%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV459+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 : n019.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 166.86s 23.04s % Output : Proof 168.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SWV459+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.30 % Computer : n019.cluster.edu % 0.14/0.30 % Model : x86_64 x86_64 % 0.14/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.30 % Memory : 8042.1875MB % 0.14/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.30 % CPULimit : 300 % 0.14/0.30 % WCLimit : 300 % 0.14/0.30 % DateTime : Tue Aug 29 04:36:13 EDT 2023 % 0.14/0.31 % CPUTime : % 0.16/0.59 ________ _____ % 0.16/0.59 ___ __ \_________(_)________________________________ % 0.16/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.59 % 0.16/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.59 (2023-06-19) % 0.16/0.59 % 0.16/0.59 (c) Philipp Rümmer, 2009-2023 % 0.16/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.59 Amanda Stjerna. % 0.16/0.59 Free software under BSD-3-Clause. % 0.16/0.59 % 0.16/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.59 % 0.16/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.16/0.61 Running up to 7 provers in parallel. % 0.16/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.06/1.39 Prover 1: Preprocessing ... % 4.06/1.39 Prover 4: Preprocessing ... % 4.06/1.47 Prover 3: Preprocessing ... % 4.06/1.47 Prover 6: Preprocessing ... % 4.06/1.47 Prover 0: Preprocessing ... % 4.06/1.47 Prover 5: Preprocessing ... % 4.06/1.47 Prover 2: Preprocessing ... % 15.56/2.97 Prover 1: Constructing countermodel ... % 15.56/2.99 Prover 3: Constructing countermodel ... % 15.98/3.04 Prover 6: Proving ... % 17.35/3.23 Prover 2: Proving ... % 17.35/3.23 Prover 5: Proving ... % 18.91/3.40 Prover 4: Constructing countermodel ... % 20.28/3.74 Prover 0: Proving ... % 29.02/4.83 Prover 3: gave up % 29.02/4.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 29.57/4.97 Prover 7: Preprocessing ... % 36.39/5.80 Prover 7: Warning: ignoring some quantifiers % 36.93/5.89 Prover 7: Constructing countermodel ... % 60.72/9.07 Prover 2: stopped % 60.72/9.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 62.56/9.28 Prover 8: Preprocessing ... % 65.80/9.72 Prover 8: Warning: ignoring some quantifiers % 65.80/9.74 Prover 8: Constructing countermodel ... % 98.36/13.97 Prover 5: stopped % 98.36/13.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 99.76/14.13 Prover 9: Preprocessing ... % 102.66/14.53 Prover 1: gave up % 102.66/14.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 102.66/14.61 Prover 10: Preprocessing ... % 102.66/14.73 Prover 10: Warning: ignoring some quantifiers % 102.66/14.74 Prover 10: Constructing countermodel ... % 106.93/15.04 Prover 9: Constructing countermodel ... % 126.61/17.87 Prover 6: stopped % 126.61/17.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 126.61/17.90 Prover 8: gave up % 126.61/17.90 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 126.61/17.97 Prover 12: Preprocessing ... % 128.71/18.02 Prover 11: Preprocessing ... % 129.86/18.15 Prover 12: Proving ... % 131.67/18.43 Prover 11: Constructing countermodel ... % 136.76/19.09 Prover 12: stopped % 137.56/19.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 138.28/19.24 Prover 13: Preprocessing ... % 139.95/19.43 Prover 13: Warning: ignoring some quantifiers % 139.95/19.44 Prover 13: Constructing countermodel ... % 161.40/22.26 Prover 13: stopped % 161.40/22.26 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379 % 161.70/22.33 Prover 14: Preprocessing ... % 164.32/22.68 Prover 14: Proving ... % 166.86/23.01 Prover 10: Found proof (size 366) % 166.86/23.01 Prover 10: proved (8475ms) % 166.86/23.01 Prover 9: stopped % 166.86/23.01 Prover 14: stopped % 166.86/23.01 Prover 11: stopped % 166.86/23.01 Prover 7: stopped % 166.86/23.01 Prover 0: stopped % 166.86/23.04 Prover 4: stopped % 166.86/23.04 % 166.86/23.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 166.86/23.04 % 166.86/23.06 % SZS output start Proof for theBenchmark % 166.86/23.07 Assumptions after simplification: % 166.86/23.07 --------------------------------- % 166.86/23.07 % 166.86/23.07 (axiom_01) % 167.44/23.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~ (host(v0) = % 167.44/23.11 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v2) & s(v2) = v3 & % 167.44/23.11 $i(v3))) % 167.44/23.11 % 167.44/23.11 (axiom_03) % 167.44/23.11 $i(nbr_proc) & $i(zero) & ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0, % 167.44/23.11 nbr_proc)) % 167.44/23.12 % 167.44/23.12 (axiom_17) % 167.44/23.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~ % 167.44/23.12 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 167.44/23.12 % 167.44/23.12 (axiom_26) % 167.44/23.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v1) = v2) | ~ % 167.44/23.12 (m_Halt(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 167.44/23.12 % 167.44/23.12 (axiom_30) % 167.44/23.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v1) = v2) | ~ % 167.44/23.12 (m_Down(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 167.44/23.12 % 167.44/23.12 (axiom_46) % 167.44/23.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 167.44/23.12 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) | % 167.44/23.12 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 167.44/23.12 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 167.44/23.12 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) % 167.44/23.12 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2)) % 167.44/23.12 % 167.44/23.12 (axiom_48) % 167.44/23.13 ! [v0: $i] : ! [v1: $i] : ( ~ (m_Down(v1) = v0) | ~ $i(v1) | ~ $i(v0) | % 167.44/23.13 pidElem(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (m_Halt(v1) = v0) | ~ $i(v1) % 167.44/23.13 | ~ $i(v0) | pidElem(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ? % 167.44/23.13 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) = % 167.44/23.13 v0) | (v2 = v0 & m_Halt(v1) = v0)))) % 167.44/23.13 % 167.44/23.13 (axiom_61) % 167.44/23.13 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) % 167.44/23.13 | ~ leq(v0, v1)) & ? [v0: $i] : ( ~ $i(v0) | leq(v0, v0)) % 167.44/23.13 % 167.44/23.13 (axiom_63) % 167.44/23.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = v3) | ~ % 167.44/23.13 (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | leq(v0, v1)) & ! % 167.44/23.13 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = v3) | ~ % 167.44/23.13 (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) | leq(v2, v3)) % 167.44/23.13 % 167.44/23.13 (axiom_64) % 167.44/23.