%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV462+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 : n005.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 22:56:35 EDT 2023 % Result : Theorem 141.24s 19.16s % Output : Proof 142.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SWV462+1 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n005.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 03:43:53 EDT 2023 % 0.13/0.35 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.91/1.29 Prover 1: Preprocessing ... % 4.42/1.29 Prover 4: Preprocessing ... % 4.42/1.32 Prover 5: Preprocessing ... % 4.42/1.32 Prover 3: Preprocessing ... % 4.42/1.32 Prover 0: Preprocessing ... % 4.42/1.32 Prover 2: Preprocessing ... % 4.42/1.32 Prover 6: Preprocessing ... % 10.78/2.23 Prover 1: Constructing countermodel ... % 11.33/2.26 Prover 6: Proving ... % 11.59/2.28 Prover 3: Constructing countermodel ... % 13.06/2.48 Prover 2: Proving ... % 13.06/2.52 Prover 5: Proving ... % 15.03/2.75 Prover 0: Proving ... % 15.26/2.76 Prover 4: Constructing countermodel ... % 18.36/3.25 Prover 3: gave up % 18.36/3.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 19.60/3.37 Prover 7: Preprocessing ... % 24.20/4.00 Prover 7: Warning: ignoring some quantifiers % 24.87/4.04 Prover 7: Constructing countermodel ... % 25.50/4.12 Prover 1: gave up % 25.50/4.12 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 26.06/4.26 Prover 8: Preprocessing ... % 27.82/4.45 Prover 8: Warning: ignoring some quantifiers % 27.82/4.48 Prover 8: Constructing countermodel ... % 39.63/5.94 Prover 8: gave up % 39.63/5.94 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 39.63/5.98 Prover 9: Preprocessing ... % 42.64/6.35 Prover 9: Constructing countermodel ... % 60.64/8.66 Prover 2: stopped % 60.64/8.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 61.01/8.74 Prover 10: Preprocessing ... % 62.20/8.91 Prover 10: Warning: ignoring some quantifiers % 62.20/8.91 Prover 10: Constructing countermodel ... % 101.18/13.97 Prover 5: stopped % 101.18/13.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 101.85/14.04 Prover 11: Preprocessing ... % 105.79/14.54 Prover 11: Constructing countermodel ... % 130.84/17.88 Prover 6: stopped % 130.84/17.90 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 130.84/17.94 Prover 12: Preprocessing ... % 132.98/18.11 Prover 12: Proving ... % 140.73/19.14 Prover 10: Found proof (size 809) % 140.73/19.14 Prover 10: proved (10480ms) % 140.73/19.15 Prover 9: stopped % 140.73/19.15 Prover 7: stopped % 140.73/19.15 Prover 0: stopped % 140.73/19.15 Prover 11: stopped % 140.73/19.15 Prover 12: stopped % 141.24/19.16 Prover 4: stopped % 141.24/19.16 % 141.24/19.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 141.24/19.16 % 141.24/19.18 % SZS output start Proof for theBenchmark % 141.24/19.19 Assumptions after simplification: % 141.24/19.19 --------------------------------- % 141.24/19.19 % 141.24/19.19 (axiom_01) % 141.24/19.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~ (host(v0) = % 141.24/19.22 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v2) & s(v2) = v3 & % 141.24/19.22 $i(v3))) % 141.24/19.22 % 141.24/19.22 (axiom_04) % 141.24/19.22 $i(nbr_proc) & ! [v0: $i] : ! [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) | % 141.24/19.22 leq(v1, nbr_proc)) % 141.24/19.22 % 141.24/19.22 (axiom_09) % 141.24/19.22 ~ (norm = elec_2) & $i(norm) & $i(elec_2) % 141.24/19.22 % 141.24/19.22 (axiom_12) % 141.24/19.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v2) = v3) % 141.24/19.22 | ~ (m_Ack(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 141.24/19.22 % 141.24/19.22 (axiom_17) % 141.24/19.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~ % 141.24/19.22 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 141.24/19.22 % 141.24/19.22 (axiom_26) % 141.24/19.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v1) = v2) | ~ % 141.24/19.22 (m_Halt(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 141.24/19.22 % 141.24/19.22 (axiom_31) % 141.24/19.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 141.24/19.22 | ~ (m_Ack(v1, v3) = v4) | ~ (m_Ack(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) % 141.24/19.22 | ~ $i(v1) | ~ $i(v0)) % 141.24/19.22 % 141.24/19.22 (axiom_32) % 141.24/19.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2 % 141.24/19.23 | ~ (m_Ack(v1, v3) = v4) | ~ (m_Ack(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) % 141.24/19.23 | ~ $i(v1) | ~ $i(v0)) % 141.24/19.23 % 141.24/19.23 (axiom_46) % 141.24/19.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 141.24/19.23 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) | % 141.24/19.23 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 141.24/19.23 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 141.24/19.23 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) % 141.24/19.23 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2)) % 141.24/19.23 % 141.24/19.23 (axiom_47) % 141.47/19.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 141.47/19.23 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) | % 141.47/19.23 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 141.47/19.23 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 141.47/19.23 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (snoc(v1, v0) % 141.47/19.23 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2)) % 141.47/19.23 % 141.47/19.23 (axiom_48) % 141.47/19.23 ! [v0: $i] : ! [v1: $i] : ( ~ (m_Down(v1) = v0) | ~ $i(v1) | ~ $i(v0) | % 141.47/19.23 pidElem(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (m_Halt(v1) = v0) | ~ $i(v1) % 141.47/19.23 | ~ $i(v0) | pidElem(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ? % 141.47/19.23 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) = % 141.47/19.23 v0) | (v2 = v0 & m_Halt(v1) = v0)))) % 141.47/19.23 % 141.47/19.23 (axiom_61) % 141.47/19.23 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) % 141.47/19.23 | ~ leq(v0, v1)) & ? [v0: $i] : ( ~ $i(v0) | leq(v0, v0)) % 141.47/19.23 % 141.47/19.23 (axiom_62) % 141.47/19.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 141.47/19.24 ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2)) % 141.47/19.24 % 141.47/19.24 (axiom_63) % 141.47/19.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = v3) | ~ % 141.47/19.24 (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | leq(v0, v1)) & ! % 141.47/19.24 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = v3) | ~ % 141.47/19.24 (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) | leq(v2, v3)) % 141.47/19.24 % 141.47/19.24 (axiom_64) % 141.47/19.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (s(v1) = v2) | ~ % 141.47/19.24 $i(v1) | ~ $i(v0) | ~ leq(v0, v2) | leq(v0, v1)) & ! [v0: $i] : ! [v1: % 141.47/19.24 $i] : ! [v2: $i] : ( ~ (s(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 141.47/19.24 v1) | leq(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ (s(v1) = v0) | ~ % 141.47/19.24 $i(v1) | ~ $i(v0) | leq(v0, v0)) % 141.47/19.24 % 141.47/19.24 (conj) % 141.47/19.26 $i(down) & $i(ldr) & $i(elid) & $i(status) & $i(pendack) & $i(alive) & % 141.47/19.26 $i(norm) & $i(elec_1) & $i(elec_2) & $i(nbr_proc) & $i(zero) & ? [v0: $i] : % 141.47/19.26 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 141.47/19.26 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] % 141.47/19.26 : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : % 141.47/19.26 ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ( ~ (v10 = v4) & ~ (v7 = v4) & % 141.47/19.26 index(ldr, v10) = v10 & index(status, v10) = norm & index(status, v7) = % 141.47/19.26 elec_2 & index(pendack, v7) = v14 & snoc(v17, v8) = v18 & cons(v6, v1) = v5 % 141.47/19.26 & m_Down(v12) = v16 & m_Halt(v3) = v6 & s(v14) = v15 & s(zero) = v0 & % 141.47/19.26 m_Ack(v13, v11) = v19 & m_Ack(v3, v2) = v8 & host(v13) = v7 & host(v12) = % 141.47/19.26 v15 & host(v11) = v14 & host(v9) = v10 & host(v3) = v7 & host(v2) = v4 & % 141.47/19.26 queue(v7) = v17 & queue(v4) = v5 & $i(v19) & $i(v18) & $i(v17) & $i(v16) & % 141.47/19.26 $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) % 141.47/19.26 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 141.47/19.26 leq(nbr_proc, v15) & setIn(v13, alive) & setIn(v9, alive) & setIn(v2, alive) % 141.47/19.26 & elem(v19, v18) & elem(v16, v18) & ! [v20: $i] : ! [v21: $i] : ! [v22: % 141.47/19.26 $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ % 141.47/19.26 (m_Down(v22) = v25) | ~ (m_Ack(v23, v21) = v24) | ~ (host(v20) = v26) | % 141.47/19.26 ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v23, alive) | % 141.47/19.26 ~ setIn(v20, alive) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? % 141.47/19.26 [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : ? [v34: $i] : ? % 141.47/19.26 [v35: $i] : (( ~ (v35 = norm) & index(status, v26) = v35 & $i(v35)) | ( ~ % 141.47/19.26 (v34 = v26) & index(ldr, v26) = v34 & $i(v34)) | (host(v23) = v27 & % 141.47/19.26 $i(v27) & (( ~ (v33 = v30) & index(pendack, v27) = v29 & s(v29) = v30 % 141.47/19.26 & host(v22) = v33 & $i(v33) & $i(v30) & $i(v29)) | ( ~ (v32 = v29) % 141.47/19.26 & index(pendack, v27) = v29 & host(v21) = v32 & $i(v32) & $i(v29)) % 141.47/19.26 | ( ~ (v31 = elec_2) & index(status, v27) = v31 & $i(v31)) | % 141.47/19.26 (index(pendack, v27) = v29 & s(v29) = v30 & $i(v30) & $i(v29) & ~ % 141.47/19.26 leq(nbr_proc, v30)) | (queue(v27) = v28 & $i(v28) & ( ~ elem(v25, % 141.47/19.26 v28) | ~ elem(v24, v28))))))) & ! [v20: $i] : ! [v21: $i] : % 141.47/19.26 ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( % 141.47/19.26 ~ (m_Down(v22) = v24) | ~ (m_Down(v21) = v25) | ~ (host(v23) = nbr_proc) % 141.47/19.26 | ~ (host(v20) = v26) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) % 141.47/19.26 | ~ setIn(v20, alive) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? % 141.47/19.26 [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : ($i(v33) & (( ~ % 141.47/19.26 (v33 = v28) & index(down, nbr_proc) = v27 & host(v22) = v28 & % 141.47/19.26 $i(v28) & $i(v27) & leq(v0, v33) & ~ leq(nbr_proc, v33) & ~ % 141.47/19.26 setIn(v33, v27)) | ( ~ (v31 = elec_1) & index(status, nbr_proc) = % 141.47/19.26 v31 & $i(v31)) | ( ~ (v30 = nbr_proc) & host(v21) = v30 & $i(v30)) | % 141.47/19.26 (queue(v26) = v32 & $i(v32) & ~ elem(v25, v32)) | (queue(nbr_proc) = % 141.47/19.26 v29 & $i(v29) & ~ elem(v24, v29))))) & ! [v20: $i] : ! [v21: $i] % 141.47/19.26 : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ % 141.47/19.26 (m_Down(v21) = v23) | ~ (host(v22) = v24) | ~ (host(v20) = v25) | ~ % 141.47/19.26 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~ setIn(v20, % 141.47/19.26 alive) | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( % 141.47/19.26 ~ (v29 = norm) & index(status, v25) = v29 & $i(v29)) | ( ~ (v28 = v25) % 141.47/19.26 & index(ldr, v25) = v28 & $i(v28)) | ( ~ (v27 = v25) & host(v21) = v27 % 141.47/19.26 & $i(v27)) | (queue(v24) = v26 & $i(v26) & ~ elem(v23, v26)))) & ! % 141.47/19.26 [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! % 141.47/19.26 [v25: $i] : ( ~ (m_Halt(v22) = v24) | ~ (host(v21) = v25) | ~ (host(v20) = % 141.47/19.26 v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~ % 141.47/19.26 setIn(v20, alive) | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: % 141.47/19.26 $i] : ? [v30: $i] : ? [v31: $i] : (( ~ (v31 = norm) & index(status, % 141.47/19.26 v23) = v31 & $i(v31)) | ( ~ (v30 = v23) & index(ldr, v23) = v30 & % 141.47/19.26 $i(v30)) | ( ~ (v29 = elec_2) & index(status, v26) = v29 & host(v22) = % 141.47/19.26 v26 & $i(v29) & $i(v26)) | (index(pendack, v26) = v27 & host(v22) = % 141.47/19.26 v26 & $i(v27) & $i(v26) & leq(v27, v23)) | (queue(v25) = v28 & $i(v28) % 141.47/19.26 & ~ elem(v24, v28)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : % 141.47/19.26 ! [v23: $i] : ! [v24: $i] : ( ~ (m_Ack(v22, v20) = v23) | ~ (host(v21) = % 141.47/19.26 v24) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ? [v25: $i] : ? [v26: % 141.47/19.26 $i] : ? [v27: $i] : ((host(v22) = v27 & host(v20) = v26 & $i(v27) & % 141.47/19.26 $i(v26) & ~ leq(v26, v27)) | (queue(v24) = v25 & $i(v25) & ~ % 141.47/19.26 elem(v23, v25)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! % 141.47/19.26 [v23: $i] : ! [v24: $i] : ( ~ (m_Ack(v20, v21) = v24) | ~ (host(v22) = % 141.47/19.26 v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~ % 141.47/19.26 setIn(v20, alive) | ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 141.47/19.26 $i] : ? [v29: $i] : (( ~ (v28 = elec_2) & index(status, v23) = v28 & % 141.47/19.26 $i(v28)) | ( ~ (v27 = elec_2) & index(status, v26) = v27 & host(v20) = % 141.47/19.26 v26 & $i(v27) & $i(v26)) | ( ~ (v25 = v23) & host(v21) = v25 & % 141.47/19.26 $i(v25)) | (host(v20) = v26 & queue(v26) = v29 & $i(v29) & $i(v26) & % 141.47/19.26 ~ elem(v24, v29)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! % 141.47/19.26 [v23: $i] : ( ~ (m_Ldr(v21) = v22) | ~ (host(v20) = v23) | ~ $i(v21) | ~ % 141.47/19.26 $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) = v25 & $i(v25) & ~ % 141.47/19.26 leq(v23, v25)) | (queue(v23) = v24 & $i(v24) & ~ elem(v22, v24)))) & % 141.47/19.26 ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (m_Down(v21) % 141.47/19.26 = v22) | ~ (host(v20) = v23) | ~ $i(v21) | ~ $i(v20) | ? [v24: $i] : % 141.47/19.26 ? [v25: $i] : (( ~ (v25 = v23) & host(v21) = v25 & $i(v25)) | (queue(v23) % 141.47/19.26 = v24 & $i(v24) & ~ elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : % 141.47/19.26 ! [v22: $i] : ! [v23: $i] : ( ~ (m_Halt(v21) = v22) | ~ (host(v20) = v23) % 141.47/19.26 | ~ $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) = % 141.47/19.26 v25 & $i(v25) & ~ leq(v23, v25)) | (queue(v23) = v24 & $i(v24) & ~ % 141.47/19.26 elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! % 141.47/19.26 [v23: $i] : ( ~ (host(v21) = v23) | ~ (host(v20) = v22) | ~ $i(v21) | ~ % 141.47/19.26 $i(v20) | ~ setIn(v21, alive) | ~ setIn(v20, alive) | leq(v22, v23) | ? % 141.47/19.26 [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : (( ~ (v25 = % 141.47/19.26 elec_2) & index(status, v23) = v25 & $i(v25)) | ( ~ (v24 = elec_2) & % 141.47/19.26 index(status, v22) = v24 & $i(v24)) | (index(pendack, v23) = v27 & % 141.47/19.26 index(pendack, v22) = v26 & $i(v27) & $i(v26) & ~ leq(v26, v27)))) & % 141.47/19.26 ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (host(v21) = % 141.47/19.26 v23) | ~ (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, % 141.47/19.26 alive) | ~ setIn(v20, alive) | leq(v22, v23) | ? [v24: $i] : ? [v25: % 141.47/19.26 $i] : ? [v26: $i] : (( ~ (v25 = elec_2) & index(status, v23) = v25 & % 141.47/19.26 $i(v25)) | ( ~ (v24 = elec_2) & index(status, v22) = v24 & $i(v24)) | % 141.47/19.27 (index(pendack, v23) = v26 & $i(v26) & leq(v26, v22)))) & ! [v20: $i] : % 141.47/19.27 ! [v21: $i] : ! [v22: $i] : (v21 = v20 | ~ (host(v21) = v22) | ~ % 141.47/19.27 (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) | ~ % 141.47/19.27 setIn(v20, alive)) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ % 141.47/19.27 (m_Ack(v21, v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) | % 141.47/19.27 ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : (host(v21) = % 141.47/19.27 v23 & $i(v23) & ((index(pendack, v23) = v26 & host(v20) = v25 & $i(v26) % 141.47/19.27 & $i(v25) & leq(v25, v26)) | (queue(v23) = v24 & $i(v24) & ~ % 141.47/19.27 elem(v22, v24))))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( % 141.47/19.27 ~ (m_Ack(v21, v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) % 141.47/19.27 | ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : (host(v21) = v23 & $i(v23) % 141.47/19.27 & (( ~ (v24 = elec_1) & index(status, v23) = v24 & $i(v24)) | % 141.47/19.27 (queue(v23) = v25 & $i(v25) & ~ elem(v22, v25))))) & ! [v20: $i] : % 141.47/19.27 ! [v21: $i] : ( ~ (host(v20) = v21) | ~ $i(v20) | ~ setIn(v20, alive) | ? % 141.47/19.27 [v22: $i] : ? [v23: $i] : ((v23 = v20 & index(elid, v21) = v20) | ( ~ % 141.47/19.27 (v22 = elec_1) & ~ (v22 = elec_2) & index(status, v21) = v22 & % 141.47/19.27 $i(v22))))) % 141.47/19.27 % 141.47/19.27 (function-axioms) % 141.47/19.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 141.47/19.27 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 141.47/19.27 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3, % 141.47/19.27 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 141.47/19.27 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! % 141.47/19.27 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~ % 141.47/19.27 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 141.47/19.27 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 141.47/19.27 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i] % 141.47/19.27 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) = % 141.47/19.27 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) = % 141.47/19.27 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 141.47/19.27 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 141.47/19.27 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & ! % 141.47/19.27 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~ % 141.47/19.27 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 141.47/19.27 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 141.47/19.27 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & ! % 141.47/19.27 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~ % 141.47/19.27 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 141.47/19.27 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 141.47/19.27 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1: % 141.47/19.27 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0)) % 141.47/19.27 % 141.47/19.27 Further assumptions not needed in the proof: % 141.47/19.27 -------------------------------------------- % 141.79/19.27 axiom, axiom_02, axiom_03, axiom_05, axiom_06, axiom_07, axiom_08, axiom_10, % 141.79/19.27 axiom_11, axiom_13, axiom_14, axiom_15, axiom_16, axiom_18, axiom_19, axiom_20, % 141.79/19.27 axiom_21, axiom_22, axiom_23, axiom_24, axiom_25, axiom_27, axiom_28, axiom_29, % 141.79/19.27 axiom_30, axiom_33, axiom_34, axiom_35, axiom_36, axiom_37, axiom_38, axiom_39, % 141.79/19.27 axiom_40, axiom_41, axiom_42, axiom_43, axiom_44, axiom_45, axiom_49, axiom_50, % 141.79/19.27 axiom_51, axiom_52, axiom_53, axiom_54, axiom_55, axiom_56, axiom_57, axiom_58, % 141.79/19.27 axiom_59, axiom_60, axiom_65 % 141.79/19.27 % 141.79/19.27 Those formulas are unsatisfiable: % 141.79/19.27 --------------------------------- % 141.79/19.27 % 141.79/19.27 Begin of proof % 141.79/19.27 | % 141.79/19.27 | ALPHA: (axiom_04) implies: % 141.79/19.27 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) | leq(v1, % 141.79/19.27 | nbr_proc)) % 141.79/19.27 | % 141.79/19.27 | ALPHA: (axiom_09) implies: % 141.79/19.27 | (2) ~ (norm = elec_2) % 141.79/19.27 | % 141.79/19.27 | ALPHA: (axiom_46) implies: % 141.79/19.27 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) = v2) | ~ % 141.79/19.27 | $i(v1) | ~ $i(v0) | elem(v0, v2)) % 141.79/19.28 | % 141.79/19.28 | ALPHA: (axiom_47) implies: % 141.79/19.28 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 141.79/19.28 | (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, % 141.79/19.28 | v3) | elem(v0, v2)) % 141.79/19.28 | % 141.79/19.28 | ALPHA: (axiom_48) implies: % 141.79/19.28 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ? [v1: $i] : ? [v2: $i] : % 141.79/19.28 | ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) = v0) | (v2 = v0 & % 141.79/19.28 | m_Halt(v1) = v0)))) % 141.79/19.28 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (m_Halt(v1) = v0) | ~ $i(v1) | ~ % 141.79/19.28 | $i(v0) | pidElem(v0)) % 141.79/19.28 | % 141.79/19.28 | ALPHA: (axiom_61) implies: % 141.79/19.28 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 141.79/19.28 | leq(v1, v0) | ~ leq(v0, v1)) % 141.79/19.28 | % 141.79/19.28 | ALPHA: (axiom_63) implies: % 141.79/19.28 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = % 141.79/19.28 | v3) | ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | % 141.79/19.28 | leq(v0, v1)) % 141.79/19.28 | % 141.79/19.28 | ALPHA: (axiom_64) implies: % 141.79/19.28 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (s(v1) = v0) | ~ $i(v1) | ~ $i(v0) | % 141.79/19.28 | leq(v0, v0)) % 141.79/19.28 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (s(v1) = v2) | % 141.79/19.28 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v2) | leq(v0, v1)) % 141.79/19.28 | % 141.79/19.28 | ALPHA: (conj) implies: % 141.79/19.28 | (11) $i(nbr_proc) % 141.79/19.30 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 141.79/19.30 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 141.79/19.30 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 141.79/19.30 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 141.79/19.30 | [v19: $i] : ( ~ (v10 = v4) & ~ (v7 = v4) & index(ldr, v10) = v10 & % 141.79/19.30 | index(status, v10) = norm & index(status, v7) = elec_2 & % 141.79/19.30 | index(pendack, v7) = v14 & snoc(v17, v8) = v18 & cons(v6, v1) = v5 & % 141.79/19.30 | m_Down(v12) = v16 & m_Halt(v3) = v6 & s(v14) = v15 & s(zero) = v0 & % 141.79/19.30 | m_Ack(v13, v11) = v19 & m_Ack(v3, v2) = v8 & host(v13) = v7 & % 141.79/19.30 | host(v12) = v15 & host(v11) = v14 & host(v9) = v10 & host(v3) = v7 & % 141.79/19.30 | host(v2) = v4 & queue(v7) = v17 & queue(v4) = v5 & $i(v19) & $i(v18) % 141.79/19.30 | & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 141.79/19.30 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 141.79/19.30 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(nbr_proc, v15) & % 141.79/19.30 | setIn(v13, alive) & setIn(v9, alive) & setIn(v2, alive) & elem(v19, % 141.79/19.30 | v18) & elem(v16, v18) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] % 141.79/19.30 | : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ % 141.79/19.30 | (m_Down(v22) = v25) | ~ (m_Ack(v23, v21) = v24) | ~ (host(v20) = % 141.79/19.30 | v26) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ % 141.79/19.30 | setIn(v23, alive) | ~ setIn(v20, alive) | ? [v27: $i] : ? [v28: % 141.79/19.30 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] % 141.79/19.30 | : ? [v33: $i] : ? [v34: $i] : ? [v35: $i] : (( ~ (v35 = norm) & % 141.79/19.30 | index(status, v26) = v35 & $i(v35)) | ( ~ (v34 = v26) & % 141.79/19.30 | index(ldr, v26) = v34 & $i(v34)) | (host(v23) = v27 & $i(v27) % 141.79/19.30 | & (( ~ (v33 = v30) & index(pendack, v27) = v29 & s(v29) = v30 % 141.79/19.30 | & host(v22) = v33 & $i(v33) & $i(v30) & $i(v29)) | ( ~ % 141.79/19.30 | (v32 = v29) & index(pendack, v27) = v29 & host(v21) = v32 % 141.79/19.30 | & $i(v32) & $i(v29)) | ( ~ (v31 = elec_2) & index(status, % 