TSTP Solution File: SWV454+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV454+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n022.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 22:56:33 EDT 2023
% Result : Theorem 34.57s 5.27s
% Output : Proof 44.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV454+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n022.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 07:30:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.56/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.56/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.56/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.56/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.56/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.56/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.56/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.68/1.21 Prover 1: Preprocessing ...
% 3.68/1.21 Prover 4: Preprocessing ...
% 3.68/1.25 Prover 5: Preprocessing ...
% 3.68/1.25 Prover 0: Preprocessing ...
% 3.68/1.26 Prover 2: Preprocessing ...
% 3.68/1.26 Prover 3: Preprocessing ...
% 3.68/1.27 Prover 6: Preprocessing ...
% 10.68/2.17 Prover 1: Constructing countermodel ...
% 10.68/2.18 Prover 3: Constructing countermodel ...
% 10.68/2.19 Prover 6: Proving ...
% 11.23/2.21 Prover 5: Proving ...
% 11.23/2.22 Prover 4: Constructing countermodel ...
% 11.23/2.25 Prover 2: Proving ...
% 12.25/2.37 Prover 0: Proving ...
% 17.11/3.02 Prover 3: gave up
% 17.53/3.03 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.89/3.12 Prover 7: Preprocessing ...
% 19.61/3.35 Prover 7: Warning: ignoring some quantifiers
% 20.04/3.36 Prover 7: Constructing countermodel ...
% 34.57/5.27 Prover 2: proved (4628ms)
% 34.57/5.27
% 34.57/5.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.57/5.27
% 34.57/5.28 Prover 0: stopped
% 34.57/5.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 34.57/5.29 Prover 6: stopped
% 34.57/5.30 Prover 5: stopped
% 34.57/5.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 34.57/5.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 34.57/5.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 35.34/5.36 Prover 8: Preprocessing ...
% 35.34/5.38 Prover 10: Preprocessing ...
% 35.79/5.40 Prover 13: Preprocessing ...
% 35.79/5.41 Prover 11: Preprocessing ...
% 36.29/5.52 Prover 8: Warning: ignoring some quantifiers
% 36.29/5.54 Prover 8: Constructing countermodel ...
% 36.73/5.59 Prover 10: Warning: ignoring some quantifiers
% 37.29/5.62 Prover 10: Constructing countermodel ...
% 37.29/5.64 Prover 13: Warning: ignoring some quantifiers
% 37.29/5.66 Prover 13: Constructing countermodel ...
% 38.07/5.75 Prover 11: Constructing countermodel ...
% 44.05/6.54 Prover 10: Found proof (size 80)
% 44.05/6.54 Prover 10: proved (1248ms)
% 44.05/6.54 Prover 4: stopped
% 44.05/6.54 Prover 11: stopped
% 44.05/6.54 Prover 13: stopped
% 44.05/6.54 Prover 7: stopped
% 44.05/6.54 Prover 8: stopped
% 44.05/6.54 Prover 1: stopped
% 44.05/6.54
% 44.05/6.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.05/6.54
% 44.05/6.55 % SZS output start Proof for theBenchmark
% 44.05/6.55 Assumptions after simplification:
% 44.05/6.55 ---------------------------------
% 44.05/6.55
% 44.05/6.55 (axiom_46)
% 44.69/6.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.69/6.58 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) |
% 44.69/6.58 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 44.69/6.58 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 44.69/6.58 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1)
% 44.69/6.58 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2))
% 44.69/6.58
% 44.69/6.58 (conj)
% 44.69/6.59 $i(down) & $i(elid) & $i(status) & $i(ldr) & $i(alive) & $i(norm) & $i(wait) &
% 44.69/6.59 $i(elec_1) & $i(nbr_proc) & $i(zero) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 44.69/6.59 : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 44.69/6.59 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 44.69/6.59 $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18:
% 44.69/6.59 $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ( ~ (v17 = v13) & ~ (v17
% 44.77/6.59 = v5) & ~ (v13 = v5) & index(down, v5) = v12 & index(status, v5) = elec_1
% 44.77/6.59 & cons(v7, v1) = v6 & m_Down(v20) = v21 & m_Down(v15) = v18 & m_Down(v4) =
% 44.77/6.59 v7 & s(v5) = v13 & s(zero) = v0 & host(v20) = v17 & host(v16) = v17 &
% 44.77/6.59 host(v15) = v5 & host(v14) = v5 & host(v4) = v8 & host(v3) = v5 & queue(v17)
% 44.77/6.59 = v19 & queue(v5) = v6 & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) &
% 44.77/6.59 $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v8) & $i(v7) & $i(v6) &
% 44.77/6.59 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & setIn(v16, alive) &
% 44.77/6.59 setIn(v14, alive) & setIn(v3, alive) & elem(v21, v1) & elem(v18, v19) & ~
% 44.77/6.59 leq(v5, v8) & ~ leq(nbr_proc, v5) & ! [v22: $i] : ! [v23: $i] : ! [v24:
% 44.77/6.59 $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ! [v28: $i] : ! [v29:
% 44.77/6.59 $i] : (v27 = v26 | ~ (m_Down(v25) = v28) | ~ (m_Down(v23) = v29) | ~
% 44.77/6.59 (host(v24) = v26) | ~ (host(v22) = v27) | ~ $i(v25) | ~ $i(v24) | ~
% 44.77/6.59 $i(v23) | ~ $i(v22) | ~ setIn(v24, alive) | ~ setIn(v22, alive) | ?
% 44.77/6.59 [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : (( ~ (v31 = v26)
% 44.77/6.59 & host(v25) = v31 & $i(v31)) | ( ~ (v30 = v27) & host(v23) = v30 &
% 44.77/6.59 $i(v30)) | (queue(v27) = v32 & $i(v32) & ~ elem(v28, v32)) |
% 44.77/6.59 (queue(v26) = v33 & $i(v33) & ~ elem(v29, v33)))) & ! [v22: $i] : !