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (s(v1) = v2) | ~ % 167.44/23.14 $i(v1) | ~ $i(v0) | ~ leq(v0, v2) | leq(v0, v1)) & ! [v0: $i] : ! [v1: % 167.44/23.14 $i] : ! [v2: $i] : ( ~ (s(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 167.44/23.14 v1) | leq(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ (s(v1) = v0) | ~ % 167.44/23.14 $i(v1) | ~ $i(v0) | leq(v0, v0)) % 167.44/23.14 % 167.44/23.14 (conj) % 167.44/23.16 $i(down) & $i(ldr) & $i(elid) & $i(status) & $i(pendack) & $i(alive) & % 167.44/23.16 $i(norm) & $i(wait) & $i(elec_1) & $i(elec_2) & $i(nbr_proc) & $i(zero) & ? % 167.44/23.16 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 167.44/23.16 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? % 167.44/23.16 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? % 167.44/23.16 [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ( ~ % 167.44/23.16 (v17 = v13) & ~ (v17 = v5) & ~ (v15 = v5) & index(down, v5) = v12 & % 167.44/23.16 index(ldr, v15) = v15 & index(status, v15) = norm & index(status, v5) = % 167.44/23.16 elec_1 & cons(v7, v1) = v6 & m_Down(v4) = v7 & m_Halt(v19) = v20 & s(v5) = % 167.44/23.16 v13 & s(zero) = v0 & host(v19) = v5 & host(v16) = v17 & host(v14) = v15 & % 167.44/23.17 host(v4) = v8 & host(v3) = v5 & queue(v17) = v18 & queue(v5) = v6 & $i(v20) % 167.44/23.17 & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & % 167.44/23.17 $i(v12) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 167.44/23.17 $i(v1) & $i(v0) & setIn(v19, alive) & setIn(v14, alive) & setIn(v3, alive) & % 167.44/23.17 elem(v20, v18) & ~ leq(v13, v15) & ~ leq(v5, v8) & ~ leq(nbr_proc, v5) & % 167.44/23.17 ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! % 167.44/23.17 [v26: $i] : ( ~ (m_Down(v22) = v26) | ~ (host(v23) = v24) | ~ (host(v21) = % 167.44/23.17 v25) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v21, alive) | % 167.44/23.17 leq(v24, v25) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] % 167.44/23.17 : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : ($i(v33) & (( ~ (v33 = v28) % 167.44/23.17 & index(down, v24) = v27 & host(v22) = v28 & $i(v28) & $i(v27) & % 167.44/23.17 leq(v0, v33) & ~ leq(v24, v33) & ~ setIn(v33, v27)) | ( ~ (v32 = % 167.44/23.17 norm) & index(status, v25) = v32 & $i(v32)) | ( ~ (v31 = v25) & % 167.44/23.17 index(ldr, v25) = v31 & $i(v31)) | ( ~ (v30 = elec_1) & % 167.44/23.17 index(status, v24) = v30 & $i(v30)) | (queue(v24) = v29 & $i(v29) & % 167.44/23.17 ~ elem(v26, v29))))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : % 167.44/23.17 ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ (m_Down(v22) = v24) | ~ % 167.44/23.17 (host(v23) = v25) | ~ (host(v21) = v26) | ~ $i(v23) | ~ $i(v22) | ~ % 167.44/23.17 $i(v21) | ~ setIn(v23, alive) | ~ setIn(v21, alive) | ? [v27: $i] : ? % 167.44/23.17 [v28: $i] : ? [v29: $i] : ? [v30: $i] : (( ~ (v30 = norm) & % 167.44/23.17 index(status, v26) = v30 & $i(v30)) | ( ~ (v29 = v26) & index(ldr, % 167.44/23.17 v26) = v29 & $i(v29)) | ( ~ (v28 = v26) & host(v22) = v28 & $i(v28)) % 167.44/23.17 | (queue(v25) = v27 & $i(v27) & ~ elem(v24, v27)))) & ! [v21: $i] : ! % 167.44/23.17 [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ % 167.44/23.17 (m_Halt(v23) = v25) | ~ (host(v22) = v26) | ~ (host(v21) = v24) | ~ % 167.44/23.17 $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v23, alive) | ~ setIn(v21, % 167.44/23.17 alive) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? % 167.44/23.17 [v31: $i] : ? [v32: $i] : (( ~ (v32 = norm) & index(status, v24) = v32 & % 167.44/23.17 $i(v32)) | ( ~ (v31 = v24) & index(ldr, v24) = v31 & $i(v31)) | ( ~ % 167.44/23.17 (v30 = elec_2) & index(status, v27) = v30 & host(v23) = v27 & $i(v30) % 167.44/23.17 & $i(v27)) | (index(pendack, v27) = v28 & host(v23) = v27 & $i(v28) & % 167.44/23.17 $i(v27) & leq(v28, v24)) | (queue(v26) = v29 & $i(v29) & ~ elem(v25, % 167.44/23.17 v29)))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] % 167.44/23.17 : ! [v25: $i] : ( ~ (m_Ack(v23, v22) = v24) | ~ (host(v21) = v25) | ~ % 167.44/23.17 $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v23, alive) | ~ setIn(v21, % 167.44/23.17 alive) | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? % 167.44/23.17 [v30: $i] : (( ~ (v30 = norm) & index(status, v25) = v30 & $i(v30)) | ( ~ % 167.44/23.17 (v29 = v25) & index(ldr, v25) = v29 & $i(v29)) | ( ~ (v28 = v25) & % 167.44/23.17 host(v22) = v28 & $i(v28)) | (host(v23) = v26 & queue(v26) = v27 & % 167.44/23.17 $i(v27) & $i(v26) & ~ elem(v24, v27)))) & ! [v21: $i] : ! [v22: $i] % 167.44/23.17 : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ (m_Ack(v23, v21) = v24) | % 167.44/23.17 ~ (host(v22) = v25) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ? [v26: $i] % 167.44/23.17 : ? [v27: $i] : ? [v28: $i] : ((host(v23) = v28 & host(v21) = v27 & % 167.44/23.17 $i(v28) & $i(v27) & ~ leq(v27, v28)) | (queue(v25) = v26 & $i(v26) & % 167.44/23.17 ~ elem(v24, v26)))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! % 167.44/23.17 [v24: $i] : (v22 = v21 | ~ (host(v22) = v24) | ~ (host(v21) = v23) | ~ % 167.44/23.17 $i(v22) | ~ $i(v21) | ~ setIn(v22, alive) | ~ setIn(v21, alive) | ? % 167.44/23.17 [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : (( ~ (v28 = v24) % 167.44/23.17 & index(ldr, v24) = v28 & $i(v28)) | ( ~ (v27 = norm) & index(status, % 167.44/23.17 v24) = v27 & $i(v27)) | ( ~ (v26 = norm) & index(status, v23) = v26 % 167.44/23.17 & $i(v26)) | ( ~ (v25 = v23) & index(ldr, v23) = v25 & $i(v25)))) & ! % 167.44/23.17 [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (m_Ldr(v22) = % 167.44/23.17 v23) | ~ (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ? [v25: $i] : % 167.44/23.17 ? [v26: $i] : ((host(v22) = v26 & $i(v26) & ~ leq(v24, v26)) | % 167.44/23.17 (queue(v24) = v25 & $i(v25) & ~ elem(v23, v25)))) & ! [v21: $i] : ! % 167.44/23.17 [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (m_Down(v22) = v23) | ~ % 167.44/23.17 (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v22, alive) | ? % 167.44/23.17 [v25: $i] : (queue(v24) = v25 & $i(v25) & ~ elem(v23, v25))) & ! [v21: % 167.44/23.17 $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (m_Halt(v22) = v23) % 167.44/23.17 | ~ (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ? [v25: $i] : ? [v26: % 167.44/23.17 $i] : ((host(v22) = v26 & $i(v26) & ~ leq(v24, v26)) | (queue(v24) = % 167.44/23.17 v25 & $i(v25) & ~ elem(v23, v25)))) & ! [v21: $i] : ! [v22: $i] : % 167.44/23.17 ! [v23: $i] : ! [v24: $i] : ( ~ (host(v22) = v24) | ~ (host(v21) = v23) | % 167.44/23.17 ~ $i(v22) | ~ $i(v21) | ~ setIn(v22, alive) | ~ setIn(v21, alive) | % 167.44/23.17 leq(v23, v24) | ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] % 167.44/23.17 : (( ~ (v26 = elec_2) & index(status, v24) = v26 & $i(v26)) | ( ~ (v25 = % 167.44/23.17 elec_2) & index(status, v23) = v25 & $i(v25)) | (index(pendack, v24) % 167.44/23.17 = v28 & index(pendack, v23) = v27 & $i(v28) & $i(v27) & ~ leq(v27, % 167.44/23.17 v28)))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] % 167.44/23.17 : ( ~ (host(v22) = v24) | ~ (host(v21) = v23) | ~ $i(v22) | ~ $i(v21) | % 167.44/23.17 ~ setIn(v22, alive) | ~ setIn(v21, alive) | leq(v23, v24) | ? [v25: $i] % 167.44/23.17 : ? [v26: $i] : ? [v27: $i] : (( ~ (v26 = elec_2) & index(status, v24) = % 167.44/23.17 v26 & $i(v26)) | ( ~ (v25 = elec_2) & index(status, v23) = v25 & % 167.44/23.17 $i(v25)) | (index(pendack, v24) = v27 & $i(v27) & leq(v27, v23)))) & % 167.44/23.17 ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (host(v22) = % 167.44/23.17 v23) | ~ (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v22, % 167.44/23.17 alive) | ~ setIn(v21, alive) | ? [v25: $i] : ? [v26: $i] : ? [v27: % 167.44/23.17 $i] : ? [v28: $i] : (( ~ (v28 = norm) & index(status, v24) = v28 & % 167.44/23.17 $i(v28)) | ( ~ (v27 = v24) & index(ldr, v24) = v27 & $i(v27)) | ( ~ % 167.44/23.17 (v26 = elec_2) & index(status, v23) = v26 & $i(v26)) | (index(pendack, % 167.44/23.17 v23) = v25 & $i(v25) & leq(v25, v24)))) & ! [v21: $i] : ! [v22: % 167.44/23.17 $i] : ! [v23: $i] : (v22 = v21 | ~ (host(v22) = v23) | ~ (host(v21) = % 167.44/23.17 v23) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v22, alive) | ~ setIn(v21, % 167.44/23.17 alive)) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (host(v22) = % 167.44/23.17 v23) | ~ (host(v21) = v23) | ~ $i(v22) | ~ $i(v21) | ~ leq(v22, v21) % 167.44/23.17 | ~ setIn(v22, alive) | setIn(v21, alive)) & ! [v21: $i] : ! [v22: $i] % 167.44/23.17 : ( ~ (host(v21) = v22) | ~ $i(v21) | ~ setIn(v21, alive) | ? [v23: $i] : % 167.44/23.17 ? [v24: $i] : ((v24 = v21 & index(elid, v22) = v21) | ( ~ (v23 = elec_1) % 167.44/23.17 & ~ (v23 = elec_2) & index(status, v22) = v23 & $i(v23)))) & ! [v21: % 167.44/23.17 $i] : ! [v22: $i] : ( ~ (host(v21) = v22) | ~ $i(v21) | ? [v23: $i] : % 167.44/23.17 (index(pendack, v22) = v23 & $i(v23) & leq(v23, nbr_proc))) & ! [v21: $i] % 167.44/23.17 : (v21 = v8 | ~ $i(v21) | ~ leq(v0, v21) | leq(v5, v21) | setIn(v21, v12)) % 167.44/23.17 & ( ~ (norm = elec_1) | ( ~ (v9 = v8) & index(ldr, v5) = v9 & $i(v9))) & ( ~ % 167.44/23.17 (wait = elec_1) | ( ~ (v11 = v8) & index(elid, v5) = v10 & host(v10) = v11 % 167.44/23.17 & $i(v11) & $i(v10)))) % 167.44/23.17 % 167.44/23.17 (function-axioms) % 167.44/23.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 167.44/23.18 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 167.44/23.18 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3, % 167.44/23.18 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 167.44/23.18 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! % 167.44/23.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~ % 167.44/23.18 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 167.44/23.18 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 167.44/23.18 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i] % 167.44/23.18 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) = % 167.44/23.18 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) = % 167.44/23.18 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 167.44/23.18 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 167.44/23.18 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & ! % 167.44/23.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~ % 167.44/23.18 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 167.44/23.18 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 167.44/23.18 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & ! % 167.44/23.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~ % 167.44/23.18 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 167.44/23.18 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 167.44/23.18 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1: % 167.44/23.18 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0)) % 167.44/23.18 % 167.44/23.18 Further assumptions not needed in the proof: % 167.44/23.18 -------------------------------------------- % 167.44/23.18 axiom, axiom_02, axiom_04, axiom_05, axiom_06, axiom_07, axiom_08, axiom_09, % 167.44/23.18 axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15, axiom_16, axiom_18, % 167.44/23.18 axiom_19, axiom_20, axiom_21, axiom_22, axiom_23, axiom_24, axiom_25, axiom_27, % 167.44/23.18 axiom_28, axiom_29, axiom_31, axiom_32, axiom_33, axiom_34, axiom_35, axiom_36, % 167.44/23.18 axiom_37, axiom_38, axiom_39, axiom_40, axiom_41, axiom_42, axiom_43, axiom_44, % 167.44/23.18 axiom_45, axiom_47, axiom_49, axiom_50, axiom_51, axiom_52, axiom_53, axiom_54, % 167.44/23.18 axiom_55, axiom_56, axiom_57, axiom_58, axiom_59, axiom_60, axiom_62, axiom_65 % 167.44/23.18 % 167.44/23.18 Those formulas are unsatisfiable: % 167.44/23.18 --------------------------------- % 167.44/23.18 % 167.44/23.18 Begin of proof % 167.44/23.18 | % 167.44/23.18 | ALPHA: (axiom_03) implies: % 167.44/23.18 | (1) ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0, nbr_proc)) % 167.44/23.18 | % 167.44/23.18 | ALPHA: (axiom_46) implies: % 167.44/23.18 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) = v2) | ~ % 167.44/23.18 | $i(v1) | ~ $i(v0) | elem(v0, v2)) % 167.44/23.18 | % 167.44/23.18 | ALPHA: (axiom_48) implies: % 167.44/23.18 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ? [v1: $i] : ? [v2: $i] : % 167.44/23.18 | ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) = v0) | (v2 = v0 & % 167.44/23.18 | m_Halt(v1) = v0)))) % 167.44/23.19 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (m_Halt(v1) = v0) | ~ $i(v1) | ~ % 167.44/23.19 | $i(v0) | pidElem(v0)) % 167.44/23.19 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (m_Down(v1) = v0) | ~ $i(v1) | ~ % 167.44/23.19 | $i(v0) | pidElem(v0)) % 167.44/23.19 | % 167.44/23.19 | ALPHA: (axiom_61) implies: % 167.44/23.19 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 167.44/23.19 | leq(v1, v0) | ~ leq(v0, v1)) % 167.44/23.19 | % 167.44/23.19 | ALPHA: (axiom_63) implies: % 167.44/23.19 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = % 167.44/23.19 | v3) | ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) | % 167.44/23.19 | leq(v2, v3)) % 167.44/23.19 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = % 167.44/23.19 | v3) | ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | % 167.44/23.19 | leq(v0, v1)) % 167.44/23.19 | % 167.44/23.19 | ALPHA: (axiom_64) implies: % 167.44/23.19 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (s(v1) = v0) | ~ $i(v1) | ~ $i(v0) | % 167.44/23.19 | leq(v0, v0)) % 167.44/23.19 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (s(v1) = v2) | % 167.44/23.19 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v2) | leq(v0, v1)) % 167.44/23.19 | % 167.44/23.19 | ALPHA: (conj) implies: % 167.91/23.21 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 167.91/23.21 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 167.91/23.21 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 167.91/23.21 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 167.91/23.21 | [v19: $i] : ? [v20: $i] : ( ~ (v17 = v13) & ~ (v17 = v5) & ~ (v15 = % 167.91/23.21 | v5) & index(down, v5) = v12 & index(ldr, v15) = v15 & % 167.91/23.21 | index(status, v15) = norm & index(status, v5) = elec_1 & cons(v7, % 167.91/23.21 | v1) = v6 & m_Down(v4) = v7 & m_Halt(v19) = v20 & s(v5) = v13 & % 167.91/23.21 | s(zero) = v0 & host(v19) = v5 & host(v16) = v17 & host(v14) = v15 & % 167.91/23.21 | host(v4) = v8 & host(v3) = v5 & queue(v17) = v18 & queue(v5) = v6 & % 167.91/23.21 | $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) % 