TSTP Solution File: SWV381+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV381+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 : n029.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 22:56:06 EDT 2023
% Result : Theorem 19.33s 3.28s
% Output : Proof 24.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n029.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 03:58:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.50/0.61 ________ _____
% 0.50/0.61 ___ __ \_________(_)________________________________
% 0.50/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.50/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.50/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.50/0.61
% 0.50/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.50/0.61 (2023-06-19)
% 0.50/0.61
% 0.50/0.61 (c) Philipp Rümmer, 2009-2023
% 0.50/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.50/0.61 Amanda Stjerna.
% 0.50/0.61 Free software under BSD-3-Clause.
% 0.50/0.61
% 0.50/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.50/0.61
% 0.50/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.50/0.62 Running up to 7 provers in parallel.
% 0.75/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.75/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.75/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.75/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.75/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.75/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.75/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.35/1.30 Prover 1: Preprocessing ...
% 4.35/1.32 Prover 4: Preprocessing ...
% 5.11/1.37 Prover 0: Preprocessing ...
% 5.11/1.37 Prover 3: Preprocessing ...
% 5.11/1.37 Prover 2: Preprocessing ...
% 5.11/1.37 Prover 6: Preprocessing ...
% 5.11/1.37 Prover 5: Preprocessing ...
% 13.08/2.50 Prover 1: Warning: ignoring some quantifiers
% 13.83/2.55 Prover 5: Proving ...
% 13.83/2.56 Prover 6: Proving ...
% 13.83/2.57 Prover 3: Warning: ignoring some quantifiers
% 14.28/2.60 Prover 3: Constructing countermodel ...
% 14.28/2.61 Prover 1: Constructing countermodel ...
% 14.79/2.67 Prover 2: Proving ...
% 15.47/2.84 Prover 4: Constructing countermodel ...
% 16.22/2.88 Prover 0: Proving ...
% 19.19/3.25 Prover 0: proved (2623ms)
% 19.33/3.28
% 19.33/3.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.33/3.28
% 19.33/3.28 Prover 3: stopped
% 19.33/3.29 Prover 2: stopped
% 19.33/3.29 Prover 5: stopped
% 19.33/3.30 Prover 6: stopped
% 19.33/3.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.33/3.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 19.33/3.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 19.33/3.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 19.33/3.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 20.13/3.39 Prover 8: Preprocessing ...
% 20.13/3.41 Prover 10: Preprocessing ...
% 20.13/3.43 Prover 7: Preprocessing ...
% 20.13/3.44 Prover 11: Preprocessing ...
% 20.13/3.45 Prover 13: Preprocessing ...
% 22.50/3.74 Prover 8: Warning: ignoring some quantifiers
% 23.01/3.76 Prover 7: Warning: ignoring some quantifiers
% 23.01/3.77 Prover 10: Warning: ignoring some quantifiers
% 23.13/3.81 Prover 13: Warning: ignoring some quantifiers
% 23.13/3.81 Prover 8: Constructing countermodel ...
% 23.13/3.82 Prover 10: Constructing countermodel ...
% 23.56/3.83 Prover 7: Constructing countermodel ...
% 23.56/3.85 Prover 4: Found proof (size 78)
% 23.56/3.85 Prover 4: proved (3215ms)
% 23.56/3.85 Prover 8: stopped
% 23.56/3.85 Prover 10: stopped
% 23.80/3.86 Prover 7: stopped
% 23.80/3.86 Prover 1: stopped
% 23.80/3.86 Prover 13: Constructing countermodel ...
% 23.80/3.88 Prover 13: stopped
% 23.80/3.92 Prover 11: Constructing countermodel ...
% 24.23/3.94 Prover 11: stopped
% 24.23/3.94
% 24.23/3.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.23/3.94
% 24.23/3.95 % SZS output start Proof for theBenchmark
% 24.23/3.96 Assumptions after simplification:
% 24.23/3.96 ---------------------------------
% 24.23/3.96
% 24.23/3.96 (ax10)
% 24.43/3.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 24.43/3.99 (issmallestelement_pq(v0, v1) = 0) | ~ (less_than(v1, v2) = v3) | ~ $i(v2)
% 24.43/3.99 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & contains_pq(v0, v2)
% 24.43/3.99 = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 24.43/3.99 (issmallestelement_pq(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 24.43/3.99 ? [v4: int] : ( ~ (v4 = 0) & contains_pq(v0, v3) = 0 & less_than(v1, v3) =
% 24.43/3.99 v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 24.43/3.99 (issmallestelement_pq(v0, v1) = 0) | ~ (contains_pq(v0, v2) = 0) | ~
% 24.43/3.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | less_than(v1, v2) = 0)
% 24.43/3.99
% 24.43/3.99 (ax52)
% 24.43/3.99 ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) | ?
