TSTP Solution File: SWV409+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV409+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 22:56:13 EDT 2023
% Result : Theorem 10.84s 2.27s
% Output : Proof 17.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV409+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Tue Aug 29 03:09:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.63/0.61 ________ _____
% 0.63/0.61 ___ __ \_________(_)________________________________
% 0.63/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.63/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.63/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.63/0.61
% 0.63/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.63/0.61 (2023-06-19)
% 0.63/0.61
% 0.63/0.61 (c) Philipp Rümmer, 2009-2023
% 0.63/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.63/0.61 Amanda Stjerna.
% 0.63/0.61 Free software under BSD-3-Clause.
% 0.63/0.61
% 0.63/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.63/0.61
% 0.63/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.62 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 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 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 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
% 3.33/1.17 Prover 4: Preprocessing ...
% 3.33/1.17 Prover 1: Preprocessing ...
% 3.47/1.23 Prover 5: Preprocessing ...
% 3.47/1.23 Prover 2: Preprocessing ...
% 3.47/1.23 Prover 6: Preprocessing ...
% 3.66/1.23 Prover 3: Preprocessing ...
% 3.66/1.23 Prover 0: Preprocessing ...
% 7.05/1.77 Prover 6: Proving ...
% 7.05/1.77 Prover 5: Proving ...
% 7.66/1.79 Prover 3: Constructing countermodel ...
% 7.66/1.80 Prover 2: Proving ...
% 7.66/1.80 Prover 1: Constructing countermodel ...
% 7.92/1.84 Prover 4: Constructing countermodel ...
% 8.02/1.88 Prover 0: Proving ...
% 9.04/1.99 Prover 3: gave up
% 9.04/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.04/2.00 Prover 1: gave up
% 9.04/2.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.68/2.07 Prover 8: Preprocessing ...
% 9.68/2.08 Prover 7: Preprocessing ...
% 10.84/2.21 Prover 7: Warning: ignoring some quantifiers
% 10.84/2.21 Prover 8: Warning: ignoring some quantifiers
% 10.84/2.23 Prover 8: Constructing countermodel ...
% 10.84/2.25 Prover 7: Constructing countermodel ...
% 10.84/2.27 Prover 0: proved (1642ms)
% 10.84/2.27
% 10.84/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.84/2.27
% 10.84/2.28 Prover 6: stopped
% 10.84/2.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.84/2.29 Prover 2: stopped
% 11.42/2.30 Prover 5: stopped
% 11.42/2.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.42/2.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.42/2.36 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 11.42/2.37 Prover 11: Preprocessing ...
% 11.42/2.37 Prover 13: Preprocessing ...
% 12.17/2.40 Prover 10: Preprocessing ...
% 12.17/2.40 Prover 16: Preprocessing ...
% 12.17/2.42 Prover 8: gave up
% 12.30/2.42 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.30/2.45 Prover 19: Preprocessing ...
% 13.06/2.53 Prover 10: Warning: ignoring some quantifiers
% 13.06/2.56 Prover 13: Warning: ignoring some quantifiers
% 13.06/2.56 Prover 16: Warning: ignoring some quantifiers
% 13.06/2.56 Prover 10: Constructing countermodel ...
% 13.06/2.57 Prover 16: Constructing countermodel ...
% 13.06/2.58 Prover 13: Constructing countermodel ...
% 13.71/2.61 Prover 10: gave up
% 13.71/2.62 Prover 7: gave up
% 13.71/2.66 Prover 19: Warning: ignoring some quantifiers
% 13.71/2.68 Prover 19: Constructing countermodel ...
% 14.46/2.69 Prover 11: Constructing countermodel ...
% 16.15/2.94 Prover 4: Found proof (size 108)
% 16.15/2.94 Prover 4: proved (2310ms)
% 16.15/2.94 Prover 13: stopped
% 16.15/2.94 Prover 11: stopped
% 16.15/2.95 Prover 19: stopped
% 16.15/2.95 Prover 16: stopped
% 16.15/2.95
% 16.15/2.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.15/2.95
% 16.15/2.97 % SZS output start Proof for theBenchmark
% 16.15/2.98 Assumptions after simplification:
% 16.15/2.98 ---------------------------------
% 16.15/2.98
% 16.15/2.98 (l45_co)
% 16.74/3.02 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 16.74/3.02 = 0) & update_slb(v0, v2) = v3 & pair_in_list(v3, v1, v2) = v4 &
% 16.74/3.02 contains_slb(v0, v1) = 0 & strictly_less_than(v1, v2) = 0 & $i(v3) & $i(v2)
% 16.74/3.02 & $i(v1) & $i(v0) & ! [v5: $i] : ( ~ (pair_in_list(v3, v1, v5) = 0) | ~
% 16.74/3.02 $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & less_than(v2, v5) = v6)) & ! [v5:
% 16.74/3.02 $i] : ( ~ (less_than(v2, v5) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 =
% 16.74/3.02 0) & pair_in_list(v3, v1, v5) = v6)))
% 16.74/3.02
% 16.74/3.02 (l45_l48)
% 16.74/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.74/3.04 int] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v3)
% 16.74/3.04 = v5) | ~ (pair_in_list(v0, v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 16.74/3.04 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (strictly_less_than(v2,
% 16.74/3.04 v3) = v7 & strictly_less_than(v1, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 =
% 16.74/3.04 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 16.74/3.04 [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~
% 16.74/3.04 (pair_in_list(v4, v1, v3) = v5) | ~ (strictly_less_than(v2, v3) = 0) | ~
% 16.74/3.04 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 16.74/3.04 (pair_in_list(v0, v1, v2) = v6 & strictly_less_than(v1, v3) = v7 & ( ~ (v7 =
% 16.74/3.04 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 16.74/3.04 [v3: $i] : ( ~ (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v2, v3)
% 16.74/3.04 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 16.74/3.04 [v5: $i] : ? [v6: any] : (update_slb(v0, v3) = v5 & pair_in_list(v5, v1,
% 16.74/3.04 v3) = v6 & strictly_less_than(v1, v3) = v4 & $i(v5) & ( ~ (v4 = 0) | v6
% 16.74/3.04 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 16.74/3.04 (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v1, v3) = 0) | ~
% 16.74/3.04 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ?
