TSTP Solution File: MGT044+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT044+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n018.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 09:16:25 EDT 2023
% Result : Theorem 8.94s 1.86s
% Output : Proof 13.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT044+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 06:40:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 ________ _____
% 0.20/0.58 ___ __ \_________(_)________________________________
% 0.20/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58 (2023-06-19)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2023
% 0.20/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58 Amanda Stjerna.
% 0.20/0.58 Free software under BSD-3-Clause.
% 0.20/0.58
% 0.20/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58
% 0.20/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.59 Running up to 7 provers in parallel.
% 0.20/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.25/0.99 Prover 1: Preprocessing ...
% 2.25/1.00 Prover 4: Preprocessing ...
% 2.83/1.04 Prover 2: Preprocessing ...
% 2.83/1.04 Prover 6: Preprocessing ...
% 2.83/1.04 Prover 0: Preprocessing ...
% 2.83/1.04 Prover 3: Preprocessing ...
% 2.83/1.04 Prover 5: Preprocessing ...
% 4.42/1.32 Prover 3: Constructing countermodel ...
% 4.42/1.32 Prover 1: Constructing countermodel ...
% 4.42/1.33 Prover 6: Constructing countermodel ...
% 4.42/1.41 Prover 2: Proving ...
% 5.60/1.46 Prover 4: Constructing countermodel ...
% 6.16/1.50 Prover 0: Proving ...
% 6.16/1.53 Prover 5: Proving ...
% 6.16/1.53 Prover 3: gave up
% 6.16/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.76/1.57 Prover 1: gave up
% 6.76/1.58 Prover 7: Preprocessing ...
% 6.76/1.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.76/1.60 Prover 6: gave up
% 6.76/1.60 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 7.09/1.62 Prover 8: Preprocessing ...
% 7.09/1.63 Prover 9: Preprocessing ...
% 7.35/1.70 Prover 8: Warning: ignoring some quantifiers
% 7.35/1.72 Prover 8: Constructing countermodel ...
% 8.02/1.76 Prover 7: Warning: ignoring some quantifiers
% 8.02/1.77 Prover 7: Constructing countermodel ...
% 8.45/1.81 Prover 9: Constructing countermodel ...
% 8.45/1.85 Prover 8: gave up
% 8.94/1.86 Prover 0: proved (1257ms)
% 8.94/1.86
% 8.94/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.94/1.86
% 8.94/1.86 Prover 9: stopped
% 8.94/1.86 Prover 5: stopped
% 9.03/1.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.03/1.86 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.03/1.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.03/1.86 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.03/1.87 Prover 2: stopped
% 9.03/1.90 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.33/1.91 Prover 11: Preprocessing ...
% 9.33/1.92 Prover 19: Preprocessing ...
% 9.33/1.92 Prover 16: Preprocessing ...
% 9.33/1.93 Prover 10: Preprocessing ...
% 9.33/1.93 Prover 13: Preprocessing ...
% 9.33/1.97 Prover 16: Warning: ignoring some quantifiers
% 9.33/1.97 Prover 13: Warning: ignoring some quantifiers
% 9.33/1.98 Prover 16: Constructing countermodel ...
% 9.33/1.99 Prover 13: Constructing countermodel ...
% 9.33/1.99 Prover 10: Warning: ignoring some quantifiers
% 9.33/2.00 Prover 10: Constructing countermodel ...
% 10.10/2.05 Prover 19: Warning: ignoring some quantifiers
% 10.10/2.06 Prover 19: Constructing countermodel ...
% 10.10/2.11 Prover 11: Constructing countermodel ...
% 10.97/2.15 Prover 19: gave up
% 11.39/2.20 Prover 16: gave up
% 12.21/2.31 Prover 10: gave up
% 12.49/2.37 Prover 11: Found proof (size 76)
% 12.49/2.37 Prover 11: proved (509ms)
% 12.49/2.37 Prover 4: stopped
% 12.49/2.37 Prover 13: stopped
% 12.49/2.37 Prover 7: stopped
% 12.49/2.37
% 12.49/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.49/2.37
% 12.49/2.38 % SZS output start Proof for theBenchmark
% 12.49/2.38 Assumptions after simplification:
% 12.49/2.38 ---------------------------------
% 12.49/2.38
% 12.49/2.38 (assumption_5)
% 13.03/2.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.03/2.45 any] : ( ~ (internal_friction(v0, v2) = v3) | ~ (internal_friction(v0, v1)
% 13.03/2.45 = v4) | ~ (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 13.03/2.45 [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ?
% 13.03/2.45 [v11: $i] : ? [v12: $i] : ? [v13: int] : ? [v14: int] : ? [v15: int] :
% 13.03/2.45 (( ~ (v6 = 0) & organization(v0) = v6) | (( ~ (v5 = 0) | (v15 = 0 &
% 13.03/2.45 capability(v0, v2) = v11 & capability(v0, v1) = v12 & smaller(v11,
% 13.03/2.45 v12) = 0 & $i(v12) & $i(v11)) | ( ~ (v14 = 0) &
% 13.03/2.45 stock_of_knowledge(v0, v2) = v7 & stock_of_knowledge(v0, v1) = v8 &
% 13.03/2.45 smaller_or_equal(v7, v8) = v14 & $i(v8) & $i(v7))) & ( ~ (v4 = v3) |
% 13.03/2.45 (v12 = v11 & capability(v0, v2) = v11 & capability(v0, v1) = v11 &
% 13.03/2.45 $i(v11)) | ( ~ (v8 = v7) & stock_of_knowledge(v0, v2) = v7 &
% 13.03/2.45 stock_of_knowledge(v0, v1) = v8 & $i(v8) & $i(v7))) & ((v13 = 0 &
% 13.03/2.45 capability(v0, v2) = v11 & capability(v0, v1) = v12 & greater(v11,
% 13.03/2.45 v12) = 0 & $i(v12) & $i(v11)) | ( ~ (v10 = 0) &
% 13.03/2.45 smaller_or_equal(v3, v4) = v10) | ( ~ (v9 = 0) &
% 13.03/2.45 stock_of_knowledge(v0, v2) = v7 & stock_of_knowledge(v0, v1) = v8 &
% 13.03/2.45 greater(v7, v8) = v9 & $i(v8) & $i(v7)))))) & ! [v0: $i] : ! [v1:
% 13.03/2.45 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~
% 13.03/2.45 (internal_friction(v0, v2) = v3) | ~ (internal_friction(v0, v1) = v4) | ~
% 13.03/2.45 (smaller_or_equal(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 13.03/2.45 [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ?
