%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV448+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 : n028.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 22:56:31 EDT 2023 % Result : Theorem 74.56s 10.50s % Output : Proof 75.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV448+1 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Aug 29 10:08:55 EDT 2023 % 0.13/0.33 % CPUTime : % 0.18/0.60 ________ _____ % 0.18/0.60 ___ __ \_________(_)________________________________ % 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.60 % 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.60 (2023-06-19) % 0.18/0.60 % 0.18/0.60 (c) Philipp Rümmer, 2009-2023 % 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.60 Amanda Stjerna. % 0.18/0.60 Free software under BSD-3-Clause. % 0.18/0.60 % 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.60 % 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.61 Running up to 7 provers in parallel. % 0.51/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.51/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.51/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.51/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.51/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.51/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.51/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.59/1.23 Prover 1: Preprocessing ... % 3.59/1.25 Prover 4: Preprocessing ... % 4.21/1.29 Prover 3: Preprocessing ... % 4.21/1.29 Prover 6: Preprocessing ... % 4.21/1.30 Prover 2: Preprocessing ... % 4.21/1.30 Prover 0: Preprocessing ... % 4.21/1.30 Prover 5: Preprocessing ... % 10.67/2.16 Prover 1: Constructing countermodel ... % 10.67/2.20 Prover 3: Constructing countermodel ... % 11.52/2.26 Prover 6: Proving ... % 11.52/2.28 Prover 5: Proving ... % 12.50/2.42 Prover 2: Proving ... % 14.50/2.72 Prover 4: Constructing countermodel ... % 15.29/2.81 Prover 3: gave up % 15.29/2.83 Prover 0: Proving ... % 15.29/2.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.18/2.88 Prover 7: Preprocessing ... % 19.64/3.38 Prover 7: Warning: ignoring some quantifiers % 20.03/3.41 Prover 7: Constructing countermodel ... % 23.45/3.88 Prover 1: gave up % 23.83/3.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 24.34/3.95 Prover 8: Preprocessing ... % 25.14/4.12 Prover 8: Warning: ignoring some quantifiers % 25.14/4.13 Prover 8: Constructing countermodel ... % 30.22/4.73 Prover 8: gave up % 30.22/4.74 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 30.87/4.83 Prover 9: Preprocessing ... % 33.87/5.21 Prover 9: Constructing countermodel ... % 59.04/8.48 Prover 2: stopped % 59.04/8.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 59.87/8.58 Prover 10: Preprocessing ... % 59.87/8.74 Prover 10: Warning: ignoring some quantifiers % 60.55/8.75 Prover 10: Constructing countermodel ... % 74.56/10.49 Prover 10: Found proof (size 97) % 74.56/10.49 Prover 10: proved (1996ms) % 74.56/10.50 Prover 5: stopped % 74.56/10.50 Prover 6: stopped % 74.56/10.50 Prover 9: stopped % 74.56/10.50 Prover 0: stopped % 74.56/10.50 Prover 7: stopped % 74.56/10.50 Prover 4: stopped % 74.56/10.50 % 74.56/10.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 74.56/10.50 % 74.56/10.51 % SZS output start Proof for theBenchmark % 74.56/10.52 Assumptions after simplification: % 74.56/10.52 --------------------------------- % 74.56/10.52 % 74.56/10.52 (axiom_03) % 74.56/10.54 $i(nbr_proc) & $i(zero) & ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0, % 74.56/10.54 nbr_proc)) % 74.56/10.54 % 74.56/10.54 (axiom_04) % 74.56/10.54 $i(nbr_proc) & ! [v0: $i] : ! [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) | % 74.56/10.54 leq(v1, nbr_proc)) % 74.56/10.54 % 74.56/10.54 (axiom_17) % 74.56/10.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~ % 74.56/10.55 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 74.56/10.55 % 74.56/10.55 (axiom_30) % 74.56/10.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v1) = v2) | ~ % 74.56/10.55 (m_Down(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 74.56/10.55 % 74.56/10.55 (axiom_46) % 74.56/10.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.56/10.55 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) | % 74.56/10.55 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 74.56/10.55 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 74.56/10.55 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) % 74.56/10.55 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2)) % 74.56/10.55 % 74.56/10.55 (axiom_48) % 74.56/10.55 ! [v0: $i] : ! [v1: $i] : ( ~ (m_Down(v1) = v0) | ~ $i(v1) | ~ $i(v0) | % 74.56/10.55 pidElem(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (m_Halt(v1) = v0) | ~ $i(v1) % 74.56/10.55 | ~ $i(v0) | pidElem(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ? % 74.56/10.55 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) = % 74.56/10.55 v0) | (v2 = v0 & m_Halt(v1) = v0)))) % 74.56/10.55 % 74.56/10.55 (axiom_61) % 74.56/10.55 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) % 74.56/10.55 | ~ leq(v0, v1)) & ? [v0: $i] : ( ~ $i(v0) | leq(v0, v0)) % 74.56/10.55 % 74.56/10.56 (axiom_62) % 74.56/10.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 74.56/10.56 ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2)) % 74.56/10.56 % 74.56/10.56 (conj) % 75.09/10.58 $i(down) & $i(pendack) & $i(ldr) & $i(elid) & $i(status) & $i(setEmpty) & % 75.09/10.58 $i(alive) & $i(norm) & $i(wait) & $i(elec_1) & $i(elec_2) & $i(nbr_proc) & % 75.09/10.58 $i(zero) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 75.09/10.58 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 75.09/10.58 [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? % 75.09/10.58 [v15: $i] : ? [v16: $i] : ? [v17: $i] : ( ~ (v17 = v5) & ~ (v16 = v15) & % 75.09/10.58 index(down, v5) = v12 & index(ldr, v17) = v17 & index(status, v17) = norm & % 75.09/10.58 index(status, v5) = elec_1 & cons(v7, v1) = v6 & m_Down(v4) = v7 & s(zero) = % 75.09/10.58 v0 & host(v16) = v17 & host(v15) = v5 & host(v13) = v14 & host(v4) = v8 & % 75.09/10.58 host(v3) = v5 & queue(v5) = v6 & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 75.09/10.58 $i(v13) & $i(v12) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 75.09/10.58 $i(v2) & $i(v1) & $i(v0) & leq(nbr_proc, v5) & setIn(v16, alive) & % 75.09/10.58 setIn(v15, alive) & setIn(v3, alive) & ~ leq(v5, v8) & ~ setIn(v14, % 75.09/10.58 setEmpty) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! % 75.09/10.58 [v22: $i] : ! [v23: $i] : ( ~ (m_Down(v19) = v23) | ~ (host(v20) = v21) | % 75.09/10.58 ~ (host(v18) = v22) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v18, % 75.09/10.58 alive) | leq(v21, v22) | ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? % 75.09/10.58 [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ($i(v30) & (( ~ % 75.09/10.58 (v30 = v25) & index(down, v21) = v24 & host(v19) = v25 & $i(v25) & % 75.09/10.58 $i(v24) & leq(v0, v30) & ~ leq(v21, v30) & ~ setIn(v30, v24)) | ( % 75.09/10.58 ~ (v29 = norm) & index(status, v22) = v29 & $i(v29)) | ( ~ (v28 = % 75.09/10.58 v22) & index(ldr, v22) = v28 & $i(v28)) | ( ~ (v27 = elec_1) & % 75.09/10.58 index(status, v21) = v27 & $i(v27)) | (queue(v21) = v26 & $i(v26) & % 75.09/10.58 ~ elem(v23, v26))))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : % 75.09/10.58 ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (m_Down(v19) = v21) | ~ % 75.09/10.58 (host(v20) = v22) | ~ (host(v18) = v23) | ~ $i(v20) | ~ $i(v19) | ~ % 75.09/10.58 $i(v18) | ~ setIn(v20, alive) | ~ setIn(v18, alive) | ? [v24: $i] : ? % 75.09/10.58 [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( % 75.09/10.58 ~ (v29 = norm) & index(status, v23) = v29 & $i(v29)) | ( ~ (v28 = v23) % 75.09/10.58 & index(ldr, v23) = v28 & $i(v28)) | ( ~ (v27 = v25) & index(pendack, % 75.09/10.58 v22) = v25 & host(v19) = v27 & $i(v27) & $i(v25)) | ( ~ (v26 = % 75.09/10.58 elec_2) & index(status, v22) = v26 & $i(v26)) | (index(pendack, v22) % 75.09/10.58 = v25 & $i(v25) & ~ leq(nbr_proc, v25)) | (queue(v22) = v24 & $i(v24) % 75.09/10.58 & ~ elem(v21, v24)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : % 75.09/10.58 ! [v21: $i] : ! [v22: $i] : ( ~ (m_Ack(v20, v19) = v21) | ~ (host(v18) = % 75.09/10.58 v22) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v20, alive) | ~ % 75.09/10.58 setIn(v18, alive) | ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: % 75.09/10.58 $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( ~ (v29 = norm) & % 75.09/10.58 index(status, v22) = v29 & $i(v29)) | ( ~ (v28 = v22) & index(ldr, % 75.09/10.58 v22) = v28 & $i(v28)) | (host(v20) = v23 & $i(v23) & (( ~ (v27 = % 75.09/10.58 v25) & index(pendack, v23) = v25 & host(v19) = v27 & $i(v27) & % 75.09/10.58 $i(v25)) | ( ~ (v26 = elec_2) & index(status, v23) = v26 & % 75.09/10.58 $i(v26)) | (index(pendack, v23) = v25 & $i(v25) & ~ leq(nbr_proc, % 75.09/10.58 v25)) | (queue(v23) = v24 & $i(v24) & ~ elem(v21, v24)))))) & % 75.09/10.58 ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : (v19 = v18 | ~ % 75.09/10.58 (host(v19) = v21) | ~ (host(v18) = v20) | ~ $i(v19) | ~ $i(v18) | ~ % 75.09/10.58 setIn(v19, alive) | ~ setIn(v18, alive) | ? [v22: $i] : ? [v23: $i] : % 75.09/10.58 ? [v24: $i] : ? [v25: $i] : (( ~ (v25 = v21) & index(ldr, v21) = v25 & % 75.09/10.58 $i(v25)) | ( ~ (v24 = norm) & index(status, v21) = v24 & $i(v24)) | ( % 75.09/10.58 ~ (v23 = norm) & index(status, v20) = v23 & $i(v23)) | ( ~ (v22 = v20) % 75.09/10.58 & index(ldr, v20) = v22 & $i(v22)))) & ! [v18: $i] : ! [v19: $i] : % 75.09/10.58 ! [v20: $i] : ! [v21: $i] : ( ~ (m_Ldr(v19) = v20) | ~ (host(v18) = v21) | % 75.09/10.58 ~ $i(v19) | ~ $i(v18) | ? [v22: $i] : ? [v23: $i] : ((host(v19) = v23 % 75.09/10.58 & $i(v23) & ~ leq(v21, v23)) | (queue(v21) = v22 & $i(v22) & ~ % 75.09/10.58 elem(v20, v22)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : (v19 % 75.09/10.58 = v18 | ~ (host(v19) = v20) | ~ (host(v18) = v20) | ~ $i(v19) | ~ % 75.09/10.58 $i(v18) | ~ setIn(v19, alive) | ~ setIn(v18, alive)) & ! [v18: $i] : ! % 75.09/10.58 [v19: $i] : ( ~ (host(v18) = v19) | ~ $i(v18) | ~ setIn(v18, alive) | ? % 75.09/10.58 [v20: $i] : ? [v21: $i] : ((v21 = v18 & index(elid, v19) = v18) | ( ~ % 75.09/10.58 (v20 = elec_1) & ~ (v20 = elec_2) & index(status, v19) = v20 & % 75.09/10.58 $i(v20)))) & ! [v18: $i] : (v18 = v8 | ~ $i(v18) | ~ leq(v0, v18) | % 75.09/10.58 leq(v5, v18) | setIn(v18, v12)) & ( ~ (norm = elec_1) | ( ~ (v9 = v8) & % 75.09/10.58 index(ldr, v5) = v9 & $i(v9))) & ( ~ (wait = elec_1) | ( ~ (v11 = v8) & % 75.09/10.58 index(elid, v5) = v10 & host(v10) = v11 & $i(v11) & $i(v10)))) % 75.09/10.58 % 75.09/10.58 (function-axioms) % 75.09/10.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.09/10.58 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 75.09/10.58 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3, % 75.09/10.58 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 75.09/10.58 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! % 75.09/10.58 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~ % 75.09/10.58 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 75.09/10.58 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 75.09/10.58 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i] % 75.09/10.58 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) = % 75.09/10.58 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) = % 75.09/10.58 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 75.09/10.58 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 75.09/10.58 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & ! % 75.09/10.58 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~ % 75.09/10.58 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 75.09/10.58 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 75.09/10.58 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & ! % 75.09/10.58 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~ % 75.09/10.58 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 75.09/10.58 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 75.09/10.58 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1: % 75.09/10.58 