TSTP Solution File: SWV370+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV370+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 : n031.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 22:56:03 EDT 2023
% Result : Theorem 13.59s 2.66s
% Output : Proof 17.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n031.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 05:16:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.65 Running up to 7 provers in parallel.
% 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.69/1.33 Prover 1: Preprocessing ...
% 3.69/1.33 Prover 4: Preprocessing ...
% 3.69/1.37 Prover 6: Preprocessing ...
% 3.69/1.37 Prover 0: Preprocessing ...
% 3.69/1.37 Prover 5: Preprocessing ...
% 3.69/1.37 Prover 2: Preprocessing ...
% 3.69/1.37 Prover 3: Preprocessing ...
% 9.46/2.12 Prover 1: Warning: ignoring some quantifiers
% 10.51/2.20 Prover 3: Warning: ignoring some quantifiers
% 10.51/2.21 Prover 6: Proving ...
% 10.84/2.24 Prover 1: Constructing countermodel ...
% 10.84/2.24 Prover 3: Constructing countermodel ...
% 10.84/2.25 Prover 5: Proving ...
% 10.84/2.28 Prover 2: Proving ...
% 10.84/2.30 Prover 4: Constructing countermodel ...
% 12.39/2.46 Prover 0: Proving ...
% 13.59/2.66 Prover 3: proved (1989ms)
% 13.59/2.66
% 13.59/2.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.59/2.66
% 13.59/2.67 Prover 2: stopped
% 14.00/2.68 Prover 0: stopped
% 14.00/2.68 Prover 6: stopped
% 14.00/2.68 Prover 5: stopped
% 14.00/2.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.00/2.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.00/2.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.00/2.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.00/2.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.56/2.76 Prover 7: Preprocessing ...
% 14.69/2.78 Prover 8: Preprocessing ...
% 14.69/2.79 Prover 11: Preprocessing ...
% 14.69/2.80 Prover 13: Preprocessing ...
% 14.69/2.81 Prover 10: Preprocessing ...
% 15.74/2.92 Prover 1: Found proof (size 75)
% 15.74/2.92 Prover 1: proved (2257ms)
% 15.74/2.93 Prover 4: stopped
% 15.74/2.94 Prover 13: stopped
% 15.74/2.96 Prover 7: Warning: ignoring some quantifiers
% 15.74/2.97 Prover 10: Warning: ignoring some quantifiers
% 16.16/2.99 Prover 7: Constructing countermodel ...
% 16.16/3.00 Prover 10: Constructing countermodel ...
% 16.16/3.00 Prover 8: Warning: ignoring some quantifiers
% 16.16/3.01 Prover 10: stopped
% 16.16/3.02 Prover 8: Constructing countermodel ...
% 16.16/3.03 Prover 7: stopped
% 16.16/3.03 Prover 8: stopped
% 16.69/3.12 Prover 11: Constructing countermodel ...
% 16.69/3.14 Prover 11: stopped
% 16.69/3.14
% 16.69/3.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.69/3.14
% 16.69/3.15 % SZS output start Proof for theBenchmark
% 16.69/3.16 Assumptions after simplification:
% 16.69/3.16 ---------------------------------
% 16.69/3.16
% 16.69/3.16 (ax21)
% 16.69/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.69/3.19 $i] : ! [v6: int] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | ~ (pair(v1,
% 16.69/3.19 v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 16.69/3.19 $i(v1) | ~ $i(v0) | ( ~ (v2 = v1) & ? [v7: int] : ( ~ (v7 = 0) &
% 16.69/3.19 contains_slb(v0, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.69/3.19 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = v1 | ~ (contains_slb(v5, v2)
% 16.69/3.19 = 0) | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) |
% 16.69/3.19 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | contains_slb(v0, v2) = 0)
% 16.69/3.19
% 16.69/3.19 (ax37)
% 16.69/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.69/3.19 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~
% 16.69/3.19 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) |
% 16.69/3.19 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10:
% 16.69/3.19 $i] : ? [v11: any] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 &
% 16.69/3.19 check_cpq(v7) = v9 & less_than(v4, v3) = v8 & $i(v10) & ( ~ (v8 = 0) | ((
% 16.69/3.19 ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0)))))
% 16.69/3.19
% 16.69/3.19 (ax39)
% 16.69/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.69/3.19 int] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) =
% 16.69/3.19 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~
% 16.69/3.19 (v6 = 0) & contains_slb(v1, v3) = v6)) & ! [v0: $i] : ! [v1: $i] : !