% 13.03/2.45 [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14: int] : ? [v15: int] :
% 13.03/2.45 (( ~ (v6 = 0) & organization(v0) = v6) | (( ~ (v5 = 0) | (v12 = 0 &
% 13.03/2.45 capability(v0, v2) = v10 & capability(v0, v1) = v11 & greater(v10,
% 13.03/2.45 v11) = 0 & $i(v11) & $i(v10)) | ( ~ (v9 = 0) &
% 13.03/2.45 stock_of_knowledge(v0, v2) = v7 & stock_of_knowledge(v0, v1) = v8 &
% 13.03/2.45 greater(v7, v8) = v9 & $i(v8) & $i(v7))) & ( ~ (v4 = v3) | (v11 =
% 13.03/2.45 v10 & capability(v0, v2) = v10 & capability(v0, v1) = v10 & $i(v10))
% 13.03/2.45 | ( ~ (v8 = v7) & stock_of_knowledge(v0, v2) = v7 &
% 13.03/2.45 stock_of_knowledge(v0, v1) = v8 & $i(v8) & $i(v7))) & ((v15 = 0 &
% 13.03/2.45 capability(v0, v2) = v10 & capability(v0, v1) = v11 & smaller(v10,
% 13.03/2.45 v11) = 0 & $i(v11) & $i(v10)) | ( ~ (v14 = 0) & greater(v3, v4) =
% 13.03/2.45 v14) | ( ~ (v13 = 0) & stock_of_knowledge(v0, v2) = v7 &
% 13.03/2.45 stock_of_knowledge(v0, v1) = v8 & smaller_or_equal(v7, v8) = v13 &
% 13.03/2.45 $i(v8) & $i(v7)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.03/2.45 [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (stock_of_knowledge(v0, v2) = v3)
% 13.03/2.45 | ~ (stock_of_knowledge(v0, v1) = v4) | ~ (greater(v3, v4) = v5) | ~
% 13.03/2.45 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] :
% 13.03/2.45 ? [v9: int] : ? [v10: $i] : ? [v11: $i] : ? [v12: int] : ? [v13: int] :
% 13.03/2.45 ? [v14: int] : ? [v15: int] : (( ~ (v6 = 0) & organization(v0) = v6) | (( ~
% 13.03/2.45 (v5 = 0) | (v12 = 0 & capability(v0, v2) = v10 & capability(v0, v1) =
% 13.03/2.45 v11 & greater(v10, v11) = 0 & $i(v11) & $i(v10)) | ( ~ (v9 = 0) &
% 13.03/2.45 internal_friction(v0, v2) = v7 & internal_friction(v0, v1) = v8 &
% 13.03/2.45 smaller_or_equal(v7, v8) = v9 & $i(v8) & $i(v7))) & ( ~ (v4 = v3) |
% 13.03/2.45 (v11 = v10 & capability(v0, v2) = v10 & capability(v0, v1) = v10 &
% 13.03/2.45 $i(v10)) | ( ~ (v8 = v7) & internal_friction(v0, v2) = v7 &
% 13.03/2.45 internal_friction(v0, v1) = v8 & $i(v8) & $i(v7))) & ((v15 = 0 &
% 13.03/2.45 capability(v0, v2) = v10 & capability(v0, v1) = v11 & smaller(v10,
% 13.03/2.45 v11) = 0 & $i(v11) & $i(v10)) | ( ~ (v14 = 0) &
% 13.03/2.45 internal_friction(v0, v2) = v7 & internal_friction(v0, v1) = v8 &
% 13.03/2.45 greater(v7, v8) = v14 & $i(v8) & $i(v7)) | ( ~ (v13 = 0) &
% 13.03/2.45 smaller_or_equal(v3, v4) = v13))))) & ! [v0: $i] : ! [v1: $i] : !
% 13.03/2.45 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~
% 13.03/2.45 (stock_of_knowledge(v0, v2) = v3) | ~ (stock_of_knowledge(v0, v1) = v4) |
% 13.03/2.45 ~ (smaller_or_equal(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 13.03/2.45 [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] : ?
% 13.03/2.45 [v11: $i] : ? [v12: $i] : ? [v13: int] : ? [v14: int] : ? [v15: int] :
% 13.03/2.45 (( ~ (v6 = 0) & organization(v0) = v6) | (( ~ (v5 = 0) | (v15 = 0 &
% 13.03/2.45 capability(v0, v2) = v11 & capability(v0, v1) = v12 & smaller(v11,
% 13.03/2.45 v12) = 0 & $i(v12) & $i(v11)) | ( ~ (v14 = 0) &
% 13.03/2.45 internal_friction(v0, v2) = v8 & internal_friction(v0, v1) = v9 &
% 13.03/2.45 greater(v8, v9) = v14 & $i(v9) & $i(v8))) & ( ~ (v4 = v3) | (v12 =
% 13.03/2.45 v11 & capability(v0, v2) = v11 & capability(v0, v1) = v11 & $i(v11))
% 13.03/2.45 | ( ~ (v9 = v8) & internal_friction(v0, v2) = v8 &
% 13.03/2.45 internal_friction(v0, v1) = v9 & $i(v9) & $i(v8))) & ((v13 = 0 &
% 13.03/2.45 capability(v0, v2) = v11 & capability(v0, v1) = v12 & greater(v11,
% 13.03/2.45 v12) = 0 & $i(v12) & $i(v11)) | ( ~ (v10 = 0) &
% 13.03/2.45 internal_friction(v0, v2) = v8 & internal_friction(v0, v1) = v9 &
% 13.03/2.45 smaller_or_equal(v8, v9) = v10 & $i(v9) & $i(v8)) | ( ~ (v7 = 0) &
% 13.03/2.45 greater(v3, v4) = v7))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.03/2.45 : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (capability(v0, v2) = v3) |
% 13.03/2.45 ~ (capability(v0, v1) = v4) | ~ (greater(v3, v4) = v5) | ~ $i(v2) | ~
% 13.03/2.45 $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: int]
% 13.03/2.45 : ? [v10: $i] : ? [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14:
% 13.03/2.45 int] : ? [v15: int] : (( ~ (v6 = 0) & organization(v0) = v6) | ((v5 = 0 |
% 13.03/2.45 ( ~ (v12 = 0) & internal_friction(v0, v2) = v10 &
% 13.03/2.45 internal_friction(v0, v1) = v11 & smaller_or_equal(v10, v11) = v12 &
% 13.03/2.45 $i(v11) & $i(v10)) | ( ~ (v9 = 0) & stock_of_knowledge(v0, v2) = v7
% 13.03/2.45 & stock_of_knowledge(v0, v1) = v8 & greater(v7, v8) = v9 & $i(v8) &
% 13.03/2.45 $i(v7))) & (v4 = v3 | ( ~ (v11 = v10) & internal_friction(v0, v2) =
% 13.03/2.45 v10 & internal_friction(v0, v1) = v11 & $i(v11) & $i(v10)) | ( ~ (v8
% 13.03/2.45 = v7) & stock_of_knowledge(v0, v2) = v7 & stock_of_knowledge(v0,
% 13.03/2.45 v1) = v8 & $i(v8) & $i(v7))) & ((v15 = 0 & smaller(v3, v4) = 0) |
% 13.03/2.45 ( ~ (v14 = 0) & internal_friction(v0, v2) = v10 &
% 13.03/2.45 internal_friction(v0, v1) = v11 & greater(v10, v11) = v14 & $i(v11)
% 13.03/2.45 & $i(v10)) | ( ~ (v13 = 0) & stock_of_knowledge(v0, v2) = v7 &
% 13.03/2.45 stock_of_knowledge(v0, v1) = v8 & smaller_or_equal(v7, v8) = v13 &
% 13.03/2.45 $i(v8) & $i(v7)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.03/2.45 [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (capability(v0, v2) = v3) | ~
% 13.03/2.45 (capability(v0, v1) = v4) | ~ (smaller(v3, v4) = v5) | ~ $i(v2) | ~
% 13.03/2.45 $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: int]
% 13.03/2.45 : ? [v10: $i] : ? [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14:
% 13.03/2.45 int] : ? [v15: int] : (( ~ (v6 = 0) & organization(v0) = v6) | ((v5 = 0 |
% 13.03/2.45 ( ~ (v15 = 0) & internal_friction(v0, v2) = v10 &
% 13.03/2.45 internal_friction(v0, v1) = v11 & greater(v10, v11) = v15 & $i(v11)
% 13.03/2.45 & $i(v10)) | ( ~ (v14 = 0) & stock_of_knowledge(v0, v2) = v7 &
% 13.03/2.45 stock_of_knowledge(v0, v1) = v8 & smaller_or_equal(v7, v8) = v14 &
% 13.03/2.45 $i(v8) & $i(v7))) & (v4 = v3 | ( ~ (v11 = v10) &
% 13.03/2.45 internal_friction(v0, v2) = v10 & internal_friction(v0, v1) = v11 &
% 13.03/2.45 $i(v11) & $i(v10)) | ( ~ (v8 = v7) & stock_of_knowledge(v0, v2) = v7
% 13.03/2.45 & stock_of_knowledge(v0, v1) = v8 & $i(v8) & $i(v7))) & ((v13 = 0 &
% 13.03/2.45 greater(v3, v4) = 0) | ( ~ (v12 = 0) & internal_friction(v0, v2) =
