TSTP Solution File: SWV406+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV406+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n007.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 22:56:12 EDT 2023
% Result : Theorem 12.31s 2.33s
% Output : Proof 17.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV406+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 06:23:58 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.52/0.61 ________ _____
% 0.52/0.61 ___ __ \_________(_)________________________________
% 0.52/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.52/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.52/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.52/0.61
% 0.52/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.52/0.61 (2023-06-19)
% 0.52/0.61
% 0.52/0.61 (c) Philipp Rümmer, 2009-2023
% 0.52/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.52/0.61 Amanda Stjerna.
% 0.52/0.61 Free software under BSD-3-Clause.
% 0.52/0.61
% 0.52/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.52/0.61
% 0.52/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.52/0.62 Running up to 7 provers in parallel.
% 0.71/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.71/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.71/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.71/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.71/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.71/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.71/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.82/1.17 Prover 1: Preprocessing ...
% 3.82/1.18 Prover 4: Preprocessing ...
% 3.82/1.21 Prover 3: Preprocessing ...
% 3.82/1.21 Prover 0: Preprocessing ...
% 3.82/1.21 Prover 2: Preprocessing ...
% 3.82/1.21 Prover 6: Preprocessing ...
% 3.82/1.21 Prover 5: Preprocessing ...
% 7.65/1.73 Prover 1: Warning: ignoring some quantifiers
% 8.39/1.79 Prover 5: Proving ...
% 8.39/1.80 Prover 1: Constructing countermodel ...
% 8.39/1.81 Prover 6: Proving ...
% 8.39/1.81 Prover 3: Warning: ignoring some quantifiers
% 8.83/1.83 Prover 0: Proving ...
% 8.83/1.83 Prover 3: Constructing countermodel ...
% 9.06/1.87 Prover 4: Constructing countermodel ...
% 9.06/1.88 Prover 2: Proving ...
% 12.31/2.33 Prover 0: proved (1702ms)
% 12.31/2.33
% 12.31/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.31/2.33
% 12.31/2.34 Prover 3: stopped
% 12.31/2.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.31/2.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.31/2.34 Prover 5: stopped
% 12.31/2.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.31/2.34 Prover 2: stopped
% 12.76/2.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.76/2.34 Prover 6: stopped
% 12.90/2.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.90/2.41 Prover 10: Preprocessing ...
% 12.90/2.41 Prover 8: Preprocessing ...
% 12.90/2.41 Prover 7: Preprocessing ...
% 12.90/2.41 Prover 11: Preprocessing ...
% 13.34/2.44 Prover 13: Preprocessing ...
% 14.31/2.56 Prover 10: Warning: ignoring some quantifiers
% 14.31/2.58 Prover 10: Constructing countermodel ...
% 14.65/2.61 Prover 7: Warning: ignoring some quantifiers
% 14.65/2.63 Prover 7: Constructing countermodel ...
% 14.65/2.64 Prover 8: Warning: ignoring some quantifiers
% 15.25/2.66 Prover 8: Constructing countermodel ...
% 15.25/2.67 Prover 13: Warning: ignoring some quantifiers
% 15.25/2.69 Prover 11: Constructing countermodel ...
% 15.25/2.70 Prover 13: Constructing countermodel ...
% 16.74/2.87 Prover 10: gave up
% 16.74/2.87 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 16.99/2.90 Prover 4: Found proof (size 155)
% 16.99/2.90 Prover 4: proved (2268ms)
% 16.99/2.90 Prover 7: stopped
% 16.99/2.90 Prover 13: stopped
% 16.99/2.90 Prover 11: stopped
% 16.99/2.90 Prover 1: stopped
% 16.99/2.90 Prover 8: stopped
% 16.99/2.91 Prover 16: Preprocessing ...
% 17.38/2.95 Prover 16: stopped
% 17.38/2.95
% 17.38/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.38/2.95
% 17.38/2.97 % SZS output start Proof for theBenchmark
% 17.38/2.97 Assumptions after simplification:
% 17.38/2.97 ---------------------------------
% 17.38/2.97
% 17.38/2.97 (ax23)
% 17.38/3.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.38/3.00 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (pair_in_list(v6, v2, v4) =
% 17.38/3.00 v7) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ $i(v4) |
% 17.38/3.00 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) &
% 17.38/3.00 pair_in_list(v0, v2, v4) = v8)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.38/3.00 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v3 | ~
% 17.38/3.00 (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0,
% 17.38/3.00 v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.38/3.00 pair_in_list(v0, v2, v4) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.38/3.00 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v2 = v1 | ~
% 17.38/3.00 (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0,
% 17.38/3.00 v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.38/3.00 pair_in_list(v0, v2, v4) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.38/3.00 [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2)
% 17.38/3.00 = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | ~ $i(v2)
% 17.38/3.00 | ~ $i(v1) | ~ $i(v0))
% 17.38/3.00
% 17.38/3.00 (ax37)
% 17.38/3.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.38/3.00 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~
% 17.38/3.00 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) |
% 17.38/3.00 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10:
% 17.38/3.00 $i] : ? [v11: any] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 &
% 17.38/3.00 check_cpq(v7) = v9 & less_than(v4, v3) = v8 & $i(v10) & ( ~ (v8 = 0) | ((
% 17.38/3.00 ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0)))))
% 17.38/3.00
% 17.38/3.00 (ax38)
% 17.38/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.38/3.01 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~
% 17.38/3.01 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) |
% 17.38/3.01 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: any] :
% 17.38/3.01 (check_cpq(v7) = v9 & strictly_less_than(v3, v4) = v8 & ( ~ (v9 = 0) | ~
% 17.38/3.01 (v8 = 0))))
% 17.38/3.01
% 17.38/3.01 (l42_co)
% 17.72/3.01 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 17.72/3.01 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i]
% 17.72/3.01 : ? [v11: int] : ? [v12: int] : (triple(v1, v6, v2) = v7 & check_cpq(v7) =
% 17.72/3.01 v8 & pair(v3, v4) = v5 & insert_slb(v0, v5) = v6 & $i(v10) & $i(v9) & $i(v7)
% 17.72/3.01 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v13:
% 17.72/3.01 $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18:
% 17.72/3.01 int] : (v18 = 0 | ~ (triple(v13, v0, v14) = v15) | ~ (less_than(v17,
% 17.72/3.01 v16) = v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v14) | ~ $i(v13) | ?
% 17.72/3.01 [v19: int] : (( ~ (v19 = 0) & check_cpq(v15) = v19) | ( ~ (v19 = 0) &
% 17.72/3.01 pair_in_list(v0, v16, v17) = v19))) & ! [v13: $i] : ! [v14: $i] : !
% 17.72/3.01 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ (triple(v13, v0, v14) = v15) |
% 17.72/3.01 ~ (pair_in_list(v0, v16, v17) = 0) | ~ $i(v17) | ~ $i(v16) | ~ $i(v14)
% 17.72/3.01 | ~ $i(v13) | ? [v18: int] : ((v18 = 0 & less_than(v17, v16) = 0) | ( ~
% 17.72/3.01 (v18 = 0) & check_cpq(v15) = v18))) & ! [v13: $i] : ! [v14: $i] : !
% 17.72/3.01 [v15: $i] : ( ~ (triple(v13, v0, v14) = v15) | ~ $i(v14) | ~ $i(v13) | ?