% 24.43/3.99 [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) =
% 24.43/3.99 v3 & remove_cpq(v3, v1) = v2 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1:
% 24.43/3.99 $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 24.43/3.99 $i] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 &
% 24.43/3.99 remove_cpq(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : !
% 24.43/3.99 [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 24.43/3.99 $i] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 &
% 24.43/3.99 remove_cpq(v1, v3) = v2 & $i(v3) & $i(v2)))
% 24.43/3.99
% 24.43/3.99 (l17_co)
% 24.43/3.99 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 24.43/3.99 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & phi(v4) = 0 & i(v3) = v5 &
% 24.43/3.99 findmin_cpq_res(v3) = v6 & triple(v0, v1, v2) = v3 & findmin_cpq_eff(v3) =
% 24.43/3.99 v4 & issmallestelement_pq(v5, v6) = v7 & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 24.43/3.99 $i(v2) & $i(v1) & $i(v0))
% 24.43/3.99
% 24.43/3.99 (l17_l18)
% 24.43/4.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1,
% 24.43/4.00 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5:
% 24.43/4.00 $i] : ? [v6: any] : (phi(v5) = v6 & findmin_cpq_res(v3) = v4 &
% 24.43/4.00 findmin_cpq_eff(v3) = v5 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | ( ! [v7: $i] :
% 24.43/4.00 ( ~ (contains_cpq(v3, v7) = 0) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 =
% 24.43/4.00 0) & strictly_less_than(v7, v4) = v8)) & ! [v7: $i] : ( ~
% 24.43/4.00 (strictly_less_than(v7, v4) = 0) | ~ $i(v7) | ? [v8: int] : ( ~
% 24.43/4.00 (v8 = 0) & contains_cpq(v3, v7) = v8))))))
% 24.43/4.00
% 24.43/4.00 (l17_li56)
% 24.43/4.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 24.43/4.00 $i] : ! [v6: int] : (v6 = 0 | ~ (i(v4) = v5) | ~ (triple(v0, v1, v2) =
% 24.43/4.00 v4) | ~ (contains_pq(v5, v3) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 24.43/4.00 ~ $i(v0) | ? [v7: int] : ( ~ (v7 = 0) & contains_cpq(v4, v3) = v7)) & !
% 24.43/4.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 24.43/4.00 int] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) =
% 24.43/4.00 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ?
% 24.43/4.00 [v7: int] : ( ~ (v7 = 0) & i(v4) = v6 & contains_pq(v6, v3) = v7 & $i(v6)))
% 24.43/4.00 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 24.43/4.00 [v5: $i] : ( ~ (i(v4) = v5) | ~ (triple(v0, v1, v2) = v4) | ~
% 24.43/4.00 (contains_pq(v5, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.43/4.00 contains_cpq(v4, v3) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.43/4.00 [v3: $i] : ! [v4: $i] : ( ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1,
% 24.43/4.00 v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i]
% 24.43/4.00 : (i(v4) = v5 & contains_pq(v5, v3) = 0 & $i(v5)))
% 24.43/4.00
% 24.43/4.00 (stricly_smaller_definition)
% 24.43/4.00 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 24.43/4.00 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 24.43/4.00 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 24.43/4.00 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 |
% 24.43/4.00 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 24.43/4.00 any] : (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3
% 24.43/4.00 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 24.43/4.00 (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 24.43/4.00 any] : (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3
% 24.43/4.00 = 0) | (v4 = 0 & ~ (v2 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 24.43/4.00 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 24.43/4.00 ? [v4: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & (
% 24.43/4.00 ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 24.43/4.00 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : (
% 24.43/4.00 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0:
% 24.43/4.00 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 24.43/4.00 [v2: any] : ? [v3: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1,
% 24.43/4.00 v0) = v2 & (v3 = 0 | v2 = 0)))
% 24.43/4.00
% 24.43/4.00 (totality)
% 24.43/4.01 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) =
% 24.43/4.01 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : !
% 24.43/4.01 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) |
% 24.43/4.01 ~ $i(v0) | less_than(v1, v0) = 0)
% 24.43/4.01
% 24.43/4.01 (function-axioms)
% 24.43/4.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 24.43/4.02 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 24.43/4.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.43/4.02 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 24.43/4.02 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.43/4.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.43/4.02 (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) &
% 24.43/4.02 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 24.43/4.02 $i] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~
% 24.43/4.02 (pi_sharp_find_min(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.43/4.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.43/4.02 (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0:
% 24.43/4.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.43/4.02 : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) =
% 24.43/4.02 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 24.43/4.02 ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] :
% 24.43/4.02 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) =
% 24.43/4.02 v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.43/4.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.43/4.02 (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0: $i]
% 24.43/4.02 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2)
% 24.43/4.02 = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 24.43/4.02 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~
% 24.43/4.02 (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.43/4.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 24.43/4.02 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 24.43/4.02 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 24.43/4.02 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.43/4.02 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 24.43/4.02 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 24.43/4.02 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 24.43/4.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.43/4.02 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 24.43/4.02 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.43/4.02 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 24.43/4.02 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 24.43/4.02 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.43/4.02 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~
% 24.43/4.02 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 24.43/4.02 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~
% 24.43/4.02 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 24.43/4.02 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~
% 24.43/4.02 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 24.43/4.02 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~
% 24.43/4.02 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 24.43/4.02 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) =
% 24.43/4.02 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 24.43/4.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~
% 24.43/4.02 (issmallestelement_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.43/4.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.43/4.02 (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0: $i] :
% 24.43/4.02 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pq(v3, v2) =
% 24.43/4.02 v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.43/4.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.43/4.02 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 24.43/4.02 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 24.43/4.02 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 24.43/4.02 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 24.43/4.02 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0: MultipleValueBool] :
% 24.43/4.02 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_removemin(v2) =
% 24.43/4.02 v1) | ~ (pi_removemin(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.43/4.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~
% 24.43/4.02 (pi_find_min(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 24.43/4.02 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 24.43/4.02 $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2)
% 24.43/4.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.43/4.02 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] :
% 24.43/4.02 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~
% 24.43/4.02 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.43/4.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2)