% 13.03/2.45 v10 & internal_friction(v0, v1) = v11 & smaller_or_equal(v10, v11) =
% 13.03/2.45 v12 & $i(v11) & $i(v10)) | ( ~ (v9 = 0) & stock_of_knowledge(v0, v2)
% 13.03/2.45 = v7 & stock_of_knowledge(v0, v1) = v8 & greater(v7, v8) = v9 &
% 13.03/2.45 $i(v8) & $i(v7))))))
% 13.03/2.45
% 13.03/2.45 (assumption_7)
% 13.03/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.03/2.46 int] : (v5 = 0 | ~ (stock_of_knowledge(v0, v2) = v3) | ~
% 13.03/2.46 (stock_of_knowledge(v0, v1) = v4) | ~ (greater(v3, v4) = v5) | ~ $i(v2) |
% 13.03/2.46 ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 13.03/2.46 int] : (( ~ (v9 = 0) & age(v0, v2) = v7 & age(v0, v1) = v8 & greater(v7,
% 13.03/2.46 v8) = v9 & $i(v8) & $i(v7)) | ( ~ (v6 = 0) & organization(v0) = v6)))
% 13.03/2.46 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 13.03/2.46 (age(v0, v2) = v3) | ~ (age(v0, v1) = v4) | ~ (greater(v3, v4) = 0) | ~
% 13.03/2.46 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] :
% 13.03/2.46 ? [v8: int] : ((v8 = 0 & stock_of_knowledge(v0, v2) = v6 &
% 13.03/2.46 stock_of_knowledge(v0, v1) = v7 & greater(v6, v7) = 0 & $i(v7) & $i(v6))
% 13.03/2.46 | ( ~ (v5 = 0) & organization(v0) = v5)))
% 13.03/2.46
% 13.03/2.46 (assumption_9)
% 13.03/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3
% 13.03/2.46 | ~ (internal_friction(v0, v2) = v3) | ~ (internal_friction(v0, v1) = v4)
% 13.03/2.46 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 13.03/2.46 organization(v0) = v5))
% 13.03/2.46
% 13.03/2.46 (definition_smaller_or_equal)
% 13.03/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (smaller(v0,
% 13.03/2.46 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.03/2.46 smaller_or_equal(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int]
% 13.03/2.46 : (v2 = 0 | ~ (smaller_or_equal(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 13.03/2.46 [v3: int] : ( ~ (v3 = 0) & smaller(v0, v1) = v3)) & ! [v0: $i] : ! [v1:
% 13.03/2.46 $i] : (v1 = v0 | ~ (smaller_or_equal(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 13.03/2.46 smaller(v0, v1) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 13.03/2.46 (smaller_or_equal(v0, v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : (
% 13.03/2.46 ~ (smaller(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | smaller_or_equal(v0, v1) =
% 13.03/2.46 0) & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (smaller(v0, v0) = v1) |
% 13.03/2.46 ~ $i(v0) | smaller_or_equal(v0, v0) = 0)
% 13.03/2.46
% 13.03/2.46 (lemma_3)
% 13.03/2.46 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 13.03/2.46 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & age(v0, v2) = v3 & age(v0,
% 13.03/2.46 v1) = v4 & organization(v0) = 0 & capability(v0, v2) = v5 & capability(v0,
% 13.03/2.46 v1) = v6 & greater(v5, v6) = v7 & greater(v3, v4) = 0 & $i(v6) & $i(v5) &
% 13.03/2.46 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.03/2.46
% 13.03/2.46 (function-axioms)
% 13.03/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (age(v3,
% 13.03/2.46 v2) = v1) | ~ (age(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.03/2.46 $i] : ! [v3: $i] : (v1 = v0 | ~ (internal_friction(v3, v2) = v1) | ~
% 13.03/2.46 (internal_friction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.03/2.46 : ! [v3: $i] : (v1 = v0 | ~ (stock_of_knowledge(v3, v2) = v1) | ~
% 13.03/2.46 (stock_of_knowledge(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.03/2.46 : ! [v3: $i] : (v1 = v0 | ~ (capability(v3, v2) = v1) | ~ (capability(v3,
% 13.03/2.46 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 13.03/2.46 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~
% 13.03/2.46 (greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.03/2.46 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.03/2.46 (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) = v0)) & !
% 13.03/2.46 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.03/2.46 $i] : (v1 = v0 | ~ (smaller(v3, v2) = v1) | ~ (smaller(v3, v2) = v0)) & !
% 13.03/2.46 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.03/2.46 $i] : (v1 = v0 | ~ (smaller_or_equal(v3, v2) = v1) | ~
% 13.03/2.46 (smaller_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.03/2.46 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (organization(v2) = v1) |
% 13.03/2.46 ~ (organization(v2) = v0))
% 13.03/2.46
% 13.03/2.46 Further assumptions not needed in the proof:
% 13.03/2.46 --------------------------------------------
% 13.03/2.46 definition_greater_or_equal, definition_smaller,
% 13.03/2.46 meaning_postulate_greater_comparable, meaning_postulate_greater_strict,
% 13.03/2.46 meaning_postulate_greater_transitive
% 13.03/2.46
% 13.03/2.46 Those formulas are unsatisfiable:
% 13.03/2.46 ---------------------------------
% 13.03/2.46
% 13.03/2.46 Begin of proof
% 13.03/2.46 |
% 13.03/2.46 | ALPHA: (definition_smaller_or_equal) implies:
% 13.03/2.46 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (smaller_or_equal(v0, v0) =
% 13.03/2.46 | v1) | ~ $i(v0))
% 13.03/2.46 |
% 13.03/2.46 | ALPHA: (assumption_5) implies:
% 13.03/2.47 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 13.03/2.47 | ! [v5: any] : ( ~ (capability(v0, v2) = v3) | ~ (capability(v0, v1) =
% 13.03/2.47 | v4) | ~ (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 13.03/2.47 | | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10:
% 13.03/2.47 | $i] : ? [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14: int]
% 13.03/2.47 | : ? [v15: int] : (( ~ (v6 = 0) & organization(v0) = v6) | ((v5 = 0 |
% 13.03/2.47 | ( ~ (v12 = 0) & internal_friction(v0, v2) = v10 &
% 13.03/2.47 | internal_friction(v0, v1) = v11 & smaller_or_equal(v10, v11)
% 13.03/2.47 | = v12 & $i(v11) & $i(v10)) | ( ~ (v9 = 0) &
% 13.03/2.47 | stock_of_knowledge(v0, v2) = v7 & stock_of_knowledge(v0, v1)
% 13.03/2.47 | = v8 & greater(v7, v8) = v9 & $i(v8) & $i(v7))) & (v4 = v3 |
% 13.03/2.47 | ( ~ (v11 = v10) & internal_friction(v0, v2) = v10 &
% 13.03/2.47 | internal_friction(v0, v1) = v11 & $i(v11) & $i(v10)) | ( ~
% 13.03/2.47 | (v8 = v7) & stock_of_knowledge(v0, v2) = v7 &
% 13.03/2.47 | stock_of_knowledge(v0, v1) = v8 & $i(v8) & $i(v7))) & ((v15 =
% 13.03/2.47 | 0 & smaller(v3, v4) = 0) | ( ~ (v14 = 0) &
% 13.03/2.47 | internal_friction(v0, v2) = v10 & internal_friction(v0, v1) =
% 13.03/2.47 | v11 & greater(v10, v11) = v14 & $i(v11) & $i(v10)) | ( ~ (v13
% 13.03/2.47 | = 0) & stock_of_knowledge(v0, v2) = v7 &