% 17.72/3.01 [v16: int] : ? [v17: $i] : ? [v18: $i] : ? [v19: int] : ? [v20: int] :
% 17.72/3.01 ($i(v18) & $i(v17) & ((v19 = 0 & ~ (v20 = 0) & pair_in_list(v0, v17, v18)
% 17.72/3.01 = 0 & less_than(v18, v17) = v20) | (v16 = 0 & check_cpq(v15) = 0))))
% 17.72/3.01 & ((v11 = 0 & v8 = 0 & ~ (v12 = 0) & pair_in_list(v6, v9, v10) = 0 &
% 17.72/3.01 less_than(v10, v9) = v12) | ( ~ (v8 = 0) & ! [v13: $i] : ! [v14: $i] :
% 17.72/3.01 ! [v15: int] : (v15 = 0 | ~ (less_than(v14, v13) = v15) | ~ $i(v14) |
% 17.72/3.01 ~ $i(v13) | ? [v16: int] : ( ~ (v16 = 0) & pair_in_list(v6, v13,
% 17.72/3.01 v14) = v16)) & ! [v13: $i] : ! [v14: $i] : ( ~ (pair_in_list(v6,
% 17.72/3.01 v13, v14) = 0) | ~ $i(v14) | ~ $i(v13) | less_than(v14, v13) =
% 17.72/3.01 0))))
% 17.72/3.01
% 17.72/3.01 (stricly_smaller_definition)
% 17.72/3.02 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 17.72/3.02 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 17.72/3.02 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 17.72/3.02 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 |
% 17.72/3.02 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 17.72/3.02 any] : (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3
% 17.72/3.02 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 17.72/3.02 (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 17.72/3.02 any] : (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3
% 17.72/3.02 = 0) | (v4 = 0 & ~ (v2 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.72/3.02 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 17.72/3.02 ? [v4: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & (
% 17.72/3.02 ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 17.72/3.02 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : (
% 17.72/3.02 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0:
% 17.72/3.02 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 17.72/3.02 [v2: any] : ? [v3: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1,
% 17.72/3.02 v0) = v2 & (v3 = 0 | v2 = 0)))
% 17.72/3.02
% 17.72/3.02 (totality)
% 17.72/3.02 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) =
% 17.72/3.02 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : !
% 17.72/3.02 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) |
% 17.72/3.02 ~ $i(v0) | less_than(v1, v0) = 0)
% 17.72/3.02
% 17.72/3.02 (function-axioms)
% 17.72/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 17.72/3.03 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 17.72/3.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.72/3.03 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 17.72/3.03 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.72/3.03 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2)
% 17.72/3.03 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 17.72/3.03 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0:
% 17.72/3.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.72/3.03 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 17.72/3.03 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.72/3.03 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : !
% 17.72/3.03 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1)
% 17.72/3.03 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.72/3.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 17.72/3.03 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.72/3.03 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 17.72/3.03 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.72/3.03 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 17.72/3.03 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 17.72/3.03 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 17.72/3.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.72/3.03 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 17.72/3.03 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.72/3.03 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 17.72/3.03 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 17.72/3.03 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.72/3.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.72/3.03 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 17.72/3.03 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.72/3.03 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 17.72/3.03 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.72/3.03 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0:
% 17.72/3.03 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) |
% 17.72/3.03 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.72/3.03 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & !
% 17.72/3.03 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 17.72/3.03 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 17.72/3.03 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) |
% 17.72/3.03 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 17.72/3.03 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & !
% 17.72/3.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) =
% 17.72/3.03 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 17.72/3.03 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) =
% 17.72/3.03 v1) | ~ (isnonempty_slb(v2) = v0))
% 17.72/3.03
% 17.72/3.03 Further assumptions not needed in the proof:
% 17.72/3.03 --------------------------------------------
% 17.72/3.03 ax18, ax19, ax20, ax21, ax22, ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31,
% 17.72/3.03 ax32, ax33, ax34, ax35, ax36, ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax46,
% 17.72/3.03 ax47, ax48, ax49, ax50, ax51, ax52, ax53, bottom_smallest, reflexivity,
% 17.72/3.03 transitivity
% 17.72/3.03
% 17.72/3.03 Those formulas are unsatisfiable:
% 17.72/3.03 ---------------------------------
% 17.72/3.03
% 17.72/3.03 Begin of proof
% 17.72/3.03 |
% 17.72/3.03 | ALPHA: (totality) implies:
% 17.72/3.03 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1,
% 17.72/3.03 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0)
% 17.72/3.03 |
% 17.72/3.03 | ALPHA: (stricly_smaller_definition) implies:
% 17.72/3.03 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v0, v1) = v2)
% 17.72/3.03 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 17.72/3.03 | (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( ~ (v3 =
% 17.72/3.03 | 0) | (v2 = 0 & ~ (v4 = 0)))))
% 17.72/3.03 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v1, v0) = v2)
% 17.72/3.03 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 17.72/3.03 | (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 =
% 17.72/3.03 | 0) | (v4 = 0 & ~ (v2 = 0)))))
% 17.72/3.03 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1,
% 17.72/3.03 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 17.72/3.03 | (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 17.72/3.03 | 0) | v4 = 0)))
% 17.72/3.03 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 17.72/3.03 | (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 17.72/3.03 | any] : ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) =
% 17.72/3.03 | v3 & ( ~ (v3 = 0) | v4 = 0)))
% 17.72/3.03 |
% 17.72/3.03 | ALPHA: (ax23) implies:
% 17.72/3.03 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.72/3.03 | ! [v5: int] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2) = v5) | ~
% 17.72/3.03 | (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | ~ $i(v2) | ~
% 17.72/3.03 | $i(v1) | ~ $i(v0))
% 17.72/3.04 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.72/3.04 | ! [v5: $i] : ! [v6: $i] : (v2 = v1 | ~ (pair_in_list(v6, v2, v4) = 0)
% 17.72/3.04 | | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ $i(v4) |
% 17.72/3.04 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | pair_in_list(v0, v2,
% 17.72/3.04 | v4) = 0)
% 17.72/3.04 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.72/3.04 | ! [v5: $i] : ! [v6: $i] : (v4 = v3 | ~ (pair_in_list(v6, v2, v4) = 0)
% 17.72/3.04 | | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ $i(v4) |
% 17.72/3.04 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | pair_in_list(v0, v2,
% 17.72/3.04 | v4) = 0)
% 17.72/3.04 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.72/3.04 | ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~
% 17.72/3.04 | (pair_in_list(v6, v2, v4) = v7) | ~ (pair(v1, v3) = v5) | ~
% 17.72/3.04 | (insert_slb(v0, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 17.72/3.04 | $i(v1) | ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) & pair_in_list(v0,
% 17.72/3.04 | v2, v4) = v8))
% 17.72/3.04 |
% 17.72/3.04 | ALPHA: (function-axioms) implies:
% 17.72/3.04 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.72/3.04 | : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 17.72/3.04 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.72/3.04 | : ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~
% 17.72/3.04 | (less_than(v3, v2) = v0))
% 17.72/3.04 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.72/3.04 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2)
% 17.72/3.04 | = v1) | ~ (pair_in_list(v4, v3, v2) = v0))
% 17.72/3.04 |
% 17.72/3.04 | DELTA: instantiating (l42_co) with fresh symbols all_46_0, all_46_1, all_46_2,
% 17.72/3.04 | all_46_3, all_46_4, all_46_5, all_46_6, all_46_7, all_46_8, all_46_9,
% 17.72/3.04 | all_46_10, all_46_11, all_46_12 gives:
% 17.72/3.04 | (13) triple(all_46_11, all_46_6, all_46_10) = all_46_5 &
% 17.72/3.04 | check_cpq(all_46_5) = all_46_4 & pair(all_46_9, all_46_8) = all_46_7 &
% 17.72/3.04 | insert_slb(all_46_12, all_46_7) = all_46_6 & $i(all_46_2) &
% 17.72/3.04 | $i(all_46_3) & $i(all_46_5) & $i(all_46_6) & $i(all_46_7) &
% 17.72/3.04 | $i(all_46_8) & $i(all_46_9) & $i(all_46_10) & $i(all_46_11) &
% 17.72/3.04 | $i(all_46_12) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 17.72/3.04 | : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (triple(v0, all_46_12, v1)
% 17.72/3.04 | = v2) | ~ (less_than(v4, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 17.72/3.04 | $i(v1) | ~ $i(v0) | ? [v6: int] : (( ~ (v6 = 0) & check_cpq(v2) =
% 17.72/3.04 | v6) | ( ~ (v6 = 0) & pair_in_list(all_46_12, v3, v4) = v6))) &
% 17.72/3.04 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 17.72/3.04 | ~ (triple(v0, all_46_12, v1) = v2) | ~ (pair_in_list(all_46_12, v3,
% 17.72/3.04 | v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ?