% 24.43/4.02 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 24.43/4.02 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & !
% 24.43/4.02 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) =
% 24.43/4.02 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 24.43/4.02 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2)
% 24.43/4.02 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 24.43/4.02 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) =
% 24.43/4.02 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 24.43/4.02 $i] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0))
% 24.43/4.02
% 24.43/4.02 Further assumptions not needed in the proof:
% 24.43/4.02 --------------------------------------------
% 24.43/4.02 ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax21, ax22, ax23,
% 24.43/4.02 ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, ax36,
% 24.43/4.02 ax37, ax38, ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49,
% 24.43/4.02 ax50, ax51, ax53, ax54, ax55, ax56, ax57, ax58, ax59, ax6, ax60, ax61, ax62,
% 24.43/4.02 ax7, ax8, ax9, bottom_smallest, reflexivity, transitivity
% 24.43/4.02
% 24.43/4.02 Those formulas are unsatisfiable:
% 24.43/4.02 ---------------------------------
% 24.43/4.02
% 24.43/4.02 Begin of proof
% 24.43/4.02 |
% 24.43/4.02 | ALPHA: (totality) implies:
% 24.43/4.02 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1,
% 24.43/4.02 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0)
% 24.43/4.02 |
% 24.43/4.02 | ALPHA: (stricly_smaller_definition) implies:
% 24.43/4.02 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v0, v1) = v2)
% 24.43/4.02 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 24.43/4.02 | (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( ~ (v3 =
% 24.43/4.02 | 0) | (v2 = 0 & ~ (v4 = 0)))))
% 24.43/4.02 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v1, v0) = v2)
% 24.43/4.02 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 24.43/4.02 | (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 =
% 24.43/4.02 | 0) | (v4 = 0 & ~ (v2 = 0)))))
% 24.43/4.02 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1,
% 24.43/4.02 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 24.43/4.02 | (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 24.43/4.02 | 0) | v4 = 0)))
% 24.43/4.02 |
% 24.43/4.02 | ALPHA: (ax10) implies:
% 24.43/4.02 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 24.43/4.02 | (issmallestelement_pq(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 24.43/4.02 | $i] : ? [v4: int] : ( ~ (v4 = 0) & contains_pq(v0, v3) = 0 &
% 24.43/4.02 | less_than(v1, v3) = v4 & $i(v3)))
% 24.43/4.02 |
% 24.43/4.02 | ALPHA: (ax52) implies:
% 24.43/4.03 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0)
% 24.43/4.03 | | ? [v2: $i] : ? [v3: $i] : (findmin_cpq_res(v0) = v3 &
% 24.43/4.03 | removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2 & $i(v3) &
% 24.43/4.03 | $i(v2)))
% 24.43/4.03 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0)
% 24.43/4.03 | | ? [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 &
% 24.43/4.03 | findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2 & $i(v3) &
% 24.43/4.03 | $i(v2)))
% 24.43/4.03 |
% 24.43/4.03 | ALPHA: (l17_li56) implies:
% 24.43/4.03 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 24.43/4.03 | ! [v5: $i] : ( ~ (i(v4) = v5) | ~ (triple(v0, v1, v2) = v4) | ~
% 24.43/4.03 | (contains_pq(v5, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 24.43/4.03 | $i(v0) | contains_cpq(v4, v3) = 0)
% 24.43/4.03 |
% 24.43/4.03 | ALPHA: (function-axioms) implies:
% 24.43/4.03 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.43/4.03 | (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 24.43/4.03 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.43/4.03 | (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 24.43/4.03 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.43/4.03 | : (v1 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0))
% 24.43/4.03 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.43/4.03 | : ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~
% 24.43/4.03 | (less_than(v3, v2) = v0))
% 24.43/4.03 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.43/4.03 | : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~
% 24.43/4.03 | (strictly_less_than(v3, v2) = v0))
% 24.43/4.03 |
% 24.43/4.03 | DELTA: instantiating (l17_co) with fresh symbols all_70_0, all_70_1, all_70_2,
% 24.43/4.03 | all_70_3, all_70_4, all_70_5, all_70_6, all_70_7 gives:
% 24.43/4.03 | (14) ~ (all_70_0 = 0) & phi(all_70_3) = 0 & i(all_70_4) = all_70_2 &
% 24.43/4.03 | findmin_cpq_res(all_70_4) = all_70_1 & triple(all_70_7, all_70_6,
% 24.43/4.03 | all_70_5) = all_70_4 & findmin_cpq_eff(all_70_4) = all_70_3 &
% 24.43/4.03 | issmallestelement_pq(all_70_2, all_70_1) = all_70_0 & $i(all_70_1) &