% 16.74/3.04 [v6: any] : (update_slb(v0, v3) = v5 & pair_in_list(v5, v1, v3) = v6 &
% 16.74/3.04 strictly_less_than(v2, v3) = v4 & $i(v5) & ( ~ (v4 = 0) | v6 = 0)))
% 16.74/3.04
% 16.74/3.04 (l45_l49)
% 16.74/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 16.74/3.05 (update_slb(v0, v3) = v4) | ~ (pair_in_list(v0, v1, v2) = 0) | ~ $i(v3) |
% 16.74/3.05 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i]
% 16.74/3.05 : ? [v8: int] : ? [v9: int] : ($i(v7) & ((v9 = 0 & v8 = 0 &
% 16.74/3.05 pair_in_list(v4, v1, v7) = 0 & less_than(v3, v7) = 0) |
% 16.74/3.05 (strictly_less_than(v1, v3) = v5 & less_than(v3, v2) = v6 & ( ~ (v6 = 0)
% 16.74/3.05 | ~ (v5 = 0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 16.74/3.05 [v3: $i] : ! [v4: $i] : ( ~ (update_slb(v0, v3) = v4) | ~
% 16.74/3.05 (strictly_less_than(v1, v3) = 0) | ~ (less_than(v3, v2) = 0) | ~ $i(v3) |
% 16.74/3.05 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: int]
% 16.74/3.05 : ? [v8: int] : ($i(v6) & ((v8 = 0 & v7 = 0 & pair_in_list(v4, v1, v6) = 0
% 16.74/3.06 & less_than(v3, v6) = 0) | ( ~ (v5 = 0) & pair_in_list(v0, v1, v2) =
% 16.74/3.06 v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 16.74/3.06 (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v1, v3) = 0) | ~
% 16.74/3.06 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ?
% 16.74/3.06 [v6: $i] : ? [v7: int] : ? [v8: int] : (update_slb(v0, v3) = v5 &
% 16.74/3.06 less_than(v3, v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | (v8 = 0 & v7 = 0
% 16.74/3.06 & pair_in_list(v5, v1, v6) = 0 & less_than(v3, v6) = 0)))) & ! [v0:
% 16.74/3.06 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (pair_in_list(v0, v1,
% 16.74/3.06 v2) = 0) | ~ (less_than(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 16.74/3.06 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: int]
% 16.74/3.06 : ? [v8: int] : (update_slb(v0, v3) = v5 & strictly_less_than(v1, v3) = v4
% 16.74/3.06 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | (v8 = 0 & v7 = 0 & pair_in_list(v5, v1,
% 16.74/3.06 v6) = 0 & less_than(v3, v6) = 0))))
% 16.74/3.06
% 16.74/3.06 (l45_li4647)
% 16.74/3.06 ! [v0: $i] : ! [v1: $i] : ( ~ (contains_slb(v0, v1) = 0) | ~ $i(v1) | ~
% 16.74/3.06 $i(v0) | ? [v2: $i] : (pair_in_list(v0, v1, v2) = 0 & $i(v2)))
% 16.74/3.06
% 16.74/3.06 (stricly_smaller_definition)
% 16.74/3.07 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 16.74/3.07 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 16.74/3.07 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 16.74/3.07 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 |
% 16.74/3.07 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 16.74/3.07 any] : (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3
% 16.74/3.07 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 16.74/3.07 (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 16.74/3.07 any] : (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3
% 16.74/3.07 = 0) | (v4 = 0 & ~ (v2 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 16.74/3.07 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 16.74/3.07 ? [v4: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & (
% 16.74/3.07 ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 16.74/3.07 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : (
% 16.74/3.07 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0:
% 16.74/3.07 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 16.74/3.07 [v2: any] : ? [v3: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1,
% 16.74/3.07 v0) = v2 & (v3 = 0 | v2 = 0)))
% 16.74/3.07
% 16.74/3.07 (totality)
% 16.74/3.07 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) =
% 16.74/3.07 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : !
% 16.74/3.07 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) |
% 16.74/3.07 ~ $i(v0) | less_than(v1, v0) = 0)
% 16.74/3.07
% 16.74/3.07 (function-axioms)
% 16.74/3.08 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 16.74/3.08 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 16.74/3.08 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.74/3.08 ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2)
% 16.74/3.08 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 16.74/3.08 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) & ! [v0: $i]
% 16.74/3.08 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_slb(v3, v2)
% 16.74/3.08 = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 16.74/3.08 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.74/3.08 (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) & ! [v0: $i]
% 16.74/3.08 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (pair(v3, v2) = v1)
% 16.74/3.08 | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 16.74/3.08 [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) =
% 16.74/3.08 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.74/3.08 $i] : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~
% 16.74/3.08 (strictly_less_than(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.74/3.08 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.74/3.08 (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) & ! [v0:
% 16.74/3.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 16.74/3.08 ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0))
% 16.74/3.08
% 16.74/3.08 Further assumptions not needed in the proof:
% 16.74/3.08 --------------------------------------------
% 16.74/3.08 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30,
% 16.74/3.08 bottom_smallest, reflexivity, transitivity
% 16.74/3.08
% 16.74/3.08 Those formulas are unsatisfiable:
% 16.74/3.08 ---------------------------------
% 16.74/3.08
% 16.74/3.08 Begin of proof
% 16.74/3.08 |
% 16.74/3.08 | ALPHA: (totality) implies:
% 16.74/3.09 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1,
% 16.74/3.09 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0)
% 16.74/3.09 |
% 16.74/3.09 | ALPHA: (stricly_smaller_definition) implies:
% 16.74/3.09 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v0, v1) = v2)
% 16.74/3.09 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 16.74/3.09 | (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( ~ (v3 =
% 16.74/3.09 | 0) | (v2 = 0 & ~ (v4 = 0)))))
% 16.74/3.09 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v1, v0) = v2)
% 16.74/3.09 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 16.74/3.09 | (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 =
% 16.74/3.09 | 0) | (v4 = 0 & ~ (v2 = 0)))))
% 16.74/3.09 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1,
% 16.74/3.09 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 16.74/3.09 | (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 16.74/3.09 | 0) | v4 = 0)))
% 16.74/3.09 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 16.74/3.09 | (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 16.74/3.09 | any] : ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) =
% 16.74/3.09 | v3 & ( ~ (v3 = 0) | v4 = 0)))
% 16.74/3.09 |
% 16.74/3.09 | ALPHA: (l45_l48) implies:
% 16.74/3.10 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 16.74/3.10 | (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v1, v3) = 0)
% 16.74/3.10 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 16.74/3.10 | [v5: $i] : ? [v6: any] : (update_slb(v0, v3) = v5 & pair_in_list(v5,
% 16.74/3.10 | v1, v3) = v6 & strictly_less_than(v2, v3) = v4 & $i(v5) & ( ~ (v4
% 16.74/3.10 | = 0) | v6 = 0)))
% 16.74/3.10 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.74/3.10 | ! [v5: int] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~
% 16.74/3.10 | (pair_in_list(v4, v1, v3) = v5) | ~ (pair_in_list(v0, v1, v2) = 0) |
% 16.74/3.10 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 16.74/3.10 | [v7: any] : (strictly_less_than(v2, v3) = v7 & strictly_less_than(v1,
% 16.74/3.10 | v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 16.74/3.10 |
% 16.74/3.10 | ALPHA: (l45_l49) implies:
% 17.20/3.10 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 17.20/3.10 | (pair_in_list(v0, v1, v2) = 0) | ~ (strictly_less_than(v1, v3) = 0)
% 17.20/3.10 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 17.20/3.10 | [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: int] :
% 17.20/3.10 | (update_slb(v0, v3) = v5 & less_than(v3, v2) = v4 & $i(v6) & $i(v5) &
% 17.20/3.10 | ( ~ (v4 = 0) | (v8 = 0 & v7 = 0 & pair_in_list(v5, v1, v6) = 0 &
% 17.20/3.10 | less_than(v3, v6) = 0))))
% 17.20/3.10 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 17.20/3.10 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v0, v1, v2) = 0) | ~
% 17.20/3.10 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 17.20/3.10 | any] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : ($i(v7) & ((v9 =
% 17.20/3.10 | 0 & v8 = 0 & pair_in_list(v4, v1, v7) = 0 & less_than(v3, v7) =
% 17.20/3.10 | 0) | (strictly_less_than(v1, v3) = v5 & less_than(v3, v2) = v6
% 17.20/3.10 | & ( ~ (v6 = 0) | ~ (v5 = 0))))))
% 17.20/3.10 |
% 17.20/3.10 | ALPHA: (function-axioms) implies:
% 17.20/3.10 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.20/3.10 | : ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~
% 17.20/3.10 | (less_than(v3, v2) = v0))
% 17.20/3.10 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.20/3.10 | : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~
% 17.20/3.10 | (strictly_less_than(v3, v2) = v0))
% 17.20/3.11 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.20/3.11 | (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 17.20/3.11 |
% 17.20/3.11 | DELTA: instantiating (l45_co) with fresh symbols all_26_0, all_26_1, all_26_2,
% 17.20/3.11 | all_26_3, all_26_4 gives:
% 17.20/3.11 | (13) ~ (all_26_0 = 0) & update_slb(all_26_4, all_26_2) = all_26_1 &
% 17.20/3.11 | pair_in_list(all_26_1, all_26_3, all_26_2) = all_26_0 &
% 17.20/3.11 | contains_slb(all_26_4, all_26_3) = 0 & strictly_less_than(all_26_3,
% 17.20/3.11 | all_26_2) = 0 & $i(all_26_1) & $i(all_26_2) & $i(all_26_3) &
% 17.20/3.11 | $i(all_26_4) & ! [v0: $i] : ( ~ (pair_in_list(all_26_1, all_26_3, v0)
% 17.20/3.11 | = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 17.20/3.11 | less_than(all_26_2, v0) = v1)) & ! [v0: $i] : ( ~
% 17.20/3.11 | (less_than(all_26_2, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 17.20/3.11 | 0) & pair_in_list(all_26_1, all_26_3, v0) = v1))
% 17.20/3.11 |
% 17.20/3.11 | ALPHA: (13) implies:
% 17.20/3.11 | (14) ~ (all_26_0 = 0)
% 17.20/3.11 | (15) $i(all_26_4)
% 17.20/3.11 | (16) $i(all_26_3)
% 17.20/3.11 | (17) $i(all_26_2)
% 17.20/3.11 | (18) strictly_less_than(all_26_3, all_26_2) = 0
% 17.20/3.11 | (19) contains_slb(all_26_4, all_26_3) = 0
% 17.20/3.11 | (20) pair_in_list(all_26_1, all_26_3, all_26_2) = all_26_0
% 17.20/3.11 | (21) update_slb(all_26_4, all_26_2) = all_26_1