% 17.72/3.04 | [v5: int] : ((v5 = 0 & less_than(v4, v3) = 0) | ( ~ (v5 = 0) &
% 17.72/3.04 | check_cpq(v2) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.72/3.04 | : ( ~ (triple(v0, all_46_12, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 17.72/3.04 | [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int]
% 17.72/3.04 | : ($i(v5) & $i(v4) & ((v6 = 0 & ~ (v7 = 0) &
% 17.72/3.04 | pair_in_list(all_46_12, v4, v5) = 0 & less_than(v5, v4) = v7)
% 17.72/3.04 | | (v3 = 0 & check_cpq(v2) = 0)))) & ((all_46_1 = 0 & all_46_4 =
% 17.72/3.04 | 0 & ~ (all_46_0 = 0) & pair_in_list(all_46_6, all_46_3, all_46_2)
% 17.72/3.04 | = 0 & less_than(all_46_2, all_46_3) = all_46_0) | ( ~ (all_46_4 =
% 17.72/3.04 | 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 17.72/3.04 | (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int]
% 17.72/3.04 | : ( ~ (v3 = 0) & pair_in_list(all_46_6, v0, v1) = v3)) & ! [v0:
% 17.72/3.04 | $i] : ! [v1: $i] : ( ~ (pair_in_list(all_46_6, v0, v1) = 0) |
% 17.72/3.04 | ~ $i(v1) | ~ $i(v0) | less_than(v1, v0) = 0)))
% 17.72/3.04 |
% 17.72/3.04 | ALPHA: (13) implies:
% 17.72/3.04 | (14) $i(all_46_12)
% 17.72/3.04 | (15) $i(all_46_11)
% 17.72/3.04 | (16) $i(all_46_10)
% 17.72/3.04 | (17) $i(all_46_9)
% 17.72/3.04 | (18) $i(all_46_8)
% 17.72/3.04 | (19) $i(all_46_3)
% 17.72/3.04 | (20) $i(all_46_2)
% 17.72/3.04 | (21) insert_slb(all_46_12, all_46_7) = all_46_6
% 17.72/3.05 | (22) pair(all_46_9, all_46_8) = all_46_7
% 17.72/3.05 | (23) check_cpq(all_46_5) = all_46_4
% 17.72/3.05 | (24) triple(all_46_11, all_46_6, all_46_10) = all_46_5
% 17.72/3.05 | (25) (all_46_1 = 0 & all_46_4 = 0 & ~ (all_46_0 = 0) &
% 17.72/3.05 | pair_in_list(all_46_6, all_46_3, all_46_2) = 0 & less_than(all_46_2,
% 17.72/3.05 | all_46_3) = all_46_0) | ( ~ (all_46_4 = 0) & ! [v0: $i] : ! [v1:
% 17.72/3.05 | $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) = v2) | ~
% 17.72/3.05 | $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 17.72/3.05 | pair_in_list(all_46_6, v0, v1) = v3)) & ! [v0: $i] : ! [v1:
% 17.72/3.05 | $i] : ( ~ (pair_in_list(all_46_6, v0, v1) = 0) | ~ $i(v1) | ~
% 17.72/3.05 | $i(v0) | less_than(v1, v0) = 0))
% 17.72/3.05 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, all_46_12,
% 17.72/3.05 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] :
% 17.72/3.05 | ? [v5: $i] : ? [v6: int] : ? [v7: int] : ($i(v5) & $i(v4) & ((v6
% 17.72/3.05 | = 0 & ~ (v7 = 0) & pair_in_list(all_46_12, v4, v5) = 0 &
% 17.72/3.05 | less_than(v5, v4) = v7) | (v3 = 0 & check_cpq(v2) = 0))))
% 17.72/3.05 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.72/3.05 | ! [v5: int] : (v5 = 0 | ~ (triple(v0, all_46_12, v1) = v2) | ~
% 17.72/3.05 | (less_than(v4, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~
% 17.72/3.05 | $i(v0) | ? [v6: int] : (( ~ (v6 = 0) & check_cpq(v2) = v6) | ( ~
% 17.72/3.05 | (v6 = 0) & pair_in_list(all_46_12, v3, v4) = v6)))
% 17.72/3.05 |
% 17.72/3.05 | GROUND_INST: instantiating (ax37) with all_46_11, all_46_12, all_46_10,
% 17.72/3.05 | all_46_9, all_46_8, all_46_7, all_46_6, all_46_5, simplifying
% 17.72/3.05 | with (14), (15), (16), (17), (18), (21), (22), (24) gives:
% 17.72/3.05 | (28) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 17.72/3.05 | (triple(all_46_11, all_46_12, all_46_10) = v2 & check_cpq(v2) = v3 &
% 17.72/3.05 | check_cpq(all_46_5) = v1 & less_than(all_46_8, all_46_9) = v0 &
% 17.72/3.05 | $i(v2) & ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3
% 17.72/3.05 | = 0))))
% 17.72/3.05 |
% 17.72/3.05 | GROUND_INST: instantiating (ax38) with all_46_11, all_46_12, all_46_10,
% 17.72/3.05 | all_46_9, all_46_8, all_46_7, all_46_6, all_46_5, simplifying
% 17.72/3.05 | with (14), (15), (16), (17), (18), (21), (22), (24) gives:
% 17.72/3.05 | (29) ? [v0: any] : ? [v1: any] : (check_cpq(all_46_5) = v1 &
% 17.72/3.05 | strictly_less_than(all_46_9, all_46_8) = v0 & ( ~ (v1 = 0) | ~ (v0
% 17.72/3.05 | = 0)))
% 17.72/3.05 |
% 17.72/3.05 | DELTA: instantiating (29) with fresh symbols all_55_0, all_55_1 gives:
% 17.72/3.05 | (30) check_cpq(all_46_5) = all_55_0 & strictly_less_than(all_46_9,
% 17.72/3.05 | all_46_8) = all_55_1 & ( ~ (all_55_0 = 0) | ~ (all_55_1 = 0))
% 17.72/3.05 |
% 17.72/3.05 | ALPHA: (30) implies:
% 17.72/3.05 | (31) strictly_less_than(all_46_9, all_46_8) = all_55_1
% 17.72/3.05 | (32) check_cpq(all_46_5) = all_55_0
% 17.72/3.05 | (33) ~ (all_55_0 = 0) | ~ (all_55_1 = 0)
% 17.72/3.05 |
% 17.72/3.05 | DELTA: instantiating (28) with fresh symbols all_57_0, all_57_1, all_57_2,
% 17.72/3.05 | all_57_3 gives:
% 17.72/3.05 | (34) triple(all_46_11, all_46_12, all_46_10) = all_57_1 &
% 17.72/3.05 | check_cpq(all_57_1) = all_57_0 & check_cpq(all_46_5) = all_57_2 &
% 17.72/3.05 | less_than(all_46_8, all_46_9) = all_57_3 & $i(all_57_1) & ( ~
% 17.72/3.05 | (all_57_3 = 0) | (( ~ (all_57_0 = 0) | all_57_2 = 0) & ( ~ (all_57_2
% 17.72/3.05 | = 0) | all_57_0 = 0)))
% 17.72/3.05 |
% 17.72/3.05 | ALPHA: (34) implies:
% 17.72/3.05 | (35) less_than(all_46_8, all_46_9) = all_57_3
% 17.72/3.05 | (36) check_cpq(all_46_5) = all_57_2
% 17.72/3.05 | (37) check_cpq(all_57_1) = all_57_0
% 17.72/3.05 | (38) triple(all_46_11, all_46_12, all_46_10) = all_57_1
% 17.72/3.05 | (39) ~ (all_57_3 = 0) | (( ~ (all_57_0 = 0) | all_57_2 = 0) & ( ~
% 17.72/3.05 | (all_57_2 = 0) | all_57_0 = 0))
% 17.72/3.05 |
% 17.72/3.05 | GROUND_INST: instantiating (10) with all_46_4, all_57_2, all_46_5, simplifying
% 17.72/3.05 | with (23), (36) gives:
% 17.72/3.06 | (40) all_57_2 = all_46_4
% 17.72/3.06 |
% 17.72/3.06 | GROUND_INST: instantiating (10) with all_55_0, all_57_2, all_46_5, simplifying
% 17.72/3.06 | with (32), (36) gives:
% 17.72/3.06 | (41) all_57_2 = all_55_0
% 17.72/3.06 |
