v5) | ~ r1(v5, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 135.57/18.57 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 135.57/18.57 | r1(all_3_8, v0) | p1(v7) | ? [v8: $i] : ? [v9: $i] : ($i(v9) &
% 135.57/18.57 | $i(v8) & ((p1(v8) & r1(v8, v9) & r1(v6, v8) & ~ p1(v9)) | (p1(v8)
% 135.57/18.57 | & r1(v8, v9) & r1(v5, v8) & ~ p1(v9) & ! [v10: $i] : !
% 135.57/18.58 | [v11: $i] : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~
% 135.57/18.58 | $i(v10) | ~ p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) |
% 135.57/18.58 | ~ r1(v8, v10) | p1(v12) | p1(v10)) & ! [v10: $i] : ! [v11:
% 135.57/18.58 | $i] : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~ $i(v10) |
% 135.57/18.58 | ~ p1(v11) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v8,
% 135.57/18.58 | v10) | p1(v12) | ? [v13: $i] : ($i(v13) & r1(v10, v13) &
% 135.57/18.58 | ~ p1(v13)))))))
% 135.57/18.58 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 135.57/18.58 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~
% 135.57/18.58 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 135.57/18.58 | ~ $i(v1) | ~ $i(v0) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5,
% 135.57/18.58 | v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1,
% 135.57/18.58 | v2) | ~ r1(v0, v1) | ~ r1(all_3_8, v0) | p1(v8) | ? [v9: $i] :
% 135.57/18.58 | ($i(v9) & r1(v6, v9) & ~ p1(v9)))
% 135.57/18.58 |
% 135.57/18.58 | GROUND_INST: instantiating (21) with all_3_7, all_3_6, all_3_5, all_3_4,
% 135.57/18.58 | all_3_3, all_3_2, all_3_1, simplifying with (3), (4), (5), (6),
% 135.57/18.58 | (7), (8), (9), (11), (12), (13), (14), (15), (16), (17) gives:
% 135.57/18.58 | (25) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) |
% 135.57/18.58 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 135.57/18.58 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1)
% 135.57/18.58 | | p1(v2)))))
% 135.57/18.58 |
% 135.57/18.58 | GROUND_INST: instantiating (21) with all_3_7, all_3_6, all_3_5, all_3_4,
% 135.57/18.58 | all_3_3, all_3_2, all_3_0, simplifying with (3), (4), (5), (6),
% 135.57/18.58 | (7), (8), (10), (11), (12), (13), (14), (15), (16), (18) gives:
% 136.02/18.58 | (26) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_0, v0) & ~ p1(v0)) |
% 136.02/18.58 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 136.02/18.58 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1)
% 136.02/18.58 | | p1(v2)))))
% 136.02/18.58 |
% 136.02/18.58 | BETA: splitting (26) gives:
% 136.02/18.58 |
% 136.02/18.58 | Case 1:
% 136.02/18.58 | |
% 136.02/18.58 | | (27) p1(all_3_2)
% 136.02/18.58 | |
% 136.02/18.59 | | GROUND_INST: instantiating (23) with all_3_7, all_3_6, all_3_5, all_3_4,
% 136.02/18.59 | | all_3_3, all_3_2, all_3_1, all_3_0, simplifying with (2), (3),
% 136.02/18.59 | | (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 136.02/18.59 | | (15), (16), (17), (18), (27) gives:
% 136.05/18.59 | | (28) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0, v1)
% 136.05/18.59 | | & r1(all_3_1, v0) & ~ p1(v1)) | (p1(v0) & r1(v0, v1) &
% 136.05/18.59 | | r1(all_3_2, v0) & ~ p1(v1) & ! [v2: $i] : ! [v3: $i] : !
% 136.05/18.59 | | [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~
% 136.05/18.59 | | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) |
% 136.05/18.59 | | p1(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 136.05/18.59 | | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~ r1(v3, v4) |
% 136.05/18.59 | | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | ? [v5: $i] :
% 136.05/18.59 | | ($i(v5) & r1(v2, v5) & ~ p1(v5))))))
% 136.05/18.59 | |
% 136.05/18.59 | | DELTA: instantiating (28) with fresh symbols all_66_0, all_66_1 gives:
% 136.05/18.59 | | (29) $i(all_66_0) & $i(all_66_1) & ((p1(all_66_1) & r1(all_66_1,
% 136.05/18.59 | | all_66_0) & r1(all_3_1, all_66_1) & ~ p1(all_66_0)) |
% 136.05/18.59 | | (p1(all_66_1) & r1(all_66_1, all_66_0) & r1(all_3_2, all_66_1) &
% 136.05/18.59 | | ~ p1(all_66_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 136.05/18.59 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) |
% 136.05/18.59 | | ~ r1(v0, v1) | ~ r1(all_66_1, v0) | p1(v2) | p1(v0)) & !