% 24.43/4.03 | $i(all_70_2) & $i(all_70_3) & $i(all_70_4) & $i(all_70_5) &
% 24.43/4.03 | $i(all_70_6) & $i(all_70_7)
% 24.43/4.03 |
% 24.43/4.03 | ALPHA: (14) implies:
% 24.43/4.03 | (15) ~ (all_70_0 = 0)
% 24.43/4.03 | (16) $i(all_70_7)
% 24.43/4.03 | (17) $i(all_70_6)
% 24.43/4.03 | (18) $i(all_70_5)
% 24.43/4.03 | (19) $i(all_70_4)
% 24.43/4.03 | (20) $i(all_70_2)
% 24.43/4.03 | (21) $i(all_70_1)
% 24.43/4.03 | (22) issmallestelement_pq(all_70_2, all_70_1) = all_70_0
% 24.43/4.03 | (23) findmin_cpq_eff(all_70_4) = all_70_3
% 24.43/4.03 | (24) triple(all_70_7, all_70_6, all_70_5) = all_70_4
% 24.43/4.03 | (25) findmin_cpq_res(all_70_4) = all_70_1
% 24.43/4.03 | (26) i(all_70_4) = all_70_2
% 24.43/4.03 | (27) phi(all_70_3) = 0
% 24.43/4.03 |
% 24.43/4.03 | GROUND_INST: instantiating (5) with all_70_2, all_70_1, all_70_0, simplifying
% 24.43/4.03 | with (20), (21), (22) gives:
% 24.43/4.03 | (28) all_70_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 24.43/4.03 | contains_pq(all_70_2, v0) = 0 & less_than(all_70_1, v0) = v1 &
% 24.43/4.03 | $i(v0))
% 24.43/4.03 |
% 24.43/4.03 | GROUND_INST: instantiating (6) with all_70_4, all_70_3, simplifying with (19),
% 24.43/4.04 | (23) gives:
% 24.43/4.04 | (29) ? [v0: $i] : ? [v1: $i] : (findmin_cpq_res(all_70_4) = v1 &
% 24.43/4.04 | removemin_cpq_eff(all_70_4) = v0 & remove_cpq(all_70_3, v1) = v0 &
% 24.43/4.04 | $i(v1) & $i(v0))
% 24.43/4.04 |
% 24.43/4.04 | GROUND_INST: instantiating (l17_l18) with all_70_7, all_70_6, all_70_5,
% 24.43/4.04 | all_70_4, simplifying with (16), (17), (18), (24) gives:
% 24.43/4.04 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (phi(v1) = v2 &
% 24.43/4.04 | findmin_cpq_res(all_70_4) = v0 & findmin_cpq_eff(all_70_4) = v1 &
% 24.43/4.04 | $i(v1) & $i(v0) & ( ~ (v2 = 0) | ( ! [v3: $i] : ( ~
% 24.43/4.04 | (contains_cpq(all_70_4, v3) = 0) | ~ $i(v3) | ? [v4: int] :
% 24.43/4.04 | ( ~ (v4 = 0) & strictly_less_than(v3, v0) = v4)) & ! [v3: $i]
% 24.43/4.04 | : ( ~ (strictly_less_than(v3, v0) = 0) | ~ $i(v3) | ? [v4:
% 24.43/4.04 | int] : ( ~ (v4 = 0) & contains_cpq(all_70_4, v3) = v4)))))
% 24.43/4.04 |
% 24.43/4.04 | GROUND_INST: instantiating (7) with all_70_4, all_70_1, simplifying with (19),
% 24.43/4.04 | (25) gives:
% 24.72/4.04 | (31) ? [v0: $i] : ? [v1: $i] : (removemin_cpq_eff(all_70_4) = v0 &
% 24.72/4.04 | findmin_cpq_eff(all_70_4) = v1 & remove_cpq(v1, all_70_1) = v0 &
% 24.72/4.04 | $i(v1) & $i(v0))
% 24.72/4.04 |
% 24.72/4.04 | DELTA: instantiating (29) with fresh symbols all_80_0, all_80_1 gives:
% 24.72/4.04 | (32) findmin_cpq_res(all_70_4) = all_80_0 & removemin_cpq_eff(all_70_4) =
% 24.72/4.04 | all_80_1 & remove_cpq(all_70_3, all_80_0) = all_80_1 & $i(all_80_0) &
% 24.72/4.04 | $i(all_80_1)
% 24.72/4.04 |
% 24.72/4.04 | ALPHA: (32) implies:
% 24.72/4.04 | (33) $i(all_80_0)
% 24.72/4.04 | (34) findmin_cpq_res(all_70_4) = all_80_0
% 24.72/4.04 |
% 24.72/4.04 | DELTA: instantiating (31) with fresh symbols all_90_0, all_90_1 gives:
% 24.72/4.04 | (35) removemin_cpq_eff(all_70_4) = all_90_1 & findmin_cpq_eff(all_70_4) =
% 24.72/4.04 | all_90_0 & remove_cpq(all_90_0, all_70_1) = all_90_1 & $i(all_90_0) &
% 24.72/4.04 | $i(all_90_1)
% 24.72/4.04 |
% 24.72/4.04 | ALPHA: (35) implies:
% 24.72/4.04 | (36) findmin_cpq_eff(all_70_4) = all_90_0
% 24.72/4.04 |
% 24.72/4.04 | DELTA: instantiating (30) with fresh symbols all_92_0, all_92_1, all_92_2
% 24.72/4.04 | gives:
% 24.72/4.04 | (37) phi(all_92_1) = all_92_0 & findmin_cpq_res(all_70_4) = all_92_2 &
% 24.72/4.04 | findmin_cpq_eff(all_70_4) = all_92_1 & $i(all_92_1) & $i(all_92_2) & (
% 24.72/4.04 | ~ (all_92_0 = 0) | ( ! [v0: $i] : ( ~ (contains_cpq(all_70_4, v0) =
% 24.72/4.04 | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 24.72/4.04 | strictly_less_than(v0, all_92_2) = v1)) & ! [v0: $i] : ( ~
% 24.72/4.04 | (strictly_less_than(v0, all_92_2) = 0) | ~ $i(v0) | ? [v1:
% 24.72/4.04 | int] : ( ~ (v1 = 0) & contains_cpq(all_70_4, v0) = v1))))
% 24.72/4.04 |
% 24.72/4.04 | ALPHA: (37) implies:
% 24.72/4.04 | (38) findmin_cpq_eff(all_70_4) = all_92_1
% 24.72/4.04 | (39) findmin_cpq_res(all_70_4) = all_92_2
% 24.72/4.04 | (40) phi(all_92_1) = all_92_0
% 24.72/4.04 | (41) ~ (all_92_0 = 0) | ( ! [v0: $i] : ( ~ (contains_cpq(all_70_4, v0) =
% 24.72/4.04 | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 24.72/4.04 | strictly_less_than(v0, all_92_2) = v1)) & ! [v0: $i] : ( ~
% 24.72/4.04 | (strictly_less_than(v0, all_92_2) = 0) | ~ $i(v0) | ? [v1: int]
% 24.72/4.04 | : ( ~ (v1 = 0) & contains_cpq(all_70_4, v0) = v1)))
% 24.72/4.04 |
% 24.72/4.04 | BETA: splitting (28) gives:
% 24.72/4.04 |
% 24.72/4.04 | Case 1:
% 24.72/4.04 | |
% 24.72/4.04 | | (42) all_70_0 = 0
% 24.72/4.04 | |
% 24.72/4.04 | | REDUCE: (15), (42) imply:
% 24.72/4.04 | | (43) $false
% 24.72/4.04 | |
% 24.72/4.04 | | CLOSE: (43) is inconsistent.
