%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV470+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 : n003.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 22:56:37 EDT 2023 % Result : Theorem 97.03s 13.35s % Output : Proof 98.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWV470+1 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n003.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 08:04:25 EDT 2023 % 0.12/0.33 % CPUTime : % 0.54/0.59 ________ _____ % 0.54/0.59 ___ __ \_________(_)________________________________ % 0.54/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.54/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.54/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.54/0.59 % 0.54/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.54/0.59 (2023-06-19) % 0.54/0.59 % 0.54/0.59 (c) Philipp Rümmer, 2009-2023 % 0.54/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.54/0.59 Amanda Stjerna. % 0.54/0.59 Free software under BSD-3-Clause. % 0.54/0.59 % 0.54/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.54/0.59 % 0.54/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.54/0.60 Running up to 7 provers in parallel. % 0.54/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.54/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.54/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.54/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.54/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.54/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.54/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.55/1.20 Prover 4: Preprocessing ... % 3.55/1.20 Prover 1: Preprocessing ... % 3.79/1.24 Prover 5: Preprocessing ... % 3.79/1.24 Prover 2: Preprocessing ... % 3.79/1.24 Prover 6: Preprocessing ... % 3.79/1.24 Prover 0: Preprocessing ... % 3.79/1.24 Prover 3: Preprocessing ... % 10.52/2.17 Prover 6: Proving ... % 10.52/2.18 Prover 1: Constructing countermodel ... % 10.52/2.18 Prover 3: Constructing countermodel ... % 11.19/2.24 Prover 5: Proving ... % 11.92/2.31 Prover 2: Proving ... % 12.48/2.41 Prover 4: Constructing countermodel ... % 13.22/2.47 Prover 0: Proving ... % 15.73/2.81 Prover 3: gave up % 15.73/2.82 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.36/2.95 Prover 7: Preprocessing ... % 20.72/3.46 Prover 7: Warning: ignoring some quantifiers % 20.72/3.49 Prover 7: Constructing countermodel ... % 22.18/3.66 Prover 1: gave up % 22.18/3.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.27/3.78 Prover 8: Preprocessing ... % 24.19/3.91 Prover 8: Warning: ignoring some quantifiers % 24.46/3.92 Prover 8: Constructing countermodel ... % 32.22/4.95 Prover 8: gave up % 32.22/4.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 32.56/5.00 Prover 9: Preprocessing ... % 34.87/5.35 Prover 9: Constructing countermodel ... % 59.90/8.54 Prover 2: stopped % 59.90/8.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 60.62/8.61 Prover 10: Preprocessing ... % 61.21/8.75 Prover 10: Warning: ignoring some quantifiers % 61.21/8.75 Prover 10: Constructing countermodel ... % 97.03/13.33 Prover 10: Found proof (size 127) % 97.03/13.33 Prover 10: proved (4780ms) % 97.03/13.33 Prover 5: stopped % 97.03/13.33 Prover 9: stopped % 97.03/13.33 Prover 6: stopped % 97.03/13.33 Prover 7: stopped % 97.03/13.34 Prover 0: stopped % 97.03/13.35 Prover 4: stopped % 97.03/13.35 % 97.03/13.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 97.03/13.35 % 97.03/13.36 % SZS output start Proof for theBenchmark % 97.03/13.36 Assumptions after simplification: % 97.03/13.36 --------------------------------- % 97.03/13.36 % 97.03/13.36 (axiom_03) % 97.64/13.39 $i(nbr_proc) & $i(zero) & ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0, % 97.64/13.39 nbr_proc)) % 97.64/13.39 % 97.64/13.39 (axiom_12) % 97.64/13.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v2) = v3) % 97.64/13.39 | ~ (m_Ack(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 97.64/13.39 % 97.64/13.39 (axiom_17) % 97.64/13.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~ % 97.64/13.39 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 97.64/13.39 % 97.64/13.39 (axiom_30) % 97.64/13.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v1) = v2) | ~ % 97.64/13.39 (m_Down(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 97.64/13.39 % 97.64/13.39 (axiom_46) % 97.80/13.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.80/13.40 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) | % 97.80/13.40 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 97.80/13.40 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 97.80/13.40 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) % 97.80/13.40 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2)) % 97.80/13.40 % 97.80/13.40 (axiom_47) % 97.80/13.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.80/13.40 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) | % 97.80/13.40 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 97.80/13.40 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 97.80/13.40 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (snoc(v1, v0) % 97.80/13.40 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2)) % 97.80/13.40 % 97.80/13.40 (axiom_48) % 97.80/13.40 ! [v0: $i] : ! [v1: $i] : ( ~ (m_Down(v1) = v0) | ~ $i(v1) | ~ $i(v0) | % 97.80/13.40 pidElem(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (m_Halt(v1) = v0) | ~ $i(v1) % 97.80/13.40 | ~ $i(v0) | pidElem(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ? % 97.80/13.40 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) = % 97.80/13.40 v0) | (v2 = v0 & m_Halt(v1) = v0)))) % 97.80/13.40 % 97.80/13.40 (conj) % 97.80/13.42 $i(down) & $i(ldr) & $i(elid) & $i(status) & $i(alive) & $i(norm) & $i(wait) & % 97.80/13.42 $i(elec_1) & $i(elec_2) & $i(nbr_proc) & $i(zero) & ? [v0: $i] : ? [v1: $i] % 97.80/13.42 : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? % 97.80/13.42 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 97.80/13.42 $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: % 97.80/13.42 $i] : ( ~ (v4 = nbr_proc) & index(down, nbr_proc) = v13 & index(status, % 97.80/13.42 nbr_proc) = elec_1 & snoc(v1, v7) = v8 & cons(v6, v1) = v5 & m_Down(v11) = % 97.80/13.42 v15 & m_Down(v10) = v17 & m_Halt(v3) = v6 & s(zero) = v0 & m_Ack(v3, v2) = % 97.80/13.42 v7 & host(v12) = nbr_proc & host(v11) = v14 & host(v10) = nbr_proc & % 97.80/13.42 host(v9) = v4 & host(v3) = v4 & host(v2) = v4 & queue(v4) = v5 & % 97.80/13.42 queue(nbr_proc) = v16 & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & % 97.80/13.42 $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 97.80/13.42 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & setIn(v9, alive) & setIn(v2, % 97.80/13.42 alive) & elem(v17, v8) & elem(v15, v16) & ! [v18: $i] : ! [v19: $i] : ! % 97.80/13.42 [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! % 97.80/13.42 [v25: $i] : (v23 = v22 | ~ (m_Down(v21) = v24) | ~ (m_Down(v19) = v25) | % 97.80/13.42 ~ (host(v20) = v22) | ~ (host(v18) = v23) | ~ $i(v21) | ~ $i(v20) | ~ % 97.80/13.42 $i(v19) | ~ $i(v18) | ~ setIn(v20, alive) | ~ setIn(v18, alive) | ? % 97.80/13.42 [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( ~ (v27 = v22) % 97.80/13.42 & host(v21) = v27 & $i(v27)) | ( ~ (v26 = v23) & host(v19) = v26 & % 97.80/13.42 $i(v26)) | (queue(v23) = v28 & $i(v28) & ~ elem(v24, v28)) | % 97.80/13.42 (queue(v22) = v29 & $i(v29) & ~ elem(v25, v29)))) & ! [v18: $i] : ! % 97.80/13.42 [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! % 97.80/13.42 [v24: $i] : (v23 = v22 | ~ (m_Down(v21) = v24) | ~ (host(v20) = v22) | ~ % 97.80/13.42 (host(v19) = v23) | ~ (host(v18) = v23) | ~ $i(v21) | ~ $i(v20) | ~ % 97.80/13.42 $i(v19) | ~ $i(v18) | ~ setIn(v20, alive) | ~ setIn(v18, alive) | ? % 97.80/13.42 [v25: $i] : ? [v26: $i] : ? [v27: $i] : (( ~ (v25 = v22) & host(v21) = % 97.80/13.42 v25 & $i(v25)) | (index(down, v22) = v27 & $i(v27) & ~ setIn(v23, % 97.80/13.42 v27)) | (queue(v23) = v26 & $i(v26) & ~ elem(v24, v26)))) & ! % 97.80/13.42 [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! % 97.80/13.42 [v23: $i] : ! [v24: $i] : ( ~ (m_Down(v20) = v22) | ~ (m_Down(v19) = v23) % 97.80/13.42 | ~ (host(v21) = nbr_proc) | ~ (host(v18) = v24) | ~ $i(v21) | ~ % 97.80/13.42 $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v18, alive) | ? [v25: $i] : % 97.80/13.42 ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : % 97.80/13.42 ($i(v30) & ((v27 = v16 & ~ elem(v22, v16)) | (v25 = v13 & ~ (v30 = v26) % 97.80/13.42 & host(v20) = v26 & $i(v26) & leq(v0, v30) & ~ leq(nbr_proc, v30) & % 97.80/13.42 ~ setIn(v30, v13)) | ( ~ (v28 = nbr_proc) & host(v19) = v28 & % 97.80/13.42 $i(v28)) | (queue(v24) = v29 & $i(v29) & ~ elem(v23, v29))))) & ! % 97.80/13.42 [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! % 97.80/13.42 [v23: $i] : (v22 = v21 | ~ (m_Down(v18) = v23) | ~ (host(v20) = v21) | ~ % 97.80/13.42 (host(v19) = v22) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v20, % 97.80/13.42 alive) | ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? % 97.80/13.42 [v28: $i] : (( ~ (v27 = v22) & index(elid, v21) = v26 & host(v26) = v27 & % 97.80/13.42 $i(v27) & $i(v26)) | ( ~ (v25 = wait) & index(status, v21) = v25 & % 97.80/13.42 $i(v25)) | ( ~ (v24 = v21) & host(v18) = v24 & $i(v24)) | (queue(v22) % 97.80/13.42 = v28 & $i(v28) & ~ elem(v23, v28)))) & ! [v18: $i] : ! [v19: $i] : % 97.80/13.42 ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : (v22 = v21 | ~ % 97.80/13.42 (m_Down(v18) = v23) | ~ (host(v20) = v21) | ~ (host(v19) = v22) | ~ % 97.80/13.42 $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v20, alive) | ? [v24: $i] : % 97.80/13.42 ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : (( ~ (v26 = norm) & % 97.80/13.42 index(status, v21) = v26 & $i(v26)) | ( ~ (v25 = v22) & index(ldr, % 97.80/13.42 v21) = v25 & $i(v25)) | ( ~ (v24 = v21) & host(v18) = v24 & $i(v24)) % 97.80/13.42 | (queue(v22) = v27 & $i(v27) & ~ elem(v23, v27)))) & ! [v18: $i] : ! % 97.80/13.42 [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (m_Ldr(v19) = v20) | ~ % 97.80/13.42 (host(v18) = v21) | ~ $i(v19) | ~ $i(v18) | ? [v22: $i] : ? [v23: $i] % 97.80/13.42 : ((host(v19) = v23 & $i(v23) & ~ leq(v21, v23)) | (queue(v21) = v22 & % 97.80/13.42 $i(v22) & ~ elem(v20, v22)))) & ! [v18: $i] : ! [v19: $i] : ! % 97.80/13.42 [v20: $i] : ! [v21: $i] : ( ~ (m_Down(v19) = v20) | ~ (host(v18) = v21) | % 97.80/13.42 ~ $i(v19) | ~ $i(v18) | ? [v22: $i] : ? [v23: $i] : (( ~ (v23 = v21) & % 97.80/13.42 host(v19) = v23 & $i(v23)) | (queue(v21) = v22 & $i(v22) & ~ % 97.80/13.42 elem(v20, v22)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : (v19 % 97.80/13.42 = v18 | ~ (host(v19) = v20) | ~ (host(v18) = v20) | ~ $i(v19) | ~ % 97.80/13.42 $i(v18) | ~ setIn(v19, alive) | ~ setIn(v18, alive)) & ! [v18: $i] : ! % 97.80/13.42 [v19: $i] : ! [v20: $i] : ( ~ (m_NotNorm(v18) = v20) | ~ (host(v19) = % 97.80/13.42 nbr_proc) | ~ $i(v19) | ~ $i(v18) | ~ elem(v20, v16)) & ! [v18: $i] % 97.80/13.42 : ! [v19: $i] : ( ~ (host(v18) = v19) | ~ $i(v18) | ~ setIn(v18, alive) | % 97.80/13.42 ? [v20: $i] : ? [v21: $i] : ((v21 = v18 & index(elid, v19) = v18) | ( ~ % 97.80/13.42 (v20 = elec_1) & ~ (v20 = elec_2) & index(status, v19) = v20 & % 97.80/13.42 $i(v20)))) & ! [v18: $i] : (v18 = v14 | ~ $i(v18) | ~ leq(v0, v18) % 97.80/13.42 | leq(nbr_proc, v18) | setIn(v18, v13))) % 97.80/13.42 % 97.80/13.42 (function-axioms) % 97.80/13.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.80/13.43 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 97.80/13.43 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3, % 97.80/13.43 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 97.80/13.43 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! % 97.80/13.43 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~ % 97.80/13.43 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 97.80/13.43 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 97.80/13.43 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i] % 97.80/13.43 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) = % 97.80/13.43 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) = % 97.80/13.43 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 97.80/13.43 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 97.80/13.43 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & ! % 97.80/13.43 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~ % 97.80/13.43 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 97.80/13.43 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 97.80/13.43 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & ! % 97.80/13.43 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~ % 97.80/13.43 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 97.80/13.43 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 97.80/13.43 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1: % 97.80/13.43 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0)) % 97.80/13.43 % 97.80/13.43 Further assumptions not needed in the proof: % 97.80/13.43 -------------------------------------------- % 97.80/13.43 axiom, axiom_01, axiom_02, axiom_04, axiom_05, axiom_06, axiom_07, axiom_08, % 97.80/13.43 axiom_09, axiom_10, axiom_11, axiom_13, axiom_14, axiom_15, axiom_16, axiom_18, % 97.80/13.43 axiom_19, axiom_20, axiom_21, axiom_22, axiom_23, axiom_24, axiom_25, axiom_26, % 97.80/13.43 axiom_27, axiom_28, axiom_29, axiom_31, axiom_32, axiom_33, axiom_34, axiom_35, % 97.80/13.43 axiom_36, axiom_37, axiom_38, axiom_39, axiom_40, axiom_41, axiom_42, axiom_43, % 97.80/13.43 