% 17.20/3.11 | (22) ! [v0: $i] : ( ~ (pair_in_list(all_26_1, all_26_3, v0) = 0) | ~
% 17.20/3.11 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & less_than(all_26_2, v0) =
% 17.20/3.11 | v1))
% 17.20/3.11 |
% 17.20/3.11 | GROUND_INST: instantiating (l45_li4647) with all_26_4, all_26_3, simplifying
% 17.20/3.11 | with (15), (16), (19) gives:
% 17.20/3.11 | (23) ? [v0: $i] : (pair_in_list(all_26_4, all_26_3, v0) = 0 & $i(v0))
% 17.20/3.11 |
% 17.20/3.11 | DELTA: instantiating (23) with fresh symbol all_34_0 gives:
% 17.20/3.11 | (24) pair_in_list(all_26_4, all_26_3, all_34_0) = 0 & $i(all_34_0)
% 17.20/3.12 |
% 17.20/3.12 | ALPHA: (24) implies:
% 17.20/3.12 | (25) $i(all_34_0)
% 17.20/3.12 | (26) pair_in_list(all_26_4, all_26_3, all_34_0) = 0
% 17.20/3.12 |
% 17.20/3.12 | GROUND_INST: instantiating (7) with all_26_4, all_26_3, all_34_0, all_26_2,
% 17.20/3.12 | all_26_1, all_26_0, simplifying with (15), (16), (17), (20),
% 17.20/3.12 | (21), (25), (26) gives:
% 17.20/3.12 | (27) all_26_0 = 0 | ? [v0: any] : ? [v1: any] :
% 17.20/3.12 | (strictly_less_than(all_34_0, all_26_2) = v1 &
% 17.20/3.12 | strictly_less_than(all_26_3, all_26_2) = v0 & ( ~ (v1 = 0) | ~ (v0
% 17.20/3.12 | = 0)))
% 17.20/3.12 |
% 17.20/3.12 | GROUND_INST: instantiating (9) with all_26_4, all_26_3, all_34_0, all_26_2,
% 17.20/3.12 | all_26_1, simplifying with (15), (16), (17), (21), (25), (26)
% 17.20/3.12 | gives:
% 17.20/3.12 | (28) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ? [v4:
% 17.20/3.12 | int] : ($i(v2) & ((v4 = 0 & v3 = 0 & pair_in_list(all_26_1,
% 17.20/3.12 | all_26_3, v2) = 0 & less_than(all_26_2, v2) = 0) |
% 17.20/3.12 | (strictly_less_than(all_26_3, all_26_2) = v0 & less_than(all_26_2,
% 17.20/3.12 | all_34_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 17.20/3.12 |
% 17.20/3.12 | GROUND_INST: instantiating (8) with all_26_4, all_26_3, all_34_0, all_26_2,
% 17.20/3.12 | simplifying with (15), (16), (17), (18), (25), (26) gives:
% 17.20/3.12 | (29) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int]
% 17.20/3.12 | : (update_slb(all_26_4, all_26_2) = v1 & less_than(all_26_2, all_34_0)
% 17.20/3.12 | = v0 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | (v4 = 0 & v3 = 0 &
% 17.20/3.12 | pair_in_list(v1, all_26_3, v2) = 0 & less_than(all_26_2, v2) =
% 17.20/3.12 | 0)))
% 17.20/3.13 |
% 17.20/3.13 | GROUND_INST: instantiating (6) with all_26_4, all_26_3, all_34_0, all_26_2,
% 17.20/3.13 | simplifying with (15), (16), (17), (18), (25), (26) gives:
% 17.20/3.13 | (30) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (update_slb(all_26_4,
% 17.20/3.13 | all_26_2) = v1 & pair_in_list(v1, all_26_3, all_26_2) = v2 &
% 17.20/3.13 | strictly_less_than(all_34_0, all_26_2) = v0 & $i(v1) & ( ~ (v0 = 0)
% 17.20/3.13 | | v2 = 0))
% 17.20/3.13 |
% 17.20/3.13 | DELTA: instantiating (30) with fresh symbols all_61_0, all_61_1, all_61_2
% 17.20/3.13 | gives:
% 17.20/3.13 | (31) update_slb(all_26_4, all_26_2) = all_61_1 & pair_in_list(all_61_1,
% 17.20/3.13 | all_26_3, all_26_2) = all_61_0 & strictly_less_than(all_34_0,
% 17.20/3.13 | all_26_2) = all_61_2 & $i(all_61_1) & ( ~ (all_61_2 = 0) | all_61_0
% 17.20/3.13 | = 0)
% 17.20/3.13 |
% 17.20/3.13 | ALPHA: (31) implies:
% 17.20/3.13 | (32) $i(all_61_1)
% 17.20/3.13 | (33) strictly_less_than(all_34_0, all_26_2) = all_61_2
% 17.20/3.13 | (34) update_slb(all_26_4, all_26_2) = all_61_1
% 17.20/3.13 |
% 17.20/3.13 | DELTA: instantiating (29) with fresh symbols all_63_0, all_63_1, all_63_2,
% 17.20/3.13 | all_63_3, all_63_4 gives:
% 17.20/3.13 | (35) update_slb(all_26_4, all_26_2) = all_63_3 & less_than(all_26_2,
% 17.20/3.13 | all_34_0) = all_63_4 & $i(all_63_2) & $i(all_63_3) & ( ~ (all_63_4 =
% 17.20/3.13 | 0) | (all_63_0 = 0 & all_63_1 = 0 & pair_in_list(all_63_3,
% 17.20/3.13 | all_26_3, all_63_2) = 0 & less_than(all_26_2, all_63_2) = 0))
% 17.20/3.13 |
% 17.20/3.13 | ALPHA: (35) implies:
% 17.20/3.13 | (36) less_than(all_26_2, all_34_0) = all_63_4
% 17.20/3.13 | (37) update_slb(all_26_4, all_26_2) = all_63_3
% 17.20/3.13 | (38) ~ (all_63_4 = 0) | (all_63_0 = 0 & all_63_1 = 0 &
% 17.20/3.13 | pair_in_list(all_63_3, all_26_3, all_63_2) = 0 & less_than(all_26_2,
% 17.20/3.13 | all_63_2) = 0)
% 17.20/3.13 |
% 17.20/3.13 | DELTA: instantiating (28) with fresh symbols all_65_0, all_65_1, all_65_2,
% 17.20/3.13 | all_65_3, all_65_4 gives:
% 17.20/3.14 | (39) $i(all_65_2) & ((all_65_0 = 0 & all_65_1 = 0 & pair_in_list(all_26_1,
% 17.20/3.14 | all_26_3, all_65_2) = 0 & less_than(all_26_2, all_65_2) = 0) |
% 17.20/3.14 | (strictly_less_than(all_26_3, all_26_2) = all_65_4 &
% 17.20/3.14 | less_than(all_26_2, all_34_0) = all_65_3 & ( ~ (all_65_3 = 0) | ~
% 17.20/3.14 | (all_65_4 = 0))))
% 17.20/3.14 |
% 17.20/3.14 | ALPHA: (39) implies:
% 17.20/3.14 | (40) $i(all_65_2)
% 17.20/3.14 | (41) (all_65_0 = 0 & all_65_1 = 0 & pair_in_list(all_26_1, all_26_3,
% 17.20/3.14 | all_65_2) = 0 & less_than(all_26_2, all_65_2) = 0) |
% 17.20/3.14 | (strictly_less_than(all_26_3, all_26_2) = all_65_4 &
% 17.20/3.14 | less_than(all_26_2, all_34_0) = all_65_3 & ( ~ (all_65_3 = 0) | ~
% 17.20/3.14 | (all_65_4 = 0)))
% 17.20/3.14 |
% 17.20/3.14 | BETA: splitting (27) gives:
% 17.20/3.14 |
% 17.20/3.14 | Case 1:
% 17.20/3.14 | |
% 17.20/3.14 | | (42) all_26_0 = 0
% 17.20/3.14 | |
% 17.20/3.14 | | REDUCE: (14), (42) imply:
% 17.20/3.14 | | (43) $false
% 17.20/3.14 | |
% 17.20/3.14 | | CLOSE: (43) is inconsistent.