% 17.72/3.06 | COMBINE_EQS: (40), (41) imply:
% 17.72/3.06 | (42) all_55_0 = all_46_4
% 17.72/3.06 |
% 17.72/3.06 | GROUND_INST: instantiating (1) with all_46_9, all_46_8, all_57_3, simplifying
% 17.72/3.06 | with (17), (18), (35) gives:
% 17.72/3.06 | (43) all_57_3 = 0 | less_than(all_46_9, all_46_8) = 0
% 17.72/3.06 |
% 17.72/3.06 | GROUND_INST: instantiating (4) with all_46_9, all_46_8, all_57_3, simplifying
% 17.72/3.06 | with (17), (18), (35) gives:
% 17.72/3.06 | (44) all_57_3 = 0 | ? [v0: any] : ? [v1: any] :
% 17.72/3.06 | (strictly_less_than(all_46_9, all_46_8) = v1 & less_than(all_46_9,
% 17.72/3.06 | all_46_8) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 17.72/3.06 |
% 17.72/3.06 | GROUND_INST: instantiating (3) with all_46_9, all_46_8, all_57_3, simplifying
% 17.72/3.06 | with (17), (18), (35) gives:
% 17.72/3.06 | (45) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_9, all_46_8)
% 17.72/3.06 | = v0 & less_than(all_46_9, all_46_8) = v1 & ( ~ (v0 = 0) | (v1 = 0 &
% 17.72/3.06 | ~ (all_57_3 = 0))))
% 17.72/3.06 |
% 17.72/3.06 | GROUND_INST: instantiating (2) with all_46_8, all_46_9, all_57_3, simplifying
% 17.72/3.06 | with (17), (18), (35) gives:
% 17.72/3.06 | (46) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_8, all_46_9)
% 17.72/3.06 | = v0 & less_than(all_46_9, all_46_8) = v1 & ( ~ (v0 = 0) | (all_57_3
% 17.72/3.06 | = 0 & ~ (v1 = 0))))
% 17.72/3.06 |
% 17.72/3.06 | GROUND_INST: instantiating (5) with all_46_9, all_46_8, all_55_1, simplifying
% 17.72/3.06 | with (17), (18), (31) gives:
% 17.72/3.06 | (47) all_55_1 = 0 | ? [v0: any] : ? [v1: any] : (less_than(all_46_8,
% 17.72/3.06 | all_46_9) = v1 & less_than(all_46_9, all_46_8) = v0 & ( ~ (v0 = 0)
% 17.72/3.06 | | v1 = 0))
% 17.72/3.06 |
% 17.72/3.06 | GROUND_INST: instantiating (26) with all_46_11, all_46_10, all_57_1,
% 17.72/3.06 | simplifying with (15), (16), (38) gives:
% 17.72/3.06 | (48) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int]
% 17.72/3.06 | : ($i(v2) & $i(v1) & ((v3 = 0 & ~ (v4 = 0) & pair_in_list(all_46_12,
% 17.72/3.06 | v1, v2) = 0 & less_than(v2, v1) = v4) | (v0 = 0 &
% 17.72/3.06 | check_cpq(all_57_1) = 0)))
% 17.72/3.06 |
% 17.72/3.06 | DELTA: instantiating (46) with fresh symbols all_68_0, all_68_1 gives:
% 17.72/3.06 | (49) strictly_less_than(all_46_8, all_46_9) = all_68_1 &
% 17.72/3.06 | less_than(all_46_9, all_46_8) = all_68_0 & ( ~ (all_68_1 = 0) |
% 17.72/3.06 | (all_57_3 = 0 & ~ (all_68_0 = 0)))
% 17.72/3.06 |
% 17.72/3.06 | ALPHA: (49) implies:
% 17.72/3.06 | (50) less_than(all_46_9, all_46_8) = all_68_0
% 17.72/3.06 |
% 17.72/3.06 | DELTA: instantiating (45) with fresh symbols all_70_0, all_70_1 gives:
% 17.72/3.06 | (51) strictly_less_than(all_46_9, all_46_8) = all_70_1 &
% 17.72/3.06 | less_than(all_46_9, all_46_8) = all_70_0 & ( ~ (all_70_1 = 0) |
% 17.72/3.06 | (all_70_0 = 0 & ~ (all_57_3 = 0)))
% 17.72/3.06 |
% 17.72/3.06 | ALPHA: (51) implies:
% 17.72/3.06 | (52) less_than(all_46_9, all_46_8) = all_70_0
% 17.72/3.06 |
% 17.72/3.06 | DELTA: instantiating (48) with fresh symbols all_72_0, all_72_1, all_72_2,
% 17.72/3.06 | all_72_3, all_72_4 gives:
% 17.72/3.06 | (53) $i(all_72_2) & $i(all_72_3) & ((all_72_1 = 0 & ~ (all_72_0 = 0) &
% 17.97/3.06 | pair_in_list(all_46_12, all_72_3, all_72_2) = 0 &
% 17.97/3.06 | less_than(all_72_2, all_72_3) = all_72_0) | (all_72_4 = 0 &
% 17.97/3.06 | check_cpq(all_57_1) = 0))
% 17.97/3.06 |
% 17.97/3.06 | ALPHA: (53) implies:
% 17.97/3.06 | (54) $i(all_72_3)
% 17.97/3.06 | (55) $i(all_72_2)
% 17.97/3.06 | (56) (all_72_1 = 0 & ~ (all_72_0 = 0) & pair_in_list(all_46_12, all_72_3,
% 17.97/3.06 | all_72_2) = 0 & less_than(all_72_2, all_72_3) = all_72_0) |
% 17.97/3.06 | (all_72_4 = 0 & check_cpq(all_57_1) = 0)
% 17.97/3.06 |
% 17.97/3.06 | GROUND_INST: instantiating (11) with all_68_0, all_70_0, all_46_8, all_46_9,
% 17.97/3.06 | simplifying with (50), (52) gives:
% 17.97/3.06 | (57) all_70_0 = all_68_0
% 17.97/3.06 |
% 17.97/3.06 | GROUND_INST: instantiating (3) with all_46_8, all_46_9, all_68_0, simplifying
% 17.97/3.06 | with (17), (18), (50) gives:
% 17.97/3.06 | (58) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_8, all_46_9)
% 17.97/3.06 | = v0 & less_than(all_46_8, all_46_9) = v1 & ( ~ (v0 = 0) | (v1 = 0 &
% 17.97/3.06 | ~ (all_68_0 = 0))))
% 17.97/3.07 |
% 17.97/3.07 | GROUND_INST: instantiating (2) with all_46_9, all_46_8, all_68_0, simplifying
% 17.97/3.07 | with (17), (18), (50) gives:
% 17.97/3.07 | (59) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_9, all_46_8)
% 17.97/3.07 | = v0 & less_than(all_46_8, all_46_9) = v1 & ( ~ (v0 = 0) | (all_68_0
% 17.97/3.07 | = 0 & ~ (v1 = 0))))
% 17.97/3.07 |
% 17.97/3.07 | DELTA: instantiating (59) with fresh symbols all_83_0, all_83_1 gives:
% 17.97/3.07 | (60) strictly_less_than(all_46_9, all_46_8) = all_83_1 &
% 17.97/3.07 | less_than(all_46_8, all_46_9) = all_83_0 & ( ~ (all_83_1 = 0) |
% 17.97/3.07 | (all_68_0 = 0 & ~ (all_83_0 = 0)))
% 17.97/3.07 |
% 17.97/3.07 | ALPHA: (60) implies:
% 17.97/3.07 | (61) less_than(all_46_8, all_46_9) = all_83_0
% 17.97/3.07 |
% 17.97/3.07 | DELTA: instantiating (58) with fresh symbols all_85_0, all_85_1 gives:
% 17.97/3.07 | (62) strictly_less_than(all_46_8, all_46_9) = all_85_1 &
% 17.97/3.07 | less_than(all_46_8, all_46_9) = all_85_0 & ( ~ (all_85_1 = 0) |
% 17.97/3.07 | (all_85_0 = 0 & ~ (all_68_0 = 0)))
% 17.97/3.07 |
% 17.97/3.07 | ALPHA: (62) implies:
% 17.97/3.07 | (63) less_than(all_46_8, all_46_9) = all_85_0
% 17.97/3.07 |
% 17.97/3.07 | GROUND_INST: instantiating (11) with all_57_3, all_85_0, all_46_9, all_46_8,
% 17.97/3.07 | simplifying with (35), (63) gives:
% 17.97/3.07 | (64) all_85_0 = all_57_3
% 17.97/3.07 |
% 17.97/3.07 | GROUND_INST: instantiating (11) with all_83_0, all_85_0, all_46_9, all_46_8,