% 24.72/4.04 | |
% 24.72/4.04 | Case 2:
% 24.72/4.04 | |
% 24.72/4.05 | | (44) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & contains_pq(all_70_2,
% 24.72/4.05 | | v0) = 0 & less_than(all_70_1, v0) = v1 & $i(v0))
% 24.72/4.05 | |
% 24.72/4.05 | | DELTA: instantiating (44) with fresh symbols all_101_0, all_101_1 gives:
% 24.72/4.05 | | (45) ~ (all_101_0 = 0) & contains_pq(all_70_2, all_101_1) = 0 &
% 24.72/4.05 | | less_than(all_70_1, all_101_1) = all_101_0 & $i(all_101_1)
% 24.72/4.05 | |
% 24.72/4.05 | | ALPHA: (45) implies:
% 24.72/4.05 | | (46) ~ (all_101_0 = 0)
% 24.72/4.05 | | (47) $i(all_101_1)
% 24.72/4.05 | | (48) less_than(all_70_1, all_101_1) = all_101_0
% 24.72/4.05 | | (49) contains_pq(all_70_2, all_101_1) = 0
% 24.72/4.05 | |
% 24.72/4.05 | | GROUND_INST: instantiating (9) with all_70_3, all_92_1, all_70_4,
% 24.72/4.05 | | simplifying with (23), (38) gives:
% 24.72/4.05 | | (50) all_92_1 = all_70_3
% 24.72/4.05 | |
% 24.72/4.05 | | GROUND_INST: instantiating (9) with all_90_0, all_92_1, all_70_4,
% 24.72/4.05 | | simplifying with (36), (38) gives:
% 24.72/4.05 | | (51) all_92_1 = all_90_0
% 24.72/4.05 | |
% 24.72/4.05 | | GROUND_INST: instantiating (10) with all_70_1, all_92_2, all_70_4,
% 24.72/4.05 | | simplifying with (25), (39) gives:
% 24.72/4.05 | | (52) all_92_2 = all_70_1
% 24.72/4.05 | |
% 24.72/4.05 | | GROUND_INST: instantiating (10) with all_80_0, all_92_2, all_70_4,
% 24.72/4.05 | | simplifying with (34), (39) gives:
% 24.72/4.05 | | (53) all_92_2 = all_80_0
% 24.72/4.05 | |
% 24.72/4.05 | | COMBINE_EQS: (50), (51) imply:
% 24.72/4.05 | | (54) all_90_0 = all_70_3
% 24.72/4.05 | |
% 24.72/4.05 | | COMBINE_EQS: (52), (53) imply:
% 24.72/4.05 | | (55) all_80_0 = all_70_1
% 24.72/4.05 | |
% 24.72/4.05 | | REDUCE: (40), (50) imply:
% 24.72/4.05 | | (56) phi(all_70_3) = all_92_0
% 24.72/4.05 | |
% 24.72/4.05 | | GROUND_INST: instantiating (11) with 0, all_92_0, all_70_3, simplifying with
% 24.72/4.05 | | (27), (56) gives:
% 24.72/4.05 | | (57) all_92_0 = 0
% 24.72/4.05 | |
% 24.72/4.05 | | BETA: splitting (41) gives:
% 24.72/4.05 | |
% 24.72/4.05 | | Case 1:
% 24.72/4.05 | | |
% 24.72/4.05 | | | (58) ~ (all_92_0 = 0)
% 24.72/4.05 | | |
% 24.72/4.05 | | | REDUCE: (57), (58) imply:
% 24.72/4.05 | | | (59) $false
% 24.72/4.05 | | |
% 24.72/4.05 | | | CLOSE: (59) is inconsistent.
% 24.72/4.05 | | |
% 24.72/4.05 | | Case 2:
% 24.72/4.05 | | |
% 24.72/4.05 | | | (60) ! [v0: $i] : ( ~ (contains_cpq(all_70_4, v0) = 0) | ~ $i(v0) |
% 24.72/4.05 | | | ? [v1: int] : ( ~ (v1 = 0) & strictly_less_than(v0, all_92_2) =
% 24.72/4.05 | | | v1)) & ! [v0: $i] : ( ~ (strictly_less_than(v0, all_92_2) =
% 24.72/4.05 | | | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 24.72/4.05 | | | contains_cpq(all_70_4, v0) = v1))
% 24.72/4.05 | | |
% 24.72/4.05 | | | ALPHA: (60) implies:
% 24.72/4.05 | | | (61) ! [v0: $i] : ( ~ (contains_cpq(all_70_4, v0) = 0) | ~ $i(v0) |
% 24.72/4.05 | | | ? [v1: int] : ( ~ (v1 = 0) & strictly_less_than(v0, all_92_2) =
% 24.72/4.05 | | | v1))
% 24.72/4.05 | | |
% 24.72/4.05 | | | GROUND_INST: instantiating (1) with all_101_1, all_70_1, all_101_0,
% 24.72/4.05 | | | simplifying with (21), (47), (48) gives:
% 24.72/4.05 | | | (62) all_101_0 = 0 | less_than(all_101_1, all_70_1) = 0
% 24.72/4.05 | | |
% 24.72/4.05 | | | GROUND_INST: instantiating (4) with all_101_1, all_70_1, all_101_0,
% 24.72/4.05 | | | simplifying with (21), (47), (48) gives:
% 24.72/4.05 | | | (63) all_101_0 = 0 | ? [v0: any] : ? [v1: any] :
