%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV458+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 : n016.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 22:56:34 EDT 2023 % Result : Theorem 122.94s 16.54s % Output : Proof 123.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.11 % Problem : SWV458+1 : TPTP v8.1.2. Released v4.0.0. % 0.08/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n016.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 09:13:15 EDT 2023 % 0.12/0.33 % CPUTime : % 0.67/0.63 ________ _____ % 0.67/0.63 ___ __ \_________(_)________________________________ % 0.67/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.67/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.67/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.67/0.63 % 0.67/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.67/0.63 (2023-06-19) % 0.67/0.63 % 0.67/0.63 (c) Philipp Rümmer, 2009-2023 % 0.67/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.67/0.63 Amanda Stjerna. % 0.67/0.63 Free software under BSD-3-Clause. % 0.67/0.63 % 0.67/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.67/0.63 % 0.67/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.67/0.65 Running up to 7 provers in parallel. % 0.67/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.09/1.26 Prover 1: Preprocessing ... % 4.09/1.27 Prover 4: Preprocessing ... % 4.09/1.30 Prover 3: Preprocessing ... % 4.09/1.30 Prover 6: Preprocessing ... % 4.09/1.30 Prover 0: Preprocessing ... % 4.09/1.30 Prover 5: Preprocessing ... % 4.09/1.30 Prover 2: Preprocessing ... % 11.41/2.27 Prover 3: Constructing countermodel ... % 11.79/2.32 Prover 1: Constructing countermodel ... % 11.79/2.34 Prover 6: Proving ... % 13.01/2.46 Prover 5: Proving ... % 13.01/2.51 Prover 2: Proving ... % 14.51/2.65 Prover 4: Constructing countermodel ... % 15.30/2.78 Prover 0: Proving ... % 19.23/3.27 Prover 3: gave up % 19.23/3.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.02/3.38 Prover 7: Preprocessing ... % 24.69/3.97 Prover 7: Warning: ignoring some quantifiers % 24.95/3.99 Prover 7: Constructing countermodel ... % 68.22/9.52 Prover 2: stopped % 68.22/9.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 68.63/9.64 Prover 8: Preprocessing ... % 70.58/9.84 Prover 8: Warning: ignoring some quantifiers % 70.58/9.86 Prover 8: Constructing countermodel ... % 86.41/11.93 Prover 8: gave up % 86.41/11.94 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 87.75/12.03 Prover 9: Preprocessing ... % 90.12/12.32 Prover 9: Constructing countermodel ... % 103.07/13.99 Prover 5: stopped % 103.07/14.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 103.60/14.06 Prover 10: Preprocessing ... % 104.39/14.22 Prover 10: Warning: ignoring some quantifiers % 104.39/14.23 Prover 10: Constructing countermodel ... % 118.43/16.01 Prover 1: stopped % 119.03/16.04 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 119.45/16.13 Prover 11: Preprocessing ... % 121.80/16.40 Prover 11: Constructing countermodel ... % 122.66/16.51 Prover 10: Found proof (size 154) % 122.66/16.51 Prover 10: proved (2504ms) % 122.66/16.51 Prover 11: stopped % 122.66/16.51 Prover 9: stopped % 122.66/16.51 Prover 6: stopped % 122.66/16.51 Prover 7: stopped % 122.66/16.52 Prover 0: stopped % 122.94/16.54 Prover 4: stopped % 122.94/16.54 % 122.94/16.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 122.94/16.54 % 123.03/16.55 % SZS output start Proof for theBenchmark % 123.03/16.56 Assumptions after simplification: % 123.03/16.56 --------------------------------- % 123.03/16.56 % 123.03/16.56 (axiom_01) % 123.03/16.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~ (host(v0) = % 123.03/16.58 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v2) & s(v2) = v3 & % 123.03/16.58 $i(v3))) % 123.03/16.58 % 123.03/16.58 (axiom_03) % 123.03/16.58 $i(nbr_proc) & $i(zero) & ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0, % 123.03/16.58 nbr_proc)) % 123.03/16.58 % 123.03/16.59 (axiom_17) % 123.03/16.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~ % 123.03/16.59 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 123.03/16.59 % 123.03/16.59 (axiom_46) % 123.03/16.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 123.03/16.59 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) | % 123.03/16.59 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 123.03/16.59 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 123.03/16.59 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) % 123.03/16.59 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2)) % 123.03/16.59 % 123.03/16.59 (axiom_48) % 123.03/16.59 ! [v0: $i] : ! [v1: $i] : ( ~ (m_Down(v1) = v0) | ~ $i(v1) | ~ $i(v0) | % 123.03/16.59 pidElem(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (m_Halt(v1) = v0) | ~ $i(v1) % 123.03/16.59 | ~ $i(v0) | pidElem(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ? % 123.03/16.59 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) = % 123.03/16.59 v0) | (v2 = v0 & m_Halt(v1) = v0)))) % 123.03/16.59 % 123.03/16.59 (axiom_61) % 123.03/16.59 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) % 123.03/16.59 | ~ leq(v0, v1)) & ? [v0: $i] : ( ~ $i(v0) | leq(v0, v0)) % 123.03/16.59 % 123.03/16.59 (axiom_63) % 123.03/16.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = v3) | ~ % 123.03/16.60 (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | leq(v0, v1)) & ! % 123.03/16.60 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = v3) | ~ % 123.03/16.60 (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) | leq(v2, v3)) % 123.03/16.60 % 123.03/16.60 (axiom_64) % 123.03/16.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (s(v1) = v2) | ~ % 123.03/16.60 $i(v1) | ~ $i(v0) | ~ leq(v0, v2) | leq(v0, v1)) & ! [v0: $i] : ! [v1: % 123.03/16.60 $i] : ! [v2: $i] : ( ~ (s(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 123.03/16.60 v1) | leq(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ (s(v1) = v0) | ~ % 123.03/16.60 $i(v1) | ~ $i(v0) | leq(v0, v0)) % 123.03/16.60 % 123.03/16.60 (conj) % 123.03/16.62 $i(down) & $i(ldr) & $i(elid) & $i(status) & $i(pendack) & $i(alive) & % 123.03/16.62 $i(norm) & $i(wait) & $i(elec_1) & $i(elec_2) & $i(nbr_proc) & $i(zero) & ? % 123.03/16.62 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 123.03/16.62 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? % 123.03/16.62 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? % 123.03/16.62 [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? % 123.03/16.62 [v21: $i] : ( ~ (v16 = v5) & ~ (v13 = v5) & index(down, v5) = v12 & % 123.03/16.62 index(ldr, v16) = v16 & index(status, v16) = norm & index(status, v5) = % 123.03/16.62 elec_1 & snoc(v18, v14) = v19 & cons(v7, v1) = v6 & m_Down(v4) = v7 & % 123.03/16.62 m_Halt(v20) = v21 & m_Halt(v3) = v14 & s(v5) = v13 & s(zero) = v0 & % 123.03/16.62 host(v20) = v5 & host(v17) = v13 & host(v15) = v16 & host(v4) = v8 & % 123.35/16.62 host(v3) = v5 & queue(v13) = v18 & queue(v5) = v6 & $i(v21) & $i(v20) & % 123.35/16.62 $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & % 123.35/16.62 $i(v12) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 123.35/16.62 $i(v1) & $i(v0) & setIn(v20, alive) & setIn(v15, alive) & setIn(v3, alive) & % 123.35/16.62 elem(v21, v19) & ~ leq(v13, v16) & ~ leq(v5, v8) & ~ leq(nbr_proc, v5) & % 123.35/16.62 ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! % 123.35/16.62 [v27: $i] : ( ~ (m_Down(v23) = v27) | ~ (host(v24) = v25) | ~ (host(v22) = % 123.35/16.62 v26) | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ setIn(v22, alive) | % 123.35/16.62 leq(v25, v26) | ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] % 123.35/16.62 : ? [v32: $i] : ? [v33: $i] : ? [v34: $i] : ($i(v34) & (( ~ (v34 = v29) % 123.35/16.62 & index(down, v25) = v28 & host(v23) = v29 & $i(v29) & $i(v28) & % 123.35/16.62 leq(v0, v34) & ~ leq(v25, v34) & ~ setIn(v34, v28)) | ( ~ (v33 = % 123.35/16.62 norm) & index(status, v26) = v33 & $i(v33)) | ( ~ (v32 = v26) & % 123.35/16.62 index(ldr, v26) = v32 & $i(v32)) | ( ~ (v31 = elec_1) & % 123.35/16.62 index(status, v25) = v31 & $i(v31)) | (queue(v25) = v30 & $i(v30) & % 123.35/16.62 ~ elem(v27, v30))))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : % 123.35/16.62 ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ( ~ (m_Down(v23) = v25) | ~ % 123.35/16.62 (host(v24) = v26) | ~ (host(v22) = v27) | ~ $i(v24) | ~ $i(v23) | ~ % 123.35/16.62 $i(v22) | ~ setIn(v24, alive) | ~ setIn(v22, alive) | ? [v28: $i] : ? % 123.35/16.62 [v29: $i] : ? [v30: $i] : ? [v31: $i] : (( ~ (v31 = norm) & % 123.35/16.62 index(status, v27) = v31 & $i(v31)) | ( ~ (v30 = v27) & index(ldr, % 123.35/16.62 v27) = v30 & $i(v30)) | ( ~ (v29 = v27) & host(v23) = v29 & $i(v29)) % 123.35/16.62 | (queue(v26) = v28 & $i(v28) & ~ elem(v25, v28)))) & ! [v22: $i] : ! % 123.35/16.62 [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ( ~ % 123.35/16.62 (m_Halt(v24) = v26) | ~ (host(v23) = v27) | ~ (host(v22) = v25) | ~ % 123.35/16.62 $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ setIn(v24, alive) | ~ setIn(v22, % 123.35/16.62 alive) | ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? % 123.35/16.62 [v32: $i] : ? [v33: $i] : (( ~ (v33 = norm) & index(status, v25) = v33 & % 123.35/16.62 $i(v33)) | ( ~ (v32 = v25) & index(ldr, v25) = v32 & $i(v32)) | ( ~ % 123.35/16.62 (v31 = elec_2) & index(status, v28) = v31 & host(v24) = v28 & $i(v31) % 123.35/16.62 & $i(v28)) | (index(pendack, v28) = v29 & host(v24) = v28 & $i(v29) & % 123.35/16.62 $i(v28) & leq(v29, v25)) | (queue(v27) = v30 & $i(v30) & ~ elem(v26, % 123.35/16.62 v30)))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] % 123.35/16.62 : ! [v26: $i] : ( ~ (m_Ack(v24, v23) = v25) | ~ (host(v22) = v26) | ~ % 123.35/16.62 $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ setIn(v24, alive) | ~ setIn(v22, % 123.35/16.62 alive) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? % 123.35/16.62 [v31: $i] : (( ~ (v31 = norm) & index(status, v26) = v31 & $i(v31)) | ( ~ % 123.35/16.62 (v30 = v26) & index(ldr, v26) = v30 & $i(v30)) | ( ~ (v29 = v26) & % 123.35/16.62 host(v23) = v29 & $i(v29)) | (host(v24) = v27 & queue(v27) = v28 & % 123.35/16.62 $i(v28) & $i(v27) & ~ elem(v25, v28)))) & ! [v22: $i] : ! [v23: $i] % 123.35/16.62 : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ (m_Ack(v24, v22) = v25) | % 123.35/16.62 ~ (host(v23) = v26) | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ? [v27: $i] % 123.35/16.62 : ? [v28: $i] : ? [v29: $i] : ((host(v24) = v29 & host(v22) = v28 & % 123.35/16.62 $i(v29) & $i(v28) & ~ leq(v28, v29)) | (queue(v26) = v27 & $i(v27) & % 123.35/16.62 ~ elem(v25, v27)))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! % 123.35/16.62 [v25: $i] : (v23 = v22 | ~ (host(v23) = v25) | ~ (host(v22) = v24) | ~ % 123.35/16.62 $i(v23) | ~ $i(v22) | ~ setIn(v23, alive) | ~ setIn(v22, alive) | ? % 123.35/16.62 [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( ~ (v29 = v25) % 123.35/16.62 & index(ldr, v25) = v29 & $i(v29)) | ( ~ (v28 = norm) & index(status, % 123.35/16.62 v25) = v28 & $i(v28)) | ( ~ (v27 = norm) & index(status, v24) = v27 % 123.35/16.62 & $i(v27)) | ( ~ (v26 = v24) & index(ldr, v24) = v26 & $i(v26)))) & ! % 123.35/16.62 [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ (m_Ldr(v23) = % 123.35/16.62 v24) | ~ (host(v22) = v25) | ~ $i(v23) | ~ $i(v22) | ? [v26: $i] : % 123.35/16.62 ? [v27: $i] : ((host(v23) = v27 & $i(v27) & ~ leq(v25, v27)) | % 123.35/16.62 (queue(v25) = v26 & $i(v26) & ~ elem(v24, v26)))) & ! [v22: $i] : ! % 123.35/16.62 [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ (m_Down(v23) = v24) | ~ % 123.35/16.62 (host(v22) = v25) | ~ $i(v23) | ~ $i(v22) | ~ setIn(v23, alive) | ? % 123.35/16.62 [v26: $i] : (queue(v25) = v26 & $i(v26) & ~ elem(v24, v26))) & ! [v22: % 123.35/16.62 $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ (m_Halt(v23) = v24) % 123.35/16.62 | ~ (host(v22) = v25) | ~ $i(v23) | ~ $i(v22) | ? [v26: $i] : ? [v27: % 123.35/16.62 $i] : ((host(v23) = v27 & $i(v27) & ~ leq(v25, v27)) | (queue(v25) = % 123.35/16.62 v26 & $i(v26) & ~ elem(v24, v26)))) & ! [v22: $i] : ! [v23: $i] : % 123.35/16.62 ! [v24: $i] : ! [v25: $i] : ( ~ (host(v23) = v25) | ~ (host(v22) = v24) | % 123.35/16.62 ~ $i(v23) | ~ $i(v22) | ~ setIn(v23, alive) | ~ setIn(v22, alive) | % 123.35/16.62 leq(v24, v25) | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] % 123.35/16.62 : (( ~ (v27 = elec_2) & index(status, v25) = v27 & $i(v27)) | ( ~ (v26 = % 123.35/16.62 elec_2) & index(status, v24) = v26 & $i(v26)) | (index(pendack, v25) % 123.35/16.62 = v29 & index(pendack, v24) = v28 & $i(v29) & $i(v28) & ~ leq(v28, % 123.35/16.62 v29)))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] % 123.35/16.62 : ( ~ (host(v23) = v25) | ~ (host(v22) = v24) | ~ $i(v23) | ~ $i(v22) | % 123.35/16.62 ~ setIn(v23, alive) | ~ setIn(v22, alive) | leq(v24, v25) | ? [v26: $i] % 123.35/16.62 : ? [v27: $i] : ? [v28: $i] : (( ~ (v27 = elec_2) & index(status, v25) = % 123.35/16.62 v27 & $i(v27)) | ( ~ (v26 = elec_2) & index(status, v24) = v26 & % 123.35/16.62 $i(v26)) | (index(pendack, v25) = v28 & $i(v28) & leq(v28, v24)))) & % 123.35/16.62 ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ (host(v23) = % 123.35/16.62 v24) | ~ (host(v22) = v25) | ~ $i(v23) | ~ $i(v22) | ~ setIn(v23, % 123.35/16.62 alive) | ~ setIn(v22, alive) | ? [v26: $i] : ? [v27: $i] : ? [v28: % 123.35/16.62 $i] : ? [v29: $i] : (( ~ (v29 = norm) & index(status, v25) = v29 & % 123.35/16.62 $i(v29)) | ( ~ (v28 = v25) & index(ldr, v25) = v28 & $i(v28)) | ( ~ % 123.35/16.62 (v27 = elec_2) & index(status, v24) = v27 & $i(v27)) | (index(pendack, % 123.35/16.62 v24) = v26 & $i(v26) & leq(v26, v25)))) & ! [v22: $i] : ! [v23: % 123.35/16.62 $i] : ! [v24: $i] : (v23 = v22 | ~ (host(v23) = v24) | ~ (host(v22) = % 123.35/16.62 v24) | ~ $i(v23) | ~ $i(v22) | ~ setIn(v23, alive) | ~ setIn(v22, % 123.35/16.62 alive)) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (host(v23) = % 123.35/16.62 v24) | ~ (host(v22) = v24) | ~ $i(v23) | ~ $i(v22) | ~ leq(v23, v22) % 123.35/16.62 | ~ setIn(v23, alive) | setIn(v22, alive)) & ! [v22: $i] : ! [v23: $i] % 123.35/16.62 : ( ~ (host(v22) = v23) | ~ $i(v22) | ~ setIn(v22, alive) | ? [v24: $i] : % 123.35/16.62 ? [v25: $i] : ((v25 = v22 & index(elid, v23) = v22) | ( ~ (v24 = elec_1) % 123.35/16.62 & ~ (v24 = elec_2) & index(status, v23) = v24 & $i(v24)))) & ! [v22: % 123.35/16.62 $i] : ! [v23: $i] : ( ~ (host(v22) = v23) | ~ $i(v22) | ? [v24: $i] : % 123.35/16.62 (index(pendack, v23) = v24 & $i(v24) & leq(v24, nbr_proc))) & ! [v22: $i] % 123.35/16.62 : (v22 = v8 | ~ $i(v22) | ~ leq(v0, v22) | leq(v5, v22) | setIn(v22, v12)) % 123.35/16.62 & ( ~ (norm = elec_1) | ( ~ (v9 = v8) & index(ldr, v5) = v9 & $i(v9))) & ( ~ % 123.35/16.62 (wait = elec_1) | ( ~ (v11 = v8) & index(elid, v5) = v10 & host(v10) = v11 % 123.35/16.62 & $i(v11) & $i(v10)))) % 123.35/16.62 % 123.35/16.62 (function-axioms) % 123.35/16.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 123.35/16.62 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 123.35/16.62 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3, % 123.35/16.62 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 123.35/16.62 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! % 123.35/16.62 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~ % 123.35/16.62 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 123.35/16.62 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 123.35/16.62 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i] % 123.35/16.62 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) = % 123.35/16.62 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) = % 123.35/16.62 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 123.35/16.62 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 123.35/16.62 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & ! % 123.35/16.62 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~ % 123.35/16.62 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 123.35/16.62 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 123.35/16.62 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & ! % 123.35/16.62 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~ % 123.35/16.62 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 123.35/16.62 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 123.35/16.62 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1: % 123.35/16.62 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0)) % 123.35/16.62 % 123.35/16.62 Further assumptions not needed in the proof: % 123.35/16.62 -------------------------------------------- % 123.35/16.62 axiom, axiom_02, axiom_04, axiom_05, axiom_06, axiom_07, axiom_08, axiom_09, % 123.35/16.62 axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15, axiom_16, axiom_18, % 123.35/16.62 axiom_19, axiom_20, axiom_21, axiom_22, axiom_23, axiom_24, axiom_25, axiom_26, % 123.35/16.62 axiom_27, axiom_28, axiom_29, axiom_30, axiom_31, axiom_32, axiom_33, axiom_34, % 123.35/16.62 axiom_35, axiom_36, axiom_37, axiom_38, axiom_39, axiom_40, axiom_41, axiom_42, % 123.35/16.62 axiom_43, axiom_44, axiom_45, axiom_47, axiom_49, axiom_50, axiom_51, axiom_52, % 123.35/16.62 axiom_53, axiom_54, axiom_55, axiom_56, axiom_57, axiom_58, axiom_59, axiom_60, % 123.35/16.62 axiom_62, axiom_65 % 123.35/16.62 % 123.35/16.62 Those formulas are unsatisfiable: % 123.35/16.62 --------------------------------- % 123.35/16.62 % 123.35/16.62 Begin of proof % 123.35/16.62 | % 123.35/16.62 | ALPHA: (axiom_03) implies: % 123.35/16.63 | (1) ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0, nbr_proc)) % 123.35/16.63 | % 123.35/16.63 | ALPHA: (axiom_46) implies: % 123.35/16.63 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) = v2) | ~ % 123.35/16.63 | $i(v1) | ~ $i(v0) | elem(v0, v2)) % 123.35/16.63 | % 123.35/16.63 | ALPHA: (axiom_48) implies: % 123.35/16.63 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ? [v1: $i] : ? [v2: $i] : % 123.35/16.63 | ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) = v0) | (v2 = v0 & % 123.35/16.63 | m_Halt(v1) = v0)))) % 123.35/16.63 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (m_Halt(v1) = v0) | ~ $i(v1) | ~ % 123.35/16.63 | $i(v0) | pidElem(v0)) % 123.35/16.63 | % 123.35/16.63 | ALPHA: (axiom_61) implies: % 123.35/16.63 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 123.35/16.63 | leq(v1, v0) | ~ leq(v0, v1)) % 123.35/16.63 | % 123.35/16.63 | ALPHA: (axiom_63) implies: % 123.35/16.63 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = % 123.35/16.63 | v3) | ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) | % 123.35/16.63 | leq(v2, v3)) % 123.35/16.63 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = % 123.35/16.63 | v3) | ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | % 123.35/16.63 | leq(v0, v1)) % 