% 17.20/3.14 | |
% 17.20/3.14 | Case 2:
% 17.20/3.14 | |
% 17.20/3.14 | | (44) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_34_0,
% 17.20/3.15 | | all_26_2) = v1 & strictly_less_than(all_26_3, all_26_2) = v0 & (
% 17.20/3.15 | | ~ (v1 = 0) | ~ (v0 = 0)))
% 17.20/3.15 | |
% 17.20/3.15 | | DELTA: instantiating (44) with fresh symbols all_71_0, all_71_1 gives:
% 17.20/3.15 | | (45) strictly_less_than(all_34_0, all_26_2) = all_71_0 &
% 17.20/3.15 | | strictly_less_than(all_26_3, all_26_2) = all_71_1 & ( ~ (all_71_0 =
% 17.20/3.15 | | 0) | ~ (all_71_1 = 0))
% 17.20/3.15 | |
% 17.20/3.15 | | ALPHA: (45) implies:
% 17.20/3.15 | | (46) strictly_less_than(all_26_3, all_26_2) = all_71_1
% 17.20/3.15 | | (47) strictly_less_than(all_34_0, all_26_2) = all_71_0
% 17.20/3.15 | | (48) ~ (all_71_0 = 0) | ~ (all_71_1 = 0)
% 17.20/3.15 | |
% 17.20/3.15 | | GROUND_INST: instantiating (11) with 0, all_71_1, all_26_2, all_26_3,
% 17.20/3.15 | | simplifying with (18), (46) gives:
% 17.20/3.15 | | (49) all_71_1 = 0
% 17.20/3.15 | |
% 17.20/3.15 | | GROUND_INST: instantiating (11) with all_61_2, all_71_0, all_26_2, all_34_0,
% 17.20/3.15 | | simplifying with (33), (47) gives:
% 17.20/3.15 | | (50) all_71_0 = all_61_2
% 17.20/3.15 | |
% 17.20/3.15 | | GROUND_INST: instantiating (12) with all_26_1, all_63_3, all_26_2, all_26_4,
% 17.20/3.15 | | simplifying with (21), (37) gives:
% 17.20/3.15 | | (51) all_63_3 = all_26_1
% 17.20/3.15 | |
% 17.20/3.15 | | GROUND_INST: instantiating (12) with all_61_1, all_63_3, all_26_2, all_26_4,
% 17.20/3.15 | | simplifying with (34), (37) gives:
% 17.20/3.15 | | (52) all_63_3 = all_61_1
% 17.20/3.15 | |
% 17.20/3.15 | | COMBINE_EQS: (51), (52) imply:
% 17.20/3.15 | | (53) all_61_1 = all_26_1
% 17.20/3.15 | |
% 17.20/3.15 | | SIMP: (53) implies:
% 17.20/3.15 | | (54) all_61_1 = all_26_1
% 17.20/3.15 | |
% 17.20/3.15 | | REDUCE: (32), (54) imply:
% 17.20/3.15 | | (55) $i(all_26_1)
% 17.20/3.15 | |
% 17.20/3.15 | | BETA: splitting (48) gives:
% 17.20/3.15 | |
% 17.20/3.15 | | Case 1:
% 17.20/3.15 | | |
% 17.20/3.15 | | | (56) ~ (all_71_0 = 0)
% 17.20/3.15 | | |
% 17.20/3.15 | | | REDUCE: (50), (56) imply:
% 17.20/3.15 | | | (57) ~ (all_61_2 = 0)
% 17.20/3.15 | | |
% 17.20/3.15 | | | GROUND_INST: instantiating (1) with all_34_0, all_26_2, all_63_4,
% 17.20/3.15 | | | simplifying with (17), (25), (36) gives:
% 17.20/3.15 | | | (58) all_63_4 = 0 | less_than(all_34_0, all_26_2) = 0
% 17.20/3.15 | | |
% 17.20/3.16 | | | GROUND_INST: instantiating (4) with all_34_0, all_26_2, all_63_4,
% 17.20/3.16 | | | simplifying with (17), (25), (36) gives:
% 17.20/3.16 | | | (59) all_63_4 = 0 | ? [v0: any] : ? [v1: any] :
% 17.20/3.16 | | | (strictly_less_than(all_34_0, all_26_2) = v1 & less_than(all_34_0,
% 17.20/3.16 | | | all_26_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 17.20/3.16 | | |
% 17.20/3.16 | | | GROUND_INST: instantiating (3) with all_34_0, all_26_2, all_63_4,
% 17.20/3.16 | | | simplifying with (17), (25), (36) gives:
% 17.20/3.16 | | | (60) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_34_0,
% 17.20/3.16 | | | all_26_2) = v0 & less_than(all_34_0, all_26_2) = v1 & ( ~ (v0
% 17.20/3.16 | | | = 0) | (v1 = 0 & ~ (all_63_4 = 0))))
% 17.20/3.16 | | |
% 17.20/3.16 | | | GROUND_INST: instantiating (2) with all_26_2, all_34_0, all_63_4,
% 17.20/3.16 | | | simplifying with (17), (25), (36) gives:
% 17.20/3.16 | | | (61) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_26_2,
% 17.20/3.16 | | | all_34_0) = v0 & less_than(all_34_0, all_26_2) = v1 & ( ~ (v0
% 17.20/3.16 | | | = 0) | (all_63_4 = 0 & ~ (v1 = 0))))
% 17.20/3.16 | | |
% 17.20/3.16 | | | GROUND_INST: instantiating (5) with all_34_0, all_26_2, all_61_2,
% 17.20/3.16 | | | simplifying with (17), (25), (33) gives:
% 17.20/3.16 | | | (62) all_61_2 = 0 | ? [v0: any] : ? [v1: any] : (less_than(all_34_0,
% 17.20/3.16 | | | all_26_2) = v0 & less_than(all_26_2, all_34_0) = v1 & ( ~ (v0
% 17.20/3.16 | | | = 0) | v1 = 0))
% 17.20/3.16 | | |
% 17.20/3.16 | | | DELTA: instantiating (61) with fresh symbols all_94_0, all_94_1 gives:
% 17.20/3.16 | | | (63) strictly_less_than(all_26_2, all_34_0) = all_94_1 &
% 17.20/3.16 | | | less_than(all_34_0, all_26_2) = all_94_0 & ( ~ (all_94_1 = 0) |
% 17.20/3.16 | | | (all_63_4 = 0 & ~ (all_94_0 = 0)))