% 16.69/3.19 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (contains_cpq(v4, v3) = 0) | ~
% 16.69/3.19 (triple(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 16.69/3.19 contains_slb(v1, v3) = 0)
% 16.69/3.19
% 16.69/3.19 (ax55)
% 16.69/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.69/3.19 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~
% 16.69/3.19 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) |
% 16.69/3.19 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i]
% 16.69/3.19 : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) =
% 16.69/3.19 v8 & $i(v10) & $i(v9) & $i(v8)))
% 16.69/3.20
% 16.69/3.20 (ax9)
% 16.69/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 16.69/3.20 | ~ (contains_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) | ~ $i(v2) |
% 16.69/3.20 ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v1) & ? [v5: int] : ( ~ (v5 = 0) &
% 16.69/3.20 contains_pq(v0, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.69/3.20 ! [v3: $i] : (v2 = v1 | ~ (contains_pq(v3, v2) = 0) | ~ (insert_pq(v0, v1) =
% 16.69/3.20 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | contains_pq(v0, v2) = 0)
% 16.69/3.20
% 16.69/3.20 (l6_co)
% 16.69/3.20 ? [v0: $i] : ($i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 16.69/3.20 : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (i(v4) = v5) | ~ (triple(v1,
% 16.69/3.20 v0, v2) = v4) | ~ (contains_pq(v5, v3) = v6) | ~ $i(v3) | ~ $i(v2)
% 16.69/3.20 | ~ $i(v1) | ? [v7: int] : ( ~ (v7 = 0) & contains_cpq(v4, v3) = v7)) &
% 16.69/3.20 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 16.69/3.20 (i(v4) = v5) | ~ (triple(v1, v0, v2) = v4) | ~ (contains_pq(v5, v3) = 0)
% 16.69/3.20 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | contains_cpq(v4, v3) = 0) & ? [v1:
% 16.69/3.20 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 16.69/3.20 : ? [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: any] :
% 16.69/3.20 (i(v8) = v10 & contains_cpq(v8, v5) = v9 & triple(v1, v7, v2) = v8 &
% 16.69/3.20 pair(v3, v4) = v6 & insert_slb(v0, v6) = v7 & contains_pq(v10, v5) = v11 &
% 16.69/3.20 $i(v10) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 16.69/3.20 $i(v1) & ((v11 = 0 & ~ (v9 = 0)) | (v9 = 0 & ~ (v11 = 0)))))
% 16.69/3.20
% 16.69/3.20 (function-axioms)
% 16.69/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 16.69/3.21 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 16.69/3.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.69/3.21 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 16.69/3.21 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.69/3.21 (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) &
% 16.69/3.21 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 16.69/3.21 $i] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~
% 16.69/3.21 (pi_sharp_find_min(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.69/3.21 (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0:
% 16.69/3.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.69/3.21 : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) =
% 16.69/3.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 16.69/3.21 ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] :
% 16.69/3.21 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) =
% 16.69/3.21 v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.69/3.21 (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0: $i]
% 16.69/3.21 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2)
% 16.69/3.21 = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 16.69/3.21 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~
% 16.69/3.21 (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 16.69/3.21 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 16.69/3.21 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 16.69/3.21 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 16.69/3.21 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 16.69/3.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 16.69/3.21 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 16.69/3.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.69/3.21 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 16.69/3.21 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.69/3.21 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 16.69/3.21 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 16.69/3.21 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 16.69/3.21 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~
% 16.69/3.21 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.69/3.21 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~
% 16.69/3.21 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.69/3.21 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~
% 16.69/3.21 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.69/3.21 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~
% 16.69/3.21 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.69/3.21 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) =
% 16.69/3.21 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.69/3.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~
% 16.69/3.21 (issmallestelement_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.69/3.21 (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0: $i] :
% 16.69/3.21 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pq(v3, v2) =
% 16.69/3.21 v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.69/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.69/3.21 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 16.69/3.21 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 16.69/3.21 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 16.69/3.21 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 16.69/3.21 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0: MultipleValueBool] :
% 16.69/3.21 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_removemin(v2) =
% 16.69/3.21 v1) | ~ (pi_removemin(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.69/3.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~
% 16.69/3.21 (pi_find_min(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 16.69/3.21 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 16.69/3.21 $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2)
% 16.69/3.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 16.69/3.21 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] :
% 16.69/3.21 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~
% 16.69/3.21 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.69/3.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2)
% 16.69/3.21 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.69/3.21 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & !
% 16.69/3.21 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) =
% 16.69/3.21 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 16.69/3.21 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2)
% 16.69/3.21 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.69/3.21 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) =
% 16.69/3.21 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.69/3.21 $i] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0))
% 16.69/3.21
% 16.69/3.21 Further assumptions not needed in the proof:
% 16.69/3.21 --------------------------------------------
% 16.69/3.21 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax22, ax23,
% 16.69/3.21 ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, ax36,
% 16.69/3.21 ax38, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax50, ax51,
% 16.69/3.21 ax52, ax53, ax54, ax56, ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax7, ax8,
% 16.69/3.21 bottom_smallest, reflexivity, stricly_smaller_definition, totality, transitivity
% 16.69/3.21
% 16.69/3.21 Those formulas are unsatisfiable:
% 16.69/3.21 ---------------------------------
% 16.69/3.21
% 16.69/3.21 Begin of proof
% 16.69/3.21 |
% 16.69/3.21 | ALPHA: (ax9) implies:
% 16.69/3.22 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 16.69/3.22 | (contains_pq(v3, v2) = 0) | ~ (insert_pq(v0, v1) = v3) | ~ $i(v2) |
% 16.69/3.22 | ~ $i(v1) | ~ $i(v0) | contains_pq(v0, v2) = 0)
% 16.69/3.22 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 16.69/3.22 | (v4 = 0 | ~ (contains_pq(v3, v2) = v4) | ~ (insert_pq(v0, v1) = v3) |
% 16.69/3.22 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v1) & ? [v5: int] : (
% 16.69/3.22 | ~ (v5 = 0) & contains_pq(v0, v2) = v5)))
% 16.69/3.22 |
% 16.69/3.22 | ALPHA: (ax21) implies:
% 16.69/3.22 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.69/3.22 | ! [v5: $i] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1,
% 16.69/3.22 | v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2)
% 16.69/3.22 | | ~ $i(v1) | ~ $i(v0) | contains_slb(v0, v2) = 0)
% 16.69/3.22 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.69/3.22 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) |
% 16.69/3.22 | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~
% 16.69/3.22 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v1) & ? [v7: int] : ( ~
% 16.69/3.22 | (v7 = 0) & contains_slb(v0, v2) = v7)))
% 16.69/3.22 |
% 16.69/3.22 | ALPHA: (ax39) implies:
% 17.00/3.22 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 17.00/3.22 | ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | ~
% 17.00/3.22 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | contains_slb(v1, v3) =
% 17.00/3.22 | 0)
% 17.00/3.22 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.00/3.22 | ! [v5: int] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0,
% 17.00/3.22 | v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.00/3.22 | ? [v6: int] : ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))
% 17.00/3.22 |
% 17.00/3.22 | ALPHA: (function-axioms) implies:
% 17.00/3.22 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (i(v2) = v1) |
% 17.00/3.22 | ~ (i(v2) = v0))
% 17.00/3.22 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.00/3.22 | ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~
% 17.00/3.22 | (contains_slb(v3, v2) = v0))
% 17.00/3.22 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.00/3.22 | (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0))
% 17.00/3.22 |
% 17.00/3.22 | DELTA: instantiating (l6_co) with fresh symbol all_72_0 gives:
% 17.00/3.22 | (10) $i(all_72_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 17.00/3.22 | ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (i(v3) = v4) | ~
% 17.00/3.22 | (triple(v0, all_72_0, v1) = v3) | ~ (contains_pq(v4, v2) = v5) | ~
% 17.00/3.22 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) &