% 24.72/4.05 | | | (strictly_less_than(all_101_1, all_70_1) = v1 &
% 24.72/4.05 | | | less_than(all_101_1, all_70_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 24.72/4.05 | | |
% 24.72/4.05 | | | GROUND_INST: instantiating (3) with all_101_1, all_70_1, all_101_0,
% 24.72/4.05 | | | simplifying with (21), (47), (48) gives:
% 24.72/4.05 | | | (64) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_101_1,
% 24.72/4.05 | | | all_70_1) = v0 & less_than(all_101_1, all_70_1) = v1 & ( ~ (v0
% 24.72/4.05 | | | = 0) | (v1 = 0 & ~ (all_101_0 = 0))))
% 24.72/4.05 | | |
% 24.72/4.05 | | | GROUND_INST: instantiating (2) with all_70_1, all_101_1, all_101_0,
% 24.72/4.05 | | | simplifying with (21), (47), (48) gives:
% 24.72/4.05 | | | (65) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_70_1,
% 24.72/4.05 | | | all_101_1) = v0 & less_than(all_101_1, all_70_1) = v1 & ( ~
% 24.72/4.05 | | | (v0 = 0) | (all_101_0 = 0 & ~ (v1 = 0))))
% 24.72/4.05 | | |
% 24.72/4.06 | | | GROUND_INST: instantiating (8) with all_70_7, all_70_6, all_70_5,
% 24.72/4.06 | | | all_101_1, all_70_4, all_70_2, simplifying with (16), (17),
% 24.72/4.06 | | | (18), (24), (26), (47), (49) gives:
% 24.72/4.06 | | | (66) contains_cpq(all_70_4, all_101_1) = 0
% 24.72/4.06 | | |
% 24.72/4.06 | | | DELTA: instantiating (65) with fresh symbols all_144_0, all_144_1 gives:
% 24.82/4.06 | | | (67) strictly_less_than(all_70_1, all_101_1) = all_144_1 &
% 24.82/4.06 | | | less_than(all_101_1, all_70_1) = all_144_0 & ( ~ (all_144_1 = 0) |
% 24.82/4.06 | | | (all_101_0 = 0 & ~ (all_144_0 = 0)))
% 24.82/4.06 | | |
% 24.82/4.06 | | | ALPHA: (67) implies:
% 24.82/4.06 | | | (68) less_than(all_101_1, all_70_1) = all_144_0
% 24.82/4.06 | | |
% 24.82/4.06 | | | DELTA: instantiating (64) with fresh symbols all_146_0, all_146_1 gives:
% 24.82/4.06 | | | (69) strictly_less_than(all_101_1, all_70_1) = all_146_1 &
% 24.82/4.06 | | | less_than(all_101_1, all_70_1) = all_146_0 & ( ~ (all_146_1 = 0) |
% 24.82/4.06 | | | (all_146_0 = 0 & ~ (all_101_0 = 0)))
% 24.82/4.06 | | |
% 24.82/4.06 | | | ALPHA: (69) implies:
% 24.82/4.06 | | | (70) less_than(all_101_1, all_70_1) = all_146_0
% 24.82/4.06 | | | (71) strictly_less_than(all_101_1, all_70_1) = all_146_1
% 24.82/4.06 | | |
% 24.82/4.06 | | | BETA: splitting (62) gives:
% 24.82/4.06 | | |
% 24.82/4.06 | | | Case 1:
% 24.82/4.06 | | | |
% 24.82/4.06 | | | | (72) less_than(all_101_1, all_70_1) = 0
% 24.82/4.06 | | | |
% 24.82/4.06 | | | | GROUND_INST: instantiating (12) with all_144_0, all_146_0, all_70_1,
% 24.82/4.06 | | | | all_101_1, simplifying with (68), (70) gives:
% 24.82/4.06 | | | | (73) all_146_0 = all_144_0
% 24.82/4.06 | | | |
% 24.82/4.06 | | | | GROUND_INST: instantiating (12) with 0, all_146_0, all_70_1, all_101_1,
% 24.82/4.06 | | | | simplifying with (70), (72) gives:
% 24.82/4.06 | | | | (74) all_146_0 = 0
% 24.82/4.06 | | | |
% 24.82/4.06 | | | | COMBINE_EQS: (73), (74) imply:
% 24.82/4.06 | | | | (75) all_144_0 = 0
% 24.82/4.06 | | | |
% 24.82/4.06 | | | | SIMP: (75) implies:
% 24.82/4.06 | | | | (76) all_144_0 = 0
% 24.82/4.06 | | | |
% 24.82/4.06 | | | | BETA: splitting (63) gives:
% 24.82/4.06 | | | |
% 24.82/4.06 | | | | Case 1:
% 24.82/4.06 | | | | |
% 24.82/4.06 | | | | | (77) all_101_0 = 0
% 24.82/4.06 | | | | |
% 24.82/4.06 | | | | | REDUCE: (46), (77) imply:
% 24.82/4.06 | | | | | (78) $false
% 24.82/4.06 | | | | |
% 24.82/4.06 | | | | | CLOSE: (78) is inconsistent.