% 44.77/6.59 [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ (m_Ack(v24,
% 44.77/6.59 v22) = v25) | ~ (host(v23) = v26) | ~ $i(v24) | ~ $i(v23) | ~
% 44.77/6.59 $i(v22) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ((host(v24) = v29 &
% 44.77/6.59 host(v22) = v28 & $i(v29) & $i(v28) & ~ leq(v28, v29)) | (queue(v26)
% 44.77/6.59 = v27 & $i(v27) & ~ elem(v25, v27)))) & ! [v22: $i] : ! [v23: $i] :
% 44.77/6.59 ! [v24: $i] : ! [v25: $i] : ( ~ (m_Down(v23) = v24) | ~ (host(v22) = v25)
% 44.77/6.59 | ~ $i(v23) | ~ $i(v22) | ~ setIn(v23, alive) | ? [v26: $i] :
% 44.77/6.59 (queue(v25) = v26 & $i(v26) & ~ elem(v24, v26))) & ! [v22: $i] : !
% 44.77/6.59 [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ (m_Down(v23) = v24) | ~
% 44.77/6.59 (host(v22) = v25) | ~ $i(v23) | ~ $i(v22) | ? [v26: $i] : ? [v27: $i]
% 44.77/6.59 : (( ~ (v27 = v25) & host(v23) = v27 & $i(v27)) | (queue(v25) = v26 &
% 44.77/6.59 $i(v26) & ~ elem(v24, v26)))) & ! [v22: $i] : ! [v23: $i] : !
% 44.77/6.59 [v24: $i] : ! [v25: $i] : ( ~ (m_Halt(v23) = v24) | ~ (host(v22) = v25) |
% 44.77/6.59 ~ $i(v23) | ~ $i(v22) | ? [v26: $i] : ? [v27: $i] : ((host(v23) = v27 &
% 44.77/6.59 $i(v27) & ~ leq(v25, v27)) | (queue(v25) = v26 & $i(v26) & ~
% 44.77/6.59 elem(v24, v26)))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : (v23
% 44.77/6.59 = v22 | ~ (host(v23) = v24) | ~ (host(v22) = v24) | ~ $i(v23) | ~
% 44.77/6.59 $i(v22) | ~ setIn(v23, alive) | ~ setIn(v22, alive)) & ! [v22: $i] : !
% 44.77/6.59 [v23: $i] : ! [v24: $i] : ( ~ (host(v23) = v24) | ~ (host(v22) = v24) | ~
% 44.77/6.59 $i(v23) | ~ $i(v22) | ~ leq(v23, v22) | ~ setIn(v23, alive) |
% 44.77/6.59 setIn(v22, alive)) & ! [v22: $i] : (v22 = v8 | ~ $i(v22) | ~ leq(v0,
% 44.77/6.59 v22) | leq(v5, v22) | setIn(v22, v12)) & ( ~ (norm = elec_1) | ( ~ (v9 =
% 44.77/6.59 v8) & index(ldr, v5) = v9 & $i(v9))) & ( ~ (wait = elec_1) | ( ~ (v11
% 44.77/6.59 = v8) & index(elid, v5) = v10 & host(v10) = v11 & $i(v11) & $i(v10))))
% 44.77/6.59
% 44.77/6.59 (function-axioms)
% 44.77/6.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.77/6.60 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 44.77/6.60 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3,
% 44.77/6.60 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 44.77/6.60 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : !
% 44.77/6.60 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~
% 44.77/6.60 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 44.77/6.60 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 44.77/6.60 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i]
% 44.77/6.60 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) =
% 44.77/6.60 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) =
% 44.77/6.60 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 44.77/6.60 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 44.77/6.60 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & !
% 44.77/6.60 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~
% 44.77/6.60 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.77/6.60 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 44.77/6.60 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & !
% 44.77/6.60 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~
% 44.77/6.60 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.77/6.60 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 44.77/6.60 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1:
% 44.77/6.60 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0))
% 44.77/6.60
% 44.77/6.60 Further assumptions not needed in the proof:
% 44.77/6.60 --------------------------------------------
% 44.77/6.60 axiom, axiom_01, axiom_02, axiom_03, axiom_04, axiom_05, axiom_06, axiom_07,
% 44.77/6.60 axiom_08, axiom_09, axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15,
% 44.77/6.60 axiom_16, axiom_17, axiom_18, axiom_19, axiom_20, axiom_21, axiom_22, axiom_23,
% 44.77/6.60 axiom_24, axiom_25, axiom_26, axiom_27, axiom_28, axiom_29, axiom_30, axiom_31,
% 44.77/6.60 axiom_32, axiom_33, axiom_34, axiom_35, axiom_36, axiom_37, axiom_38, axiom_39,
% 44.77/6.60 axiom_40, axiom_41, axiom_42, axiom_43, axiom_44, axiom_45, axiom_47, axiom_48,
% 44.77/6.60 axiom_49, axiom_50, axiom_51, axiom_52, axiom_53, axiom_54, axiom_55, axiom_56,
% 44.77/6.60 axiom_57, axiom_58, axiom_59, axiom_60, axiom_61, axiom_62, axiom_63, axiom_64,
% 44.77/6.60 axiom_65
% 44.77/6.60
% 44.77/6.60 Those formulas are unsatisfiable:
% 44.77/6.60 ---------------------------------
% 44.77/6.60
% 44.77/6.60 Begin of proof
% 44.77/6.60 |
% 44.77/6.60 | ALPHA: (axiom_46) implies:
% 44.77/6.60 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1,
% 44.77/6.60 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 44.77/6.60 | elem(v0, v3))
% 44.77/6.60 |
% 44.77/6.60 | ALPHA: (conj) implies:
% 44.87/6.61 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 44.87/6.61 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 44.87/6.61 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 44.87/6.61 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19:
% 44.87/6.61 | $i] : ? [v20: $i] : ? [v21: $i] : ( ~ (v17 = v13) & ~ (v17 = v5) &
% 44.87/6.61 | ~ (v13 = v5) & index(down, v5) = v12 & index(status, v5) = elec_1 &
% 44.87/6.61 | cons(v7, v1) = v6 & m_Down(v20) = v21 & m_Down(v15) = v18 &
% 44.87/6.61 | m_Down(v4) = v7 & s(v5) = v13 & s(zero) = v0 & host(v20) = v17 &
% 44.87/6.61 | host(v16) = v17 & host(v15) = v5 & host(v14) = v5 & host(v4) = v8 &
% 44.87/6.61 | host(v3) = v5 & queue(v17) = v19 & queue(v5) = v6 & $i(v21) & $i(v20)
% 44.87/6.61 | & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13)
% 44.87/6.61 | & $i(v12) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 44.87/6.61 | $i(v2) & $i(v1) & $i(v0) & setIn(v16, alive) & setIn(v14, alive) &
% 44.87/6.61 | setIn(v3, alive) & elem(v21, v1) & elem(v18, v19) & ~ leq(v5, v8) &
% 44.87/6.61 | ~ leq(nbr_proc, v5) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : !
% 44.87/6.61 | [v25: $i] : ! [v26: $i] : ! [v27: $i] : ! [v28: $i] : ! [v29: $i]
% 44.87/6.61 | : (v27 = v26 | ~ (m_Down(v25) = v28) | ~ (m_Down(v23) = v29) | ~
% 44.87/6.61 | (host(v24) = v26) | ~ (host(v22) = v27) | ~ $i(v25) | ~ $i(v24)
% 44.87/6.61 | | ~ $i(v23) | ~ $i(v22) | ~ setIn(v24, alive) | ~ setIn(v22,
% 44.87/6.61 | alive) | ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33:
% 44.87/6.61 | $i] : (( ~ (v31 = v26) & host(v25) = v31 & $i(v31)) | ( ~ (v30 =
% 44.87/6.61 | v27) & host(v23) = v30 & $i(v30)) | (queue(v27) = v32 &
% 44.87/6.61 | $i(v32) & ~ elem(v28, v32)) | (queue(v26) = v33 & $i(v33) & ~
% 44.87/6.61 | elem(v29, v33)))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i]
% 44.87/6.61 | : ! [v25: $i] : ! [v26: $i] : ( ~ (m_Ack(v24, v22) = v25) | ~
% 44.87/6.61 | (host(v23) = v26) | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ? [v27:
% 44.87/6.61 | $i] : ? [v28: $i] : ? [v29: $i] : ((host(v24) = v29 & host(v22)
% 44.87/6.61 | = v28 & $i(v29) & $i(v28) & ~ leq(v28, v29)) | (queue(v26) =
% 44.87/6.61 | v27 & $i(v27) & ~ elem(v25, v27)))) & ! [v22: $i] : ! [v23:
% 44.87/6.61 | $i] : ! [v24: $i] : ! [v25: $i] : ( ~ (m_Down(v23) = v24) | ~
% 44.87/6.61 | (host(v22) = v25) | ~ $i(v23) | ~ $i(v22) | ~ setIn(v23, alive)
% 44.87/6.61 | | ? [v26: $i] : (queue(v25) = v26 & $i(v26) & ~ elem(v24, v26)))
% 44.87/6.61 | & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~
% 44.87/6.61 | (m_Down(v23) = v24) | ~ (host(v22) = v25) | ~ $i(v23) | ~
% 44.87/6.61 | $i(v22) | ? [v26: $i] : ? [v27: $i] : (( ~ (v27 = v25) &
% 44.87/6.61 | host(v23) = v27 & $i(v27)) | (queue(v25) = v26 & $i(v26) & ~
% 44.87/6.61 | elem(v24, v26)))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i]
% 44.87/6.62 | : ! [v25: $i] : ( ~ (m_Halt(v23) = v24) | ~ (host(v22) = v25) | ~
% 44.87/6.62 | $i(v23) | ~ $i(v22) | ? [v26: $i] : ? [v27: $i] : ((host(v23) =
% 44.87/6.62 | v27 & $i(v27) & ~ leq(v25, v27)) | (queue(v25) = v26 & $i(v26)
% 44.87/6.62 | & ~ elem(v24, v26)))) & ! [v22: $i] : ! [v23: $i] : ! [v24:
% 44.87/6.62 | $i] : (v23 = v22 | ~ (host(v23) = v24) | ~ (host(v22) = v24) | ~
% 44.87/6.62 | $i(v23) | ~ $i(v22) | ~ setIn(v23, alive) | ~ setIn(v22, alive))
% 44.87/6.62 | & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (host(v23) = v24)
% 44.87/6.62 | | ~ (host(v22) = v24) | ~ $i(v23) | ~ $i(v22) | ~ leq(v23, v22)
% 44.87/6.62 | | ~ setIn(v23, alive) | setIn(v22, alive)) & ! [v22: $i] : (v22 =
% 44.87/6.62 | v8 | ~ $i(v22) | ~ leq(v0, v22) | leq(v5, v22) | setIn(v22, v12))
% 44.87/6.62 | & ( ~ (norm = elec_1) | ( ~ (v9 = v8) & index(ldr, v5) = v9 &
% 44.87/6.62 | $i(v9))) & ( ~ (wait = elec_1) | ( ~ (v11 = v8) & index(elid, v5)
% 44.87/6.62 | = v10 & host(v10) = v11 & $i(v11) & $i(v10))))
% 44.87/6.62 |
% 44.87/6.62 | ALPHA: (function-axioms) implies:
% 44.87/6.62 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) =
% 44.87/6.62 | v1) | ~ (queue(v2) = v0))
% 44.87/6.62 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1)
% 44.87/6.62 | | ~ (host(v2) = v0))
% 44.87/6.62 |
% 44.87/6.62 | DELTA: instantiating (2) with fresh symbols all_65_0, all_65_1, all_65_2,
% 44.87/6.62 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9,
% 44.87/6.62 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15,
% 44.87/6.62 | all_65_16, all_65_17, all_65_18, all_65_19, all_65_20, all_65_21 gives:
% 44.87/6.63 | (5) ~ (all_65_4 = all_65_8) & ~ (all_65_4 = all_65_16) & ~ (all_65_8 =
% 44.87/6.63 | all_65_16) & index(down, all_65_16) = all_65_9 & index(status,
% 44.87/6.63 | all_65_16) = elec_1 & cons(all_65_14, all_65_20) = all_65_15 &
% 44.87/6.63 | m_Down(all_65_1) = all_65_0 & m_Down(all_65_6) = all_65_3 &
% 44.87/6.63 | m_Down(all_65_17) = all_65_14 & s(all_65_16) = all_65_8 & s(zero) =
% 44.87/6.63 | all_65_21 & host(all_65_1) = all_65_4 & host(all_65_5) = all_65_4 &
% 44.87/6.63 | host(all_65_6) = all_65_16 & host(all_65_7) = all_65_16 &
% 44.87/6.63 | host(all_65_17) = all_65_13 & host(all_65_18) = all_65_16 &
% 44.87/6.63 | queue(all_65_4) = all_65_2 & queue(all_65_16) = all_65_15 &
% 44.87/6.63 | $i(all_65_0) & $i(all_65_1) & $i(all_65_2) & $i(all_65_3) &
% 44.87/6.63 | $i(all_65_4) & $i(all_65_5) & $i(all_65_6) & $i(all_65_7) &
% 44.87/6.63 | $i(all_65_8) & $i(all_65_9) & $i(all_65_13) & $i(all_65_14) &
% 44.87/6.63 | $i(all_65_15) & $i(all_65_16) & $i(all_65_17) & $i(all_65_18) &
% 44.87/6.63 | $i(all_65_19) & $i(all_65_20) & $i(all_65_21) & setIn(all_65_5, alive)
% 44.87/6.63 | & setIn(all_65_7, alive) & setIn(all_65_18, alive) & elem(all_65_0,
% 44.87/6.63 | all_65_20) & elem(all_65_3, all_65_2) & ~ leq(all_65_16, all_65_13)
% 44.87/6.63 | & ~ leq(nbr_proc, all_65_16) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 44.87/6.63 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 44.87/6.63 | (v5 = v4 | ~ (m_Down(v3) = v6) | ~ (m_Down(v1) = v7) | ~ (host(v2) =
% 44.87/6.63 | v4) | ~ (host(v0) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 44.87/6.63 | $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? [v8: $i] : ?
% 44.87/6.63 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v9 = v4) & host(v3) =
% 44.87/6.63 | v9 & $i(v9)) | ( ~ (v8 = v5) & host(v1) = v8 & $i(v8)) |
% 44.87/6.63 | (queue(v5) = v10 & $i(v10) & ~ elem(v6, v10)) | (queue(v4) = v11 &
% 44.87/6.63 | $i(v11) & ~ elem(v7, v11)))) & ! [v0: $i] : ! [v1: $i] : !
% 44.87/6.63 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (m_Ack(v2, v0) = v3) | ~
% 44.87/6.63 | (host(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] :
% 44.87/6.63 | ? [v6: $i] : ? [v7: $i] : ((host(v2) = v7 & host(v0) = v6 & $i(v7) &
% 44.87/6.63 | $i(v6) & ~ leq(v6, v7)) | (queue(v4) = v5 & $i(v5) & ~ elem(v3,
% 44.87/6.63 | v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 44.87/6.63 | : ( ~ (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 44.87/6.63 | ~ setIn(v1, alive) | ? [v4: $i] : (queue(v3) = v4 & $i(v4) & ~
% 44.87/6.63 | elem(v2, v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 44.87/6.63 | $i] : ( ~ (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~
% 44.87/6.63 | $i(v0) | ? [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 &
% 44.87/6.63 | $i(v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) & ! [v0:
% 44.87/6.63 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Halt(v1) = v2)
% 44.87/6.63 | | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5:
% 44.87/6.63 | $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3) = v4
% 44.87/6.63 | & $i(v4) & ~ elem(v2, v4)))) & ! [v0: $i] : ! [v1: $i] : !
% 44.87/6.63 | [v2: $i] : (v1 = v0 | ~ (host(v1) = v2) | ~ (host(v0) = v2) | ~
% 44.87/6.63 | $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive)) & !