% 17.00/3.22 | contains_cpq(v3, v2) = v6)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.00/3.22 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (i(v3) = v4) | ~ (triple(v0,
% 17.00/3.22 | all_72_0, v1) = v3) | ~ (contains_pq(v4, v2) = 0) | ~ $i(v2) |
% 17.00/3.22 | ~ $i(v1) | ~ $i(v0) | contains_cpq(v3, v2) = 0) & ? [v0: $i] : ?
% 17.00/3.22 | [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 17.00/3.22 | [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: any] :
% 17.00/3.22 | (i(v7) = v9 & contains_cpq(v7, v4) = v8 & triple(v0, v6, v1) = v7 &
% 17.00/3.22 | pair(v2, v3) = v5 & insert_slb(all_72_0, v5) = v6 & contains_pq(v9,
% 17.00/3.22 | v4) = v10 & $i(v9) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 17.00/3.23 | $i(v2) & $i(v1) & $i(v0) & ((v10 = 0 & ~ (v8 = 0)) | (v8 = 0 & ~
% 17.00/3.23 | (v10 = 0))))
% 17.00/3.23 |
% 17.00/3.23 | ALPHA: (10) implies:
% 17.00/3.23 | (11) $i(all_72_0)
% 17.00/3.23 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.00/3.23 | ( ~ (i(v3) = v4) | ~ (triple(v0, all_72_0, v1) = v3) | ~
% 17.00/3.23 | (contains_pq(v4, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.00/3.23 | contains_cpq(v3, v2) = 0)
% 17.00/3.23 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.00/3.23 | ! [v5: int] : (v5 = 0 | ~ (i(v3) = v4) | ~ (triple(v0, all_72_0, v1)
% 17.00/3.23 | = v3) | ~ (contains_pq(v4, v2) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 17.00/3.23 | $i(v0) | ? [v6: int] : ( ~ (v6 = 0) & contains_cpq(v3, v2) = v6))
% 17.00/3.23 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 17.00/3.23 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] :
% 17.00/3.23 | ? [v10: any] : (i(v7) = v9 & contains_cpq(v7, v4) = v8 & triple(v0,
% 17.00/3.23 | v6, v1) = v7 & pair(v2, v3) = v5 & insert_slb(all_72_0, v5) = v6 &
% 17.00/3.23 | contains_pq(v9, v4) = v10 & $i(v9) & $i(v7) & $i(v6) & $i(v5) &
% 17.00/3.23 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v10 = 0 & ~ (v8 =
% 17.00/3.23 | 0)) | (v8 = 0 & ~ (v10 = 0))))
% 17.00/3.23 |
% 17.00/3.23 | DELTA: instantiating (14) with fresh symbols all_75_0, all_75_1, all_75_2,
% 17.00/3.23 | all_75_3, all_75_4, all_75_5, all_75_6, all_75_7, all_75_8, all_75_9,
% 17.00/3.23 | all_75_10 gives:
% 17.00/3.23 | (15) i(all_75_3) = all_75_1 & contains_cpq(all_75_3, all_75_6) = all_75_2 &
% 17.00/3.23 | triple(all_75_10, all_75_4, all_75_9) = all_75_3 & pair(all_75_8,
% 17.00/3.23 | all_75_7) = all_75_5 & insert_slb(all_72_0, all_75_5) = all_75_4 &
% 17.00/3.23 | contains_pq(all_75_1, all_75_6) = all_75_0 & $i(all_75_1) &
% 17.00/3.23 | $i(all_75_3) & $i(all_75_4) & $i(all_75_5) & $i(all_75_6) &
% 17.00/3.23 | $i(all_75_7) & $i(all_75_8) & $i(all_75_9) & $i(all_75_10) &
% 17.00/3.23 | ((all_75_0 = 0 & ~ (all_75_2 = 0)) | (all_75_2 = 0 & ~ (all_75_0 =
% 17.00/3.23 | 0)))
% 17.00/3.23 |
% 17.00/3.23 | ALPHA: (15) implies:
% 17.00/3.23 | (16) $i(all_75_10)
% 17.00/3.23 | (17) $i(all_75_9)
% 17.00/3.23 | (18) $i(all_75_8)
% 17.00/3.23 | (19) $i(all_75_7)
% 17.00/3.23 | (20) $i(all_75_6)
% 17.00/3.23 | (21) $i(all_75_4)
% 17.00/3.23 | (22) contains_pq(all_75_1, all_75_6) = all_75_0
% 17.00/3.23 | (23) insert_slb(all_72_0, all_75_5) = all_75_4
% 17.00/3.23 | (24) pair(all_75_8, all_75_7) = all_75_5
% 17.00/3.23 | (25) triple(all_75_10, all_75_4, all_75_9) = all_75_3
% 17.00/3.23 | (26) contains_cpq(all_75_3, all_75_6) = all_75_2
% 17.00/3.23 | (27) i(all_75_3) = all_75_1
% 17.00/3.23 | (28) (all_75_0 = 0 & ~ (all_75_2 = 0)) | (all_75_2 = 0 & ~ (all_75_0 =
% 17.00/3.23 | 0))
% 17.00/3.23 |
% 17.00/3.23 | GROUND_INST: instantiating (ax37) with all_75_10, all_72_0, all_75_9,
% 17.00/3.23 | all_75_8, all_75_7, all_75_5, all_75_4, all_75_3, simplifying
% 17.00/3.23 | with (11), (16), (17), (18), (19), (23), (24), (25) gives:
% 17.00/3.23 | (29) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 17.00/3.23 | (triple(all_75_10, all_72_0, all_75_9) = v2 & check_cpq(v2) = v3 &