141.79/19.30 | v27) = v31 & $i(v31)) | (index(pendack, v27) = v29 & % 141.79/19.30 | s(v29) = v30 & $i(v30) & $i(v29) & ~ leq(nbr_proc, v30)) % 141.79/19.30 | | (queue(v27) = v28 & $i(v28) & ( ~ elem(v25, v28) | ~ % 141.79/19.30 | elem(v24, v28))))))) & ! [v20: $i] : ! [v21: $i] : ! % 141.79/19.30 | [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: % 141.79/19.30 | $i] : ( ~ (m_Down(v22) = v24) | ~ (m_Down(v21) = v25) | ~ % 141.79/19.30 | (host(v23) = nbr_proc) | ~ (host(v20) = v26) | ~ $i(v23) | ~ % 141.79/19.30 | $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v20, alive) | ? % 141.79/19.30 | [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: % 141.79/19.30 | $i] : ? [v32: $i] : ? [v33: $i] : ($i(v33) & (( ~ (v33 = v28) % 141.79/19.30 | & index(down, nbr_proc) = v27 & host(v22) = v28 & $i(v28) & % 141.79/19.30 | $i(v27) & leq(v0, v33) & ~ leq(nbr_proc, v33) & ~ % 141.79/19.30 | setIn(v33, v27)) | ( ~ (v31 = elec_1) & index(status, % 141.79/19.30 | nbr_proc) = v31 & $i(v31)) | ( ~ (v30 = nbr_proc) & % 141.79/19.30 | host(v21) = v30 & $i(v30)) | (queue(v26) = v32 & $i(v32) & % 141.79/19.30 | ~ elem(v25, v32)) | (queue(nbr_proc) = v29 & $i(v29) & ~ % 141.79/19.30 | elem(v24, v29))))) & ! [v20: $i] : ! [v21: $i] : ! [v22: % 141.79/19.30 | $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ % 141.79/19.30 | (m_Down(v21) = v23) | ~ (host(v22) = v24) | ~ (host(v20) = v25) % 141.79/19.30 | | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~ % 141.79/19.30 | setIn(v20, alive) | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : % 141.79/19.30 | ? [v29: $i] : (( ~ (v29 = norm) & index(status, v25) = v29 & % 141.79/19.30 | $i(v29)) | ( ~ (v28 = v25) & index(ldr, v25) = v28 & $i(v28)) % 141.79/19.30 | | ( ~ (v27 = v25) & host(v21) = v27 & $i(v27)) | (queue(v24) = % 141.79/19.30 | v26 & $i(v26) & ~ elem(v23, v26)))) & ! [v20: $i] : ! [v21: % 141.79/19.30 | $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : % 141.79/19.30 | ( ~ (m_Halt(v22) = v24) | ~ (host(v21) = v25) | ~ (host(v20) = % 141.79/19.30 | v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, % 141.79/19.30 | alive) | ~ setIn(v20, alive) | ? [v26: $i] : ? [v27: $i] : ? % 141.79/19.30 | [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (( ~ (v31 % 141.79/19.30 | = norm) & index(status, v23) = v31 & $i(v31)) | ( ~ (v30 = % 141.79/19.30 | v23) & index(ldr, v23) = v30 & $i(v30)) | ( ~ (v29 = elec_2) % 141.79/19.30 | & index(status, v26) = v29 & host(v22) = v26 & $i(v29) & % 141.79/19.30 | $i(v26)) | (index(pendack, v26) = v27 & host(v22) = v26 & % 141.79/19.30 | $i(v27) & $i(v26) & leq(v27, v23)) | (queue(v25) = v28 & % 141.79/19.30 | $i(v28) & ~ elem(v24, v28)))) & ! [v20: $i] : ! [v21: $i] : % 141.79/19.30 | ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (m_Ack(v22, v20) = % 141.79/19.30 | v23) | ~ (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ~ % 141.79/19.30 | $i(v20) | ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ((host(v22) % 141.79/19.30 | = v27 & host(v20) = v26 & $i(v27) & $i(v26) & ~ leq(v26, % 141.79/19.30 | v27)) | (queue(v24) = v25 & $i(v25) & ~ elem(v23, v25)))) & % 141.79/19.30 | ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: % 141.79/19.30 | $i] : ( ~ (m_Ack(v20, v21) = v24) | ~ (host(v22) = v23) | ~ % 141.79/19.30 | $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~ % 141.79/19.30 | setIn(v20, alive) | ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : % 141.79/19.30 | ? [v28: $i] : ? [v29: $i] : (( ~ (v28 = elec_2) & index(status, % 141.79/19.30 | v23) = v28 & $i(v28)) | ( ~ (v27 = elec_2) & index(status, % 141.79/19.30 | v26) = v27 & host(v20) = v26 & $i(v27) & $i(v26)) | ( ~ (v25 % 141.79/19.30 | = v23) & host(v21) = v25 & $i(v25)) | (host(v20) = v26 & % 141.79/19.30 | queue(v26) = v29 & $i(v29) & $i(v26) & ~ elem(v24, v29)))) & % 141.79/19.30 | ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ % 141.79/19.30 | (m_Ldr(v21) = v22) | ~ (host(v20) = v23) | ~ $i(v21) | ~ % 141.79/19.30 | $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) = v25 & % 141.79/19.30 | $i(v25) & ~ leq(v23, v25)) | (queue(v23) = v24 & $i(v24) & ~ % 141.79/19.30 | elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] % 141.79/19.30 | : ! [v23: $i] : ( ~ (m_Down(v21) = v22) | ~ (host(v20) = v23) | ~ % 141.79/19.30 | $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25: $i] : (( ~ (v25 = % 141.79/19.30 | v23) & host(v21) = v25 & $i(v25)) | (queue(v23) = v24 & % 141.79/19.30 | $i(v24) & ~ elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : % 141.79/19.30 | ! [v22: $i] : ! [v23: $i] : ( ~ (m_Halt(v21) = v22) | ~ % 141.79/19.30 | (host(v20) = v23) | ~ $i(v21) | ~ $i(v20) | ? [v24: $i] : ? % 141.79/19.30 | [v25: $i] : ((host(v21) = v25 & $i(v25) & ~ leq(v23, v25)) | % 141.79/19.30 | (queue(v23) = v24 & $i(v24) & ~ elem(v22, v24)))) & ! [v20: % 141.79/19.30 | $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (host(v21) % 141.79/19.30 | = v23) | ~ (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ % 141.79/19.30 | setIn(v21, alive) | ~ setIn(v20, alive) | leq(v22, v23) | ? % 141.79/19.30 | [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : (( ~ (v25 % 141.79/19.30 | = elec_2) & index(status, v23) = v25 & $i(v25)) | ( ~ (v24 = % 141.79/19.30 | elec_2) & index(status, v22) = v24 & $i(v24)) | % 141.79/19.30 | (index(pendack, v23) = v27 & index(pendack, v22) = v26 & $i(v27) % 141.79/19.30 | & $i(v26) & ~ leq(v26, v27)))) & ! [v20: $i] : ! [v21: $i] % 141.79/19.30 | : ! [v22: $i] : ! [v23: $i] : ( ~ (host(v21) = v23) | ~ % 141.79/19.30 | (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) % 141.79/19.30 | | ~ setIn(v20, alive) | leq(v22, v23) | ? [v24: $i] : ? [v25: % 141.79/19.30 | $i] : ? [v26: $i] : (( ~ (v25 = elec_2) & index(status, v23) = % 141.79/19.30 | v25 & $i(v25)) | ( ~ (v24 = elec_2) & index(status, v22) = v24 % 141.79/19.30 | & $i(v24)) | (index(pendack, v23) = v26 & $i(v26) & leq(v26, % 141.79/19.30 | v22)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : (v21 % 141.79/19.30 | = v20 | ~ (host(v21) = v22) | ~ (host(v20) = v22) | ~ $i(v21) | % 141.79/19.30 | ~ $i(v20) | ~ setIn(v21, alive) | ~ setIn(v20, alive)) & ! % 141.79/19.30 | [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ (m_Ack(v21, v20) = % 141.79/19.30 | v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) | ? [v23: % 141.79/19.30 | $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : (host(v21) = % 141.79/19.30 | v23 & $i(v23) & ((index(pendack, v23) = v26 & host(v20) = v25 & % 141.79/19.30 | $i(v26) & $i(v25) & leq(v25, v26)) | (queue(v23) = v24 & % 141.79/19.30 | $i(v24) & ~ elem(v22, v24))))) & ! [v20: $i] : ! [v21: % 141.79/19.30 | $i] : ! [v22: $i] : ( ~ (m_Ack(v21, v20) = v22) | ~ $i(v21) | ~ % 141.79/19.30 | $i(v20) | ~ setIn(v21, alive) | ? [v23: $i] : ? [v24: $i] : ? % 141.79/19.30 | [v25: $i] : (host(v21) = v23 & $i(v23) & (( ~ (v24 = elec_1) & % 141.79/19.30 | index(status, v23) = v24 & $i(v24)) | (queue(v23) = v25 & % 141.79/19.30 | $i(v25) & ~ elem(v22, v25))))) & ! [v20: $i] : ! [v21: % 141.79/19.30 | $i] : ( ~ (host(v20) = v21) | ~ $i(v20) | ~ setIn(v20, alive) | % 141.79/19.30 | ? [v22: $i] : ? [v23: $i] : ((v23 = v20 & index(elid, v21) = v20) % 141.79/19.30 | | ( ~ (v22 = elec_1) & ~ (v22 = elec_2) & index(status, v21) = % 141.79/19.30 | v22 & $i(v22))))) % 141.79/19.30 | % 141.79/19.30 | ALPHA: (function-axioms) implies: % 141.79/19.30 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = % 141.79/19.30 | v1) | ~ (queue(v2) = v0)) % 141.79/19.30 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = % 141.79/19.30 | v1) | ~ (host(v2) = v0)) % 141.79/19.30 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 141.79/19.30 | ~ (s(v2) = v0)) % 141.79/19.30 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 141.79/19.30 | (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) % 141.79/19.30 | % 141.79/19.30 | DELTA: instantiating (12) with fresh symbols all_65_0, all_65_1, all_65_2, % 141.79/19.30 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9, % 141.79/19.30 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15, % 141.79/19.30 | all_65_16, all_65_17, all_65_18, all_65_19 gives: % 141.94/19.32 | (17) ~ (all_65_9 = all_65_15) & ~ (all_65_12 = all_65_15) & index(ldr, % 141.94/19.32 | all_65_9) = all_65_9 & index(status, all_65_9) = norm & % 141.94/19.32 | index(status, all_65_12) = elec_2 & index(pendack, all_65_12) = % 141.94/19.32 | all_65_5 & snoc(all_65_2, all_65_11) = all_65_1 & cons(all_65_13, % 141.94/19.32 | all_65_18) = all_65_14 & m_Down(all_65_7) = all_65_3 & % 141.94/19.32 | m_Halt(all_65_16) = all_65_13 & s(all_65_5) = all_65_4 & s(zero) = % 141.94/19.32 | all_65_19 & m_Ack(all_65_6, all_65_8) = all_65_0 & m_Ack(all_65_16, % 141.94/19.32 | all_65_17) = all_65_11 & host(all_65_6) = all_65_12 & host(all_65_7) % 141.94/19.32 | = all_65_4 & host(all_65_8) = all_65_5 & host(all_65_10) = all_65_9 & % 141.94/19.32 | host(all_65_16) = all_65_12 & host(all_65_17) = all_65_15 & % 141.94/19.32 | queue(all_65_12) = all_65_2 & queue(all_65_15) = all_65_14 & % 141.94/19.32 | $i(all_65_0) & $i(all_65_1) & $i(all_65_2) & $i(all_65_3) & % 141.94/19.32 | $i(all_65_4) & $i(all_65_5) & $i(all_65_6) & $i(all_65_7) & % 141.94/19.32 | $i(all_65_8) & $i(all_65_9) & $i(all_65_10) & $i(all_65_11) & % 141.94/19.32 | $i(all_65_12) & $i(all_65_13) & $i(all_65_14) & $i(all_65_15) & % 141.94/19.32 | $i(all_65_16) & $i(all_65_17) & $i(all_65_18) & $i(all_65_19) & % 141.94/19.32 | leq(nbr_proc, all_65_4) & setIn(all_65_6, alive) & setIn(all_65_10, % 141.94/19.32 | alive) & setIn(all_65_17, alive) & elem(all_65_0, all_65_1) & % 141.94/19.32 | elem(all_65_3, all_65_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 141.94/19.32 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (m_Down(v2) % 141.94/19.32 | = v5) | ~ (m_Ack(v3, v1) = v4) | ~ (host(v0) = v6) | ~ $i(v3) | % 141.94/19.32 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v3, alive) | ~ % 141.94/19.32 | setIn(v0, alive) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 141.94/19.32 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 141.94/19.32 | $i] : ? [v15: $i] : (( ~ (v15 = norm) & index(status, v6) = v15 & % 141.94/19.32 | $i(v15)) | ( ~ (v14 = v6) & index(ldr, v6) = v14 & $i(v14)) | % 141.94/19.32 | (host(v3) = v7 & $i(v7) & (( ~ (v13 = v10) & index(pendack, v7) = % 141.94/19.32 | v9 & s(v9) = v10 & host(v2) = v13 & $i(v13) & $i(v10) & % 141.94/19.32 | $i(v9)) | ( ~ (v12 = v9) & index(pendack, v7) = v9 & % 141.94/19.32 | host(v1) = v12 & $i(v12) & $i(v9)) | ( ~ (v11 = elec_2) & % 141.94/19.32 | index(status, v7) = v11 & $i(v11)) | (index(pendack, v7) = % 141.94/19.32 | v9 & s(v9) = v10 & $i(v10) & $i(v9) & ~ leq(nbr_proc, v10)) % 141.94/19.32 | | (queue(v7) = v8 & $i(v8) & ( ~ elem(v5, v8) | ~ elem(v4, % 141.94/19.32 | v8))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 141.94/19.32 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (m_Down(v2) = % 141.94/19.32 | v4) | ~ (m_Down(v1) = v5) | ~ (host(v3) = nbr_proc) | ~ % 141.94/19.32 | (host(v0) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 141.94/19.32 | setIn(v0, alive) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 141.94/19.32 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ($i(v13) & % 141.94/19.32 | (( ~ (v13 = v8) & index(down, nbr_proc) = v7 & host(v2) = v8 & % 141.94/19.32 | $i(v8) & $i(v7) & leq(all_65_19, v13) & ~ leq(nbr_proc, v13) % 141.94/19.32 | & ~ setIn(v13, v7)) | ( ~ (v11 = elec_1) & index(status, % 141.94/19.32 | nbr_proc) = v11 & $i(v11)) | ( ~ (v10 = nbr_proc) & host(v1) % 141.94/19.32 | = v10 & $i(v10)) | (queue(v6) = v12 & $i(v12) & ~ elem(v5, % 141.94/19.32 | v12)) | (queue(nbr_proc) = v9 & $i(v9) & ~ elem(v4, v9))))) % 141.94/19.32 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 141.94/19.32 | : ! [v5: $i] : ( ~ (m_Down(v1) = v3) | ~ (host(v2) = v4) | ~ % 141.94/19.32 | (host(v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, % 141.94/19.32 | alive) | ~ setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: % 141.94/19.32 | $i] : ? [v9: $i] : (( ~ (v9 = norm) & index(status, v5) = v9 & % 141.94/19.32 | $i(v9)) | ( ~ (v8 = v5) & index(ldr, v5) = v8 & $i(v8)) | ( ~ % 141.94/19.32 | (v7 = v5) & host(v1) = v7 & $i(v7)) | (queue(v4) = v6 & $i(v6) & % 141.94/19.32 | ~ elem(v3, v6)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 141.94/19.32 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (m_Halt(v2) = v4) | ~ % 141.94/19.32 | (host(v1) = v5) | ~ (host(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 141.94/19.32 | $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? [v6: $i] : % 141.94/19.32 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] % 141.94/19.32 | : (( ~ (v11 = norm) & index(status, v3) = v11 & $i(v11)) | ( ~ (v10 % 141.94/19.32 | = v3) & index(ldr, v3) = v10 & $i(v10)) | ( ~ (v9 = elec_2) & % 141.94/19.32 | index(status, v6) = v9 & host(v2) = v6 & $i(v9) & $i(v6)) | % 141.94/19.32 | (index(pendack, v6) = v7 & host(v2) = v6 & $i(v7) & $i(v6) & % 141.94/19.32 | leq(v7, v3)) | (queue(v5) = v8 & $i(v8) & ~ elem(v4, v8)))) & % 141.94/19.32 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 141.94/19.32 | ~ (m_Ack(v2, v0) = v3) | ~ (host(v1) = v4) | ~ $i(v2) | ~ $i(v1) % 141.94/19.32 | | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((host(v2) = % 141.94/19.32 | v7 & host(v0) = v6 & $i(v7) & $i(v6) & ~ leq(v6, v7)) | % 141.94/19.32 | (queue(v4) = v5 & $i(v5) & ~ elem(v3, v5)))) & ! [v0: $i] : ! % 141.94/19.32 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (m_Ack(v0, % 141.94/19.32 | v1) = v4) | ~ (host(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 141.94/19.32 | $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? [v5: $i] : % 141.94/19.32 | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (( ~ (v8 = % 141.94/19.32 | elec_2) & index(status, v3) = v8 & $i(v8)) | ( ~ (v7 = elec_2) % 141.94/19.32 | & index(status, v6) = v7 & host(v0) = v6 & $i(v7) & $i(v6)) | ( % 141.94/19.32 | ~ (v5 = v3) & host(v1) = v5 & $i(v5)) | (host(v0) = v6 & % 141.94/19.32 | queue(v6) = v9 & $i(v9) & $i(v6) & ~ elem(v4, v9)))) & ! [v0: % 141.94/19.32 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Ldr(v1) = v2) % 141.94/19.32 | | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: % 141.94/19.32 | $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3) = v4 % 141.94/19.32 | & $i(v4) & ~ elem(v2, v4)))) & ! [v0: $i] : ! [v1: $i] : ! % 141.94/19.32 | [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v1) = v2) | ~ (host(v0) = v3) | % 141.94/19.32 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & % 141.94/19.32 | host(v1) = v5 & $i(v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, % 141.94/19.32 | v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 141.94/19.32 | : ( ~ (m_Halt(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 141.94/19.32 | ? [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, % 141.94/19.32 | v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) & ! [v0: % 141.94/19.32 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) = v3) % 141.94/19.32 | | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | % 141.94/19.32 | ~ setIn(v0, alive) | leq(v2, v3) | ? [v4: $i] : ? [v5: $i] : ? % 141.94/19.32 | [v6: $i] : ? [v7: $i] : (( ~ (v5 = elec_2) & index(status, v3) = v5 % 141.94/19.32 | & $i(v5)) | ( ~ (v4 = elec_2) & index(status, v2) = v4 & $i(v4)) % 141.94/19.32 | | (index(pendack, v3) = v7 & index(pendack, v2) = v6 & $i(v7) & % 141.94/19.32 | $i(v6) & ~ leq(v6, v7)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 141.94/19.32 | $i] : ! [v3: $i] : ( ~ (host(v1) = v3) | ~ (host(v0) = v2) | ~ % 141.94/19.32 | $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive) | % 141.94/19.32 | leq(v2, v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (( ~ (v5 = % 141.94/19.32 | elec_2) & index(status, v3) = v5 & $i(v5)) | ( ~ (v4 = elec_2) % 141.94/19.32 | & index(status, v2) = v4 & $i(v4)) | (index(pendack, v3) = v6 & % 141.94/19.32 | $i(v6) & leq(v6, v2)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 141.94/19.32 | $i] : (v1 = v0 | ~ (host(v1) = v2) | ~ (host(v0) = v2) | ~ $i(v1) % 141.94/19.32 | | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive)) & ! [v0: % 141.94/19.32 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Ack(v1, v0) = v2) | ~ % 141.94/19.32 | $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ? [v3: $i] : ? [v4: $i] % 141.94/19.32 | : ? [v5: $i] : ? [v6: $i] : (host(v1) = v3 & $i(v3) & % 141.94/19.32 | ((index(pendack, v3) = v6 & host(v0) = v5 & $i(v6) & $i(v5) & % 141.94/19.32 | leq(v5, v6)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4))))) % 141.94/19.32 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Ack(v1, v0) = v2) | % 141.94/19.32 | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ? [v3: $i] : ? [v4: % 141.94/19.32 | $i] : ? [v5: $i] : (host(v1) = v3 & $i(v3) & (( ~ (v4 = elec_1) & % 141.94/19.32 | index(status, v3) = v4 & $i(v4)) | (queue(v3) = v5 & $i(v5) & % 141.94/19.32 | ~ elem(v2, v5))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (host(v0) % 141.94/19.32 | = v1) | ~ $i(v0) | ~ setIn(v0, alive) | ? [v2: $i] : ? [v3: % 141.94/19.32 | $i] : ((v3 = v0 & index(elid, v1) = v0) | ( ~ (v2 = elec_1) & ~ % 141.94/19.32 | (v2 = elec_2) & index(status, v1) = v2 & $i(v2)))) % 141.94/19.32 | % 141.94/19.32 | ALPHA: (17) implies: % 141.94/19.32 | (18) ~ (all_65_9 = all_65_15) % 141.94/19.32 | (19) elem(all_65_3, all_65_1) % 141.94/19.32 | (20) elem(all_65_0, all_65_1) % 141.94/19.32 | (21) setIn(all_65_17, alive) % 141.94/19.32 | (22) setIn(all_65_10, alive) % 141.94/19.32 | (23) setIn(all_65_6, alive) % 141.94/19.32 | (24) leq(nbr_proc, all_65_4) % 141.94/19.32 | (25) $i(all_65_18) % 141.94/19.32 | (26) $i(all_65_17) % 141.94/19.32 | (27) $i(all_65_16) % 141.94/19.32 | (28) $i(all_65_15) % 141.94/19.32 | (29) $i(all_65_13) % 141.94/19.32 | (30) $i(all_65_11) % 141.94/19.32 | (31) $i(all_65_10) % 141.94/19.32 | (32) $i(all_65_9) % 141.94/19.32 | (33) $i(all_65_8) % 141.94/19.32 | (34) $i(all_65_7) % 141.94/19.32 | (35) $i(all_65_6) % 141.94/19.32 | (36) $i(all_65_5) % 141.94/19.32 | (37) $i(all_65_4) % 141.94/19.32 | (38) $i(all_65_3) % 141.94/19.32 | (39) $i(all_65_2) % 141.94/19.32 | (40) $i(all_65_0) % 141.94/19.32 | (41) queue(all_65_15) = all_65_14 % 141.94/19.32 | (42) queue(all_65_12) = all_65_2 % 141.94/19.32 | (43) host(all_65_17) = all_65_15 % 141.94/19.32 | (44) host(all_65_16) = all_65_12 % 141.94/19.32 | (45) host(all_65_10) = all_65_9 % 141.94/19.32 | (46) host(all_65_8) = all_65_5 % 141.94/19.32 | (47) host(all_65_7) = all_65_4 % 141.94/19.32 | (48) host(all_65_6) = all_65_12 % 141.94/19.32 | (49) m_Ack(all_65_16, all_65_17) = all_65_11 % 141.94/19.32 | (50) m_Ack(all_65_6, all_65_8) = all_65_0 % 141.94/19.32 | (51) s(all_65_5) = all_65_4 % 141.94/19.32 | (52) m_Halt(all_65_16) = all_65_13 % 141.94/19.32 | (53) m_Down(all_65_7) = all_65_3 % 141.94/19.32 | (54) cons(all_65_13, all_65_18) = all_65_14 % 141.94/19.32 | (55) snoc(all_65_2, all_65_11) = all_65_1 % 141.94/19.32 | (56) index(pendack, all_65_12) = all_65_5 % 141.94/19.32 | (57) index(status, all_65_12) = elec_2 % 141.94/19.32 | (58) index(status, all_65_9) = norm % 141.94/19.32 | (59) index(ldr, all_65_9) = all_65_9 % 141.94/19.32 | (60) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Ack(v1, v0) = v2) | % 141.94/19.32 | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ? [v3: $i] : ? [v4: % 141.94/19.32 | $i] : ? [v5: $i] : (host(v1) = v3 & $i(v3) & (( ~ (v4 = elec_1) & % 141.94/19.32 | index(status, v3) = v4 & $i(v4)) | (queue(v3) = v5 & $i(v5) & % 141.94/19.32 | ~ elem(v2, v5))))) % 141.94/19.32 | (61) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Ack(v1, v0) = v2) | % 141.94/19.32 | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ? [v3: $i] : ? [v4: % 141.94/19.32 | $i] : ? [v5: $i] : ? [v6: $i] : (host(v1) = v3 & $i(v3) & % 141.94/19.32 | ((index(pendack, v3) = v6 & host(v0) = v5 & $i(v6) & $i(v5) & % 141.94/19.32 | leq(v5, v6)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4))))) % 141.94/19.33 | (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) % 141.94/19.33 | = v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 141.94/19.33 | alive) | ~ setIn(v0, alive) | leq(v2, v3) | ? [v4: $i] : ? [v5: % 141.94/19.33 | $i] : ? [v6: $i] : (( ~ (v5 = elec_2) & index(status, v3) = v5 & % 141.94/19.33 | $i(v5)) | ( ~ (v4 = elec_2) & index(status, v2) = v4 & $i(v4)) | % 141.94/19.33 | (index(pendack, v3) = v6 & $i(v6) & leq(v6, v2)))) % 141.94/19.33 | (63) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) % 141.94/19.33 | = v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 141.94/19.33 | alive) | ~ setIn(v0, alive) | leq(v2, v3) | ? [v4: $i] : ? [v5: % 141.94/19.33 | $i] : ? [v6: $i] : ? [v7: $i] : (( ~ (v5 = elec_2) & % 141.94/19.33 | index(status, v3) = v5 & $i(v5)) | ( ~ (v4 = elec_2) & % 141.94/19.33 | index(status, v2) = v4 & $i(v4)) | (index(pendack, v3) = v7 & % 141.94/19.33 | index(pendack, v2) = v6 & $i(v7) & $i(v6) & ~ leq(v6, v7)))) % 141.94/19.33 | (64) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 141.94/19.33 | (m_Halt(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 141.94/19.33 | [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) % 141.94/19.33 | | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) % 142.05/19.33 | (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 142.05/19.33 | (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 142.05/19.33 | [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 & $i(v5)) | % 142.05/19.33 | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) % 142.05/19.33 | (66) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 142.05/19.33 | ( ~ (m_Ack(v2, v0) = v3) | ~ (host(v1) = v4) | ~ $i(v2) | ~ $i(v1) % 142.05/19.33 | | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((host(v2) = % 142.05/19.33 | v7 & host(v0) = v6 & $i(v7) & $i(v6) & ~ leq(v6, v7)) | % 142.05/19.33 | (queue(v4) = v5 & $i(v5) & ~ elem(v3, v5)))) % 142.05/19.33 | (67) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 142.05/19.33 | ! [v5: $i] : ( ~ (m_Halt(v2) = v4) | ~ (host(v1) = v5) | ~ (host(v0) % 142.05/19.33 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | % 142.05/19.33 | ~ setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 142.05/19.33 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v11 = norm) & % 142.05/19.33 | index(status, v3) = v11 & $i(v11)) | ( ~ (v10 = v3) & index(ldr, % 142.05/19.33 | v3) = v10 & $i(v10)) | ( ~ (v9 = elec_2) & index(status, v6) = % 142.05/19.33 | v9 & host(v2) = v6 & $i(v9) & $i(v6)) | (index(pendack, v6) = v7 % 142.05/19.33 | & host(v2) = v6 & $i(v7) & $i(v6) & leq(v7, v3)) | (queue(v5) = % 142.05/19.33 | v8 & $i(v8) & ~ elem(v4, v8)))) % 142.05/19.33 | (68) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 142.05/19.33 | ! [v5: $i] : ( ~ (m_Down(v1) = v3) | ~ (host(v2) = v4) | ~ (host(v0) % 142.05/19.33 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | % 142.05/19.33 | ~ setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 142.05/19.33 | [v9: $i] : (( ~ (v9 = norm) & index(status, v5) = v9 & $i(v9)) | ( ~ % 142.05/19.33 | (v8 = v5) & index(ldr, v5) = v8 & $i(v8)) | ( ~ (v7 = v5) & % 142.05/19.33 | host(v1) = v7 & $i(v7)) | (queue(v4) = v6 & $i(v6) & ~ elem(v3, % 142.05/19.33 | v6)))) % 142.05/19.33 | (69) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 142.05/19.33 | ! [v5: $i] : ! [v6: $i] : ( ~ (m_Down(v2) = v5) | ~ (m_Ack(v3, v1) = % 142.05/19.33 | v4) | ~ (host(v0) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 142.05/19.33 | $i(v0) | ~ setIn(v3, alive) | ~ setIn(v0, alive) | ? [v7: $i] : % 142.05/19.33 | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 142.05/19.33 | $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : (( ~ (v15 = % 142.05/19.33 | norm) & index(status, v6) = v15 & $i(v15)) | ( ~ (v14 = v6) & % 142.05/19.33 | index(ldr, v6) = v14 & $i(v14)) | (host(v3) = v7 & $i(v7) & (( ~ % 142.05/19.33 | (v13 = v10) & index(pendack, v7) = v9 & s(v9) = v10 & % 142.05/19.33 | host(v2) = v13 & $i(v13) & $i(v10) & $i(v9)) | ( ~ (v12 = % 142.05/19.33 | v9) & index(pendack, v7) = v9 & host(v1) = v12 & $i(v12) & % 142.05/19.33 | $i(v9)) | ( ~ (v11 = elec_2) & index(status, v7) = v11 & % 142.05/19.33 | $i(v11)) | (index(pendack, v7) = v9 & s(v9) = v10 & $i(v10) % 142.05/19.33 | & $i(v9) & ~ leq(nbr_proc, v10)) | (queue(v7) = v8 & $i(v8) % 142.05/19.33 | & ( ~ elem(v5, v8) | ~ elem(v4, v8))))))) % 142.05/19.33 | % 142.05/19.33 | GROUND_INST: instantiating (63) with all_65_17, all_65_10, all_65_15, % 142.05/19.33 | all_65_9, simplifying with (21), (22), (26), (31), (43), (45) % 142.05/19.33 | gives: % 142.05/19.34 | (70) leq(all_65_15, all_65_9) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 142.05/19.34 | ? [v3: $i] : (( ~ (v1 = elec_2) & index(status, all_65_9) = v1 & % 142.05/19.34 | $i(v1)) | ( ~ (v0 = elec_2) & index(status, all_65_15) = v0 & % 142.05/19.34 | $i(v0)) | (index(pendack, all_65_9) = v3 & index(pendack, % 142.05/19.34 | all_65_15) = v2 & $i(v3) & $i(v2) & ~ leq(v2, v3))) % 142.05/19.34 | % 142.05/19.34 | GROUND_INST: instantiating (63) with all_65_10, all_65_17, all_65_9, % 142.05/19.34 | all_65_15, simplifying with (21), (22), (26), (31), (43), (45) % 142.05/19.34 | gives: % 142.05/19.34 | (71) leq(all_65_9, all_65_15) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 142.05/19.34 | ? [v3: $i] : (( ~ (v1 = elec_2) & index(status, all_65_15) = v1 & % 142.05/19.34 | $i(v1)) | ( ~ (v0 = elec_2) & index(status, all_65_9) = v0 & % 142.05/19.34 | $i(v0)) | (index(pendack, all_65_9) = v2 & index(pendack, % 142.05/19.34 | all_65_15) = v3 & $i(v3) & $i(v2) & ~ leq(v2, v3))) % 142.05/19.34 | % 142.05/19.34 | GROUND_INST: instantiating (62) with all_65_10, all_65_17, all_65_9, % 142.05/19.34 | all_65_15, simplifying with (21), (22), (26), (31), (43), (45) % 142.05/19.34 | gives: % 142.05/19.34 | (72) leq(all_65_9, all_65_15) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 142.05/19.34 | (( ~ (v1 = elec_2) & index(status, all_65_15) = v1 & $i(v1)) | ( ~ (v0 % 142.05/19.34 | = elec_2) & index(status, all_65_9) = v0 & $i(v0)) | % 142.05/19.34 | (index(pendack, all_65_15) = v2 & $i(v2) & leq(v2, all_65_9))) % 142.05/19.34 | % 142.05/19.34 | GROUND_INST: instantiating (1) with all_65_10, all_65_9, simplifying with % 142.05/19.34 | (31), (45) gives: % 142.05/19.34 | (73) leq(all_65_9, nbr_proc) % 142.05/19.34 | % 142.05/19.34 | GROUND_INST: instantiating (axiom_01) with all_65_8, all_65_8, all_65_5, % 142.05/19.34 | simplifying with (33), (46) gives: % 142.05/19.34 | (74) ? [v0: any] : ( ~ (v0 = all_65_5) & s(all_65_5) = v0 & $i(v0)) % 142.05/19.34 | % 142.05/19.34 | GROUND_INST: instantiating (1) with all_65_7, all_65_4, simplifying with (34), % 142.05/19.34 | (47) gives: % 142.05/19.34 | (75) leq(all_65_4, nbr_proc) % 142.05/19.34 | % 142.05/19.34 | GROUND_INST: instantiating (63) with all_65_6, all_65_6, all_65_12, all_65_12, % 142.05/19.34 | simplifying with (23), (35), (48) gives: % 142.05/19.34 | (76) leq(all_65_12, all_65_12) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 142.05/19.34 | ? [v3: $i] : (( ~ (v1 = elec_2) & index(status, all_65_12) = v1 & % 142.05/19.34 | $i(v1)) | ( ~ (v0 = elec_2) & index(status, all_65_12) = v0 & % 142.05/19.34 | $i(v0)) | (index(pendack, all_65_12) = v3 & index(pendack, % 142.05/19.34 | all_65_12) = v2 & $i(v3) & $i(v2) & ~ leq(v2, v3))) % 142.05/19.34 | % 142.05/19.34 | GROUND_INST: instantiating (62) with all_65_6, all_65_6, all_65_12, all_65_12, % 142.05/19.34 | simplifying with (23), (35), (48) gives: % 142.05/19.34 | (77) leq(all_65_12, all_65_12) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 142.05/19.34 | (( ~ (v1 = elec_2) & index(status, all_65_12) = v1 & $i(v1)) | ( ~ (v0 % 142.05/19.34 | = elec_2) & index(status, all_65_12) = v0 & $i(v0)) | % 142.05/19.34 | (index(pendack, all_65_12) = v2 & $i(v2) & leq(v2, all_65_12))) % 142.05/19.34 | % 142.05/19.34 | GROUND_INST: instantiating (63) with all_65_10, all_65_6, all_65_9, all_65_12, % 142.05/19.34 | simplifying with (22), (23), (31), (35), (45), (48) gives: % 142.05/19.34 | (78) leq(all_65_9, all_65_12) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 142.05/19.34 | ? [v3: $i] : (( ~ (v1 = elec_2) & index(status, all_65_12) = v1 & % 142.05/19.34 | $i(v1)) | ( ~ (v0 = elec_2) & index(status, all_65_9) = v0 & % 142.05/19.34 | $i(v0)) | (index(pendack, all_65_9) = v2 & index(pendack, % 142.05/19.34 | all_65_12) = v3 & $i(v3) & $i(v2) & ~ leq(v2, v3))) % 142.05/19.34 | % 142.05/19.34 | GROUND_INST: instantiating (63) with all_65_6, all_65_10, all_65_12, all_65_9, % 142.05/19.34 | simplifying with (22), (23), (31), (35), (45), (48) gives: % 142.05/19.34 | (79) leq(all_65_12, all_65_9) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 142.05/19.34 | ? [v3: $i] : (( ~ (v1 = elec_2) & index(status, all_65_9) = v1 & % 142.05/19.34 | $i(v1)) | ( ~ (v0 = elec_2) & index(status, all_65_12) = v0 & % 142.05/19.34 | $i(v0)) | (index(pendack, all_65_9) = v3 & index(pendack, % 142.05/19.34 | all_65_12) = v2 & $i(v3) & $i(v2) & ~ leq(v2, v3))) % 142.05/19.34 | % 142.05/19.34 | GROUND_INST: instantiating (62) with all_65_6, all_65_10, all_65_12, all_65_9, % 142.05/19.34 | simplifying with (22), (23), (31), (35), (45), (48) gives: % 142.05/19.34 | (80) leq(all_65_12, all_65_9) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 142.05/19.34 | (( ~ (v1 = elec_2) & index(status, all_65_9) = v1 & $i(v1)) | ( ~ (v0 % 142.05/19.34 | = elec_2) & index(status, all_65_12) = v0 & $i(v0)) | % 142.05/19.34 | (index(pendack, all_65_9) = v2 & $i(v2) & leq(v2, all_65_12))) % 142.05/19.34 | % 142.05/19.34 | GROUND_INST: instantiating (66) with all_65_8, all_65_7, all_65_6, all_65_0, % 142.05/19.34 | all_65_4, simplifying with (33), (34), (35), (47), (50) gives: % 142.05/19.35 | (81) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((host(all_65_6) = v2 & % 142.05/19.35 | host(all_65_8) = v1 & $i(v2) & $i(v1) & ~ leq(v1, v2)) | % 142.05/19.35 | (queue(all_65_4) = v0 & $i(v0) & ~ elem(all_65_0, v0))) % 142.05/19.35 | % 142.05/19.35 | GROUND_INST: instantiating (61) with all_65_8, all_65_6, all_65_0, simplifying % 142.05/19.35 | with (23), (33), (35), (50) gives: % 142.05/19.35 | (82) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 142.05/19.35 | (host(all_65_6) = v0 & $i(v0) & ((index(pendack, v0) = v3 & % 142.05/19.35 | host(all_65_8) = v2 & $i(v3) & $i(v2) & leq(v2, v3)) | % 142.05/19.35 | (queue(v0) = v1 & $i(v1) & ~ elem(all_65_0, v1)))) % 142.05/19.35 | % 142.05/19.35 | GROUND_INST: instantiating (60) with all_65_8, all_65_6, all_65_0, simplifying % 142.05/19.35 | with (23), (33), (35), (50) gives: % 142.05/19.35 | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (host(all_65_6) = v0 & % 142.05/19.35 | $i(v0) & (( ~ (v1 = elec_1) & index(status, v0) = v1 & $i(v1)) | % 142.05/19.35 | (queue(v0) = v2 & $i(v2) & ~ elem(all_65_0, v2)))) % 142.05/19.35 | % 142.05/19.35 | GROUND_INST: instantiating (9) with all_65_4, all_65_5, simplifying with (36), % 142.05/19.35 | (37), (51) gives: % 142.05/19.35 | (84) leq(all_65_4, all_65_4) % 142.05/19.35 | % 142.05/19.35 | GROUND_INST: instantiating (64) with all_65_17, all_65_16, all_65_13, % 142.05/19.35 | all_65_15, simplifying with (26), (27), (43), (52) gives: % 142.05/19.35 | (85) ? [v0: $i] : ? [v1: $i] : ((host(all_65_16) = v1 & $i(v1) & ~ % 142.05/19.35 | leq(all_65_15, v1)) | (queue(all_65_15) = v0 & $i(v0) & ~ % 142.05/19.35 | elem(all_65_13, v0))) % 142.05/19.35 | % 142.05/19.35 | GROUND_INST: instantiating (6) with all_65_13, all_65_16, simplifying with % 142.05/19.35 | (27), (29), (52) gives: % 142.05/19.35 | (86) pidElem(all_65_13) % 142.05/19.35 | % 142.05/19.35 | GROUND_INST: instantiating (69) with all_65_10, all_65_8, all_65_7, all_65_6, % 142.05/19.35 | all_65_0, all_65_3, all_65_9, simplifying with (22), (23), (31), % 142.05/19.35 | (33), (34), (35), (45), (50), (53) gives: % 142.05/19.35 | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 142.05/19.35 | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : (( ~ (v8 = % 142.05/19.35 | norm) & index(status, all_65_9) = v8 & $i(v8)) | ( ~ (v7 = % 142.05/19.35 | all_65_9) & index(ldr, all_65_9) = v7 & $i(v7)) | % 142.05/19.35 | (host(all_65_6) = v0 & $i(v0) & (( ~ (v6 = v3) & index(pendack, v0) % 142.05/19.35 | = v2 & s(v2) = v3 & host(all_65_7) = v6 & $i(v6) & $i(v3) & % 142.05/19.35 | $i(v2)) | ( ~ (v5 = v2) & index(pendack, v0) = v2 & % 142.05/19.35 | host(all_65_8) = v5 & $i(v5) & $i(v2)) | ( ~ (v4 = elec_2) & % 142.05/19.35 | index(status, v0) = v4 & $i(v4)) | (index(pendack, v0) = v2 & % 142.05/19.35 | s(v2) = v3 & $i(v3) & $i(v2) & ~ leq(nbr_proc, v3)) | % 142.05/19.35 | (queue(v0) = v1 & $i(v1) & ( ~ elem(all_65_0, v1) | ~ % 142.05/19.35 | elem(all_65_3, v1)))))) % 142.05/19.35 | % 142.05/19.35 | GROUND_INST: instantiating (68) with all_65_10, all_65_7, all_65_6, all_65_3, % 142.05/19.35 | all_65_12, all_65_9, simplifying with (22), (23), (31), (34), % 142.05/19.35 | (35), (45), (48), (53) gives: % 142.05/19.35 | (88) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : (( ~ (v3 = % 142.05/19.35 | norm) & index(status, all_65_9) = v3 & $i(v3)) | ( ~ (v2 = % 142.05/19.35 | all_65_9) & index(ldr, all_65_9) = v2 & $i(v2)) | ( ~ (v1 = % 142.05/19.35 | all_65_9) & host(all_65_7) = v1 & $i(v1)) | (queue(all_65_12) = % 142.05/19.35 | v0 & $i(v0) & ~ elem(all_65_3, v0))) % 142.05/19.35 | % 142.05/19.35 | GROUND_INST: instantiating (65) with all_65_16, all_65_7, all_65_3, all_65_12, % 142.05/19.35 | simplifying with (27), (34), (44), (53) gives: % 142.05/19.35 | (89) ? [v0: $i] : ? [v1: any] : (( ~ (v1 = all_65_12) & host(all_65_7) = % 142.05/19.35 | v1 & $i(v1)) | (queue(all_65_12) = v0 & $i(v0) & ~ elem(all_65_3, % 142.05/19.35 | v0))) % 142.05/19.35 | % 142.05/19.35 | GROUND_INST: instantiating (3) with all_65_13, all_65_18, all_65_14, % 142.05/19.35 | simplifying with (25), (29), (54) gives: % 142.05/19.35 | (90) elem(all_65_13, all_65_14) % 142.05/19.35 | % 142.05/19.35 | GROUND_INST: instantiating (4) with all_65_0, all_65_11, all_65_2, all_65_1, % 142.05/19.35 | simplifying with (20), (30), (39), (40), (55) gives: % 142.05/19.35 | (91) all_65_0 = all_65_11 | elem(all_65_0, all_65_2) % 142.05/19.35 | % 142.05/19.35 | GROUND_INST: instantiating (4) with all_65_3, all_65_11, all_65_2, all_65_1, % 142.05/19.35 | simplifying with (19), (30), (38), (39), (55) gives: % 142.05/19.35 | (92) all_65_3 = all_65_11 | elem(all_65_3, all_65_2) % 142.05/19.35 | % 142.05/19.35 | DELTA: instantiating (74) with fresh symbol all_84_0 gives: % 142.05/19.35 | (93) ~ (all_84_0 = all_65_5) & s(all_65_5) = all_84_0 & $i(all_84_0) % 142.05/19.35 | % 142.05/19.35 | ALPHA: (93) implies: % 142.05/19.35 | (94) $i(all_84_0) % 142.05/19.35 | (95) s(all_65_5) = all_84_0 % 142.05/19.35 | % 142.05/19.35 | DELTA: instantiating (89) with fresh symbols all_96_0, all_96_1 gives: % 142.05/19.35 | (96) ( ~ (all_96_0 = all_65_12) & host(all_65_7) = all_96_0 & $i(all_96_0)) % 142.05/19.35 | | (queue(all_65_12) = all_96_1 & $i(all_96_1) & ~ elem(all_65_3, % 142.05/19.35 | all_96_1)) % 142.05/19.35 | % 142.05/19.35 | DELTA: instantiating (85) with fresh symbols all_97_0, all_97_1 gives: % 142.05/19.35 | (97) (host(all_65_16) = all_97_0 & $i(all_97_0) & ~ leq(all_65_15, % 142.05/19.35 | all_97_0)) | (queue(all_65_15) = all_97_1 & $i(all_97_1) & ~ % 142.05/19.35 | elem(all_65_13, all_97_1)) % 142.05/19.35 | % 142.05/19.35 | DELTA: instantiating (83) with fresh symbols all_105_0, all_105_1, all_105_2 % 142.05/19.35 | gives: % 142.05/19.35 | (98) host(all_65_6) = all_105_2 & $i(all_105_2) & (( ~ (all_105_1 = elec_1) % 142.05/19.35 | & index(status, all_105_2) = all_105_1 & $i(all_105_1)) | % 142.05/19.35 | (queue(all_105_2) = all_105_0 & $i(all_105_0) & ~ elem(all_65_0, % 142.05/19.35 | all_105_0))) % 142.05/19.35 | % 142.05/19.35 | ALPHA: (98) implies: % 142.05/19.35 | (99) host(all_65_6) = all_105_2 % 142.05/19.36 | (100) ( ~ (all_105_1 = elec_1) & index(status, all_105_2) = all_105_1 & % 142.05/19.36 | $i(all_105_1)) | (queue(all_105_2) = all_105_0 & $i(all_105_0) & ~ % 142.05/19.36 | elem(all_65_0, all_105_0)) % 142.05/19.36 | % 142.05/19.36 | DELTA: instantiating (81) with fresh symbols all_107_0, all_107_1, all_107_2 % 142.05/19.36 | gives: % 142.05/19.36 | (101) (host(all_65_6) = all_107_0 & host(all_65_8) = all_107_1 & % 142.05/19.36 | $i(all_107_0) & $i(all_107_1) & ~ leq(all_107_1, all_107_0)) | % 142.05/19.36 | (queue(all_65_4) = all_107_2 & $i(all_107_2) & ~ elem(all_65_0, % 142.05/19.36 | all_107_2)) % 142.05/19.36 | % 142.05/19.36 | DELTA: instantiating (82) with fresh symbols all_113_0, all_113_1, all_113_2, % 142.05/19.36 | all_113_3 gives: % 142.05/19.36 | (102) host(all_65_6) = all_113_3 & $i(all_113_3) & ((index(pendack, % 142.05/19.36 | all_113_3) = all_113_0 & host(all_65_8) = all_113_1 & % 142.05/19.36 | $i(all_113_0) & $i(all_113_1) & leq(all_113_1, all_113_0)) | % 142.05/19.36 | (queue(all_113_3) = all_113_2 & $i(all_113_2) & ~ elem(all_65_0, % 142.05/19.36 | all_113_2))) % 142.05/19.36 | % 142.05/19.36 | ALPHA: (102) implies: % 142.05/19.36 | (103) host(all_65_6) = all_113_3 % 142.05/19.36 | % 142.05/19.36 | DELTA: instantiating (88) with fresh symbols all_123_0, all_123_1, all_123_2, % 142.05/19.36 | all_123_3 gives: % 142.05/19.36 | (104) ( ~ (all_123_0 = norm) & index(status, all_65_9) = all_123_0 & % 142.05/19.36 | $i(all_123_0)) | ( ~ (all_123_1 = all_65_9) & index(ldr, all_65_9) % 142.05/19.36 | = all_123_1 & $i(all_123_1)) | ( ~ (all_123_2 = all_65_9) & % 142.05/19.36 | host(all_65_7) = all_123_2 & $i(all_123_2)) | (queue(all_65_12) = % 142.05/19.36 | all_123_3 & $i(all_123_3) & ~ elem(all_65_3, all_123_3)) % 142.05/19.36 | % 142.05/19.36 | DELTA: instantiating (87) with fresh symbols all_128_0, all_128_1, all_128_2, % 142.05/19.36 | all_128_3, all_128_4, all_128_5, all_128_6, all_128_7, all_128_8 gives: % 142.05/19.36 | (105) ( ~ (all_128_0 = norm) & index(status, all_65_9) = all_128_0 & % 142.05/19.36 | $i(all_128_0)) | ( ~ (all_128_1 = all_65_9) & index(ldr, all_65_9) % 142.05/19.36 | = all_128_1 & $i(all_128_1)) | (host(all_65_6) = all_128_8 & % 142.05/19.36 | $i(all_128_8) & (( ~ (all_128_2 = all_128_5) & index(pendack, % 142.05/19.36 | all_128_8) = all_128_6 & s(all_128_6) = all_128_5 & % 142.05/19.36 | host(all_65_7) = all_128_2 & $i(all_128_2) & $i(all_128_5) & % 142.05/19.36 | $i(all_128_6)) | ( ~ (all_128_3 = all_128_6) & index(pendack, % 142.05/19.36 | all_128_8) = all_128_6 & host(all_65_8) = all_128_3 & % 142.05/19.36 | $i(all_128_3) & $i(all_128_6)) | ( ~ (all_128_4 = elec_2) & % 142.05/19.36 | index(status, all_128_8) = all_128_4 & $i(all_128_4)) | % 142.05/19.36 | (index(pendack, all_128_8) = all_128_6 & s(all_128_6) = all_128_5 % 142.05/19.36 | & $i(all_128_5) & $i(all_128_6) & ~ leq(nbr_proc, all_128_5)) % 142.05/19.36 | | (queue(all_128_8) = all_128_7 & $i(all_128_7) & ( ~ % 142.05/19.36 | elem(all_65_0, all_128_7) | ~ elem(all_65_3, all_128_7))))) % 142.05/19.36 | % 142.05/19.36 | BETA: splitting (97) gives: % 142.05/19.36 | % 142.05/19.36 | Case 1: % 142.05/19.36 | | % 142.05/19.36 | | (106) host(all_65_16) = all_97_0 & $i(all_97_0) & ~ leq(all_65_15, % 142.05/19.36 | | all_97_0) % 142.05/19.36 | | % 142.05/19.36 | | ALPHA: (106) implies: % 142.05/19.36 | | (107) $i(all_97_0) % 142.05/19.36 | | (108) host(all_65_16) = all_97_0 % 142.05/19.36 | | % 142.05/19.36 | | BETA: splitting (105) gives: % 142.05/19.36 | | % 142.05/19.36 | | Case 1: % 142.05/19.36 | | | % 142.05/19.36 | | | (109) ~ (all_128_0 = norm) & index(status, all_65_9) = all_128_0 & % 142.05/19.36 | | | $i(all_128_0) % 142.05/19.36 | | | % 142.05/19.36 | | | ALPHA: (109) implies: % 142.05/19.36 | | | (110) ~ (all_128_0 = norm) % 142.05/19.36 | | | (111) index(status, all_65_9) = all_128_0 % 142.05/19.36 | | | % 142.05/19.36 | | | GROUND_INST: instantiating (16) with norm, all_128_0, all_65_9, status, % 142.05/19.36 | | | simplifying with (58), (111) gives: % 142.05/19.36 | | | (112) all_128_0 = norm % 142.05/19.36 | | | % 142.05/19.36 | | | REDUCE: (110), (112) imply: % 142.05/19.36 | | | (113) $false % 142.05/19.36 | | | % 142.05/19.36 | | | CLOSE: (113) is inconsistent. % 142.05/19.36 | | | % 142.05/19.36 | | Case 2: % 142.05/19.36 | | | % 142.05/19.36 | | | (114) ( ~ (all_128_1 = all_65_9) & index(ldr, all_65_9) = all_128_1 & % 142.05/19.36 | | | $i(all_128_1)) | (host(all_65_6) = all_128_8 & $i(all_128_8) & % 142.05/19.36 | | | (( ~ (all_128_2 = all_128_5) & index(pendack, all_128_8) = % 142.05/19.36 | | | all_128_6 & s(all_128_6) = all_128_5 & host(all_65_7) = % 142.05/19.36 | | | all_128_2 & $i(all_128_2) & $i(all_128_5) & $i(all_128_6)) % 142.05/19.36 | | | | ( ~ (all_128_3 = all_128_6) & index(pendack, all_128_8) = % 142.05/19.36 | | | all_128_6 & host(all_65_8) = all_128_3 & $i(all_128_3) & % 142.05/19.36 | | | $i(all_128_6)) | ( ~ (all_128_4 = elec_2) & index(status, % 142.05/19.36 | | | all_128_8) = all_128_4 & $i(all_128_4)) | (index(pendack, % 142.05/19.36 | | | all_128_8) = all_128_6 & s(all_128_6) = all_128_5 & % 142.05/19.36 | | | $i(all_128_5) & $i(all_128_6) & ~ leq(nbr_proc, % 142.05/19.36 | | | all_128_5)) | (queue(all_128_8) = all_128_7 & % 142.05/19.36 | | | $i(all_128_7) & ( ~ elem(all_65_0, all_128_7) | ~ % 142.05/19.36 | | | elem(all_65_3, all_128_7))))) % 142.05/19.36 | | | % 142.05/19.36 | | | BETA: splitting (114) gives: % 142.05/19.36 | | | % 142.05/19.36 | | | Case 1: % 142.05/19.36 | | | | % 142.05/19.36 | | | | (115) ~ (all_128_1 = all_65_9) & index(ldr, all_65_9) = all_128_1 & % 142.05/19.36 | | | | $i(all_128_1) % 142.05/19.36 | | | | % 142.05/19.36 | | | | ALPHA: (115) implies: % 142.05/19.36 | | | | (116) ~ (all_128_1 = all_65_9) % 142.05/19.36 | | | | (117) index(ldr, all_65_9) = all_128_1 % 142.05/19.36 | | | | % 142.05/19.36 | | | | GROUND_INST: instantiating (16) with all_65_9, all_128_1, all_65_9, ldr, % 142.05/19.36 | | | | simplifying with (59), (117) gives: % 142.05/19.36 | | | | (118) all_128_1 = all_65_9 % 142.05/19.36 | | | | % 142.05/19.36 | | | | REDUCE: (116), (118) imply: % 142.05/19.36 | | | | (119) $false % 142.05/19.36 | | | | % 142.05/19.36 | | | | CLOSE: (119) is inconsistent. % 142.05/19.36 | | | | % 142.05/19.36 | | | Case 2: % 142.05/19.36 | | | | % 142.05/19.36 | | | | (120) host(all_65_6) = all_128_8 & $i(all_128_8) & (( ~ (all_128_2 = % 142.05/19.36 | | | | all_128_5) & index(pendack, all_128_8) = all_128_6 & % 142.05/19.36 | | | | s(all_128_6) = all_128_5 & host(all_65_7) = all_128_2 & % 142.05/19.36 | | | | $i(all_128_2) & $i(all_128_5) & $i(all_128_6)) | ( ~ % 142.05/19.36 | | | | (all_128_3 = all_128_6) & index(pendack, all_128_8) = % 142.05/19.36 | | | | all_128_6 & host(all_65_8) = all_128_3 & $i(all_128_3) & % 142.05/19.36 | | | | $i(all_128_6)) | ( ~ (all_128_4 = elec_2) & index(status, % 142.05/19.36 | | | | all_128_8) = all_128_4 & $i(all_128_4)) | (index(pendack, % 142.05/19.36 | | | | all_128_8) = all_128_6 & s(all_128_6) = all_128_5 & % 142.05/19.36 | | | | $i(all_128_5) & $i(all_128_6) & ~ leq(nbr_proc, % 142.05/19.36 | | | | all_128_5)) | (queue(all_128_8) = all_128_7 & % 142.05/19.36 | | | | $i(all_128_7) & ( ~ elem(all_65_0, all_128_7) | ~ % 142.05/19.36 | | | | elem(all_65_3, all_128_7)))) % 142.05/19.36 | | | | % 142.05/19.36 | | | | ALPHA: (120) implies: % 142.05/19.36 | | | | (121) host(all_65_6) = all_128_8 % 142.05/19.37 | | | | (122) ( ~ (all_128_2 = all_128_5) & index(pendack, all_128_8) = % 142.05/19.37 | | | | all_128_6 & s(all_128_6) = all_128_5 & host(all_65_7) = % 142.05/19.37 | | | | all_128_2 & $i(all_128_2) & $i(all_128_5) & $i(all_128_6)) | % 142.05/19.37 | | | | ( ~ (all_128_3 = all_128_6) & index(pendack, all_128_8) = % 142.05/19.37 | | | | all_128_6 & host(all_65_8) = all_128_3 & $i(all_128_3) & % 142.05/19.37 | | | | $i(all_128_6)) | ( ~ (all_128_4 = elec_2) & index(status, % 142.05/19.37 | | | | all_128_8) = all_128_4 & $i(all_128_4)) | (index(pendack, % 142.05/19.37 | | | | all_128_8) = all_128_6 & s(all_128_6) = all_128_5 & % 142.05/19.37 | | | | $i(all_128_5) & $i(all_128_6) & ~ leq(nbr_proc, all_128_5)) % 142.05/19.37 | | | | | (queue(all_128_8) = all_128_7 & $i(all_128_7) & ( ~ % 142.05/19.37 | | | | elem(all_65_0, all_128_7) | ~ elem(all_65_3, all_128_7))) % 142.05/19.37 | | | | % 142.05/19.37 | | | | GROUND_INST: instantiating (14) with all_65_12, all_97_0, all_65_16, % 142.05/19.37 | | | | simplifying with (44), (108) gives: % 142.05/19.37 | | | | (123) all_97_0 = all_65_12 % 142.05/19.37 | | | | % 142.05/19.37 | | | | GROUND_INST: instantiating (14) with all_65_12, all_128_8, all_65_6, % 142.05/19.37 | | | | simplifying with (48), (121) gives: % 142.05/19.37 | | | | (124) all_128_8 = all_65_12 % 142.05/19.37 | | | | % 142.05/19.37 | | | | GROUND_INST: instantiating (14) with all_113_3, all_128_8, all_65_6, % 142.05/19.37 | | | | simplifying with (103), (121) gives: % 142.05/19.37 | | | | (125) all_128_8 = all_113_3 % 142.05/19.37 | | | | % 142.05/19.37 | | | | GROUND_INST: instantiating (14) with all_105_2, all_128_8, all_65_6, % 142.05/19.37 | | | | simplifying with (99), (121) gives: % 142.05/19.37 | | | | (126) all_128_8 = all_105_2 % 142.05/19.37 | | | | % 142.05/19.37 | | | | GROUND_INST: instantiating (15) with all_65_4, all_84_0, all_65_5, % 142.05/19.37 | | | | simplifying with (51), (95) gives: % 142.05/19.37 | | | | (127) all_84_0 = all_65_4 % 142.05/19.37 | | | | % 142.05/19.37 | | | | COMBINE_EQS: (124), (125) imply: % 142.05/19.37 | | | | (128) all_113_3 = all_65_12 % 142.05/19.37 | | | | % 142.05/19.37 | | | | COMBINE_EQS: (125), (126) imply: % 142.05/19.37 | | | | (129) all_113_3 = all_105_2 % 142.05/19.37 | | | | % 142.05/19.37 | | | | COMBINE_EQS: (128), (129) imply: % 142.05/19.37 | | | | (130) all_105_2 = all_65_12 % 142.05/19.37 | | | | % 142.05/19.37 | | | | REDUCE: (107), (123) imply: % 142.05/19.37 | | | | (131) $i(all_65_12) % 142.05/19.37 | | | | % 142.05/19.37 | | | | BETA: splitting (122) gives: % 142.05/19.37 | | | | % 142.05/19.37 | | | | Case 1: % 142.05/19.37 | | | | | % 142.05/19.37 | | | | | (132) ( ~ (all_128_2 = all_128_5) & index(pendack, all_128_8) = % 142.05/19.37 | | | | | all_128_6 & s(all_128_6) = all_128_5 & host(all_65_7) = % 142.05/19.37 | | | | | all_128_2 & $i(all_128_2) & $i(all_128_5) & $i(all_128_6)) % 142.05/19.37 | | | | | | ( ~ (all_128_3 = all_128_6) & index(pendack, all_128_8) = % 142.05/19.37 | | | | | all_128_6 & host(all_65_8) = all_128_3 & $i(all_128_3) & % 142.05/19.37 | | | | | $i(all_128_6)) % 142.05/19.37 | | | | | % 142.05/19.37 | | | | | BETA: splitting (132) gives: % 142.05/19.37 | | | | | % 142.05/19.37 | | | | | Case 1: % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | (133) ~ (all_128_2 = all_128_5) & index(pendack, all_128_8) = % 142.05/19.37 | | | | | | all_128_6 & s(all_128_6) = all_128_5 & host(all_65_7) = % 142.05/19.37 | | | | | | all_128_2 & $i(all_128_2) & $i(all_128_5) & $i(all_128_6) % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | ALPHA: (133) implies: % 142.05/19.37 | | | | | | (134) ~ (all_128_2 = all_128_5) % 142.05/19.37 | | | | | | (135) host(all_65_7) = all_128_2 % 142.05/19.37 | | | | | | (136) s(all_128_6) = all_128_5 % 142.05/19.37 | | | | | | (137) index(pendack, all_128_8) = all_128_6 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | REDUCE: (124), (137) imply: % 142.05/19.37 | | | | | | (138) index(pendack, all_65_12) = all_128_6 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | GROUND_INST: instantiating (14) with all_65_4, all_128_2, all_65_7, % 142.05/19.37 | | | | | | simplifying with (47), (135) gives: % 142.05/19.37 | | | | | | (139) all_128_2 = all_65_4 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | GROUND_INST: instantiating (16) with all_65_5, all_128_6, all_65_12, % 142.05/19.37 | | | | | | pendack, simplifying with (56), (138) gives: % 142.05/19.37 | | | | | | (140) all_128_6 = all_65_5 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | REDUCE: (134), (139) imply: % 142.05/19.37 | | | | | | (141) ~ (all_128_5 = all_65_4) % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | SIMP: (141) implies: % 142.05/19.37 | | | | | | (142) ~ (all_128_5 = all_65_4) % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | REDUCE: (136), (140) imply: % 142.05/19.37 | | | | | | (143) s(all_65_5) = all_128_5 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | GROUND_INST: instantiating (15) with all_65_4, all_128_5, all_65_5, % 142.05/19.37 | | | | | | simplifying with (51), (143) gives: % 142.05/19.37 | | | | | | (144) all_128_5 = all_65_4 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | REDUCE: (142), (144) imply: % 142.05/19.37 | | | | | | (145) $false % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | CLOSE: (145) is inconsistent. % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | Case 2: % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | (146) ~ (all_128_3 = all_128_6) & index(pendack, all_128_8) = % 142.05/19.37 | | | | | | all_128_6 & host(all_65_8) = all_128_3 & $i(all_128_3) & % 142.05/19.37 | | | | | | $i(all_128_6) % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | ALPHA: (146) implies: % 142.05/19.37 | | | | | | (147) ~ (all_128_3 = all_128_6) % 142.05/19.37 | | | | | | (148) host(all_65_8) = all_128_3 % 142.05/19.37 | | | | | | (149) index(pendack, all_128_8) = all_128_6 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | REDUCE: (124), (149) imply: % 142.05/19.37 | | | | | | (150) index(pendack, all_65_12) = all_128_6 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | GROUND_INST: instantiating (14) with all_65_5, all_128_3, all_65_8, % 142.05/19.37 | | | | | | simplifying with (46), (148) gives: % 142.05/19.37 | | | | | | (151) all_128_3 = all_65_5 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | GROUND_INST: instantiating (16) with all_65_5, all_128_6, all_65_12, % 142.05/19.37 | | | | | | pendack, simplifying with (56), (150) gives: % 142.05/19.37 | | | | | | (152) all_128_6 = all_65_5 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | REDUCE: (147), (151), (152) imply: % 142.05/19.37 | | | | | | (153) $false % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | CLOSE: (153) is inconsistent. % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | End of split % 142.05/19.37 | | | | | % 142.05/19.37 | | | | Case 2: % 142.05/19.37 | | | | | % 142.05/19.37 | | | | | (154) ( ~ (all_128_4 = elec_2) & index(status, all_128_8) = % 142.05/19.37 | | | | | all_128_4 & $i(all_128_4)) | (index(pendack, all_128_8) = % 142.05/19.37 | | | | | all_128_6 & s(all_128_6) = all_128_5 & $i(all_128_5) & % 142.05/19.37 | | | | | $i(all_128_6) & ~ leq(nbr_proc, all_128_5)) | % 142.05/19.37 | | | | | (queue(all_128_8) = all_128_7 & $i(all_128_7) & ( ~ % 142.05/19.37 | | | | | elem(all_65_0, all_128_7) | ~ elem(all_65_3, % 142.05/19.37 | | | | | all_128_7))) % 142.05/19.37 | | | | | % 142.05/19.37 | | | | | BETA: splitting (154) gives: % 142.05/19.37 | | | | | % 142.05/19.37 | | | | | Case 1: % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | (155) ~ (all_128_4 = elec_2) & index(status, all_128_8) = % 142.05/19.37 | | | | | | all_128_4 & $i(all_128_4) % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | ALPHA: (155) implies: % 142.05/19.37 | | | | | | (156) ~ (all_128_4 = elec_2) % 142.05/19.37 | | | | | | (157) index(status, all_128_8) = all_128_4 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | REDUCE: (124), (157) imply: % 142.05/19.37 | | | | | | (158) index(status, all_65_12) = all_128_4 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | GROUND_INST: instantiating (16) with elec_2, all_128_4, all_65_12, % 142.05/19.37 | | | | | | status, simplifying with (57), (158) gives: % 142.05/19.37 | | | | | | (159) all_128_4 = elec_2 % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | REDUCE: (156), (159) imply: % 142.05/19.37 | | | | | | (160) $false % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | CLOSE: (160) is inconsistent. % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | Case 2: % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | (161) (index(pendack, all_128_8) = all_128_6 & s(all_128_6) = % 142.05/19.37 | | | | | | all_128_5 & $i(all_128_5) & $i(all_128_6) & ~ % 142.05/19.37 | | | | | | leq(nbr_proc, all_128_5)) | (queue(all_128_8) = all_128_7 % 142.05/19.37 | | | | | | & $i(all_128_7) & ( ~ elem(all_65_0, all_128_7) | ~ % 142.05/19.37 | | | | | | elem(all_65_3, all_128_7))) % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | BETA: splitting (161) gives: % 142.05/19.37 | | | | | | % 142.05/19.37 | | | | | | Case 1: % 142.05/19.37 | | | | | | | % 142.05/19.37 | | | | | | | (162) index(pendack, all_128_8) = all_128_6 & s(all_128_6) = % 142.05/19.37 | | | | | | | all_128_5 & $i(all_128_5) & $i(all_128_6) & ~ % 142.05/19.37 | | | | | | | leq(nbr_proc, all_128_5) % 142.05/19.37 | | | | | | | % 142.05/19.37 | | | | | | | ALPHA: (162) implies: % 142.05/19.37 | | | | | | | (163) ~ leq(nbr_proc, all_128_5) % 142.05/19.37 | | | | | | | (164) s(all_128_6) = all_128_5 % 142.05/19.37 | | | | | | | (165) index(pendack, all_128_8) = all_128_6 % 142.05/19.37 | | | | | | | % 142.05/19.37 | | | | | | | REDUCE: (124), (165) imply: % 142.05/19.37 | | | | | | | (166) index(pendack, all_65_12) = all_128_6 % 142.05/19.37 | | | | | | | % 142.05/19.37 | | | | | | | GROUND_INST: instantiating (16) with all_65_5, all_128_6, % 142.05/19.37 | | | | | | | all_65_12, pendack, simplifying with (56), (166) % 142.05/19.37 | | | | | | | gives: % 142.05/19.37 | | | | | | | (167) all_128_6 = all_65_5 % 142.05/19.37 | | | | | | | % 142.05/19.37 | | | | | | | REDUCE: (164), (167) imply: % 142.05/19.37 | | | | | | | (168) s(all_65_5) = all_128_5 % 142.05/19.37 | | | | | | | % 142.05/19.37 | | | | | | | GROUND_INST: instantiating (15) with all_65_4, all_128_5, % 142.05/19.37 | | | | | | | all_65_5, simplifying with (51), (168) gives: % 142.05/19.37 | | | | | | | (169) all_128_5 = all_65_4 % 142.05/19.37 | | | | | | | % 142.05/19.37 | | | | | | | REDUCE: (163), (169) imply: % 142.05/19.38 | | | | | | | (170) ~ leq(nbr_proc, all_65_4) % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | PRED_UNIFY: (24), (170) imply: % 142.05/19.38 | | | | | | | (171) $false % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | CLOSE: (171) is inconsistent. % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | Case 2: % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | (172) queue(all_128_8) = all_128_7 & $i(all_128_7) & ( ~ % 142.05/19.38 | | | | | | | elem(all_65_0, all_128_7) | ~ elem(all_65_3, % 142.05/19.38 | | | | | | | all_128_7)) % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | ALPHA: (172) implies: % 142.05/19.38 | | | | | | | (173) queue(all_128_8) = all_128_7 % 142.05/19.38 | | | | | | | (174) ~ elem(all_65_0, all_128_7) | ~ elem(all_65_3, % 142.05/19.38 | | | | | | | all_128_7) % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | REDUCE: (124), (173) imply: % 142.05/19.38 | | | | | | | (175) queue(all_65_12) = all_128_7 % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | GROUND_INST: instantiating (13) with all_65_2, all_128_7, % 142.05/19.38 | | | | | | | all_65_12, simplifying with (42), (175) gives: % 142.05/19.38 | | | | | | | (176) all_128_7 = all_65_2 % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | GROUND_INST: instantiating (axiom_62) with all_65_9, nbr_proc, % 142.05/19.38 | | | | | | | all_65_4, simplifying with (11), (24), (32), (37), % 142.05/19.38 | | | | | | | (73) gives: % 142.05/19.38 | | | | | | | (177) leq(all_65_9, all_65_4) % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | GROUND_INST: instantiating (7) with nbr_proc, all_65_4, % 142.05/19.38 | | | | | | | simplifying with (11), (24), (37), (75) gives: % 142.05/19.38 | | | | | | | (178) all_65_4 = nbr_proc % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | GROUND_INST: instantiating (8) with all_65_5, all_65_5, all_65_4, % 142.05/19.38 | | | | | | | all_65_4, simplifying with (36), (51), (84) gives: % 142.05/19.38 | | | | | | | (179) leq(all_65_5, all_65_5) % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | GROUND_INST: instantiating (5) with all_65_13, simplifying with % 142.05/19.38 | | | | | | | (29), (86) gives: % 142.05/19.38 | | | | | | | (180) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ($i(v0) & % 142.05/19.38 | | | | | | | ((v2 = all_65_13 & m_Down(v0) = all_65_13) | (v1 = % 142.05/19.38 | | | | | | | all_65_13 & m_Halt(v0) = all_65_13))) % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | DELTA: instantiating (180) with fresh symbols all_174_0, % 142.05/19.38 | | | | | | | all_174_1, all_174_2 gives: % 142.05/19.38 | | | | | | | (181) $i(all_174_2) & ((all_174_0 = all_65_13 & % 142.05/19.38 | | | | | | | m_Down(all_174_2) = all_65_13) | (all_174_1 = % 142.05/19.38 | | | | | | | all_65_13 & m_Halt(all_174_2) = all_65_13)) % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | ALPHA: (181) implies: % 142.05/19.38 | | | | | | | (182) $i(all_174_2) % 142.05/19.38 | | | | | | | (183) (all_174_0 = all_65_13 & m_Down(all_174_2) = all_65_13) | % 142.05/19.38 | | | | | | | (all_174_1 = all_65_13 & m_Halt(all_174_2) = all_65_13) % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | REDUCE: (51), (178) imply: % 142.05/19.38 | | | | | | | (184) s(all_65_5) = nbr_proc % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | REDUCE: (47), (178) imply: % 142.05/19.38 | | | | | | | (185) host(all_65_7) = nbr_proc % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | BETA: splitting (76) gives: % 142.05/19.38 | | | | | | | % 142.05/19.38 | | | | | | | Case 1: % 142.05/19.38 | | | | | | | | % 142.05/19.38 | | | | | | | | (186) leq(all_65_12, all_65_12) % 142.05/19.38 | | | | | | | | % 142.05/19.38 | | | | | | | | GROUND_INST: instantiating (10) with all_65_9, all_65_5, % 142.05/19.38 | | | | | | | | nbr_proc, simplifying with (32), (36), (73), (184) % 142.05/19.38 | | | | | | | | gives: % 142.05/19.38 | | | | | | | | (187) all_65_9 = nbr_proc | leq(all_65_9, all_65_5) % 142.05/19.38 | | | | | | | | % 142.05/19.38 | | | | | | | | BETA: splitting (80) gives: % 142.05/19.38 | | | | | | | | % 142.05/19.38 | | | | | | | | Case 1: % 142.05/19.38 | | | | | | | | | % 142.05/19.38 | | | | | | | | | (188) leq(all_65_12, all_65_9) % 142.05/19.38 | | | | | | | | | % 142.05/19.38 | | | | | | | | | BETA: splitting (71) gives: % 142.05/19.38 | | | | | | | | | % 142.05/19.38 | | | | | | | | | Case 1: % 142.05/19.38 | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | (189) leq(all_65_9, all_65_15) % 142.05/19.38 | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | BETA: splitting (70) gives: % 142.05/19.38 | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | Case 1: % 142.05/19.38 | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | (190) leq(all_65_15, all_65_9) % 142.05/19.38 | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | REF_CLOSE: (7), (18), (28), (32), (189), (190) are % 142.05/19.38 | | | | | | | | | | | inconsistent by sub-proof #4. % 142.05/19.38 | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | Case 2: % 142.05/19.38 | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | (191) ~ leq(all_65_15, all_65_9) % 142.05/19.38 | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | BETA: splitting (78) gives: % 142.05/19.38 | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | Case 1: % 142.05/19.38 | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | (192) leq(all_65_9, all_65_12) % 142.05/19.38 | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_65_12, all_65_9, % 142.05/19.38 | | | | | | | | | | | | simplifying with (32), (131), (188), (192) gives: % 142.05/19.38 | | | | | | | | | | | | (193) all_65_9 = all_65_12 % 142.05/19.38 | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | REDUCE: (58), (193) imply: % 142.05/19.38 | | | | | | | | | | | | (194) index(status, all_65_12) = norm % 142.05/19.38 | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, norm, all_65_12, % 142.05/19.38 | | | | | | | | | | | | status, simplifying with (57), (194) gives: % 142.05/19.38 | | | | | | | | | | | | (195) norm = elec_2 % 142.05/19.38 | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | REDUCE: (2), (195) imply: % 142.05/19.38 | | | | | | | | | | | | (196) $false % 142.05/19.38 | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 142.05/19.38 | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | Case 2: % 142.05/19.38 | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | (197) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 142.05/19.38 | | | | | | | | | | | | $i] : (( ~ (v1 = elec_2) & index(status, % 142.05/19.38 | | | | | | | | | | | | all_65_12) = v1 & $i(v1)) | ( ~ (v0 = % 142.05/19.38 | | | | | | | | | | | | elec_2) & index(status, all_65_9) = v0 & % 142.05/19.38 | | | | | | | | | | | | $i(v0)) | (index(pendack, all_65_9) = v2 & % 142.05/19.38 | | | | | | | | | | | | index(pendack, all_65_12) = v3 & $i(v3) & % 142.05/19.38 | | | | | | | | | | | | $i(v2) & ~ leq(v2, v3))) % 142.05/19.38 | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | DELTA: instantiating (197) with fresh symbols all_254_0, % 142.05/19.38 | | | | | | | | | | | | all_254_1, all_254_2, all_254_3 gives: % 142.05/19.38 | | | | | | | | | | | | (198) ( ~ (all_254_2 = elec_2) & index(status, % 142.05/19.38 | | | | | | | | | | | | all_65_12) = all_254_2 & $i(all_254_2)) | ( ~ % 142.05/19.38 | | | | | | | | | | | | (all_254_3 = elec_2) & index(status, all_65_9) = % 142.05/19.38 | | | | | | | | | | | | all_254_3 & $i(all_254_3)) | (index(pendack, % 142.05/19.38 | | | | | | | | | | | | all_65_9) = all_254_1 & index(pendack, % 142.05/19.38 | | | | | | | | | | | | all_65_12) = all_254_0 & $i(all_254_0) & % 142.05/19.38 | | | | | | | | | | | | $i(all_254_1) & ~ leq(all_254_1, all_254_0)) % 142.05/19.38 | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | BETA: splitting (92) gives: % 142.05/19.38 | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | Case 1: % 142.05/19.38 | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | (199) elem(all_65_3, all_65_2) % 142.05/19.38 | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | BETA: splitting (174) gives: % 142.05/19.38 | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | Case 1: % 142.05/19.38 | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | (200) ~ elem(all_65_0, all_128_7) % 142.05/19.38 | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | REDUCE: (176), (200) imply: % 142.05/19.38 | | | | | | | | | | | | | | (201) ~ elem(all_65_0, all_65_2) % 142.05/19.38 | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | BETA: splitting (91) gives: % 142.05/19.38 | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | Case 1: % 142.05/19.38 | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | (202) elem(all_65_0, all_65_2) % 142.05/19.38 | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | PRED_UNIFY: (201), (202) imply: % 142.05/19.38 | | | | | | | | | | | | | | | (203) $false % 142.05/19.38 | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 142.05/19.38 | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | Case 2: % 142.05/19.38 | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | (204) all_65_0 = all_65_11 % 142.05/19.38 | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | REDUCE: (50), (204) imply: % 142.05/19.38 | | | | | | | | | | | | | | | (205) m_Ack(all_65_6, all_65_8) = all_65_11 % 142.05/19.38 | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 142.05/19.38 | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | Case 1: % 142.05/19.38 | | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | | (206) host(all_65_6) = all_107_0 & host(all_65_8) = % 142.05/19.38 | | | | | | | | | | | | | | | | all_107_1 & $i(all_107_0) & $i(all_107_1) & ~ % 142.05/19.38 | | | | | | | | | | | | | | | | leq(all_107_1, all_107_0) % 142.05/19.38 | | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | | ALPHA: (206) implies: % 142.05/19.38 | | | | | | | | | | | | | | | | (207) host(all_65_8) = all_107_1 % 142.05/19.38 | | | | | | | | | | | | | | | | (208) host(all_65_6) = all_107_0 % 142.05/19.38 | | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_65_5, all_107_1, % 142.05/19.38 | | | | | | | | | | | | | | | | all_65_8, simplifying with (46), (207) gives: % 142.05/19.38 | | | | | | | | | | | | | | | | (209) all_107_1 = all_65_5 % 142.05/19.38 | | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_65_12, all_107_0, % 142.05/19.38 | | | | | | | | | | | | | | | | all_65_6, simplifying with (48), (208) gives: % 142.05/19.38 | | | | | | | | | | | | | | | | (210) all_107_0 = all_65_12 % 142.05/19.38 | | | | | | | | | | | | | | | | % 142.05/19.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (axiom_32) with all_65_16, all_65_6, % 142.05/19.38 | | | | | | | | | | | | | | | | all_65_17, all_65_8, all_65_11, simplifying with % 142.05/19.38 | | | | | | | | | | | | | | | | (26), (27), (33), (35), (49), (205) gives: % 142.05/19.38 | | | | | | | | | | | | | | | | (211) all_65_8 = all_65_17 % 142.05/19.38 | | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (22), (23), (26), (27), (31), % 142.05/19.39 | | | | | | | | | | | | | | | | (33), (35), (41), (43), (45), (46), (48), (49), % 142.05/19.39 | | | | | | | | | | | | | | | | (52), (56), (57), (58), (59), (67), (90), (191), % 142.05/19.39 | | | | | | | | | | | | | | | | (198), (205), (211), (axiom_31) are inconsistent % 142.05/19.39 | | | | | | | | | | | | | | | | by sub-proof #3. % 142.05/19.39 | | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | Case 2: % 142.05/19.39 | | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (axiom_32) with all_65_16, all_65_6, % 142.05/19.39 | | | | | | | | | | | | | | | | all_65_17, all_65_8, all_65_11, simplifying with % 142.05/19.39 | | | | | | | | | | | | | | | | (26), (27), (33), (35), (49), (205) gives: % 142.05/19.39 | | | | | | | | | | | | | | | | (212) all_65_8 = all_65_17 % 142.05/19.39 | | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (22), (23), (26), (27), (31), % 142.05/19.39 | | | | | | | | | | | | | | | | (33), (35), (41), (43), (45), (46), (48), (49), % 142.05/19.39 | | | | | | | | | | | | | | | | (52), (56), (57), (58), (59), (67), (90), (191), % 142.05/19.39 | | | | | | | | | | | | | | | | (198), (205), (212), (axiom_31) are inconsistent % 142.05/19.39 | | | | | | | | | | | | | | | | by sub-proof #3. % 142.05/19.39 | | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | End of split % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | End of split % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | Case 2: % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | (213) ~ elem(all_65_3, all_128_7) % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | REDUCE: (176), (213) imply: % 142.05/19.39 | | | | | | | | | | | | | | (214) ~ elem(all_65_3, all_65_2) % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | PRED_UNIFY: (199), (214) imply: % 142.05/19.39 | | | | | | | | | | | | | | (215) $false % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | CLOSE: (215) is inconsistent. % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | End of split % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | Case 2: % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | (216) all_65_3 = all_65_11 % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | REDUCE: (53), (216) imply: % 142.05/19.39 | | | | | | | | | | | | | (217) m_Down(all_65_7) = all_65_11 % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | GROUND_INST: instantiating (axiom_12) with all_65_16, % 142.05/19.39 | | | | | | | | | | | | | all_65_17, all_65_7, all_65_11, simplifying with % 142.05/19.39 | | | | | | | | | | | | | (26), (27), (34), (49), (217) gives: % 142.05/19.39 | | | | | | | | | | | | | (218) $false % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | CLOSE: (218) is inconsistent. % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | End of split % 142.05/19.39 | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | End of split % 142.05/19.39 | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | End of split % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | Case 2: % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | (219) ~ leq(all_65_9, all_65_15) % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | REF_CLOSE: (13), (14), (16), (26), (27), (33), (34), (35), % 142.05/19.39 | | | | | | | | | | (42), (43), (46), (49), (50), (53), (58), (59), % 142.05/19.39 | | | | | | | | | | (91), (92), (96), (104), (174), (176), (185), % 142.05/19.39 | | | | | | | | | | (187), (219), (axiom_12), (axiom_32) are % 142.05/19.39 | | | | | | | | | | inconsistent by sub-proof #2. % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | End of split % 142.05/19.39 | | | | | | | | | % 142.05/19.39 | | | | | | | | Case 2: % 142.05/19.39 | | | | | | | | | % 142.05/19.39 | | | | | | | | | (220) ~ leq(all_65_12, all_65_9) % 142.05/19.39 | | | | | | | | | % 142.05/19.39 | | | | | | | | | BETA: splitting (79) gives: % 142.05/19.39 | | | | | | | | | % 142.05/19.39 | | | | | | | | | Case 1: % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | (221) leq(all_65_12, all_65_9) % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | PRED_UNIFY: (220), (221) imply: % 142.05/19.39 | | | | | | | | | | (222) $false % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | CLOSE: (222) is inconsistent. % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | Case 2: % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | (223) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 142.05/19.39 | | | | | | | | | | $i] : (( ~ (v1 = elec_2) & index(status, % 142.05/19.39 | | | | | | | | | | all_65_9) = v1 & $i(v1)) | ( ~ (v0 = elec_2) % 142.05/19.39 | | | | | | | | | | & index(status, all_65_12) = v0 & $i(v0)) | % 142.05/19.39 | | | | | | | | | | (index(pendack, all_65_9) = v3 & index(pendack, % 142.05/19.39 | | | | | | | | | | all_65_12) = v2 & $i(v3) & $i(v2) & ~ % 142.05/19.39 | | | | | | | | | | leq(v2, v3))) % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | DELTA: instantiating (223) with fresh symbols all_229_0, % 142.05/19.39 | | | | | | | | | | all_229_1, all_229_2, all_229_3 gives: % 142.05/19.39 | | | | | | | | | | (224) ( ~ (all_229_2 = elec_2) & index(status, all_65_9) % 142.05/19.39 | | | | | | | | | | = all_229_2 & $i(all_229_2)) | ( ~ (all_229_3 = % 142.05/19.39 | | | | | | | | | | elec_2) & index(status, all_65_12) = all_229_3 % 142.05/19.39 | | | | | | | | | | & $i(all_229_3)) | (index(pendack, all_65_9) = % 142.05/19.39 | | | | | | | | | | all_229_0 & index(pendack, all_65_12) = all_229_1 % 142.05/19.39 | | | | | | | | | | & $i(all_229_0) & $i(all_229_1) & ~ % 142.05/19.39 | | | | | | | | | | leq(all_229_1, all_229_0)) % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | BETA: splitting (70) gives: % 142.05/19.39 | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | Case 1: % 142.05/19.39 | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | (225) leq(all_65_15, all_65_9) % 142.05/19.39 | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | BETA: splitting (72) gives: % 142.05/19.39 | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | Case 1: % 142.05/19.39 | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | (226) leq(all_65_9, all_65_15) % 142.05/19.39 | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | REF_CLOSE: (7), (18), (28), (32), (225), (226) are % 142.05/19.39 | | | | | | | | | | | | inconsistent by sub-proof #4. % 142.05/19.39 | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | Case 2: % 142.05/19.39 | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | (227) ~ leq(all_65_9, all_65_15) % 142.05/19.39 | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (26), (27), (33), (34), (35), % 142.05/19.39 | | | | | | | | | | | | (42), (43), (46), (49), (50), (53), (58), (59), % 142.05/19.39 | | | | | | | | | | | | (91), (92), (96), (104), (174), (176), (185), % 142.05/19.39 | | | | | | | | | | | | (187), (227), (axiom_12), (axiom_32) are % 142.05/19.39 | | | | | | | | | | | | inconsistent by sub-proof #2. % 142.05/19.39 | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | End of split % 142.05/19.39 | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | Case 2: % 142.05/19.39 | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | (228) ~ leq(all_65_15, all_65_9) % 142.05/19.39 | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | BETA: splitting (92) gives: % 142.05/19.39 | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | Case 1: % 142.05/19.39 | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | (229) elem(all_65_3, all_65_2) % 142.05/19.39 | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | BETA: splitting (174) gives: % 142.05/19.39 | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | Case 1: % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | (230) ~ elem(all_65_0, all_128_7) % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | REDUCE: (176), (230) imply: % 142.05/19.39 | | | | | | | | | | | | | (231) ~ elem(all_65_0, all_65_2) % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | BETA: splitting (91) gives: % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | Case 1: % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | (232) elem(all_65_0, all_65_2) % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | PRED_UNIFY: (231), (232) imply: % 142.05/19.39 | | | | | | | | | | | | | | (233) $false % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | CLOSE: (233) is inconsistent. % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | Case 2: % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | (234) all_65_0 = all_65_11 % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | REDUCE: (50), (234) imply: % 142.05/19.39 | | | | | | | | | | | | | | (235) m_Ack(all_65_6, all_65_8) = all_65_11 % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | BETA: splitting (100) gives: % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | Case 1: % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | (236) ~ (all_105_1 = elec_1) & index(status, all_105_2) % 142.05/19.39 | | | | | | | | | | | | | | | = all_105_1 & $i(all_105_1) % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | ALPHA: (236) implies: % 142.05/19.39 | | | | | | | | | | | | | | | (237) index(status, all_105_2) = all_105_1 % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | REDUCE: (130), (237) imply: % 142.05/19.39 | | | | | | | | | | | | | | | (238) index(status, all_65_12) = all_105_1 % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, all_105_1, % 142.05/19.39 | | | | | | | | | | | | | | | all_65_12, status, simplifying with (57), (238) % 142.05/19.39 | | | | | | | | | | | | | | | gives: % 142.05/19.39 | | | | | | | | | | | | | | | (239) all_105_1 = elec_2 % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | GROUND_INST: instantiating (axiom_32) with all_65_16, all_65_6, % 142.05/19.39 | | | | | | | | | | | | | | | all_65_17, all_65_8, all_65_11, simplifying with % 142.05/19.39 | | | | | | | | | | | | | | | (26), (27), (33), (35), (49), (235) gives: % 142.05/19.39 | | | | | | | | | | | | | | | (240) all_65_8 = all_65_17 % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (22), (23), (26), (27), (31), % 142.05/19.39 | | | | | | | | | | | | | | | (33), (35), (41), (43), (45), (46), (48), (49), % 142.05/19.39 | | | | | | | | | | | | | | | (52), (56), (57), (58), (59), (64), (67), (90), % 142.05/19.39 | | | | | | | | | | | | | | | (182), (183), (186), (224), (228), (235), (240), % 142.05/19.39 | | | | | | | | | | | | | | | (axiom_17), (axiom_26), (axiom_31) are % 142.05/19.39 | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | Case 2: % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | GROUND_INST: instantiating (axiom_32) with all_65_16, all_65_6, % 142.05/19.39 | | | | | | | | | | | | | | | all_65_17, all_65_8, all_65_11, simplifying with % 142.05/19.39 | | | | | | | | | | | | | | | (26), (27), (33), (35), (49), (235) gives: % 142.05/19.39 | | | | | | | | | | | | | | | (241) all_65_8 = all_65_17 % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (22), (23), (26), (27), (31), % 142.05/19.39 | | | | | | | | | | | | | | | (33), (35), (41), (43), (45), (46), (48), (49), % 142.05/19.39 | | | | | | | | | | | | | | | (52), (56), (57), (58), (59), (64), (67), (90), % 142.05/19.39 | | | | | | | | | | | | | | | (182), (183), (186), (224), (228), (235), (241), % 142.05/19.39 | | | | | | | | | | | | | | | (axiom_17), (axiom_26), (axiom_31) are % 142.05/19.39 | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 142.05/19.39 | | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | | End of split % 142.05/19.39 | | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | | End of split % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.39 | | | | | | | | | | | | Case 2: % 142.05/19.39 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | (242) ~ elem(all_65_3, all_128_7) % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | REDUCE: (176), (242) imply: % 142.05/19.40 | | | | | | | | | | | | | (243) ~ elem(all_65_3, all_65_2) % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | PRED_UNIFY: (229), (243) imply: % 142.05/19.40 | | | | | | | | | | | | | (244) $false % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | CLOSE: (244) is inconsistent. % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | End of split % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | Case 2: % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | (245) all_65_3 = all_65_11 % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | REDUCE: (53), (245) imply: % 142.05/19.40 | | | | | | | | | | | | (246) m_Down(all_65_7) = all_65_11 % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | GROUND_INST: instantiating (axiom_12) with all_65_16, % 142.05/19.40 | | | | | | | | | | | | all_65_17, all_65_7, all_65_11, simplifying with % 142.05/19.40 | | | | | | | | | | | | (26), (27), (34), (49), (246) gives: % 142.05/19.40 | | | | | | | | | | | | (247) $false % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | CLOSE: (247) is inconsistent. % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | End of split % 142.05/19.40 | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | End of split % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | End of split % 142.05/19.40 | | | | | | | | | % 142.05/19.40 | | | | | | | | End of split % 142.05/19.40 | | | | | | | | % 142.05/19.40 | | | | | | | Case 2: % 142.05/19.40 | | | | | | | | % 142.05/19.40 | | | | | | | | (248) ~ leq(all_65_12, all_65_12) % 142.05/19.40 | | | | | | | | (249) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 142.05/19.40 | | | | | | | | (( ~ (v1 = elec_2) & index(status, all_65_12) = v1 & % 142.05/19.40 | | | | | | | | $i(v1)) | ( ~ (v0 = elec_2) & index(status, % 142.05/19.40 | | | | | | | | all_65_12) = v0 & $i(v0)) | (index(pendack, % 142.05/19.40 | | | | | | | | all_65_12) = v3 & index(pendack, all_65_12) = v2 % 142.05/19.40 | | | | | | | | & $i(v3) & $i(v2) & ~ leq(v2, v3))) % 142.05/19.40 | | | | | | | | % 142.05/19.40 | | | | | | | | DELTA: instantiating (249) with fresh symbols all_180_0, % 142.05/19.40 | | | | | | | | all_180_1, all_180_2, all_180_3 gives: % 142.05/19.40 | | | | | | | | (250) ( ~ (all_180_2 = elec_2) & index(status, all_65_12) = % 142.05/19.40 | | | | | | | | all_180_2 & $i(all_180_2)) | ( ~ (all_180_3 = elec_2) % 142.05/19.40 | | | | | | | | & index(status, all_65_12) = all_180_3 & % 142.05/19.40 | | | | | | | | $i(all_180_3)) | (index(pendack, all_65_12) = % 142.05/19.40 | | | | | | | | all_180_0 & index(pendack, all_65_12) = all_180_1 & % 142.05/19.40 | | | | | | | | $i(all_180_0) & $i(all_180_1) & ~ leq(all_180_1, % 142.05/19.40 | | | | | | | | all_180_0)) % 142.05/19.40 | | | | | | | | % 142.05/19.40 | | | | | | | | BETA: splitting (250) gives: % 142.05/19.40 | | | | | | | | % 142.05/19.40 | | | | | | | | Case 1: % 142.05/19.40 | | | | | | | | | % 142.05/19.40 | | | | | | | | | (251) ~ (all_180_2 = elec_2) & index(status, all_65_12) = % 142.05/19.40 | | | | | | | | | all_180_2 & $i(all_180_2) % 142.05/19.40 | | | | | | | | | % 142.05/19.40 | | | | | | | | | ALPHA: (251) implies: % 142.05/19.40 | | | | | | | | | (252) ~ (all_180_2 = elec_2) % 142.05/19.40 | | | | | | | | | (253) index(status, all_65_12) = all_180_2 % 142.05/19.40 | | | | | | | | | % 142.05/19.40 | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, all_180_2, % 142.05/19.40 | | | | | | | | | all_65_12, status, simplifying with (57), (253) % 142.05/19.40 | | | | | | | | | gives: % 142.05/19.40 | | | | | | | | | (254) all_180_2 = elec_2 % 142.05/19.40 | | | | | | | | | % 142.05/19.40 | | | | | | | | | REDUCE: (252), (254) imply: % 142.05/19.40 | | | | | | | | | (255) $false % 142.05/19.40 | | | | | | | | | % 142.05/19.40 | | | | | | | | | CLOSE: (255) is inconsistent. % 142.05/19.40 | | | | | | | | | % 142.05/19.40 | | | | | | | | Case 2: % 142.05/19.40 | | | | | | | | | % 142.05/19.40 | | | | | | | | | (256) ( ~ (all_180_3 = elec_2) & index(status, all_65_12) = % 142.05/19.40 | | | | | | | | | all_180_3 & $i(all_180_3)) | (index(pendack, % 142.05/19.40 | | | | | | | | | all_65_12) = all_180_0 & index(pendack, % 142.05/19.40 | | | | | | | | | all_65_12) = all_180_1 & $i(all_180_0) & % 142.05/19.40 | | | | | | | | | $i(all_180_1) & ~ leq(all_180_1, all_180_0)) % 142.05/19.40 | | | | | | | | | % 142.05/19.40 | | | | | | | | | BETA: splitting (256) gives: % 142.05/19.40 | | | | | | | | | % 142.05/19.40 | | | | | | | | | Case 1: % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | (257) ~ (all_180_3 = elec_2) & index(status, all_65_12) % 142.05/19.40 | | | | | | | | | | = all_180_3 & $i(all_180_3) % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | ALPHA: (257) implies: % 142.05/19.40 | | | | | | | | | | (258) ~ (all_180_3 = elec_2) % 142.05/19.40 | | | | | | | | | | (259) index(status, all_65_12) = all_180_3 % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, all_180_3, % 142.05/19.40 | | | | | | | | | | all_65_12, status, simplifying with (57), (259) % 142.05/19.40 | | | | | | | | | | gives: % 142.05/19.40 | | | | | | | | | | (260) all_180_3 = elec_2 % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | REDUCE: (258), (260) imply: % 142.05/19.40 | | | | | | | | | | (261) $false % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | CLOSE: (261) is inconsistent. % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | Case 2: % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | (262) index(pendack, all_65_12) = all_180_0 & % 142.05/19.40 | | | | | | | | | | index(pendack, all_65_12) = all_180_1 & % 142.05/19.40 | | | | | | | | | | $i(all_180_0) & $i(all_180_1) & ~ leq(all_180_1, % 142.05/19.40 | | | | | | | | | | all_180_0) % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | ALPHA: (262) implies: % 142.05/19.40 | | | | | | | | | | (263) ~ leq(all_180_1, all_180_0) % 142.05/19.40 | | | | | | | | | | (264) index(pendack, all_65_12) = all_180_1 % 142.05/19.40 | | | | | | | | | | (265) index(pendack, all_65_12) = all_180_0 % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | BETA: splitting (77) gives: % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | Case 1: % 142.05/19.40 | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | (266) leq(all_65_12, all_65_12) % 142.05/19.40 | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | PRED_UNIFY: (248), (266) imply: % 142.05/19.40 | | | | | | | | | | | (267) $false % 142.05/19.40 | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | CLOSE: (267) is inconsistent. % 142.05/19.40 | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | Case 2: % 142.05/19.40 | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | (268) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (( ~ (v1 % 142.05/19.40 | | | | | | | | | | | = elec_2) & index(status, all_65_12) = v1 & % 142.05/19.40 | | | | | | | | | | | $i(v1)) | ( ~ (v0 = elec_2) & index(status, % 142.05/19.40 | | | | | | | | | | | all_65_12) = v0 & $i(v0)) | (index(pendack, % 142.05/19.40 | | | | | | | | | | | all_65_12) = v2 & $i(v2) & leq(v2, % 142.05/19.40 | | | | | | | | | | | all_65_12))) % 142.05/19.40 | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | DELTA: instantiating (268) with fresh symbols all_189_0, % 142.05/19.40 | | | | | | | | | | | all_189_1, all_189_2 gives: % 142.05/19.40 | | | | | | | | | | | (269) ( ~ (all_189_1 = elec_2) & index(status, % 142.05/19.40 | | | | | | | | | | | all_65_12) = all_189_1 & $i(all_189_1)) | ( ~ % 142.05/19.40 | | | | | | | | | | | (all_189_2 = elec_2) & index(status, all_65_12) % 142.05/19.40 | | | | | | | | | | | = all_189_2 & $i(all_189_2)) | (index(pendack, % 142.05/19.40 | | | | | | | | | | | all_65_12) = all_189_0 & $i(all_189_0) & % 142.05/19.40 | | | | | | | | | | | leq(all_189_0, all_65_12)) % 142.05/19.40 | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | BETA: splitting (269) gives: % 142.05/19.40 | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | Case 1: % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | (270) ~ (all_189_1 = elec_2) & index(status, all_65_12) % 142.05/19.40 | | | | | | | | | | | | = all_189_1 & $i(all_189_1) % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | ALPHA: (270) implies: % 142.05/19.40 | | | | | | | | | | | | (271) ~ (all_189_1 = elec_2) % 142.05/19.40 | | | | | | | | | | | | (272) index(status, all_65_12) = all_189_1 % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, all_189_1, % 142.05/19.40 | | | | | | | | | | | | all_65_12, status, simplifying with (57), (272) % 142.05/19.40 | | | | | | | | | | | | gives: % 142.05/19.40 | | | | | | | | | | | | (273) all_189_1 = elec_2 % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | REDUCE: (271), (273) imply: % 142.05/19.40 | | | | | | | | | | | | (274) $false % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | CLOSE: (274) is inconsistent. % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | Case 2: % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | (275) ( ~ (all_189_2 = elec_2) & index(status, % 142.05/19.40 | | | | | | | | | | | | all_65_12) = all_189_2 & $i(all_189_2)) | % 142.05/19.40 | | | | | | | | | | | | (index(pendack, all_65_12) = all_189_0 & % 142.05/19.40 | | | | | | | | | | | | $i(all_189_0) & leq(all_189_0, all_65_12)) % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | BETA: splitting (275) gives: % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | Case 1: % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | (276) ~ (all_189_2 = elec_2) & index(status, all_65_12) % 142.05/19.40 | | | | | | | | | | | | | = all_189_2 & $i(all_189_2) % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | ALPHA: (276) implies: % 142.05/19.40 | | | | | | | | | | | | | (277) ~ (all_189_2 = elec_2) % 142.05/19.40 | | | | | | | | | | | | | (278) index(status, all_65_12) = all_189_2 % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, all_189_2, % 142.05/19.40 | | | | | | | | | | | | | all_65_12, status, simplifying with (57), (278) % 142.05/19.40 | | | | | | | | | | | | | gives: % 142.05/19.40 | | | | | | | | | | | | | (279) all_189_2 = elec_2 % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | REDUCE: (277), (279) imply: % 142.05/19.40 | | | | | | | | | | | | | (280) $false % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | CLOSE: (280) is inconsistent. % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | Case 2: % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | (281) index(pendack, all_65_12) = all_189_0 & % 142.05/19.40 | | | | | | | | | | | | | $i(all_189_0) & leq(all_189_0, all_65_12) % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | ALPHA: (281) implies: % 142.05/19.40 | | | | | | | | | | | | | (282) index(pendack, all_65_12) = all_189_0 % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_65_5, all_180_0, % 142.05/19.40 | | | | | | | | | | | | | all_65_12, pendack, simplifying with (56), (265) % 142.05/19.40 | | | | | | | | | | | | | gives: % 142.05/19.40 | | | | | | | | | | | | | (283) all_180_0 = all_65_5 % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_180_0, all_189_0, % 142.05/19.40 | | | | | | | | | | | | | all_65_12, pendack, simplifying with (265), (282) % 142.05/19.40 | | | | | | | | | | | | | gives: % 142.05/19.40 | | | | | | | | | | | | | (284) all_189_0 = all_180_0 % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_180_1, all_189_0, % 142.05/19.40 | | | | | | | | | | | | | all_65_12, pendack, simplifying with (264), (282) % 142.05/19.40 | | | | | | | | | | | | | gives: % 142.05/19.40 | | | | | | | | | | | | | (285) all_189_0 = all_180_1 % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | COMBINE_EQS: (284), (285) imply: % 142.05/19.40 | | | | | | | | | | | | | (286) all_180_0 = all_180_1 % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | SIMP: (286) implies: % 142.05/19.40 | | | | | | | | | | | | | (287) all_180_0 = all_180_1 % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | COMBINE_EQS: (283), (287) imply: % 142.05/19.40 | | | | | | | | | | | | | (288) all_180_1 = all_65_5 % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | REDUCE: (263), (283), (288) imply: % 142.05/19.40 | | | | | | | | | | | | | (289) ~ leq(all_65_5, all_65_5) % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | PRED_UNIFY: (179), (289) imply: % 142.05/19.40 | | | | | | | | | | | | | (290) $false % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | | CLOSE: (290) is inconsistent. % 142.05/19.40 | | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | | End of split % 142.05/19.40 | | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | | End of split % 142.05/19.40 | | | | | | | | | | | % 142.05/19.40 | | | | | | | | | | End of split % 142.05/19.40 | | | | | | | | | | % 142.05/19.40 | | | | | | | | | End of split % 142.05/19.40 | | | | | | | | | % 142.05/19.40 | | | | | | | | End of split % 142.05/19.40 | | | | | | | | % 142.05/19.40 | | | | | | | End of split % 142.05/19.40 | | | | | | | % 142.05/19.40 | | | | | | End of split % 142.05/19.40 | | | | | | % 142.05/19.40 | | | | | End of split % 142.05/19.40 | | | | | % 142.05/19.40 | | | | End of split % 142.05/19.40 | | | | % 142.05/19.40 | | | End of split % 142.05/19.40 | | | % 142.05/19.40 | | End of split % 142.05/19.40 | | % 142.05/19.40 | Case 2: % 142.05/19.40 | | % 142.05/19.40 | | (291) queue(all_65_15) = all_97_1 & $i(all_97_1) & ~ elem(all_65_13, % 142.05/19.40 | | all_97_1) % 142.05/19.40 | | % 142.05/19.40 | | ALPHA: (291) implies: % 142.05/19.41 | | (292) ~ elem(all_65_13, all_97_1) % 142.05/19.41 | | (293) queue(all_65_15) = all_97_1 % 142.05/19.41 | | % 142.05/19.41 | | GROUND_INST: instantiating (13) with all_65_14, all_97_1, all_65_15, % 142.05/19.41 | | simplifying with (41), (293) gives: % 142.05/19.41 | | (294) all_97_1 = all_65_14 % 142.05/19.41 | | % 142.05/19.41 | | REDUCE: (292), (294) imply: % 142.05/19.41 | | (295) ~ elem(all_65_13, all_65_14) % 142.05/19.41 | | % 142.05/19.41 | | PRED_UNIFY: (90), (295) imply: % 142.05/19.41 | | (296) $false % 142.05/19.41 | | % 142.05/19.41 | | CLOSE: (296) is inconsistent. % 142.05/19.41 | | % 142.05/19.41 | End of split % 142.05/19.41 | % 142.05/19.41 End of proof % 142.05/19.41 % 142.05/19.41 Sub-proof #1 shows that the following formulas are inconsistent: % 142.05/19.41 ---------------------------------------------------------------- % 142.05/19.41 (1) m_Ack(all_65_6, all_65_8) = all_65_11 % 142.05/19.41 (2) index(status, all_65_12) = elec_2 % 142.05/19.41 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~ % 142.05/19.41 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 142.05/19.41 (4) m_Halt(all_65_16) = all_65_13 % 142.05/19.41 (5) setIn(all_65_10, alive) % 142.05/19.41 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 142.05/19.41 = v0 | ~ (m_Ack(v1, v3) = v4) | ~ (m_Ack(v0, v2) = v4) | ~ $i(v3) | % 142.05/19.41 ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 142.05/19.41 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v1) = v2) % 142.05/19.41 | ~ (m_Halt(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 142.05/19.41 (8) index(pendack, all_65_12) = all_65_5 % 142.05/19.41 (9) m_Ack(all_65_16, all_65_17) = all_65_11 % 142.05/19.41 (10) host(all_65_6) = all_65_12 % 142.05/19.41 (11) leq(all_65_12, all_65_12) % 142.05/19.41 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1) % 142.05/19.41 | ~ (host(v2) = v0)) % 142.05/19.41 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 142.05/19.41 [v5: $i] : ( ~ (m_Halt(v2) = v4) | ~ (host(v1) = v5) | ~ (host(v0) = % 142.05/19.41 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ % 142.05/19.41 setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 142.05/19.41 $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v11 = norm) & % 142.05/19.41 index(status, v3) = v11 & $i(v11)) | ( ~ (v10 = v3) & index(ldr, % 142.05/19.41 v3) = v10 & $i(v10)) | ( ~ (v9 = elec_2) & index(status, v6) = % 142.05/19.41 v9 & host(v2) = v6 & $i(v9) & $i(v6)) | (index(pendack, v6) = v7 & % 142.05/19.41 host(v2) = v6 & $i(v7) & $i(v6) & leq(v7, v3)) | (queue(v5) = v8 & % 142.05/19.41 $i(v8) & ~ elem(v4, v8)))) % 142.05/19.41 (14) setIn(all_65_6, alive) % 142.05/19.41 (15) $i(all_174_2) % 142.05/19.41 (16) $i(all_65_6) % 142.05/19.41 (17) queue(all_65_15) = all_65_14 % 142.05/19.41 (18) index(status, all_65_9) = norm % 142.05/19.41 (19) host(all_65_17) = all_65_15 % 142.05/19.41 (20) $i(all_65_10) % 142.05/19.41 (21) ( ~ (all_229_2 = elec_2) & index(status, all_65_9) = all_229_2 & % 142.05/19.41 $i(all_229_2)) | ( ~ (all_229_3 = elec_2) & index(status, all_65_12) = % 142.05/19.41 all_229_3 & $i(all_229_3)) | (index(pendack, all_65_9) = all_229_0 & % 142.05/19.41 index(pendack, all_65_12) = all_229_1 & $i(all_229_0) & $i(all_229_1) % 142.05/19.41 & ~ leq(all_229_1, all_229_0)) % 142.05/19.41 (22) host(all_65_10) = all_65_9 % 142.05/19.41 (23) ~ leq(all_65_15, all_65_9) % 142.05/19.41 (24) host(all_65_8) = all_65_5 % 142.05/19.41 (25) index(ldr, all_65_9) = all_65_9 % 142.05/19.41 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Halt(v1) % 142.05/19.41 = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 142.05/19.41 ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3) = % 142.05/19.41 v4 & $i(v4) & ~ elem(v2, v4)))) % 142.05/19.41 (27) (all_174_0 = all_65_13 & m_Down(all_174_2) = all_65_13) | (all_174_1 = % 142.05/19.41 all_65_13 & m_Halt(all_174_2) = all_65_13) % 142.05/19.41 (28) $i(all_65_8) % 142.05/19.41 (29) elem(all_65_13, all_65_14) % 142.05/19.41 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) % 142.05/19.41 | ~ (queue(v2) = v0)) % 142.05/19.41 (31) $i(all_65_17) % 142.05/19.41 (32) $i(all_65_16) % 142.05/19.41 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.05/19.41 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) % 142.05/19.41 (34) all_65_8 = all_65_17 % 142.05/19.41 % 142.05/19.41 Begin of proof % 142.05/19.41 | % 142.05/19.41 | GROUND_INST: instantiating (6) with all_65_16, all_65_6, all_65_17, all_65_8, % 142.05/19.41 | all_65_11, simplifying with (1), (9), (16), (28), (31), (32) % 142.05/19.41 | gives: % 142.05/19.41 | (35) all_65_6 = all_65_16 % 142.05/19.41 | % 142.05/19.41 | REDUCE: (10), (35) imply: % 142.05/19.41 | (36) host(all_65_16) = all_65_12 % 142.05/19.41 | % 142.05/19.41 | REDUCE: (24), (34) imply: % 142.05/19.41 | (37) host(all_65_17) = all_65_5 % 142.05/19.41 | % 142.05/19.41 | REDUCE: (14), (35) imply: % 142.05/19.41 | (38) setIn(all_65_16, alive) % 142.05/19.41 | % 142.05/19.41 | GROUND_INST: instantiating (12) with all_65_15, all_65_5, all_65_17, % 142.05/19.41 | simplifying with (19), (37) gives: % 142.05/19.41 | (39) all_65_5 = all_65_15 % 142.05/19.41 | % 142.05/19.41 | REDUCE: (8), (39) imply: % 142.05/19.41 | (40) index(pendack, all_65_12) = all_65_15 % 142.05/19.41 | % 142.05/19.41 | BETA: splitting (27) gives: % 142.05/19.41 | % 142.05/19.41 | Case 1: % 142.05/19.41 | | % 142.05/19.41 | | (41) all_174_0 = all_65_13 & m_Down(all_174_2) = all_65_13 % 142.05/19.41 | | % 142.05/19.41 | | ALPHA: (41) implies: % 142.05/19.41 | | (42) m_Down(all_174_2) = all_65_13 % 142.05/19.41 | | % 142.05/19.41 | | GROUND_INST: instantiating (3) with all_174_2, all_65_16, all_65_13, % 142.05/19.41 | | simplifying with (4), (15), (32), (42) gives: % 142.05/19.41 | | (43) $false % 142.05/19.41 | | % 142.05/19.41 | | CLOSE: (43) is inconsistent. % 142.05/19.41 | | % 142.05/19.41 | Case 2: % 142.05/19.41 | | % 142.05/19.41 | | (44) all_174_1 = all_65_13 & m_Halt(all_174_2) = all_65_13 % 142.05/19.41 | | % 142.05/19.41 | | ALPHA: (44) implies: % 142.05/19.41 | | (45) m_Halt(all_174_2) = all_65_13 % 142.05/19.41 | | % 142.05/19.41 | | BETA: splitting (21) gives: % 142.05/19.41 | | % 142.05/19.41 | | Case 1: % 142.05/19.41 | | | % 142.05/19.41 | | | (46) ~ (all_229_2 = elec_2) & index(status, all_65_9) = all_229_2 & % 142.05/19.41 | | | $i(all_229_2) % 142.05/19.41 | | | % 142.05/19.41 | | | ALPHA: (46) implies: % 142.05/19.41 | | | (47) index(status, all_65_9) = all_229_2 % 142.05/19.41 | | | % 142.05/19.41 | | | GROUND_INST: instantiating (33) with norm, all_229_2, all_65_9, status, % 142.05/19.41 | | | simplifying with (18), (47) gives: % 142.05/19.41 | | | (48) all_229_2 = norm % 142.05/19.41 | | | % 142.05/19.41 | | | GROUND_INST: instantiating (13) with all_65_10, all_65_17, all_65_16, % 142.05/19.41 | | | all_65_9, all_65_13, all_65_15, simplifying with (4), (5), % 142.05/19.41 | | | (19), (20), (22), (31), (32), (38) gives: % 142.05/19.41 | | | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 142.05/19.41 | | | any] : ? [v5: $i] : (( ~ (v5 = norm) & index(status, all_65_9) % 142.05/19.41 | | | = v5 & $i(v5)) | ( ~ (v4 = all_65_9) & index(ldr, all_65_9) = % 142.05/19.41 | | | v4 & $i(v4)) | ( ~ (v3 = elec_2) & index(status, v0) = v3 & % 142.05/19.41 | | | host(all_65_16) = v0 & $i(v3) & $i(v0)) | (index(pendack, v0) % 142.05/19.41 | | | = v1 & host(all_65_16) = v0 & $i(v1) & $i(v0) & leq(v1, % 142.05/19.41 | | | all_65_9)) | (queue(all_65_15) = v2 & $i(v2) & ~ % 142.05/19.41 | | | elem(all_65_13, v2))) % 142.05/19.41 | | | % 142.05/19.41 | | | DELTA: instantiating (49) with fresh symbols all_800_0, all_800_1, % 142.05/19.41 | | | all_800_2, all_800_3, all_800_4, all_800_5 gives: % 142.05/19.42 | | | (50) ( ~ (all_800_0 = norm) & index(status, all_65_9) = all_800_0 & % 142.05/19.42 | | | $i(all_800_0)) | ( ~ (all_800_1 = all_65_9) & index(ldr, % 142.05/19.42 | | | all_65_9) = all_800_1 & $i(all_800_1)) | ( ~ (all_800_2 = % 142.05/19.42 | | | elec_2) & index(status, all_800_5) = all_800_2 & % 142.05/19.42 | | | host(all_65_16) = all_800_5 & $i(all_800_2) & $i(all_800_5)) | % 142.05/19.42 | | | (index(pendack, all_800_5) = all_800_4 & host(all_65_16) = % 142.05/19.42 | | | all_800_5 & $i(all_800_4) & $i(all_800_5) & leq(all_800_4, % 142.05/19.42 | | | all_65_9)) | (queue(all_65_15) = all_800_3 & $i(all_800_3) & % 142.05/19.42 | | | ~ elem(all_65_13, all_800_3)) % 142.05/19.42 | | | % 142.05/19.42 | | | BETA: splitting (50) gives: % 142.05/19.42 | | | % 142.05/19.42 | | | Case 1: % 142.05/19.42 | | | | % 142.05/19.42 | | | | (51) ( ~ (all_800_0 = norm) & index(status, all_65_9) = all_800_0 & % 142.05/19.42 | | | | $i(all_800_0)) | ( ~ (all_800_1 = all_65_9) & index(ldr, % 142.05/19.42 | | | | all_65_9) = all_800_1 & $i(all_800_1)) % 142.05/19.42 | | | | % 142.05/19.42 | | | | BETA: splitting (51) gives: % 142.05/19.42 | | | | % 142.05/19.42 | | | | Case 1: % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | (52) ~ (all_800_0 = norm) & index(status, all_65_9) = all_800_0 & % 142.05/19.42 | | | | | $i(all_800_0) % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | ALPHA: (52) implies: % 142.05/19.42 | | | | | (53) ~ (all_800_0 = norm) % 142.05/19.42 | | | | | (54) index(status, all_65_9) = all_800_0 % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | GROUND_INST: instantiating (33) with norm, all_800_0, all_65_9, % 142.05/19.42 | | | | | status, simplifying with (18), (54) gives: % 142.05/19.42 | | | | | (55) all_800_0 = norm % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | REDUCE: (53), (55) imply: % 142.05/19.42 | | | | | (56) $false % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | CLOSE: (56) is inconsistent. % 142.05/19.42 | | | | | % 142.05/19.42 | | | | Case 2: % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | (57) ~ (all_800_1 = all_65_9) & index(ldr, all_65_9) = all_800_1 & % 142.05/19.42 | | | | | $i(all_800_1) % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | ALPHA: (57) implies: % 142.05/19.42 | | | | | (58) ~ (all_800_1 = all_65_9) % 142.05/19.42 | | | | | (59) index(ldr, all_65_9) = all_800_1 % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | GROUND_INST: instantiating (33) with all_65_9, all_800_1, all_65_9, % 142.05/19.42 | | | | | ldr, simplifying with (25), (59) gives: % 142.05/19.42 | | | | | (60) all_800_1 = all_65_9 % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | REDUCE: (58), (60) imply: % 142.05/19.42 | | | | | (61) $false % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | CLOSE: (61) is inconsistent. % 142.05/19.42 | | | | | % 142.05/19.42 | | | | End of split % 142.05/19.42 | | | | % 142.05/19.42 | | | Case 2: % 142.05/19.42 | | | | % 142.05/19.42 | | | | (62) ( ~ (all_800_2 = elec_2) & index(status, all_800_5) = all_800_2 % 142.05/19.42 | | | | & host(all_65_16) = all_800_5 & $i(all_800_2) & $i(all_800_5)) % 142.05/19.42 | | | | | (index(pendack, all_800_5) = all_800_4 & host(all_65_16) = % 142.05/19.42 | | | | all_800_5 & $i(all_800_4) & $i(all_800_5) & leq(all_800_4, % 142.05/19.42 | | | | all_65_9)) | (queue(all_65_15) = all_800_3 & $i(all_800_3) & % 142.05/19.42 | | | | ~ elem(all_65_13, all_800_3)) % 142.05/19.42 | | | | % 142.05/19.42 | | | | BETA: splitting (62) gives: % 142.05/19.42 | | | | % 142.05/19.42 | | | | Case 1: % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | (63) ~ (all_800_2 = elec_2) & index(status, all_800_5) = all_800_2 % 142.05/19.42 | | | | | & host(all_65_16) = all_800_5 & $i(all_800_2) & $i(all_800_5) % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | ALPHA: (63) implies: % 142.05/19.42 | | | | | (64) ~ (all_800_2 = elec_2) % 142.05/19.42 | | | | | (65) host(all_65_16) = all_800_5 % 142.05/19.42 | | | | | (66) index(status, all_800_5) = all_800_2 % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | GROUND_INST: instantiating (12) with all_65_12, all_800_5, all_65_16, % 142.05/19.42 | | | | | simplifying with (36), (65) gives: % 142.05/19.42 | | | | | (67) all_800_5 = all_65_12 % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | REDUCE: (66), (67) imply: % 142.05/19.42 | | | | | (68) index(status, all_65_12) = all_800_2 % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | GROUND_INST: instantiating (33) with elec_2, all_800_2, all_65_12, % 142.05/19.42 | | | | | status, simplifying with (2), (68) gives: % 142.05/19.42 | | | | | (69) all_800_2 = elec_2 % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | REDUCE: (64), (69) imply: % 142.05/19.42 | | | | | (70) $false % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | CLOSE: (70) is inconsistent. % 142.05/19.42 | | | | | % 142.05/19.42 | | | | Case 2: % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | (71) (index(pendack, all_800_5) = all_800_4 & host(all_65_16) = % 142.05/19.42 | | | | | all_800_5 & $i(all_800_4) & $i(all_800_5) & leq(all_800_4, % 142.05/19.42 | | | | | all_65_9)) | (queue(all_65_15) = all_800_3 & $i(all_800_3) % 142.05/19.42 | | | | | & ~ elem(all_65_13, all_800_3)) % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | BETA: splitting (71) gives: % 142.05/19.42 | | | | | % 142.05/19.42 | | | | | Case 1: % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | (72) index(pendack, all_800_5) = all_800_4 & host(all_65_16) = % 142.05/19.42 | | | | | | all_800_5 & $i(all_800_4) & $i(all_800_5) & leq(all_800_4, % 142.05/19.42 | | | | | | all_65_9) % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | ALPHA: (72) implies: % 142.05/19.42 | | | | | | (73) leq(all_800_4, all_65_9) % 142.05/19.42 | | | | | | (74) host(all_65_16) = all_800_5 % 142.05/19.42 | | | | | | (75) index(pendack, all_800_5) = all_800_4 % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | GROUND_INST: instantiating (12) with all_65_12, all_800_5, % 142.05/19.42 | | | | | | all_65_16, simplifying with (36), (74) gives: % 142.05/19.42 | | | | | | (76) all_800_5 = all_65_12 % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | REDUCE: (75), (76) imply: % 142.05/19.42 | | | | | | (77) index(pendack, all_65_12) = all_800_4 % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | GROUND_INST: instantiating (33) with all_65_15, all_800_4, % 142.05/19.42 | | | | | | all_65_12, pendack, simplifying with (40), (77) gives: % 142.05/19.42 | | | | | | (78) all_800_4 = all_65_15 % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | REDUCE: (73), (78) imply: % 142.05/19.42 | | | | | | (79) leq(all_65_15, all_65_9) % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | PRED_UNIFY: (23), (79) imply: % 142.05/19.42 | | | | | | (80) $false % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | CLOSE: (80) is inconsistent. % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | Case 2: % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | (81) queue(all_65_15) = all_800_3 & $i(all_800_3) & ~ % 142.05/19.42 | | | | | | elem(all_65_13, all_800_3) % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | ALPHA: (81) implies: % 142.05/19.42 | | | | | | (82) ~ elem(all_65_13, all_800_3) % 142.05/19.42 | | | | | | (83) queue(all_65_15) = all_800_3 % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | GROUND_INST: instantiating (30) with all_65_14, all_800_3, % 142.05/19.42 | | | | | | all_65_15, simplifying with (17), (83) gives: % 142.05/19.42 | | | | | | (84) all_800_3 = all_65_14 % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | REDUCE: (82), (84) imply: % 142.05/19.42 | | | | | | (85) ~ elem(all_65_13, all_65_14) % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | PRED_UNIFY: (29), (85) imply: % 142.05/19.42 | | | | | | (86) $false % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | | CLOSE: (86) is inconsistent. % 142.05/19.42 | | | | | | % 142.05/19.42 | | | | | End of split % 142.05/19.42 | | | | | % 142.05/19.42 | | | | End of split % 142.05/19.42 | | | | % 142.05/19.42 | | | End of split % 142.05/19.42 | | | % 142.05/19.42 | | Case 2: % 142.05/19.42 | | | % 142.05/19.42 | | | (87) ( ~ (all_229_3 = elec_2) & index(status, all_65_12) = all_229_3 & % 142.05/19.42 | | | $i(all_229_3)) | (index(pendack, all_65_9) = all_229_0 & % 142.05/19.42 | | | index(pendack, all_65_12) = all_229_1 & $i(all_229_0) & % 142.05/19.42 | | | $i(all_229_1) & ~ leq(all_229_1, all_229_0)) % 142.05/19.42 | | | % 142.05/19.42 | | | BETA: splitting (87) gives: % 142.05/19.42 | | | % 142.05/19.42 | | | Case 1: % 142.05/19.42 | | | | % 142.05/19.42 | | | | (88) ~ (all_229_3 = elec_2) & index(status, all_65_12) = all_229_3 & % 142.05/19.42 | | | | $i(all_229_3) % 142.05/19.42 | | | | % 142.05/19.42 | | | | ALPHA: (88) implies: % 142.47/19.42 | | | | (89) ~ (all_229_3 = elec_2) % 142.47/19.42 | | | | (90) index(status, all_65_12) = all_229_3 % 142.47/19.42 | | | | % 142.47/19.42 | | | | GROUND_INST: instantiating (33) with elec_2, all_229_3, all_65_12, % 142.47/19.42 | | | | status, simplifying with (2), (90) gives: % 142.47/19.42 | | | | (91) all_229_3 = elec_2 % 142.47/19.42 | | | | % 142.47/19.42 | | | | REDUCE: (89), (91) imply: % 142.47/19.42 | | | | (92) $false % 142.47/19.42 | | | | % 142.47/19.42 | | | | CLOSE: (92) is inconsistent. % 142.47/19.42 | | | | % 142.47/19.42 | | | Case 2: % 142.47/19.42 | | | | % 142.47/19.42 | | | | (93) index(pendack, all_65_9) = all_229_0 & index(pendack, all_65_12) % 142.47/19.42 | | | | = all_229_1 & $i(all_229_0) & $i(all_229_1) & ~ leq(all_229_1, % 142.47/19.42 | | | | all_229_0) % 142.47/19.42 | | | | % 142.47/19.42 | | | | ALPHA: (93) implies: % 142.47/19.42 | | | | (94) index(pendack, all_65_12) = all_229_1 % 142.47/19.42 | | | | % 142.47/19.42 | | | | GROUND_INST: instantiating (33) with all_65_15, all_229_1, all_65_12, % 142.47/19.42 | | | | pendack, simplifying with (40), (94) gives: % 142.47/19.42 | | | | (95) all_229_1 = all_65_15 % 142.47/19.42 | | | | % 142.47/19.42 | | | | GROUND_INST: instantiating (13) with all_65_10, all_65_17, all_65_16, % 142.47/19.42 | | | | all_65_9, all_65_13, all_65_15, simplifying with (4), (5), % 142.47/19.42 | | | | (19), (20), (22), (31), (32), (38) gives: % 142.47/19.42 | | | | (96) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 142.47/19.42 | | | | any] : ? [v5: $i] : (( ~ (v5 = norm) & index(status, % 142.47/19.42 | | | | all_65_9) = v5 & $i(v5)) | ( ~ (v4 = all_65_9) & % 142.47/19.42 | | | | index(ldr, all_65_9) = v4 & $i(v4)) | ( ~ (v3 = elec_2) & % 142.47/19.42 | | | | index(status, v0) = v3 & host(all_65_16) = v0 & $i(v3) & % 142.47/19.42 | | | | $i(v0)) | (index(pendack, v0) = v1 & host(all_65_16) = v0 & % 142.47/19.42 | | | | $i(v1) & $i(v0) & leq(v1, all_65_9)) | (queue(all_65_15) = % 142.47/19.42 | | | | v2 & $i(v2) & ~ elem(all_65_13, v2))) % 142.47/19.42 | | | | % 142.47/19.42 | | | | GROUND_INST: instantiating (26) with all_65_16, all_174_2, all_65_13, % 142.47/19.42 | | | | all_65_12, simplifying with (15), (32), (36), (45) gives: % 142.47/19.42 | | | | (97) ? [v0: $i] : ? [v1: $i] : ((host(all_174_2) = v1 & $i(v1) & ~ % 142.47/19.42 | | | | leq(all_65_12, v1)) | (queue(all_65_12) = v0 & $i(v0) & ~ % 142.47/19.42 | | | | elem(all_65_13, v0))) % 142.47/19.42 | | | | % 142.47/19.42 | | | | GROUND_INST: instantiating (7) with all_65_16, all_174_2, all_65_13, % 142.47/19.42 | | | | simplifying with (4), (15), (32), (45) gives: % 142.47/19.42 | | | | (98) all_174_2 = all_65_16 % 142.47/19.42 | | | | % 142.47/19.42 | | | | DELTA: instantiating (97) with fresh symbols all_773_0, all_773_1 gives: % 142.47/19.43 | | | | (99) (host(all_174_2) = all_773_0 & $i(all_773_0) & ~ leq(all_65_12, % 142.47/19.43 | | | | all_773_0)) | (queue(all_65_12) = all_773_1 & $i(all_773_1) % 142.47/19.43 | | | | & ~ elem(all_65_13, all_773_1)) % 142.47/19.43 | | | | % 142.47/19.43 | | | | DELTA: instantiating (96) with fresh symbols all_804_0, all_804_1, % 142.47/19.43 | | | | all_804_2, all_804_3, all_804_4, all_804_5 gives: % 142.47/19.43 | | | | (100) ( ~ (all_804_0 = norm) & index(status, all_65_9) = all_804_0 & % 142.47/19.43 | | | | $i(all_804_0)) | ( ~ (all_804_1 = all_65_9) & index(ldr, % 142.47/19.43 | | | | all_65_9) = all_804_1 & $i(all_804_1)) | ( ~ (all_804_2 = % 142.47/19.43 | | | | elec_2) & index(status, all_804_5) = all_804_2 & % 142.47/19.43 | | | | host(all_65_16) = all_804_5 & $i(all_804_2) & $i(all_804_5)) % 142.47/19.43 | | | | | (index(pendack, all_804_5) = all_804_4 & host(all_65_16) = % 142.47/19.43 | | | | all_804_5 & $i(all_804_4) & $i(all_804_5) & leq(all_804_4, % 142.47/19.43 | | | | all_65_9)) | (queue(all_65_15) = all_804_3 & $i(all_804_3) % 142.47/19.43 | | | | & ~ elem(all_65_13, all_804_3)) % 142.47/19.43 | | | | % 142.47/19.43 | | | | BETA: splitting (100) gives: % 142.47/19.43 | | | | % 142.47/19.43 | | | | Case 1: % 142.47/19.43 | | | | | % 142.47/19.43 | | | | | (101) ( ~ (all_804_0 = norm) & index(status, all_65_9) = all_804_0 % 142.47/19.43 | | | | | & $i(all_804_0)) | ( ~ (all_804_1 = all_65_9) & index(ldr, % 142.47/19.43 | | | | | all_65_9) = all_804_1 & $i(all_804_1)) % 142.47/19.43 | | | | | % 142.47/19.43 | | | | | BETA: splitting (101) gives: % 142.47/19.43 | | | | | % 142.47/19.43 | | | | | Case 1: % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | (102) ~ (all_804_0 = norm) & index(status, all_65_9) = all_804_0 % 142.47/19.43 | | | | | | & $i(all_804_0) % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | ALPHA: (102) implies: % 142.47/19.43 | | | | | | (103) ~ (all_804_0 = norm) % 142.47/19.43 | | | | | | (104) index(status, all_65_9) = all_804_0 % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | GROUND_INST: instantiating (33) with norm, all_804_0, all_65_9, % 142.47/19.43 | | | | | | status, simplifying with (18), (104) gives: % 142.47/19.43 | | | | | | (105) all_804_0 = norm % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | REDUCE: (103), (105) imply: % 142.47/19.43 | | | | | | (106) $false % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | CLOSE: (106) is inconsistent. % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | Case 2: % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | (107) ~ (all_804_1 = all_65_9) & index(ldr, all_65_9) = % 142.47/19.43 | | | | | | all_804_1 & $i(all_804_1) % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | ALPHA: (107) implies: % 142.47/19.43 | | | | | | (108) ~ (all_804_1 = all_65_9) % 142.47/19.43 | | | | | | (109) index(ldr, all_65_9) = all_804_1 % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | GROUND_INST: instantiating (33) with all_65_9, all_804_1, all_65_9, % 142.47/19.43 | | | | | | ldr, simplifying with (25), (109) gives: % 142.47/19.43 | | | | | | (110) all_804_1 = all_65_9 % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | REDUCE: (108), (110) imply: % 142.47/19.43 | | | | | | (111) $false % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | CLOSE: (111) is inconsistent. % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | End of split % 142.47/19.43 | | | | | % 142.47/19.43 | | | | Case 2: % 142.47/19.43 | | | | | % 142.47/19.43 | | | | | (112) ( ~ (all_804_2 = elec_2) & index(status, all_804_5) = % 142.47/19.43 | | | | | all_804_2 & host(all_65_16) = all_804_5 & $i(all_804_2) & % 142.47/19.43 | | | | | $i(all_804_5)) | (index(pendack, all_804_5) = all_804_4 & % 142.47/19.43 | | | | | host(all_65_16) = all_804_5 & $i(all_804_4) & $i(all_804_5) % 142.47/19.43 | | | | | & leq(all_804_4, all_65_9)) | (queue(all_65_15) = all_804_3 % 142.47/19.43 | | | | | & $i(all_804_3) & ~ elem(all_65_13, all_804_3)) % 142.47/19.43 | | | | | % 142.47/19.43 | | | | | BETA: splitting (112) gives: % 142.47/19.43 | | | | | % 142.47/19.43 | | | | | Case 1: % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | (113) ~ (all_804_2 = elec_2) & index(status, all_804_5) = % 142.47/19.43 | | | | | | all_804_2 & host(all_65_16) = all_804_5 & $i(all_804_2) & % 142.47/19.43 | | | | | | $i(all_804_5) % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | ALPHA: (113) implies: % 142.47/19.43 | | | | | | (114) ~ (all_804_2 = elec_2) % 142.47/19.43 | | | | | | (115) host(all_65_16) = all_804_5 % 142.47/19.43 | | | | | | (116) index(status, all_804_5) = all_804_2 % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | BETA: splitting (99) gives: % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | Case 1: % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | (117) host(all_174_2) = all_773_0 & $i(all_773_0) & ~ % 142.47/19.43 | | | | | | | leq(all_65_12, all_773_0) % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | ALPHA: (117) implies: % 142.47/19.43 | | | | | | | (118) ~ leq(all_65_12, all_773_0) % 142.47/19.43 | | | | | | | (119) host(all_174_2) = all_773_0 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | REDUCE: (98), (119) imply: % 142.47/19.43 | | | | | | | (120) host(all_65_16) = all_773_0 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | GROUND_INST: instantiating (12) with all_65_12, all_804_5, % 142.47/19.43 | | | | | | | all_65_16, simplifying with (36), (115) gives: % 142.47/19.43 | | | | | | | (121) all_804_5 = all_65_12 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | GROUND_INST: instantiating (12) with all_773_0, all_804_5, % 142.47/19.43 | | | | | | | all_65_16, simplifying with (115), (120) gives: % 142.47/19.43 | | | | | | | (122) all_804_5 = all_773_0 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | COMBINE_EQS: (121), (122) imply: % 142.47/19.43 | | | | | | | (123) all_773_0 = all_65_12 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | SIMP: (123) implies: % 142.47/19.43 | | | | | | | (124) all_773_0 = all_65_12 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | REDUCE: (118), (124) imply: % 142.47/19.43 | | | | | | | (125) ~ leq(all_65_12, all_65_12) % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | PRED_UNIFY: (11), (125) imply: % 142.47/19.43 | | | | | | | (126) $false % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | CLOSE: (126) is inconsistent. % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | Case 2: % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | GROUND_INST: instantiating (12) with all_65_12, all_804_5, % 142.47/19.43 | | | | | | | all_65_16, simplifying with (36), (115) gives: % 142.47/19.43 | | | | | | | (127) all_804_5 = all_65_12 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | REDUCE: (116), (127) imply: % 142.47/19.43 | | | | | | | (128) index(status, all_65_12) = all_804_2 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | GROUND_INST: instantiating (33) with elec_2, all_804_2, all_65_12, % 142.47/19.43 | | | | | | | status, simplifying with (2), (128) gives: % 142.47/19.43 | | | | | | | (129) all_804_2 = elec_2 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | REDUCE: (114), (129) imply: % 142.47/19.43 | | | | | | | (130) $false % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | CLOSE: (130) is inconsistent. % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | End of split % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | Case 2: % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | (131) (index(pendack, all_804_5) = all_804_4 & host(all_65_16) = % 142.47/19.43 | | | | | | all_804_5 & $i(all_804_4) & $i(all_804_5) & % 142.47/19.43 | | | | | | leq(all_804_4, all_65_9)) | (queue(all_65_15) = all_804_3 % 142.47/19.43 | | | | | | & $i(all_804_3) & ~ elem(all_65_13, all_804_3)) % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | BETA: splitting (131) gives: % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | | Case 1: % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | (132) index(pendack, all_804_5) = all_804_4 & host(all_65_16) = % 142.47/19.43 | | | | | | | all_804_5 & $i(all_804_4) & $i(all_804_5) & % 142.47/19.43 | | | | | | | leq(all_804_4, all_65_9) % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | ALPHA: (132) implies: % 142.47/19.43 | | | | | | | (133) leq(all_804_4, all_65_9) % 142.47/19.43 | | | | | | | (134) host(all_65_16) = all_804_5 % 142.47/19.43 | | | | | | | (135) index(pendack, all_804_5) = all_804_4 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | GROUND_INST: instantiating (12) with all_65_12, all_804_5, % 142.47/19.43 | | | | | | | all_65_16, simplifying with (36), (134) gives: % 142.47/19.43 | | | | | | | (136) all_804_5 = all_65_12 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | REDUCE: (135), (136) imply: % 142.47/19.43 | | | | | | | (137) index(pendack, all_65_12) = all_804_4 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | GROUND_INST: instantiating (33) with all_65_15, all_804_4, % 142.47/19.43 | | | | | | | all_65_12, pendack, simplifying with (40), (137) % 142.47/19.43 | | | | | | | gives: % 142.47/19.43 | | | | | | | (138) all_804_4 = all_65_15 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | REDUCE: (133), (138) imply: % 142.47/19.43 | | | | | | | (139) leq(all_65_15, all_65_9) % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | PRED_UNIFY: (23), (139) imply: % 142.47/19.43 | | | | | | | (140) $false % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | CLOSE: (140) is inconsistent. % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | Case 2: % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | (141) queue(all_65_15) = all_804_3 & $i(all_804_3) & ~ % 142.47/19.43 | | | | | | | elem(all_65_13, all_804_3) % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | ALPHA: (141) implies: % 142.47/19.43 | | | | | | | (142) ~ elem(all_65_13, all_804_3) % 142.47/19.43 | | | | | | | (143) queue(all_65_15) = all_804_3 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | GROUND_INST: instantiating (30) with all_65_14, all_804_3, % 142.47/19.43 | | | | | | | all_65_15, simplifying with (17), (143) gives: % 142.47/19.43 | | | | | | | (144) all_804_3 = all_65_14 % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | REDUCE: (142), (144) imply: % 142.47/19.43 | | | | | | | (145) ~ elem(all_65_13, all_65_14) % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | PRED_UNIFY: (29), (145) imply: % 142.47/19.43 | | | | | | | (146) $false % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | | CLOSE: (146) is inconsistent. % 142.47/19.43 | | | | | | | % 142.47/19.43 | | | | | | End of split % 142.47/19.43 | | | | | | % 142.47/19.43 | | | | | End of split % 142.47/19.43 | | | | | % 142.47/19.43 | | | | End of split % 142.47/19.43 | | | | % 142.47/19.43 | | | End of split % 142.47/19.43 | | | % 142.47/19.43 | | End of split % 142.47/19.43 | | % 142.47/19.43 | End of split % 142.47/19.43 | % 142.47/19.43 End of proof % 142.47/19.43 % 142.47/19.43 Sub-proof #2 shows that the following formulas are inconsistent: % 142.47/19.43 ---------------------------------------------------------------- % 142.47/19.43 (1) ( ~ (all_123_0 = norm) & index(status, all_65_9) = all_123_0 & % 142.47/19.43 $i(all_123_0)) | ( ~ (all_123_1 = all_65_9) & index(ldr, all_65_9) = % 142.47/19.43 all_123_1 & $i(all_123_1)) | ( ~ (all_123_2 = all_65_9) & % 142.47/19.43 host(all_65_7) = all_123_2 & $i(all_123_2)) | (queue(all_65_12) = % 142.47/19.43 all_123_3 & $i(all_123_3) & ~ elem(all_65_3, all_123_3)) % 142.47/19.43 (2) host(all_65_7) = nbr_proc % 142.47/19.43 (3) m_Ack(all_65_6, all_65_8) = all_65_0 % 142.47/19.43 (4) m_Ack(all_65_16, all_65_17) = all_65_11 % 142.47/19.43 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1) | % 142.47/19.43 ~ (host(v2) = v0)) % 142.47/19.43 (6) $i(all_65_7) % 142.47/19.43 (7) ( ~ (all_96_0 = all_65_12) & host(all_65_7) = all_96_0 & $i(all_96_0)) | % 142.47/19.43 (queue(all_65_12) = all_96_1 & $i(all_96_1) & ~ elem(all_65_3, % 142.47/19.43 all_96_1)) % 142.47/19.43 (8) all_65_9 = nbr_proc | leq(all_65_9, all_65_5) % 142.47/19.43 (9) $i(all_65_6) % 142.47/19.43 (10) queue(all_65_12) = all_65_2 % 142.47/19.43 (11) index(status, all_65_9) = norm % 142.47/19.43 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v2) % 142.47/19.43 = v3) | ~ (m_Ack(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 142.47/19.43 (13) host(all_65_17) = all_65_15 % 142.47/19.43 (14) all_128_7 = all_65_2 % 142.47/19.43 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 142.47/19.43 (v3 = v2 | ~ (m_Ack(v1, v3) = v4) | ~ (m_Ack(v0, v2) = v4) | ~ $i(v3) % 142.47/19.44 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 142.47/19.44 (16) ~ elem(all_65_0, all_128_7) | ~ elem(all_65_3, all_128_7) % 142.47/19.44 (17) all_65_0 = all_65_11 | elem(all_65_0, all_65_2) % 142.47/19.44 (18) ~ leq(all_65_9, all_65_15) % 142.47/19.44 (19) all_65_3 = all_65_11 | elem(all_65_3, all_65_2) % 142.47/19.44 (20) host(all_65_8) = all_65_5 % 142.47/19.44 (21) m_Down(all_65_7) = all_65_3 % 142.47/19.44 (22) index(ldr, all_65_9) = all_65_9 % 142.47/19.44 (23) $i(all_65_8) % 142.47/19.44 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) % 142.47/19.44 | ~ (queue(v2) = v0)) % 142.47/19.44 (25) $i(all_65_17) % 142.47/19.44 (26) $i(all_65_16) % 142.47/19.44 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.47/19.44 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) % 142.47/19.44 % 142.47/19.44 Begin of proof % 142.47/19.44 | % 142.47/19.44 | BETA: splitting (19) gives: % 142.47/19.44 | % 142.47/19.44 | Case 1: % 142.47/19.44 | | % 142.47/19.44 | | (28) elem(all_65_3, all_65_2) % 142.47/19.44 | | % 142.47/19.44 | | BETA: splitting (16) gives: % 142.47/19.44 | | % 142.47/19.44 | | Case 1: % 142.47/19.44 | | | % 142.47/19.44 | | | (29) ~ elem(all_65_0, all_128_7) % 142.47/19.44 | | | % 142.47/19.44 | | | REDUCE: (14), (29) imply: % 142.47/19.44 | | | (30) ~ elem(all_65_0, all_65_2) % 142.47/19.44 | | | % 142.47/19.44 | | | BETA: splitting (17) gives: % 142.47/19.44 | | | % 142.47/19.44 | | | Case 1: % 142.47/19.44 | | | | % 142.47/19.44 | | | | (31) elem(all_65_0, all_65_2) % 142.47/19.44 | | | | % 142.47/19.44 | | | | PRED_UNIFY: (30), (31) imply: % 142.47/19.44 | | | | (32) $false % 142.47/19.44 | | | | % 142.47/19.44 | | | | CLOSE: (32) is inconsistent. % 142.47/19.44 | | | | % 142.47/19.44 | | | Case 2: % 142.47/19.44 | | | | % 142.47/19.44 | | | | (33) all_65_0 = all_65_11 % 142.47/19.44 | | | | % 142.47/19.44 | | | | REDUCE: (3), (33) imply: % 142.47/19.44 | | | | (34) m_Ack(all_65_6, all_65_8) = all_65_11 % 142.47/19.44 | | | | % 142.47/19.44 | | | | BETA: splitting (7) gives: % 142.47/19.44 | | | | % 142.47/19.44 | | | | Case 1: % 142.47/19.44 | | | | | % 142.47/19.44 | | | | | (35) ~ (all_96_0 = all_65_12) & host(all_65_7) = all_96_0 & % 142.47/19.44 | | | | | $i(all_96_0) % 142.47/19.44 | | | | | % 142.47/19.44 | | | | | ALPHA: (35) implies: % 142.47/19.44 | | | | | (36) host(all_65_7) = all_96_0 % 142.47/19.44 | | | | | % 142.47/19.44 | | | | | BETA: splitting (1) gives: % 142.47/19.44 | | | | | % 142.47/19.44 | | | | | Case 1: % 142.47/19.44 | | | | | | % 142.47/19.44 | | | | | | (37) ( ~ (all_123_0 = norm) & index(status, all_65_9) = all_123_0 % 142.47/19.44 | | | | | | & $i(all_123_0)) | ( ~ (all_123_1 = all_65_9) & index(ldr, % 142.47/19.44 | | | | | | all_65_9) = all_123_1 & $i(all_123_1)) % 142.47/19.44 | | | | | | % 142.47/19.44 | | | | | | BETA: splitting (37) gives: % 142.47/19.44 | | | | | | % 142.47/19.44 | | | | | | Case 1: % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | (38) ~ (all_123_0 = norm) & index(status, all_65_9) = % 142.47/19.44 | | | | | | | all_123_0 & $i(all_123_0) % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | ALPHA: (38) implies: % 142.47/19.44 | | | | | | | (39) ~ (all_123_0 = norm) % 142.47/19.44 | | | | | | | (40) index(status, all_65_9) = all_123_0 % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | GROUND_INST: instantiating (27) with norm, all_123_0, all_65_9, % 142.47/19.44 | | | | | | | status, simplifying with (11), (40) gives: % 142.47/19.44 | | | | | | | (41) all_123_0 = norm % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | REDUCE: (39), (41) imply: % 142.47/19.44 | | | | | | | (42) $false % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | CLOSE: (42) is inconsistent. % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | Case 2: % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | (43) ~ (all_123_1 = all_65_9) & index(ldr, all_65_9) = % 142.47/19.44 | | | | | | | all_123_1 & $i(all_123_1) % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | ALPHA: (43) implies: % 142.47/19.44 | | | | | | | (44) ~ (all_123_1 = all_65_9) % 142.47/19.44 | | | | | | | (45) index(ldr, all_65_9) = all_123_1 % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | GROUND_INST: instantiating (27) with all_65_9, all_123_1, % 142.47/19.44 | | | | | | | all_65_9, ldr, simplifying with (22), (45) gives: % 142.47/19.44 | | | | | | | (46) all_123_1 = all_65_9 % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | REDUCE: (44), (46) imply: % 142.47/19.44 | | | | | | | (47) $false % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | CLOSE: (47) is inconsistent. % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | End of split % 142.47/19.44 | | | | | | % 142.47/19.44 | | | | | Case 2: % 142.47/19.44 | | | | | | % 142.47/19.44 | | | | | | (48) ( ~ (all_123_2 = all_65_9) & host(all_65_7) = all_123_2 & % 142.47/19.44 | | | | | | $i(all_123_2)) | (queue(all_65_12) = all_123_3 & % 142.47/19.44 | | | | | | $i(all_123_3) & ~ elem(all_65_3, all_123_3)) % 142.47/19.44 | | | | | | % 142.47/19.44 | | | | | | BETA: splitting (48) gives: % 142.47/19.44 | | | | | | % 142.47/19.44 | | | | | | Case 1: % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | (49) ~ (all_123_2 = all_65_9) & host(all_65_7) = all_123_2 & % 142.47/19.44 | | | | | | | $i(all_123_2) % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | ALPHA: (49) implies: % 142.47/19.44 | | | | | | | (50) ~ (all_123_2 = all_65_9) % 142.47/19.44 | | | | | | | (51) host(all_65_7) = all_123_2 % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | GROUND_INST: instantiating (5) with nbr_proc, all_123_2, all_65_7, % 142.47/19.44 | | | | | | | simplifying with (2), (51) gives: % 142.47/19.44 | | | | | | | (52) all_123_2 = nbr_proc % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | GROUND_INST: instantiating (5) with all_96_0, all_123_2, all_65_7, % 142.47/19.44 | | | | | | | simplifying with (36), (51) gives: % 142.47/19.44 | | | | | | | (53) all_123_2 = all_96_0 % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | COMBINE_EQS: (52), (53) imply: % 142.47/19.44 | | | | | | | (54) all_96_0 = nbr_proc % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | REDUCE: (50), (52) imply: % 142.47/19.44 | | | | | | | (55) ~ (all_65_9 = nbr_proc) % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | SIMP: (55) implies: % 142.47/19.44 | | | | | | | (56) ~ (all_65_9 = nbr_proc) % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | BETA: splitting (8) gives: % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | Case 1: % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | | (57) leq(all_65_9, all_65_5) % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | | GROUND_INST: instantiating (15) with all_65_16, all_65_6, % 142.47/19.44 | | | | | | | | all_65_17, all_65_8, all_65_11, simplifying with % 142.47/19.44 | | | | | | | | (4), (9), (23), (25), (26), (34) gives: % 142.47/19.44 | | | | | | | | (58) all_65_8 = all_65_17 % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | | REDUCE: (20), (58) imply: % 142.47/19.44 | | | | | | | | (59) host(all_65_17) = all_65_5 % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | | GROUND_INST: instantiating (5) with all_65_15, all_65_5, % 142.47/19.44 | | | | | | | | all_65_17, simplifying with (13), (59) gives: % 142.47/19.44 | | | | | | | | (60) all_65_5 = all_65_15 % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | | REDUCE: (57), (60) imply: % 142.47/19.44 | | | | | | | | (61) leq(all_65_9, all_65_15) % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | | PRED_UNIFY: (18), (61) imply: % 142.47/19.44 | | | | | | | | (62) $false % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | | CLOSE: (62) is inconsistent. % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | Case 2: % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | | (63) all_65_9 = nbr_proc % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | | REDUCE: (56), (63) imply: % 142.47/19.44 | | | | | | | | (64) $false % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | | CLOSE: (64) is inconsistent. % 142.47/19.44 | | | | | | | | % 142.47/19.44 | | | | | | | End of split % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | Case 2: % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | (65) queue(all_65_12) = all_123_3 & $i(all_123_3) & ~ % 142.47/19.44 | | | | | | | elem(all_65_3, all_123_3) % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | ALPHA: (65) implies: % 142.47/19.44 | | | | | | | (66) ~ elem(all_65_3, all_123_3) % 142.47/19.44 | | | | | | | (67) queue(all_65_12) = all_123_3 % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | GROUND_INST: instantiating (24) with all_65_2, all_123_3, % 142.47/19.44 | | | | | | | all_65_12, simplifying with (10), (67) gives: % 142.47/19.44 | | | | | | | (68) all_123_3 = all_65_2 % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | REDUCE: (66), (68) imply: % 142.47/19.44 | | | | | | | (69) ~ elem(all_65_3, all_65_2) % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | PRED_UNIFY: (28), (69) imply: % 142.47/19.44 | | | | | | | (70) $false % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | | CLOSE: (70) is inconsistent. % 142.47/19.44 | | | | | | | % 142.47/19.44 | | | | | | End of split % 142.47/19.44 | | | | | | % 142.47/19.44 | | | | | End of split % 142.47/19.44 | | | | | % 142.47/19.44 | | | | Case 2: % 142.47/19.44 | | | | | % 142.47/19.44 | | | | | (71) queue(all_65_12) = all_96_1 & $i(all_96_1) & ~ elem(all_65_3, % 142.47/19.44 | | | | | all_96_1) % 142.47/19.44 | | | | | % 142.47/19.44 | | | | | ALPHA: (71) implies: % 142.47/19.44 | | | | | (72) ~ elem(all_65_3, all_96_1) % 142.47/19.44 | | | | | (73) queue(all_65_12) = all_96_1 % 142.47/19.44 | | | | | % 142.47/19.44 | | | | | GROUND_INST: instantiating (24) with all_65_2, all_96_1, all_65_12, % 142.47/19.44 | | | | | simplifying with (10), (73) gives: % 142.47/19.44 | | | | | (74) all_96_1 = all_65_2 % 142.47/19.44 | | | | | % 142.47/19.44 | | | | | REDUCE: (72), (74) imply: % 142.47/19.44 | | | | | (75) ~ elem(all_65_3, all_65_2) % 142.47/19.44 | | | | | % 142.47/19.44 | | | | | PRED_UNIFY: (28), (75) imply: % 142.47/19.44 | | | | | (76) $false % 142.47/19.44 | | | | | % 142.47/19.44 | | | | | CLOSE: (76) is inconsistent. % 142.47/19.44 | | | | | % 142.47/19.44 | | | | End of split % 142.47/19.44 | | | | % 142.47/19.44 | | | End of split % 142.47/19.44 | | | % 142.47/19.44 | | Case 2: % 142.47/19.44 | | | % 142.47/19.44 | | | (77) ~ elem(all_65_3, all_128_7) % 142.47/19.44 | | | % 142.47/19.44 | | | REDUCE: (14), (77) imply: % 142.47/19.44 | | | (78) ~ elem(all_65_3, all_65_2) % 142.47/19.44 | | | % 142.47/19.44 | | | PRED_UNIFY: (28), (78) imply: % 142.47/19.44 | | | (79) $false % 142.47/19.44 | | | % 142.47/19.44 | | | CLOSE: (79) is inconsistent. % 142.47/19.44 | | | % 142.47/19.44 | | End of split % 142.47/19.44 | | % 142.47/19.44 | Case 2: % 142.47/19.44 | | % 142.47/19.44 | | (80) all_65_3 = all_65_11 % 142.47/19.44 | | % 142.47/19.44 | | REDUCE: (21), (80) imply: % 142.47/19.44 | | (81) m_Down(all_65_7) = all_65_11 % 142.47/19.44 | | % 142.47/19.44 | | GROUND_INST: instantiating (12) with all_65_16, all_65_17, all_65_7, % 142.47/19.44 | | all_65_11, simplifying with (4), (6), (25), (26), (81) gives: % 142.47/19.44 | | (82) $false % 142.47/19.44 | | % 142.47/19.44 | | CLOSE: (82) is inconsistent. % 142.47/19.44 | | % 142.47/19.44 | End of split % 142.47/19.44 | % 142.47/19.44 End of proof % 142.47/19.44 % 142.47/19.44 Sub-proof #3 shows that the following formulas are inconsistent: % 142.47/19.44 ---------------------------------------------------------------- % 142.47/19.44 (1) m_Ack(all_65_6, all_65_8) = all_65_11 % 142.47/19.44 (2) index(status, all_65_12) = elec_2 % 142.47/19.44 (3) m_Halt(all_65_16) = all_65_13 % 142.47/19.44 (4) setIn(all_65_10, alive) % 142.47/19.44 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 % 142.47/19.44 = v0 | ~ (m_Ack(v1, v3) = v4) | ~ (m_Ack(v0, v2) = v4) | ~ $i(v3) | % 142.47/19.44 ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 142.47/19.44 (6) index(pendack, all_65_12) = all_65_5 % 142.47/19.44 (7) m_Ack(all_65_16, all_65_17) = all_65_11 % 142.47/19.44 (8) host(all_65_6) = all_65_12 % 142.47/19.44 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1) | % 142.47/19.44 ~ (host(v2) = v0)) % 142.47/19.45 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 142.47/19.45 [v5: $i] : ( ~ (m_Halt(v2) = v4) | ~ (host(v1) = v5) | ~ (host(v0) = % 142.47/19.45 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ % 142.47/19.45 setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 142.47/19.45 $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v11 = norm) & % 142.47/19.45 index(status, v3) = v11 & $i(v11)) | ( ~ (v10 = v3) & index(ldr, % 142.47/19.45 v3) = v10 & $i(v10)) | ( ~ (v9 = elec_2) & index(status, v6) = % 142.47/19.45 v9 & host(v2) = v6 & $i(v9) & $i(v6)) | (index(pendack, v6) = v7 & % 142.47/19.45 host(v2) = v6 & $i(v7) & $i(v6) & leq(v7, v3)) | (queue(v5) = v8 & % 142.47/19.45 $i(v8) & ~ elem(v4, v8)))) % 142.47/19.45 (11) setIn(all_65_6, alive) % 142.47/19.45 (12) $i(all_65_6) % 142.47/19.45 (13) queue(all_65_15) = all_65_14 % 142.47/19.45 (14) index(status, all_65_9) = norm % 142.47/19.45 (15) ( ~ (all_254_2 = elec_2) & index(status, all_65_12) = all_254_2 & % 142.47/19.45 $i(all_254_2)) | ( ~ (all_254_3 = elec_2) & index(status, all_65_9) = % 142.47/19.45 all_254_3 & $i(all_254_3)) | (index(pendack, all_65_9) = all_254_1 & % 142.47/19.45 index(pendack, all_65_12) = all_254_0 & $i(all_254_0) & $i(all_254_1) % 142.47/19.45 & ~ leq(all_254_1, all_254_0)) % 142.47/19.45 (16) host(all_65_17) = all_65_15 % 142.47/19.45 (17) $i(all_65_10) % 142.47/19.45 (18) host(all_65_10) = all_65_9 % 142.47/19.45 (19) ~ leq(all_65_15, all_65_9) % 142.47/19.45 (20) host(all_65_8) = all_65_5 % 142.47/19.45 (21) index(ldr, all_65_9) = all_65_9 % 142.47/19.45 (22) $i(all_65_8) % 142.47/19.45 (23) elem(all_65_13, all_65_14) % 142.47/19.45 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) % 142.47/19.45 | ~ (queue(v2) = v0)) % 142.47/19.45 (25) $i(all_65_17) % 142.47/19.45 (26) $i(all_65_16) % 142.47/19.45 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 142.47/19.45 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) % 