% 44.87/6.63 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~
% 44.87/6.63 | (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) | ~
% 44.87/6.63 | setIn(v1, alive) | setIn(v0, alive)) & ! [v0: any] : (v0 = all_65_13
% 44.87/6.63 | | ~ $i(v0) | ~ leq(all_65_21, v0) | leq(all_65_16, v0) | setIn(v0,
% 44.87/6.63 | all_65_9)) & ( ~ (norm = elec_1) | ( ~ (all_65_12 = all_65_13) &
% 44.87/6.63 | index(ldr, all_65_16) = all_65_12 & $i(all_65_12))) & ( ~ (wait =
% 44.87/6.63 | elec_1) | ( ~ (all_65_10 = all_65_13) & index(elid, all_65_16) =
% 44.87/6.63 | all_65_11 & host(all_65_11) = all_65_10 & $i(all_65_10) &
% 44.87/6.63 | $i(all_65_11)))
% 44.87/6.63 |
% 44.87/6.63 | ALPHA: (5) implies:
% 44.87/6.63 | (6) ~ (all_65_4 = all_65_16)
% 44.87/6.63 | (7) elem(all_65_3, all_65_2)
% 44.87/6.63 | (8) elem(all_65_0, all_65_20)
% 44.87/6.63 | (9) setIn(all_65_18, alive)
% 44.87/6.63 | (10) setIn(all_65_5, alive)
% 44.87/6.63 | (11) $i(all_65_20)
% 44.87/6.63 | (12) $i(all_65_18)
% 44.87/6.63 | (13) $i(all_65_14)
% 44.87/6.63 | (14) $i(all_65_6)
% 44.87/6.63 | (15) $i(all_65_5)
% 44.87/6.63 | (16) $i(all_65_1)
% 44.87/6.63 | (17) $i(all_65_0)
% 44.87/6.63 | (18) queue(all_65_16) = all_65_15
% 44.87/6.63 | (19) queue(all_65_4) = all_65_2
% 44.87/6.63 | (20) host(all_65_18) = all_65_16
% 44.87/6.63 | (21) host(all_65_6) = all_65_16
% 44.87/6.63 | (22) host(all_65_5) = all_65_4
% 44.87/6.63 | (23) host(all_65_1) = all_65_4
% 44.87/6.63 | (24) m_Down(all_65_6) = all_65_3
% 44.87/6.63 | (25) m_Down(all_65_1) = all_65_0
% 44.87/6.63 | (26) cons(all_65_14, all_65_20) = all_65_15
% 44.87/6.63 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 44.87/6.63 | (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 44.87/6.63 | [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 & $i(v5)) |
% 44.87/6.63 | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4))))
% 44.87/6.63 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 44.87/6.63 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ (m_Down(v3) =
% 44.87/6.63 | v6) | ~ (m_Down(v1) = v7) | ~ (host(v2) = v4) | ~ (host(v0) =
% 44.87/6.63 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2,
% 44.87/6.63 | alive) | ~ setIn(v0, alive) | ? [v8: $i] : ? [v9: $i] : ?
% 44.87/6.63 | [v10: $i] : ? [v11: $i] : (( ~ (v9 = v4) & host(v3) = v9 & $i(v9))
% 44.87/6.63 | | ( ~ (v8 = v5) & host(v1) = v8 & $i(v8)) | (queue(v5) = v10 &
% 44.87/6.63 | $i(v10) & ~ elem(v6, v10)) | (queue(v4) = v11 & $i(v11) & ~
% 44.87/6.63 | elem(v7, v11))))
% 44.87/6.63 |
% 44.87/6.64 | GROUND_INST: instantiating (27) with all_65_18, all_65_6, all_65_3, all_65_16,
% 44.87/6.64 | simplifying with (12), (14), (20), (24) gives:
% 44.87/6.64 | (29) ? [v0: $i] : ? [v1: any] : (( ~ (v1 = all_65_16) & host(all_65_6) =
% 44.87/6.64 | v1 & $i(v1)) | (queue(all_65_16) = v0 & $i(v0) & ~ elem(all_65_3,
% 44.87/6.64 | v0)))
% 44.87/6.64 |
% 44.87/6.64 | GROUND_INST: instantiating (28) with all_65_18, all_65_6, all_65_5, all_65_1,
% 44.87/6.64 | all_65_4, all_65_16, all_65_0, all_65_3, simplifying with (9),
% 44.87/6.64 | (10), (12), (14), (15), (16), (20), (22), (24), (25) gives:
% 44.87/6.64 | (30) all_65_4 = all_65_16 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 44.87/6.64 | [v3: $i] : (( ~ (v1 = all_65_4) & host(all_65_1) = v1 & $i(v1)) | ( ~
% 44.87/6.64 | (v0 = all_65_16) & host(all_65_6) = v0 & $i(v0)) |
% 44.87/6.64 | (queue(all_65_4) = v3 & $i(v3) & ~ elem(all_65_3, v3)) |
% 44.87/6.64 | (queue(all_65_16) = v2 & $i(v2) & ~ elem(all_65_0, v2)))
% 44.87/6.64 |
% 44.87/6.64 | GROUND_INST: instantiating (28) with all_65_5, all_65_1, all_65_18, all_65_6,
% 44.87/6.64 | all_65_16, all_65_4, all_65_3, all_65_0, simplifying with (9),
% 44.87/6.64 | (10), (12), (14), (15), (16), (20), (22), (24), (25) gives:
% 44.87/6.64 | (31) all_65_4 = all_65_16 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 44.87/6.64 | [v3: $i] : (( ~ (v1 = all_65_16) & host(all_65_6) = v1 & $i(v1)) | ( ~
% 44.87/6.64 | (v0 = all_65_4) & host(all_65_1) = v0 & $i(v0)) | (queue(all_65_4)
% 44.87/6.64 | = v2 & $i(v2) & ~ elem(all_65_3, v2)) | (queue(all_65_16) = v3 &
% 44.87/6.64 | $i(v3) & ~ elem(all_65_0, v3)))
% 44.87/6.64 |
% 44.87/6.64 | GROUND_INST: instantiating (1) with all_65_0, all_65_14, all_65_20, all_65_15,
% 44.87/6.64 | simplifying with (8), (11), (13), (17), (26) gives:
% 44.87/6.64 | (32) elem(all_65_0, all_65_15)
% 44.87/6.64 |
% 44.87/6.64 | DELTA: instantiating (29) with fresh symbols all_89_0, all_89_1 gives:
% 44.87/6.64 | (33) ( ~ (all_89_0 = all_65_16) & host(all_65_6) = all_89_0 & $i(all_89_0))
% 44.87/6.64 | | (queue(all_65_16) = all_89_1 & $i(all_89_1) & ~ elem(all_65_3,
% 44.87/6.64 | all_89_1))
% 44.87/6.64 |
% 44.87/6.64 | BETA: splitting (33) gives:
% 44.87/6.64 |
% 44.87/6.64 | Case 1:
% 44.87/6.64 | |
% 44.87/6.64 | | (34) ~ (all_89_0 = all_65_16) & host(all_65_6) = all_89_0 & $i(all_89_0)
% 44.87/6.64 | |
% 44.87/6.64 | | ALPHA: (34) implies:
% 44.87/6.64 | | (35) ~ (all_89_0 = all_65_16)
% 44.87/6.64 | | (36) host(all_65_6) = all_89_0
% 44.87/6.64 | |
% 44.87/6.64 | | GROUND_INST: instantiating (4) with all_65_16, all_89_0, all_65_6,
% 44.87/6.64 | | simplifying with (21), (36) gives:
% 44.87/6.64 | | (37) all_89_0 = all_65_16
% 44.87/6.64 | |
% 44.87/6.64 | | REDUCE: (35), (37) imply:
% 44.87/6.64 | | (38) $false
% 44.87/6.64 | |
% 44.87/6.64 | | CLOSE: (38) is inconsistent.