% 17.00/3.23 | check_cpq(all_75_3) = v1 & less_than(all_75_7, all_75_8) = v0 &
% 17.00/3.23 | $i(v2) & ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3
% 17.00/3.23 | = 0))))
% 17.00/3.23 |
% 17.00/3.23 | GROUND_INST: instantiating (ax55) with all_75_10, all_72_0, all_75_9,
% 17.00/3.23 | all_75_8, all_75_7, all_75_5, all_75_4, all_75_3, simplifying
% 17.00/3.23 | with (11), (16), (17), (18), (19), (23), (24), (25) gives:
% 17.00/3.24 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (i(v1) = v2 & i(all_75_3) =
% 17.00/3.24 | v0 & triple(all_75_10, all_72_0, all_75_9) = v1 & insert_pq(v2,
% 17.00/3.24 | all_75_8) = v0 & $i(v2) & $i(v1) & $i(v0))
% 17.00/3.24 |
% 17.00/3.24 | GROUND_INST: instantiating (6) with all_75_10, all_75_4, all_75_9, all_75_6,
% 17.00/3.24 | all_75_3, all_75_2, simplifying with (16), (17), (20), (21),
% 17.00/3.24 | (25), (26) gives:
% 17.00/3.24 | (31) all_75_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_75_4,
% 17.00/3.24 | all_75_6) = v0)
% 17.00/3.24 |
% 17.00/3.24 | DELTA: instantiating (30) with fresh symbols all_85_0, all_85_1, all_85_2
% 17.00/3.24 | gives:
% 17.00/3.24 | (32) i(all_85_1) = all_85_0 & i(all_75_3) = all_85_2 & triple(all_75_10,
% 17.00/3.24 | all_72_0, all_75_9) = all_85_1 & insert_pq(all_85_0, all_75_8) =
% 17.00/3.24 | all_85_2 & $i(all_85_0) & $i(all_85_1) & $i(all_85_2)
% 17.00/3.24 |
% 17.00/3.24 | ALPHA: (32) implies:
% 17.00/3.24 | (33) $i(all_85_0)
% 17.00/3.24 | (34) insert_pq(all_85_0, all_75_8) = all_85_2
% 17.00/3.24 | (35) triple(all_75_10, all_72_0, all_75_9) = all_85_1
% 17.00/3.24 | (36) i(all_75_3) = all_85_2
% 17.00/3.24 | (37) i(all_85_1) = all_85_0
% 17.00/3.24 |
% 17.00/3.24 | DELTA: instantiating (29) with fresh symbols all_87_0, all_87_1, all_87_2,
% 17.00/3.24 | all_87_3 gives:
% 17.00/3.24 | (38) triple(all_75_10, all_72_0, all_75_9) = all_87_1 & check_cpq(all_87_1)
% 17.00/3.24 | = all_87_0 & check_cpq(all_75_3) = all_87_2 & less_than(all_75_7,
% 17.00/3.24 | all_75_8) = all_87_3 & $i(all_87_1) & ( ~ (all_87_3 = 0) | (( ~
% 17.00/3.24 | (all_87_0 = 0) | all_87_2 = 0) & ( ~ (all_87_2 = 0) | all_87_0 =
% 17.00/3.24 | 0)))
% 17.00/3.24 |
% 17.00/3.24 | ALPHA: (38) implies:
% 17.00/3.24 | (39) triple(all_75_10, all_72_0, all_75_9) = all_87_1
% 17.00/3.24 |
% 17.00/3.24 | GROUND_INST: instantiating (9) with all_85_1, all_87_1, all_75_9, all_72_0,
% 17.00/3.24 | all_75_10, simplifying with (35), (39) gives:
% 17.00/3.24 | (40) all_87_1 = all_85_1
% 17.00/3.24 |
% 17.00/3.24 | GROUND_INST: instantiating (7) with all_75_1, all_85_2, all_75_3, simplifying
% 17.00/3.24 | with (27), (36) gives:
% 17.00/3.24 | (41) all_85_2 = all_75_1
% 17.00/3.24 |
% 17.00/3.24 | REDUCE: (34), (41) imply:
% 17.00/3.24 | (42) insert_pq(all_85_0, all_75_8) = all_75_1
% 17.00/3.24 |
% 17.00/3.24 | GROUND_INST: instantiating (2) with all_85_0, all_75_8, all_75_6, all_75_1,
% 17.00/3.24 | all_75_0, simplifying with (18), (20), (22), (33), (42) gives:
% 17.00/3.24 | (43) all_75_0 = 0 | ( ~ (all_75_6 = all_75_8) & ? [v0: int] : ( ~ (v0 = 0)
% 17.00/3.24 | & contains_pq(all_85_0, all_75_6) = v0))
% 17.00/3.24 |
% 17.00/3.24 | BETA: splitting (28) gives:
% 17.00/3.24 |
% 17.48/3.24 | Case 1:
% 17.48/3.24 | |
% 17.48/3.24 | | (44) all_75_0 = 0 & ~ (all_75_2 = 0)
% 17.48/3.24 | |
% 17.48/3.24 | | ALPHA: (44) implies:
% 17.48/3.24 | | (45) all_75_0 = 0
% 17.48/3.24 | | (46) ~ (all_75_2 = 0)
% 17.48/3.24 | |
% 17.48/3.24 | | REDUCE: (22), (45) imply:
% 17.48/3.24 | | (47) contains_pq(all_75_1, all_75_6) = 0
% 17.48/3.24 | |
% 17.48/3.24 | | BETA: splitting (31) gives:
% 17.48/3.24 | |
% 17.48/3.24 | | Case 1:
% 17.48/3.24 | | |
% 17.48/3.24 | | | (48) all_75_2 = 0
% 17.48/3.24 | | |
% 17.48/3.24 | | | REDUCE: (46), (48) imply:
% 17.48/3.24 | | | (49) $false
% 17.48/3.24 | | |
% 17.48/3.24 | | | CLOSE: (49) is inconsistent.