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0)) % 75.09/10.58 % 75.09/10.58 Further assumptions not needed in the proof: % 75.09/10.58 -------------------------------------------- % 75.09/10.58 axiom, axiom_01, axiom_02, axiom_05, axiom_06, axiom_07, axiom_08, axiom_09, % 75.09/10.58 axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15, axiom_16, axiom_18, % 75.09/10.58 axiom_19, axiom_20, axiom_21, axiom_22, axiom_23, axiom_24, axiom_25, axiom_26, % 75.09/10.58 axiom_27, axiom_28, axiom_29, axiom_31, axiom_32, axiom_33, axiom_34, axiom_35, % 75.09/10.58 axiom_36, axiom_37, axiom_38, axiom_39, axiom_40, axiom_41, axiom_42, axiom_43, % 75.09/10.58 axiom_44, axiom_45, axiom_47, axiom_49, axiom_50, axiom_51, axiom_52, axiom_53, % 75.09/10.58 axiom_54, axiom_55, axiom_56, axiom_57, axiom_58, axiom_59, axiom_60, axiom_63, % 75.09/10.58 axiom_64, axiom_65 % 75.09/10.58 % 75.09/10.58 Those formulas are unsatisfiable: % 75.09/10.58 --------------------------------- % 75.09/10.58 % 75.09/10.58 Begin of proof % 75.09/10.58 | % 75.09/10.59 | ALPHA: (axiom_03) implies: % 75.09/10.59 | (1) ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0, nbr_proc)) % 75.09/10.59 | % 75.09/10.59 | ALPHA: (axiom_04) implies: % 75.09/10.59 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) | leq(v1, % 75.09/10.59 | nbr_proc)) % 75.09/10.59 | % 75.09/10.59 | ALPHA: (axiom_46) implies: % 75.09/10.59 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) = v2) | ~ % 75.09/10.59 | $i(v1) | ~ $i(v0) | elem(v0, v2)) % 75.09/10.59 | % 75.09/10.59 | ALPHA: (axiom_48) implies: % 75.09/10.59 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ? [v1: $i] : ? [v2: $i] : % 75.09/10.59 | ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) = v0) | (v2 = v0 & % 75.09/10.59 | m_Halt(v1) = v0)))) % 75.09/10.59 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (m_Down(v1) = v0) | ~ $i(v1) | ~ % 75.09/10.59 | $i(v0) | pidElem(v0)) % 75.09/10.59 | % 75.09/10.59 | ALPHA: (axiom_61) implies: % 75.09/10.59 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 75.09/10.59 | leq(v1, v0) | ~ leq(v0, v1)) % 75.09/10.59 | % 75.09/10.59 | ALPHA: (conj) implies: % 75.09/10.59 | (7) $i(nbr_proc) % 75.09/10.60 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 75.09/10.60 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 75.09/10.60 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 75.09/10.60 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ( ~ (v17 = v5) & ~ (v16 = % 75.09/10.60 | v15) & index(down, v5) = v12 & index(ldr, v17) = v17 & % 75.09/10.60 | index(status, v17) = norm & index(status, v5) = elec_1 & cons(v7, v1) % 75.09/10.60 | = v6 & m_Down(v4) = v7 & s(zero) = v0 & host(v16) = v17 & host(v15) = % 75.09/10.60 | v5 & host(v13) = v14 & host(v4) = v8 & host(v3) = v5 & queue(v5) = v6 % 75.09/10.60 | & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v8) % 75.09/10.60 | & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 75.09/10.60 | $i(v0) & leq(nbr_proc, v5) & setIn(v16, alive) & setIn(v15, alive) & % 75.09/10.60 | setIn(v3, alive) & ~ leq(v5, v8) & ~ setIn(v14, setEmpty) & ! % 75.09/10.60 | [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] % 75.09/10.60 | : ! [v23: $i] : ( ~ (m_Down(v19) = v23) | ~ (host(v20) = v21) | ~ % 75.09/10.60 | (host(v18) = v22) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ % 75.09/10.60 | setIn(v18, alive) | leq(v21, v22) | ? [v24: $i] : ? [v25: $i] : % 75.09/10.60 | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: % 75.09/10.60 | $i] : ($i(v30) & (( ~ (v30 = v25) & index(down, v21) = v24 & % 75.09/10.60 | host(v19) = v25 & $i(v25) & $i(v24) & leq(v0, v30) & ~ % 75.09/10.60 | leq(v21, v30) & ~ setIn(v30, v24)) | ( ~ (v29 = norm) & % 75.09/10.60 | index(status, v22) = v29 & $i(v29)) | ( ~ (v28 = v22) & % 75.09/10.60 | index(ldr, v22) = v28 & $i(v28)) | ( ~ (v27 = elec_1) & % 75.09/10.60 | index(status, v21) = v27 & $i(v27)) | (queue(v21) = v26 & % 75.09/10.60 | $i(v26) & ~ elem(v23, v26))))) & ! [v18: $i] : ! [v19: $i] % 75.09/10.60 | : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ % 75.09/10.60 | (m_Down(v19) = v21) | ~ (host(v20) = v22) | ~ (host(v18) = v23) | % 75.09/10.60 | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v20, alive) | ~ % 75.09/10.60 | setIn(v18, alive) | ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? % 75.09/10.60 | [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( ~ (v29 = norm) & % 75.09/10.60 | index(status, v23) = v29 & $i(v29)) | ( ~ (v28 = v23) & % 75.09/10.60 | index(ldr, v23) = v28 & $i(v28)) | ( ~ (v27 = v25) & % 75.09/10.60 | index(pendack, v22) = v25 & host(v19) = v27 & $i(v27) & % 75.09/10.60 | $i(v25)) | ( ~ (v26 = elec_2) & index(status, v22) = v26 & % 75.09/10.60 | $i(v26)) | (index(pendack, v22) = v25 & $i(v25) & ~ % 75.09/10.60 | leq(nbr_proc, v25)) | (queue(v22) = v24 & $i(v24) & ~ % 75.09/10.60 | elem(v21, v24)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] % 75.09/10.60 | : ! [v21: $i] : ! [v22: $i] : ( ~ (m_Ack(v20, v19) = v21) | ~ % 75.09/10.60 | (host(v18) = v22) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ % 75.09/10.60 | setIn(v20, alive) | ~ setIn(v18, alive) | ? [v23: $i] : ? [v24: % 75.09/10.60 | $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : % 75.09/10.60 | ? [v29: $i] : (( ~ (v29 = norm) & index(status, v22) = v29 & % 75.09/10.60 | $i(v29)) | ( ~ (v28 = v22) & index(ldr, v22) = v28 & $i(v28)) | % 75.09/10.60 | (host(v20) = v23 & $i(v23) & (( ~ (v27 = v25) & index(pendack, % 75.09/10.60 | v23) = v25 & host(v19) = v27 & $i(v27) & $i(v25)) | ( ~ % 75.09/10.60 | (v26 = elec_2) & index(status, v23) = v26 & $i(v26)) | % 75.09/10.60 | (index(pendack, v23) = v25 & $i(v25) & ~ leq(nbr_proc, v25)) % 75.09/10.60 | | (queue(v23) = v24 & $i(v24) & ~ elem(v21, v24)))))) & ! % 75.09/10.60 | [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : (v19 = v18 | % 75.09/10.60 | ~ (host(v19) = v21) | ~ (host(v18) = v20) | ~ $i(v19) | ~ % 75.09/10.60 | $i(v18) | ~ setIn(v19, alive) | ~ setIn(v18, alive) | ? [v22: % 75.09/10.60 | $i] : ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : (( ~ (v25 = % 75.09/10.60 | v21) & index(ldr, v21) = v25 & $i(v25)) | ( ~ (v24 = norm) & % 75.09/10.61 | index(status, v21) = v24 & $i(v24)) | ( ~ (v23 = norm) & % 75.09/10.61 | index(status, v20) = v23 & $i(v23)) | ( ~ (v22 = v20) & % 75.09/10.61 | index(ldr, v20) = v22 & $i(v22)))) & ! [v18: $i] : ! [v19: % 75.09/10.61 | $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (m_Ldr(v19) = v20) | ~ % 75.09/10.61 | (host(v18) = v21) | ~ $i(v19) | ~ $i(v18) | ? [v22: $i] : ? % 75.09/10.61 | [v23: $i] : ((host(v19) = v23 & $i(v23) & ~ leq(v21, v23)) | % 75.09/10.61 | (queue(v21) = v22 & $i(v22) & ~ elem(v20, v22)))) & ! [v18: $i] % 75.09/10.61 | : ! [v19: $i] : ! [v20: $i] : (v19 = v18 | ~ (host(v19) = v20) | % 75.09/10.61 | ~ (host(v18) = v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v19, % 75.09/10.61 | alive) | ~ setIn(v18, alive)) & ! [v18: $i] : ! [v19: $i] : ( % 75.09/10.61 | ~ (host(v18) = v19) | ~ $i(v18) | ~ setIn(v18, alive) | ? [v20: % 75.09/10.61 | $i] : ? [v21: $i] : ((v21 = v18 & index(elid, v19) = v18) | ( ~ % 75.09/10.61 | (v20 = elec_1) & ~ (v20 = elec_2) & index(status, v19) = v20 & % 75.09/10.61 | $i(v20)))) & ! [v18: $i] : (v18 = v8 | ~ $i(v18) | ~ leq(v0, % 75.09/10.61 | v18) | leq(v5, v18) | setIn(v18, v12)) & ( ~ (norm = elec_1) | ( % 75.09/10.61 | ~ (v9 = v8) & index(ldr, v5) = v9 & $i(v9))) & ( ~ (wait = % 75.09/10.61 | elec_1) | ( ~ (v11 = v8) & index(elid, v5) = v10 & host(v10) = % 75.09/10.61 | v11 & $i(v11) & $i(v10)))) % 75.09/10.61 | % 75.09/10.61 | ALPHA: (function-axioms) implies: % 75.09/10.61 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = % 75.09/10.61 | v1) | ~ (queue(v2) = v0)) % 75.09/10.61 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = % 75.09/10.61 | v1) | ~ (host(v2) = v0)) % 75.09/10.61 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 75.09/10.61 | ~ (s(v2) = v0)) % 75.09/10.61 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.09/10.61 | (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) % 75.09/10.61 | % 75.09/10.61 | DELTA: instantiating (1) with fresh symbol all_59_0 gives: % 75.09/10.61 | (13) s(zero) = all_59_0 & $i(all_59_0) & leq(all_59_0, nbr_proc) % 75.09/10.61 | % 75.09/10.61 | ALPHA: (13) implies: % 75.09/10.61 | (14) s(zero) = all_59_0 % 75.09/10.61 | % 75.09/10.61 | DELTA: instantiating (8) with fresh symbols all_65_0, all_65_1, all_65_2, % 75.09/10.61 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9, % 75.09/10.61 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15, % 75.09/10.61 | all_65_16, all_65_17 gives: % 75.09/10.62 | (15) ~ (all_65_0 = all_65_12) & ~ (all_65_1 = all_65_2) & index(down, % 75.09/10.62 | all_65_12) = all_65_5 & index(ldr, all_65_0) = all_65_0 & % 75.09/10.62 | index(status, all_65_0) = norm & index(status, all_65_12) = elec_1 & % 75.09/10.62 | cons(all_65_10, all_65_16) = all_65_11 & m_Down(all_65_13) = all_65_10 % 75.09/10.62 | & s(zero) = all_65_17 & host(all_65_1) = all_65_0 & host(all_65_2) = % 75.09/10.62 | all_65_12 & host(all_65_4) = all_65_3 & host(all_65_13) = all_65_9 & % 75.09/10.62 | host(all_65_14) = all_65_12 & queue(all_65_12) = all_65_11 & % 75.09/10.62 | $i(all_65_0) & $i(all_65_1) & $i(all_65_2) & $i(all_65_3) & % 75.09/10.62 | $i(all_65_4) & $i(all_65_5) & $i(all_65_9) & $i(all_65_10) & % 75.09/10.62 | $i(all_65_11) & $i(all_65_12) & $i(all_65_13) & $i(all_65_14) & % 75.09/10.62 | $i(all_65_15) & $i(all_65_16) & $i(all_65_17) & leq(nbr_proc, % 75.09/10.62 | all_65_12) & setIn(all_65_1, alive) & setIn(all_65_2, alive) & % 75.09/10.62 | setIn(all_65_14, alive) & ~ leq(all_65_12, all_65_9) & ~ % 75.09/10.62 | setIn(all_65_3, setEmpty) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 75.09/10.62 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (m_Down(v1) = v5) | ~ % 75.09/10.62 | (host(v2) = v3) | ~ (host(v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 75.09/10.62 | $i(v0) | ~ setIn(v0, alive) | leq(v3, v4) | ? [v6: $i] : ? [v7: % 75.09/10.62 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 75.09/10.62 | [v12: $i] : ($i(v12) & (( ~ (v12 = v7) & index(down, v3) = v6 & % 75.09/10.62 | host(v1) = v7 & $i(v7) & $i(v6) & leq(all_65_17, v12) & ~ % 75.09/10.62 | leq(v3, v12) & ~ setIn(v12, v6)) | ( ~ (v11 = norm) & % 75.09/10.62 | index(status, v4) = v11 & $i(v11)) | ( ~ (v10 = v4) & % 75.09/10.62 | index(ldr, v4) = v10 & $i(v10)) | ( ~ (v9 = elec_1) & % 75.09/10.62 | index(status, v3) = v9 & $i(v9)) | (queue(v3) = v8 & $i(v8) & % 75.09/10.62 | ~ elem(v5, v8))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 75.09/10.62 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (m_Down(v1) = v3) | ~ % 75.09/10.62 | (host(v2) = v4) | ~ (host(v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 75.09/10.62 | $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? [v6: $i] : % 75.09/10.62 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] % 75.09/10.62 | : (( ~ (v11 = norm) & index(status, v5) = v11 & $i(v11)) | ( ~ (v10 % 75.09/10.62 | = v5) & index(ldr, v5) = v10 & $i(v10)) | ( ~ (v9 = v7) & % 75.09/10.62 | index(pendack, v4) = v7 & host(v1) = v9 & $i(v9) & $i(v7)) | ( ~ % 75.09/10.62 | (v8 = elec_2) & index(status, v4) = v8 & $i(v8)) | % 75.09/10.62 | (index(pendack, v4) = v7 & $i(v7) & ~ leq(nbr_proc, v7)) | % 75.09/10.62 | (queue(v4) = v6 & $i(v6) & ~ elem(v3, v6)))) & ! [v0: $i] : ! % 75.09/10.62 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (m_Ack(v2, % 75.09/10.62 | v1) = v3) | ~ (host(v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 75.09/10.62 | $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? [v5: $i] : % 75.09/10.62 | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] % 75.09/10.62 | : ? [v11: $i] : (( ~ (v11 = norm) & index(status, v4) = v11 & % 75.09/10.62 | $i(v11)) | ( ~ (v10 = v4) & index(ldr, v4) = v10 & $i(v10)) | % 75.09/10.62 | (host(v2) = v5 & $i(v5) & (( ~ (v9 = v7) & index(pendack, v5) = v7 % 75.09/10.62 | & host(v1) = v9 & $i(v9) & $i(v7)) | ( ~ (v8 = elec_2) & % 75.09/10.62 | index(status, v5) = v8 & $i(v8)) | (index(pendack, v5) = v7 % 75.09/10.62 | & $i(v7) & ~ leq(nbr_proc, v7)) | (queue(v5) = v6 & $i(v6) % 75.09/10.62 | & ~ elem(v3, v6)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 75.09/10.62 | $i] : ! [v3: $i] : (v1 = v0 | ~ (host(v1) = v3) | ~ (host(v0) = % 75.09/10.62 | v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, % 75.09/10.62 | alive) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 75.09/10.62 | (( ~ (v7 = v3) & index(ldr, v3) = v7 & $i(v7)) | ( ~ (v6 = norm) & % 75.09/10.62 | index(status, v3) = v6 & $i(v6)) | ( ~ (v5 = norm) & % 75.09/10.62 | index(status, v2) = v5 & $i(v5)) | ( ~ (v4 = v2) & index(ldr, % 75.09/10.62 | v2) = v4 & $i(v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 75.09/10.62 | : ! [v3: $i] : ( ~ (m_Ldr(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) % 75.09/10.62 | | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & % 75.09/10.62 | ~ leq(v3, v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) % 75.09/10.62 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v1) = % 75.09/10.62 | v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 75.09/10.62 | alive) | ~ setIn(v0, alive)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 75.09/10.62 | (host(v0) = v1) | ~ $i(v0) | ~ setIn(v0, alive) | ? [v2: $i] : ? % 75.09/10.62 | [v3: $i] : ((v3 = v0 & index(elid, v1) = v0) | ( ~ (v2 = elec_1) & % 75.09/10.62 | ~ (v2 = elec_2) & index(status, v1) = v2 & $i(v2)))) & ! [v0: % 75.09/10.62 | any] : (v0 = all_65_9 | ~ $i(v0) | ~ leq(all_65_17, v0) | % 75.09/10.62 | leq(all_65_12, v0) | setIn(v0, all_65_5)) & ( ~ (norm = elec_1) | ( % 75.09/10.62 | ~ (all_65_8 = all_65_9) & index(ldr, all_65_12) = all_65_8 & % 75.09/10.62 | $i(all_65_8))) & ( ~ (wait = elec_1) | ( ~ (all_65_6 = all_65_9) & % 75.09/10.62 | index(elid, all_65_12) = all_65_7 & host(all_65_7) = all_65_6 & % 75.09/10.62 | $i(all_65_6) & $i(all_65_7))) % 75.09/10.62 | % 75.09/10.62 | ALPHA: (15) implies: % 75.09/10.62 | (16) ~ (all_65_1 = all_65_2) % 75.09/10.62 | (17) ~ (all_65_0 = all_65_12) % 75.09/10.62 | (18) setIn(all_65_14, alive) % 75.09/10.63 | (19) setIn(all_65_2, alive) % 75.09/10.63 | (20) setIn(all_65_1, alive) % 75.09/10.63 | (21) leq(nbr_proc, all_65_12) % 75.09/10.63 | (22) $i(all_65_16) % 75.09/10.63 | (23) $i(all_65_14) % 75.09/10.63 | (24) $i(all_65_13) % 75.09/10.63 | (25) $i(all_65_12) % 75.09/10.63 | (26) $i(all_65_10) % 75.09/10.63 | (27) $i(all_65_2) % 75.09/10.63 | (28) $i(all_65_1) % 75.09/10.63 | (29) $i(all_65_0) % 75.09/10.63 | (30) queue(all_65_12) = all_65_11 % 75.09/10.63 | (31) host(all_65_14) = all_65_12 % 75.09/10.63 | (32) host(all_65_13) = all_65_9 % 75.09/10.63 | (33) host(all_65_2) = all_65_12 % 75.09/10.63 | (34) host(all_65_1) = all_65_0 % 75.09/10.63 | (35) s(zero) = all_65_17 % 75.09/10.63 | (36) m_Down(all_65_13) = all_65_10 % 75.09/10.63 | (37) cons(all_65_10, all_65_16) = all_65_11 % 75.09/10.63 | (38) index(status, all_65_12) = elec_1 % 75.09/10.63 | (39) index(status, all_65_0) = norm % 75.09/10.63 | (40) index(ldr, all_65_0) = all_65_0 % 75.09/10.63 | (41) index(down, all_65_12) = all_65_5 % 75.09/10.63 | (42) ! [v0: any] : (v0 = all_65_9 | ~ $i(v0) | ~ leq(all_65_17, v0) | % 75.09/10.63 | leq(all_65_12, v0) | setIn(v0, all_65_5)) % 75.09/10.63 | (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v1) = % 75.09/10.63 | v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 75.09/10.63 | alive) | ~ setIn(v0, alive)) % 75.09/10.63 | (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.09/10.63 | (host(v1) = v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 75.09/10.63 | setIn(v1, alive) | ~ setIn(v0, alive) | ? [v4: $i] : ? [v5: $i] : % 75.09/10.63 | ? [v6: $i] : ? [v7: $i] : (( ~ (v7 = v3) & index(ldr, v3) = v7 & % 75.09/10.63 | $i(v7)) | ( ~ (v6 = norm) & index(status, v3) = v6 & $i(v6)) | ( % 75.09/10.63 | ~ (v5 = norm) & index(status, v2) = v5 & $i(v5)) | ( ~ (v4 = v2) % 75.09/10.63 | & index(ldr, v2) = v4 & $i(v4)))) % 75.09/10.63 | (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 75.09/10.63 | ! [v5: $i] : ( ~ (m_Down(v1) = v5) | ~ (host(v2) = v3) | ~ (host(v0) % 75.09/10.63 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v0, alive) | % 75.09/10.63 | leq(v3, v4) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 75.09/10.63 | : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ($i(v12) & (( ~ (v12 % 75.09/10.63 | = v7) & index(down, v3) = v6 & host(v1) = v7 & $i(v7) & % 75.09/10.63 | $i(v6) & leq(all_65_17, v12) & ~ leq(v3, v12) & ~ setIn(v12, % 75.09/10.63 | v6)) | ( ~ (v11 = norm) & index(status, v4) = v11 & $i(v11)) % 75.09/10.63 | | ( ~ (v10 = v4) & index(ldr, v4) = v10 & $i(v10)) | ( ~ (v9 = % 75.09/10.63 | elec_1) & index(status, v3) = v9 & $i(v9)) | (queue(v3) = v8 % 75.09/10.63 | & $i(v8) & ~ elem(v5, v8))))) % 75.09/10.63 | % 75.09/10.63 | GROUND_INST: instantiating (11) with all_59_0, all_65_17, zero, simplifying % 75.09/10.63 | with (14), (35) gives: % 75.09/10.63 | (46) all_65_17 = all_59_0 % 75.09/10.63 | % 75.09/10.63 | GROUND_INST: instantiating (43) with all_65_14, all_65_2, all_65_12, % 75.09/10.63 | simplifying with (18), (19), (23), (27), (31), (33) gives: % 75.09/10.63 | (47) all_65_2 = all_65_14 % 75.09/10.63 | % 75.09/10.63 | GROUND_INST: instantiating (2) with all_65_2, all_65_12, simplifying with % 75.09/10.63 | (27), (33) gives: % 75.09/10.63 | (48) leq(all_65_12, nbr_proc) % 75.09/10.63 | % 75.09/10.63 | GROUND_INST: instantiating (44) with all_65_1, all_65_14, all_65_0, all_65_12, % 75.09/10.63 | simplifying with (18), (20), (23), (28), (31), (34) gives: % 75.09/10.64 | (49) all_65_1 = all_65_14 | ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? % 75.09/10.64 | [v3: any] : (( ~ (v3 = all_65_12) & index(ldr, all_65_12) = v3 & % 75.09/10.64 | $i(v3)) | ( ~ (v2 = norm) & index(status, all_65_12) = v2 & % 75.09/10.64 | $i(v2)) | ( ~ (v1 = norm) & index(status, all_65_0) = v1 & $i(v1)) % 75.09/10.64 | | ( ~ (v0 = all_65_0) & index(ldr, all_65_0) = v0 & $i(v0))) % 75.09/10.64 | % 75.09/10.64 | GROUND_INST: instantiating (2) with all_65_1, all_65_0, simplifying with (28), % 75.09/10.64 | (34) gives: % 75.09/10.64 | (50) leq(all_65_0, nbr_proc) % 75.09/10.64 | % 75.09/10.64 | GROUND_INST: instantiating (45) with all_65_1, all_65_13, all_65_14, % 