% 44.87/6.64 | |
% 44.87/6.64 | Case 2:
% 44.87/6.64 | |
% 44.87/6.64 | | (39) queue(all_65_16) = all_89_1 & $i(all_89_1) & ~ elem(all_65_3,
% 44.87/6.64 | | all_89_1)
% 44.87/6.64 | |
% 44.87/6.64 | | ALPHA: (39) implies:
% 44.87/6.64 | | (40) queue(all_65_16) = all_89_1
% 44.87/6.64 | |
% 44.87/6.64 | | BETA: splitting (30) gives:
% 44.87/6.64 | |
% 44.87/6.64 | | Case 1:
% 44.87/6.64 | | |
% 44.87/6.64 | | | (41) all_65_4 = all_65_16
% 44.87/6.64 | | |
% 44.87/6.64 | | | REDUCE: (6), (41) imply:
% 44.87/6.64 | | | (42) $false
% 44.87/6.64 | | |
% 44.87/6.64 | | | CLOSE: (42) is inconsistent.
% 44.87/6.64 | | |
% 44.87/6.64 | | Case 2:
% 44.87/6.64 | | |
% 44.87/6.64 | | | (43) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : (( ~ (v1
% 44.87/6.64 | | | = all_65_4) & host(all_65_1) = v1 & $i(v1)) | ( ~ (v0 =
% 44.87/6.64 | | | all_65_16) & host(all_65_6) = v0 & $i(v0)) |
% 44.87/6.64 | | | (queue(all_65_4) = v3 & $i(v3) & ~ elem(all_65_3, v3)) |
% 44.87/6.64 | | | (queue(all_65_16) = v2 & $i(v2) & ~ elem(all_65_0, v2)))
% 44.87/6.64 | | |
% 44.87/6.64 | | | DELTA: instantiating (43) with fresh symbols all_143_0, all_143_1,
% 44.87/6.64 | | | all_143_2, all_143_3 gives:
% 44.87/6.65 | | | (44) ( ~ (all_143_2 = all_65_4) & host(all_65_1) = all_143_2 &
% 44.87/6.65 | | | $i(all_143_2)) | ( ~ (all_143_3 = all_65_16) & host(all_65_6) =
% 44.87/6.65 | | | all_143_3 & $i(all_143_3)) | (queue(all_65_4) = all_143_0 &
% 44.87/6.65 | | | $i(all_143_0) & ~ elem(all_65_3, all_143_0)) |
% 44.87/6.65 | | | (queue(all_65_16) = all_143_1 & $i(all_143_1) & ~ elem(all_65_0,
% 44.87/6.65 | | | all_143_1))
% 44.87/6.65 | | |
% 44.87/6.65 | | | BETA: splitting (44) gives:
% 44.87/6.65 | | |
% 44.87/6.65 | | | Case 1:
% 44.87/6.65 | | | |
% 44.87/6.65 | | | | (45) ( ~ (all_143_2 = all_65_4) & host(all_65_1) = all_143_2 &
% 44.87/6.65 | | | | $i(all_143_2)) | ( ~ (all_143_3 = all_65_16) & host(all_65_6)
% 44.87/6.65 | | | | = all_143_3 & $i(all_143_3))
% 44.87/6.65 | | | |
% 44.87/6.65 | | | | BETA: splitting (45) gives:
% 44.87/6.65 | | | |
% 44.87/6.65 | | | | Case 1:
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | (46) ~ (all_143_2 = all_65_4) & host(all_65_1) = all_143_2 &
% 44.87/6.65 | | | | | $i(all_143_2)
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | ALPHA: (46) implies:
% 44.87/6.65 | | | | | (47) ~ (all_143_2 = all_65_4)
% 44.87/6.65 | | | | | (48) host(all_65_1) = all_143_2
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | GROUND_INST: instantiating (4) with all_65_4, all_143_2, all_65_1,
% 44.87/6.65 | | | | | simplifying with (23), (48) gives:
% 44.87/6.65 | | | | | (49) all_143_2 = all_65_4
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | REDUCE: (47), (49) imply:
% 44.87/6.65 | | | | | (50) $false
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | CLOSE: (50) is inconsistent.
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | Case 2:
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | (51) ~ (all_143_3 = all_65_16) & host(all_65_6) = all_143_3 &
% 44.87/6.65 | | | | | $i(all_143_3)
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | ALPHA: (51) implies:
% 44.87/6.65 | | | | | (52) ~ (all_143_3 = all_65_16)
% 44.87/6.65 | | | | | (53) host(all_65_6) = all_143_3
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | GROUND_INST: instantiating (4) with all_65_16, all_143_3, all_65_6,
% 44.87/6.65 | | | | | simplifying with (21), (53) gives:
% 44.87/6.65 | | | | | (54) all_143_3 = all_65_16
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | REDUCE: (52), (54) imply:
% 44.87/6.65 | | | | | (55) $false
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | CLOSE: (55) is inconsistent.