% 13.03/2.47 | stock_of_knowledge(v0, v1) = v8 & smaller_or_equal(v7, v8) =
% 13.03/2.47 | v13 & $i(v8) & $i(v7))))))
% 13.03/2.47 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 13.03/2.47 | ! [v5: any] : ( ~ (stock_of_knowledge(v0, v2) = v3) | ~
% 13.03/2.47 | (stock_of_knowledge(v0, v1) = v4) | ~ (greater(v3, v4) = v5) | ~
% 13.03/2.47 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8:
% 13.03/2.47 | $i] : ? [v9: int] : ? [v10: $i] : ? [v11: $i] : ? [v12: int] :
% 13.03/2.47 | ? [v13: int] : ? [v14: int] : ? [v15: int] : (( ~ (v6 = 0) &
% 13.03/2.47 | organization(v0) = v6) | (( ~ (v5 = 0) | (v12 = 0 &
% 13.03/2.47 | capability(v0, v2) = v10 & capability(v0, v1) = v11 &
% 13.03/2.47 | greater(v10, v11) = 0 & $i(v11) & $i(v10)) | ( ~ (v9 = 0) &
% 13.03/2.47 | internal_friction(v0, v2) = v7 & internal_friction(v0, v1) =
% 13.03/2.47 | v8 & smaller_or_equal(v7, v8) = v9 & $i(v8) & $i(v7))) & ( ~
% 13.03/2.47 | (v4 = v3) | (v11 = v10 & capability(v0, v2) = v10 &
% 13.03/2.47 | capability(v0, v1) = v10 & $i(v10)) | ( ~ (v8 = v7) &
% 13.03/2.47 | internal_friction(v0, v2) = v7 & internal_friction(v0, v1) =
% 13.03/2.47 | v8 & $i(v8) & $i(v7))) & ((v15 = 0 & capability(v0, v2) = v10
% 13.03/2.47 | & capability(v0, v1) = v11 & smaller(v10, v11) = 0 & $i(v11)
% 13.03/2.47 | & $i(v10)) | ( ~ (v14 = 0) & internal_friction(v0, v2) = v7 &
% 13.03/2.47 | internal_friction(v0, v1) = v8 & greater(v7, v8) = v14 &
% 13.03/2.47 | $i(v8) & $i(v7)) | ( ~ (v13 = 0) & smaller_or_equal(v3, v4) =
% 13.03/2.47 | v13)))))
% 13.03/2.47 |
% 13.03/2.47 | ALPHA: (assumption_7) implies:
% 13.03/2.47 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 13.03/2.47 | ~ (age(v0, v2) = v3) | ~ (age(v0, v1) = v4) | ~ (greater(v3, v4) =
% 13.03/2.47 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i]
% 13.03/2.47 | : ? [v7: $i] : ? [v8: int] : ((v8 = 0 & stock_of_knowledge(v0, v2)
% 13.03/2.47 | = v6 & stock_of_knowledge(v0, v1) = v7 & greater(v6, v7) = 0 &
% 13.03/2.47 | $i(v7) & $i(v6)) | ( ~ (v5 = 0) & organization(v0) = v5)))
% 13.03/2.47 |
% 13.03/2.47 | ALPHA: (function-axioms) implies:
% 13.03/2.47 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.03/2.47 | (v1 = v0 | ~ (organization(v2) = v1) | ~ (organization(v2) = v0))
% 13.03/2.47 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.03/2.47 | ! [v3: $i] : (v1 = v0 | ~ (smaller_or_equal(v3, v2) = v1) | ~
% 13.03/2.47 | (smaller_or_equal(v3, v2) = v0))
% 13.03/2.48 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.03/2.48 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 13.03/2.48 | v2) = v0))
% 13.03/2.48 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.03/2.48 | (capability(v3, v2) = v1) | ~ (capability(v3, v2) = v0))
% 13.03/2.48 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.03/2.48 | (stock_of_knowledge(v3, v2) = v1) | ~ (stock_of_knowledge(v3, v2) =
% 13.03/2.48 | v0))
% 13.03/2.48 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.03/2.48 | (internal_friction(v3, v2) = v1) | ~ (internal_friction(v3, v2) =
% 13.03/2.48 | v0))
% 13.03/2.48 |
% 13.03/2.48 | DELTA: instantiating (lemma_3) with fresh symbols all_12_0, all_12_1,
% 13.03/2.48 | all_12_2, all_12_3, all_12_4, all_12_5, all_12_6, all_12_7 gives:
% 13.03/2.48 | (11) ~ (all_12_0 = 0) & age(all_12_7, all_12_5) = all_12_4 & age(all_12_7,
% 13.03/2.48 | all_12_6) = all_12_3 & organization(all_12_7) = 0 &
% 13.03/2.48 | capability(all_12_7, all_12_5) = all_12_2 & capability(all_12_7,
% 13.03/2.48 | all_12_6) = all_12_1 & greater(all_12_2, all_12_1) = all_12_0 &
% 13.03/2.48 | greater(all_12_4, all_12_3) = 0 & $i(all_12_1) & $i(all_12_2) &
% 13.03/2.48 | $i(all_12_3) & $i(all_12_4) & $i(all_12_5) & $i(all_12_6) &
% 13.03/2.48 | $i(all_12_7)
% 13.03/2.48 |
% 13.03/2.48 | ALPHA: (11) implies:
% 13.03/2.48 | (12) ~ (all_12_0 = 0)
% 13.03/2.48 | (13) $i(all_12_7)
% 13.03/2.48 | (14) $i(all_12_6)
% 13.03/2.48 | (15) $i(all_12_5)
% 13.03/2.48 | (16) greater(all_12_4, all_12_3) = 0
% 13.03/2.48 | (17) greater(all_12_2, all_12_1) = all_12_0
% 13.03/2.48 | (18) capability(all_12_7, all_12_6) = all_12_1
% 13.03/2.48 | (19) capability(all_12_7, all_12_5) = all_12_2
% 13.03/2.48 | (20) organization(all_12_7) = 0
% 13.03/2.48 | (21) age(all_12_7, all_12_6) = all_12_3
% 13.03/2.48 | (22) age(all_12_7, all_12_5) = all_12_4
% 13.03/2.48 |
% 13.03/2.48 | GROUND_INST: instantiating (2) with all_12_7, all_12_6, all_12_5, all_12_2,
% 13.03/2.48 | all_12_1, all_12_0, simplifying with (13), (14), (15), (17),
% 13.03/2.48 | (18), (19) gives:
% 13.03/2.48 | (23) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i]
% 13.03/2.48 | : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9:
% 13.03/2.48 | int] : (( ~ (v0 = 0) & organization(all_12_7) = v0) | ((all_12_0 = 0
% 13.03/2.48 | | ( ~ (v6 = 0) & internal_friction(all_12_7, all_12_5) = v4 &
% 13.03/2.48 | internal_friction(all_12_7, all_12_6) = v5 &
% 13.03/2.48 | smaller_or_equal(v4, v5) = v6 & $i(v5) & $i(v4)) | ( ~ (v3 =
% 13.03/2.48 | 0) & stock_of_knowledge(all_12_7, all_12_5) = v1 &
% 13.03/2.48 | stock_of_knowledge(all_12_7, all_12_6) = v2 & greater(v1, v2)
% 13.03/2.48 | = v3 & $i(v2) & $i(v1))) & (all_12_1 = all_12_2 | ( ~ (v5 =
% 13.03/2.48 | v4) & internal_friction(all_12_7, all_12_5) = v4 &
% 13.03/2.48 | internal_friction(all_12_7, all_12_6) = v5 & $i(v5) & $i(v4))
% 13.03/2.48 | | ( ~ (v2 = v1) & stock_of_knowledge(all_12_7, all_12_5) = v1 &
% 13.03/2.48 | stock_of_knowledge(all_12_7, all_12_6) = v2 & $i(v2) &
% 13.03/2.48 | $i(v1))) & ((v9 = 0 & smaller(all_12_2, all_12_1) = 0) | ( ~
% 13.03/2.48 | (v8 = 0) & internal_friction(all_12_7, all_12_5) = v4 &
% 13.03/2.49 | internal_friction(all_12_7, all_12_6) = v5 & greater(v4, v5) =
% 13.03/2.49 | v8 & $i(v5) & $i(v4)) | ( ~ (v7 = 0) &
% 13.03/2.49 | stock_of_knowledge(all_12_7, all_12_5) = v1 &
% 13.03/2.49 | stock_of_knowledge(all_12_7, all_12_6) = v2 &
% 13.03/2.49 | smaller_or_equal(v1, v2) = v7 & $i(v2) & $i(v1)))))
% 13.03/2.49 |
% 13.03/2.49 | GROUND_INST: instantiating (4) with all_12_7, all_12_6, all_12_5, all_12_4,
% 13.03/2.49 | all_12_3, simplifying with (13), (14), (15), (16), (21), (22)
% 13.03/2.49 | gives:
% 13.03/2.49 | (24) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ((v3 = 0 &
% 13.03/2.49 | stock_of_knowledge(all_12_7, all_12_5) = v1 &
% 13.03/2.49 | stock_of_knowledge(all_12_7, all_12_6) = v2 & greater(v1, v2) = 0