axiom_44, axiom_45, axiom_49, axiom_50, axiom_51, axiom_52, axiom_53, axiom_54, % 97.80/13.43 axiom_55, axiom_56, axiom_57, axiom_58, axiom_59, axiom_60, axiom_61, axiom_62, % 97.80/13.43 axiom_63, axiom_64, axiom_65 % 97.80/13.43 % 97.80/13.43 Those formulas are unsatisfiable: % 97.80/13.43 --------------------------------- % 97.80/13.43 % 97.80/13.43 Begin of proof % 97.80/13.43 | % 97.80/13.43 | ALPHA: (axiom_03) implies: % 97.80/13.43 | (1) ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0, nbr_proc)) % 97.80/13.43 | % 97.80/13.43 | ALPHA: (axiom_46) implies: % 97.80/13.43 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, % 97.80/13.43 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 97.80/13.43 | elem(v0, v3)) % 97.80/13.43 | % 97.80/13.43 | ALPHA: (axiom_47) implies: % 97.80/13.43 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.80/13.43 | (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, % 97.80/13.43 | v3) | elem(v0, v2)) % 97.80/13.43 | % 97.80/13.43 | ALPHA: (axiom_48) implies: % 97.80/13.43 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ? [v1: $i] : ? [v2: $i] : % 97.80/13.43 | ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) = v0) | (v2 = v0 & % 97.80/13.43 | m_Halt(v1) = v0)))) % 97.80/13.43 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (m_Down(v1) = v0) | ~ $i(v1) | ~ % 97.80/13.43 | $i(v0) | pidElem(v0)) % 97.80/13.43 | % 97.80/13.43 | ALPHA: (conj) implies: % 97.80/13.45 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.80/13.45 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 97.80/13.45 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 97.80/13.45 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ( ~ (v4 = nbr_proc) & % 97.80/13.45 | index(down, nbr_proc) = v13 & index(status, nbr_proc) = elec_1 & % 97.80/13.45 | snoc(v1, v7) = v8 & cons(v6, v1) = v5 & m_Down(v11) = v15 & % 97.80/13.45 | m_Down(v10) = v17 & m_Halt(v3) = v6 & s(zero) = v0 & m_Ack(v3, v2) = % 97.80/13.45 | v7 & host(v12) = nbr_proc & host(v11) = v14 & host(v10) = nbr_proc & % 97.80/13.45 | host(v9) = v4 & host(v3) = v4 & host(v2) = v4 & queue(v4) = v5 & % 97.80/13.45 | queue(nbr_proc) = v16 & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 97.80/13.45 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 97.80/13.45 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 97.80/13.45 | setIn(v9, alive) & setIn(v2, alive) & elem(v17, v8) & elem(v15, v16) % 97.80/13.45 | & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! % 97.80/13.45 | [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : (v23 = v22 | % 97.80/13.45 | ~ (m_Down(v21) = v24) | ~ (m_Down(v19) = v25) | ~ (host(v20) = % 97.80/13.45 | v22) | ~ (host(v18) = v23) | ~ $i(v21) | ~ $i(v20) | ~ % 97.80/13.45 | $i(v19) | ~ $i(v18) | ~ setIn(v20, alive) | ~ setIn(v18, alive) % 97.80/13.45 | | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( ~ % 97.80/13.45 | (v27 = v22) & host(v21) = v27 & $i(v27)) | ( ~ (v26 = v23) & % 97.80/13.45 | host(v19) = v26 & $i(v26)) | (queue(v23) = v28 & $i(v28) & ~ % 97.80/13.45 | elem(v24, v28)) | (queue(v22) = v29 & $i(v29) & ~ elem(v25, % 97.80/13.45 | v29)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! % 97.80/13.45 | [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : (v23 = v22 | % 97.80/13.45 | ~ (m_Down(v21) = v24) | ~ (host(v20) = v22) | ~ (host(v19) = % 97.80/13.45 | v23) | ~ (host(v18) = v23) | ~ $i(v21) | ~ $i(v20) | ~ % 97.80/13.45 | $i(v19) | ~ $i(v18) | ~ setIn(v20, alive) | ~ setIn(v18, alive) % 97.80/13.45 | | ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : (( ~ (v25 = v22) & % 97.80/13.45 | host(v21) = v25 & $i(v25)) | (index(down, v22) = v27 & $i(v27) % 97.80/13.45 | & ~ setIn(v23, v27)) | (queue(v23) = v26 & $i(v26) & ~ % 97.80/13.45 | elem(v24, v26)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] % 97.80/13.45 | : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ % 97.80/13.45 | (m_Down(v20) = v22) | ~ (m_Down(v19) = v23) | ~ (host(v21) = % 97.80/13.45 | nbr_proc) | ~ (host(v18) = v24) | ~ $i(v21) | ~ $i(v20) | ~ % 97.80/13.45 | $i(v19) | ~ $i(v18) | ~ setIn(v18, alive) | ? [v25: $i] : ? % 97.80/13.45 | [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: % 97.80/13.45 | $i] : ($i(v30) & ((v27 = v16 & ~ elem(v22, v16)) | (v25 = v13 & % 97.80/13.45 | ~ (v30 = v26) & host(v20) = v26 & $i(v26) & leq(v0, v30) & ~ % 97.80/13.45 | leq(nbr_proc, v30) & ~ setIn(v30, v13)) | ( ~ (v28 = % 97.80/13.45 | nbr_proc) & host(v19) = v28 & $i(v28)) | (queue(v24) = v29 % 97.80/13.45 | & $i(v29) & ~ elem(v23, v29))))) & ! [v18: $i] : ! [v19: % 97.80/13.45 | $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : % 97.80/13.45 | (v22 = v21 | ~ (m_Down(v18) = v23) | ~ (host(v20) = v21) | ~ % 97.80/13.45 | (host(v19) = v22) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ % 97.80/13.45 | setIn(v20, alive) | ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? % 97.80/13.45 | [v27: $i] : ? [v28: $i] : (( ~ (v27 = v22) & index(elid, v21) = % 97.80/13.45 | v26 & host(v26) = v27 & $i(v27) & $i(v26)) | ( ~ (v25 = wait) & % 97.80/13.45 | index(status, v21) = v25 & $i(v25)) | ( ~ (v24 = v21) & % 97.80/13.45 | host(v18) = v24 & $i(v24)) | (queue(v22) = v28 & $i(v28) & ~ % 97.80/13.45 | elem(v23, v28)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] % 97.80/13.45 | : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : (v22 = v21 | ~ % 97.80/13.45 | (m_Down(v18) = v23) | ~ (host(v20) = v21) | ~ (host(v19) = v22) | % 97.80/13.45 | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v20, alive) | ? % 97.80/13.45 | [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : (( ~ (v26 % 97.80/13.45 | = norm) & index(status, v21) = v26 & $i(v26)) | ( ~ (v25 = % 97.80/13.45 | v22) & index(ldr, v21) = v25 & $i(v25)) | ( ~ (v24 = v21) & % 97.80/13.45 | host(v18) = v24 & $i(v24)) | (queue(v22) = v27 & $i(v27) & ~ % 97.80/13.45 | elem(v23, v27)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] % 97.80/13.45 | : ! [v21: $i] : ( ~ (m_Ldr(v19) = v20) | ~ (host(v18) = v21) | ~ % 97.80/13.45 | $i(v19) | ~ $i(v18) | ? [v22: $i] : ? [v23: $i] : ((host(v19) = % 97.80/13.45 | v23 & $i(v23) & ~ leq(v21, v23)) | (queue(v21) = v22 & $i(v22) % 97.80/13.45 | & ~ elem(v20, v22)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: % 97.80/13.45 | $i] : ! [v21: $i] : ( ~ (m_Down(v19) = v20) | ~ (host(v18) = v21) % 97.80/13.45 | | ~ $i(v19) | ~ $i(v18) | ? [v22: $i] : ? [v23: $i] : (( ~ (v23 % 97.80/13.45 | = v21) & host(v19) = v23 & $i(v23)) | (queue(v21) = v22 & % 97.80/13.45 | $i(v22) & ~ elem(v20, v22)))) & ! [v18: $i] : ! [v19: $i] : % 97.80/13.45 | ! [v20: $i] : (v19 = v18 | ~ (host(v19) = v20) | ~ (host(v18) = % 97.80/13.45 | v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v19, alive) | ~ % 97.80/13.45 | setIn(v18, alive)) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( % 