% 24.82/4.06 | | | | |
% 24.82/4.06 | | | | Case 2:
% 24.82/4.06 | | | | |
% 24.82/4.06 | | | | | (79) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_101_1,
% 24.82/4.06 | | | | | all_70_1) = v1 & less_than(all_101_1, all_70_1) = v0 & ( ~
% 24.82/4.06 | | | | | (v0 = 0) | v1 = 0))
% 24.82/4.06 | | | | |
% 24.82/4.06 | | | | | DELTA: instantiating (79) with fresh symbols all_176_0, all_176_1
% 24.82/4.06 | | | | | gives:
% 24.82/4.06 | | | | | (80) strictly_less_than(all_101_1, all_70_1) = all_176_0 &
% 24.82/4.06 | | | | | less_than(all_101_1, all_70_1) = all_176_1 & ( ~ (all_176_1 =
% 24.82/4.06 | | | | | 0) | all_176_0 = 0)
% 24.82/4.06 | | | | |
% 24.82/4.06 | | | | | ALPHA: (80) implies:
% 24.82/4.06 | | | | | (81) less_than(all_101_1, all_70_1) = all_176_1
% 24.82/4.06 | | | | | (82) strictly_less_than(all_101_1, all_70_1) = all_176_0
% 24.82/4.06 | | | | | (83) ~ (all_176_1 = 0) | all_176_0 = 0
% 24.82/4.06 | | | | |
% 24.82/4.06 | | | | | GROUND_INST: instantiating (12) with 0, all_176_1, all_70_1,
% 24.82/4.06 | | | | | all_101_1, simplifying with (72), (81) gives:
% 24.82/4.06 | | | | | (84) all_176_1 = 0
% 24.82/4.06 | | | | |
% 24.82/4.06 | | | | | GROUND_INST: instantiating (13) with all_146_1, all_176_0, all_70_1,
% 24.82/4.06 | | | | | all_101_1, simplifying with (71), (82) gives:
% 24.82/4.06 | | | | | (85) all_176_0 = all_146_1
% 24.82/4.06 | | | | |
% 24.82/4.06 | | | | | BETA: splitting (83) gives:
% 24.82/4.06 | | | | |
% 24.82/4.06 | | | | | Case 1:
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | (86) ~ (all_176_1 = 0)
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | REDUCE: (84), (86) imply:
% 24.82/4.06 | | | | | | (87) $false
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | CLOSE: (87) is inconsistent.
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | Case 2:
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | (88) all_176_0 = 0
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | COMBINE_EQS: (85), (88) imply:
% 24.82/4.06 | | | | | | (89) all_146_1 = 0
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | REDUCE: (71), (89) imply:
% 24.82/4.06 | | | | | | (90) strictly_less_than(all_101_1, all_70_1) = 0
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | GROUND_INST: instantiating (61) with all_101_1, simplifying with
% 24.82/4.06 | | | | | | (47), (66) gives:
% 24.82/4.06 | | | | | | (91) ? [v0: int] : ( ~ (v0 = 0) & strictly_less_than(all_101_1,
% 24.82/4.06 | | | | | | all_92_2) = v0)
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | DELTA: instantiating (91) with fresh symbol all_192_0 gives:
% 24.82/4.06 | | | | | | (92) ~ (all_192_0 = 0) & strictly_less_than(all_101_1, all_92_2)
% 24.82/4.06 | | | | | | = all_192_0
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | ALPHA: (92) implies:
% 24.82/4.06 | | | | | | (93) ~ (all_192_0 = 0)
% 24.82/4.06 | | | | | | (94) strictly_less_than(all_101_1, all_92_2) = all_192_0
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | REDUCE: (52), (94) imply:
% 24.82/4.06 | | | | | | (95) strictly_less_than(all_101_1, all_70_1) = all_192_0
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | GROUND_INST: instantiating (13) with 0, all_192_0, all_70_1,
% 24.82/4.06 | | | | | | all_101_1, simplifying with (90), (95) gives:
% 24.82/4.06 | | | | | | (96) all_192_0 = 0
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | REDUCE: (93), (96) imply:
% 24.82/4.06 | | | | | | (97) $false
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | | CLOSE: (97) is inconsistent.
% 24.82/4.06 | | | | | |
% 24.82/4.06 | | | | | End of split
% 24.82/4.06 | | | | |
% 24.82/4.07 | | | | End of split
% 24.82/4.07 | | | |
% 24.82/4.07 | | | Case 2:
% 24.82/4.07 | | | |
% 24.82/4.07 | | | | (98) all_101_0 = 0
% 24.82/4.07 | | | |
% 24.82/4.07 | | | | REDUCE: (46), (98) imply:
% 24.82/4.07 | | | | (99) $false
% 24.82/4.07 | | | |
% 24.82/4.07 | | | | CLOSE: (99) is inconsistent.
% 24.82/4.07 | | | |
% 24.82/4.07 | | | End of split
% 24.82/4.07 | | |
% 24.82/4.07 | | End of split
% 24.82/4.07 | |
% 24.82/4.07 | End of split
% 24.82/4.07 |
% 24.82/4.07 End of proof
% 24.82/4.07 % SZS output end Proof for theBenchmark
% 24.82/4.07
% 24.82/4.07 3458ms
%------------------------------------------------------------------------------