% 17.97/3.07 | simplifying with (61), (63) gives:
% 17.97/3.07 | (65) all_85_0 = all_83_0
% 17.97/3.07 |
% 17.97/3.07 | COMBINE_EQS: (64), (65) imply:
% 17.97/3.07 | (66) all_83_0 = all_57_3
% 17.97/3.07 |
% 17.97/3.07 | BETA: splitting (25) gives:
% 17.97/3.07 |
% 17.97/3.07 | Case 1:
% 17.97/3.07 | |
% 17.97/3.07 | | (67) all_46_1 = 0 & all_46_4 = 0 & ~ (all_46_0 = 0) &
% 17.97/3.07 | | pair_in_list(all_46_6, all_46_3, all_46_2) = 0 & less_than(all_46_2,
% 17.97/3.07 | | all_46_3) = all_46_0
% 17.97/3.07 | |
% 17.97/3.07 | | ALPHA: (67) implies:
% 17.97/3.07 | | (68) all_46_4 = 0
% 17.97/3.07 | | (69) ~ (all_46_0 = 0)
% 17.97/3.07 | | (70) less_than(all_46_2, all_46_3) = all_46_0
% 17.97/3.07 | | (71) pair_in_list(all_46_6, all_46_3, all_46_2) = 0
% 17.97/3.07 | |
% 17.97/3.07 | | COMBINE_EQS: (42), (68) imply:
% 17.97/3.07 | | (72) all_55_0 = 0
% 17.97/3.07 | |
% 17.97/3.07 | | COMBINE_EQS: (40), (68) imply:
% 17.97/3.07 | | (73) all_57_2 = 0
% 17.97/3.07 | |
% 17.97/3.07 | | BETA: splitting (33) gives:
% 17.97/3.07 | |
% 17.97/3.07 | | Case 1:
% 17.97/3.07 | | |
% 17.97/3.07 | | | (74) ~ (all_55_0 = 0)
% 17.97/3.07 | | |
% 17.97/3.07 | | | REDUCE: (72), (74) imply:
% 17.97/3.07 | | | (75) $false
% 17.97/3.07 | | |
% 17.97/3.07 | | | CLOSE: (75) is inconsistent.
% 17.97/3.07 | | |
% 17.97/3.07 | | Case 2:
% 17.97/3.07 | | |
% 17.97/3.07 | | | (76) ~ (all_55_1 = 0)
% 17.97/3.07 | | |
% 17.97/3.07 | | | GROUND_INST: instantiating (27) with all_46_11, all_46_10, all_57_1,
% 17.97/3.07 | | | all_46_3, all_46_2, all_46_0, simplifying with (15), (16),
% 17.97/3.07 | | | (19), (20), (38), (70) gives:
% 17.97/3.07 | | | (77) all_46_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & check_cpq(all_57_1)
% 17.97/3.07 | | | = v0) | ( ~ (v0 = 0) & pair_in_list(all_46_12, all_46_3,
% 17.97/3.07 | | | all_46_2) = v0))
% 17.97/3.07 | | |
% 17.97/3.07 | | | GROUND_INST: instantiating (8) with all_46_12, all_46_9, all_46_3,
% 17.97/3.07 | | | all_46_8, all_46_2, all_46_7, all_46_6, simplifying with
% 17.97/3.07 | | | (14), (17), (18), (19), (20), (21), (22), (71) gives:
% 17.97/3.07 | | | (78) all_46_2 = all_46_8 | pair_in_list(all_46_12, all_46_3, all_46_2)
% 17.97/3.07 | | | = 0
% 17.97/3.07 | | |
% 17.97/3.07 | | | GROUND_INST: instantiating (7) with all_46_12, all_46_9, all_46_3,
% 17.97/3.07 | | | all_46_8, all_46_2, all_46_7, all_46_6, simplifying with
% 17.97/3.07 | | | (14), (17), (18), (19), (20), (21), (22), (71) gives:
% 17.97/3.07 | | | (79) all_46_3 = all_46_9 | pair_in_list(all_46_12, all_46_3, all_46_2)
% 17.97/3.07 | | | = 0
% 17.97/3.07 | | |
% 17.97/3.07 | | | BETA: splitting (77) gives:
% 17.97/3.07 | | |
% 17.97/3.07 | | | Case 1:
% 17.97/3.07 | | | |
% 17.97/3.07 | | | | (80) all_46_0 = 0
% 17.97/3.07 | | | |
% 17.97/3.07 | | | | REDUCE: (69), (80) imply:
% 17.97/3.07 | | | | (81) $false
% 17.97/3.07 | | | |
% 17.97/3.07 | | | | CLOSE: (81) is inconsistent.
% 17.97/3.07 | | | |
% 17.97/3.07 | | | Case 2:
% 17.97/3.07 | | | |
% 17.97/3.07 | | | | (82) ? [v0: int] : (( ~ (v0 = 0) & check_cpq(all_57_1) = v0) | ( ~
% 17.97/3.07 | | | | (v0 = 0) & pair_in_list(all_46_12, all_46_3, all_46_2) =
% 17.97/3.07 | | | | v0))
% 17.97/3.07 | | | |
% 17.97/3.07 | | | | DELTA: instantiating (82) with fresh symbol all_123_0 gives:
% 17.97/3.08 | | | | (83) ( ~ (all_123_0 = 0) & check_cpq(all_57_1) = all_123_0) | ( ~
% 17.97/3.08 | | | | (all_123_0 = 0) & pair_in_list(all_46_12, all_46_3, all_46_2)
% 17.97/3.08 | | | | = all_123_0)
% 17.97/3.08 | | | |
% 17.97/3.08 | | | | BETA: splitting (39) gives:
% 17.97/3.08 | | | |
% 17.97/3.08 | | | | Case 1:
% 17.97/3.08 | | | | |
% 17.97/3.08 | | | | | (84) ~ (all_57_3 = 0)
% 17.97/3.08 | | | | |
% 17.97/3.08 | | | | | BETA: splitting (43) gives:
% 17.97/3.08 | | | | |
% 17.97/3.08 | | | | | Case 1:
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | (85) less_than(all_46_9, all_46_8) = 0
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | BETA: splitting (47) gives:
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | Case 1:
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | (86) all_55_1 = 0
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | REDUCE: (76), (86) imply:
% 17.97/3.08 | | | | | | | (87) $false
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | CLOSE: (87) is inconsistent.
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | Case 2:
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | (88) ? [v0: any] : ? [v1: any] : (less_than(all_46_8,
% 17.97/3.08 | | | | | | | all_46_9) = v1 & less_than(all_46_9, all_46_8) = v0 &
% 17.97/3.08 | | | | | | | ( ~ (v0 = 0) | v1 = 0))
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | DELTA: instantiating (88) with fresh symbols all_159_0, all_159_1
% 17.97/3.08 | | | | | | | gives:
% 17.97/3.08 | | | | | | | (89) less_than(all_46_8, all_46_9) = all_159_0 &
% 17.97/3.08 | | | | | | | less_than(all_46_9, all_46_8) = all_159_1 & ( ~ (all_159_1
% 17.97/3.08 | | | | | | | = 0) | all_159_0 = 0)
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | ALPHA: (89) implies:
% 17.97/3.08 | | | | | | | (90) less_than(all_46_9, all_46_8) = all_159_1
% 17.97/3.08 | | | | | | | (91) less_than(all_46_8, all_46_9) = all_159_0
% 17.97/3.08 | | | | | | | (92) ~ (all_159_1 = 0) | all_159_0 = 0
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | BETA: splitting (44) gives:
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | Case 1:
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | (93) all_57_3 = 0
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | REDUCE: (84), (93) imply:
% 17.97/3.08 | | | | | | | | (94) $false
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | CLOSE: (94) is inconsistent.