123.35/16.63 | % 123.35/16.63 | ALPHA: (axiom_64) implies: % 123.35/16.63 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (s(v1) = v2) | % 123.35/16.63 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v2) | leq(v0, v1)) % 123.35/16.63 | % 123.35/16.63 | ALPHA: (conj) implies: % 123.35/16.64 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 123.35/16.64 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 123.35/16.64 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 123.35/16.64 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 123.35/16.64 | $i] : ? [v20: $i] : ? [v21: $i] : ( ~ (v16 = v5) & ~ (v13 = v5) & % 123.35/16.64 | index(down, v5) = v12 & index(ldr, v16) = v16 & index(status, v16) = % 123.35/16.64 | norm & index(status, v5) = elec_1 & snoc(v18, v14) = v19 & cons(v7, % 123.35/16.64 | v1) = v6 & m_Down(v4) = v7 & m_Halt(v20) = v21 & m_Halt(v3) = v14 & % 123.35/16.64 | s(v5) = v13 & s(zero) = v0 & host(v20) = v5 & host(v17) = v13 & % 123.35/16.64 | host(v15) = v16 & host(v4) = v8 & host(v3) = v5 & queue(v13) = v18 & % 123.35/16.64 | queue(v5) = v6 & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & % 123.35/16.64 | $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v8) & $i(v7) & % 123.35/16.64 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 123.35/16.64 | setIn(v20, alive) & setIn(v15, alive) & setIn(v3, alive) & elem(v21, % 123.35/16.64 | v19) & ~ leq(v13, v16) & ~ leq(v5, v8) & ~ leq(nbr_proc, v5) & % 123.35/16.64 | ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: % 123.35/16.64 | $i] : ! [v27: $i] : ( ~ (m_Down(v23) = v27) | ~ (host(v24) = v25) % 123.35/16.64 | | ~ (host(v22) = v26) | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ % 123.35/16.64 | setIn(v22, alive) | leq(v25, v26) | ? [v28: $i] : ? [v29: $i] : % 123.35/16.64 | ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : ? [v34: % 123.35/16.64 | $i] : ($i(v34) & (( ~ (v34 = v29) & index(down, v25) = v28 & % 123.35/16.64 | host(v23) = v29 & $i(v29) & $i(v28) & leq(v0, v34) & ~ % 123.35/16.64 | leq(v25, v34) & ~ setIn(v34, v28)) | ( ~ (v33 = norm) & % 123.35/16.64 | index(status, v26) = v33 & $i(v33)) | ( ~ (v32 = v26) & % 123.35/16.64 | index(ldr, v26) = v32 & $i(v32)) | ( ~ (v31 = elec_1) & % 123.35/16.64 | index(status, v25) = v31 & $i(v31)) | (queue(v25) = v30 & % 123.35/16.64 | $i(v30) & ~ elem(v27, v30))))) & ! [v22: $i] : ! [v23: $i] % 123.35/16.64 | : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ( ~ % 123.35/16.64 | (m_Down(v23) = v25) | ~ (host(v24) = v26) | ~ (host(v22) = v27) | % 123.35/16.64 | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ setIn(v24, alive) | ~ % 123.35/16.64 | setIn(v22, alive) | ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? % 123.35/16.64 | [v31: $i] : (( ~ (v31 = norm) & index(status, v27) = v31 & $i(v31)) % 123.35/16.64 | | ( ~ (v30 = v27) & index(ldr, v27) = v30 & $i(v30)) | ( ~ (v29 = % 123.35/16.64 | v27) & host(v23) = v29 & $i(v29)) | (queue(v26) = v28 & % 123.35/16.64 | $i(v28) & ~ elem(v25, v28)))) & ! [v22: $i] : ! [v23: $i] : % 123.35/16.64 | ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ( ~ % 123.35/16.64 | (m_Halt(v24) = v26) | ~ (host(v23) = v27) | ~ (host(v22) = v25) | % 123.35/16.64 | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ setIn(v24, alive) | ~ % 123.35/16.64 | setIn(v22, alive) | ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? % 123.35/16.64 | [v31: $i] : ? [v32: $i] : ? [v33: $i] : (( ~ (v33 = norm) & % 123.35/16.64 | index(status, v25) = v33 & $i(v33)) | ( ~ (v32 = v25) & % 123.35/16.64 | index(ldr, v25) = v32 & $i(v32)) | ( ~ (v31 = elec_2) & % 123.35/16.64 | index(status, v28) = v31 & host(v24) = v28 & $i(v31) & $i(v28)) % 123.35/16.64 | | (index(pendack, v28) = v29 & host(v24) = v28 & $i(v29) & % 123.35/16.64 | $i(v28) & leq(v29, v25)) | (queue(v27) = v30 & $i(v30) & ~ % 123.35/16.64 | elem(v26, v30)))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] % 123.35/16.64 | : ! [v25: $i] : ! [v26: $i] : ( ~ (m_Ack(v24, v23) = v25) | ~ % 123.35/16.64 | (host(v22) = v26) | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ % 123.35/16.64 | setIn(v24, alive) | ~ setIn(v22, alive) | ? [v27: $i] : ? [v28: % 123.35/16.64 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (( ~ (v31 = % 123.35/16.64 | norm) & index(status, v26) = v31 & $i(v31)) | ( ~ (v30 = v26) % 123.35/16.64 | & index(ldr, v26) = v30 & $i(v30)) | ( ~ (v29 = v26) & % 123.35/16.64 | host(v23) = v29 & $i(v29)) | (host(v24) = v27 & queue(v27) = % 123.35/16.64 | v28 & $i(v28) & $i(v27) & ~ elem(v25, v28)))) & ! [v22: $i] : % 123.35/16.64 | ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ % 123.35/16.64 | (m_Ack(v24, v22) = v25) | ~ (host(v23) = v26) | ~ $i(v24) | ~ % 123.35/16.64 | $i(v23) | ~ $i(v22) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : % 123.35/16.64 | ((host(v24) = v29 & host(v22) = v28 & $i(v29) & $i(v28) & ~ % 123.35/16.64 | leq(v28, v29)) | (queue(v26) = v27 & $i(v27) & ~ elem(v25, % 123.35/16.64 | v27)))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! % 123.35/16.64 | [v25: $i] : (v23 = v22 | ~ (host(v23) = v25) | ~ (host(v22) = v24) % 123.35/16.64 | | ~ $i(v23) | ~ $i(v22) | ~ setIn(v23, alive) | ~ setIn(v22, % 123.35/16.64 | alive) | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: % 123.35/16.64 | $i] : (( ~ (v29 = v25) & index(ldr, v25) = v29 & $i(v29)) | ( ~ % 123.35/16.64 | (v28 = norm) & index(status, v25) = v28 & $i(v28)) | ( ~ (v27 = % 123.35/16.64 | norm) & index(status, v24) = v27 & $i(v27)) | ( ~ (v26 = v24) % 123.35/16.64 | & index(ldr, v24) = v26 & $i(v26)))) & ! [v22: $i] : ! [v23: % 123.35/16.64 | $i] : ! [v24: $i] : ! [v25: $i] : ( ~ (m_Ldr(v23) = v24) | ~ % 123.35/16.64 | (host(v22) = v25) | ~ $i(v23) | ~ $i(v22) | ? [v26: $i] : ? % 123.35/16.64 | [v27: $i] : ((host(v23) = v27 & $i(v27) & ~ leq(v25, v27)) | % 123.35/16.64 | (queue(v25) = v26 & $i(v26) & ~ elem(v24, v26)))) & ! [v22: $i] % 123.35/16.64 | : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ (m_Down(v23) = % 123.35/16.64 | v24) | ~ (host(v22) = v25) | ~ $i(v23) | ~ $i(v22) | ~ % 123.35/16.64 | setIn(v23, alive) | ? [v26: $i] : (queue(v25) = v26 & $i(v26) & ~ % 123.35/16.64 | elem(v24, v26))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : % 123.35/16.64 | ! [v25: $i] : ( ~ (m_Halt(v23) = v24) | ~ (host(v22) = v25) | ~ % 123.35/16.64 | $i(v23) | ~ $i(v22) | ? [v26: $i] : ? [v27: $i] : ((host(v23) = % 123.35/16.64 | v27 & $i(v27) & ~ leq(v25, v27)) | (queue(v25) = v26 & $i(v26) % 123.35/16.64 | & ~ elem(v24, v26)))) & ! [v22: $i] : ! [v23: $i] : ! [v24: % 123.35/16.64 | $i] : ! [v25: $i] : ( ~ (host(v23) = v25) | ~ (host(v22) = v24) | % 123.35/16.64 | ~ $i(v23) | ~ $i(v22) | ~ setIn(v23, alive) | ~ setIn(v22, % 123.35/16.64 | alive) | leq(v24, v25) | ? [v26: $i] : ? [v27: $i] : ? [v28: % 123.35/16.64 | $i] : ? [v29: $i] : (( ~ (v27 = elec_2) & index(status, v25) = % 123.35/16.64 | v27 & $i(v27)) | ( ~ (v26 = elec_2) & index(status, v24) = v26 % 123.35/16.64 | & $i(v26)) | (index(pendack, v25) = v29 & index(pendack, v24) = % 123.35/16.64 | v28 & $i(v29) & $i(v28) & ~ leq(v28, v29)))) & ! [v22: $i] : % 123.35/16.64 | ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ (host(v23) = v25) | % 123.35/16.64 | ~ (host(v22) = v24) | ~ $i(v23) | ~ $i(v22) | ~ setIn(v23, % 123.35/16.64 | alive) | ~ setIn(v22, alive) | leq(v24, v25) | ? [v26: $i] : ? % 123.35/16.64 | [v27: $i] : ? [v28: $i] : (( ~ (v27 = elec_2) & index(status, v25) % 123.35/16.64 | = v27 & $i(v27)) | ( ~ (v26 = elec_2) & index(status, v24) = % 123.35/16.64 | v26 & $i(v26)) | (index(pendack, v25) = v28 & $i(v28) & % 123.35/16.64 | leq(v28, v24)))) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : % 123.35/16.64 | ! [v25: $i] : ( ~ (host(v23) = v24) | ~ (host(v22) = v25) | ~ % 123.35/16.64 | $i(v23) | ~ $i(v22) | ~ setIn(v23, alive) | ~ setIn(v22, alive) % 123.35/16.64 | | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( ~ % 123.35/16.64 | (v29 = norm) & index(status, v25) = v29 & $i(v29)) | ( ~ (v28 = % 123.35/16.64 | v25) & index(ldr, v25) = v28 & $i(v28)) | ( ~ (v27 = elec_2) % 123.35/16.64 | & index(status, v24) = v27 & $i(v27)) | (index(pendack, v24) = % 123.35/16.64 | v26 & $i(v26) & leq(v26, v25)))) & ! [v22: $i] : ! [v23: $i] % 123.35/16.64 | : ! [v24: $i] : (v23 = v22 | ~ (host(v23) = v24) | ~ (host(v22) = % 123.35/16.64 | v24) | ~ $i(v23) | ~ $i(v22) | ~ setIn(v23, alive) | ~ % 123.35/16.64 | setIn(v22, alive)) & ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( % 123.35/16.64 | ~ (host(v23) = v24) | ~ (host(v22) = v24) | ~ $i(v23) | ~ % 123.35/16.64 | $i(v22) | ~ leq(v23, v22) | ~ setIn(v23, alive) | setIn(v22, % 123.35/16.64 | alive)) & ! [v22: $i] : ! [v23: $i] : ( ~ (host(v22) = v23) | % 123.35/16.64 | ~ $i(v22) | ~ setIn(v22, alive) | ? [v24: $i] : ? [v25: $i] : % 123.35/16.64 | ((v25 = v22 & index(elid, v23) = v22) | ( ~ (v24 = elec_1) & ~ % 123.35/16.64 | (v24 = elec_2) & index(status, v23) = v24 & $i(v24)))) & ! % 123.35/16.64 | [v22: $i] : ! [v23: $i] : ( ~ (host(v22) = v23) | ~ $i(v22) | ? % 123.35/16.64 | [v24: $i] : (index(pendack, v23) = v24 & $i(v24) & leq(v24, % 123.35/16.64 | nbr_proc))) & ! [v22: $i] : (v22 = v8 | ~ $i(v22) | ~ % 123.35/16.65 | leq(v0, v22) | leq(v5, v22) | setIn(v22, v12)) & ( ~ (norm = % 123.35/16.65 | elec_1) | ( ~ (v9 = v8) & index(ldr, v5) = v9 & $i(v9))) & ( ~ % 123.35/16.65 | (wait = elec_1) | ( ~ (v11 = v8) & index(elid, v5) = v10 & % 123.35/16.65 | host(v10) = v11 & $i(v11) & $i(v10)))) % 123.35/16.65 | % 123.35/16.65 | ALPHA: (function-axioms) implies: % 123.35/16.65 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = % 123.35/16.65 | v1) | ~ (queue(v2) = v0)) % 123.35/16.65 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = % 123.35/16.65 | v1) | ~ (host(v2) = v0)) % 123.35/16.65 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 123.35/16.65 | ~ (s(v2) = v0)) % 123.35/16.65 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = % 123.35/16.65 | v1) | ~ (m_Halt(v2) = v0)) % 123.35/16.65 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 123.35/16.65 | (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) % 123.35/16.65 | % 123.35/16.65 | DELTA: instantiating (1) with fresh symbol all_59_0 gives: % 123.35/16.65 | (15) s(zero) = all_59_0 & $i(all_59_0) & leq(all_59_0, nbr_proc) % 123.35/16.65 | % 123.35/16.65 | ALPHA: (15) implies: % 123.35/16.65 | (16) s(zero) = all_59_0 % 123.35/16.65 | % 123.35/16.65 | DELTA: instantiating (9) with fresh symbols all_65_0, all_65_1, all_65_2, % 123.35/16.65 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9, % 123.35/16.65 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15, % 123.35/16.65 | all_65_16, all_65_17, all_65_18, all_65_19, all_65_20, all_65_21 gives: % 123.35/16.66 | (17) ~ (all_65_5 = all_65_16) & ~ (all_65_8 = all_65_16) & index(down, % 123.35/16.66 | all_65_16) = all_65_9 & index(ldr, all_65_5) = all_65_5 & % 123.35/16.66 | index(status, all_65_5) = norm & index(status, all_65_16) = elec_1 & % 123.35/16.66 | snoc(all_65_3, all_65_7) = all_65_2 & cons(all_65_14, all_65_20) = % 123.35/16.66 | all_65_15 & m_Down(all_65_17) = all_65_14 & m_Halt(all_65_1) = % 123.35/16.66 | all_65_0 & m_Halt(all_65_18) = all_65_7 & s(all_65_16) = all_65_8 & % 123.35/16.66 | s(zero) = all_65_21 & host(all_65_1) = all_65_16 & host(all_65_4) = % 123.35/16.66 | all_65_8 & host(all_65_6) = all_65_5 & host(all_65_17) = all_65_13 & % 123.35/16.66 | host(all_65_18) = all_65_16 & queue(all_65_8) = all_65_3 & % 123.35/16.66 | queue(all_65_16) = all_65_15 & $i(all_65_0) & $i(all_65_1) & % 123.35/16.66 | $i(all_65_2) & $i(all_65_3) & $i(all_65_4) & $i(all_65_5) & % 123.35/16.66 | $i(all_65_6) & $i(all_65_7) & $i(all_65_8) & $i(all_65_9) & % 123.35/16.66 | $i(all_65_13) & $i(all_65_14) & $i(all_65_15) & $i(all_65_16) & % 123.35/16.66 | $i(all_65_17) & $i(all_65_18) & $i(all_65_19) & $i(all_65_20) & % 123.35/16.66 | $i(all_65_21) & setIn(all_65_1, alive) & setIn(all_65_6, alive) & % 123.35/16.66 | setIn(all_65_18, alive) & elem(all_65_0, all_65_2) & ~ leq(all_65_8, % 123.35/16.66 | all_65_5) & ~ leq(all_65_16, all_65_13) & ~ leq(nbr_proc, % 123.35/16.66 | all_65_16) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 123.35/16.66 | ! [v4: $i] : ! [v5: $i] : ( ~ (m_Down(v1) = v5) | ~ (host(v2) = v3) % 123.35/16.66 | | ~ (host(v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 123.35/16.66 | setIn(v0, alive) | leq(v3, v4) | ? [v6: $i] : ? [v7: $i] : ? [v8: % 123.35/16.66 | $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : % 123.35/16.66 | ($i(v12) & (( ~ (v12 = v7) & index(down, v3) = v6 & host(v1) = v7 & % 123.35/16.66 | $i(v7) & $i(v6) & leq(all_65_21, v12) & ~ leq(v3, v12) & ~ % 123.35/16.66 | setIn(v12, v6)) | ( ~ (v11 = norm) & index(status, v4) = v11 & % 123.35/16.66 | $i(v11)) | ( ~ (v10 = v4) & index(ldr, v4) = v10 & $i(v10)) | % 123.35/16.66 | ( ~ (v9 = elec_1) & index(status, v3) = v9 & $i(v9)) | % 123.35/16.66 | (queue(v3) = v8 & $i(v8) & ~ elem(v5, v8))))) & ! [v0: $i] : % 123.35/16.66 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 123.35/16.66 | ~ (m_Down(v1) = v3) | ~ (host(v2) = v4) | ~ (host(v0) = v5) | ~ % 123.35/16.66 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, % 123.35/16.66 | alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 123.35/16.66 | (( ~ (v9 = norm) & index(status, v5) = v9 & $i(v9)) | ( ~ (v8 = v5) % 123.35/16.66 | & index(ldr, v5) = v8 & $i(v8)) | ( ~ (v7 = v5) & host(v1) = v7 % 123.35/16.66 | & $i(v7)) | (queue(v4) = v6 & $i(v6) & ~ elem(v3, v6)))) & ! % 123.35/16.66 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 123.35/16.66 | [v5: $i] : ( ~ (m_Halt(v2) = v4) | ~ (host(v1) = v5) | ~ (host(v0) = % 123.35/16.66 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ % 123.35/16.66 | setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 123.35/16.66 | $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v11 = norm) & % 123.35/16.66 | index(status, v3) = v11 & $i(v11)) | ( ~ (v10 = v3) & index(ldr, % 123.35/16.66 | v3) = v10 & $i(v10)) | ( ~ (v9 = elec_2) & index(status, v6) = % 123.35/16.66 | v9 & host(v2) = v6 & $i(v9) & $i(v6)) | (index(pendack, v6) = v7 % 123.35/16.66 | & host(v2) = v6 & $i(v7) & $i(v6) & leq(v7, v3)) | (queue(v5) = % 123.35/16.66 | v8 & $i(v8) & ~ elem(v4, v8)))) & ! [v0: $i] : ! [v1: $i] : % 123.35/16.66 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (m_Ack(v2, v1) = v3) | ~ % 123.35/16.66 | (host(v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, % 123.35/16.66 | alive) | ~ setIn(v0, alive) | ? [v5: $i] : ? [v6: $i] : ? [v7: % 123.35/16.66 | $i] : ? [v8: $i] : ? [v9: $i] : (( ~ (v9 = norm) & index(status, % 123.35/16.66 | v4) = v9 & $i(v9)) | ( ~ (v8 = v4) & index(ldr, v4) = v8 & % 123.35/16.66 | $i(v8)) | ( ~ (v7 = v4) & host(v1) = v7 & $i(v7)) | (host(v2) = % 123.35/16.66 | v5 & queue(v5) = v6 & $i(v6) & $i(v5) & ~ elem(v3, v6)))) & ! % 123.35/16.66 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 123.35/16.66 | (m_Ack(v2, v0) = v3) | ~ (host(v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 123.35/16.66 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((host(v2) = v7 % 123.35/16.66 | & host(v0) = v6 & $i(v7) & $i(v6) & ~ leq(v6, v7)) | (queue(v4) % 123.35/16.66 | = v5 & $i(v5) & ~ elem(v3, v5)))) & ! [v0: $i] : ! [v1: $i] : % 123.35/16.66 | ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (host(v1) = v3) | ~ % 123.35/16.66 | (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ % 123.35/16.66 | setIn(v0, alive) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 123.35/16.66 | $i] : (( ~ (v7 = v3) & index(ldr, v3) = v7 & $i(v7)) | ( ~ (v6 = % 123.35/16.66 | norm) & index(status, v3) = v6 & $i(v6)) | ( ~ (v5 = norm) & % 123.35/16.66 | index(status, v2) = v5 & $i(v5)) | ( ~ (v4 = v2) & index(ldr, % 123.35/16.66 | v2) = v4 & $i(v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 123.35/16.66 | : ! [v3: $i] : ( ~ (m_Ldr(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) % 123.35/16.66 | | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & % 123.35/16.66 | ~ leq(v3, v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) % 123.35/16.66 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 123.35/16.66 | (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 123.35/16.66 | setIn(v1, alive) | ? [v4: $i] : (queue(v3) = v4 & $i(v4) & ~ % 123.35/16.66 | elem(v2, v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 123.35/16.66 | $i] : ( ~ (m_Halt(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ % 123.35/16.66 | $i(v0) | ? [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ % 123.35/16.66 | leq(v3, v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) & % 123.35/16.66 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) = % 123.35/16.66 | v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 123.35/16.66 | alive) | ~ setIn(v0, alive) | leq(v2, v3) | ? [v4: $i] : ? [v5: % 123.35/16.66 | $i] : ? [v6: $i] : ? [v7: $i] : (( ~ (v5 = elec_2) & % 123.35/16.66 | index(status, v3) = v5 & $i(v5)) | ( ~ (v4 = elec_2) & % 123.35/16.66 | index(status, v2) = v4 & $i(v4)) | (index(pendack, v3) = v7 & % 123.35/16.66 | index(pendack, v2) = v6 & $i(v7) & $i(v6) & ~ leq(v6, v7)))) & % 123.35/16.66 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) = % 123.35/16.66 | v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 123.35/16.66 | alive) | ~ setIn(v0, alive) | leq(v2, v3) | ? [v4: $i] : ? [v5: % 123.35/16.66 | $i] : ? [v6: $i] : (( ~ (v5 = elec_2) & index(status, v3) = v5 & % 123.35/16.66 | $i(v5)) | ( ~ (v4 = elec_2) & index(status, v2) = v4 & $i(v4)) | % 123.35/16.66 | (index(pendack, v3) = v6 & $i(v6) & leq(v6, v2)))) & ! [v0: $i] : % 123.35/16.66 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) = v2) | ~ % 123.35/16.66 | (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ % 123.35/16.66 | setIn(v0, alive) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 123.35/16.66 | $i] : (( ~ (v7 = norm) & index(status, v3) = v7 & $i(v7)) | ( ~ % 123.35/16.66 | (v6 = v3) & index(ldr, v3) = v6 & $i(v6)) | ( ~ (v5 = elec_2) & % 123.35/16.66 | index(status, v2) = v5 & $i(v5)) | (index(pendack, v2) = v4 & % 123.35/16.66 | $i(v4) & leq(v4, v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 123.35/16.66 | $i] : (v1 = v0 | ~ (host(v1) = v2) | ~ (host(v0) = v2) | ~ $i(v1) % 123.35/16.66 | | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive)) & ! [v0: % 123.35/16.66 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~ (host(v0) % 123.35/16.66 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) | ~ setIn(v1, % 123.35/16.66 | alive) | setIn(v0, alive)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 123.35/16.66 | (host(v0) = v1) | ~ $i(v0) | ~ setIn(v0, alive) | ? [v2: $i] : ? % 123.35/16.66 | [v3: $i] : ((v3 = v0 & index(elid, v1) = v0) | ( ~ (v2 = elec_1) & % 123.35/16.66 | ~ (v2 = elec_2) & index(status, v1) = v2 & $i(v2)))) & ! [v0: % 123.35/16.66 | $i] : ! [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 123.35/16.66 | (index(pendack, v1) = v2 & $i(v2) & leq(v2, nbr_proc))) & ! [v0: % 123.35/16.66 | any] : (v0 = all_65_13 | ~ $i(v0) | ~ leq(all_65_21, v0) | % 123.35/16.66 | leq(all_65_16, v0) | setIn(v0, all_65_9)) & ( ~ (norm = elec_1) | ( % 123.35/16.66 | ~ (all_65_12 = all_65_13) & index(ldr, all_65_16) = all_65_12 & % 123.35/16.66 | $i(all_65_12))) & ( ~ (wait = elec_1) | ( ~ (all_65_10 = % 123.35/16.66 | all_65_13) & index(elid, all_65_16) = all_65_11 & % 123.35/16.66 | host(all_65_11) = all_65_10 & $i(all_65_10) & $i(all_65_11))) % 123.35/16.66 | % 123.35/16.66 | ALPHA: (17) implies: % 123.35/16.66 | (18) ~ (all_65_5 = all_65_16) % 123.59/16.66 | (19) ~ leq(all_65_8, all_65_5) % 123.59/16.66 | (20) setIn(all_65_18, alive) % 123.59/16.66 | (21) setIn(all_65_6, alive) % 123.59/16.66 | (22) setIn(all_65_1, alive) % 123.59/16.66 | (23) $i(all_65_20) % 123.59/16.66 | (24) $i(all_65_18) % 123.59/16.66 | (25) $i(all_65_17) % 123.59/16.66 | (26) $i(all_65_16) % 123.59/16.67 | (27) $i(all_65_14) % 123.59/16.67 | (28) $i(all_65_8) % 123.59/16.67 | (29) $i(all_65_6) % 123.59/16.67 | (30) $i(all_65_5) % 123.59/16.67 | (31) $i(all_65_1) % 123.59/16.67 | (32) $i(all_65_0) % 123.59/16.67 | (33) queue(all_65_16) = all_65_15 % 123.59/16.67 | (34) host(all_65_18) = all_65_16 % 123.59/16.67 | (35) host(all_65_17) = all_65_13 % 123.59/16.67 | (36) host(all_65_6) = all_65_5 % 123.59/16.67 | (37) host(all_65_1) = all_65_16 % 123.59/16.67 | (38) s(zero) = all_65_21 % 123.59/16.67 | (39) s(all_65_16) = all_65_8 % 123.59/16.67 | (40) m_Halt(all_65_18) = all_65_7 % 123.59/16.67 | (41) m_Halt(all_65_1) = all_65_0 % 123.59/16.67 | (42) m_Down(all_65_17) = all_65_14 % 123.59/16.67 | (43) cons(all_65_14, all_65_20) = all_65_15 % 123.59/16.67 | (44) index(status, all_65_16) = elec_1 % 123.59/16.67 | (45) index(status, all_65_5) = norm % 123.59/16.67 | (46) index(ldr, all_65_5) = all_65_5 % 123.59/16.67 | (47) index(down, all_65_16) = all_65_9 % 123.59/16.67 | (48) ! [v0: any] : (v0 = all_65_13 | ~ $i(v0) | ~ leq(all_65_21, v0) | % 123.59/16.67 | leq(all_65_16, v0) | setIn(v0, all_65_9)) % 123.59/16.67 | (49) ! [v0: $i] : ! [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) | ~ % 123.59/16.67 | setIn(v0, alive) | ? [v2: $i] : ? [v3: $i] : ((v3 = v0 & % 123.59/16.67 | index(elid, v1) = v0) | ( ~ (v2 = elec_1) & ~ (v2 = elec_2) & % 123.59/16.67 | index(status, v1) = v2 & $i(v2)))) % 123.59/16.67 | (50) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v1) = % 123.59/16.67 | v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 123.59/16.67 | alive) | ~ setIn(v0, alive)) % 123.59/16.67 | (51) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) % 123.59/16.67 | = v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 123.59/16.67 | alive) | ~ setIn(v0, alive) | leq(v2, v3) | ? [v4: $i] : ? [v5: % 123.59/16.67 | $i] : ? [v6: $i] : (( ~ (v5 = elec_2) & index(status, v3) = v5 & % 123.59/16.67 | $i(v5)) | ( ~ (v4 = elec_2) & index(status, v2) = v4 & $i(v4)) | % 123.59/16.67 | (index(pendack, v3) = v6 & $i(v6) & leq(v6, v2)))) % 123.59/16.67 | (52) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 123.59/16.67 | (m_Halt(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 123.59/16.67 | [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) % 123.59/16.67 | | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) % 123.59/16.67 | (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 123.59/16.67 | ! [v5: $i] : ( ~ (m_Down(v1) = v3) | ~ (host(v2) = v4) | ~ (host(v0) % 123.59/16.67 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | % 123.59/16.67 | ~ setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 123.59/16.67 | [v9: $i] : (( ~ (v9 = norm) & index(status, v5) = v9 & $i(v9)) | ( ~ % 123.59/16.67 | (v8 = v5) & index(ldr, v5) = v8 & $i(v8)) | ( ~ (v7 = v5) & % 123.59/16.67 | host(v1) = v7 & $i(v7)) | (queue(v4) = v6 & $i(v6) & ~ elem(v3, % 123.59/16.67 | v6)))) % 123.59/16.67 | (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 123.59/16.67 | ! [v5: $i] : ( ~ (m_Down(v1) = v5) | ~ (host(v2) = v3) | ~ (host(v0) % 123.59/16.67 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v0, alive) | % 123.59/16.67 | leq(v3, v4) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 123.59/16.67 | : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ($i(v12) & (( ~ (v12 % 123.59/16.67 | = v7) & index(down, v3) = v6 & host(v1) = v7 & $i(v7) & % 123.59/16.67 | $i(v6) & leq(all_65_21, v12) & ~ leq(v3, v12) & ~ setIn(v12, % 123.59/16.67 | v6)) | ( ~ (v11 = norm) & index(status, v4) = v11 & $i(v11)) % 123.59/16.67 | | ( ~ (v10 = v4) & index(ldr, v4) = v10 & $i(v10)) | ( ~ (v9 = % 123.59/16.67 | elec_1) & index(status, v3) = v9 & $i(v9)) | (queue(v3) = v8 % 123.59/16.67 | & $i(v8) & ~ elem(v5, v8))))) % 123.59/16.67 | % 123.59/16.67 | GROUND_INST: instantiating (12) with all_59_0, all_65_21, zero, simplifying % 123.59/16.67 | with (16), (38) gives: % 123.59/16.67 | (55) all_65_21 = all_59_0 % 123.59/16.67 | % 123.59/16.67 | GROUND_INST: instantiating (axiom_01) with all_65_6, all_65_6, all_65_5, % 123.59/16.67 | simplifying with (29), (36) gives: % 123.59/16.67 | (56) ? [v0: any] : ( ~ (v0 = all_65_5) & s(all_65_5) = v0 & $i(v0)) % 123.59/16.67 | % 123.59/16.67 | GROUND_INST: instantiating (51) with all_65_1, all_65_6, all_65_16, all_65_5, % 123.59/16.67 | simplifying with (21), (22), (29), (31), (36), (37) gives: % 123.59/16.67 | (57) leq(all_65_16, all_65_5) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 123.59/16.67 | (( ~ (v1 = elec_2) & index(status, all_65_5) = v1 & $i(v1)) | ( ~ (v0 % 123.59/16.67 | = elec_2) & index(status, all_65_16) = v0 & $i(v0)) | % 123.59/16.67 | (index(pendack, all_65_5) = v2 & $i(v2) & leq(v2, all_65_16))) % 123.59/16.67 | % 123.59/16.67 | GROUND_INST: instantiating (50) with all_65_18, all_65_1, all_65_16, % 123.59/16.67 | simplifying with (20), (22), (24), (31), (34), (37) gives: % 123.59/16.67 | (58) all_65_1 = all_65_18 % 123.59/16.67 | % 123.59/16.67 | GROUND_INST: instantiating (49) with all_65_1, all_65_16, simplifying with % 123.59/16.67 | (22), (31), (37) gives: % 123.59/16.67 | (59) ? [v0: $i] : ? [v1: int] : ((v1 = all_65_1 & index(elid, all_65_16) % 123.59/16.67 | = all_65_1) | ( ~ (v0 = elec_1) & ~ (v0 = elec_2) & index(status, % 123.59/16.67 | all_65_16) = v0 & $i(v0))) % 123.59/16.67 | % 123.59/16.67 | GROUND_INST: instantiating (52) with all_65_17, all_65_18, all_65_7, % 123.59/16.67 | all_65_13, simplifying with (24), (25), (35), (40) gives: % 123.59/16.67 | (60) ? [v0: $i] : ? [v1: $i] : ((host(all_65_18) = v1 & $i(v1) & ~ % 123.59/16.67 | leq(all_65_13, v1)) | (queue(all_65_13) = v0 & $i(v0) & ~ % 123.59/16.67 | elem(all_65_7, v0))) % 123.59/16.67 | % 123.59/16.67 | GROUND_INST: instantiating (4) with all_65_0, all_65_1, simplifying with (31), % 123.59/16.67 | (32), (41) gives: % 123.59/16.67 | (61) pidElem(all_65_0) % 123.59/16.67 | % 123.59/16.68 | GROUND_INST: instantiating (54) with all_65_18, all_65_17, all_65_6, all_65_5, % 123.59/16.68 | all_65_16, all_65_14, simplifying with (20), (24), (25), (29), % 123.59/16.68 | (34), (36), (42) gives: % 123.59/16.68 | (62) leq(all_65_5, all_65_16) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 123.59/16.68 | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & (( ~ % 123.59/16.68 | (v6 = v1) & index(down, all_65_5) = v0 & host(all_65_17) = v1 & % 123.59/16.68 | $i(v1) & $i(v0) & leq(all_65_21, v6) & ~ leq(all_65_5, v6) & ~ % 123.59/16.68 | setIn(v6, v0)) | ( ~ (v5 = norm) & index(status, all_65_16) = v5 % 123.59/16.68 | & $i(v5)) | ( ~ (v4 = all_65_16) & index(ldr, all_65_16) = v4 & % 123.59/16.68 | $i(v4)) | ( ~ (v3 = elec_1) & index(status, all_65_5) = v3 & % 123.59/16.68 | $i(v3)) | (queue(all_65_5) = v2 & $i(v2) & ~ elem(all_65_14, % 123.59/16.68 | v2)))) % 123.59/16.68 | % 123.59/16.68 | GROUND_INST: instantiating (54) with all_65_18, all_65_17, all_65_17, % 123.59/16.68 | all_65_13, all_65_16, all_65_14, simplifying with (20), (24), % 123.59/16.68 | (25), (34), (35), (42) gives: % 123.59/16.68 | (63) leq(all_65_13, all_65_16) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 123.59/16.68 | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & (( ~ % 123.59/16.68 | (v6 = v1) & index(down, all_65_13) = v0 & host(all_65_17) = v1 & % 123.59/16.68 | $i(v1) & $i(v0) & leq(all_65_21, v6) & ~ leq(all_65_13, v6) & % 123.59/16.68 | ~ setIn(v6, v0)) | ( ~ (v5 = norm) & index(status, all_65_16) = % 123.59/16.68 | v5 & $i(v5)) | ( ~ (v4 = all_65_16) & index(ldr, all_65_16) = v4 % 123.59/16.68 | & $i(v4)) | ( ~ (v3 = elec_1) & index(status, all_65_13) = v3 & % 123.59/16.68 | $i(v3)) | (queue(all_65_13) = v2 & $i(v2) & ~ elem(all_65_14, % 123.59/16.68 | v2)))) % 123.59/16.68 | % 123.59/16.68 | GROUND_INST: instantiating (54) with all_65_6, all_65_17, all_65_18, % 123.59/16.68 | all_65_16, all_65_5, all_65_14, simplifying with (21), (24), % 123.59/16.68 | (25), (29), (34), (36), (42) gives: % 123.59/16.68 | (64) leq(all_65_16, all_65_5) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 123.59/16.68 | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & (( ~ % 123.59/16.68 | (v6 = v1) & index(down, all_65_16) = v0 & host(all_65_17) = v1 & % 123.59/16.68 | $i(v1) & $i(v0) & leq(all_65_21, v6) & ~ leq(all_65_16, v6) & % 123.59/16.68 | ~ setIn(v6, v0)) | ( ~ (v5 = norm) & index(status, all_65_5) = % 123.59/16.68 | v5 & $i(v5)) | ( ~ (v4 = all_65_5) & index(ldr, all_65_5) = v4 & % 123.59/16.68 | $i(v4)) | ( ~ (v3 = elec_1) & index(status, all_65_16) = v3 & % 123.59/16.68 | $i(v3)) | (queue(all_65_16) = v2 & $i(v2) & ~ elem(all_65_14, % 123.59/16.68 | v2)))) % 123.59/16.68 | % 123.59/16.68 | GROUND_INST: instantiating (53) with all_65_6, all_65_17, all_65_18, % 123.59/16.68 | all_65_14, all_65_16, all_65_5, simplifying with (20), (21), % 123.59/16.68 | (24), (25), (29), (34), (36), (42) gives: % 123.59/16.68 | (65) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : (( ~ (v3 = % 123.59/16.68 | norm) & index(status, all_65_5) = v3 & $i(v3)) | ( ~ (v2 = % 123.59/16.68 | all_65_5) & index(ldr, all_65_5) = v2 & $i(v2)) | ( ~ (v1 = % 123.59/16.68 | all_65_5) & host(all_65_17) = v1 & $i(v1)) | (queue(all_65_16) = % 123.59/16.68 | v0 & $i(v0) & ~ elem(all_65_14, v0))) % 123.59/16.68 | % 123.59/16.68 | GROUND_INST: instantiating (2) with all_65_14, all_65_20, all_65_15, % 123.59/16.68 | simplifying with (23), (27), (43) gives: % 123.59/16.68 | (66) elem(all_65_14, all_65_15) % 123.59/16.68 | % 123.59/16.68 | DELTA: instantiating (56) with fresh symbol all_80_0 gives: % 123.59/16.68 | (67) ~ (all_80_0 = all_65_5) & s(all_65_5) = all_80_0 & $i(all_80_0) % 123.59/16.68 | % 123.59/16.68 | ALPHA: (67) implies: % 123.59/16.68 | (68) s(all_65_5) = all_80_0 % 123.59/16.68 | % 123.59/16.68 | DELTA: instantiating (60) with fresh symbols all_93_0, all_93_1 gives: % 123.59/16.68 | (69) (host(all_65_18) = all_93_0 & $i(all_93_0) & ~ leq(all_65_13, % 123.59/16.68 | all_93_0)) | (queue(all_65_13) = all_93_1 & $i(all_93_1) & ~ % 123.59/16.68 | elem(all_65_7, all_93_1)) % 123.59/16.68 | % 123.59/16.68 | DELTA: instantiating (59) with fresh symbols all_96_0, all_96_1 gives: % 123.59/16.68 | (70) (all_96_0 = all_65_1 & index(elid, all_65_16) = all_65_1) | ( ~ % 123.59/16.68 | (all_96_1 = elec_1) & ~ (all_96_1 = elec_2) & index(status, % 123.59/16.68 | all_65_16) = all_96_1 & $i(all_96_1)) % 123.59/16.68 | % 123.59/16.68 | DELTA: instantiating (65) with fresh symbols all_108_0, all_108_1, all_108_2, % 123.59/16.68 | all_108_3 gives: % 123.59/16.68 | (71) ( ~ (all_108_0 = norm) & index(status, all_65_5) = all_108_0 & % 123.59/16.68 | $i(all_108_0)) | ( ~ (all_108_1 = all_65_5) & index(ldr, all_65_5) = % 123.59/16.68 | all_108_1 & $i(all_108_1)) | ( ~ (all_108_2 = all_65_5) & % 123.59/16.68 | host(all_65_17) = all_108_2 & $i(all_108_2)) | (queue(all_65_16) = % 123.59/16.68 | all_108_3 & $i(all_108_3) & ~ elem(all_65_14, all_108_3)) % 123.59/16.68 | % 123.59/16.68 | REDUCE: (41), (58) imply: % 123.59/16.68 | (72) m_Halt(all_65_18) = all_65_0 % 123.59/16.68 | % 123.59/16.68 | BETA: splitting (71) gives: % 123.59/16.68 | % 123.59/16.68 | Case 1: % 123.59/16.68 | | % 123.59/16.68 | | (73) ( ~ (all_108_0 = norm) & index(status, all_65_5) = all_108_0 & % 123.59/16.68 | | $i(all_108_0)) | ( ~ (all_108_1 = all_65_5) & index(ldr, all_65_5) % 123.59/16.68 | | = all_108_1 & $i(all_108_1)) % 123.59/16.68 | | % 123.59/16.68 | | BETA: splitting (73) gives: % 123.59/16.68 | | % 123.59/16.68 | | Case 1: % 123.59/16.68 | | | % 123.59/16.68 | | | (74) ~ (all_108_0 = norm) & index(status, all_65_5) = all_108_0 & % 123.59/16.68 | | | $i(all_108_0) % 123.59/16.68 | | | % 123.59/16.68 | | | ALPHA: (74) implies: % 123.59/16.68 | | | (75) ~ (all_108_0 = norm) % 123.59/16.68 | | | (76) index(status, all_65_5) = all_108_0 % 123.59/16.68 | | | % 123.59/16.68 | | | GROUND_INST: instantiating (14) with norm, all_108_0, all_65_5, status, % 123.59/16.68 | | | simplifying with (45), (76) gives: % 123.59/16.68 | | | (77) all_108_0 = norm % 123.59/16.68 | | | % 123.59/16.68 | | | REDUCE: (75), (77) imply: % 123.59/16.68 | | | (78) $false % 123.59/16.68 | | | % 123.59/16.68 | | | CLOSE: (78) is inconsistent. % 123.59/16.68 | | | % 123.59/16.68 | | Case 2: % 123.59/16.68 | | | % 123.59/16.68 | | | (79) ~ (all_108_1 = all_65_5) & index(ldr, all_65_5) = all_108_1 & % 123.59/16.68 | | | $i(all_108_1) % 123.59/16.68 | | | % 123.59/16.68 | | | ALPHA: (79) implies: % 123.59/16.68 | | | (80) ~ (all_108_1 = all_65_5) % 123.59/16.68 | | | (81) index(ldr, all_65_5) = all_108_1 % 123.59/16.68 | | | % 123.59/16.68 | | | GROUND_INST: instantiating (14) with all_65_5, all_108_1, all_65_5, ldr, % 123.59/16.68 | | | simplifying with (46), (81) gives: % 123.59/16.68 | | | (82) all_108_1 = all_65_5 % 123.59/16.68 | | | % 123.59/16.68 | | | REDUCE: (80), (82) imply: % 123.59/16.68 | | | (83) $false % 123.59/16.68 | | | % 123.59/16.68 | | | CLOSE: (83) is inconsistent. % 123.59/16.68 | | | % 123.59/16.68 | | End of split % 123.59/16.68 | | % 123.59/16.68 | Case 2: % 123.59/16.68 | | % 123.59/16.68 | | (84) ( ~ (all_108_2 = all_65_5) & host(all_65_17) = all_108_2 & % 123.59/16.68 | | $i(all_108_2)) | (queue(all_65_16) = all_108_3 & $i(all_108_3) & % 123.59/16.68 | | ~ elem(all_65_14, all_108_3)) % 123.59/16.69 | | % 123.59/16.69 | | BETA: splitting (84) gives: % 123.59/16.69 | | % 123.59/16.69 | | Case 1: % 123.59/16.69 | | | % 123.59/16.69 | | | (85) ~ (all_108_2 = all_65_5) & host(all_65_17) = all_108_2 & % 123.59/16.69 | | | $i(all_108_2) % 123.59/16.69 | | | % 123.59/16.69 | | | ALPHA: (85) implies: % 123.59/16.69 | | | (86) host(all_65_17) = all_108_2 % 123.59/16.69 | | | % 123.59/16.69 | | | BETA: splitting (70) gives: % 123.59/16.69 | | | % 123.59/16.69 | | | Case 1: % 123.59/16.69 | | | | % 123.59/16.69 | | | | % 123.59/16.69 | | | | GROUND_INST: instantiating (11) with all_65_13, all_108_2, all_65_17, % 123.59/16.69 | | | | simplifying with (35), (86) gives: % 123.59/16.69 | | | | (87) all_108_2 = all_65_13 % 123.59/16.69 | | | | % 123.59/16.69 | | | | GROUND_INST: instantiating (13) with all_65_7, all_65_0, all_65_18, % 123.59/16.69 | | | | simplifying with (40), (72) gives: % 123.59/16.69 | | | | (88) all_65_0 = all_65_7 % 123.59/16.69 | | | | % 123.59/16.69 | | | | REDUCE: (32), (88) imply: % 123.59/16.69 | | | | (89) $i(all_65_7) % 123.59/16.69 | | | | % 123.59/16.69 | | | | REDUCE: (61), (88) imply: % 123.59/16.69 | | | | (90) pidElem(all_65_7) % 123.59/16.69 | | | | % 123.59/16.69 | | | | GROUND_INST: instantiating (3) with all_65_7, simplifying with (89), % 123.59/16.69 | | | | (90) gives: % 123.59/16.69 | | | | (91) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ($i(v0) & ((v2 = % 123.59/16.69 | | | | all_65_7 & m_Down(v0) = all_65_7) | (v1 = all_65_7 & % 123.59/16.69 | | | | m_Halt(v0) = all_65_7))) % 123.59/16.69 | | | | % 123.59/16.69 | | | | DELTA: instantiating (91) with fresh symbols all_153_0, all_153_1, % 123.59/16.69 | | | | all_153_2 gives: % 123.59/16.69 | | | | (92) $i(all_153_2) & ((all_153_0 = all_65_7 & m_Down(all_153_2) = % 123.59/16.69 | | | | all_65_7) | (all_153_1 = all_65_7 & m_Halt(all_153_2) = % 123.59/16.69 | | | | all_65_7)) % 123.59/16.69 | | | | % 123.59/16.69 | | | | ALPHA: (92) implies: % 123.59/16.69 | | | | (93) $i(all_153_2) % 123.59/16.69 | | | | (94) (all_153_0 = all_65_7 & m_Down(all_153_2) = all_65_7) | % 123.59/16.69 | | | | (all_153_1 = all_65_7 & m_Halt(all_153_2) = all_65_7) % 123.59/16.69 | | | | % 123.59/16.69 | | | | BETA: splitting (64) gives: % 123.59/16.69 | | | | % 123.59/16.69 | | | | Case 1: % 123.59/16.69 | | | | | % 123.59/16.69 | | | | | (95) leq(all_65_16, all_65_5) % 123.59/16.69 | | | | | % 123.59/16.69 | | | | | BETA: splitting (62) gives: % 123.59/16.69 | | | | | % 123.59/16.69 | | | | | Case 1: % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | | (96) leq(all_65_5, all_65_16) % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | | GROUND_INST: instantiating (5) with all_65_16, all_65_5, simplifying % 123.59/16.69 | | | | | | with (26), (30), (95), (96) gives: % 123.59/16.69 | | | | | | (97) all_65_5 = all_65_16 % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | | REDUCE: (18), (97) imply: % 123.59/16.69 | | | | | | (98) $false % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | | CLOSE: (98) is inconsistent. % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | Case 2: % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | | (99) ~ leq(all_65_5, all_65_16) % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | | BETA: splitting (63) gives: % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | | Case 1: % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | | (100) leq(all_65_13, all_65_16) % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | | BETA: splitting (69) gives: % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | | Case 1: % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | (101) host(all_65_18) = all_93_0 & $i(all_93_0) & ~ % 123.59/16.69 | | | | | | | | leq(all_65_13, all_93_0) % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | ALPHA: (101) implies: % 123.59/16.69 | | | | | | | | (102) ~ leq(all_65_13, all_93_0) % 123.59/16.69 | | | | | | | | (103) host(all_65_18) = all_93_0 % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | GROUND_INST: instantiating (11) with all_65_16, all_93_0, % 123.59/16.69 | | | | | | | | all_65_18, simplifying with (34), (103) gives: % 123.59/16.69 | | | | | | | | (104) all_93_0 = all_65_16 % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | REDUCE: (102), (104) imply: % 123.59/16.69 | | | | | | | | (105) ~ leq(all_65_13, all_65_16) % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | PRED_UNIFY: (100), (105) imply: % 123.59/16.69 | | | | | | | | (106) $false % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | CLOSE: (106) is