% 17.20/3.16 | | |
% 17.20/3.16 | | | ALPHA: (63) implies:
% 17.20/3.16 | | | (64) less_than(all_34_0, all_26_2) = all_94_0
% 17.20/3.16 | | |
% 17.20/3.16 | | | DELTA: instantiating (60) with fresh symbols all_96_0, all_96_1 gives:
% 17.20/3.16 | | | (65) strictly_less_than(all_34_0, all_26_2) = all_96_1 &
% 17.20/3.16 | | | less_than(all_34_0, all_26_2) = all_96_0 & ( ~ (all_96_1 = 0) |
% 17.20/3.16 | | | (all_96_0 = 0 & ~ (all_63_4 = 0)))
% 17.20/3.16 | | |
% 17.20/3.16 | | | ALPHA: (65) implies:
% 17.20/3.16 | | | (66) less_than(all_34_0, all_26_2) = all_96_0
% 17.20/3.16 | | | (67) strictly_less_than(all_34_0, all_26_2) = all_96_1
% 17.20/3.16 | | |
% 17.20/3.16 | | | GROUND_INST: instantiating (10) with all_94_0, all_96_0, all_26_2,
% 17.20/3.16 | | | all_34_0, simplifying with (64), (66) gives:
% 17.20/3.17 | | | (68) all_96_0 = all_94_0
% 17.20/3.17 | | |
% 17.20/3.17 | | | GROUND_INST: instantiating (11) with all_61_2, all_96_1, all_26_2,
% 17.20/3.17 | | | all_34_0, simplifying with (33), (67) gives:
% 17.20/3.17 | | | (69) all_96_1 = all_61_2
% 17.20/3.17 | | |
% 17.20/3.17 | | | GROUND_INST: instantiating (3) with all_26_2, all_34_0, all_94_0,
% 17.20/3.17 | | | simplifying with (17), (25), (64) gives:
% 17.20/3.17 | | | (70) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_26_2,
% 17.20/3.17 | | | all_34_0) = v0 & less_than(all_26_2, all_34_0) = v1 & ( ~ (v0
% 17.20/3.17 | | | = 0) | (v1 = 0 & ~ (all_94_0 = 0))))
% 17.20/3.17 | | |
% 17.20/3.17 | | | DELTA: instantiating (70) with fresh symbols all_107_0, all_107_1 gives:
% 17.20/3.17 | | | (71) strictly_less_than(all_26_2, all_34_0) = all_107_1 &
% 17.20/3.17 | | | less_than(all_26_2, all_34_0) = all_107_0 & ( ~ (all_107_1 = 0) |
% 17.20/3.17 | | | (all_107_0 = 0 & ~ (all_94_0 = 0)))
% 17.20/3.17 | | |
% 17.20/3.17 | | | ALPHA: (71) implies:
% 17.20/3.17 | | | (72) less_than(all_26_2, all_34_0) = all_107_0
% 17.20/3.17 | | |
% 17.20/3.17 | | | GROUND_INST: instantiating (10) with all_63_4, all_107_0, all_34_0,
% 17.20/3.17 | | | all_26_2, simplifying with (36), (72) gives:
% 17.20/3.17 | | | (73) all_107_0 = all_63_4
% 17.20/3.17 | | |
% 17.20/3.17 | | | BETA: splitting (38) gives:
% 17.20/3.17 | | |
% 17.20/3.17 | | | Case 1:
% 17.20/3.17 | | | |
% 17.20/3.17 | | | | (74) ~ (all_63_4 = 0)
% 17.20/3.17 | | | |
% 17.20/3.17 | | | | BETA: splitting (58) gives:
% 17.20/3.17 | | | |
% 17.20/3.17 | | | | Case 1:
% 17.20/3.17 | | | | |
% 17.20/3.17 | | | | | (75) less_than(all_34_0, all_26_2) = 0
% 17.20/3.17 | | | | |
% 17.20/3.17 | | | | | BETA: splitting (59) gives:
% 17.20/3.17 | | | | |
% 17.20/3.17 | | | | | Case 1:
% 17.20/3.17 | | | | | |
% 17.20/3.17 | | | | | | (76) all_63_4 = 0
% 17.20/3.17 | | | | | |
% 17.20/3.17 | | | | | | REDUCE: (74), (76) imply:
% 17.20/3.17 | | | | | | (77) $false
% 17.20/3.17 | | | | | |
% 17.20/3.17 | | | | | | CLOSE: (77) is inconsistent.
% 17.20/3.17 | | | | | |
% 17.20/3.17 | | | | | Case 2:
% 17.20/3.17 | | | | | |
% 17.20/3.17 | | | | | | (78) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_34_0,
% 17.20/3.17 | | | | | | all_26_2) = v1 & less_than(all_34_0, all_26_2) = v0 & (
% 17.20/3.17 | | | | | | ~ (v0 = 0) | v1 = 0))
% 17.20/3.17 | | | | | |
% 17.20/3.17 | | | | | | DELTA: instantiating (78) with fresh symbols all_128_0, all_128_1
% 17.20/3.17 | | | | | | gives:
% 17.20/3.17 | | | | | | (79) strictly_less_than(all_34_0, all_26_2) = all_128_0 &
% 17.20/3.17 | | | | | | less_than(all_34_0, all_26_2) = all_128_1 & ( ~ (all_128_1 =
% 17.20/3.17 | | | | | | 0) | all_128_0 = 0)
% 17.20/3.17 | | | | | |
% 17.20/3.17 | | | | | | ALPHA: (79) implies:
% 17.20/3.17 | | | | | | (80) less_than(all_34_0, all_26_2) = all_128_1
% 17.20/3.17 | | | | | | (81) strictly_less_than(all_34_0, all_26_2) = all_128_0
% 17.20/3.17 | | | | | | (82) ~ (all_128_1 = 0) | all_128_0 = 0
% 17.20/3.17 | | | | | |
% 17.20/3.17 | | | | | | BETA: splitting (62) gives:
% 17.20/3.17 | | | | | |
% 17.20/3.17 | | | | | | Case 1:
% 17.20/3.17 | | | | | | |
% 17.20/3.17 | | | | | | | (83) all_61_2 = 0
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | REDUCE: (57), (83) imply:
% 17.20/3.18 | | | | | | | (84) $false
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | CLOSE: (84) is inconsistent.