% 17.48/3.24 | | |
% 17.48/3.24 | | Case 2:
% 17.48/3.24 | | |
% 17.48/3.25 | | | (50) ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_75_4, all_75_6) =
% 17.48/3.25 | | | v0)
% 17.48/3.25 | | |
% 17.48/3.25 | | | DELTA: instantiating (50) with fresh symbol all_110_0 gives:
% 17.48/3.25 | | | (51) ~ (all_110_0 = 0) & contains_slb(all_75_4, all_75_6) = all_110_0
% 17.48/3.25 | | |
% 17.48/3.25 | | | ALPHA: (51) implies:
% 17.48/3.25 | | | (52) ~ (all_110_0 = 0)
% 17.48/3.25 | | | (53) contains_slb(all_75_4, all_75_6) = all_110_0
% 17.48/3.25 | | |
% 17.48/3.25 | | | GROUND_INST: instantiating (1) with all_85_0, all_75_8, all_75_6,
% 17.48/3.25 | | | all_75_1, simplifying with (18), (20), (33), (42), (47)
% 17.48/3.25 | | | gives:
% 17.48/3.25 | | | (54) all_75_6 = all_75_8 | contains_pq(all_85_0, all_75_6) = 0
% 17.48/3.25 | | |
% 17.48/3.25 | | | GROUND_INST: instantiating (4) with all_72_0, all_75_8, all_75_6,
% 17.48/3.25 | | | all_75_7, all_75_5, all_75_4, all_110_0, simplifying with
% 17.48/3.25 | | | (11), (18), (19), (20), (23), (24), (53) gives:
% 17.48/3.25 | | | (55) all_110_0 = 0 | ( ~ (all_75_6 = all_75_8) & ? [v0: int] : ( ~ (v0
% 17.48/3.25 | | | = 0) & contains_slb(all_72_0, all_75_6) = v0))
% 17.48/3.25 | | |
% 17.48/3.25 | | | BETA: splitting (55) gives:
% 17.48/3.25 | | |
% 17.48/3.25 | | | Case 1:
% 17.48/3.25 | | | |
% 17.48/3.25 | | | | (56) all_110_0 = 0
% 17.48/3.25 | | | |
% 17.48/3.25 | | | | REDUCE: (52), (56) imply:
% 17.48/3.25 | | | | (57) $false
% 17.48/3.25 | | | |
% 17.48/3.25 | | | | CLOSE: (57) is inconsistent.
% 17.48/3.25 | | | |
% 17.48/3.25 | | | Case 2:
% 17.48/3.25 | | | |
% 17.48/3.25 | | | | (58) ~ (all_75_6 = all_75_8) & ? [v0: int] : ( ~ (v0 = 0) &
% 17.48/3.25 | | | | contains_slb(all_72_0, all_75_6) = v0)
% 17.48/3.25 | | | |
% 17.48/3.25 | | | | ALPHA: (58) implies:
% 17.48/3.25 | | | | (59) ~ (all_75_6 = all_75_8)
% 17.48/3.25 | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_72_0, all_75_6) =
% 17.48/3.25 | | | | v0)
% 17.48/3.25 | | | |
% 17.48/3.25 | | | | BETA: splitting (54) gives:
% 17.48/3.25 | | | |
% 17.48/3.25 | | | | Case 1:
% 17.48/3.25 | | | | |
% 17.48/3.25 | | | | | (61) contains_pq(all_85_0, all_75_6) = 0
% 17.48/3.25 | | | | |
% 17.48/3.25 | | | | | GROUND_INST: instantiating (12) with all_75_10, all_75_9, all_75_6,
% 17.48/3.25 | | | | | all_85_1, all_85_0, simplifying with (16), (17), (20),
% 17.48/3.25 | | | | | (35), (37), (61) gives:
% 17.48/3.25 | | | | | (62) contains_cpq(all_85_1, all_75_6) = 0
% 17.48/3.25 | | | | |
% 17.48/3.25 | | | | | GROUND_INST: instantiating (5) with all_75_10, all_72_0, all_75_9,
% 17.48/3.25 | | | | | all_75_6, all_85_1, simplifying with (11), (16), (17),
% 17.48/3.25 | | | | | (20), (35), (62) gives:
% 17.48/3.25 | | | | | (63) contains_slb(all_72_0, all_75_6) = 0
% 17.48/3.25 | | | | |
% 17.48/3.25 | | | | | DELTA: instantiating (60) with fresh symbol all_139_0 gives:
% 17.48/3.25 | | | | | (64) ~ (all_139_0 = 0) & contains_slb(all_72_0, all_75_6) =
% 17.48/3.25 | | | | | all_139_0
% 17.48/3.25 | | | | |
% 17.48/3.25 | | | | | REF_CLOSE: (8), (63), (64) are inconsistent by sub-proof #1.
% 17.48/3.25 | | | | |
% 17.48/3.25 | | | | Case 2:
% 17.48/3.25 | | | | |
% 17.48/3.25 | | | | | (65) all_75_6 = all_75_8
% 17.48/3.25 | | | | |
% 17.48/3.25 | | | | | REDUCE: (59), (65) imply:
% 17.48/3.25 | | | | | (66) $false
% 17.48/3.25 | | | | |
% 17.48/3.25 | | | | | CLOSE: (66) is inconsistent.