97.80/13.45 | ~ (m_NotNorm(v18) = v20) | ~ (host(v19) = nbr_proc) | ~ $i(v19) | % 97.80/13.45 | ~ $i(v18) | ~ elem(v20, v16)) & ! [v18: $i] : ! [v19: $i] : ( ~ % 97.80/13.45 | (host(v18) = v19) | ~ $i(v18) | ~ setIn(v18, alive) | ? [v20: % 97.80/13.45 | $i] : ? [v21: $i] : ((v21 = v18 & index(elid, v19) = v18) | ( ~ % 97.80/13.45 | (v20 = elec_1) & ~ (v20 = elec_2) & index(status, v19) = v20 & % 97.80/13.45 | $i(v20)))) & ! [v18: $i] : (v18 = v14 | ~ $i(v18) | ~ % 97.80/13.45 | leq(v0, v18) | leq(nbr_proc, v18) | setIn(v18, v13))) % 97.80/13.45 | % 97.80/13.45 | ALPHA: (function-axioms) implies: % 97.80/13.45 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = % 97.80/13.45 | v1) | ~ (queue(v2) = v0)) % 97.80/13.45 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1) % 97.80/13.45 | | ~ (host(v2) = v0)) % 97.80/13.45 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 97.80/13.45 | ~ (s(v2) = v0)) % 97.80/13.45 | % 97.80/13.45 | DELTA: instantiating (1) with fresh symbol all_59_0 gives: % 97.80/13.45 | (10) s(zero) = all_59_0 & $i(all_59_0) & leq(all_59_0, nbr_proc) % 97.80/13.45 | % 97.80/13.45 | ALPHA: (10) implies: % 97.80/13.45 | (11) s(zero) = all_59_0 % 97.80/13.45 | % 97.80/13.45 | DELTA: instantiating (6) with fresh symbols all_65_0, all_65_1, all_65_2, % 97.80/13.45 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9, % 97.80/13.45 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15, % 97.80/13.45 | all_65_16, all_65_17 gives: % 97.80/13.46 | (12) ~ (all_65_13 = nbr_proc) & index(down, nbr_proc) = all_65_4 & % 97.80/13.46 | index(status, nbr_proc) = elec_1 & snoc(all_65_16, all_65_10) = % 97.80/13.46 | all_65_9 & cons(all_65_11, all_65_16) = all_65_12 & m_Down(all_65_6) = % 97.80/13.46 | all_65_2 & m_Down(all_65_7) = all_65_0 & m_Halt(all_65_14) = all_65_11 % 97.80/13.46 | & s(zero) = all_65_17 & m_Ack(all_65_14, all_65_15) = all_65_10 & % 97.80/13.46 | host(all_65_5) = nbr_proc & host(all_65_6) = all_65_3 & host(all_65_7) % 97.80/13.46 | = nbr_proc & host(all_65_8) = all_65_13 & host(all_65_14) = all_65_13 % 97.80/13.46 | & host(all_65_15) = all_65_13 & queue(all_65_13) = all_65_12 & % 97.80/13.46 | queue(nbr_proc) = all_65_1 & $i(all_65_0) & $i(all_65_1) & % 97.80/13.46 | $i(all_65_2) & $i(all_65_3) & $i(all_65_4) & $i(all_65_5) & % 97.80/13.46 | $i(all_65_6) & $i(all_65_7) & $i(all_65_8) & $i(all_65_9) & % 97.80/13.46 | $i(all_65_10) & $i(all_65_11) & $i(all_65_12) & $i(all_65_13) & % 97.80/13.46 | $i(all_65_14) & $i(all_65_15) & $i(all_65_16) & $i(all_65_17) & % 97.80/13.46 | setIn(all_65_8, alive) & setIn(all_65_15, alive) & elem(all_65_0, % 97.80/13.46 | all_65_9) & elem(all_65_2, all_65_1) & ! [v0: $i] : ! [v1: $i] : % 97.80/13.46 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 97.80/13.46 | ! [v7: $i] : (v5 = v4 | ~ (m_Down(v3) = v6) | ~ (m_Down(v1) = v7) | % 97.80/13.46 | ~ (host(v2) = v4) | ~ (host(v0) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 97.80/13.46 | $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? % 97.80/13.46 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v9 = % 97.80/13.46 | v4) & host(v3) = v9 & $i(v9)) | ( ~ (v8 = v5) & host(v1) = v8 % 97.80/13.46 | & $i(v8)) | (queue(v5) = v10 & $i(v10) & ~ elem(v6, v10)) | % 97.80/13.46 | (queue(v4) = v11 & $i(v11) & ~ elem(v7, v11)))) & ! [v0: $i] : % 97.80/13.46 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 97.80/13.46 | ! [v6: $i] : (v5 = v4 | ~ (m_Down(v3) = v6) | ~ (host(v2) = v4) | ~ % 97.80/13.46 | (host(v1) = v5) | ~ (host(v0) = v5) | ~ $i(v3) | ~ $i(v2) | ~ % 97.80/13.46 | $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? % 97.80/13.46 | [v7: $i] : ? [v8: $i] : ? [v9: $i] : (( ~ (v7 = v4) & host(v3) = % 97.80/13.46 | v7 & $i(v7)) | (index(down, v4) = v9 & $i(v9) & ~ setIn(v5, % 97.80/13.46 | v9)) | (queue(v5) = v8 & $i(v8) & ~ elem(v6, v8)))) & ! [v0: % 97.80/13.46 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 97.80/13.46 | [v5: $i] : ! [v6: $i] : ( ~ (m_Down(v2) = v4) | ~ (m_Down(v1) = v5) % 97.80/13.46 | | ~ (host(v3) = nbr_proc) | ~ (host(v0) = v6) | ~ $i(v3) | ~ % 97.80/13.46 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v0, alive) | ? [v7: int] % 97.80/13.46 | : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: $i] : ? % 97.80/13.46 | [v12: $i] : ($i(v12) & ((v9 = all_65_1 & ~ elem(v4, all_65_1)) | % 97.80/13.46 | (v7 = all_65_4 & ~ (v12 = v8) & host(v2) = v8 & $i(v8) & % 97.80/13.46 | leq(all_65_17, v12) & ~ leq(nbr_proc, v12) & ~ setIn(v12, % 98.15/13.46 | all_65_4)) | ( ~ (v10 = nbr_proc) & host(v1) = v10 & % 98.15/13.46 | $i(v10)) | (queue(v6) = v11 & $i(v11) & ~ elem(v5, v11))))) & % 98.15/13.46 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 98.15/13.46 | ! [v5: $i] : (v4 = v3 | ~ (m_Down(v0) = v5) | ~ (host(v2) = v3) | ~ % 98.15/13.47 | (host(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, % 98.15/13.47 | alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 98.15/13.47 | ? [v10: $i] : (( ~ (v9 = v4) & index(elid, v3) = v8 & host(v8) = v9 % 98.15/13.47 | & $i(v9) & $i(v8)) | ( ~ (v7 = wait) & index(status, v3) = v7 & % 98.15/13.47 | $i(v7)) | ( ~ (v6 = v3) & host(v0) = v6 & $i(v6)) | (queue(v4) = % 98.15/13.47 | v10 & $i(v10) & ~ elem(v5, v10)))) & ! [v0: $i] : ! [v1: $i] % 98.15/13.47 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | % 98.15/13.47 | ~ (m_Down(v0) = v5) | ~ (host(v2) = v3) | ~ (host(v1) = v4) | ~ % 98.15/13.47 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ? [v6: $i] : % 98.15/13.47 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (( ~ (v8 = norm) & % 98.15/13.47 | index(status, v3) = v8 & $i(v8)) | ( ~ (v7 = v4) & index(ldr, % 98.15/13.47 | v3) = v7 & $i(v7)) | ( ~ (v6 = v3) & host(v0) = v6 & $i(v6)) | % 98.15/13.47 | (queue(v4) = v9 & $i(v9) & ~ elem(v5, v9)))) & ! [v0: $i] : ! % 98.15/13.47 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Ldr(v1) = v2) | ~ % 98.15/13.47 | (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] % 98.15/13.47 | : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3) = v4 & % 98.15/13.47 | $i(v4) & ~ elem(v2, v4)))) & ! [v0: $i] : ! [v1: $i] : ! % 98.15/13.47 | [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v1) = v2) | ~ (host(v0) = v3) | % 98.15/13.47 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & % 98.15/13.47 | host(v1) = v5 & $i(v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, % 98.15/13.47 | v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 98.15/13.47 | ~ (host(v1) = v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 98.15/13.47 | setIn(v1, alive) | ~ setIn(v0, alive)) & ! [v0: $i] : ! [v1: $i] % 98.15/13.47 | : ! [v2: $i] : ( ~ (m_NotNorm(v0) = v2) | ~ (host(v1) = nbr_proc) | % 98.15/13.47 | ~ $i(v1) | ~ $i(v0) | ~ elem(v2, all_65_1)) & ! [v0: $i] : ! % 98.15/13.47 | [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) | ~ setIn(v0, alive) | ? % 98.15/13.47 | [v2: $i] : ? [v3: $i] : ((v3 = v0 & index(elid, v1) = v0) | ( ~ (v2 % 98.15/13.47 | = elec_1) & ~ (v2 = elec_2) & index(status, v1) = v2 & % 98.15/13.47 | $i(v2)))) & ! [v0: any] : (v0 = all_65_3 | ~ $i(v0) | ~ % 98.15/13.47 | leq(all_65_17, v0) | leq(nbr_proc, v0) | setIn(v0, all_65_4)) % 98.15/13.47 | % 98.15/13.47 | ALPHA: (12) implies: % 98.15/13.47 | (13) elem(all_65_2, all_65_1) % 98.16/13.47 | (14) elem(all_65_0, all_65_9) % 98.16/13.47 | (15) setIn(all_65_15, alive) % 98.16/13.47 | (16) setIn(all_65_8, alive) % 98.16/13.47 | (17) $i(all_65_16) % 98.16/13.47 | (18) $i(all_65_15) % 98.16/13.47 | (19) $i(all_65_14) % 98.16/13.47 | (20) $i(all_65_11) % 98.16/13.47 | (21) $i(all_65_10) % 98.16/13.47 | (22) $i(all_65_8) % 98.16/13.47 | (23) $i(all_65_7) % 98.16/13.47 | (24) $i(all_65_6) % 98.16/13.47 | (25) $i(all_65_0) % 98.16/13.47 | (26) queue(nbr_proc) = all_65_1 % 98.16/13.47 | (27) queue(all_65_13) = all_65_12 % 98.16/13.47 | (28) host(all_65_15) = all_65_13 % 98.16/13.47 | (29) host(all_65_8) = all_65_13 % 98.16/13.47 | (30) host(all_65_7) = nbr_proc % 98.16/13.47 | (31) host(all_65_6) = all_65_3 % 98.16/13.47 | (32) m_Ack(all_65_14, all_65_15) = all_65_10 % 98.16/13.47 | (33) s(zero) = all_65_17 % 98.16/13.47 | (34) m_Down(all_65_7) = all_65_0 % 98.16/13.47 | (35) m_Down(all_65_6) = all_65_2 % 98.16/13.47 | (36) cons(all_65_11, all_65_16) = all_65_12 % 98.16/13.47 | (37) snoc(all_65_16, all_65_10) = all_65_9 % 98.16/13.47 | (38) ! [v0: any] : (v0 = all_65_3 | ~ $i(v0) | ~ leq(all_65_17, v0) | % 98.16/13.47 | leq(nbr_proc, v0) | setIn(v0, all_65_4)) % 98.16/13.47 | (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v1) = % 98.16/13.47 | v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 98.16/13.47 | alive) | ~ setIn(v0, alive)) % 98.16/13.47 | (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 98.16/13.47 | (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 98.16/13.47 | [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 & $i(v5)) | % 98.16/13.47 | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) % 98.16/13.47 | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 98.16/13.47 | ! [v5: $i] : ! [v6: $i] : ( ~ (m_Down(v2) = v4) | ~ (m_Down(v1) = % 98.16/13.47 | v5) | ~ (host(v3) = nbr_proc) | ~ (host(v0) = v6) | ~ $i(v3) | % 98.16/13.47 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v0, alive) | ? [v7: % 98.16/13.47 | int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: $i] : % 98.16/13.47 | ? [v12: $i] : ($i(v12) & ((v9 = all_65_1 & ~ elem(v4, all_65_1)) | % 98.16/13.47 | (v7 = all_65_4 & ~ (v12 = v8) & host(v2) = v8 & $i(v8) & % 98.16/13.47 | leq(all_65_17, v12) & ~ leq(nbr_proc, v12) & ~ setIn(v12, % 98.16/13.47 | all_65_4)) | ( ~ (v10 = nbr_proc) & host(v1) = v10 & % 98.16/13.47 | $i(v10)) | (queue(v6) = v11 & $i(v11) & ~ elem(v5, v11))))) % 98.16/13.47 | % 98.16/13.47 | GROUND_INST: instantiating (9) with all_59_0, all_65_17, zero, simplifying % 98.16/13.47 | with (11), (33) gives: % 98.16/13.47 | (42) all_65_17 = all_59_0 % 98.16/13.47 | % 98.16/13.47 | GROUND_INST: instantiating (39) with all_65_15, all_65_8, all_65_13, % 98.16/13.47 | simplifying with (15), (16), (18), (22), (28), (29) gives: % 98.16/13.47 | (43) all_65_8 = all_65_15 % 98.16/13.47 | % 98.16/13.47 | GROUND_INST: instantiating (40) with all_65_7, all_65_7, all_65_0, nbr_proc, % 98.16/13.47 | simplifying with (23), (30), (34) gives: % 98.16/13.48 | (44) ? [v0: $i] : ? [v1: $i] : (( ~ (v1 = nbr_proc) & host(all_65_7) = v1 % 98.16/13.48 | & $i(v1)) | (queue(nbr_proc) = v0 & $i(v0) & ~ elem(all_65_0, % 98.16/13.48 | v0))) % 98.16/13.48 | % 98.16/13.48 | GROUND_INST: instantiating (40) with all_65_15, all_65_7, all_65_0, all_65_13, % 98.16/13.48 | simplifying with (18), (23), (28), (34) gives: % 98.16/13.48 | (45) ? [v0: $i] : ? [v1: any] : (( ~ (v1 = all_65_13) & host(all_65_7) = % 98.16/13.48 | v1 & $i(v1)) | (queue(all_65_13) = v0 & $i(v0) & ~ elem(all_65_0, % 98.16/13.48 | v0))) % 98.16/13.48 | % 98.16/13.48 | GROUND_INST: instantiating (5) with all_65_0, all_65_7, simplifying with (23), % 98.16/13.48 | (25), (34) gives: % 98.16/13.48 | (46) pidElem(all_65_0) % 98.16/13.48 | % 98.16/13.48 | GROUND_INST: instantiating (41) with all_65_15, all_65_7, all_65_6, all_65_7, % 98.16/13.48 | all_65_2, all_65_0, all_65_13, simplifying with (15), (18), (23), % 98.16/13.48 | (24), (28), (30), (34), (35) gives: % 98.16/13.48 | (47) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] % 98.16/13.48 | : ? [v5: $i] : ($i(v5) & ((v2 = all_65_1 & ~ elem(all_65_2, % 98.16/13.48 | all_65_1)) | (v0 = all_65_4 & ~ (v5 = v1) & host(all_65_6) = % 98.16/13.48 | v1 & $i(v1) & leq(all_65_17, v5) & ~ leq(nbr_proc, v5) & ~ % 98.16/13.48 | setIn(v5, all_65_4)) | ( ~ (v3 = nbr_proc) & host(all_65_7) = v3 % 98.16/13.48 | & $i(v3)) | (queue(all_65_13) = v4 & $i(v4) & ~ elem(all_65_0, % 98.16/13.48 | v4)))) % 98.16/13.48 | % 98.16/13.48 | GROUND_INST: instantiating (40) with all_65_7, all_65_6, all_65_2, nbr_proc, % 98.16/13.48 | simplifying with (23), (24), (30), (35) gives: % 98.16/13.48 | (48) ? [v0: $i] : ? [v1: $i] : (( ~ (v1 = nbr_proc) & host(all_65_6) = v1 % 98.16/13.48 | & $i(v1)) | (queue(nbr_proc) = v0 & $i(v0) & ~ elem(all_65_2, % 98.16/13.48 | v0))) % 98.16/13.48 | % 98.16/13.48 | GROUND_INST: instantiating (3) with all_65_0, all_65_10, all_65_16, all_65_9, % 98.16/13.48 | simplifying with (14), (17), (21), (25), (37) gives: % 98.16/13.48 | (49) all_65_0 = all_65_10 | elem(all_65_0, all_65_16) % 98.16/13.48 | % 98.16/13.48 | DELTA: instantiating (44) with fresh symbols all_85_0, all_85_1 gives: % 98.16/13.48 | (50) ( ~ (all_85_0 = nbr_proc) & host(all_65_7) = all_85_0 & $i(all_85_0)) % 98.16/13.48 | | (queue(nbr_proc) = all_85_1 & $i(all_85_1) & ~ elem(all_65_0, % 98.16/13.48 | all_85_1)) % 98.16/13.48 | % 98.16/13.48 | DELTA: instantiating (45) with fresh symbols all_86_0, all_86_1 gives: % 98.16/13.48 | (51) ( ~ (all_86_0 = all_65_13) & host(all_65_7) = all_86_0 & $i(all_86_0)) % 98.16/13.48 | | (queue(all_65_13) = all_86_1 & $i(all_86_1) & ~ elem(all_65_0, % 98.16/13.48 | all_86_1)) % 98.16/13.48 | % 98.16/13.48 | DELTA: instantiating (48) with fresh symbols all_91_0, all_91_1 gives: % 98.16/13.48 | (52) ( ~ (all_91_0 = nbr_proc) & host(all_65_6) = all_91_0 & $i(all_91_0)) % 98.16/13.48 | | (queue(nbr_proc) = all_91_1 & $i(all_91_1) & ~ elem(all_65_2, % 98.16/13.48 | all_91_1)) % 98.16/13.48 | % 98.16/13.48 | DELTA: instantiating (47) with fresh symbols all_92_0, all_92_1, all_92_2, % 98.16/13.48 | all_92_3, all_92_4, all_92_5 gives: % 98.16/13.48 | (53) $i(all_92_0) & ((all_92_3 = all_65_1 & ~ elem(all_65_2, all_65_1)) | % 98.16/13.48 | (all_92_5 = all_65_4 & ~ (all_92_0 = all_92_4) & host(all_65_6) = % 98.16/13.48 | all_92_4 & $i(all_92_4) & leq(all_65_17, all_92_0) & ~ % 98.16/13.48 | leq(nbr_proc, all_92_0) & ~ setIn(all_92_0, all_65_4)) | ( ~ % 98.16/13.48 | (all_92_2 = nbr_proc) & host(all_65_7) = all_92_2 & $i(all_92_2)) % 98.16/13.48 | | (queue(all_65_13) = all_92_1 & $i(all_92_1) & ~ elem(all_65_0, % 98.16/13.48 | all_92_1))) % 98.16/13.48 | % 98.16/13.48 | ALPHA: (53) implies: % 98.16/13.48 | (54) $i(all_92_0) % 98.16/13.48 | (55) (all_92_3 = all_65_1 & ~ elem(all_65_2, all_65_1)) | (all_92_5 = % 98.16/13.48 | all_65_4 & ~ (all_92_0 = all_92_4) & host(all_65_6) = all_92_4 & % 98.16/13.48 | $i(all_92_4) & leq(all_65_17, all_92_0) & ~ leq(nbr_proc, all_92_0) % 98.16/13.48 | & ~ setIn(all_92_0, all_65_4)) | ( ~ (all_92_2 = nbr_proc) & % 98.16/13.48 | host(all_65_7) = all_92_2 & $i(all_92_2)) | (queue(all_65_13) = % 98.16/13.48 | all_92_1 & $i(all_92_1) & ~ elem(all_65_0, all_92_1)) % 98.16/13.48 | % 98.16/13.48 | BETA: splitting (50) gives: % 98.16/13.48 | % 98.16/13.48 | Case 1: % 98.16/13.48 | | % 98.16/13.48 | | (56) ~ (all_85_0 = nbr_proc) & host(all_65_7) = all_85_0 & $i(all_85_0) % 98.16/13.48 | | % 98.16/13.48 | | ALPHA: (56) implies: % 98.16/13.48 | | (57) ~ (all_85_0 = nbr_proc) % 98.16/13.48 | | (58) host(all_65_7) = all_85_0 % 98.16/13.48 | | % 98.16/13.48 | | GROUND_INST: instantiating (8) with nbr_proc, all_85_0, all_65_7, % 98.16/13.48 | | simplifying with (30), (58) gives: % 98.16/13.48 | | (59) all_85_0 = nbr_proc % 98.16/13.48 | | % 98.16/13.48 | | REDUCE: (57), (59) imply: % 98.16/13.48 | | (60) $false % 98.16/13.48 | | % 98.16/13.48 | | CLOSE: (60) is inconsistent. % 98.16/13.48 | | % 98.16/13.48 | Case 2: % 98.16/13.48 | | % 98.16/13.48 | | (61) queue(nbr_proc) = all_85_1 & $i(all_85_1) & ~ elem(all_65_0, % 98.16/13.48 | | all_85_1) % 98.16/13.48 | | % 98.16/13.48 | | ALPHA: (61) implies: % 98.16/13.48 | | (62) queue(nbr_proc) = all_85_1 % 98.16/13.48 | | % 98.16/13.48 | | GROUND_INST: instantiating (7) with all_65_1, all_85_1, nbr_proc, % 98.16/13.48 | | simplifying with (26), (62) gives: % 98.16/13.49 | | (63) all_85_1 = all_65_1 % 98.16/13.49 | | % 98.16/13.49 | | BETA: splitting (52) gives: % 98.16/13.49 | | % 98.16/13.49 | | Case 1: % 98.16/13.49 | | | % 98.16/13.49 | | | (64) ~ (all_91_0 = nbr_proc) & host(all_65_6) = all_91_0 & % 98.16/13.49 | | | $i(all_91_0) % 98.16/13.49 | | | % 98.16/13.49 | | | ALPHA: (64) implies: % 98.16/13.49 | | | (65) host(all_65_6) = all_91_0 % 98.16/13.49 | | | % 98.16/13.49 | | | GROUND_INST: instantiating (8) with all_65_3, all_91_0, all_65_6, % 98.16/13.49 | | | simplifying with (31), (65) gives: % 98.16/13.49 | | | (66) all_91_0 = all_65_3 % 98.16/13.49 | | | % 98.16/13.49 | | | GROUND_INST: instantiating (4) with all_65_0, simplifying with (25), (46) % 98.16/13.49 | | | gives: % 98.16/13.49 | | | (67) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ($i(v0) & ((v2 = % 98.16/13.49 | | | all_65_0 & m_Down(v0) = all_65_0) | (v1 = all_65_0 & % 98.16/13.49 | | | m_Halt(v0) = all_65_0))) % 98.16/13.49 | | | % 98.16/13.49 | | | DELTA: instantiating (67) with fresh symbols all_145_0, all_145_1, % 98.16/13.49 | | | all_145_2 gives: % 98.16/13.49 | | | (68) $i(all_145_2) & ((all_145_0 = all_65_0 & m_Down(all_145_2) = % 98.16/13.49 | | | all_65_0) | (all_145_1 = all_65_0 & m_Halt(all_145_2) = % 98.16/13.49 | | | all_65_0)) % 98.16/13.49 | | | % 98.16/13.49 | | | ALPHA: (68) implies: % 98.16/13.49 | | | (69) $i(all_145_2) % 98.16/13.49 | | | (70) (all_145_0 = all_65_0 & m_Down(all_145_2) = all_65_0) | (all_145_1 % 98.16/13.49 | | | = all_65_0 & m_Halt(all_145_2) = all_65_0) % 98.16/13.49 | | | % 98.16/13.49 | | | BETA: splitting (49) gives: % 98.16/13.49 | | | % 98.16/13.49 | | | Case 1: % 98.16/13.49 | | | | % 98.16/13.49 | | | | (71) elem(all_65_0, all_65_16) % 98.16/13.49 | | | | % 98.16/13.49 | | | | GROUND_INST: instantiating (2) with all_65_0, all_65_11, all_65_16, % 98.16/13.49 | | | | all_65_12, simplifying with (17), (20), (25), (36), (71) % 98.16/13.49 | | | | gives: % 98.16/13.49 | | | | (72) elem(all_65_0, all_65_12) % 98.16/13.49 | | | | % 98.16/13.49 | | | | BETA: splitting (51) gives: % 98.16/13.49 | | | | % 98.16/13.49 | | | | Case 1: % 98.16/13.49 | | | | | % 98.16/13.49 | | | | | (73) ~ (all_86_0 = all_65_13) & host(all_65_7) = all_86_0 & % 98.16/13.49 | | | | | $i(all_86_0) % 98.16/13.49 | | | | | % 98.16/13.49 | | | | | ALPHA: (73) implies: % 98.16/13.49 | | | | | (74) host(all_65_7) = all_86_0 % 98.16/13.49 | | | | | % 98.16/13.49 | | | | | BETA: splitting (55) gives: % 98.16/13.49 | | | | | % 98.16/13.49 | | | | | Case 1: % 98.16/13.49 | | | | | | % 98.16/13.49 | | | | | | (75) (all_92_3 = all_65_1 & ~ elem(all_65_2, all_65_1)) | % 98.16/13.49 | | | | | | (all_92_5 = all_65_4 & ~ (all_92_0 = all_92_4) & % 98.16/13.49 | | | | | | host(all_65_6) = all_92_4 & $i(all_92_4) & leq(all_65_17, % 98.16/13.49 | | | | | | all_92_0) & ~ leq(nbr_proc, all_92_0) & ~ % 98.16/13.49 | | | | | | setIn(all_92_0, all_65_4)) % 98.16/13.49 | | | | | | % 98.16/13.49 | | | | | | BETA: splitting (75) gives: % 98.16/13.49 | | | | | | % 98.16/13.49 | | | | | | Case 1: % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | (76) all_92_3 = all_65_1 & ~ elem(all_65_2, all_65_1) % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | ALPHA: (76) implies: % 98.16/13.49 | | | | | | | (77) ~ elem(all_65_2, all_65_1) % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | PRED_UNIFY: (13), (77) imply: % 98.16/13.49 | | | | | | | (78) $false % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | CLOSE: (78) is inconsistent. % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | Case 2: % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | (79) all_92_5 = all_65_4 & ~ (all_92_0 = all_92_4) & % 98.16/13.49 | | | | | | | host(all_65_6) = all_92_4 & $i(all_92_4) & leq(all_65_17, % 98.16/13.49 | | | | | | | all_92_0) & ~ leq(nbr_proc, all_92_0) & ~ % 98.16/13.49 | | | | | | | setIn(all_92_0, all_65_4) % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | ALPHA: (79) implies: % 98.16/13.49 | | | | | | | (80) ~ (all_92_0 = all_92_4) % 98.16/13.49 | | | | | | | (81) ~ setIn(all_92_0, all_65_4) % 98.16/13.49 | | | | | | | (82) ~ leq(nbr_proc, all_92_0) % 98.16/13.49 | | | | | | | (83) leq(all_65_17, all_92_0) % 98.16/13.49 | | | | | | | (84) host(all_65_6) = all_92_4 % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | REDUCE: (42), (83) imply: % 98.16/13.49 | | | | | | | (85) leq(all_59_0, all_92_0) % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | GROUND_INST: instantiating (8) with nbr_proc, all_86_0, all_65_7, % 98.16/13.49 | | | | | | | simplifying with (30), (74) gives: % 98.16/13.49 | | | | | | | (86) all_86_0 = nbr_proc % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | GROUND_INST: instantiating (8) with all_65_3, all_92_4, all_65_6, % 98.16/13.49 | | | | | | | simplifying with (31), (84) gives: % 98.16/13.49 | | | | | | | (87) all_92_4 = all_65_3 % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | REDUCE: (80), (87) imply: % 98.16/13.49 | | | | | | | (88) ~ (all_92_0 = all_65_3) % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | BETA: splitting (70) gives: % 98.16/13.49 | | | | | | | % 98.16/13.49 | | | | | | | Case 1: % 98.16/13.49 | | | | | | | | % 98.16/13.49 | | | | | | | | (89) all_145_0 = all_65_0 & m_Down(all_145_2) = all_65_0 % 98.16/13.49 | | | | | | | | % 98.16/13.49 | | | | | | | | ALPHA: (89) implies: % 98.16/13.49 | | | | | | | | (90) m_Down(all_145_2) = all_65_0 % 98.16/13.49 | | | | | | | | % 98.16/13.49 | | | | | | | | GROUND_INST: instantiating (axiom_30) with all_65_7, all_145_2, % 98.16/13.49 | | | | | | | | all_65_0, simplifying with (23), (34), (69), (90) % 98.16/13.49 | | | | | | | | gives: % 98.16/13.49 | | | | | | | | (91) all_145_2 = all_65_7 % 98.16/13.49 | | | | | | | | % 98.16/13.49 | | | | | | | | GROUND_INST: instantiating (40) with all_65_7, all_145_2, % 98.16/13.49 | | | | | | | | all_65_0, nbr_proc, simplifying with (23), (30), % 98.16/13.49 | | | | | | | | (69), (90) gives: % 98.16/13.49 | | | | | | | | (92) ? [v0: $i] : ? [v1: $i] : (( ~ (v1 = nbr_proc) & % 98.16/13.49 | | | | | | | | host(all_145_2) = v1 & $i(v1)) | (queue(nbr_proc) = % 98.16/13.49 | | | | | | | | v0 & $i(v0) & ~ elem(all_65_0, v0))) % 98.16/13.49 | | | | | | | | % 98.16/13.49 | | | | | | | | GROUND_INST: instantiating (40) with all_65_15, all_145_2, % 98.16/13.49 | | | | | | | | all_65_0, all_65_13, simplifying with (18), (28), % 98.16/13.49 | | | | | | | | (69), (90) gives: % 98.16/13.49 | | | | | | | | (93) ? [v0: $i] : ? [v1: any] : (( ~ (v1 = all_65_13) & % 98.16/13.49 | | | | | | | | host(all_145_2) = v1 & $i(v1)) | (queue(all_65_13) = % 98.16/13.49 | | | | | | | | v0 & $i(v0) & ~ elem(all_65_0, v0))) % 98.16/13.49 | | | | | | | | % 98.16/13.49 | | | | | | | | DELTA: instantiating (93) with fresh symbols all_419_0, % 98.16/13.49 | | | | | | | | all_419_1 gives: % 98.16/13.49 | | | | | | | | (94) ( ~ (all_419_0 = all_65_13) & host(all_145_2) = % 98.16/13.49 | | | | | | | | all_419_0 & $i(all_419_0)) | (queue(all_65_13) = % 98.16/13.49 | | | | | | | | all_419_1 & $i(all_419_1) & ~ elem(all_65_0, % 98.16/13.49 | | | | | | | | all_419_1)) % 98.16/13.49 | | | | | | | | % 98.16/13.49 | | | | | | | | DELTA: instantiating (92) with fresh symbols all_421_0, % 98.16/13.49 | | | | | | | | all_421_1 gives: % 98.16/13.49 | | | | | | | | (95) ( ~ (all_421_0 = nbr_proc) & host(all_145_2) = all_421_0 % 98.16/13.49 | | | | | | | | & $i(all_421_0)) | (queue(nbr_proc) = all_421_1 & % 98.16/13.49 | | | | | | | | $i(all_421_1) & ~ elem(all_65_0, all_421_1)) % 98.16/13.49 | | | | | | | | % 98.16/13.49 | | | | | | | | BETA: splitting (94) gives: % 98.16/13.49 | | | | | | | | % 98.16/13.49 | | | | | | | | Case 1: % 98.16/13.49 | | | | | | | | | % 98.16/13.49 | | | | | | | | | (96) ~ (all_419_0 = all_65_13) & host(all_145_2) = % 98.16/13.49 | | | | | | | | | all_419_0 & $i(all_419_0) % 98.16/13.49 | | | | | | | | | % 98.16/13.49 | | | | | | | | | ALPHA: (96) implies: % 98.16/13.49 | | | | | | | | | (97) host(all_145_2) = all_419_0 % 98.16/13.49 | | | | | | | | | % 98.16/13.49 | | | | | | | | | REDUCE: (91), (97) imply: % 98.16/13.49 | | | | | | | | | (98) host(all_65_7) = all_419_0 % 98.16/13.49 | | | | | | | | | % 98.16/13.50 | | | | | | | | | GROUND_INST: instantiating (8) with nbr_proc, all_419_0, % 98.16/13.50 | | | | | | | | | all_65_7, simplifying with (30), (98) gives: % 98.16/13.50 | | | | | | | | | (99) all_419_0 = nbr_proc % 98.16/13.50 | | | | | | | | | % 98.16/13.50 | | | | | | | | | BETA: splitting (95) gives: % 98.16/13.50 | | | | | | | | | % 98.16/13.50 | | | | | | | | | Case 1: % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | (100) ~ (all_421_0 = nbr_proc) & host(all_145_2) = % 98.16/13.50 | | | | | | | | | | all_421_0 & $i(all_421_0) % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | ALPHA: (100) implies: % 98.16/13.50 | | | | | | | | | | (101) ~ (all_421_0 = nbr_proc) % 98.16/13.50 | | | | | | | | | | (102) host(all_145_2) = all_421_0 % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | REDUCE: (91), (102) imply: % 98.16/13.50 | | | | | | | | | | (103) host(all_65_7) = all_421_0 % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | GROUND_INST: instantiating (8) with nbr_proc, all_421_0, % 98.16/13.50 | | | | | | | | | | all_65_7, simplifying with (30), (103) gives: % 98.16/13.50 | | | | | | | | | | (104) all_421_0 = nbr_proc % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | REDUCE: (101), (104) imply: % 98.16/13.50 | | | | | | | | | | (105) $false % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | CLOSE: (105) is inconsistent. % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | Case 2: % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | GROUND_INST: instantiating (38) with all_92_0, simplifying with % 98.16/13.50 | | | | | | | | | | (54), (81), (82) gives: % 98.16/13.50 | | | | | | | | | | (106) all_92_0 = all_65_3 | ~ leq(all_65_17, all_92_0) % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | BETA: splitting (106) gives: % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | Case 1: % 98.16/13.50 | | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | | (107) ~ leq(all_65_17, all_92_0) % 98.16/13.50 | | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | | REDUCE: (42), (107) imply: % 98.16/13.50 | | | | | | | | | | | (108) ~ leq(all_59_0, all_92_0) % 98.16/13.50 | | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | | PRED_UNIFY: (85), (108) imply: % 98.16/13.50 | | | | | | | | | | | (109) $false % 98.16/13.50 | | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | | CLOSE: (109) is inconsistent. % 98.16/13.50 | | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | Case 2: % 98.16/13.50 | | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | | (110) all_92_0 = all_65_3 % 98.16/13.50 | | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | | REDUCE: (88), (110) imply: % 98.16/13.50 | | | | | | | | | | | (111) $false % 98.16/13.50 | | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | | CLOSE: (111) is inconsistent. % 98.16/13.50 | | | | | | | | | | | % 98.16/13.50 | | | | | | | | | | End of split % 98.16/13.50 | | | | | | | | | | % 98.16/13.50 | | | | | | | | | End of split % 98.16/13.50 | | | | | | | | | % 98.16/13.50 | | | | | | | | Case 2: % 98.16/13.50 | | | | | | | | | % 98.16/13.50 | | | | | | | | | (112) queue(all_65_13) = all_419_1 & $i(all_419_1) & ~ % 98.16/13.50 | | | | | | | | | elem(all_65_0, all_419_1) % 98.16/13.50 | | | | | | | | | % 98.16/13.50 | | | | | | | | | ALPHA: (112) implies: % 98.16/13.50 | | | | | | | | | (113) ~ elem(all_65_0, all_419_1) % 98.16/13.50 | | | | | | | | | (114) queue(all_65_13) = all_419_1 % 98.16/13.50 | | | | | | | | | % 98.16/13.50 | | | | | | | | | GROUND_INST: instantiating (7) with all_65_12, all_419_1, % 98.16/13.50 | | | | | | | | | all_65_13, simplifying with (27), (114) gives: % 98.16/13.50 | | | | | | | | | (115) all_419_1 = all_65_12 % 98.16/13.50 | | | | | | | | | % 98.16/13.50 | | | | | | | | | REDUCE: (113), (115) imply: % 98.16/13.50 | | | | | | | | | (116) ~ elem(all_65_0, all_65_12) % 98.16/13.50 | | | | | | | | | % 98.16/13.50 | | | | | | | | | PRED_UNIFY: (72), (116) imply: % 98.16/13.50 | | | | | | | | | (117) $false % 98.16/13.50 | | | | | | | | | % 98.16/13.50 | | | | | | | | | CLOSE: (117) is inconsistent. % 98.16/13.50 | | | | | | | | | % 98.30/13.50 | | | | | | | | End of split % 98.30/13.50 | | | | | | | | % 98.30/13.50 | | | | | | | Case 2: % 98.30/13.50 | | | | | | | | % 98.30/13.50 | | | | | | | | (118) all_145_1 = all_65_0 & m_Halt(all_145_2) = all_65_0 % 98.30/13.50 | | | | | | | | % 98.30/13.50 | | | | | | | | ALPHA: (118) implies: % 98.30/13.50 | | | | | | | | (119) m_Halt(all_145_2) = all_65_0 % 98.30/13.50 | | | | | | | | % 98.30/13.50 | | | | | | | | GROUND_INST: instantiating (axiom_17) with all_65_7, all_145_2, % 98.30/13.50 | | | | | | | | all_65_0, simplifying with (23), (34), (69), (119) % 98.30/13.50 | | | | | | | | gives: % 98.30/13.50 | | | | | | | | (120) $false % 98.30/13.50 | | | | | | | | % 98.30/13.50 | | | | | | | | CLOSE: (120) is inconsistent. % 98.30/13.50 | | | | | | | | % 98.30/13.50 | | | | | | | End of split % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | End of split % 98.30/13.50 | | | | | | % 98.30/13.50 | | | | | Case 2: % 98.30/13.50 | | | | | | % 98.30/13.50 | | | | | | (121) ( ~ (all_92_2 = nbr_proc) & host(all_65_7) = all_92_2 & % 98.30/13.50 | | | | | | $i(all_92_2)) | (queue(all_65_13) = all_92_1 & % 98.30/13.50 | | | | | | $i(all_92_1) & ~ elem(all_65_0, all_92_1)) % 98.30/13.50 | | | | | | % 98.30/13.50 | | | | | | BETA: splitting (121) gives: % 98.30/13.50 | | | | | | % 98.30/13.50 | | | | | | Case 1: % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | | (122) ~ (all_92_2 = nbr_proc) & host(all_65_7) = all_92_2 & % 98.30/13.50 | | | | | | | $i(all_92_2) % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | | ALPHA: (122) implies: % 98.30/13.50 | | | | | | | (123) ~ (all_92_2 = nbr_proc) % 98.30/13.50 | | | | | | | (124) host(all_65_7) = all_92_2 % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | | GROUND_INST: instantiating (8) with nbr_proc, all_92_2, all_65_7, % 98.30/13.50 | | | | | | | simplifying with (30), (124) gives: % 98.30/13.50 | | | | | | | (125) all_92_2 = nbr_proc % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | | REDUCE: (123), (125) imply: % 98.30/13.50 | | | | | | | (126) $false % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | | CLOSE: (126) is inconsistent. % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | Case 2: % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | | (127) queue(all_65_13) = all_92_1 & $i(all_92_1) & ~ % 98.30/13.50 | | | | | | | elem(all_65_0, all_92_1) % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | | ALPHA: (127) implies: % 98.30/13.50 | | | | | | | (128) ~ elem(all_65_0, all_92_1) % 98.30/13.50 | | | | | | | (129) queue(all_65_13) = all_92_1 % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | | GROUND_INST: instantiating (7) with all_65_12, all_92_1, % 98.30/13.50 | | | | | | | all_65_13, simplifying with (27), (129) gives: % 98.30/13.50 | | | | | | | (130) all_92_1 = all_65_12 % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | | REDUCE: (128), (130) imply: % 98.30/13.50 | | | | | | | (131) ~ elem(all_65_0, all_65_12) % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | | PRED_UNIFY: (72), (131) imply: % 98.30/13.50 | | | | | | | (132) $false % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | | CLOSE: (132) is inconsistent. % 98.30/13.50 | | | | | | | % 98.30/13.50 | | | | | | End of split % 98.30/13.50 | | | | | | % 98.30/13.50 | | | | | End of split % 98.30/13.50 | | | | | % 98.30/13.50 | | | | Case 2: % 98.30/13.50 | | | | | % 98.30/13.50 | | | | | (133) queue(all_65_13) = all_86_1 & $i(all_86_1) & ~ % 98.30/13.50 | | | | | elem(all_65_0, all_86_1) % 98.30/13.50 | | | | | % 98.30/13.50 | | | | | ALPHA: (133) implies: % 98.30/13.50 | | | | | (134) ~ elem(all_65_0, all_86_1) % 98.30/13.50 | | | | | (135) queue(all_65_13) = all_86_1 % 98.30/13.50 | | | | | % 98.30/13.50 | | | | | GROUND_INST: instantiating (7) with all_65_12, all_86_1, all_65_13, % 98.30/13.50 | | | | | simplifying with (27), (135) gives: % 98.30/13.50 | | | | | (136) all_86_1 = all_65_12 % 98.30/13.50 | | | | | % 98.30/13.50 | | | | | REDUCE: (134), (136) imply: % 98.30/13.50 | | | | | (137) ~ elem(all_65_0, all_65_12) % 98.30/13.50 | | | | | % 98.30/13.50 | | | | | PRED_UNIFY: (72), (137) imply: % 98.30/13.50 | | | | | (138) $false % 98.30/13.50 | | | | | % 98.30/13.50 | | | | | CLOSE: (138) is inconsistent. % 98.30/13.50 | | | | | % 98.30/13.50 | | | | End of split % 98.30/13.50 | | | | % 98.30/13.50 | | | Case 2: % 98.30/13.50 | | | | % 98.30/13.50 | | | | (139) all_65_0 = all_65_10 % 98.30/13.50 | | | | % 98.30/13.50 | | | | REDUCE: (34), (139) imply: % 98.30/13.50 | | | | (140) m_Down(all_65_7) = all_65_10 % 98.30/13.50 | | | | % 98.30/13.50 | | | | GROUND_INST: instantiating (axiom_12) with all_65_14, all_65_15, % 98.30/13.50 | | | | all_65_7, all_65_10, simplifying with (18), (19), (23), % 98.30/13.50 | | | | (32), (140) gives: % 98.30/13.50 | | | | (141) $false % 98.30/13.50 | | | | % 98.30/13.50 | | | | CLOSE: (141) is inconsistent. % 98.30/13.50 | | | | % 98.30/13.50 | | | End of split % 98.30/13.50 | | | % 98.30/13.50 | | Case 2: % 98.30/13.50 | | | % 98.30/13.50 | | | (142) queue(nbr_proc) = all_91_1 & $i(all_91_1) & ~ elem(all_65_2, % 98.30/13.50 | | | all_91_1) % 98.30/13.50 | | | % 98.30/13.50 | | | ALPHA: (142) implies: % 98.30/13.50 | | | (143) ~ elem(all_65_2, all_91_1) % 98.30/13.50 | | | (144) queue(nbr_proc) = all_91_1 % 98.30/13.50 | | | % 98.30/13.50 | | | GROUND_INST: instantiating (7) with all_65_1, all_91_1, nbr_proc, % 98.30/13.50 | | | simplifying with (26), (144) gives: % 98.30/13.50 | | | (145) all_91_1 = all_65_1 % 98.30/13.50 | | | % 98.30/13.50 | | | REDUCE: (143), (145) imply: % 98.30/13.50 | | | (146) ~ elem(all_65_2, all_65_1) % 98.30/13.50 | | | % 98.30/13.50 | | | PRED_UNIFY: (13), (146) imply: % 98.30/13.50 | | | (147) $false % 98.30/13.50 | | | % 98.30/13.50 | | | CLOSE: (147) is inconsistent. % 98.30/13.50 | | | % 98.30/13.50 | | End of split % 98.30/13.50 | | % 98.30/13.50 | End of split % 98.30/13.50 | % 98.30/13.50 End of proof % 98.30/13.51 % SZS output end Proof for theBenchmark % 98.30/13.51 % 98.30/13.51 12917ms %------------------------------------------------------------------------------