167.91/23.21 | & $i(v13) & $i(v12) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 167.91/23.21 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & setIn(v19, alive) & setIn(v14, % 167.91/23.21 | alive) & setIn(v3, alive) & elem(v20, v18) & ~ leq(v13, v15) & ~ % 167.91/23.21 | leq(v5, v8) & ~ leq(nbr_proc, v5) & ! [v21: $i] : ! [v22: $i] : % 167.91/23.21 | ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ % 167.91/23.21 | (m_Down(v22) = v26) | ~ (host(v23) = v24) | ~ (host(v21) = v25) % 167.91/23.22 | | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v21, alive) | % 167.91/23.22 | leq(v24, v25) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? % 167.91/23.22 | [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : ($i(v33) % 167.91/23.22 | & (( ~ (v33 = v28) & index(down, v24) = v27 & host(v22) = v28 & % 167.91/23.22 | $i(v28) & $i(v27) & leq(v0, v33) & ~ leq(v24, v33) & ~ % 167.91/23.22 | setIn(v33, v27)) | ( ~ (v32 = norm) & index(status, v25) = % 167.91/23.22 | v32 & $i(v32)) | ( ~ (v31 = v25) & index(ldr, v25) = v31 & % 167.91/23.22 | $i(v31)) | ( ~ (v30 = elec_1) & index(status, v24) = v30 & % 167.91/23.22 | $i(v30)) | (queue(v24) = v29 & $i(v29) & ~ elem(v26, % 167.91/23.22 | v29))))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! % 167.91/23.22 | [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ (m_Down(v22) = v24) | % 167.91/23.22 | ~ (host(v23) = v25) | ~ (host(v21) = v26) | ~ $i(v23) | ~ % 167.91/23.22 | $i(v22) | ~ $i(v21) | ~ setIn(v23, alive) | ~ setIn(v21, alive) % 167.91/23.22 | | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : (( ~ % 167.91/23.22 | (v30 = norm) & index(status, v26) = v30 & $i(v30)) | ( ~ (v29 % 167.91/23.22 | = v26) & index(ldr, v26) = v29 & $i(v29)) | ( ~ (v28 = v26) % 167.91/23.22 | & host(v22) = v28 & $i(v28)) | (queue(v25) = v27 & $i(v27) & % 167.91/23.22 | ~ elem(v24, v27)))) & ! [v21: $i] : ! [v22: $i] : ! [v23: % 167.91/23.22 | $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ % 167.91/23.22 | (m_Halt(v23) = v25) | ~ (host(v22) = v26) | ~ (host(v21) = v24) % 167.91/23.22 | | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v23, alive) | ~ % 167.91/23.22 | setIn(v21, alive) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : % 167.91/23.22 | ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : (( ~ (v32 = norm) & % 167.91/23.22 | index(status, v24) = v32 & $i(v32)) | ( ~ (v31 = v24) & % 167.91/23.22 | index(ldr, v24) = v31 & $i(v31)) | ( ~ (v30 = elec_2) & % 167.91/23.22 | index(status, v27) = v30 & host(v23) = v27 & $i(v30) & % 167.91/23.22 | $i(v27)) | (index(pendack, v27) = v28 & host(v23) = v27 & % 167.91/23.22 | $i(v28) & $i(v27) & leq(v28, v24)) | (queue(v26) = v29 & % 167.91/23.22 | $i(v29) & ~ elem(v25, v29)))) & ! [v21: $i] : ! [v22: $i] : % 167.91/23.22 | ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ (m_Ack(v23, v22) = % 167.91/23.22 | v24) | ~ (host(v21) = v25) | ~ $i(v23) | ~ $i(v22) | ~ % 167.91/23.22 | $i(v21) | ~ setIn(v23, alive) | ~ setIn(v21, alive) | ? [v26: % 167.91/23.22 | $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] % 167.91/23.22 | : (( ~ (v30 = norm) & index(status, v25) = v30 & $i(v30)) | ( ~ % 167.91/23.22 | (v29 = v25) & index(ldr, v25) = v29 & $i(v29)) | ( ~ (v28 = % 167.91/23.22 | v25) & host(v22) = v28 & $i(v28)) | (host(v23) = v26 & % 167.91/23.22 | queue(v26) = v27 & $i(v27) & $i(v26) & ~ elem(v24, v27)))) & % 167.91/23.22 | ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: % 167.91/23.22 | $i] : ( ~ (m_Ack(v23, v21) = v24) | ~ (host(v22) = v25) | ~ % 167.91/23.22 | $i(v23) | ~ $i(v22) | ~ $i(v21) | ? [v26: $i] : ? [v27: $i] : % 167.91/23.22 | ? [v28: $i] : ((host(v23) = v28 & host(v21) = v27 & $i(v28) & % 167.91/23.22 | $i(v27) & ~ leq(v27, v28)) | (queue(v25) = v26 & $i(v26) & ~ % 167.91/23.22 | elem(v24, v26)))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] % 167.91/23.22 | : ! [v24: $i] : (v22 = v21 | ~ (host(v22) = v24) | ~ (host(v21) = % 167.91/23.22 | v23) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v22, alive) | ~ % 167.91/23.22 | setIn(v21, alive) | ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : % 167.91/23.22 | ? [v28: $i] : (( ~ (v28 = v24) & index(ldr, v24) = v28 & $i(v28)) % 167.91/23.22 | | ( ~ (v27 = norm) & index(status, v24) = v27 & $i(v27)) | ( ~ % 167.91/23.22 | (v26 = norm) & index(status, v23) = v26 & $i(v26)) | ( ~ (v25 % 167.91/23.22 | = v23) & index(ldr, v23) = v25 & $i(v25)))) & ! [v21: $i] : % 167.91/23.22 | ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (m_Ldr(v22) = v23) % 167.91/23.22 | | ~ (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ? [v25: $i] : % 167.91/23.22 | ? [v26: $i] : ((host(v22) = v26 & $i(v26) & ~ leq(v24, v26)) | % 167.91/23.22 | (queue(v24) = v25 & $i(v25) & ~ elem(v23, v25)))) & ! [v21: % 167.91/23.22 | $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ % 167.91/23.22 | (m_Down(v22) = v23) | ~ (host(v21) = v24) | ~ $i(v22) | ~ % 167.91/23.22 | $i(v21) | ~ setIn(v22, alive) | ? [v25: $i] : (queue(v24) = v25 % 167.91/23.22 | & $i(v25) & ~ elem(v23, v25))) & ! [v21: $i] : ! [v22: $i] : % 167.91/23.22 | ! [v23: $i] : ! [v24: $i] : ( ~ (m_Halt(v22) = v23) | ~ (host(v21) % 167.91/23.22 | = v24) | ~ $i(v22) | ~ $i(v21) | ? [v25: $i] : ? [v26: $i] : % 167.91/23.22 | ((host(v22) = v26 & $i(v26) & ~ leq(v24, v26)) | (queue(v24) = % 167.91/23.22 | v25 & $i(v25) & ~ elem(v23, v25)))) & ! [v21: $i] : ! [v22: % 167.91/23.22 | $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (host(v22) = v24) | ~ % 167.91/23.22 | (host(v21) = v23) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v22, alive) % 167.91/23.22 | | ~ setIn(v21, alive) | leq(v23, v24) | ? [v25: $i] : ? [v26: % 167.91/23.22 | $i] : ? [v27: $i] : ? [v28: $i] : (( ~ (v26 = elec_2) & % 167.91/23.22 | index(status, v24) = v26 & $i(v26)) | ( ~ (v25 = elec_2) & % 167.91/23.22 | index(status, v23) = v25 & $i(v25)) | (index(pendack, v24) = % 167.91/23.22 | v28 & index(pendack, v23) = v27 & $i(v28) & $i(v27) & ~ % 167.91/23.22 | leq(v27, v28)))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] % 167.91/23.22 | : ! [v24: $i] : ( ~ (host(v22) = v24) | ~ (host(v21) = v23) | ~ % 167.91/23.22 | $i(v22) | ~ $i(v21) | ~ setIn(v22, alive) | ~ setIn(v21, alive) % 167.91/23.22 | | leq(v23, v24) | ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : (( % 167.91/23.22 | ~ (v26 = elec_2) & index(status, v24) = v26 & $i(v26)) | ( ~ % 167.91/23.22 | (v25 = elec_2) & index(status, v23) = v25 & $i(v25)) | % 167.91/23.22 | (index(pendack, v24) = v27 & $i(v27) & leq(v27, v23)))) & ! % 167.91/23.22 | [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ % 167.91/23.22 | (host(v22) = v23) | ~ (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) % 167.91/23.22 | | ~ setIn(v22, alive) | ~ setIn(v21, alive) | ? [v25: $i] : ? % 167.91/23.22 | [v26: $i] : ? [v27: $i] : ? [v28: $i] : (( ~ (v28 = norm) & % 167.91/23.22 | index(status, v24) = v28 & $i(v28)) | ( ~ (v27 = v24) & % 167.91/23.22 | index(ldr, v24) = v27 & $i(v27)) | ( ~ (v26 = elec_2) & % 167.91/23.22 | index(status, v23) = v26 & $i(v26)) | (index(pendack, v23) = % 167.91/23.22 | v25 & $i(v25) & leq(v25, v24)))) & ! [v21: $i] : ! [v22: $i] % 167.91/23.22 | : ! [v23: $i] : (v22 = v21 | ~ (host(v22) = v23) | ~ (host(v21) = % 167.91/23.22 | v23) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v22, alive) | ~ % 167.91/23.22 | setIn(v21, alive)) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : % 167.91/23.22 | ( ~ (host(v22) = v23) | ~ (host(v21) = v23) | ~ $i(v22) | ~ % 167.91/23.22 | $i(v21) | ~ leq(v22, v21) | ~ setIn(v22, alive) | setIn(v21, % 167.91/23.22 | alive)) & ! [v21: $i] : ! [v22: $i] : ( ~ (host(v21) = v22) | % 167.91/23.22 | ~ $i(v21) | ~ setIn(v21, alive) | ? [v23: $i] : ? [v24: $i] : % 167.91/23.22 | ((v24 = v21 & index(elid, v22) = v21) | ( ~ (v23 = elec_1) & ~ % 167.91/23.22 | (v23 = elec_2) & index(status, v22) = v23 & $i(v23)))) & ! % 167.91/23.22 | [v21: $i] : ! [v22: $i] : ( ~ (host(v21) = v22) | ~ $i(v21) | ? % 167.91/23.22 | [v23: $i] : (index(pendack, v22) = v23 & $i(v23) & leq(v23, % 167.91/23.22 | nbr_proc))) & ! [v21: $i] : (v21 = v8 | ~ $i(v21) | ~ % 167.91/23.22 | leq(v0, v21) | leq(v5, v21) | setIn(v21, v12)) & ( ~ (norm = % 167.91/23.22 | elec_1) | ( ~ (v9 = v8) & index(ldr, v5) = v9 & $i(v9))) & ( ~ % 167.91/23.22 | (wait = elec_1) | ( ~ (v11 = v8) & index(elid, v5) = v10 & % 167.91/23.22 | host(v10) = v11 & $i(v11) & $i(v10)))) % 167.91/23.22 | % 167.91/23.22 | ALPHA: (function-axioms) implies: % 167.91/23.22 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = % 167.91/23.22 | v1) | ~ (queue(v2) = v0)) % 167.91/23.22 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = % 167.91/23.22 | v1) | ~ (host(v2) = v0)) % 167.91/23.22 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 167.91/23.22 | ~ (s(v2) = v0)) % 167.91/23.23 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 167.91/23.23 | (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) % 167.91/23.23 | % 167.91/23.23 | DELTA: instantiating (1) with fresh symbol all_59_0 gives: % 167.91/23.23 | (16) s(zero) = all_59_0 & $i(all_59_0) & leq(all_59_0, nbr_proc) % 167.91/23.23 | % 167.91/23.23 | ALPHA: (16) implies: % 167.91/23.23 | (17) s(zero) = all_59_0 % 167.91/23.23 | % 167.91/23.23 | DELTA: instantiating (11) with fresh symbols all_65_0, all_65_1, all_65_2, % 167.91/23.23 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9, % 167.91/23.23 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15, % 167.91/23.23 | all_65_16, all_65_17, all_65_18, all_65_19, all_65_20 gives: % 167.91/23.25 | (18) ~ (all_65_3 = all_65_7) & ~ (all_65_3 = all_65_15) & ~ (all_65_5 = % 167.91/23.25 | all_65_15) & index(down, all_65_15) = all_65_8 & index(ldr, % 167.91/23.25 | all_65_5) = all_65_5 & index(status, all_65_5) = norm & % 167.91/23.25 | index(status, all_65_15) = elec_1 & cons(all_65_13, all_65_19) = % 167.91/23.25 | all_65_14 & m_Down(all_65_16) = all_65_13 & m_Halt(all_65_1) = % 167.91/23.25 | all_65_0 & s(all_65_15) = all_65_7 & s(zero) = all_65_20 & % 167.91/23.25 | host(all_65_1) = all_65_15 & host(all_65_4) = all_65_3 & % 167.91/23.25 | host(all_65_6) = all_65_5 & host(all_65_16) = all_65_12 & % 167.91/23.25 | host(all_65_17) = all_65_15 & queue(all_65_3) = all_65_2 & % 167.91/23.25 | queue(all_65_15) = all_65_14 & $i(all_65_0) & $i(all_65_1) & % 167.91/23.25 | $i(all_65_2) & $i(all_65_3) & $i(all_65_4) & $i(all_65_5) & % 167.91/23.25 | $i(all_65_6) & $i(all_65_7) & $i(all_65_8) & $i(all_65_12) & % 167.91/23.25 | $i(all_65_13) & $i(all_65_14) & $i(all_65_15) & $i(all_65_16) & % 167.91/23.25 | $i(all_65_17) & $i(all_65_18) & $i(all_65_19) & $i(all_65_20) & % 167.91/23.25 | setIn(all_65_1, alive) & setIn(all_65_6, alive) & setIn(all_65_17, % 167.91/23.25 | alive) & elem(all_65_0, all_65_2) & ~ leq(all_65_7, all_65_5) & ~ % 167.91/23.25 | leq(all_65_15, all_65_12) & ~ leq(nbr_proc, all_65_15) & ! [v0: $i] % 167.91/23.25 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 167.91/23.25 | : ( ~ (m_Down(v1) = v5) | ~ (host(v2) = v3) | ~ (host(v0) = v4) | ~ % 167.91/23.25 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v0, alive) | leq(v3, v4) | % 167.91/23.25 | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] % 167.91/23.25 | : ? [v11: $i] : ? [v12: $i] : ($i(v12) & (( ~ (v12 = v7) & % 167.91/23.25 | index(down, v3) = v6 & host(v1) = v7 & $i(v7) & $i(v6) & % 167.91/23.25 | leq(all_65_20, v12) & ~ leq(v3, v12) & ~ setIn(v12, v6)) | ( % 167.91/23.25 | ~ (v11 = norm) & index(status, v4) = v11 & $i(v11)) | ( ~ (v10 % 167.91/23.25 | = v4) & index(ldr, v4) = v10 & $i(v10)) | ( ~ (v9 = elec_1) % 167.91/23.25 | & index(status, v3) = v9 & $i(v9)) | (queue(v3) = v8 & $i(v8) % 167.91/23.25 | & ~ elem(v5, v8))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 167.91/23.25 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (m_Down(v1) = % 167.91/23.25 | v3) | ~ (host(v2) = v4) | ~ (host(v0) = v5) | ~ $i(v2) | ~ % 167.91/23.25 | $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? % 167.91/23.25 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (( ~ (v9 = % 167.91/23.25 | norm) & index(status, v5) = v9 & $i(v9)) | ( ~ (v8 = v5) & % 167.91/23.25 | index(ldr, v5) = v8 & $i(v8)) | ( ~ (v7 = v5) & host(v1) = v7 & % 167.91/23.25 | $i(v7)) | (queue(v4) = v6 & $i(v6) & ~ elem(v3, v6)))) & ! % 167.91/23.25 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 167.91/23.25 | [v5: $i] : ( ~ (m_Halt(v2) = v4) | ~ (host(v1) = v5) | ~ (host(v0) = % 167.91/23.25 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ % 167.91/23.25 | setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 167.91/23.25 | $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v11 = norm) & % 167.91/23.25 | index(status, v3) = v11 & $i(v11)) | ( ~ (v10 = v3) & index(ldr, % 167.91/23.25 | v3) = v10 & $i(v10)) | ( ~ (v9 = elec_2) & index(status, v6) = % 167.91/23.25 | v9 & host(v2) = v6 & $i(v9) & $i(v6)) | (index(pendack, v6) = v7 % 167.91/23.25 | & host(v2) = v6 & $i(v7) & $i(v6) & leq(v7, v3)) | (queue(v5) = % 167.91/23.25 | v8 & $i(v8) & ~ elem(v4, v8)))) & ! [v0: $i] : ! [v1: $i] : % 167.91/23.25 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (m_Ack(v2, v1) = v3) | ~ % 167.91/23.25 | (host(v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, % 167.91/23.25 | alive) | ~ setIn(v0, alive) | ? [v5: $i] : ? [v6: $i] : ? [v7: % 167.91/23.25 | $i] : ? [v8: $i] : ? [v9: $i] : (( ~ (v9 = norm) & index(status, % 167.91/23.25 | v4) = v9 & $i(v9)) | ( ~ (v8 = v4) & index(ldr, v4) = v8 & % 167.91/23.25 | $i(v8)) | ( ~ (v7 = v4) & host(v1) = v7 & $i(v7)) | (host(v2) = % 167.91/23.25 | v5 & queue(v5) = v6 & $i(v6) & $i(v5) & ~ elem(v3, v6)))) & ! % 167.91/23.25 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 167.91/23.25 | (m_Ack(v2, v0) = v3) | ~ (host(v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 167.91/23.25 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((host(v2) = v7 % 167.91/23.25 | & host(v0) = v6 & $i(v7) & $i(v6) & ~ leq(v6, v7)) | (queue(v4) % 167.91/23.25 | = v5 & $i(v5) & ~ elem(v3, v5)))) & ! [v0: $i] : ! [v1: $i] : % 167.91/23.25 | ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (host(v1) = v3) | ~ % 167.91/23.25 | (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ % 167.91/23.25 | setIn(v0, alive) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 167.91/23.25 | $i] : (( ~ (v7 = v3) & index(ldr, v3) = v7 & $i(v7)) | ( ~ (v6 = % 167.91/23.25 | norm) & index(status, v3) = v6 & $i(v6)) | ( ~ (v5 = norm) & % 167.91/23.25 | index(status, v2) = v5 & $i(v5)) | ( ~ (v4 = v2) & index(ldr, % 167.91/23.25 | v2) = v4 & $i(v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 167.91/23.25 | : ! [v3: $i] : ( ~ (m_Ldr(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) % 167.91/23.25 | | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & % 167.91/23.25 | ~ leq(v3, v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) % 167.91/23.25 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 167.91/23.25 | (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 167.91/23.25 | setIn(v1, alive) | ? [v4: $i] : (queue(v3) = v4 & $i(v4) & ~ % 167.91/23.25 | elem(v2, v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 167.91/23.25 | $i] : ( ~ (m_Halt(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ % 167.91/23.25 | $i(v0) | ? [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ % 167.91/23.25 | leq(v3, v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) & % 167.91/23.25 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) = % 167.91/23.25 | v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 167.91/23.25 | alive) | ~ setIn(v0, alive) | leq(v2, v3) | ? [v4: $i] : ? [v5: % 167.91/23.25 | $i] : ? [v6: $i] : ? [v7: $i] : (( ~ (v5 = elec_2) & % 167.91/23.25 | index(status, v3) = v5 & $i(v5)) | ( ~ (v4 = elec_2) & % 167.91/23.25 | index(status, v2) = v4 & $i(v4)) | (index(pendack, v3) = v7 & % 167.91/23.25 | index(pendack, v2) = v6 & $i(v7) & $i(v6) & ~ leq(v6, v7)))) & % 167.91/23.25 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) = % 167.91/23.25 | v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 167.91/23.25 | alive) | ~ setIn(v0, alive) | leq(v2, v3) | ? [v4: $i] : ? [v5: % 167.91/23.25 | $i] : ? [v6: $i] : (( ~ (v5 = elec_2) & index(status, v3) = v5 & % 167.91/23.25 | $i(v5)) | ( ~ (v4 = elec_2) & index(status, v2) = v4 & $i(v4)) | % 167.91/23.25 | (index(pendack, v3) = v6 & $i(v6) & leq(v6, v2)))) & ! [v0: $i] : % 167.91/23.25 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) = v2) | ~ % 167.91/23.25 | (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ % 167.91/23.25 | setIn(v0, alive) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 167.91/23.25 | $i] : (( ~ (v7 = norm) & index(status, v3) = v7 & $i(v7)) | ( ~ % 167.91/23.25 | (v6 = v3) & index(ldr, v3) = v6 & $i(v6)) | ( ~ (v5 = elec_2) & % 167.91/23.25 | index(status, v2) = v5 & $i(v5)) | (index(pendack, v2) = v4 & % 167.91/23.25 | $i(v4) & leq(v4, v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 167.91/23.25 | $i] : (v1 = v0 | ~ (host(v1) = v2) | ~ (host(v0) = v2) | ~ $i(v1) % 167.91/23.25 | | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive)) & ! [v0: % 167.91/23.25 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~ (host(v0) % 167.91/23.26 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) | ~ setIn(v1, % 167.91/23.26 | alive) | setIn(v0, alive)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 167.91/23.26 | (host(v0) = v1) | ~ $i(v0) | ~ setIn(v0, alive) | ? [v2: $i] : ? % 167.91/23.26 | [v3: $i] : ((v3 = v0 & index(elid, v1) = v0) | ( ~ (v2 = elec_1) & % 167.91/23.26 | ~ (v2 = elec_2) & index(status, v1) = v2 & $i(v2)))) & ! [v0: % 167.91/23.26 | $i] : ! [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 167.91/23.26 | (index(pendack, v1) = v2 & $i(v2) & leq(v2, nbr_proc))) & ! [v0: % 167.91/23.26 | any] : (v0 = all_65_12 | ~ $i(v0) | ~ leq(all_65_20, v0) | % 167.91/23.26 | leq(all_65_15, v0) | setIn(v0, all_65_8)) & ( ~ (norm = elec_1) | ( % 167.91/23.26 | ~ (all_65_11 = all_65_12) & index(ldr, all_65_15) = all_65_11 & % 167.91/23.26 | $i(all_65_11))) & ( ~ (wait = elec_1) | ( ~ (all_65_9 = all_65_12) % 167.91/23.26 | & index(elid, all_65_15) = all_65_10 & host(all_65_10) = all_65_9 % 167.91/23.26 | & $i(all_65_9) & $i(all_65_10))) % 167.91/23.26 | % 167.91/23.26 | ALPHA: (18) implies: % 167.91/23.26 | (19) ~ (all_65_5 = all_65_15) % 167.91/23.26 | (20) ~ leq(all_65_7, all_65_5) % 167.91/23.26 | (21) elem(all_65_0, all_65_2) % 167.91/23.26 | (22) setIn(all_65_17, alive) % 167.91/23.26 | (23) setIn(all_65_6, alive) % 167.91/23.26 | (24) setIn(all_65_1, alive) % 167.91/23.26 | (25) $i(all_65_19) % 167.91/23.26 | (26) $i(all_65_17) % 167.91/23.26 | (27) $i(all_65_16) % 167.91/23.26 | (28) $i(all_65_15) % 167.91/23.26 | (29) $i(all_65_13) % 167.91/23.26 | (30) $i(all_65_7) % 167.91/23.26 | (31) $i(all_65_6) % 167.91/23.26 | (32) $i(all_65_5) % 167.91/23.26 | (33) $i(all_65_4) % 167.91/23.26 | (34) $i(all_65_1) % 167.91/23.26 | (35) $i(all_65_0) % 167.91/23.26 | (36) queue(all_65_15) = all_65_14 % 167.91/23.26 | (37) queue(all_65_3) = all_65_2 % 167.91/23.26 | (38) host(all_65_17) = all_65_15 % 167.91/23.26 | (39) host(all_65_16) = all_65_12 % 167.91/23.26 | (40) host(all_65_6) = all_65_5 % 167.91/23.26 | (41) host(all_65_4) = all_65_3 % 167.91/23.26 | (42) host(all_65_1) = all_65_15 % 167.91/23.26 | (43) s(zero) = all_65_20 % 167.91/23.26 | (44) s(all_65_15) = all_65_7 % 167.91/23.26 | (45) m_Halt(all_65_1) = all_65_0 % 167.91/23.26 | (46) m_Down(all_65_16) = all_65_13 % 167.91/23.26 | (47) cons(all_65_13, all_65_19) = all_65_14 % 167.91/23.26 | (48) index(status, all_65_15) = elec_1 % 167.91/23.26 | (49) index(status, all_65_5) = norm % 167.91/23.26 | (50) index(ldr, all_65_5) = all_65_5 % 167.91/23.26 | (51) index(down, all_65_15) = all_65_8 % 167.91/23.26 | (52) ! [v0: any] : (v0 = all_65_12 | ~ $i(v0) | ~ leq(all_65_20, v0) | % 167.91/23.26 | leq(all_65_15, v0) | setIn(v0, all_65_8)) % 167.91/23.26 | (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v1) = % 167.91/23.26 | v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 167.91/23.26 | alive) | ~ setIn(v0, alive)) % 167.91/23.27 | (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 167.91/23.27 | (m_Halt(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 167.91/23.27 | [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) % 167.91/23.27 | | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) % 167.91/23.27 | (55) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 167.91/23.27 | (host(v1) = v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 167.91/23.27 | setIn(v1, alive) | ~ setIn(v0, alive) | ? [v4: $i] : ? [v5: $i] : % 167.91/23.27 | ? [v6: $i] : ? [v7: $i] : (( ~ (v7 = v3) & index(ldr, v3) = v7 & % 167.91/23.27 | $i(v7)) | ( ~ (v6 = norm) & index(status, v3) = v6 & $i(v6)) | ( % 167.91/23.27 | ~ (v5 = norm) & index(status, v2) = v5 & $i(v5)) | ( ~ (v4 = v2) % 167.91/23.27 | & index(ldr, v2) = v4 & $i(v4)))) % 167.91/23.27 | (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 167.91/23.27 | ! [v5: $i] : ( ~ (m_Down(v1) = v3) | ~ (host(v2) = v4) | ~ (host(v0) % 167.91/23.27 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | % 167.91/23.27 | ~ setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 167.91/23.27 | [v9: $i] : (( ~ (v9 = norm) & index(status, v5) = v9 & $i(v9)) | ( ~ % 167.91/23.27 | (v8 = v5) & index(ldr, v5) = v8 & $i(v8)) | ( ~ (v7 = v5) & % 167.91/23.27 | host(v1) = v7 & $i(v7)) | (queue(v4) = v6 & $i(v6) & ~ elem(v3, % 167.91/23.27 | v6)))) % 167.91/23.27 | (57) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 167.91/23.27 | ! [v5: $i] : ( ~ (m_Down(v1) = v5) | ~ (host(v2) = v3) | ~ (host(v0) % 167.91/23.27 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v0, alive) | % 167.91/23.27 | leq(v3, v4) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 167.91/23.27 | : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ($i(v12) & (( ~ (v12 % 167.91/23.27 | = v7) & index(down, v3) = v6 & host(v1) = v7 & $i(v7) & % 167.91/23.27 | $i(v6) & leq(all_65_20, v12) & ~ leq(v3, v12) & ~ setIn(v12, % 167.91/23.27 | v6)) | ( ~ (v11 = norm) & index(status, v4) = v11 & $i(v11)) % 167.91/23.27 | | ( ~ (v10 = v4) & index(ldr, v4) = v10 & $i(v10)) | ( ~ (v9 = % 167.91/23.27 | elec_1) & index(status, v3) = v9 & $i(v9)) | (queue(v3) = v8 % 167.91/23.27 | & $i(v8) & ~ elem(v5, v8))))) % 167.91/23.27 | % 167.91/23.28 | GROUND_INST: instantiating (14) with all_59_0, all_65_20, zero, simplifying % 167.91/23.28 | with (17), (43) gives: % 167.91/23.28 | (58) all_65_20 = all_59_0 % 167.91/23.28 | % 167.91/23.28 | GROUND_INST: instantiating (axiom_01) with all_65_6, all_65_6, all_65_5, % 167.91/23.28 | simplifying with (31), (40) gives: % 167.91/23.28 | (59) ? [v0: any] : ( ~ (v0 = all_65_5) & s(all_65_5) = v0 & $i(v0)) % 167.91/23.28 | % 167.91/23.28 | GROUND_INST: instantiating (55) with all_65_6, all_65_1, all_65_5, all_65_15, % 167.91/23.28 | simplifying with (23), (24), (31), (34), (40), (42) gives: % 167.91/23.28 | (60) all_65_1 = all_65_6 | ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? % 167.91/23.28 | [v3: any] : (( ~ (v3 = all_65_15) & index(ldr, all_65_15) = v3 & % 167.91/23.28 | $i(v3)) | ( ~ (v2 = norm) & index(status, all_65_15) = v2 & % 167.91/23.28 | $i(v2)) | ( ~ (v1 = norm) & index(status, all_65_5) = v1 & $i(v1)) % 167.91/23.28 | | ( ~ (v0 = all_65_5) & index(ldr, all_65_5) = v0 & $i(v0))) % 167.91/23.28 | % 167.91/23.28 | GROUND_INST: instantiating (55) with all_65_1, all_65_6, all_65_15, all_65_5, % 167.91/23.28 | simplifying with (23), (24), (31), (34), (40), (42) gives: % 167.91/23.28 | (61) all_65_1 = all_65_6 | ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? % 167.91/23.28 | [v3: any] : (( ~ (v3 = all_65_5) & index(ldr, all_65_5) = v3 & $i(v3)) % 167.91/23.28 | | ( ~ (v2 = norm) & index(status, all_65_5) = v2 & $i(v2)) | ( ~ (v1 % 167.91/23.28 | = norm) & index(status, all_65_15) = v1 & $i(v1)) | ( ~ (v0 = % 167.91/23.28 | all_65_15) & index(ldr, all_65_15) = v0 & $i(v0))) % 167.91/23.28 | % 167.91/23.28 | GROUND_INST: instantiating (53) with all_65_17, all_65_1, all_65_15, % 167.91/23.28 | simplifying with (22), (24), (26), (34), (38), (42) gives: % 167.91/23.28 | (62) all_65_1 = all_65_17 % 167.91/23.28 | % 167.91/23.28 | GROUND_INST: instantiating (axiom_01) with all_65_17, all_65_1, all_65_15, % 167.91/23.28 | simplifying with (26), (34), (38), (42) gives: % 167.91/23.28 | (63) ? [v0: any] : ( ~ (v0 = all_65_15) & s(all_65_15) = v0 & $i(v0)) % 167.91/23.28 | % 167.91/23.28 | GROUND_INST: instantiating (9) with all_65_7, all_65_15, simplifying with % 167.91/23.28 | (28), (30), (44) gives: % 167.91/23.28 | (64) leq(all_65_7, all_65_7) % 167.91/23.28 | % 167.91/23.28 | GROUND_INST: instantiating (54) with all_65_4, all_65_1, all_65_0, all_65_3, % 167.91/23.28 | simplifying with (33), (34), (41), (45) gives: % 167.91/23.29 | (65) ? [v0: $i] : ? [v1: $i] : ((host(all_65_1) = v1 & $i(v1) & ~ % 167.91/23.29 | leq(all_65_3, v1)) | (queue(all_65_3) = v0 & $i(v0) & ~ % 167.91/23.29 | elem(all_65_0, v0))) % 167.91/23.29 | % 167.91/23.29 | GROUND_INST: instantiating (4) with all_65_0, all_65_1, simplifying with (34), % 167.91/23.29 | (35), (45) gives: % 167.91/23.29 | (66) pidElem(all_65_0) % 167.91/23.29 | % 167.91/23.29 | GROUND_INST: instantiating (57) with all_65_17, all_65_16, all_65_6, all_65_5, % 167.91/23.29 | all_65_15, all_65_13, simplifying with (22), (26), (27), (31), % 167.91/23.29 | (38), (40), (46) gives: % 167.91/23.29 | (67) leq(all_65_5, all_65_15) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 168.34/23.29 | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & (( ~ % 168.34/23.29 | (v6 = v1) & index(down, all_65_5) = v0 & host(all_65_16) = v1 & % 168.34/23.29 | $i(v1) & $i(v0) & leq(all_65_20, v6) & ~ leq(all_65_5, v6) & ~ % 168.34/23.29 | setIn(v6, v0)) | ( ~ (v5 = norm) & index(status, all_65_15) = v5 % 168.34/23.29 | & $i(v5)) | ( ~ (v4 = all_65_15) & index(ldr, all_65_15) = v4 & % 168.34/23.29 | $i(v4)) | ( ~ (v3 = elec_1) & index(status, all_65_5) = v3 & % 168.34/23.29 | $i(v3)) | (queue(all_65_5) = v2 & $i(v2) & ~ elem(all_65_13, % 168.34/23.29 | v2)))) % 168.34/23.29 | % 168.34/23.29 | GROUND_INST: instantiating (57) with all_65_6, all_65_16, all_65_17, % 168.34/23.29 | all_65_15, all_65_5, all_65_13, simplifying with (23), (26), % 168.34/23.29 | (27), (31), (38), (40), (46) gives: % 168.34/23.29 | (68) leq(all_65_15, all_65_5) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 168.34/23.29 | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & (( ~ % 168.34/23.29 | (v6 = v1) & index(down, all_65_15) = v0 & host(all_65_16) = v1 & % 168.34/23.29 | $i(v1) & $i(v0) & leq(all_65_20, v6) & ~ leq(all_65_15, v6) & % 168.34/23.29 | ~ setIn(v6, v0)) | ( ~ (v5 = norm) & index(status, all_65_5) = % 168.34/23.29 | v5 & $i(v5)) | ( ~ (v4 = all_65_5) & index(ldr, all_65_5) = v4 & % 168.34/23.29 | $i(v4)) | ( ~ (v3 = elec_1) & index(status, all_65_15) = v3 & % 168.34/23.29 | $i(v3)) | (queue(all_65_15) = v2 & $i(v2) & ~ elem(all_65_13, % 168.34/23.29 | v2)))) % 168.34/23.29 | % 168.34/23.29 | GROUND_INST: instantiating (56) with all_65_6, all_65_16, all_65_17, % 168.34/23.29 | all_65_13, all_65_15, all_65_5, simplifying with (22), (23), % 168.34/23.29 | (26), (27), (31), (38), (40), (46) gives: % 168.34/23.30 | (69) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : (( ~ (v3 = % 168.34/23.30 | norm) & index(status, all_65_5) = v3 & $i(v3)) | ( ~ (v2 = % 168.34/23.30 | all_65_5) & index(ldr, all_65_5) = v2 & $i(v2)) | ( ~ (v1 = % 168.34/23.30 | all_65_5) & host(all_65_16) = v1 & $i(v1)) | (queue(all_65_15) = % 168.34/23.30 | v0 & $i(v0) & ~ elem(all_65_13, v0))) % 168.34/23.30 | % 168.34/23.30 | GROUND_INST: instantiating (5) with all_65_13, all_65_16, simplifying with % 168.34/23.30 | (27), (29), (46) gives: % 168.34/23.30 | (70) pidElem(all_65_13) % 168.34/23.30 | % 168.34/23.30 | GROUND_INST: instantiating (2) with all_65_13, all_65_19, all_65_14, % 168.34/23.30 | simplifying with (25), (29), (47) gives: % 168.34/23.30 | (71) elem(all_65_13, all_65_14) % 168.34/23.30 | % 168.34/23.30 | DELTA: instantiating (63) with fresh symbol all_78_0 gives: % 168.34/23.30 | (72) ~ (all_78_0 = all_65_15) & s(all_65_15) = all_78_0 & $i(all_78_0) % 