% 13.03/2.49 | & $i(v2) & $i(v1)) | ( ~ (v0 = 0) & organization(all_12_7) = v0))
% 13.03/2.49 |
% 13.03/2.49 | DELTA: instantiating (24) with fresh symbols all_22_0, all_22_1, all_22_2,
% 13.03/2.49 | all_22_3 gives:
% 13.03/2.49 | (25) (all_22_0 = 0 & stock_of_knowledge(all_12_7, all_12_5) = all_22_2 &
% 13.03/2.49 | stock_of_knowledge(all_12_7, all_12_6) = all_22_1 &
% 13.03/2.49 | greater(all_22_2, all_22_1) = 0 & $i(all_22_1) & $i(all_22_2)) | ( ~
% 13.03/2.49 | (all_22_3 = 0) & organization(all_12_7) = all_22_3)
% 13.03/2.49 |
% 13.03/2.49 | DELTA: instantiating (23) with fresh symbols all_23_0, all_23_1, all_23_2,
% 13.03/2.49 | all_23_3, all_23_4, all_23_5, all_23_6, all_23_7, all_23_8, all_23_9
% 13.03/2.49 | gives:
% 13.31/2.49 | (26) ( ~ (all_23_9 = 0) & organization(all_12_7) = all_23_9) | ((all_12_0 =
% 13.31/2.49 | 0 | ( ~ (all_23_3 = 0) & internal_friction(all_12_7, all_12_5) =
% 13.31/2.49 | all_23_5 & internal_friction(all_12_7, all_12_6) = all_23_4 &
% 13.31/2.49 | smaller_or_equal(all_23_5, all_23_4) = all_23_3 & $i(all_23_4) &
% 13.31/2.49 | $i(all_23_5)) | ( ~ (all_23_6 = 0) &
% 13.31/2.49 | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 &
% 13.31/2.49 | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 &
% 13.31/2.49 | greater(all_23_8, all_23_7) = all_23_6 & $i(all_23_7) &
% 13.31/2.49 | $i(all_23_8))) & (all_12_1 = all_12_2 | ( ~ (all_23_4 =
% 13.31/2.49 | all_23_5) & internal_friction(all_12_7, all_12_5) = all_23_5 &
% 13.31/2.49 | internal_friction(all_12_7, all_12_6) = all_23_4 & $i(all_23_4)
% 13.31/2.49 | & $i(all_23_5)) | ( ~ (all_23_7 = all_23_8) &
% 13.31/2.49 | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 &
% 13.31/2.49 | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 & $i(all_23_7)
% 13.31/2.49 | & $i(all_23_8))) & ((all_23_0 = 0 & smaller(all_12_2, all_12_1)
% 13.31/2.49 | = 0) | ( ~ (all_23_1 = 0) & internal_friction(all_12_7,
% 13.31/2.49 | all_12_5) = all_23_5 & internal_friction(all_12_7, all_12_6) =
% 13.31/2.49 | all_23_4 & greater(all_23_5, all_23_4) = all_23_1 & $i(all_23_4)
% 13.31/2.49 | & $i(all_23_5)) | ( ~ (all_23_2 = 0) &
% 13.31/2.49 | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 &
% 13.31/2.49 | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 &
% 13.31/2.49 | smaller_or_equal(all_23_8, all_23_7) = all_23_2 & $i(all_23_7) &
% 13.31/2.49 | $i(all_23_8))))
% 13.31/2.49 |
% 13.31/2.49 | BETA: splitting (25) gives:
% 13.31/2.49 |
% 13.31/2.49 | Case 1:
% 13.31/2.49 | |
% 13.31/2.49 | | (27) all_22_0 = 0 & stock_of_knowledge(all_12_7, all_12_5) = all_22_2 &
% 13.31/2.49 | | stock_of_knowledge(all_12_7, all_12_6) = all_22_1 &
% 13.31/2.49 | | greater(all_22_2, all_22_1) = 0 & $i(all_22_1) & $i(all_22_2)
% 13.31/2.49 | |
% 13.31/2.49 | | ALPHA: (27) implies:
% 13.31/2.49 | | (28) greater(all_22_2, all_22_1) = 0
% 13.31/2.49 | | (29) stock_of_knowledge(all_12_7, all_12_6) = all_22_1
% 13.31/2.49 | | (30) stock_of_knowledge(all_12_7, all_12_5) = all_22_2
% 13.31/2.49 | |
% 13.31/2.49 | | BETA: splitting (26) gives:
% 13.31/2.49 | |
% 13.31/2.49 | | Case 1:
% 13.31/2.49 | | |
% 13.31/2.49 | | | (31) ~ (all_23_9 = 0) & organization(all_12_7) = all_23_9
% 13.31/2.49 | | |
% 13.31/2.49 | | | ALPHA: (31) implies:
% 13.31/2.49 | | | (32) ~ (all_23_9 = 0)
% 13.31/2.49 | | | (33) organization(all_12_7) = all_23_9
% 13.31/2.49 | | |
% 13.31/2.49 | | | GROUND_INST: instantiating (5) with 0, all_23_9, all_12_7, simplifying
% 13.31/2.49 | | | with (20), (33) gives:
% 13.31/2.49 | | | (34) all_23_9 = 0
% 13.31/2.49 | | |
% 13.31/2.49 | | | REDUCE: (32), (34) imply:
% 13.31/2.49 | | | (35) $false
% 13.31/2.49 | | |
% 13.31/2.49 | | | CLOSE: (35) is inconsistent.
% 13.31/2.49 | | |
% 13.31/2.50 | | Case 2:
% 13.31/2.50 | | |
% 13.31/2.50 | | | (36) (all_12_0 = 0 | ( ~ (all_23_3 = 0) & internal_friction(all_12_7,
% 13.31/2.50 | | | all_12_5) = all_23_5 & internal_friction(all_12_7, all_12_6)
% 13.31/2.50 | | | = all_23_4 & smaller_or_equal(all_23_5, all_23_4) = all_23_3 &
% 13.31/2.50 | | | $i(all_23_4) & $i(all_23_5)) | ( ~ (all_23_6 = 0) &
% 13.31/2.50 | | | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 &
% 13.31/2.50 | | | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 &
% 13.31/2.50 | | | greater(all_23_8, all_23_7) = all_23_6 & $i(all_23_7) &
% 13.31/2.50 | | | $i(all_23_8))) & (all_12_1 = all_12_2 | ( ~ (all_23_4 =
% 13.31/2.50 | | | all_23_5) & internal_friction(all_12_7, all_12_5) = all_23_5
% 13.31/2.50 | | | & internal_friction(all_12_7, all_12_6) = all_23_4 &
% 13.31/2.50 | | | $i(all_23_4) & $i(all_23_5)) | ( ~ (all_23_7 = all_23_8) &
% 13.31/2.50 | | | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 &
% 13.31/2.50 | | | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 &
% 13.31/2.50 | | | $i(all_23_7) & $i(all_23_8))) & ((all_23_0 = 0 &
% 13.31/2.50 | | | smaller(all_12_2, all_12_1) = 0) | ( ~ (all_23_1 = 0) &
% 13.31/2.50 | | | internal_friction(all_12_7, all_12_5) = all_23_5 &
% 13.31/2.50 | | | internal_friction(all_12_7, all_12_6) = all_23_4 &
% 13.31/2.50 | | | greater(all_23_5, all_23_4) = all_23_1 & $i(all_23_4) &
% 13.31/2.50 | | | $i(all_23_5)) | ( ~ (all_23_2 = 0) &
% 13.31/2.50 | | | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 &
% 13.31/2.50 | | | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 &
% 13.31/2.50 | | | smaller_or_equal(all_23_8, all_23_7) = all_23_2 & $i(all_23_7)
% 13.31/2.50 | | | & $i(all_23_8)))
% 13.31/2.50 | | |
% 13.31/2.50 | | | ALPHA: (36) implies:
% 13.31/2.50 | | | (37) all_12_0 = 0 | ( ~ (all_23_3 = 0) & internal_friction(all_12_7,
% 13.31/2.50 | | | all_12_5) = all_23_5 & internal_friction(all_12_7, all_12_6) =
% 13.31/2.50 | | | all_23_4 & smaller_or_equal(all_23_5, all_23_4) = all_23_3 &
% 13.31/2.50 | | | $i(all_23_4) & $i(all_23_5)) | ( ~ (all_23_6 = 0) &
% 13.31/2.50 | | | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 &
% 13.31/2.50 | | | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 &
% 13.31/2.50 | | | greater(all_23_8, all_23_7) = all_23_6 & $i(all_23_7) &
% 13.31/2.50 | | | $i(all_23_8))
% 13.31/2.50 | | |
% 13.31/2.50 | | | BETA: splitting (37) gives:
% 13.31/2.50 | | |
% 13.31/2.50 | | | Case 1:
% 13.31/2.50 | | | |
% 13.31/2.50 | | | | (38) all_12_0 = 0
% 13.31/2.50 | | | |
% 13.31/2.50 | | | | REDUCE: (12), (38) imply:
% 13.31/2.50 | | | | (39) $false
% 13.31/2.50 | | | |
% 13.31/2.50 | | | | CLOSE: (39) is inconsistent.