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | Case 2:
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | (95) ? [v0: any] : ? [v1: any] :
% 17.97/3.08 | | | | | | | | (strictly_less_than(all_46_9, all_46_8) = v1 &
% 17.97/3.08 | | | | | | | | less_than(all_46_9, all_46_8) = v0 & ( ~ (v0 = 0) | v1
% 17.97/3.08 | | | | | | | | = 0))
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | DELTA: instantiating (95) with fresh symbols all_165_0,
% 17.97/3.08 | | | | | | | | all_165_1 gives:
% 17.97/3.08 | | | | | | | | (96) strictly_less_than(all_46_9, all_46_8) = all_165_0 &
% 17.97/3.08 | | | | | | | | less_than(all_46_9, all_46_8) = all_165_1 & ( ~
% 17.97/3.08 | | | | | | | | (all_165_1 = 0) | all_165_0 = 0)
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | ALPHA: (96) implies:
% 17.97/3.08 | | | | | | | | (97) less_than(all_46_9, all_46_8) = all_165_1
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | GROUND_INST: instantiating (11) with all_159_1, all_165_1,
% 17.97/3.08 | | | | | | | | all_46_8, all_46_9, simplifying with (90), (97)
% 17.97/3.08 | | | | | | | | gives:
% 17.97/3.08 | | | | | | | | (98) all_165_1 = all_159_1
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | GROUND_INST: instantiating (11) with 0, all_165_1, all_46_8,
% 17.97/3.08 | | | | | | | | all_46_9, simplifying with (85), (97) gives:
% 17.97/3.08 | | | | | | | | (99) all_165_1 = 0
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | GROUND_INST: instantiating (11) with all_57_3, all_159_0,
% 17.97/3.08 | | | | | | | | all_46_9, all_46_8, simplifying with (35), (91)
% 17.97/3.08 | | | | | | | | gives:
% 17.97/3.08 | | | | | | | | (100) all_159_0 = all_57_3
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | COMBINE_EQS: (98), (99) imply:
% 17.97/3.08 | | | | | | | | (101) all_159_1 = 0
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | SIMP: (101) implies:
% 17.97/3.08 | | | | | | | | (102) all_159_1 = 0
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | BETA: splitting (92) gives:
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | Case 1:
% 17.97/3.08 | | | | | | | | |
% 17.97/3.08 | | | | | | | | | (103) ~ (all_159_1 = 0)
% 17.97/3.08 | | | | | | | | |
% 17.97/3.08 | | | | | | | | | REDUCE: (102), (103) imply:
% 17.97/3.08 | | | | | | | | | (104) $false
% 17.97/3.08 | | | | | | | | |
% 17.97/3.08 | | | | | | | | | CLOSE: (104) is inconsistent.
% 17.97/3.08 | | | | | | | | |
% 17.97/3.08 | | | | | | | | Case 2:
% 17.97/3.08 | | | | | | | | |
% 17.97/3.08 | | | | | | | | | (105) all_159_0 = 0
% 17.97/3.08 | | | | | | | | |
% 17.97/3.08 | | | | | | | | | COMBINE_EQS: (100), (105) imply:
% 17.97/3.08 | | | | | | | | | (106) all_57_3 = 0
% 17.97/3.08 | | | | | | | | |
% 17.97/3.08 | | | | | | | | | SIMP: (106) implies:
% 17.97/3.08 | | | | | | | | | (107) all_57_3 = 0
% 17.97/3.08 | | | | | | | | |
% 17.97/3.08 | | | | | | | | | REDUCE: (84), (107) imply:
% 17.97/3.08 | | | | | | | | | (108) $false
% 17.97/3.08 | | | | | | | | |
% 17.97/3.08 | | | | | | | | | CLOSE: (108) is inconsistent.
% 17.97/3.08 | | | | | | | | |
% 17.97/3.08 | | | | | | | | End of split
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | End of split
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | End of split
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | Case 2:
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | (109) all_57_3 = 0
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | REDUCE: (84), (109) imply:
% 17.97/3.08 | | | | | | (110) $false
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | CLOSE: (110) is inconsistent.
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | End of split
% 17.97/3.08 | | | | |
% 17.97/3.08 | | | | Case 2:
% 17.97/3.08 | | | | |
% 17.97/3.08 | | | | | (111) all_57_3 = 0
% 17.97/3.08 | | | | | (112) ( ~ (all_57_0 = 0) | all_57_2 = 0) & ( ~ (all_57_2 = 0) |
% 17.97/3.08 | | | | | all_57_0 = 0)
% 17.97/3.08 | | | | |
% 17.97/3.08 | | | | | ALPHA: (112) implies:
% 17.97/3.08 | | | | | (113) ~ (all_57_2 = 0) | all_57_0 = 0
% 17.97/3.08 | | | | |
% 17.97/3.08 | | | | | REDUCE: (35), (111) imply:
% 17.97/3.08 | | | | | (114) less_than(all_46_8, all_46_9) = 0
% 17.97/3.08 | | | | |
% 17.97/3.08 | | | | | BETA: splitting (113) gives:
% 17.97/3.08 | | | | |
% 17.97/3.08 | | | | | Case 1:
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | (115) ~ (all_57_2 = 0)
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | REDUCE: (73), (115) imply:
% 17.97/3.08 | | | | | | (116) $false
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | CLOSE: (116) is inconsistent.
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | Case 2:
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | (117) all_57_0 = 0
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | REDUCE: (37), (117) imply:
% 17.97/3.08 | | | | | | (118) check_cpq(all_57_1) = 0
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | BETA: splitting (83) gives:
% 17.97/3.08 | | | | | |
% 17.97/3.08 | | | | | | Case 1:
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | (119) ~ (all_123_0 = 0) & check_cpq(all_57_1) = all_123_0
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | ALPHA: (119) implies:
% 17.97/3.08 | | | | | | | (120) ~ (all_123_0 = 0)
% 17.97/3.08 | | | | | | | (121) check_cpq(all_57_1) = all_123_0
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | GROUND_INST: instantiating (10) with 0, all_123_0, all_57_1,
% 17.97/3.08 | | | | | | | simplifying with (118), (121) gives:
% 17.97/3.08 | | | | | | | (122) all_123_0 = 0
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | REDUCE: (120), (122) imply:
% 17.97/3.08 | | | | | | | (123) $false
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | CLOSE: (123) is inconsistent.
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | Case 2:
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | (124) ~ (all_123_0 = 0) & pair_in_list(all_46_12, all_46_3,
% 17.97/3.08 | | | | | | | all_46_2) = all_123_0
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | ALPHA: (124) implies:
% 17.97/3.08 | | | | | | | (125) ~ (all_123_0 = 0)
% 17.97/3.08 | | | | | | | (126) pair_in_list(all_46_12, all_46_3, all_46_2) = all_123_0
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | BETA: splitting (78) gives:
% 17.97/3.08 | | | | | | |
% 17.97/3.08 | | | | | | | Case 1:
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | (127) pair_in_list(all_46_12, all_46_3, all_46_2) = 0
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | GROUND_INST: instantiating (12) with 0, all_123_0, all_46_2,
% 17.97/3.08 | | | | | | | | all_46_3, all_46_12, simplifying with (126), (127)
% 17.97/3.08 | | | | | | | | gives:
% 17.97/3.08 | | | | | | | | (128) all_123_0 = 0
% 17.97/3.08 | | | | | | | |
% 17.97/3.08 | | | | | | | | REDUCE: (125), (128) imply:
% 17.97/3.09 | | | | | | | | (129) $false
% 17.97/3.09 | | | | | | | |
% 17.97/3.09 | | | | | | | | CLOSE: (129) is inconsistent.