% 136.05/18.59 | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) |
% 136.05/18.59 | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 136.05/18.59 | | r1(all_66_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, v3)
% 136.05/18.59 | | & ~ p1(v3)))))
% 136.05/18.59 | |
% 136.05/18.59 | | ALPHA: (29) implies:
% 136.05/18.59 | | (30) $i(all_66_1)
% 136.05/18.59 | | (31) $i(all_66_0)
% 136.05/18.60 | | (32) (p1(all_66_1) & r1(all_66_1, all_66_0) & r1(all_3_1, all_66_1) & ~
% 136.05/18.60 | | p1(all_66_0)) | (p1(all_66_1) & r1(all_66_1, all_66_0) &
% 136.05/18.60 | | r1(all_3_2, all_66_1) & ~ p1(all_66_0) & ! [v0: $i] : ! [v1:
% 136.05/18.60 | | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 136.05/18.60 | | p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_66_1, v0) |
% 136.05/18.60 | | p1(v2) | p1(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 136.05/18.60 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~
% 136.05/18.60 | | r1(v0, v1) | ~ r1(all_66_1, v0) | p1(v2) | ? [v3: $i] :
% 136.05/18.60 | | ($i(v3) & r1(v0, v3) & ~ p1(v3))))
% 136.05/18.60 | |
% 136.05/18.60 | | BETA: splitting (32) gives:
% 136.05/18.60 | |
% 136.05/18.60 | | Case 1:
% 136.05/18.60 | | |
% 136.05/18.60 | | | (33) p1(all_66_1) & r1(all_66_1, all_66_0) & r1(all_3_1, all_66_1) & ~
% 136.05/18.60 | | | p1(all_66_0)
% 136.05/18.60 | | |
% 136.05/18.60 | | | ALPHA: (33) implies:
% 136.05/18.60 | | | (34) ~ p1(all_66_0)
% 136.05/18.60 | | | (35) r1(all_3_1, all_66_1)
% 136.05/18.60 | | | (36) r1(all_66_1, all_66_0)
% 136.05/18.60 | | |
% 136.05/18.60 | | | GROUND_INST: instantiating (24) with all_3_7, all_3_6, all_3_5, all_3_4,
% 136.05/18.60 | | | all_3_3, all_3_2, all_3_1, all_66_1, all_66_0, simplifying
% 136.05/18.60 | | | with (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 136.05/18.60 | | | (14), (15), (16), (17), (30), (31), (34), (35), (36) gives:
% 136.05/18.60 | | | (37) ? [v0: $i] : ($i(v0) & r1(all_3_1, v0) & ~ p1(v0))
% 136.05/18.60 | | |
% 136.05/18.60 | | | DELTA: instantiating (37) with fresh symbol all_140_0 gives:
% 136.05/18.60 | | | (38) $i(all_140_0) & r1(all_3_1, all_140_0) & ~ p1(all_140_0)
% 136.05/18.60 | | |
% 136.05/18.60 | | | ALPHA: (38) implies:
% 136.05/18.60 | | | (39) ~ p1(all_140_0)
% 136.05/18.60 | | | (40) r1(all_3_1, all_140_0)
% 136.05/18.60 | | | (41) $i(all_140_0)
% 136.05/18.60 | | |
% 136.05/18.60 | | | GROUND_INST: instantiating (20) with all_140_0, simplifying with (39),
% 136.05/18.60 | | | (40), (41) gives:
% 136.05/18.60 | | | (42) $false
% 136.05/18.60 | | |
% 136.05/18.60 | | | CLOSE: (42) is inconsistent.