% 13.31/2.50 | | | |
% 13.31/2.50 | | | Case 2:
% 13.31/2.50 | | | |
% 13.31/2.50 | | | | (40) ( ~ (all_23_3 = 0) & internal_friction(all_12_7, all_12_5) =
% 13.31/2.50 | | | | all_23_5 & internal_friction(all_12_7, all_12_6) = all_23_4 &
% 13.31/2.50 | | | | smaller_or_equal(all_23_5, all_23_4) = all_23_3 & $i(all_23_4)
% 13.31/2.50 | | | | & $i(all_23_5)) | ( ~ (all_23_6 = 0) &
% 13.31/2.50 | | | | stock_of_knowledge(all_12_7, all_12_5) = all_23_8 &
% 13.31/2.50 | | | | stock_of_knowledge(all_12_7, all_12_6) = all_23_7 &
% 13.31/2.50 | | | | greater(all_23_8, all_23_7) = all_23_6 & $i(all_23_7) &
% 13.31/2.50 | | | | $i(all_23_8))
% 13.31/2.50 | | | |
% 13.31/2.50 | | | | BETA: splitting (40) gives:
% 13.31/2.50 | | | |
% 13.31/2.50 | | | | Case 1:
% 13.31/2.50 | | | | |
% 13.31/2.50 | | | | | (41) ~ (all_23_3 = 0) & internal_friction(all_12_7, all_12_5) =
% 13.31/2.50 | | | | | all_23_5 & internal_friction(all_12_7, all_12_6) = all_23_4 &
% 13.31/2.50 | | | | | smaller_or_equal(all_23_5, all_23_4) = all_23_3 & $i(all_23_4)
% 13.31/2.50 | | | | | & $i(all_23_5)
% 13.31/2.50 | | | | |
% 13.31/2.50 | | | | | ALPHA: (41) implies:
% 13.31/2.50 | | | | | (42) smaller_or_equal(all_23_5, all_23_4) = all_23_3
% 13.31/2.50 | | | | | (43) internal_friction(all_12_7, all_12_6) = all_23_4
% 13.31/2.50 | | | | | (44) internal_friction(all_12_7, all_12_5) = all_23_5
% 13.31/2.50 | | | | |
% 13.31/2.50 | | | | | GROUND_INST: instantiating (3) with all_12_7, all_12_6, all_12_5,
% 13.31/2.50 | | | | | all_22_2, all_22_1, 0, simplifying with (13), (14), (15),
% 13.31/2.50 | | | | | (28), (29), (30) gives:
% 13.31/2.50 | | | | | (45) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ?
% 13.31/2.50 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8:
% 13.31/2.50 | | | | | int] : ? [v9: int] : (( ~ (v0 = 0) & organization(all_12_7)
% 13.31/2.50 | | | | | = v0) | (( ~ (all_22_1 = all_22_2) | (v5 = v4 &
% 13.31/2.50 | | | | | capability(all_12_7, all_12_5) = v4 &
% 13.31/2.50 | | | | | capability(all_12_7, all_12_6) = v4 & $i(v4)) | ( ~
% 13.31/2.50 | | | | | (v2 = v1) & internal_friction(all_12_7, all_12_5) = v1
% 13.31/2.50 | | | | | & internal_friction(all_12_7, all_12_6) = v2 & $i(v2)
% 13.31/2.50 | | | | | & $i(v1))) & ((v9 = 0 & capability(all_12_7, all_12_5)
% 13.31/2.50 | | | | | = v4 & capability(all_12_7, all_12_6) = v5 &
% 13.31/2.50 | | | | | smaller(v4, v5) = 0 & $i(v5) & $i(v4)) | ( ~ (v8 = 0)
% 13.31/2.50 | | | | | & internal_friction(all_12_7, all_12_5) = v1 &
% 13.31/2.50 | | | | | internal_friction(all_12_7, all_12_6) = v2 &
% 13.31/2.50 | | | | | greater(v1, v2) = v8 & $i(v2) & $i(v1)) | ( ~ (v7 = 0)
% 13.31/2.50 | | | | | & smaller_or_equal(all_22_2, all_22_1) = v7)) & ((v6 =
% 13.31/2.50 | | | | | 0 & capability(all_12_7, all_12_5) = v4 &
% 13.31/2.50 | | | | | capability(all_12_7, all_12_6) = v5 & greater(v4, v5)
% 13.31/2.50 | | | | | = 0 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) &
% 13.31/2.50 | | | | | internal_friction(all_12_7, all_12_5) = v1 &
% 13.31/2.50 | | | | | internal_friction(all_12_7, all_12_6) = v2 &
% 13.31/2.50 | | | | | smaller_or_equal(v1, v2) = v3 & $i(v2) & $i(v1)))))
% 13.31/2.50 | | | | |
% 13.31/2.51 | | | | | GROUND_INST: instantiating (assumption_9) with all_12_7, all_12_6,
% 13.31/2.51 | | | | | all_12_5, all_23_5, all_23_4, simplifying with (13),
% 13.31/2.51 | | | | | (14), (15), (43), (44) gives:
% 13.31/2.51 | | | | | (46) all_23_4 = all_23_5 | ? [v0: int] : ( ~ (v0 = 0) &
% 13.31/2.51 | | | | | organization(all_12_7) = v0)
% 13.31/2.51 | | | | |
% 13.31/2.51 | | | | | DELTA: instantiating (45) with fresh symbols all_51_0, all_51_1,
% 13.31/2.51 | | | | | all_51_2, all_51_3, all_51_4, all_51_5, all_51_6, all_51_7,
% 13.31/2.51 | | | | | all_51_8, all_51_9 gives:
% 13.31/2.51 | | | | | (47) ( ~ (all_51_9 = 0) & organization(all_12_7) = all_51_9) | (( ~
% 13.31/2.51 | | | | | (all_22_1 = all_22_2) | (all_51_4 = all_51_5 &
% 13.31/2.51 | | | | | capability(all_12_7, all_12_5) = all_51_5 &
% 13.31/2.51 | | | | | capability(all_12_7, all_12_6) = all_51_5 &
% 13.31/2.51 | | | | | $i(all_51_5)) | ( ~ (all_51_7 = all_51_8) &
% 13.31/2.51 | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 &
% 13.31/2.51 | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 &
% 13.31/2.51 | | | | | $i(all_51_7) & $i(all_51_8))) & ((all_51_0 = 0 &
% 13.31/2.51 | | | | | capability(all_12_7, all_12_5) = all_51_5 &
% 13.31/2.51 | | | | | capability(all_12_7, all_12_6) = all_51_4 &
% 13.31/2.51 | | | | | smaller(all_51_5, all_51_4) = 0 & $i(all_51_4) &
% 13.31/2.51 | | | | | $i(all_51_5)) | ( ~ (all_51_1 = 0) &
% 13.31/2.51 | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 &
% 13.31/2.51 | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 &
% 13.31/2.51 | | | | | greater(all_51_8, all_51_7) = all_51_1 & $i(all_51_7) &
% 13.31/2.51 | | | | | $i(all_51_8)) | ( ~ (all_51_2 = 0) &
% 13.31/2.51 | | | | | smaller_or_equal(all_22_2, all_22_1) = all_51_2)) &
% 13.31/2.51 | | | | | ((all_51_3 = 0 & capability(all_12_7, all_12_5) = all_51_5 &
% 13.31/2.51 | | | | | capability(all_12_7, all_12_6) = all_51_4 &
% 13.31/2.51 | | | | | greater(all_51_5, all_51_4) = 0 & $i(all_51_4) &
% 13.31/2.51 | | | | | $i(all_51_5)) | ( ~ (all_51_6 = 0) &
% 13.31/2.51 | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 &
% 13.31/2.51 | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 &
% 13.31/2.51 | | | | | smaller_or_equal(all_51_8, all_51_7) = all_51_6 &
% 13.31/2.51 | | | | | $i(all_51_7) & $i(all_51_8))))
% 13.31/2.51 | | | | |
% 13.31/2.51 | | | | | BETA: splitting (47) gives:
% 13.31/2.51 | | | | |
% 13.31/2.51 | | | | | Case 1:
% 13.31/2.51 | | | | | |
% 13.31/2.51 | | | | | | (48) ~ (all_51_9 = 0) & organization(all_12_7) = all_51_9
% 13.31/2.51 | | | | | |
% 13.31/2.51 | | | | | | ALPHA: (48) implies:
% 13.31/2.51 | | | | | | (49) ~ (all_51_9 = 0)
% 13.31/2.51 | | | | | | (50) organization(all_12_7) = all_51_9
% 13.31/2.51 | | | | | |
% 13.31/2.51 | | | | | | GROUND_INST: instantiating (5) with 0, all_51_9, all_12_7,
% 13.31/2.51 | | | | | | simplifying with (20), (50) gives:
% 13.31/2.51 | | | | | | (51) all_51_9 = 0
% 13.31/2.51 | | | | | |
% 13.31/2.51 | | | | | | REDUCE: (49), (51) imply:
% 13.31/2.51 | | | | | | (52) $false
% 13.31/2.51 | | | | | |
% 13.31/2.51 | | | | | | CLOSE: (52) is inconsistent.