% 17.97/3.09 | | | | | | | |
% 17.97/3.09 | | | | | | | Case 2:
% 17.97/3.09 | | | | | | | |
% 17.97/3.09 | | | | | | | | (130) all_46_2 = all_46_8
% 17.97/3.09 | | | | | | | |
% 17.97/3.09 | | | | | | | | REDUCE: (70), (130) imply:
% 17.97/3.09 | | | | | | | | (131) less_than(all_46_8, all_46_3) = all_46_0
% 17.97/3.09 | | | | | | | |
% 17.97/3.09 | | | | | | | | BETA: splitting (79) gives:
% 17.97/3.09 | | | | | | | |
% 17.97/3.09 | | | | | | | | Case 1:
% 17.97/3.09 | | | | | | | | |
% 17.97/3.09 | | | | | | | | | (132) pair_in_list(all_46_12, all_46_3, all_46_2) = 0
% 17.97/3.09 | | | | | | | | |
% 17.97/3.09 | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_123_0, all_46_2,
% 17.97/3.09 | | | | | | | | | all_46_3, all_46_12, simplifying with (126), (132)
% 17.97/3.09 | | | | | | | | | gives:
% 17.97/3.09 | | | | | | | | | (133) all_123_0 = 0
% 17.97/3.09 | | | | | | | | |
% 17.97/3.09 | | | | | | | | | REDUCE: (125), (133) imply:
% 17.97/3.09 | | | | | | | | | (134) $false
% 17.97/3.09 | | | | | | | | |
% 17.97/3.09 | | | | | | | | | CLOSE: (134) is inconsistent.
% 17.97/3.09 | | | | | | | | |
% 17.97/3.09 | | | | | | | | Case 2:
% 17.97/3.09 | | | | | | | | |
% 17.97/3.09 | | | | | | | | | (135) all_46_3 = all_46_9
% 17.97/3.09 | | | | | | | | |
% 17.97/3.09 | | | | | | | | | REDUCE: (131), (135) imply:
% 17.97/3.09 | | | | | | | | | (136) less_than(all_46_8, all_46_9) = all_46_0
% 17.97/3.09 | | | | | | | | |
% 17.97/3.09 | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_46_0, all_46_9,
% 17.97/3.09 | | | | | | | | | all_46_8, simplifying with (114), (136) gives:
% 17.97/3.09 | | | | | | | | | (137) all_46_0 = 0
% 17.97/3.09 | | | | | | | | |
% 17.97/3.09 | | | | | | | | | REDUCE: (69), (137) imply:
% 17.97/3.09 | | | | | | | | | (138) $false
% 17.97/3.09 | | | | | | | | |
% 17.97/3.09 | | | | | | | | | CLOSE: (138) is inconsistent.
% 17.97/3.09 | | | | | | | | |
% 17.97/3.09 | | | | | | | | End of split
% 17.97/3.09 | | | | | | | |
% 17.97/3.09 | | | | | | | End of split
% 17.97/3.09 | | | | | | |
% 17.97/3.09 | | | | | | End of split
% 17.97/3.09 | | | | | |
% 17.97/3.09 | | | | | End of split
% 17.97/3.09 | | | | |
% 17.97/3.09 | | | | End of split
% 17.97/3.09 | | | |
% 17.97/3.09 | | | End of split
% 17.97/3.09 | | |
% 17.97/3.09 | | End of split
% 17.97/3.09 | |
% 17.97/3.09 | Case 2:
% 17.97/3.09 | |
% 17.97/3.09 | | (139) ~ (all_46_4 = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2
% 17.97/3.09 | | = 0 | ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 17.97/3.09 | | [v3: int] : ( ~ (v3 = 0) & pair_in_list(all_46_6, v0, v1) = v3))
% 17.97/3.09 | | & ! [v0: $i] : ! [v1: $i] : ( ~ (pair_in_list(all_46_6, v0, v1) =
% 17.97/3.09 | | 0) | ~ $i(v1) | ~ $i(v0) | less_than(v1, v0) = 0)
% 17.97/3.09 | |
% 17.97/3.09 | | ALPHA: (139) implies:
% 17.97/3.09 | | (140) ~ (all_46_4 = 0)
% 17.97/3.09 | | (141) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 17.97/3.09 | | (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 17.97/3.09 | | ( ~ (v3 = 0) & pair_in_list(all_46_6, v0, v1) = v3))
% 17.97/3.09 | |
% 17.97/3.09 | | GROUND_INST: instantiating (141) with all_46_9, all_46_8, all_57_3,
% 17.97/3.09 | | simplifying with (17), (18), (35) gives:
% 17.97/3.09 | | (142) all_57_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) & pair_in_list(all_46_6,
% 17.97/3.09 | | all_46_9, all_46_8) = v0)
% 17.97/3.09 | |
% 17.97/3.09 | | BETA: splitting (39) gives:
% 17.97/3.09 | |
% 17.97/3.09 | | Case 1:
% 17.97/3.09 | | |
% 17.97/3.09 | | | (143) ~ (all_57_3 = 0)
% 17.97/3.09 | | |
% 17.97/3.09 | | | BETA: splitting (142) gives:
% 17.97/3.09 | | |
% 17.97/3.09 | | | Case 1:
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | (144) all_57_3 = 0
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | REDUCE: (143), (144) imply:
% 17.97/3.09 | | | | (145) $false
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | CLOSE: (145) is inconsistent.
% 17.97/3.09 | | | |
% 17.97/3.09 | | | Case 2:
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | (146) ? [v0: int] : ( ~ (v0 = 0) & pair_in_list(all_46_6, all_46_9,
% 17.97/3.09 | | | | all_46_8) = v0)
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | DELTA: instantiating (146) with fresh symbol all_153_0 gives:
% 17.97/3.09 | | | | (147) ~ (all_153_0 = 0) & pair_in_list(all_46_6, all_46_9, all_46_8)
% 17.97/3.09 | | | | = all_153_0
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | ALPHA: (147) implies:
% 17.97/3.09 | | | | (148) ~ (all_153_0 = 0)
% 17.97/3.09 | | | | (149) pair_in_list(all_46_6, all_46_9, all_46_8) = all_153_0
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | GROUND_INST: instantiating (6) with all_46_12, all_46_9, all_46_8,
% 17.97/3.09 | | | | all_46_7, all_46_6, all_153_0, simplifying with (14), (17),
% 17.97/3.09 | | | | (18), (21), (22), (149) gives:
% 17.97/3.09 | | | | (150) all_153_0 = 0
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | REDUCE: (148), (150) imply:
% 17.97/3.09 | | | | (151) $false
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | CLOSE: (151) is inconsistent.