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | End of split
% 44.87/6.65 | | | |
% 44.87/6.65 | | | Case 2:
% 44.87/6.65 | | | |
% 44.87/6.65 | | | | (56) (queue(all_65_4) = all_143_0 & $i(all_143_0) & ~ elem(all_65_3,
% 44.87/6.65 | | | | all_143_0)) | (queue(all_65_16) = all_143_1 & $i(all_143_1)
% 44.87/6.65 | | | | & ~ elem(all_65_0, all_143_1))
% 44.87/6.65 | | | |
% 44.87/6.65 | | | | BETA: splitting (56) gives:
% 44.87/6.65 | | | |
% 44.87/6.65 | | | | Case 1:
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | (57) queue(all_65_4) = all_143_0 & $i(all_143_0) & ~
% 44.87/6.65 | | | | | elem(all_65_3, all_143_0)
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | ALPHA: (57) implies:
% 44.87/6.65 | | | | | (58) ~ elem(all_65_3, all_143_0)
% 44.87/6.65 | | | | | (59) queue(all_65_4) = all_143_0
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | BETA: splitting (31) gives:
% 44.87/6.65 | | | | |
% 44.87/6.65 | | | | | Case 1:
% 44.87/6.65 | | | | | |
% 44.87/6.65 | | | | | | (60) all_65_4 = all_65_16
% 44.87/6.65 | | | | | |
% 44.87/6.65 | | | | | | REDUCE: (6), (60) imply:
% 44.87/6.65 | | | | | | (61) $false
% 44.87/6.65 | | | | | |
% 44.87/6.65 | | | | | | CLOSE: (61) is inconsistent.
% 44.87/6.65 | | | | | |
% 44.87/6.65 | | | | | Case 2:
% 44.87/6.65 | | | | | |
% 44.87/6.65 | | | | | | (62) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ((
% 44.87/6.65 | | | | | | ~ (v1 = all_65_16) & host(all_65_6) = v1 & $i(v1)) | ( ~
% 44.87/6.65 | | | | | | (v0 = all_65_4) & host(all_65_1) = v0 & $i(v0)) |
% 44.87/6.65 | | | | | | (queue(all_65_4) = v2 & $i(v2) & ~ elem(all_65_3, v2)) |
% 44.87/6.65 | | | | | | (queue(all_65_16) = v3 & $i(v3) & ~ elem(all_65_0, v3)))
% 44.87/6.65 | | | | | |
% 44.87/6.65 | | | | | | DELTA: instantiating (62) with fresh symbols all_155_0, all_155_1,
% 44.87/6.65 | | | | | | all_155_2, all_155_3 gives:
% 44.87/6.65 | | | | | | (63) ( ~ (all_155_2 = all_65_16) & host(all_65_6) = all_155_2 &
% 44.87/6.65 | | | | | | $i(all_155_2)) | ( ~ (all_155_3 = all_65_4) &
% 44.87/6.65 | | | | | | host(all_65_1) = all_155_3 & $i(all_155_3)) |
% 44.87/6.65 | | | | | | (queue(all_65_4) = all_155_1 & $i(all_155_1) & ~
% 44.87/6.65 | | | | | | elem(all_65_3, all_155_1)) | (queue(all_65_16) = all_155_0
% 44.87/6.65 | | | | | | & $i(all_155_0) & ~ elem(all_65_0, all_155_0))
% 44.87/6.65 | | | | | |
% 44.87/6.65 | | | | | | BETA: splitting (63) gives:
% 44.87/6.65 | | | | | |
% 44.87/6.65 | | | | | | Case 1:
% 44.87/6.65 | | | | | | |
% 44.87/6.65 | | | | | | | (64) ( ~ (all_155_2 = all_65_16) & host(all_65_6) = all_155_2 &
% 44.87/6.65 | | | | | | | $i(all_155_2)) | ( ~ (all_155_3 = all_65_4) &
% 44.87/6.65 | | | | | | | host(all_65_1) = all_155_3 & $i(all_155_3))
% 44.87/6.65 | | | | | | |
% 44.87/6.65 | | | | | | | BETA: splitting (64) gives:
% 44.87/6.65 | | | | | | |
% 44.87/6.65 | | | | | | | Case 1:
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | (65) ~ (all_155_2 = all_65_16) & host(all_65_6) = all_155_2
% 44.87/6.65 | | | | | | | | & $i(all_155_2)
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | ALPHA: (65) implies:
% 44.87/6.65 | | | | | | | | (66) ~ (all_155_2 = all_65_16)
% 44.87/6.65 | | | | | | | | (67) host(all_65_6) = all_155_2
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | GROUND_INST: instantiating (4) with all_65_16, all_155_2,
% 44.87/6.65 | | | | | | | | all_65_6, simplifying with (21), (67) gives:
% 44.87/6.65 | | | | | | | | (68) all_155_2 = all_65_16
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | REDUCE: (66), (68) imply:
% 44.87/6.65 | | | | | | | | (69) $false
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | CLOSE: (69) is inconsistent.
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | Case 2:
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | (70) ~ (all_155_3 = all_65_4) & host(all_65_1) = all_155_3 &
% 44.87/6.65 | | | | | | | | $i(all_155_3)
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | ALPHA: (70) implies:
% 44.87/6.65 | | | | | | | | (71) ~ (all_155_3 = all_65_4)
% 44.87/6.65 | | | | | | | | (72) host(all_65_1) = all_155_3
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | GROUND_INST: instantiating (4) with all_65_4, all_155_3,
% 44.87/6.65 | | | | | | | | all_65_1, simplifying with (23), (72) gives:
% 44.87/6.65 | | | | | | | | (73) all_155_3 = all_65_4
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | REDUCE: (71), (73) imply:
% 44.87/6.65 | | | | | | | | (74) $false
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | CLOSE: (74) is inconsistent.