% 13.31/2.51 | | | | | |
% 13.31/2.51 | | | | | Case 2:
% 13.31/2.51 | | | | | |
% 13.31/2.51 | | | | | | (53) ( ~ (all_22_1 = all_22_2) | (all_51_4 = all_51_5 &
% 13.31/2.51 | | | | | | capability(all_12_7, all_12_5) = all_51_5 &
% 13.31/2.51 | | | | | | capability(all_12_7, all_12_6) = all_51_5 &
% 13.31/2.51 | | | | | | $i(all_51_5)) | ( ~ (all_51_7 = all_51_8) &
% 13.31/2.51 | | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 &
% 13.31/2.51 | | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 &
% 13.31/2.51 | | | | | | $i(all_51_7) & $i(all_51_8))) & ((all_51_0 = 0 &
% 13.31/2.51 | | | | | | capability(all_12_7, all_12_5) = all_51_5 &
% 13.31/2.51 | | | | | | capability(all_12_7, all_12_6) = all_51_4 &
% 13.31/2.51 | | | | | | smaller(all_51_5, all_51_4) = 0 & $i(all_51_4) &
% 13.31/2.51 | | | | | | $i(all_51_5)) | ( ~ (all_51_1 = 0) &
% 13.31/2.51 | | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 &
% 13.31/2.51 | | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 &
% 13.31/2.51 | | | | | | greater(all_51_8, all_51_7) = all_51_1 & $i(all_51_7) &
% 13.31/2.51 | | | | | | $i(all_51_8)) | ( ~ (all_51_2 = 0) &
% 13.31/2.51 | | | | | | smaller_or_equal(all_22_2, all_22_1) = all_51_2)) &
% 13.31/2.51 | | | | | | ((all_51_3 = 0 & capability(all_12_7, all_12_5) = all_51_5 &
% 13.31/2.51 | | | | | | capability(all_12_7, all_12_6) = all_51_4 &
% 13.31/2.51 | | | | | | greater(all_51_5, all_51_4) = 0 & $i(all_51_4) &
% 13.31/2.51 | | | | | | $i(all_51_5)) | ( ~ (all_51_6 = 0) &
% 13.31/2.51 | | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 &
% 13.31/2.51 | | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 &
% 13.31/2.51 | | | | | | smaller_or_equal(all_51_8, all_51_7) = all_51_6 &
% 13.31/2.51 | | | | | | $i(all_51_7) & $i(all_51_8)))
% 13.31/2.51 | | | | | |
% 13.31/2.51 | | | | | | ALPHA: (53) implies:
% 13.31/2.51 | | | | | | (54) (all_51_3 = 0 & capability(all_12_7, all_12_5) = all_51_5 &
% 13.31/2.51 | | | | | | capability(all_12_7, all_12_6) = all_51_4 &
% 13.31/2.51 | | | | | | greater(all_51_5, all_51_4) = 0 & $i(all_51_4) &
% 13.31/2.51 | | | | | | $i(all_51_5)) | ( ~ (all_51_6 = 0) &
% 13.31/2.51 | | | | | | internal_friction(all_12_7, all_12_5) = all_51_8 &
% 13.31/2.51 | | | | | | internal_friction(all_12_7, all_12_6) = all_51_7 &
% 13.31/2.51 | | | | | | smaller_or_equal(all_51_8, all_51_7) = all_51_6 &
% 13.31/2.51 | | | | | | $i(all_51_7) & $i(all_51_8))
% 13.31/2.51 | | | | | |
% 13.31/2.51 | | | | | | BETA: splitting (46) gives:
% 13.31/2.51 | | | | | |
% 13.31/2.51 | | | | | | Case 1:
% 13.31/2.51 | | | | | | |
% 13.31/2.51 | | | | | | | (55) all_23_4 = all_23_5
% 13.31/2.51 | | | | | | |
% 13.31/2.51 | | | | | | | REDUCE: (43), (55) imply:
% 13.31/2.51 | | | | | | | (56) internal_friction(all_12_7, all_12_6) = all_23_5
% 13.31/2.51 | | | | | | |
% 13.31/2.51 | | | | | | | REDUCE: (42), (55) imply:
% 13.31/2.51 | | | | | | | (57) smaller_or_equal(all_23_5, all_23_5) = all_23_3
% 13.31/2.51 | | | | | | |
% 13.31/2.51 | | | | | | | BETA: splitting (54) gives:
% 13.31/2.51 | | | | | | |
% 13.31/2.51 | | | | | | | Case 1:
% 13.31/2.51 | | | | | | | |
% 13.31/2.51 | | | | | | | | (58) all_51_3 = 0 & capability(all_12_7, all_12_5) = all_51_5
% 13.31/2.51 | | | | | | | | & capability(all_12_7, all_12_6) = all_51_4 &
% 13.31/2.51 | | | | | | | | greater(all_51_5, all_51_4) = 0 & $i(all_51_4) &
% 13.31/2.51 | | | | | | | | $i(all_51_5)
% 13.31/2.51 | | | | | | | |
% 13.31/2.51 | | | | | | | | ALPHA: (58) implies:
% 13.31/2.51 | | | | | | | | (59) greater(all_51_5, all_51_4) = 0
% 13.31/2.51 | | | | | | | | (60) capability(all_12_7, all_12_6) = all_51_4
% 13.31/2.51 | | | | | | | | (61) capability(all_12_7, all_12_5) = all_51_5
% 13.31/2.51 | | | | | | | |
% 13.31/2.51 | | | | | | | | GROUND_INST: instantiating (8) with all_12_1, all_51_4,
% 13.31/2.51 | | | | | | | | all_12_6, all_12_7, simplifying with (18), (60)
% 13.31/2.51 | | | | | | | | gives:
% 13.31/2.51 | | | | | | | | (62) all_51_4 = all_12_1
% 13.31/2.51 | | | | | | | |
% 13.31/2.52 | | | | | | | | GROUND_INST: instantiating (8) with all_12_2, all_51_5,
% 13.31/2.52 | | | | | | | | all_12_5, all_12_7, simplifying with (19), (61)
% 13.31/2.52 | | | | | | | | gives:
% 13.31/2.52 | | | | | | | | (63) all_51_5 = all_12_2
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | REDUCE: (59), (62), (63) imply:
% 13.31/2.52 | | | | | | | | (64) greater(all_12_2, all_12_1) = 0
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | GROUND_INST: instantiating (7) with all_12_0, 0, all_12_1,
% 13.31/2.52 | | | | | | | | all_12_2, simplifying with (17), (64) gives:
% 13.31/2.52 | | | | | | | | (65) all_12_0 = 0
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | REDUCE: (12), (65) imply:
% 13.31/2.52 | | | | | | | | (66) $false
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | CLOSE: (66) is inconsistent.