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | Case 2:
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | (85) ? [v0: any] : ? [v1: any] : (less_than(all_34_0,
% 17.20/3.18 | | | | | | | all_26_2) = v0 & less_than(all_26_2, all_34_0) = v1 &
% 17.20/3.18 | | | | | | | ( ~ (v0 = 0) | v1 = 0))
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | DELTA: instantiating (85) with fresh symbols all_134_0, all_134_1
% 17.20/3.18 | | | | | | | gives:
% 17.20/3.18 | | | | | | | (86) less_than(all_34_0, all_26_2) = all_134_1 &
% 17.20/3.18 | | | | | | | less_than(all_26_2, all_34_0) = all_134_0 & ( ~ (all_134_1
% 17.20/3.18 | | | | | | | = 0) | all_134_0 = 0)
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | ALPHA: (86) implies:
% 17.20/3.18 | | | | | | | (87) less_than(all_34_0, all_26_2) = all_134_1
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | GROUND_INST: instantiating (10) with all_128_1, all_134_1,
% 17.20/3.18 | | | | | | | all_26_2, all_34_0, simplifying with (80), (87)
% 17.20/3.18 | | | | | | | gives:
% 17.20/3.18 | | | | | | | (88) all_134_1 = all_128_1
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | GROUND_INST: instantiating (10) with 0, all_134_1, all_26_2,
% 17.20/3.18 | | | | | | | all_34_0, simplifying with (75), (87) gives:
% 17.20/3.18 | | | | | | | (89) all_134_1 = 0
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | GROUND_INST: instantiating (11) with all_61_2, all_128_0,
% 17.20/3.18 | | | | | | | all_26_2, all_34_0, simplifying with (33), (81)
% 17.20/3.18 | | | | | | | gives:
% 17.20/3.18 | | | | | | | (90) all_128_0 = all_61_2
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | COMBINE_EQS: (88), (89) imply:
% 17.20/3.18 | | | | | | | (91) all_128_1 = 0
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | SIMP: (91) implies:
% 17.20/3.18 | | | | | | | (92) all_128_1 = 0
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | BETA: splitting (82) gives:
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | | Case 1:
% 17.20/3.18 | | | | | | | |
% 17.20/3.18 | | | | | | | | (93) ~ (all_128_1 = 0)
% 17.20/3.18 | | | | | | | |
% 17.20/3.18 | | | | | | | | REDUCE: (92), (93) imply:
% 17.20/3.18 | | | | | | | | (94) $false
% 17.20/3.18 | | | | | | | |
% 17.20/3.18 | | | | | | | | CLOSE: (94) is inconsistent.
% 17.20/3.18 | | | | | | | |
% 17.20/3.18 | | | | | | | Case 2:
% 17.20/3.18 | | | | | | | |
% 17.20/3.18 | | | | | | | | (95) all_128_0 = 0
% 17.20/3.18 | | | | | | | |
% 17.20/3.18 | | | | | | | | COMBINE_EQS: (90), (95) imply:
% 17.20/3.18 | | | | | | | | (96) all_61_2 = 0
% 17.20/3.18 | | | | | | | |
% 17.20/3.18 | | | | | | | | SIMP: (96) implies:
% 17.20/3.18 | | | | | | | | (97) all_61_2 = 0
% 17.20/3.18 | | | | | | | |
% 17.20/3.18 | | | | | | | | REDUCE: (57), (97) imply:
% 17.20/3.18 | | | | | | | | (98) $false
% 17.20/3.18 | | | | | | | |
% 17.20/3.18 | | | | | | | | CLOSE: (98) is inconsistent.
% 17.20/3.18 | | | | | | | |
% 17.20/3.18 | | | | | | | End of split
% 17.20/3.18 | | | | | | |
% 17.20/3.18 | | | | | | End of split
% 17.20/3.18 | | | | | |
% 17.20/3.18 | | | | | End of split
% 17.20/3.18 | | | | |
% 17.20/3.18 | | | | Case 2:
% 17.20/3.18 | | | | |
% 17.20/3.18 | | | | | (99) all_63_4 = 0
% 17.20/3.18 | | | | |
% 17.20/3.18 | | | | | REDUCE: (74), (99) imply:
% 17.20/3.18 | | | | | (100) $false
% 17.20/3.18 | | | | |
% 17.20/3.18 | | | | | CLOSE: (100) is inconsistent.
% 17.20/3.18 | | | | |
% 17.20/3.18 | | | | End of split
% 17.20/3.18 | | | |
% 17.20/3.18 | | | Case 2:
% 17.20/3.18 | | | |
% 17.20/3.18 | | | | (101) all_63_4 = 0
% 17.20/3.18 | | | |
% 17.20/3.18 | | | | REDUCE: (36), (101) imply:
% 17.20/3.18 | | | | (102) less_than(all_26_2, all_34_0) = 0
% 17.20/3.18 | | | |
% 17.20/3.19 | | | | BETA: splitting (41) gives:
% 17.20/3.19 | | | |
% 17.20/3.19 | | | | Case 1:
% 17.20/3.19 | | | | |
% 17.20/3.19 | | | | | (103) all_65_0 = 0 & all_65_1 = 0 & pair_in_list(all_26_1,
% 17.20/3.19 | | | | | all_26_3, all_65_2) = 0 & less_than(all_26_2, all_65_2) = 0
% 17.20/3.19 | | | | |
% 17.20/3.19 | | | | | ALPHA: (103) implies:
% 17.20/3.19 | | | | | (104) less_than(all_26_2, all_65_2) = 0
% 17.20/3.19 | | | | | (105) pair_in_list(all_26_1, all_26_3, all_65_2) = 0
% 17.20/3.19 | | | | |
% 17.20/3.19 | | | | | GROUND_INST: instantiating (8) with all_26_1, all_26_3, all_65_2,
% 17.20/3.19 | | | | | all_26_2, simplifying with (16), (17), (18), (40), (55),
% 17.20/3.19 | | | | | (105) gives:
% 17.20/3.19 | | | | | (106) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ?