142.47/19.45 (28) all_65_8 = all_65_17 % 142.47/19.45 % 142.47/19.45 Begin of proof % 142.47/19.45 | % 142.47/19.45 | GROUND_INST: instantiating (5) with all_65_16, all_65_6, all_65_17, all_65_8, % 142.47/19.45 | all_65_11, simplifying with (1), (7), (12), (22), (25), (26) % 142.47/19.45 | gives: % 142.47/19.45 | (29) all_65_6 = all_65_16 % 142.47/19.45 | % 142.47/19.45 | REDUCE: (8), (29) imply: % 142.47/19.45 | (30) host(all_65_16) = all_65_12 % 142.47/19.45 | % 142.47/19.45 | REDUCE: (20), (28) imply: % 142.47/19.45 | (31) host(all_65_17) = all_65_5 % 142.47/19.45 | % 142.47/19.45 | REDUCE: (11), (29) imply: % 142.47/19.45 | (32) setIn(all_65_16, alive) % 142.47/19.45 | % 142.47/19.45 | GROUND_INST: instantiating (9) with all_65_15, all_65_5, all_65_17, % 142.47/19.45 | simplifying with (16), (31) gives: % 142.47/19.45 | (33) all_65_5 = all_65_15 % 142.47/19.45 | % 142.47/19.45 | REDUCE: (6), (33) imply: % 142.47/19.45 | (34) index(pendack, all_65_12) = all_65_15 % 142.47/19.45 | % 142.47/19.45 | BETA: splitting (15) gives: % 142.47/19.45 | % 142.47/19.45 | Case 1: % 142.47/19.45 | | % 142.47/19.45 | | (35) ~ (all_254_2 = elec_2) & index(status, all_65_12) = all_254_2 & % 142.47/19.45 | | $i(all_254_2) % 142.47/19.45 | | % 142.47/19.45 | | ALPHA: (35) implies: % 142.47/19.45 | | (36) ~ (all_254_2 = elec_2) % 142.47/19.45 | | (37) index(status, all_65_12) = all_254_2 % 142.47/19.45 | | % 142.47/19.45 | | GROUND_INST: instantiating (27) with elec_2, all_254_2, all_65_12, status, % 142.47/19.45 | | simplifying with (2), (37) gives: % 142.47/19.45 | | (38) all_254_2 = elec_2 % 142.47/19.45 | | % 142.47/19.45 | | REDUCE: (36), (38) imply: % 142.47/19.45 | | (39) $false % 142.47/19.45 | | % 142.47/19.45 | | CLOSE: (39) is inconsistent. % 142.47/19.45 | | % 142.47/19.45 | Case 2: % 142.47/19.45 | | % 142.47/19.45 | | (40) ( ~ (all_254_3 = elec_2) & index(status, all_65_9) = all_254_3 & % 142.47/19.45 | | $i(all_254_3)) | (index(pendack, all_65_9) = all_254_1 & % 142.47/19.45 | | index(pendack, all_65_12) = all_254_0 & $i(all_254_0) & % 142.47/19.45 | | $i(all_254_1) & ~ leq(all_254_1, all_254_0)) % 142.47/19.45 | | % 142.47/19.45 | | BETA: splitting (40) gives: % 142.47/19.45 | | % 142.47/19.45 | | Case 1: % 142.47/19.45 | | | % 142.47/19.45 | | | (41) ~ (all_254_3 = elec_2) & index(status, all_65_9) = all_254_3 & % 142.47/19.45 | | | $i(all_254_3) % 142.47/19.45 | | | % 142.47/19.45 | | | ALPHA: (41) implies: % 142.47/19.45 | | | (42) index(status, all_65_9) = all_254_3 % 142.47/19.45 | | | % 142.47/19.45 | | | GROUND_INST: instantiating (27) with norm, all_254_3, all_65_9, status, % 142.47/19.45 | | | simplifying with (14), (42) gives: % 142.47/19.45 | | | (43) all_254_3 = norm % 142.47/19.45 | | | % 142.47/19.45 | | | GROUND_INST: instantiating (10) with all_65_10, all_65_17, all_65_16, % 142.47/19.45 | | | all_65_9, all_65_13, all_65_15, simplifying with (3), (4), % 142.47/19.45 | | | (16), (17), (18), (25), (26), (32) gives: % 142.47/19.45 | | | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 142.47/19.45 | | | any] : ? [v5: $i] : (( ~ (v5 = norm) & index(status, all_65_9) % 142.47/19.45 | | | = v5 & $i(v5)) | ( ~ (v4 = all_65_9) & index(ldr, all_65_9) = % 142.47/19.45 | | | v4 & $i(v4)) | ( ~ (v3 = elec_2) & index(status, v0) = v3 & % 142.47/19.45 | | | host(all_65_16) = v0 & $i(v3) & $i(v0)) | (index(pendack, v0) % 142.47/19.45 | | | = v1 & host(all_65_16) = v0 & $i(v1) & $i(v0) & leq(v1, % 142.47/19.45 | | | all_65_9)) | (queue(all_65_15) = v2 & $i(v2) & ~ % 142.47/19.45 | | | elem(all_65_13, v2))) % 142.47/19.45 | | | % 142.47/19.45 | | | DELTA: instantiating (44) with fresh symbols all_801_0, all_801_1, % 142.47/19.45 | | | all_801_2, all_801_3, all_801_4, all_801_5 gives: % 142.47/19.45 | | | (45) ( ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 & % 142.47/19.45 | | | $i(all_801_0)) | ( ~ (all_801_1 = all_65_9) & index(ldr, % 142.47/19.45 | | | all_65_9) = all_801_1 & $i(all_801_1)) | ( ~ (all_801_2 = % 142.47/19.45 | | | elec_2) & index(status, all_801_5) = all_801_2 & % 142.47/19.45 | | | host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5)) | % 142.47/19.45 | | | (index(pendack, all_801_5) = all_801_4 & host(all_65_16) = % 142.47/19.45 | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4, % 142.47/19.45 | | | all_65_9)) | (queue(all_65_15) = all_801_3 & $i(all_801_3) & % 142.47/19.45 | | | ~ elem(all_65_13, all_801_3)) % 142.47/19.45 | | | % 142.47/19.45 | | | BETA: splitting (45) gives: % 142.47/19.45 | | | % 142.47/19.45 | | | Case 1: % 142.47/19.45 | | | | % 142.47/19.45 | | | | (46) ( ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 & % 142.47/19.45 | | | | $i(all_801_0)) | ( ~ (all_801_1 = all_65_9) & index(ldr, % 142.47/19.45 | | | | all_65_9) = all_801_1 & $i(all_801_1)) % 142.47/19.45 | | | | % 142.47/19.45 | | | | BETA: splitting (46) gives: % 142.47/19.45 | | | | % 142.47/19.45 | | | | Case 1: % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | (47) ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 & % 142.47/19.45 | | | | | $i(all_801_0) % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | ALPHA: (47) implies: % 142.47/19.45 | | | | | (48) ~ (all_801_0 = norm) % 142.47/19.45 | | | | | (49) index(status, all_65_9) = all_801_0 % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | GROUND_INST: instantiating (27) with norm, all_801_0, all_65_9, % 142.47/19.45 | | | | | status, simplifying with (14), (49) gives: % 142.47/19.45 | | | | | (50) all_801_0 = norm % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | REDUCE: (48), (50) imply: % 142.47/19.45 | | | | | (51) $false % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | CLOSE: (51) is inconsistent. % 142.47/19.45 | | | | | % 142.47/19.45 | | | | Case 2: % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | (52) ~ (all_801_1 = all_65_9) & index(ldr, all_65_9) = all_801_1 & % 142.47/19.45 | | | | | $i(all_801_1) % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | ALPHA: (52) implies: % 142.47/19.45 | | | | | (53) ~ (all_801_1 = all_65_9) % 142.47/19.45 | | | | | (54) index(ldr, all_65_9) = all_801_1 % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | GROUND_INST: instantiating (27) with all_65_9, all_801_1, all_65_9, % 142.47/19.45 | | | | | ldr, simplifying with (21), (54) gives: % 142.47/19.45 | | | | | (55) all_801_1 = all_65_9 % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | REDUCE: (53), (55) imply: % 142.47/19.45 | | | | | (56) $false % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | CLOSE: (56) is inconsistent. % 142.47/19.45 | | | | | % 142.47/19.45 | | | | End of split % 142.47/19.45 | | | | % 142.47/19.45 | | | Case 2: % 142.47/19.45 | | | | % 142.47/19.45 | | | | (57) ( ~ (all_801_2 = elec_2) & index(status, all_801_5) = all_801_2 % 142.47/19.45 | | | | & host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5)) % 142.47/19.45 | | | | | (index(pendack, all_801_5) = all_801_4 & host(all_65_16) = % 142.47/19.45 | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4, % 142.47/19.45 | | | | all_65_9)) | (queue(all_65_15) = all_801_3 & $i(all_801_3) & % 142.47/19.45 | | | | ~ elem(all_65_13, all_801_3)) % 142.47/19.45 | | | | % 142.47/19.45 | | | | BETA: splitting (57) gives: % 142.47/19.45 | | | | % 142.47/19.45 | | | | Case 1: % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | (58) ~ (all_801_2 = elec_2) & index(status, all_801_5) = all_801_2 % 142.47/19.45 | | | | | & host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5) % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | ALPHA: (58) implies: % 142.47/19.45 | | | | | (59) ~ (all_801_2 = elec_2) % 142.47/19.45 | | | | | (60) host(all_65_16) = all_801_5 % 142.47/19.45 | | | | | (61) index(status, all_801_5) = all_801_2 % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | GROUND_INST: instantiating (9) with all_65_12, all_801_5, all_65_16, % 142.47/19.45 | | | | | simplifying with (30), (60) gives: % 142.47/19.45 | | | | | (62) all_801_5 = all_65_12 % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | REDUCE: (61), (62) imply: % 142.47/19.45 | | | | | (63) index(status, all_65_12) = all_801_2 % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | GROUND_INST: instantiating (27) with elec_2, all_801_2, all_65_12, % 142.47/19.45 | | | | | status, simplifying with (2), (63) gives: % 142.47/19.45 | | | | | (64) all_801_2 = elec_2 % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | REDUCE: (59), (64) imply: % 142.47/19.45 | | | | | (65) $false % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | CLOSE: (65) is inconsistent. % 142.47/19.45 | | | | | % 142.47/19.45 | | | | Case 2: % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | (66) (index(pendack, all_801_5) = all_801_4 & host(all_65_16) = % 142.47/19.45 | | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4, % 142.47/19.45 | | | | | all_65_9)) | (queue(all_65_15) = all_801_3 & $i(all_801_3) % 142.47/19.45 | | | | | & ~ elem(all_65_13, all_801_3)) % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | BETA: splitting (66) gives: % 142.47/19.45 | | | | | % 142.47/19.45 | | | | | Case 1: % 142.47/19.45 | | | | | | % 142.47/19.45 | | | | | | (67) index(pendack, all_801_5) = all_801_4 & host(all_65_16) = % 142.47/19.45 | | | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4, % 142.47/19.45 | | | | | | all_65_9) % 142.47/19.45 | | | | | | % 142.47/19.45 | | | | | | ALPHA: (67) implies: % 142.47/19.45 | | | | | | (68) leq(all_801_4, all_65_9) % 142.47/19.45 | | | | | | (69) host(all_65_16) = all_801_5 % 142.47/19.45 | | | | | | (70) index(pendack, all_801_5) = all_801_4 % 142.47/19.45 | | | | | | % 142.47/19.45 | | | | | | GROUND_INST: instantiating (9) with all_65_12, all_801_5, all_65_16, % 142.47/19.45 | | | | | | simplifying with (30), (69) gives: % 142.47/19.45 | | | | | | (71) all_801_5 = all_65_12 % 142.47/19.45 | | | | | | % 142.47/19.45 | | | | | | REDUCE: (70), (71) imply: % 142.47/19.45 | | | | | | (72) index(pendack, all_65_12) = all_801_4 % 142.47/19.45 | | | | | | % 142.47/19.45 | | | | | | GROUND_INST: instantiating (27) with all_65_15, all_801_4, % 142.47/19.45 | | | | | | all_65_12, pendack, simplifying with (34), (72) gives: % 142.47/19.45 | | | | | | (73) all_801_4 = all_65_15 % 142.47/19.45 | | | | | | % 142.47/19.45 | | | | | | REDUCE: (68), (73) imply: % 142.47/19.45 | | | | | | (74) leq(all_65_15, all_65_9) % 142.47/19.45 | | | | | | % 142.47/19.45 | | | | | | PRED_UNIFY: (19), (74) imply: % 142.47/19.45 | | | | | | (75) $false % 142.47/19.45 | | | | | | % 142.47/19.45 | | | | | | CLOSE: (75) is inconsistent. % 142.47/19.45 | | | | | | % 142.47/19.45 | | | | | Case 2: % 142.47/19.45 | | | | | | % 142.47/19.46 | | | | | | (76) queue(all_65_15) = all_801_3 & $i(all_801_3) & ~ % 142.47/19.46 | | | | | | elem(all_65_13, all_801_3) % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | ALPHA: (76) implies: % 142.47/19.46 | | | | | | (77) ~ elem(all_65_13, all_801_3) % 142.47/19.46 | | | | | | (78) queue(all_65_15) = all_801_3 % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | GROUND_INST: instantiating (24) with all_65_14, all_801_3, % 142.47/19.46 | | | | | | all_65_15, simplifying with (13), (78) gives: % 142.47/19.46 | | | | | | (79) all_801_3 = all_65_14 % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | REDUCE: (77), (79) imply: % 142.47/19.46 | | | | | | (80) ~ elem(all_65_13, all_65_14) % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | PRED_UNIFY: (23), (80) imply: % 142.47/19.46 | | | | | | (81) $false % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | CLOSE: (81) is inconsistent. % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | End of split % 142.47/19.46 | | | | | % 142.47/19.46 | | | | End of split % 142.47/19.46 | | | | % 142.47/19.46 | | | End of split % 142.47/19.46 | | | % 142.47/19.46 | | Case 2: % 142.47/19.46 | | | % 142.47/19.46 | | | (82) index(pendack, all_65_9) = all_254_1 & index(pendack, all_65_12) = % 142.47/19.46 | | | all_254_0 & $i(all_254_0) & $i(all_254_1) & ~ leq(all_254_1, % 142.47/19.46 | | | all_254_0) % 142.47/19.46 | | | % 142.47/19.46 | | | ALPHA: (82) implies: % 142.47/19.46 | | | (83) index(pendack, all_65_12) = all_254_0 % 142.47/19.46 | | | % 142.47/19.46 | | | GROUND_INST: instantiating (27) with all_65_15, all_254_0, all_65_12, % 142.47/19.46 | | | pendack, simplifying with (34), (83) gives: % 142.47/19.46 | | | (84) all_254_0 = all_65_15 % 142.47/19.46 | | | % 142.47/19.46 | | | GROUND_INST: instantiating (10) with all_65_10, all_65_17, all_65_16, % 142.47/19.46 | | | all_65_9, all_65_13, all_65_15, simplifying with (3), (4), % 142.47/19.46 | | | (16), (17), (18), (25), (26), (32) gives: % 142.47/19.46 | | | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 142.47/19.46 | | | any] : ? [v5: $i] : (( ~ (v5 = norm) & index(status, all_65_9) % 142.47/19.46 | | | = v5 & $i(v5)) | ( ~ (v4 = all_65_9) & index(ldr, all_65_9) = % 142.47/19.46 | | | v4 & $i(v4)) | ( ~ (v3 = elec_2) & index(status, v0) = v3 & % 142.47/19.46 | | | host(all_65_16) = v0 & $i(v3) & $i(v0)) | (index(pendack, v0) % 142.47/19.46 | | | = v1 & host(all_65_16) = v0 & $i(v1) & $i(v0) & leq(v1, % 142.47/19.46 | | | all_65_9)) | (queue(all_65_15) = v2 & $i(v2) & ~ % 142.47/19.46 | | | elem(all_65_13, v2))) % 142.47/19.46 | | | % 142.47/19.46 | | | DELTA: instantiating (85) with fresh symbols all_801_0, all_801_1, % 142.47/19.46 | | | all_801_2, all_801_3, all_801_4, all_801_5 gives: % 142.47/19.46 | | | (86) ( ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 & % 142.47/19.46 | | | $i(all_801_0)) | ( ~ (all_801_1 = all_65_9) & index(ldr, % 142.47/19.46 | | | all_65_9) = all_801_1 & $i(all_801_1)) | ( ~ (all_801_2 = % 142.47/19.46 | | | elec_2) & index(status, all_801_5) = all_801_2 & % 142.47/19.46 | | | host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5)) | % 142.47/19.46 | | | (index(pendack, all_801_5) = all_801_4 & host(all_65_16) = % 142.47/19.46 | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4, % 142.47/19.46 | | | all_65_9)) | (queue(all_65_15) = all_801_3 & $i(all_801_3) & % 142.47/19.46 | | | ~ elem(all_65_13, all_801_3)) % 142.47/19.46 | | | % 142.47/19.46 | | | BETA: splitting (86) gives: % 142.47/19.46 | | | % 142.47/19.46 | | | Case 1: % 142.47/19.46 | | | | % 142.47/19.46 | | | | (87) ( ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 & % 142.47/19.46 | | | | $i(all_801_0)) | ( ~ (all_801_1 = all_65_9) & index(ldr, % 142.47/19.46 | | | | all_65_9) = all_801_1 & $i(all_801_1)) % 142.47/19.46 | | | | % 142.47/19.46 | | | | BETA: splitting (87) gives: % 142.47/19.46 | | | | % 142.47/19.46 | | | | Case 1: % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | (88) ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 & % 142.47/19.46 | | | | | $i(all_801_0) % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | ALPHA: (88) implies: % 142.47/19.46 | | | | | (89) ~ (all_801_0 = norm) % 142.47/19.46 | | | | | (90) index(status, all_65_9) = all_801_0 % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | GROUND_INST: instantiating (27) with norm, all_801_0, all_65_9, % 142.47/19.46 | | | | | status, simplifying with (14), (90) gives: % 142.47/19.46 | | | | | (91) all_801_0 = norm % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | REDUCE: (89), (91) imply: % 142.47/19.46 | | | | | (92) $false % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | CLOSE: (92) is inconsistent. % 142.47/19.46 | | | | | % 142.47/19.46 | | | | Case 2: % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | (93) ~ (all_801_1 = all_65_9) & index(ldr, all_65_9) = all_801_1 & % 142.47/19.46 | | | | | $i(all_801_1) % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | ALPHA: (93) implies: % 142.47/19.46 | | | | | (94) ~ (all_801_1 = all_65_9) % 142.47/19.46 | | | | | (95) index(ldr, all_65_9) = all_801_1 % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | GROUND_INST: instantiating (27) with all_65_9, all_801_1, all_65_9, % 142.47/19.46 | | | | | ldr, simplifying with (21), (95) gives: % 142.47/19.46 | | | | | (96) all_801_1 = all_65_9 % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | REDUCE: (94), (96) imply: % 142.47/19.46 | | | | | (97) $false % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | CLOSE: (97) is inconsistent. % 142.47/19.46 | | | | | % 142.47/19.46 | | | | End of split % 142.47/19.46 | | | | % 142.47/19.46 | | | Case 2: % 142.47/19.46 | | | | % 142.47/19.46 | | | | (98) ( ~ (all_801_2 = elec_2) & index(status, all_801_5) = all_801_2 % 142.47/19.46 | | | | & host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5)) % 142.47/19.46 | | | | | (index(pendack, all_801_5) = all_801_4 & host(all_65_16) = % 142.47/19.46 | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4, % 142.47/19.46 | | | | all_65_9)) | (queue(all_65_15) = all_801_3 & $i(all_801_3) & % 142.47/19.46 | | | | ~ elem(all_65_13, all_801_3)) % 142.47/19.46 | | | | % 142.47/19.46 | | | | BETA: splitting (98) gives: % 142.47/19.46 | | | | % 142.47/19.46 | | | | Case 1: % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | (99) ~ (all_801_2 = elec_2) & index(status, all_801_5) = all_801_2 % 142.47/19.46 | | | | | & host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5) % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | ALPHA: (99) implies: % 142.47/19.46 | | | | | (100) ~ (all_801_2 = elec_2) % 142.47/19.46 | | | | | (101) host(all_65_16) = all_801_5 % 142.47/19.46 | | | | | (102) index(status, all_801_5) = all_801_2 % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | GROUND_INST: instantiating (9) with all_65_12, all_801_5, all_65_16, % 142.47/19.46 | | | | | simplifying with (30), (101) gives: % 142.47/19.46 | | | | | (103) all_801_5 = all_65_12 % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | REDUCE: (102), (103) imply: % 142.47/19.46 | | | | | (104) index(status, all_65_12) = all_801_2 % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | GROUND_INST: instantiating (27) with elec_2, all_801_2, all_65_12, % 142.47/19.46 | | | | | status, simplifying with (2), (104) gives: % 142.47/19.46 | | | | | (105) all_801_2 = elec_2 % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | REDUCE: (100), (105) imply: % 142.47/19.46 | | | | | (106) $false % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | CLOSE: (106) is inconsistent. % 142.47/19.46 | | | | | % 142.47/19.46 | | | | Case 2: % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | (107) (index(pendack, all_801_5) = all_801_4 & host(all_65_16) = % 142.47/19.46 | | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4, % 142.47/19.46 | | | | | all_65_9)) | (queue(all_65_15) = all_801_3 & % 142.47/19.46 | | | | | $i(all_801_3) & ~ elem(all_65_13, all_801_3)) % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | BETA: splitting (107) gives: % 142.47/19.46 | | | | | % 142.47/19.46 | | | | | Case 1: % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | (108) index(pendack, all_801_5) = all_801_4 & host(all_65_16) = % 142.47/19.46 | | | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4, % 142.47/19.46 | | | | | | all_65_9) % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | ALPHA: (108) implies: % 142.47/19.46 | | | | | | (109) leq(all_801_4, all_65_9) % 142.47/19.46 | | | | | | (110) host(all_65_16) = all_801_5 % 142.47/19.46 | | | | | | (111) index(pendack, all_801_5) = all_801_4 % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | GROUND_INST: instantiating (9) with all_65_12, all_801_5, all_65_16, % 142.47/19.46 | | | | | | simplifying with (30), (110) gives: % 142.47/19.46 | | | | | | (112) all_801_5 = all_65_12 % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | REDUCE: (111), (112) imply: % 142.47/19.46 | | | | | | (113) index(pendack, all_65_12) = all_801_4 % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | GROUND_INST: instantiating (27) with all_65_15, all_801_4, % 142.47/19.46 | | | | | | all_65_12, pendack, simplifying with (34), (113) gives: % 142.47/19.46 | | | | | | (114) all_801_4 = all_65_15 % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | REDUCE: (109), (114) imply: % 142.47/19.46 | | | | | | (115) leq(all_65_15, all_65_9) % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | PRED_UNIFY: (19), (115) imply: % 142.47/19.46 | | | | | | (116) $false % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | CLOSE: (116) is inconsistent. % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | Case 2: % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | (117) queue(all_65_15) = all_801_3 & $i(all_801_3) & ~ % 142.47/19.46 | | | | | | elem(all_65_13, all_801_3) % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | ALPHA: (117) implies: % 142.47/19.46 | | | | | | (118) ~ elem(all_65_13, all_801_3) % 142.47/19.46 | | | | | | (119) queue(all_65_15) = all_801_3 % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | GROUND_INST: instantiating (24) with all_65_14, all_801_3, % 142.47/19.46 | | | | | | all_65_15, simplifying with (13), (119) gives: % 142.47/19.46 | | | | | | (120) all_801_3 = all_65_14 % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | REDUCE: (118), (120) imply: % 142.47/19.46 | | | | | | (121) ~ elem(all_65_13, all_65_14) % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | PRED_UNIFY: (23), (121) imply: % 142.47/19.46 | | | | | | (122) $false % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | | CLOSE: (122) is inconsistent. % 142.47/19.46 | | | | | | % 142.47/19.46 | | | | | End of split % 142.47/19.46 | | | | | % 142.47/19.46 | | | | End of split % 142.47/19.46 | | | | % 142.47/19.46 | | | End of split % 142.47/19.46 | | | % 142.47/19.46 | | End of split % 142.47/19.46 | | % 142.47/19.46 | End of split % 142.47/19.46 | % 142.47/19.46 End of proof % 142.47/19.46 % 142.47/19.46 Sub-proof #4 shows that the following formulas are inconsistent: % 142.47/19.46 ---------------------------------------------------------------- % 142.47/19.46 (1) $i(all_65_15) % 142.47/19.46 (2) $i(all_65_9) % 142.47/19.46 (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, % 142.47/19.46 v0) | ~ leq(v0, v1)) % 142.47/19.46 (4) ~ (all_65_9 = all_65_15) % 142.47/19.46 (5) leq(all_65_9, all_65_15) % 142.47/19.46 (6) leq(all_65_15, all_65_9) % 142.47/19.46 % 142.47/19.46 Begin of proof % 142.47/19.46 | % 142.47/19.46 | GROUND_INST: instantiating (3) with all_65_15, all_65_9, simplifying with (1), % 142.47/19.46 | (2), (5), (6) gives: % 142.47/19.46 | (7) all_65_9 = all_65_15 % 142.47/19.46 | % 142.47/19.46 | REDUCE: (4), (7) imply: % 142.47/19.46 | (8) $false % 142.47/19.46 | % 142.47/19.46 | CLOSE: (8) is inconsistent. % 142.47/19.46 | % 142.47/19.46 End of proof % 142.47/19.46 % SZS output end Proof for theBenchmark % 142.47/19.46 % 142.47/19.46 18852ms %------------------------------------------------------------------------------