% 17.48/3.25 | | | | |
% 17.48/3.25 | | | | End of split
% 17.48/3.25 | | | |
% 17.48/3.25 | | | End of split
% 17.48/3.25 | | |
% 17.48/3.25 | | End of split
% 17.48/3.25 | |
% 17.48/3.25 | Case 2:
% 17.48/3.25 | |
% 17.48/3.25 | | (67) all_75_2 = 0 & ~ (all_75_0 = 0)
% 17.48/3.25 | |
% 17.48/3.25 | | ALPHA: (67) implies:
% 17.48/3.25 | | (68) all_75_2 = 0
% 17.48/3.25 | | (69) ~ (all_75_0 = 0)
% 17.48/3.25 | |
% 17.48/3.25 | | REDUCE: (26), (68) imply:
% 17.48/3.25 | | (70) contains_cpq(all_75_3, all_75_6) = 0
% 17.48/3.25 | |
% 17.48/3.25 | | BETA: splitting (43) gives:
% 17.48/3.25 | |
% 17.48/3.25 | | Case 1:
% 17.48/3.25 | | |
% 17.48/3.25 | | | (71) all_75_0 = 0
% 17.48/3.25 | | |
% 17.48/3.25 | | | REDUCE: (69), (71) imply:
% 17.48/3.25 | | | (72) $false
% 17.48/3.25 | | |
% 17.48/3.25 | | | CLOSE: (72) is inconsistent.
% 17.48/3.25 | | |
% 17.48/3.25 | | Case 2:
% 17.48/3.25 | | |
% 17.48/3.25 | | | (73) ~ (all_75_6 = all_75_8) & ? [v0: int] : ( ~ (v0 = 0) &
% 17.48/3.25 | | | contains_pq(all_85_0, all_75_6) = v0)
% 17.48/3.25 | | |
% 17.48/3.25 | | | ALPHA: (73) implies:
% 17.48/3.25 | | | (74) ~ (all_75_6 = all_75_8)
% 17.48/3.25 | | | (75) ? [v0: int] : ( ~ (v0 = 0) & contains_pq(all_85_0, all_75_6) =
% 17.48/3.25 | | | v0)
% 17.48/3.25 | | |
% 17.48/3.25 | | | DELTA: instantiating (75) with fresh symbol all_110_0 gives:
% 17.48/3.25 | | | (76) ~ (all_110_0 = 0) & contains_pq(all_85_0, all_75_6) = all_110_0
% 17.48/3.25 | | |
% 17.48/3.25 | | | ALPHA: (76) implies:
% 17.48/3.26 | | | (77) ~ (all_110_0 = 0)
% 17.48/3.26 | | | (78) contains_pq(all_85_0, all_75_6) = all_110_0
% 17.48/3.26 | | |
% 17.48/3.26 | | | GROUND_INST: instantiating (13) with all_75_10, all_75_9, all_75_6,
% 17.48/3.26 | | | all_85_1, all_85_0, all_110_0, simplifying with (16), (17),
% 17.48/3.26 | | | (20), (35), (37), (78) gives:
% 17.48/3.26 | | | (79) all_110_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 17.48/3.26 | | | contains_cpq(all_85_1, all_75_6) = v0)
% 17.48/3.26 | | |
% 17.48/3.26 | | | GROUND_INST: instantiating (5) with all_75_10, all_75_4, all_75_9,
% 17.48/3.26 | | | all_75_6, all_75_3, simplifying with (16), (17), (20), (21),
% 17.48/3.26 | | | (25), (70) gives:
% 17.48/3.26 | | | (80) contains_slb(all_75_4, all_75_6) = 0
% 17.48/3.26 | | |
% 17.48/3.26 | | | BETA: splitting (79) gives:
% 17.48/3.26 | | |
% 17.48/3.26 | | | Case 1:
% 17.48/3.26 | | | |
% 17.48/3.26 | | | | (81) all_110_0 = 0
% 17.48/3.26 | | | |
% 17.48/3.26 | | | | REDUCE: (77), (81) imply:
% 17.48/3.26 | | | | (82) $false
% 17.48/3.26 | | | |
% 17.48/3.26 | | | | CLOSE: (82) is inconsistent.