% 17.20/3.19 | | | | | [v4: int] : (update_slb(all_26_1, all_26_2) = v1 &
% 17.20/3.19 | | | | | less_than(all_26_2, all_65_2) = v0 & $i(v2) & $i(v1) & ( ~
% 17.20/3.19 | | | | | (v0 = 0) | (v4 = 0 & v3 = 0 & pair_in_list(v1, all_26_3,
% 17.20/3.19 | | | | | v2) = 0 & less_than(all_26_2, v2) = 0)))
% 17.20/3.19 | | | | |
% 17.20/3.19 | | | | | GROUND_INST: instantiating (22) with all_65_2, simplifying with (40),
% 17.20/3.19 | | | | | (105) gives:
% 17.20/3.19 | | | | | (107) ? [v0: int] : ( ~ (v0 = 0) & less_than(all_26_2, all_65_2) =
% 17.20/3.19 | | | | | v0)
% 17.20/3.19 | | | | |
% 17.20/3.19 | | | | | DELTA: instantiating (107) with fresh symbol all_130_0 gives:
% 17.20/3.19 | | | | | (108) ~ (all_130_0 = 0) & less_than(all_26_2, all_65_2) =
% 17.20/3.19 | | | | | all_130_0
% 17.20/3.19 | | | | |
% 17.20/3.19 | | | | | ALPHA: (108) implies:
% 17.20/3.19 | | | | | (109) ~ (all_130_0 = 0)
% 17.20/3.19 | | | | | (110) less_than(all_26_2, all_65_2) = all_130_0
% 17.20/3.19 | | | | |
% 17.20/3.19 | | | | | DELTA: instantiating (106) with fresh symbols all_164_0, all_164_1,
% 17.20/3.19 | | | | | all_164_2, all_164_3, all_164_4 gives:
% 17.20/3.19 | | | | | (111) update_slb(all_26_1, all_26_2) = all_164_3 &
% 17.20/3.19 | | | | | less_than(all_26_2, all_65_2) = all_164_4 & $i(all_164_2) &
% 17.20/3.19 | | | | | $i(all_164_3) & ( ~ (all_164_4 = 0) | (all_164_0 = 0 &
% 17.20/3.19 | | | | | all_164_1 = 0 & pair_in_list(all_164_3, all_26_3,
% 17.64/3.19 | | | | | all_164_2) = 0 & less_than(all_26_2, all_164_2) = 0))
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | ALPHA: (111) implies:
% 17.64/3.19 | | | | | (112) less_than(all_26_2, all_65_2) = all_164_4
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | GROUND_INST: instantiating (10) with 0, all_164_4, all_65_2, all_26_2,
% 17.64/3.19 | | | | | simplifying with (104), (112) gives:
% 17.64/3.19 | | | | | (113) all_164_4 = 0
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | GROUND_INST: instantiating (10) with all_130_0, all_164_4, all_65_2,
% 17.64/3.19 | | | | | all_26_2, simplifying with (110), (112) gives:
% 17.64/3.19 | | | | | (114) all_164_4 = all_130_0
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | COMBINE_EQS: (113), (114) imply:
% 17.64/3.19 | | | | | (115) all_130_0 = 0
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | REDUCE: (109), (115) imply:
% 17.64/3.19 | | | | | (116) $false
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | CLOSE: (116) is inconsistent.
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | Case 2:
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | (117) strictly_less_than(all_26_3, all_26_2) = all_65_4 &
% 17.64/3.19 | | | | | less_than(all_26_2, all_34_0) = all_65_3 & ( ~ (all_65_3 = 0)
% 17.64/3.19 | | | | | | ~ (all_65_4 = 0))
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | ALPHA: (117) implies:
% 17.64/3.19 | | | | | (118) less_than(all_26_2, all_34_0) = all_65_3
% 17.64/3.19 | | | | | (119) strictly_less_than(all_26_3, all_26_2) = all_65_4
% 17.64/3.19 | | | | | (120) ~ (all_65_3 = 0) | ~ (all_65_4 = 0)
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | GROUND_INST: instantiating (10) with 0, all_65_3, all_34_0, all_26_2,
% 17.64/3.19 | | | | | simplifying with (102), (118) gives:
% 17.64/3.19 | | | | | (121) all_65_3 = 0
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | GROUND_INST: instantiating (11) with 0, all_65_4, all_26_2, all_26_3,
% 17.64/3.19 | | | | | simplifying with (18), (119) gives:
% 17.64/3.19 | | | | | (122) all_65_4 = 0
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | BETA: splitting (120) gives:
% 17.64/3.19 | | | | |
% 17.64/3.19 | | | | | Case 1:
% 17.64/3.19 | | | | | |
% 17.64/3.19 | | | | | | (123) ~ (all_65_3 = 0)
% 17.64/3.19 | | | | | |
% 17.64/3.19 | | | | | | REDUCE: (121), (123) imply:
% 17.64/3.20 | | | | | | (124) $false
% 17.64/3.20 | | | | | |
% 17.64/3.20 | | | | | | CLOSE: (124) is inconsistent.
% 17.64/3.20 | | | | | |
% 17.64/3.20 | | | | | Case 2:
% 17.64/3.20 | | | | | |
% 17.64/3.20 | | | | | | (125) ~ (all_65_4 = 0)
% 17.64/3.20 | | | | | |
% 17.64/3.20 | | | | | | REDUCE: (122), (125) imply:
% 17.64/3.20 | | | | | | (126) $false
% 17.64/3.20 | | | | | |
% 17.64/3.20 | | | | | | CLOSE: (126) is inconsistent.
% 17.64/3.20 | | | | | |
% 17.64/3.20 | | | | | End of split
% 17.64/3.20 | | | | |
% 17.64/3.20 | | | | End of split
% 17.64/3.20 | | | |
% 17.64/3.20 | | | End of split
% 17.64/3.20 | | |
% 17.64/3.20 | | Case 2:
% 17.64/3.20 | | |
% 17.64/3.20 | | | (127) ~ (all_71_1 = 0)
% 17.64/3.20 | | |
% 17.64/3.20 | | | REDUCE: (49), (127) imply:
% 17.64/3.20 | | | (128) $false
% 17.64/3.20 | | |
% 17.64/3.20 | | | CLOSE: (128) is inconsistent.
% 17.64/3.20 | | |
% 17.64/3.20 | | End of split
% 17.64/3.20 | |
% 17.64/3.20 | End of split
% 17.64/3.20 |
% 17.64/3.20 End of proof
% 17.64/3.20 % SZS output end Proof for theBenchmark
% 17.64/3.20
% 17.64/3.20 2585ms
%------------------------------------------------------------------------------