75.09/10.64 | all_65_12, all_65_0, all_65_10, simplifying with (20), (23), % 75.09/10.64 | (24), (28), (31), (34), (36) gives: % 75.09/10.64 | (51) leq(all_65_12, all_65_0) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 75.09/10.64 | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & (( ~ % 75.09/10.64 | (v6 = v1) & index(down, all_65_12) = v0 & host(all_65_13) = v1 & % 75.09/10.64 | $i(v1) & $i(v0) & leq(all_65_17, v6) & ~ leq(all_65_12, v6) & % 75.09/10.64 | ~ setIn(v6, v0)) | ( ~ (v5 = norm) & index(status, all_65_0) = % 75.09/10.64 | v5 & $i(v5)) | ( ~ (v4 = all_65_0) & index(ldr, all_65_0) = v4 & % 75.09/10.64 | $i(v4)) | ( ~ (v3 = elec_1) & index(status, all_65_12) = v3 & % 75.09/10.64 | $i(v3)) | (queue(all_65_12) = v2 & $i(v2) & ~ elem(all_65_10, % 75.09/10.64 | v2)))) % 75.09/10.64 | % 75.09/10.64 | GROUND_INST: instantiating (5) with all_65_10, all_65_13, simplifying with % 75.09/10.64 | (24), (26), (36) gives: % 75.09/10.64 | (52) pidElem(all_65_10) % 75.09/10.64 | % 75.09/10.64 | GROUND_INST: instantiating (3) with all_65_10, all_65_16, all_65_11, % 75.09/10.64 | simplifying with (22), (26), (37) gives: % 75.09/10.64 | (53) elem(all_65_10, all_65_11) % 75.09/10.64 | % 75.09/10.64 | REDUCE: (16), (47) imply: % 75.09/10.64 | (54) ~ (all_65_1 = all_65_14) % 75.09/10.64 | % 75.09/10.64 | BETA: splitting (49) gives: % 75.09/10.64 | % 75.09/10.64 | Case 1: % 75.09/10.64 | | % 75.09/10.64 | | (55) all_65_1 = all_65_14 % 75.09/10.64 | | % 75.09/10.64 | | REDUCE: (54), (55) imply: % 75.09/10.64 | | (56) $false % 75.09/10.64 | | % 75.09/10.64 | | CLOSE: (56) is inconsistent. % 75.09/10.64 | | % 75.09/10.64 | Case 2: % 75.09/10.64 | | % 75.09/10.64 | | % 75.09/10.64 | | GROUND_INST: instantiating (6) with nbr_proc, all_65_12, simplifying with % 75.09/10.64 | | (7), (21), (25), (48) gives: % 75.09/10.64 | | (57) all_65_12 = nbr_proc % 75.09/10.64 | | % 75.09/10.64 | | GROUND_INST: instantiating (axiom_62) with all_65_0, nbr_proc, all_65_12, % 75.09/10.64 | | simplifying with (7), (21), (25), (29), (50) gives: % 75.09/10.64 | | (58) leq(all_65_0, all_65_12) % 75.09/10.64 | | % 75.09/10.64 | | GROUND_INST: instantiating (4) with all_65_10, simplifying with (26), (52) % 75.09/10.64 | | gives: % 75.09/10.64 | | (59) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ($i(v0) & ((v2 = % 75.09/10.64 | | all_65_10 & m_Down(v0) = all_65_10) | (v1 = all_65_10 & % 75.09/10.64 | | m_Halt(v0) = all_65_10))) % 75.09/10.64 | | % 75.09/10.64 | | DELTA: instantiating (59) with fresh symbols all_123_0, all_123_1, all_123_2 % 75.09/10.64 | | gives: % 75.09/10.64 | | (60) $i(all_123_2) & ((all_123_0 = all_65_10 & m_Down(all_123_2) = % 75.09/10.64 | | all_65_10) | (all_123_1 = all_65_10 & m_Halt(all_123_2) = % 75.09/10.64 | | all_65_10)) % 75.09/10.64 | | % 75.09/10.64 | | ALPHA: (60) implies: % 75.09/10.64 | | (61) $i(all_123_2) % 75.09/10.64 | | (62) (all_123_0 = all_65_10 & m_Down(all_123_2) = all_65_10) | (all_123_1 % 75.09/10.64 | | = all_65_10 & m_Halt(all_123_2) = all_65_10) % 75.09/10.64 | | % 75.09/10.64 | | REDUCE: (17), (57) imply: % 75.09/10.64 | | (63) ~ (all_65_0 = nbr_proc) % 75.09/10.64 | | % 75.09/10.64 | | REDUCE: (41), (57) imply: % 75.09/10.64 | | (64) index(down, nbr_proc) = all_65_5 % 75.09/10.64 | | % 75.09/10.64 | | REDUCE: (38), (57) imply: % 75.09/10.64 | | (65) index(status, nbr_proc) = elec_1 % 75.09/10.64 | | % 75.09/10.64 | | REDUCE: (31), (57) imply: % 75.09/10.64 | | (66) host(all_65_14) = nbr_proc % 75.09/10.64 | | % 75.09/10.64 | | REDUCE: (30), (57) imply: % 75.09/10.64 | | (67) queue(nbr_proc) = all_65_11 % 75.09/10.64 | | % 75.09/10.64 | | BETA: splitting (51) gives: % 75.09/10.64 | | % 75.09/10.64 | | Case 1: % 75.09/10.64 | | | % 75.09/10.64 | | | (68) leq(all_65_12, all_65_0) % 75.09/10.64 | | | % 75.09/10.64 | | | REDUCE: (57), (68) imply: % 75.09/10.64 | | | (69) leq(nbr_proc, all_65_0) % 75.09/10.64 | | | % 75.09/10.64 | | | GROUND_INST: instantiating (6) with all_65_0, nbr_proc, simplifying with % 75.09/10.64 | | | (7), (29), (50), (69) gives: % 75.09/10.64 | | | (70) all_65_0 = nbr_proc % 75.09/10.64 | | | % 75.09/10.64 | | | REDUCE: (63), (70) imply: % 75.09/10.64 | | | (71) $false % 75.09/10.64 | | | % 75.09/10.64 | | | CLOSE: (71) is inconsistent. % 75.09/10.64 | | | % 75.09/10.64 | | Case 2: % 75.09/10.64 | | | % 75.09/10.64 | | | (72) ~ leq(all_65_12, all_65_0) % 75.09/10.64 | | | % 75.09/10.64 | | | REDUCE: (57), (72) imply: % 75.09/10.65 | | | (73) ~ leq(nbr_proc, all_65_0) % 75.09/10.65 | | | % 75.09/10.65 | | | BETA: splitting (62) gives: % 75.09/10.65 | | | % 75.09/10.65 | | | Case 1: % 75.09/10.65 | | | | % 75.09/10.65 | | | | (74) all_123_0 = all_65_10 & m_Down(all_123_2) = all_65_10 % 75.09/10.65 | | | | % 75.09/10.65 | | | | ALPHA: (74) implies: % 75.09/10.65 | | | | (75) m_Down(all_123_2) = all_65_10 % 75.09/10.65 | | | | % 75.09/10.65 | | | | GROUND_INST: instantiating (45) with all_65_1, all_123_2, all_65_14, % 75.09/10.65 | | | | nbr_proc, all_65_0, all_65_10, simplifying with (20), (23), % 75.09/10.65 | | | | (28), (34), (61), (66), (73), (75) gives: % 75.09/10.65 | | | | (76) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 75.09/10.65 | | | | any] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & (( ~ (v6 = v1) & % 75.09/10.65 | | | | index(down, nbr_proc) = v0 & host(all_123_2) = v1 & $i(v1) % 75.09/10.65 | | | | & $i(v0) & leq(all_65_17, v6) & ~ leq(nbr_proc, v6) & ~ % 75.09/10.65 | | | | setIn(v6, v0)) | ( ~ (v5 = norm) & index(status, all_65_0) % 75.09/10.65 | | | | = v5 & $i(v5)) | ( ~ (v4 = all_65_0) & index(ldr, % 75.09/10.65 | | | | all_65_0) = v4 & $i(v4)) | ( ~ (v3 = elec_1) & % 75.09/10.65 | | | | index(status, nbr_proc) = v3 & $i(v3)) | (queue(nbr_proc) % 75.09/10.65 | | | | = v2 & $i(v2) & ~ elem(all_65_10, v2)))) % 75.09/10.65 | | | | % 75.09/10.65 | | | | GROUND_INST: instantiating (axiom_30) with all_65_13, all_123_2, % 75.09/10.65 | | | | all_65_10, simplifying with (24), (36), (61), (75) gives: % 75.09/10.65 | | | | (77) all_123_2 = all_65_13 % 75.09/10.65 | | | | % 75.09/10.65 | | | | DELTA: instantiating (76) with fresh symbols