% 17.48/3.26 | | | |
% 17.48/3.26 | | | Case 2:
% 17.48/3.26 | | | |
% 17.48/3.26 | | | | (83) ? [v0: int] : ( ~ (v0 = 0) & contains_cpq(all_85_1, all_75_6) =
% 17.48/3.26 | | | | v0)
% 17.48/3.26 | | | |
% 17.48/3.26 | | | | DELTA: instantiating (83) with fresh symbol all_122_0 gives:
% 17.48/3.26 | | | | (84) ~ (all_122_0 = 0) & contains_cpq(all_85_1, all_75_6) =
% 17.48/3.26 | | | | all_122_0
% 17.48/3.26 | | | |
% 17.48/3.26 | | | | ALPHA: (84) implies:
% 17.48/3.26 | | | | (85) ~ (all_122_0 = 0)
% 17.48/3.26 | | | | (86) contains_cpq(all_85_1, all_75_6) = all_122_0
% 17.48/3.26 | | | |
% 17.48/3.26 | | | | GROUND_INST: instantiating (3) with all_72_0, all_75_8, all_75_6,
% 17.48/3.26 | | | | all_75_7, all_75_5, all_75_4, simplifying with (11), (18),
% 17.48/3.26 | | | | (19), (20), (23), (24), (80) gives:
% 17.48/3.26 | | | | (87) all_75_6 = all_75_8 | contains_slb(all_72_0, all_75_6) = 0
% 17.48/3.26 | | | |
% 17.48/3.26 | | | | GROUND_INST: instantiating (6) with all_75_10, all_72_0, all_75_9,
% 17.48/3.26 | | | | all_75_6, all_85_1, all_122_0, simplifying with (11), (16),
% 17.48/3.26 | | | | (17), (20), (35), (86) gives:
% 17.48/3.26 | | | | (88) all_122_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 17.48/3.26 | | | | contains_slb(all_72_0, all_75_6) = v0)
% 17.48/3.26 | | | |
% 17.48/3.26 | | | | BETA: splitting (87) gives:
% 17.48/3.26 | | | |
% 17.48/3.26 | | | | Case 1:
% 17.48/3.26 | | | | |
% 17.48/3.26 | | | | | (89) contains_slb(all_72_0, all_75_6) = 0
% 17.48/3.26 | | | | |
% 17.48/3.26 | | | | | BETA: splitting (88) gives:
% 17.48/3.26 | | | | |
% 17.48/3.26 | | | | | Case 1:
% 17.48/3.26 | | | | | |
% 17.48/3.26 | | | | | | (90) all_122_0 = 0
% 17.48/3.26 | | | | | |
% 17.48/3.26 | | | | | | REDUCE: (85), (90) imply:
% 17.48/3.26 | | | | | | (91) $false
% 17.48/3.26 | | | | | |
% 17.48/3.26 | | | | | | CLOSE: (91) is inconsistent.
% 17.48/3.26 | | | | | |
% 17.48/3.26 | | | | | Case 2:
% 17.48/3.26 | | | | | |
% 17.48/3.26 | | | | | | (92) ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_72_0,
% 17.48/3.26 | | | | | | all_75_6) = v0)
% 17.48/3.26 | | | | | |
% 17.48/3.26 | | | | | | DELTA: instantiating (92) with fresh symbol all_139_0 gives:
% 17.48/3.26 | | | | | | (93) ~ (all_139_0 = 0) & contains_slb(all_72_0, all_75_6) =
% 17.48/3.26 | | | | | | all_139_0
% 17.48/3.26 | | | | | |
% 17.48/3.26 | | | | | | REF_CLOSE: (8), (89), (93) are inconsistent by sub-proof #1.
% 17.48/3.26 | | | | | |
% 17.48/3.26 | | | | | End of split
% 17.48/3.26 | | | | |
% 17.48/3.26 | | | | Case 2:
% 17.48/3.26 | | | | |
% 17.48/3.26 | | | | | (94) all_75_6 = all_75_8
% 17.48/3.26 | | | | |
% 17.48/3.26 | | | | | REDUCE: (74), (94) imply:
% 17.48/3.26 | | | | | (95) $false
% 17.48/3.26 | | | | |
% 17.48/3.26 | | | | | CLOSE: (95) is inconsistent.
% 17.48/3.26 | | | | |
% 17.48/3.26 | | | | End of split
% 17.48/3.26 | | | |
% 17.48/3.26 | | | End of split
% 17.48/3.26 | | |
% 17.48/3.26 | | End of split
% 17.48/3.26 | |
% 17.48/3.26 | End of split
% 17.48/3.26 |
% 17.48/3.26 End of proof
% 17.48/3.26
% 17.48/3.26 Sub-proof #1 shows that the following formulas are inconsistent:
% 17.48/3.26 ----------------------------------------------------------------
% 17.48/3.26 (1) ~ (all_139_0 = 0) & contains_slb(all_72_0, all_75_6) = all_139_0
% 17.48/3.26 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.48/3.26 ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~
% 17.48/3.26 (contains_slb(v3, v2) = v0))
% 17.48/3.26 (3) contains_slb(all_72_0, all_75_6) = 0
% 17.48/3.26
% 17.48/3.26 Begin of proof
% 17.48/3.26 |
% 17.48/3.26 | ALPHA: (1) implies:
% 17.48/3.26 | (4) ~ (all_139_0 = 0)
% 17.48/3.26 | (5) contains_slb(all_72_0, all_75_6) = all_139_0
% 17.48/3.26 |
% 17.48/3.26 | GROUND_INST: instantiating (2) with 0, all_139_0, all_75_6, all_72_0,
% 17.48/3.26 | simplifying with (3), (5) gives:
% 17.48/3.26 | (6) all_139_0 = 0
% 17.48/3.26 |
% 17.48/3.26 | REDUCE: (4), (6) imply:
% 17.48/3.26 | (7) $false
% 17.48/3.26 |
% 17.48/3.26 | CLOSE: (7) is inconsistent.
% 17.48/3.26 |
% 17.48/3.26 End of proof
% 17.48/3.26 % SZS output end Proof for theBenchmark
% 17.48/3.26
% 17.48/3.26 2631ms
%------------------------------------------------------------------------------