% 17.97/3.09 | | | |
% 17.97/3.09 | | | End of split
% 17.97/3.09 | | |
% 17.97/3.09 | | Case 2:
% 17.97/3.09 | | |
% 17.97/3.09 | | | (152) ( ~ (all_57_0 = 0) | all_57_2 = 0) & ( ~ (all_57_2 = 0) |
% 17.97/3.09 | | | all_57_0 = 0)
% 17.97/3.09 | | |
% 17.97/3.09 | | | ALPHA: (152) implies:
% 17.97/3.09 | | | (153) ~ (all_57_0 = 0) | all_57_2 = 0
% 17.97/3.09 | | |
% 17.97/3.09 | | | BETA: splitting (153) gives:
% 17.97/3.09 | | |
% 17.97/3.09 | | | Case 1:
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | (154) ~ (all_57_0 = 0)
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | BETA: splitting (56) gives:
% 17.97/3.09 | | | |
% 17.97/3.09 | | | | Case 1:
% 17.97/3.09 | | | | |
% 17.97/3.09 | | | | | (155) all_72_1 = 0 & ~ (all_72_0 = 0) & pair_in_list(all_46_12,
% 17.97/3.09 | | | | | all_72_3, all_72_2) = 0 & less_than(all_72_2, all_72_3) =
% 17.97/3.09 | | | | | all_72_0
% 17.97/3.09 | | | | |
% 17.97/3.09 | | | | | ALPHA: (155) implies:
% 17.97/3.09 | | | | | (156) ~ (all_72_0 = 0)
% 17.97/3.09 | | | | | (157) less_than(all_72_2, all_72_3) = all_72_0
% 17.97/3.09 | | | | | (158) pair_in_list(all_46_12, all_72_3, all_72_2) = 0
% 17.97/3.09 | | | | |
% 17.97/3.09 | | | | | GROUND_INST: instantiating (141) with all_72_3, all_72_2, all_72_0,
% 17.97/3.09 | | | | | simplifying with (54), (55), (157) gives:
% 17.97/3.09 | | | | | (159) all_72_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 17.97/3.09 | | | | | pair_in_list(all_46_6, all_72_3, all_72_2) = v0)
% 17.97/3.09 | | | | |
% 17.97/3.09 | | | | | BETA: splitting (159) gives:
% 17.97/3.09 | | | | |
% 17.97/3.09 | | | | | Case 1:
% 17.97/3.09 | | | | | |
% 17.97/3.09 | | | | | | (160) all_72_0 = 0
% 17.97/3.09 | | | | | |
% 17.97/3.09 | | | | | | REDUCE: (156), (160) imply:
% 17.97/3.09 | | | | | | (161) $false
% 17.97/3.09 | | | | | |
% 17.97/3.09 | | | | | | CLOSE: (161) is inconsistent.
% 17.97/3.09 | | | | | |
% 17.97/3.09 | | | | | Case 2:
% 17.97/3.09 | | | | | |
% 17.97/3.09 | | | | | | (162) ? [v0: int] : ( ~ (v0 = 0) & pair_in_list(all_46_6,
% 17.97/3.09 | | | | | | all_72_3, all_72_2) = v0)
% 17.97/3.09 | | | | | |
% 17.97/3.09 | | | | | | DELTA: instantiating (162) with fresh symbol all_148_0 gives:
% 17.97/3.09 | | | | | | (163) ~ (all_148_0 = 0) & pair_in_list(all_46_6, all_72_3,
% 17.97/3.09 | | | | | | all_72_2) = all_148_0
% 17.97/3.09 | | | | | |
% 17.97/3.09 | | | | | | ALPHA: (163) implies:
% 17.97/3.09 | | | | | | (164) ~ (all_148_0 = 0)
% 17.97/3.09 | | | | | | (165) pair_in_list(all_46_6, all_72_3, all_72_2) = all_148_0
% 17.97/3.09 | | | | | |
% 17.97/3.09 | | | | | | GROUND_INST: instantiating (9) with all_46_12, all_46_9, all_72_3,
% 17.97/3.09 | | | | | | all_46_8, all_72_2, all_46_7, all_46_6, all_148_0,
% 17.97/3.09 | | | | | | simplifying with (14), (17), (18), (21), (22), (54),
% 17.97/3.09 | | | | | | (55), (165) gives:
% 17.97/3.09 | | | | | | (166) all_148_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 17.97/3.09 | | | | | | pair_in_list(all_46_12, all_72_3, all_72_2) = v0)
% 17.97/3.09 | | | | | |
% 17.97/3.09 | | | | | | BETA: splitting (166) gives:
% 17.97/3.09 | | | | | |
% 17.97/3.09 | | | | | | Case 1:
% 17.97/3.09 | | | | | | |
% 17.97/3.09 | | | | | | | (167) all_148_0 = 0
% 17.97/3.09 | | | | | | |
% 17.97/3.09 | | | | | | | REDUCE: (164), (167) imply:
% 17.97/3.09 | | | | | | | (168) $false
% 17.97/3.09 | | | | | | |
% 17.97/3.09 | | | | | | | CLOSE: (168) is inconsistent.
% 17.97/3.09 | | | | | | |
% 17.97/3.09 | | | | | | Case 2:
% 17.97/3.09 | | | | | | |
% 17.97/3.09 | | | | | | | (169) ? [v0: int] : ( ~ (v0 = 0) & pair_in_list(all_46_12,
% 17.97/3.09 | | | | | | | all_72_3, all_72_2) = v0)
% 17.97/3.09 | | | | | | |
% 17.97/3.09 | | | | | | | DELTA: instantiating (169) with fresh symbol all_179_0 gives:
% 17.97/3.09 | | | | | | | (170) ~ (all_179_0 = 0) & pair_in_list(all_46_12, all_72_3,
% 17.97/3.09 | | | | | | | all_72_2) = all_179_0
% 17.97/3.09 | | | | | | |
% 17.97/3.09 | | | | | | | ALPHA: (170) implies:
% 17.97/3.09 | | | | | | | (171) ~ (all_179_0 = 0)
% 17.97/3.09 | | | | | | | (172) pair_in_list(all_46_12, all_72_3, all_72_2) = all_179_0
% 17.97/3.09 | | | | | | |
% 17.97/3.10 | | | | | | | GROUND_INST: instantiating (12) with 0, all_179_0, all_72_2,
% 17.97/3.10 | | | | | | | all_72_3, all_46_12, simplifying with (158), (172)
% 17.97/3.10 | | | | | | | gives:
% 17.97/3.10 | | | | | | | (173) all_179_0 = 0
% 17.97/3.10 | | | | | | |
% 17.97/3.10 | | | | | | | REDUCE: (171), (173) imply:
% 17.97/3.10 | | | | | | | (174) $false
% 17.97/3.10 | | | | | | |
% 17.97/3.10 | | | | | | | CLOSE: (174) is inconsistent.
% 17.97/3.10 | | | | | | |
% 17.97/3.10 | | | | | | End of split
% 17.97/3.10 | | | | | |
% 17.97/3.10 | | | | | End of split
% 17.97/3.10 | | | | |
% 17.97/3.10 | | | | Case 2:
% 17.97/3.10 | | | | |
% 17.97/3.10 | | | | | (175) all_72_4 = 0 & check_cpq(all_57_1) = 0
% 17.97/3.10 | | | | |
% 17.97/3.10 | | | | | ALPHA: (175) implies:
% 17.97/3.10 | | | | | (176) check_cpq(all_57_1) = 0
% 17.97/3.10 | | | | |
% 17.97/3.10 | | | | | GROUND_INST: instantiating (10) with all_57_0, 0, all_57_1,
% 17.97/3.10 | | | | | simplifying with (37), (176) gives:
% 17.97/3.10 | | | | | (177) all_57_0 = 0
% 17.97/3.10 | | | | |
% 17.97/3.10 | | | | | REDUCE: (154), (177) imply:
% 17.97/3.10 | | | | | (178) $false
% 17.97/3.10 | | | | |
% 17.97/3.10 | | | | | CLOSE: (178) is inconsistent.
% 17.97/3.10 | | | | |
% 17.97/3.10 | | | | End of split
% 17.97/3.10 | | | |
% 17.97/3.10 | | | Case 2:
% 17.97/3.10 | | | |
% 17.97/3.10 | | | | (179) all_57_2 = 0
% 17.97/3.10 | | | |
% 17.97/3.10 | | | | COMBINE_EQS: (40), (179) imply:
% 17.97/3.10 | | | | (180) all_46_4 = 0
% 17.97/3.10 | | | |
% 17.97/3.10 | | | | REDUCE: (140), (180) imply:
% 17.97/3.10 | | | | (181) $false
% 17.97/3.10 | | | |
% 17.97/3.10 | | | | CLOSE: (181) is inconsistent.
% 17.97/3.10 | | | |
% 17.97/3.10 | | | End of split
% 17.97/3.10 | | |
% 17.97/3.10 | | End of split
% 17.97/3.10 | |
% 17.97/3.10 | End of split
% 17.97/3.10 |
% 17.97/3.10 End of proof
% 17.97/3.10 % SZS output end Proof for theBenchmark
% 17.97/3.10
% 17.97/3.10 2485ms
%------------------------------------------------------------------------------