all_333_0, all_333_1, % 75.09/10.65 | | | | all_333_2, all_333_3, all_333_4, all_333_5, all_333_6 gives: % 75.09/10.65 | | | | (78) $i(all_333_0) & (( ~ (all_333_0 = all_333_5) & index(down, % 75.09/10.65 | | | | nbr_proc) = all_333_6 & host(all_123_2) = all_333_5 & % 75.09/10.65 | | | | $i(all_333_5) & $i(all_333_6) & leq(all_65_17, all_333_0) & % 75.09/10.65 | | | | ~ leq(nbr_proc, all_333_0) & ~ setIn(all_333_0, all_333_6)) % 75.09/10.65 | | | | | ( ~ (all_333_1 = norm) & index(status, all_65_0) = all_333_1 % 75.09/10.65 | | | | & $i(all_333_1)) | ( ~ (all_333_2 = all_65_0) & index(ldr, % 75.09/10.65 | | | | all_65_0) = all_333_2 & $i(all_333_2)) | ( ~ (all_333_3 = % 75.09/10.65 | | | | elec_1) & index(status, nbr_proc) = all_333_3 & % 75.09/10.65 | | | | $i(all_333_3)) | (queue(nbr_proc) = all_333_4 & % 75.09/10.65 | | | | $i(all_333_4) & ~ elem(all_65_10, all_333_4))) % 75.09/10.65 | | | | % 75.09/10.65 | | | | ALPHA: (78) implies: % 75.09/10.65 | | | | (79) $i(all_333_0) % 75.09/10.65 | | | | (80) ( ~ (all_333_0 = all_333_5) & index(down, nbr_proc) = all_333_6 % 75.09/10.65 | | | | & host(all_123_2) = all_333_5 & $i(all_333_5) & $i(all_333_6) % 75.09/10.65 | | | | & leq(all_65_17, all_333_0) & ~ leq(nbr_proc, all_333_0) & ~ % 75.09/10.65 | | | | setIn(all_333_0, all_333_6)) | ( ~ (all_333_1 = norm) & % 75.09/10.65 | | | | index(status, all_65_0) = all_333_1 & $i(all_333_1)) | ( ~ % 75.09/10.65 | | | | (all_333_2 = all_65_0) & index(ldr, all_65_0) = all_333_2 & % 75.09/10.65 | | | | $i(all_333_2)) | ( ~ (all_333_3 = elec_1) & index(status, % 75.09/10.65 | | | | nbr_proc) = all_333_3 & $i(all_333_3)) | (queue(nbr_proc) = % 75.09/10.65 | | | | all_333_4 & $i(all_333_4) & ~ elem(all_65_10, all_333_4)) % 75.09/10.65 | | | | % 75.09/10.65 | | | | BETA: splitting (80) gives: % 75.09/10.65 | | | | % 75.09/10.65 | | | | Case 1: % 75.09/10.65 | | | | | % 75.09/10.65 | | | | | (81) ( ~ (all_333_0 = all_333_5) & index(down, nbr_proc) = % 75.09/10.65 | | | | | all_333_6 & host(all_123_2) = all_333_5 & $i(all_333_5) & % 75.09/10.65 | | | | | $i(all_333_6) & leq(all_65_17, all_333_0) & ~ leq(nbr_proc, % 75.09/10.65 | | | | | all_333_0) & ~ setIn(all_333_0, all_333_6)) | ( ~ % 75.09/10.65 | | | | | (all_333_1 = norm) & index(status, all_65_0) = all_333_1 & % 75.09/10.65 | | | | | $i(all_333_1)) % 75.09/10.65 | | | | | % 75.09/10.65 | | | | | BETA: splitting (81) gives: % 75.09/10.65 | | | | | % 75.09/10.65 | | | | | Case 1: % 75.09/10.65 | | | | | | % 75.09/10.65 | | | | | | (82) ~ (all_333_0 = all_333_5) & index(down, nbr_proc) = % 75.09/10.65 | | | | | | all_333_6 & host(all_123_2) = all_333_5 & $i(all_333_5) & % 75.09/10.65 | | | | | | $i(all_333_6) & leq(all_65_17, all_333_0) & ~ leq(nbr_proc, % 75.09/10.65 | | | | | | all_333_0) & ~ setIn(all_333_0, all_333_6) % 75.09/10.65 | | | | | | % 75.09/10.65 | | | | | | ALPHA: (82) implies: % 75.09/10.65 | | | | | | (83) ~ (all_333_0 = all_333_5) % 75.09/10.65 | | | | | | (84) ~ setIn(all_333_0, all_333_6) % 75.09/10.65 | | | | | | (85) ~ leq(nbr_proc, all_333_0) % 75.09/10.65 | | | | | | (86) leq(all_65_17, all_333_0) % 75.09/10.65 | | | | | | (87) host(all_123_2) = all_333_5 % 75.09/10.65 | | | | | | (88) index(down, nbr_proc) = all_333_6 % 75.09/10.65 | | | | | | % 75.09/10.65 | | | | | | REDUCE: (77), (87) imply: % 75.09/10.65 | | | | | | (89) host(all_65_13) = all_333_5 % 75.09/10.65 | | | | | | % 75.09/10.65 | | | | | | REDUCE: (46), (86) imply: % 75.09/10.65 | | | | | | (90) leq(all_59_0, all_333_0) % 75.09/10.65 | | | | | | % 75.09/10.65 | | | | | | GROUND_INST: instantiating (10) with all_65_9, all_333_5, all_65_13, % 75.09/10.65 | | | | | | simplifying with (32), (89) gives: % 75.09/10.65 | | | | | | (91) all_333_5 = all_65_9 % 75.09/10.65 | | | | | | % 75.09/10.65 | | | | | | GROUND_INST: instantiating (12) with all_65_5, all_333_6, nbr_proc, % 75.09/10.65 | | | | | | down, simplifying with (64), (88) gives: % 75.09/10.65 | | | | | | (92) all_333_6 = all_65_5 % 75.09/10.65 | | | | | | % 75.09/10.65 | | | | | | REDUCE: (83), (91) imply: % 75.09/10.65 | | | | | | (93) ~ (all_333_0 = all_65_9) % 75.09/10.65 | | | | | | % 75.09/10.65 | | | | | | REDUCE: (84), (92) imply: % 75.09/10.65 | | | | | | (94) ~ setIn(all_333_0, all_65_5) % 75.09/10.65 | | | | | | % 75.09/10.65 | | | | | | GROUND_INST: instantiating (42) with all_333_0, simplifying with % 75.09/10.65 | | | | | | (79), (94) gives: % 75.09/10.65 | | | | | | (95) all_333_0 = all_65_9 | ~ leq(all_65_17, all_333_0) | % 75.09/10.65 | | | | | | leq(all_65_12, all_333_0) % 75.09/10.65 | | | | | | % 75.09/10.65 | | | | | | BETA: splitting (95) gives: % 75.09/10.65 | | | | | | % 75.09/10.65 | | | | | | Case 1: % 75.09/10.65 | | | | | | | % 75.09/10.65 | | | | | | | (96) ~ leq(all_65_17, all_333_0) % 75.09/10.65 | | | | | | | % 75.09/10.65 | | | | | | | REDUCE: (46), (96) imply: % 75.09/10.65 | | | | | | | (97) ~ leq(all_59_0, all_333_0) % 75.09/10.65 | | | | | | | % 75.09/10.65 | | | | | | | PRED_UNIFY: (90), (97) imply: % 75.09/10.65 | | | | | | | (98) $false % 75.09/10.65 | | | | | | | % 75.09/10.65 | | | | | | | CLOSE: (98) is inconsistent. % 75.09/10.65 | | | | | | | % 75.09/10.65 | | | | | | Case 2: % 75.09/10.65 | | | | | | | % 75.09/10.65 | | | | | | | (99) all_333_0 = all_65_9 | leq(all_65_12, all_333_0) % 75.09/10.65 | | | | | | | % 75.09/10.65 | | | | | | | BETA: splitting (99) gives: % 75.09/10.65 | | | | | | | % 75.09/10.65 | | | | | | | Case 1: % 75.09/10.65 | | | | | | | | % 75.09/10.65 | | | | | | | | (100) leq(all_65_12, all_333_0) % 75.09/10.65 | | | | | | | | % 75.09/10.65 | | | | | | | | REDUCE: (57), (100) imply: % 75.09/10.65 | | | | | | | | (101) leq(nbr_proc, all_333_0) % 75.09/10.65 | | | | | | | | % 75.09/10.65 | | | | | | | | PRED_UNIFY: (85), (101) imply: % 75.09/10.65 | | | | | | | | (102) $false % 75.09/10.65 | | | | | | | | % 75.09/10.65 | | | | | | | | CLOSE: (102) is inconsistent. % 75.09/10.65 | | | | | | | | % 75.09/10.65 | | | | | | | Case 2: % 75.09/10.65 | | | | | | | | % 75.09/10.66 | | | | | | | | (103) all_333_0 = all_65_9 % 75.09/10.66 | | | | | | | | % 75.09/10.66 | | | | | | | | REDUCE: (93), (103) imply: % 75.09/10.66 | | | | | | | | (104) $false % 75.09/10.66 | | | | | | | | % 75.09/10.66 | | | | | | | | CLOSE: (104) is inconsistent. % 75.09/10.66 | | | | | | | | % 75.09/10.66 | | | | | | | End of split % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | End of split % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | Case 2: % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | (105) ~ (all_333_1 = norm) & index(status, all_65_0) = all_333_1 % 75.09/10.66 | | | | | | & $i(all_333_1) % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | ALPHA: (105) implies: % 75.09/10.66 | | | | | | (106) ~ (all_333_1 = norm) % 75.09/10.66 | | | | | | (107) index(status, all_65_0) = all_333_1 % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | GROUND_INST: instantiating (12) with norm, all_333_1, all_65_0, % 75.09/10.66 | | | | | | status, simplifying with (39), (107) gives: % 75.09/10.66 | | | | | | (108) all_333_1 = norm % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | REDUCE: (106), (108) imply: % 75.09/10.66 | | | | | | (109) $false % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | CLOSE: (109) is inconsistent. % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | End of split % 75.09/10.66 | | | | | % 75.09/10.66 | | | | Case 2: % 75.09/10.66 | | | | | % 75.09/10.66 | | | | | (110) ( ~ (all_333_2 = all_65_0) & index(ldr, all_65_0) = all_333_2 % 75.09/10.66 | | | | | & $i(all_333_2)) | ( ~ (all_333_3 = elec_1) & index(status, % 75.09/10.66 | | | | | nbr_proc) = all_333_3 & $i(all_333_3)) | (queue(nbr_proc) % 75.09/10.66 | | | | | = all_333_4 & $i(all_333_4) & ~ elem(all_65_10, % 75.09/10.66 | | | | | all_333_4)) % 75.09/10.66 | | | | | % 75.09/10.66 | | | | | BETA: splitting (110) gives: % 75.09/10.66 | | | | | % 75.09/10.66 | | | | | Case 1: % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | (111) ~ (all_333_2 = all_65_0) & index(ldr, all_65_0) = % 75.09/10.66 | | | | | | all_333_2 & $i(all_333_2) % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | ALPHA: (111) implies: % 75.09/10.66 | | | | | | (112) ~ (all_333_2 = all_65_0) % 75.09/10.66 | | | | | | (113) index(ldr, all_65_0) = all_333_2 % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | GROUND_INST: instantiating (12) with all_65_0, all_333_2, all_65_0, % 75.09/10.66 | | | | | | ldr, simplifying with (40), (113) gives: % 75.09/10.66 | | | | | | (114) all_333_2 = all_65_0 % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | REDUCE: (112), (114) imply: % 75.09/10.66 | | | | | | (115) $false % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | CLOSE: (115) is inconsistent. % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | Case 2: % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | (116) ( ~ (all_333_3 = elec_1) & index(status, nbr_proc) = % 75.09/10.66 | | | | | | all_333_3 & $i(all_333_3)) | (queue(nbr_proc) = all_333_4 % 75.09/10.66 | | | | | | & $i(all_333_4) & ~ elem(all_65_10, all_333_4)) % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | BETA: splitting (116) gives: % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | | Case 1: % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | | (117) ~ (all_333_3 = elec_1) & index(status, nbr_proc) = % 75.09/10.66 | | | | | | | all_333_3 & $i(all_333_3) % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | | ALPHA: (117) implies: % 75.09/10.66 | | | | | | | (118) ~ (all_333_3 = elec_1) % 75.09/10.66 | | | | | | | (119) index(status, nbr_proc) = all_333_3 % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | | GROUND_INST: instantiating (12) with elec_1, all_333_3, nbr_proc, % 75.09/10.66 | | | | | | | status, simplifying with (65), (119) gives: % 75.09/10.66 | | | | | | | (120) all_333_3 = elec_1 % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | | REDUCE: (118), (120) imply: % 75.09/10.66 | | | | | | | (121) $false % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | | CLOSE: (121) is inconsistent. % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | Case 2: % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | | (122) queue(nbr_proc) = all_333_4 & $i(all_333_4) & ~ % 75.09/10.66 | | | | | | | elem(all_65_10, all_333_4) % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | | ALPHA: (122) implies: % 75.09/10.66 | | | | | | | (123) ~ elem(all_65_10, all_333_4) % 75.09/10.66 | | | | | | | (124) queue(nbr_proc) = all_333_4 % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | | GROUND_INST: instantiating (9) with all_65_11, all_333_4, % 75.09/10.66 | | | | | | | nbr_proc, simplifying with (67), (124) gives: % 75.09/10.66 | | | | | | | (125) all_333_4 = all_65_11 % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | | REDUCE: (123), (125) imply: % 75.09/10.66 | | | | | | | (126) ~ elem(all_65_10, all_65_11) % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | | PRED_UNIFY: (53), (126) imply: % 75.09/10.66 | | | | | | | (127) $false % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | | CLOSE: (127) is inconsistent. % 75.09/10.66 | | | | | | | % 75.09/10.66 | | | | | | End of split % 75.09/10.66 | | | | | | % 75.09/10.66 | | | | | End of split % 75.09/10.66 | | | | | % 75.09/10.66 | | | | End of split % 75.09/10.66 | | | | % 75.09/10.66 | | | Case 2: % 75.09/10.66 | | | | % 75.09/10.66 | | | | (128) all_123_1 = all_65_10 & m_Halt(all_123_2) = all_65_10 % 75.09/10.66 | | | | % 75.09/10.66 | | | | ALPHA: (128) implies: % 75.09/10.66 | | | | (129) m_Halt(all_123_2) = all_65_10 % 75.09/10.66 | | | | % 75.09/10.66 | | | | GROUND_INST: instantiating (axiom_17) with all_65_13, all_123_2, % 75.09/10.66 | | | | all_65_10, simplifying with (24), (36), (61), (129) gives: % 75.09/10.66 | | | | (130) $false % 75.09/10.66 | | | | % 75.09/10.66 | | | | CLOSE: (130) is inconsistent. % 75.09/10.66 | | | | % 75.09/10.66 | | | End of split % 75.09/10.66 | | | % 75.09/10.66 | | End of split % 75.09/10.66 | | % 75.09/10.66 | End of split % 75.09/10.66 | % 75.09/10.66 End of proof % 75.35/10.66 % SZS output end Proof for theBenchmark % 75.35/10.66 % 75.35/10.66 10059ms %------------------------------------------------------------------------------