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | End of split
% 44.87/6.65 | | | | | | |
% 44.87/6.65 | | | | | | Case 2:
% 44.87/6.65 | | | | | | |
% 44.87/6.65 | | | | | | | (75) (queue(all_65_4) = all_155_1 & $i(all_155_1) & ~
% 44.87/6.65 | | | | | | | elem(all_65_3, all_155_1)) | (queue(all_65_16) =
% 44.87/6.65 | | | | | | | all_155_0 & $i(all_155_0) & ~ elem(all_65_0,
% 44.87/6.65 | | | | | | | all_155_0))
% 44.87/6.65 | | | | | | |
% 44.87/6.65 | | | | | | | BETA: splitting (75) gives:
% 44.87/6.65 | | | | | | |
% 44.87/6.65 | | | | | | | Case 1:
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | (76) queue(all_65_4) = all_155_1 & $i(all_155_1) & ~
% 44.87/6.65 | | | | | | | | elem(all_65_3, all_155_1)
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | ALPHA: (76) implies:
% 44.87/6.65 | | | | | | | | (77) queue(all_65_4) = all_155_1
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | GROUND_INST: instantiating (3) with all_65_2, all_155_1,
% 44.87/6.65 | | | | | | | | all_65_4, simplifying with (19), (77) gives:
% 44.87/6.65 | | | | | | | | (78) all_155_1 = all_65_2
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | GROUND_INST: instantiating (3) with all_143_0, all_155_1,
% 44.87/6.65 | | | | | | | | all_65_4, simplifying with (59), (77) gives:
% 44.87/6.65 | | | | | | | | (79) all_155_1 = all_143_0
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | COMBINE_EQS: (78), (79) imply:
% 44.87/6.65 | | | | | | | | (80) all_143_0 = all_65_2
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | SIMP: (80) implies:
% 44.87/6.65 | | | | | | | | (81) all_143_0 = all_65_2
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | REDUCE: (58), (81) imply:
% 44.87/6.65 | | | | | | | | (82) ~ elem(all_65_3, all_65_2)
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | PRED_UNIFY: (7), (82) imply:
% 44.87/6.65 | | | | | | | | (83) $false
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | CLOSE: (83) is inconsistent.
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | Case 2:
% 44.87/6.65 | | | | | | | |
% 44.87/6.65 | | | | | | | | (84) queue(all_65_16) = all_155_0 & $i(all_155_0) & ~
% 44.87/6.65 | | | | | | | | elem(all_65_0, all_155_0)
% 44.87/6.65 | | | | | | | |
% 44.87/6.66 | | | | | | | | ALPHA: (84) implies:
% 44.87/6.66 | | | | | | | | (85) ~ elem(all_65_0, all_155_0)
% 44.87/6.66 | | | | | | | | (86) queue(all_65_16) = all_155_0
% 44.87/6.66 | | | | | | | |
% 44.87/6.66 | | | | | | | | GROUND_INST: instantiating (3) with all_65_15, all_155_0,
% 44.87/6.66 | | | | | | | | all_65_16, simplifying with (18), (86) gives:
% 44.87/6.66 | | | | | | | | (87) all_155_0 = all_65_15
% 44.87/6.66 | | | | | | | |
% 44.87/6.66 | | | | | | | | GROUND_INST: instantiating (3) with all_89_1, all_155_0,
% 44.87/6.66 | | | | | | | | all_65_16, simplifying with (40), (86) gives:
% 44.87/6.66 | | | | | | | | (88) all_155_0 = all_89_1
% 44.87/6.66 | | | | | | | |
% 44.87/6.66 | | | | | | | | COMBINE_EQS: (87), (88) imply:
% 44.87/6.66 | | | | | | | | (89) all_89_1 = all_65_15
% 44.87/6.66 | | | | | | | |
% 44.87/6.66 | | | | | | | | REDUCE: (85), (87) imply:
% 44.87/6.66 | | | | | | | | (90) ~ elem(all_65_0, all_65_15)
% 44.87/6.66 | | | | | | | |
% 44.87/6.66 | | | | | | | | PRED_UNIFY: (32), (90) imply:
% 44.87/6.66 | | | | | | | | (91) $false
% 44.87/6.66 | | | | | | | |
% 44.87/6.66 | | | | | | | | CLOSE: (91) is inconsistent.
% 44.87/6.66 | | | | | | | |
% 44.87/6.66 | | | | | | | End of split
% 44.87/6.66 | | | | | | |
% 44.87/6.66 | | | | | | End of split
% 44.87/6.66 | | | | | |
% 44.87/6.66 | | | | | End of split
% 44.87/6.66 | | | | |
% 44.87/6.66 | | | | Case 2:
% 44.87/6.66 | | | | |
% 44.87/6.66 | | | | | (92) queue(all_65_16) = all_143_1 & $i(all_143_1) & ~
% 44.87/6.66 | | | | | elem(all_65_0, all_143_1)
% 44.87/6.66 | | | | |
% 44.87/6.66 | | | | | ALPHA: (92) implies:
% 44.87/6.66 | | | | | (93) ~ elem(all_65_0, all_143_1)
% 44.87/6.66 | | | | | (94) queue(all_65_16) = all_143_1
% 44.87/6.66 | | | | |
% 44.87/6.66 | | | | | GROUND_INST: instantiating (3) with all_65_15, all_143_1, all_65_16,
% 44.87/6.66 | | | | | simplifying with (18), (94) gives:
% 44.87/6.66 | | | | | (95) all_143_1 = all_65_15
% 44.87/6.66 | | | | |
% 44.87/6.66 | | | | | REDUCE: (93), (95) imply:
% 44.87/6.66 | | | | | (96) ~ elem(all_65_0, all_65_15)
% 44.87/6.66 | | | | |
% 44.87/6.66 | | | | | PRED_UNIFY: (32), (96) imply:
% 44.87/6.66 | | | | | (97) $false
% 44.87/6.66 | | | | |
% 44.87/6.66 | | | | | CLOSE: (97) is inconsistent.
% 44.87/6.66 | | | | |
% 44.87/6.66 | | | | End of split
% 44.87/6.66 | | | |
% 44.87/6.66 | | | End of split
% 44.87/6.66 | | |
% 44.87/6.66 | | End of split
% 44.87/6.66 | |
% 44.87/6.66 | End of split
% 44.87/6.66 |
% 44.87/6.66 End of proof
% 44.87/6.66 % SZS output end Proof for theBenchmark
% 44.87/6.66
% 44.87/6.66 6046ms
%------------------------------------------------------------------------------