% 136.05/18.60 | | |
% 136.05/18.60 | | Case 2:
% 136.05/18.60 | | |
% 136.12/18.60 | | | (43) p1(all_66_1) & r1(all_66_1, all_66_0) & r1(all_3_2, all_66_1) & ~
% 136.12/18.60 | | | p1(all_66_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 136.12/18.60 | | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~
% 136.12/18.60 | | | r1(v0, v1) | ~ r1(all_66_1, v0) | p1(v2) | p1(v0)) & ! [v0:
% 136.12/18.60 | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 136.12/18.60 | | | $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 136.12/18.60 | | | r1(all_66_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, v3) &
% 136.12/18.60 | | | ~ p1(v3)))
% 136.12/18.60 | | |
% 136.12/18.60 | | | ALPHA: (43) implies:
% 136.12/18.60 | | | (44) ~ p1(all_66_0)
% 136.12/18.60 | | | (45) r1(all_3_2, all_66_1)
% 136.12/18.60 | | | (46) r1(all_66_1, all_66_0)
% 136.12/18.60 | | | (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) |
% 136.12/18.60 | | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 136.12/18.60 | | | r1(all_66_1, v0) | p1(v2) | p1(v0))
% 136.12/18.60 | | |
% 136.12/18.60 | | | GROUND_INST: instantiating (22) with all_3_7, all_3_6, all_3_5, all_3_4,
% 136.12/18.60 | | | all_3_3, all_3_2, all_66_1, all_66_0, simplifying with (3),
% 136.12/18.60 | | | (4), (5), (6), (7), (8), (11), (12), (13), (14), (15), (16),
% 136.12/18.60 | | | (30), (31), (44), (45), (46) gives:
% 136.12/18.61 | | | (48) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0,
% 136.12/18.61 | | | v1) & r1(all_66_0, v0) & ~ p1(v1)) | (r1(all_3_2, v0) &
% 136.12/18.61 | | | ~ p1(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 136.12/18.61 | | | $i(v2) | ~ p1(v2) | ~ r1(v2, v3) | ~ r1(v0, v2) |
% 136.12/18.61 | | | p1(v3)))))
% 136.12/18.61 | | |
% 136.12/18.61 | | | DELTA: instantiating (48) with fresh symbols all_141_0, all_141_1 gives:
% 136.12/18.61 | | | (49) $i(all_141_0) & $i(all_141_1) & ((p1(all_141_1) & r1(all_141_1,
% 136.12/18.61 | | | all_141_0) & r1(all_66_0, all_141_1) & ~ p1(all_141_0)) |
% 136.12/18.61 | | | (r1(all_3_2, all_141_1) & ~ p1(all_141_1) & ! [v0: $i] : !
% 136.12/18.61 | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1)
% 136.12/18.61 | | | | ~ r1(all_141_1, v0) | p1(v1))))
% 136.12/18.61 | | |
% 136.12/18.61 | | | ALPHA: (49) implies:
% 136.12/18.61 | | | (50) $i(all_141_1)
% 136.12/18.61 | | | (51) $i(all_141_0)
% 136.12/18.61 | | | (52) (p1(all_141_1) & r1(all_141_1, all_141_0) & r1(all_66_0,
% 136.12/18.61 | | | all_141_1) & ~ p1(all_141_0)) | (r1(all_3_2, all_141_1) & ~
% 136.12/18.61 | | | p1(all_141_1) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 136.12/18.61 | | | $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_141_1, v0) |
% 136.12/18.61 | | | p1(v1)))
% 136.12/18.61 | | |
% 136.12/18.61 | | | BETA: splitting (52) gives:
% 136.12/18.61 | | |
% 136.12/18.61 | | | Case 1:
% 136.12/18.61 | | | |
% 136.12/18.61 | | | | (53) p1(all_141_1) & r1(all_141_1, all_141_0) & r1(all_66_0,
% 136.12/18.61 | | | | all_141_1) & ~ p1(all_141_0)
% 136.12/18.61 | | | |
% 136.12/18.61 | | | | ALPHA: (53) implies:
% 136.12/18.61 | | | | (54) ~ p1(all_141_0)
% 136.12/18.61 | | | | (55) r1(all_66_0, all_141_1)
% 136.12/18.61 | | | | (56) r1(all_141_1, all_141_0)
% 136.12/18.61 | | | | (57) p1(all_141_1)
% 136.12/18.61 | | | |
% 136.12/18.61 | | | | GROUND_INST: instantiating (47) with all_66_0, all_141_1, all_141_0,
% 136.12/18.61 | | | | simplifying with (31), (44), (46), (50), (51), (54), (55),
% 136.12/18.61 | | | | (56), (57) gives:
% 136.12/18.61 | | | | (58) $false
% 136.15/18.61 | | | |
% 136.15/18.61 | | | | CLOSE: (58) is inconsistent.