inconsistent. % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | Case 2: % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | GROUND_INST: instantiating (6) with all_65_16, all_65_5, % 123.59/16.69 | | | | | | | | all_65_8, all_80_0, simplifying with (26), (30), % 123.59/16.69 | | | | | | | | (39), (68), (95) gives: % 123.59/16.69 | | | | | | | | (107) leq(all_65_8, all_80_0) % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | REF_CLOSE: (7), (8), (19), (24), (26), (28), (30), (39), (40), % 123.59/16.69 | | | | | | | | (68), (93), (94), (99), (107), (axiom_17) are % 123.59/16.69 | | | | | | | | inconsistent by sub-proof #1. % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | End of split % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | Case 2: % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | | GROUND_INST: instantiating (6) with all_65_16, all_65_5, all_65_8, % 123.59/16.69 | | | | | | | all_80_0, simplifying with (26), (30), (39), (68), % 123.59/16.69 | | | | | | | (95) gives: % 123.59/16.69 | | | | | | | (108) leq(all_65_8, all_80_0) % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | | REF_CLOSE: (7), (8), (19), (24), (26), (28), (30), (39), (40), % 123.59/16.69 | | | | | | | (68), (93), (94), (99), (108), (axiom_17) are % 123.59/16.69 | | | | | | | inconsistent by sub-proof #1. % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | End of split % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | End of split % 123.59/16.69 | | | | | % 123.59/16.69 | | | | Case 2: % 123.59/16.69 | | | | | % 123.59/16.69 | | | | | (109) ~ leq(all_65_16, all_65_5) % 123.59/16.69 | | | | | (110) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 123.59/16.69 | | | | | [v4: any] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & (( ~ (v6 = % 123.59/16.69 | | | | | v1) & index(down, all_65_16) = v0 & host(all_65_17) = % 123.59/16.69 | | | | | v1 & $i(v1) & $i(v0) & leq(all_65_21, v6) & ~ % 123.59/16.69 | | | | | leq(all_65_16, v6) & ~ setIn(v6, v0)) | ( ~ (v5 = % 123.59/16.69 | | | | | norm) & index(status, all_65_5) = v5 & $i(v5)) | ( ~ % 123.59/16.69 | | | | | (v4 = all_65_5) & index(ldr, all_65_5) = v4 & $i(v4)) | % 123.59/16.69 | | | | | ( ~ (v3 = elec_1) & index(status, all_65_16) = v3 & % 123.59/16.69 | | | | | $i(v3)) | (queue(all_65_16) = v2 & $i(v2) & ~ % 123.59/16.69 | | | | | elem(all_65_14, v2)))) % 123.59/16.69 | | | | | % 123.59/16.69 | | | | | DELTA: instantiating (110) with fresh symbols all_211_0, all_211_1, % 123.59/16.69 | | | | | all_211_2, all_211_3, all_211_4, all_211_5, all_211_6 gives: % 123.59/16.69 | | | | | (111) $i(all_211_0) & (( ~ (all_211_0 = all_211_5) & index(down, % 123.59/16.69 | | | | | all_65_16) = all_211_6 & host(all_65_17) = all_211_5 & % 123.59/16.69 | | | | | $i(all_211_5) & $i(all_211_6) & leq(all_65_21, all_211_0) % 123.59/16.69 | | | | | & ~ leq(all_65_16, all_211_0) & ~ setIn(all_211_0, % 123.59/16.69 | | | | | all_211_6)) | ( ~ (all_211_1 = norm) & index(status, % 123.59/16.69 | | | | | all_65_5) = all_211_1 & $i(all_211_1)) | ( ~ (all_211_2 % 123.59/16.69 | | | | | = all_65_5) & index(ldr, all_65_5) = all_211_2 & % 123.59/16.69 | | | | | $i(all_211_2)) | ( ~ (all_211_3 = elec_1) & index(status, % 123.59/16.69 | | | | | all_65_16) = all_211_3 & $i(all_211_3)) | % 123.59/16.69 | | | | | (queue(all_65_16) = all_211_4 & $i(all_211_4) & ~ % 123.59/16.69 | | | | | elem(all_65_14, all_211_4))) % 123.59/16.69 | | | | | % 123.59/16.69 | | | | | ALPHA: (111) implies: % 123.59/16.69 | | | | | (112) $i(all_211_0) % 123.59/16.69 | | | | | (113) ( ~ (all_211_0 = all_211_5) & index(down, all_65_16) = % 123.59/16.69 | | | | | all_211_6 & host(all_65_17) = all_211_5 & $i(all_211_5) & % 123.59/16.69 | | | | | $i(all_211_6) & leq(all_65_21, all_211_0) & ~ % 123.59/16.69 | | | | | leq(all_65_16, all_211_0) & ~ setIn(all_211_0, all_211_6)) % 123.59/16.69 | | | | | | ( ~ (all_211_1 = norm) & index(status, all_65_5) = % 123.59/16.69 | | | | | all_211_1 & $i(all_211_1)) | ( ~ (all_211_2 = all_65_5) & % 123.59/16.69 | | | | | index(ldr, all_65_5) = all_211_2 & $i(all_211_2)) | ( ~ % 123.59/16.69 | | | | | (all_211_3 = elec_1) & index(status, all_65_16) = all_211_3 % 123.59/16.69 | | | | | & $i(all_211_3)) | (queue(all_65_16) = all_211_4 & % 123.59/16.69 | | | | | $i(all_211_4) & ~ elem(all_65_14, all_211_4)) % 123.59/16.69 | | | | | % 123.59/16.69 | | | | | BETA: splitting (113) gives: % 123.59/16.69 | | | | | % 123.59/16.69 | | | | | Case 1: % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | | (114) ( ~ (all_211_0 = all_211_5) & index(down, all_65_16) = % 123.59/16.69 | | | | | | all_211_6 & host(all_65_17) = all_211_5 & $i(all_211_5) & % 123.59/16.69 | | | | | | $i(all_211_6) & leq(all_65_21, all_211_0) & ~ % 123.59/16.69 | | | | | | leq(all_65_16, all_211_0) & ~ setIn(all_211_0, % 123.59/16.69 | | | | | | all_211_6)) | ( ~ (all_211_1 = norm) & index(status, % 123.59/16.69 | | | | | | all_65_5) = all_211_1 & $i(all_211_1)) % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | | BETA: splitting (114) gives: % 123.59/16.69 | | | | | | % 123.59/16.69 | | | | | | Case 1: % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | | (115) ~ (all_211_0 = all_211_5) & index(down, all_65_16) = % 123.59/16.69 | | | | | | | all_211_6 & host(all_65_17) = all_211_5 & $i(all_211_5) & % 123.59/16.69 | | | | | | | $i(all_211_6) & leq(all_65_21, all_211_0) & ~ % 123.59/16.69 | | | | | | | leq(all_65_16, all_211_0) & ~ setIn(all_211_0, % 123.59/16.69 | | | | | | | all_211_6) % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | | ALPHA: (115) implies: % 123.59/16.69 | | | | | | | (116) ~ (all_211_0 = all_211_5) % 123.59/16.69 | | | | | | | (117) ~ setIn(all_211_0, all_211_6) % 123.59/16.69 | | | | | | | (118) ~ leq(all_65_16, all_211_0) % 123.59/16.69 | | | | | | | (119) leq(all_65_21, all_211_0) % 123.59/16.69 | | | | | | | (120) host(all_65_17) = all_211_5 % 123.59/16.69 | | | | | | | (121) index(down, all_65_16) = all_211_6 % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | | REDUCE: (55), (119) imply: % 123.59/16.69 | | | | | | | (122) leq(all_59_0, all_211_0) % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | | BETA: splitting (57) gives: % 123.59/16.69 | | | | | | | % 123.59/16.69 | | | | | | | Case 1: % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | (123) leq(all_65_16, all_65_5) % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | PRED_UNIFY: (109), (123) imply: % 123.59/16.69 | | | | | | | | (124) $false % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | CLOSE: (124) is inconsistent. % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | Case 2: % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | % 123.59/16.69 | | | | | | | | GROUND_INST: instantiating (11) with all_65_13, all_211_5, % 123.59/16.69 | | | | | | | | all_65_17, simplifying with (35), (120) gives: % 123.59/16.69 | | | | | | | | (125) all_211_5 = all_65_13 % 123.59/16.69 | | | | | | | | % 123.59/16.70 | | | | | | | | GROUND_INST: instantiating (14) with all_65_9, all_211_6, % 123.59/16.70 | | | | | | | | all_65_16, down, simplifying with (47), (121) % 123.59/16.70 | | | | | | | | gives: % 123.59/16.70 | | | | | | | | (126) all_211_6 = all_65_9 % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | REDUCE: (116), (125) imply: % 123.59/16.70 | | | | | | | | (127) ~ (all_211_0 = all_65_13) % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | REDUCE: (117), (126) imply: % 123.59/16.70 | | | | | | | | (128) ~ setIn(all_211_0, all_65_9) % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | GROUND_INST: instantiating (48) with all_211_0, simplifying with % 123.59/16.70 | | | | | | | | (112), (118), (128) gives: % 123.59/16.70 | | | | | | | | (129) all_211_0 = all_65_13 | ~ leq(all_65_21, all_211_0) % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | BETA: splitting (129) gives: % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | Case 1: % 123.59/16.70 | | | | | | | | | % 123.59/16.70 | | | | | | | | | (130) ~ leq(all_65_21, all_211_0) % 123.59/16.70 | | | | | | | | | % 123.59/16.70 | | | | | | | | | REDUCE: (55), (130) imply: % 123.59/16.70 | | | | | | | | | (131) ~ leq(all_59_0, all_211_0) % 123.59/16.70 | | | | | | | | | % 123.59/16.70 | | | | | | | | | PRED_UNIFY: (122), (131) imply: % 123.59/16.70 | | | | | | | | | (132) $false % 123.59/16.70 | | | | | | | | | % 123.59/16.70 | | | | | | | | | CLOSE: (132) is inconsistent. % 123.59/16.70 | | | | | | | | | % 123.59/16.70 | | | | | | | | Case 2: % 123.59/16.70 | | | | | | | | | % 123.59/16.70 | | | | | | | | | (133) all_211_0 = all_65_13 % 123.59/16.70 | | | | | | | | | % 123.59/16.70 | | | | | | | | | REDUCE: (127), (133) imply: % 123.59/16.70 | | | | | | | | | (134) $false % 123.59/16.70 | | | | | | | | | % 123.59/16.70 | | | | | | | | | CLOSE: (134) is inconsistent. % 123.59/16.70 | | | | | | | | | % 123.59/16.70 | | | | | | | | End of split % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | End of split % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | Case 2: % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | (135) ~ (all_211_1 = norm) & index(status, all_65_5) = % 123.59/16.70 | | | | | | | all_211_1 & $i(all_211_1) % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | ALPHA: (135) implies: % 123.59/16.70 | | | | | | | (136) ~ (all_211_1 = norm) % 123.59/16.70 | | | | | | | (137) index(status, all_65_5) = all_211_1 % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | GROUND_INST: instantiating (14) with norm, all_211_1, all_65_5, % 123.59/16.70 | | | | | | | status, simplifying with (45), (137) gives: % 123.59/16.70 | | | | | | | (138) all_211_1 = norm % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | REDUCE: (136), (138) imply: % 123.59/16.70 | | | | | | | (139) $false % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | CLOSE: (139) is inconsistent. % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | End of split % 123.59/16.70 | | | | | | % 123.59/16.70 | | | | | Case 2: % 123.59/16.70 | | | | | | % 123.59/16.70 | | | | | | (140) ( ~ (all_211_2 = all_65_5) & index(ldr, all_65_5) = % 123.59/16.70 | | | | | | all_211_2 & $i(all_211_2)) | ( ~ (all_211_3 = elec_1) & % 123.59/16.70 | | | | | | index(status, all_65_16) = all_211_3 & $i(all_211_3)) | % 123.59/16.70 | | | | | | (queue(all_65_16) = all_211_4 & $i(all_211_4) & ~ % 123.59/16.70 | | | | | | elem(all_65_14, all_211_4)) % 123.59/16.70 | | | | | | % 123.59/16.70 | | | | | | BETA: splitting (140) gives: % 123.59/16.70 | | | | | | % 123.59/16.70 | | | | | | Case 1: % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | (141) ~ (all_211_2 = all_65_5) & index(ldr, all_65_5) = % 123.59/16.70 | | | | | | | all_211_2 & $i(all_211_2) % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | ALPHA: (141) implies: % 123.59/16.70 | | | | | | | (142) ~ (all_211_2 = all_65_5) % 123.59/16.70 | | | | | | | (143) index(ldr, all_65_5) = all_211_2 % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | GROUND_INST: instantiating (14) with all_65_5, all_211_2, % 123.59/16.70 | | | | | | | all_65_5, ldr, simplifying with (46), (143) gives: % 123.59/16.70 | | | | | | | (144) all_211_2 = all_65_5 % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | REDUCE: (142), (144) imply: % 123.59/16.70 | | | | | | | (145) $false % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | CLOSE: (145) is inconsistent. % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | Case 2: % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | (146) ( ~ (all_211_3 = elec_1) & index(status, all_65_16) = % 123.59/16.70 | | | | | | | all_211_3 & $i(all_211_3)) | (queue(all_65_16) = % 123.59/16.70 | | | | | | | all_211_4 & $i(all_211_4) & ~ elem(all_65_14, % 123.59/16.70 | | | | | | | all_211_4)) % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | BETA: splitting (146) gives: % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | | Case 1: % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | (147) ~ (all_211_3 = elec_1) & index(status, all_65_16) = % 123.59/16.70 | | | | | | | | all_211_3 & $i(all_211_3) % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | ALPHA: (147) implies: % 123.59/16.70 | | | | | | | | (148) ~ (all_211_3 = elec_1) % 123.59/16.70 | | | | | | | | (149) index(status, all_65_16) = all_211_3 % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | GROUND_INST: instantiating (14) with elec_1, all_211_3, % 123.59/16.70 | | | | | | | | all_65_16, status, simplifying with (44), (149) % 123.59/16.70 | | | | | | | | gives: % 123.59/16.70 | | | | | | | | (150) all_211_3 = elec_1 % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | REDUCE: (148), (150) imply: % 123.59/16.70 | | | | | | | | (151) $false % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | CLOSE: (151) is inconsistent. % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | Case 2: % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | (152) queue(all_65_16) = all_211_4 & $i(all_211_4) & ~ % 123.59/16.70 | | | | | | | | elem(all_65_14, all_211_4) % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | ALPHA: (152) implies: % 123.59/16.70 | | | | | | | | (153) ~ elem(all_65_14, all_211_4) % 123.59/16.70 | | | | | | | | (154) queue(all_65_16) = all_211_4 % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | GROUND_INST: instantiating (10) with all_65_15, all_211_4, % 123.59/16.70 | | | | | | | | all_65_16, simplifying with (33), (154) gives: % 123.59/16.70 | | | | | | | | (155) all_211_4 = all_65_15 % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | REDUCE: (153), (155) imply: % 123.59/16.70 | | | | | | | | (156) ~ elem(all_65_14, all_65_15) % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | PRED_UNIFY: (66), (156) imply: % 123.59/16.70 | | | | | | | | (157) $false % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | | CLOSE: (157) is inconsistent. % 123.59/16.70 | | | | | | | | % 123.59/16.70 | | | | | | | End of split % 123.59/16.70 | | | | | | | % 123.59/16.70 | | | | | | End of split % 123.59/16.70 | | | | | | % 123.59/16.70 | | | | | End of split % 123.59/16.70 | | | | | % 123.59/16.70 | | | | End of split % 123.59/16.70 | | | | % 123.59/16.70 | | | Case 2: % 123.59/16.70 | | | | % 123.59/16.70 | | | | (158) ~ (all_96_1 = elec_1) & ~ (all_96_1 = elec_2) & index(status, % 123.59/16.70 | | | | all_65_16) = all_96_1 & $i(all_96_1) % 123.59/16.70 | | | | % 123.59/16.70 | | | | ALPHA: (158) implies: % 123.59/16.70 | | | | (159) ~ (all_96_1 = elec_1) % 123.59/16.70 | | | | (160) index(status, all_65_16) = all_96_1 % 123.59/16.70 | | | | % 123.59/16.70 | | | | GROUND_INST: instantiating (14) with elec_1, all_96_1, all_65_16, % 123.59/16.70 | | | | status, simplifying with (44), (160) gives: % 123.59/16.70 | | | | (161) all_96_1 = elec_1 % 123.59/16.70 | | | | % 123.59/16.70 | | | | REDUCE: (159), (161) imply: % 123.59/16.70 | | | | (162) $false % 123.59/16.70 | | | | % 123.59/16.70 | | | | CLOSE: (162) is inconsistent. % 123.59/16.70 | | | | % 123.59/16.70 | | | End of split % 123.59/16.70 | | | % 123.59/16.70 | | Case 2: % 123.59/16.70 | | | % 123.59/16.70 | | | (163) queue(all_65_16) = all_108_3 & $i(all_108_3) & ~ elem(all_65_14, % 123.59/16.70 | | | all_108_3) % 123.59/16.70 | | | % 123.59/16.70 | | | ALPHA: (163) implies: % 123.59/16.70 | | | (164) ~ elem(all_65_14, all_108_3) % 123.59/16.70 | | | (165) queue(all_65_16) = all_108_3 % 123.59/16.70 | | | % 123.59/16.70 | | | GROUND_INST: instantiating (10) with all_65_15, all_108_3, all_65_16, % 123.59/16.70 | | | simplifying with (33), (165) gives: % 123.59/16.70 | | | (166) all_108_3 = all_65_15 % 123.59/16.70 | | | % 123.59/16.70 | | | REDUCE: (164), (166) imply: % 123.59/16.70 | | | (167) ~ elem(all_65_14, all_65_15) % 123.59/16.70 | | | % 123.59/16.70 | | | PRED_UNIFY: (66), (167) imply: % 123.59/16.70 | | | (168) $false % 123.59/16.70 | | | % 123.59/16.70 | | | CLOSE: (168) is inconsistent. % 123.59/16.70 | | | % 123.59/16.70 | | End of split % 123.59/16.70 | | % 123.59/16.70 | End of split % 123.59/16.70 | % 123.59/16.70 End of proof % 123.59/16.70 % 123.59/16.70 Sub-proof #1 shows that the following formulas are inconsistent: % 123.59/16.70 ---------------------------------------------------------------- % 123.59/16.70 (1) ~ leq(all_65_8, all_65_5) % 123.59/16.70 (2) s(all_65_16) = all_65_8 % 123.59/16.70 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (s(v1) = v2) | ~ % 123.59/16.70 $i(v1) | ~ $i(v0) | ~ leq(v0, v2) | leq(v0, v1)) % 123.59/16.70 (4) leq(all_65_8, all_80_0) % 123.59/16.70 (5) s(all_65_5) = all_80_0 % 123.59/16.70 (6) $i(all_65_16) % 123.59/16.70 (7) ~ leq(all_65_5, all_65_16) % 123.59/16.70 (8) $i(all_65_8) % 123.59/16.70 (9) $i(all_65_18) % 123.59/16.70 (10) $i(all_153_2) % 123.59/16.70 (11) m_Halt(all_65_18) = all_65_7 % 123.59/16.70 (12) (all_153_0 = all_65_7 & m_Down(all_153_2) = all_65_7) | (all_153_1 = % 123.59/16.70 all_65_7 & m_Halt(all_153_2) = all_65_7) % 123.59/16.70 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = v3) % 123.59/16.70 | ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | leq(v0, % 123.59/16.70 v1)) % 123.59/16.70 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~ % 123.59/16.70 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 123.59/16.70 (15) $i(all_65_5) % 123.59/16.70 % 123.59/16.70 Begin of proof % 123.59/16.70 | % 123.59/16.70 | BETA: splitting (12) gives: % 123.59/16.70 | % 123.59/16.70 | Case 1: % 123.59/16.70 | | % 123.59/16.70 | | (16) all_153_0 = all_65_7 & m_Down(all_153_2) = all_65_7 % 123.59/16.70 | | % 123.59/16.70 | | ALPHA: (16) implies: % 123.59/16.70 | | (17) m_Down(all_153_2) = all_65_7 % 123.59/16.70 | | % 123.59/16.70 | | GROUND_INST: instantiating (14) with all_153_2, all_65_18, all_65_7, % 123.59/16.70 | | simplifying with (9), (10), (11), (17) gives: % 123.59/16.70 | | (18) $false % 123.59/16.70 | | % 123.59/16.70 | | CLOSE: (18) is inconsistent. % 123.59/16.70 | | % 123.59/16.70 | Case 2: % 123.59/16.70 | | % 123.59/16.70 | | % 123.59/16.71 | | GROUND_INST: instantiating (3) with all_65_8, all_65_5, all_80_0, % 123.59/16.71 | | simplifying with (1), (4), (5), (8), (15) gives: % 123.59/16.71 | | (19) all_80_0 = all_65_8 % 123.59/16.71 | | % 123.59/16.71 | | REDUCE: (5), (19) imply: % 123.59/16.71 | | (20) s(all_65_5) = all_65_8 % 123.59/16.71 | | % 123.59/16.71 | | REDUCE: (4), (19) imply: % 123.59/16.71 | | (21) leq(all_65_8, all_65_8) % 123.59/16.71 | | % 123.59/16.71 | | GROUND_INST: instantiating (13) with all_65_5, all_65_16, all_65_8, % 123.59/16.71 | | all_65_8, simplifying with (2), (6), (7), (15), (20), (21) % 123.59/16.71 | | gives: % 123.59/16.71 | | (22) $false % 123.59/16.71 | | % 123.59/16.71 | | CLOSE: (22) is inconsistent. % 123.59/16.71 | | % 123.59/16.71 | End of split % 123.59/16.71 | % 123.59/16.71 End of proof % 123.59/16.71 % SZS output end Proof for theBenchmark % 123.59/16.71 % 123.59/16.71 16072ms %------------------------------------------------------------------------------