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | Case 2:
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | (67) ~ (all_51_6 = 0) & internal_friction(all_12_7,
% 13.31/2.52 | | | | | | | | all_12_5) = all_51_8 & internal_friction(all_12_7,
% 13.31/2.52 | | | | | | | | all_12_6) = all_51_7 & smaller_or_equal(all_51_8,
% 13.31/2.52 | | | | | | | | all_51_7) = all_51_6 & $i(all_51_7) & $i(all_51_8)
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | ALPHA: (67) implies:
% 13.31/2.52 | | | | | | | | (68) ~ (all_51_6 = 0)
% 13.31/2.52 | | | | | | | | (69) $i(all_51_8)
% 13.31/2.52 | | | | | | | | (70) smaller_or_equal(all_51_8, all_51_7) = all_51_6
% 13.31/2.52 | | | | | | | | (71) internal_friction(all_12_7, all_12_6) = all_51_7
% 13.31/2.52 | | | | | | | | (72) internal_friction(all_12_7, all_12_5) = all_51_8
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | GROUND_INST: instantiating (10) with all_23_5, all_51_7,
% 13.31/2.52 | | | | | | | | all_12_6, all_12_7, simplifying with (56), (71)
% 13.31/2.52 | | | | | | | | gives:
% 13.31/2.52 | | | | | | | | (73) all_51_7 = all_23_5
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | GROUND_INST: instantiating (10) with all_23_5, all_51_8,
% 13.31/2.52 | | | | | | | | all_12_5, all_12_7, simplifying with (44), (72)
% 13.31/2.52 | | | | | | | | gives:
% 13.31/2.52 | | | | | | | | (74) all_51_8 = all_23_5
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | REDUCE: (70), (73), (74) imply:
% 13.31/2.52 | | | | | | | | (75) smaller_or_equal(all_23_5, all_23_5) = all_51_6
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | REDUCE: (69), (74) imply:
% 13.31/2.52 | | | | | | | | (76) $i(all_23_5)
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | GROUND_INST: instantiating (6) with all_23_3, all_51_6,
% 13.31/2.52 | | | | | | | | all_23_5, all_23_5, simplifying with (57), (75)
% 13.31/2.52 | | | | | | | | gives:
% 13.31/2.52 | | | | | | | | (77) all_51_6 = all_23_3
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | REDUCE: (68), (77) imply:
% 13.31/2.52 | | | | | | | | (78) ~ (all_23_3 = 0)
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | GROUND_INST: instantiating (1) with all_23_5, all_23_3,
% 13.31/2.52 | | | | | | | | simplifying with (57), (76) gives:
% 13.31/2.52 | | | | | | | | (79) all_23_3 = 0
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | REDUCE: (78), (79) imply:
% 13.31/2.52 | | | | | | | | (80) $false
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | | CLOSE: (80) is inconsistent.
% 13.31/2.52 | | | | | | | |
% 13.31/2.52 | | | | | | | End of split
% 13.31/2.52 | | | | | | |
% 13.31/2.52 | | | | | | Case 2:
% 13.31/2.52 | | | | | | |
% 13.31/2.52 | | | | | | | (81) ? [v0: int] : ( ~ (v0 = 0) & organization(all_12_7) = v0)
% 13.31/2.52 | | | | | | |
% 13.31/2.52 | | | | | | | DELTA: instantiating (81) with fresh symbol all_65_0 gives:
% 13.31/2.52 | | | | | | | (82) ~ (all_65_0 = 0) & organization(all_12_7) = all_65_0
% 13.31/2.52 | | | | | | |
% 13.31/2.52 | | | | | | | ALPHA: (82) implies:
% 13.31/2.52 | | | | | | | (83) ~ (all_65_0 = 0)
% 13.31/2.52 | | | | | | | (84) organization(all_12_7) = all_65_0
% 13.31/2.52 | | | | | | |
% 13.31/2.52 | | | | | | | GROUND_INST: instantiating (5) with 0, all_65_0, all_12_7,
% 13.31/2.52 | | | | | | | simplifying with (20), (84) gives:
% 13.31/2.52 | | | | | | | (85) all_65_0 = 0
% 13.31/2.52 | | | | | | |
% 13.31/2.52 | | | | | | | REDUCE: (83), (85) imply:
% 13.31/2.52 | | | | | | | (86) $false
% 13.31/2.52 | | | | | | |
% 13.31/2.52 | | | | | | | CLOSE: (86) is inconsistent.
% 13.31/2.52 | | | | | | |
% 13.31/2.52 | | | | | | End of split
% 13.31/2.52 | | | | | |
% 13.31/2.52 | | | | | End of split
% 13.31/2.52 | | | | |
% 13.31/2.52 | | | | Case 2:
% 13.31/2.52 | | | | |
% 13.31/2.52 | | | | | (87) ~ (all_23_6 = 0) & stock_of_knowledge(all_12_7, all_12_5) =
% 13.31/2.52 | | | | | all_23_8 & stock_of_knowledge(all_12_7, all_12_6) = all_23_7 &
% 13.31/2.52 | | | | | greater(all_23_8, all_23_7) = all_23_6 & $i(all_23_7) &
% 13.31/2.52 | | | | | $i(all_23_8)
% 13.31/2.52 | | | | |
% 13.31/2.52 | | | | | ALPHA: (87) implies:
% 13.31/2.52 | | | | | (88) ~ (all_23_6 = 0)
% 13.31/2.52 | | | | | (89) greater(all_23_8, all_23_7) = all_23_6
% 13.31/2.52 | | | | | (90) stock_of_knowledge(all_12_7, all_12_6) = all_23_7
% 13.31/2.52 | | | | | (91) stock_of_knowledge(all_12_7, all_12_5) = all_23_8
% 13.31/2.52 | | | | |
% 13.31/2.52 | | | | | GROUND_INST: instantiating (9) with all_22_1, all_23_7, all_12_6,
% 13.31/2.52 | | | | | all_12_7, simplifying with (29), (90) gives:
% 13.31/2.52 | | | | | (92) all_23_7 = all_22_1
% 13.31/2.52 | | | | |
% 13.31/2.52 | | | | | GROUND_INST: instantiating (9) with all_22_2, all_23_8, all_12_5,
% 13.31/2.52 | | | | | all_12_7, simplifying with (30), (91) gives:
% 13.31/2.52 | | | | | (93) all_23_8 = all_22_2
% 13.31/2.52 | | | | |
% 13.31/2.52 | | | | | REDUCE: (89), (92), (93) imply:
% 13.31/2.52 | | | | | (94) greater(all_22_2, all_22_1) = all_23_6
% 13.31/2.52 | | | | |
% 13.31/2.52 | | | | | GROUND_INST: instantiating (7) with 0, all_23_6, all_22_1, all_22_2,
% 13.31/2.52 | | | | | simplifying with (28), (94) gives:
% 13.31/2.52 | | | | | (95) all_23_6 = 0
% 13.31/2.52 | | | | |
% 13.31/2.52 | | | | | REDUCE: (88), (95) imply:
% 13.31/2.52 | | | | | (96) $false
% 13.31/2.52 | | | | |
% 13.31/2.53 | | | | | CLOSE: (96) is inconsistent.
% 13.31/2.53 | | | | |
% 13.31/2.53 | | | | End of split
% 13.31/2.53 | | | |
% 13.31/2.53 | | | End of split
% 13.31/2.53 | | |
% 13.31/2.53 | | End of split
% 13.31/2.53 | |
% 13.31/2.53 | Case 2:
% 13.31/2.53 | |
% 13.31/2.53 | | (97) ~ (all_22_3 = 0) & organization(all_12_7) = all_22_3
% 13.31/2.53 | |
% 13.31/2.53 | | ALPHA: (97) implies:
% 13.31/2.53 | | (98) ~ (all_22_3 = 0)
% 13.31/2.53 | | (99) organization(all_12_7) = all_22_3
% 13.31/2.53 | |
% 13.31/2.53 | | GROUND_INST: instantiating (5) with 0, all_22_3, all_12_7, simplifying with
% 13.31/2.53 | | (20), (99) gives:
% 13.31/2.53 | | (100) all_22_3 = 0
% 13.31/2.53 | |
% 13.31/2.53 | | REDUCE: (98), (100) imply:
% 13.31/2.53 | | (101) $false
% 13.31/2.53 | |
% 13.31/2.53 | | CLOSE: (101) is inconsistent.
% 13.31/2.53 | |
% 13.31/2.53 | End of split
% 13.31/2.53 |
% 13.31/2.53 End of proof
% 13.31/2.53 % SZS output end Proof for theBenchmark
% 13.31/2.53
% 13.31/2.53 1947ms
%------------------------------------------------------------------------------