% 136.15/18.61 | | | |
% 136.15/18.61 | | | Case 2:
% 136.15/18.61 | | | |
% 136.15/18.61 | | | | (59) r1(all_3_2, all_141_1) & ~ p1(all_141_1) & ! [v0: $i] : !
% 136.15/18.61 | | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) |
% 136.15/18.61 | | | | ~ r1(all_141_1, v0) | p1(v1))
% 136.15/18.61 | | | |
% 136.15/18.61 | | | | ALPHA: (59) implies:
% 136.15/18.61 | | | | (60) ~ p1(all_141_1)
% 136.15/18.61 | | | | (61) r1(all_3_2, all_141_1)
% 136.15/18.61 | | | | (62) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) |
% 136.15/18.61 | | | | ~ r1(v0, v1) | ~ r1(all_141_1, v0) | p1(v1))
% 136.15/18.61 | | | |
% 136.15/18.61 | | | | GROUND_INST: instantiating (19) with all_141_1, simplifying with (50),
% 136.15/18.61 | | | | (60), (61) gives:
% 136.15/18.61 | | | | (63) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0,
% 136.15/18.61 | | | | v1) & r1(all_141_1, v0) & ~ p1(v1))
% 136.15/18.61 | | | |
% 136.15/18.61 | | | | DELTA: instantiating (63) with fresh symbols all_205_0, all_205_1 gives:
% 136.15/18.61 | | | | (64) $i(all_205_0) & $i(all_205_1) & p1(all_205_1) & r1(all_205_1,
% 136.15/18.61 | | | | all_205_0) & r1(all_141_1, all_205_1) & ~ p1(all_205_0)
% 136.15/18.61 | | | |
% 136.15/18.61 | | | | ALPHA: (64) implies:
% 136.15/18.61 | | | | (65) ~ p1(all_205_0)
% 136.15/18.61 | | | | (66) r1(all_141_1, all_205_1)
% 136.15/18.61 | | | | (67) r1(all_205_1, all_205_0)
% 136.15/18.61 | | | | (68) p1(all_205_1)
% 136.15/18.61 | | | | (69) $i(all_205_1)
% 136.15/18.61 | | | | (70) $i(all_205_0)
% 136.15/18.61 | | | |
% 136.15/18.61 | | | | GROUND_INST: instantiating (62) with all_205_1, all_205_0, simplifying
% 136.15/18.61 | | | | with (65), (66), (67), (68), (69), (70) gives:
% 136.15/18.61 | | | | (71) $false
% 136.15/18.61 | | | |
% 136.15/18.61 | | | | CLOSE: (71) is inconsistent.
% 136.15/18.61 | | | |
% 136.15/18.61 | | | End of split
% 136.15/18.61 | | |
% 136.15/18.61 | | End of split
% 136.15/18.61 | |
% 136.15/18.61 | Case 2:
% 136.15/18.61 | |
% 136.15/18.61 | | (72) ~ p1(all_3_2)
% 136.15/18.61 | |
% 136.15/18.61 | | BETA: splitting (25) gives:
% 136.15/18.61 | |
% 136.15/18.61 | | Case 1:
% 136.15/18.61 | | |
% 136.15/18.61 | | | (73) p1(all_3_2)
% 136.15/18.61 | | |
% 136.15/18.61 | | | PRED_UNIFY: (72), (73) imply:
% 136.15/18.61 | | | (74) $false
% 136.15/18.61 | | |
% 136.15/18.61 | | | CLOSE: (74) is inconsistent.
% 136.15/18.61 | | |
% 136.15/18.61 | | Case 2:
% 136.15/18.61 | | |
% 136.15/18.61 | | | (75) ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) |
% 136.15/18.61 | | | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 136.15/18.61 | | | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0,
% 136.15/18.61 | | | v1) | p1(v2)))))
% 136.15/18.61 | | |
% 136.15/18.61 | | | DELTA: instantiating (75) with fresh symbol all_72_0 gives:
% 136.15/18.62 | | | (76) $i(all_72_0) & ((r1(all_3_1, all_72_0) & ~ p1(all_72_0)) |
% 136.15/18.62 | | | (r1(all_3_2, all_72_0) & ~ p1(all_72_0) & ! [v0: $i] : ! [v1:
% 136.15/18.62 | | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) |
% 136.15/18.62 | | | ~ r1(all_72_0, v0) | p1(v1))))
% 136.15/18.62 | | |
% 136.15/18.62 | | | ALPHA: (76) implies:
% 136.15/18.62 | | | (77) $i(all_72_0)
% 136.15/18.62 | | | (78) (r1(all_3_1, all_72_0) & ~ p1(all_72_0)) | (r1(all_3_2, all_72_0)
% 136.15/18.62 | | | & ~ p1(all_72_0) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 136.15/18.62 | | | $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_72_0, v0) |
% 136.15/18.62 | | | p1(v1)))
% 136.15/18.62 | | |
% 136.15/18.62 | | | BETA: splitting (78) gives:
% 136.15/18.62 | | |
% 136.15/18.62 | | | Case 1:
% 136.15/18.62 | | | |
% 136.15/18.62 | | | | (79) r1(all_3_1, all_72_0) & ~ p1(all_72_0)
% 136.15/18.62 | | | |
% 136.15/18.62 | | | | ALPHA: (79) implies:
% 136.15/18.62 | | | | (80) ~ p1(all_72_0)
% 136.15/18.62 | | | | (81) r1(all_3_1, all_72_0)
% 136.15/18.62 | | | |
% 136.15/18.62 | | | | GROUND_INST: instantiating (20) with all_72_0, simplifying with (77),
% 136.15/18.62 | | | | (80), (81) gives:
% 136.15/18.62 | | | | (82) $false
% 136.15/18.62 | | | |
% 136.15/18.62 | | | | CLOSE: (82) is inconsistent.
% 136.15/18.62 | | | |
% 136.15/18.62 | | | Case 2:
% 136.15/18.62 | | | |
% 136.15/18.62 | | | | (83) r1(all_3_2, all_72_0) & ~ p1(all_72_0) & ! [v0: $i] : ! [v1:
% 136.15/18.62 | | | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~
% 136.15/18.62 | | | | r1(all_72_0, v0) | p1(v1))
% 136.15/18.62 | | | |
% 136.15/18.62 | | | | ALPHA: (83) implies:
% 136.15/18.62 | | | | (84) ~ p1(all_72_0)
% 136.15/18.62 | | | | (85) r1(all_3_2, all_72_0)
% 136.15/18.62 | | | | (86) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) |
% 136.15/18.62 | | | | ~ r1(v0, v1) | ~ r1(all_72_0, v0) | p1(v1))
% 136.15/18.62 | | | |
% 136.15/18.62 | | | | GROUND_INST: instantiating (19) with all_72_0, simplifying with (77),
% 136.15/18.62 | | | | (84), (85) gives:
% 136.15/18.62 | | | | (87) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0,
% 136.15/18.62 | | | | v1) & r1(all_72_0, v0) & ~ p1(v1))
% 136.15/18.62 | | | |
% 136.15/18.62 | | | | DELTA: instantiating (87) with fresh symbols all_178_0, all_178_1 gives:
% 136.15/18.62 | | | | (88) $i(all_178_0) & $i(all_178_1) & p1(all_178_1) & r1(all_178_1,
% 136.15/18.62 | | | | all_178_0) & r1(all_72_0, all_178_1) & ~ p1(all_178_0)
% 136.15/18.62 | | | |
% 136.15/18.62 | | | | ALPHA: (88) implies:
% 136.15/18.62 | | | | (89) ~ p1(all_178_0)
% 136.15/18.62 | | | | (90) r1(all_72_0, all_178_1)
% 136.15/18.62 | | | | (91) r1(all_178_1, all_178_0)
% 136.15/18.62 | | | | (92) p1(all_178_1)
% 136.15/18.62 | | | | (93) $i(all_178_1)
% 136.15/18.62 | | | | (94) $i(all_178_0)
% 136.15/18.62 | | | |
% 136.15/18.62 | | | | GROUND_INST: instantiating (86) with all_178_1, all_178_0, simplifying
% 136.15/18.62 | | | | with (89), (90), (91), (92), (93), (94) gives:
% 136.15/18.62 | | | | (95) $false
% 136.15/18.62 | | | |
% 136.15/18.62 | | | | CLOSE: (95) is inconsistent.
% 136.15/18.62 | | | |
% 136.15/18.62 | | | End of split
% 136.15/18.62 | | |
% 136.15/18.62 | | End of split
% 136.15/18.62 | |
% 136.15/18.62 | End of split
% 136.15/18.62 |
% 136.15/18.62 End of proof
% 136.15/18.62 % SZS output end Proof for theBenchmark
% 136.15/18.62
% 136.15/18.62 18020ms
%------------------------------------------------------------------------------