168.34/23.30 | % 168.34/23.30 | ALPHA: (72) implies: % 168.34/23.30 | (73) $i(all_78_0) % 168.34/23.30 | (74) s(all_65_15) = all_78_0 % 168.34/23.30 | % 168.34/23.30 | DELTA: instantiating (59) with fresh symbol all_82_0 gives: % 168.34/23.30 | (75) ~ (all_82_0 = all_65_5) & s(all_65_5) = all_82_0 & $i(all_82_0) % 168.34/23.30 | % 168.34/23.30 | ALPHA: (75) implies: % 168.34/23.30 | (76) s(all_65_5) = all_82_0 % 168.34/23.30 | % 168.34/23.30 | DELTA: instantiating (65) with fresh symbols all_99_0, all_99_1 gives: % 168.34/23.30 | (77) (host(all_65_1) = all_99_0 & $i(all_99_0) & ~ leq(all_65_3, % 168.34/23.30 | all_99_0)) | (queue(all_65_3) = all_99_1 & $i(all_99_1) & ~ % 168.34/23.30 | elem(all_65_0, all_99_1)) % 168.34/23.30 | % 168.34/23.30 | DELTA: instantiating (69) with fresh symbols all_107_0, all_107_1, all_107_2, % 168.34/23.30 | all_107_3 gives: % 168.34/23.30 | (78) ( ~ (all_107_0 = norm) & index(status, all_65_5) = all_107_0 & % 168.34/23.30 | $i(all_107_0)) | ( ~ (all_107_1 = all_65_5) & index(ldr, all_65_5) = % 168.34/23.30 | all_107_1 & $i(all_107_1)) | ( ~ (all_107_2 = all_65_5) & % 168.34/23.30 | host(all_65_16) = all_107_2 & $i(all_107_2)) | (queue(all_65_15) = % 168.34/23.30 | all_107_3 & $i(all_107_3) & ~ elem(all_65_13, all_107_3)) % 168.34/23.30 | % 168.34/23.30 | REDUCE: (45), (62) imply: % 168.34/23.30 | (79) m_Halt(all_65_17) = all_65_0 % 168.34/23.30 | % 168.34/23.30 | BETA: splitting (77) gives: % 168.34/23.30 | % 168.34/23.30 | Case 1: % 168.34/23.30 | | % 168.34/23.30 | | (80) host(all_65_1) = all_99_0 & $i(all_99_0) & ~ leq(all_65_3, % 168.34/23.30 | | all_99_0) % 168.34/23.30 | | % 168.34/23.30 | | ALPHA: (80) implies: % 168.34/23.30 | | (81) $i(all_99_0) % 168.34/23.30 | | (82) host(all_65_1) = all_99_0 % 168.34/23.30 | | % 168.34/23.30 | | REDUCE: (62), (82) imply: % 168.34/23.30 | | (83) host(all_65_17) = all_99_0 % 168.34/23.30 | | % 168.34/23.30 | | BETA: splitting (78) gives: % 168.34/23.30 | | % 168.34/23.30 | | Case 1: % 168.34/23.30 | | | % 168.34/23.30 | | | (84) ( ~ (all_107_0 = norm) & index(status, all_65_5) = all_107_0 & % 168.34/23.30 | | | $i(all_107_0)) | ( ~ (all_107_1 = all_65_5) & index(ldr, % 168.34/23.30 | | | all_65_5) = all_107_1 & $i(all_107_1)) % 168.34/23.30 | | | % 168.34/23.30 | | | BETA: splitting (84) gives: % 168.34/23.30 | | | % 168.34/23.30 | | | Case 1: % 168.34/23.30 | | | | % 168.34/23.30 | | | | (85) ~ (all_107_0 = norm) & index(status, all_65_5) = all_107_0 & % 168.34/23.30 | | | | $i(all_107_0) % 168.34/23.30 | | | | % 168.34/23.30 | | | | ALPHA: (85) implies: % 168.34/23.30 | | | | (86) ~ (all_107_0 = norm) % 168.34/23.31 | | | | (87) index(status, all_65_5) = all_107_0 % 168.34/23.31 | | | | % 168.34/23.31 | | | | GROUND_INST: instantiating (15) with norm, all_107_0, all_65_5, status, % 168.34/23.31 | | | | simplifying with (49), (87) gives: % 168.34/23.31 | | | | (88) all_107_0 = norm % 168.34/23.31 | | | | % 168.34/23.31 | | | | REDUCE: (86), (88) imply: % 168.34/23.31 | | | | (89) $false % 168.34/23.31 | | | | % 168.34/23.31 | | | | CLOSE: (89) is inconsistent. % 168.34/23.31 | | | | % 168.34/23.31 | | | Case 2: % 168.34/23.31 | | | | % 168.34/23.31 | | | | (90) ~ (all_107_1 = all_65_5) & index(ldr, all_65_5) = all_107_1 & % 168.34/23.31 | | | | $i(all_107_1) % 168.34/23.31 | | | | % 168.34/23.31 | | | | ALPHA: (90) implies: % 168.34/23.31 | | | | (91) ~ (all_107_1 = all_65_5) % 168.34/23.31 | | | | (92) index(ldr, all_65_5) = all_107_1 % 168.34/23.31 | | | | % 168.34/23.31 | | | | GROUND_INST: instantiating (15) with all_65_5, all_107_1, all_65_5, ldr, % 168.34/23.31 | | | | simplifying with (50), (92) gives: % 168.34/23.31 | | | | (93) all_107_1 = all_65_5 % 168.34/23.31 | | | | % 168.34/23.31 | | | | REDUCE: (91), (93) imply: % 168.34/23.31 | | | | (94) $false % 168.34/23.31 | | | | % 168.34/23.31 | | | | CLOSE: (94) is inconsistent. % 168.34/23.31 | | | | % 168.34/23.31 | | | End of split % 168.34/23.31 | | | % 168.34/23.31 | | Case 2: % 168.34/23.31 | | | % 168.34/23.31 | | | (95) ( ~ (all_107_2 = all_65_5) & host(all_65_16) = all_107_2 & % 168.34/23.31 | | | $i(all_107_2)) | (queue(all_65_15) = all_107_3 & $i(all_107_3) & % 168.34/23.31 | | | ~ elem(all_65_13, all_107_3)) % 168.34/23.31 | | | % 168.34/23.31 | | | BETA: splitting (95) gives: % 168.34/23.31 | | | % 168.34/23.31 | | | Case 1: % 168.34/23.31 | | | | % 168.34/23.31 | | | | (96) ~ (all_107_2 = all_65_5) & host(all_65_16) = all_107_2 & % 168.34/23.31 | | | | $i(all_107_2) % 168.34/23.31 | | | | % 168.34/23.31 | | | | ALPHA: (96) implies: % 168.34/23.31 | | | | (97) host(all_65_16) = all_107_2 % 168.34/23.31 | | | | % 168.34/23.31 | | | | GROUND_INST: instantiating (13) with all_65_15, all_99_0, all_65_17, % 168.34/23.31 | | | | simplifying with (38), (83) gives: % 168.34/23.31 | | | | (98) all_99_0 = all_65_15 % 168.34/23.31 | | | | % 168.34/23.31 | | | | GROUND_INST: instantiating (13) with all_65_12, all_107_2, all_65_16, % 168.34/23.31 | | | | simplifying with (39), (97) gives: % 168.34/23.31 | | | | (99) all_107_2 = all_65_12 % 168.34/23.31 | | | | % 168.34/23.31 | | | | GROUND_INST: instantiating (14) with all_65_7, all_78_0, all_65_15, % 168.34/23.31 | | | | simplifying with (44), (74) gives: % 168.34/23.31 | | | | (100) all_78_0 = all_65_7 % 168.34/23.31 | | | | % 168.34/23.31 | | | | GROUND_INST: instantiating (8) with all_65_15, all_65_15, all_65_7, % 168.34/23.31 | | | | all_65_7, simplifying with (28), (44), (64) gives: % 168.34/23.31 | | | | (101) leq(all_65_15, all_65_15) % 168.34/23.31 | | | | % 168.34/23.31 | | | | GROUND_INST: instantiating (3) with all_65_13, simplifying with (29), % 168.34/23.31 | | | | (70) gives: % 168.34/23.31 | | | | (102) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ($i(v0) & ((v2 = % 168.34/23.31 | | | | all_65_13 & m_Down(v0) = all_65_13) | (v1 = all_65_13 & % 168.34/23.31 | | | | m_Halt(v0) = all_65_13))) % 168.34/23.31 | | | | % 168.34/23.31 | | | | GROUND_INST: instantiating (3) with all_65_0, simplifying with (35), % 168.34/23.31 | | | | (66) gives: % 168.34/23.32 | | | | (103) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ($i(v0) & ((v2 = % 168.34/23.32 | | | | all_65_0 & m_Down(v0) = all_65_0) | (v1 = all_65_0 & % 168.34/23.32 | | | | m_Halt(v0) = all_65_0))) % 168.34/23.32 | | | | % 168.34/23.32 | | | | DELTA: instantiating (102) with fresh symbols all_149_0, all_149_1, % 168.34/23.32 | | | | all_149_2 gives: % 168.34/23.32 | | | | (104) $i(all_149_2) & ((all_149_0 = all_65_13 & m_Down(all_149_2) = % 168.34/23.32 | | | | all_65_13) | (all_149_1 = all_65_13 & m_Halt(all_149_2) = % 168.34/23.32 | | | | all_65_13)) % 168.34/23.32 | | | | % 168.34/23.32 | | | | ALPHA: (104) implies: % 168.34/23.32 | | | | (105) $i(all_149_2) % 168.34/23.32 | | | | (106) (all_149_0 = all_65_13 & m_Down(all_149_2) = all_65_13) | % 168.34/23.32 | | | | (all_149_1 = all_65_13 & m_Halt(all_149_2) = all_65_13) % 168.34/23.32 | | | | % 168.34/23.32 | | | | DELTA: instantiating (103) with fresh symbols all_151_0, all_151_1, % 168.34/23.32 | | | | all_151_2 gives: % 168.34/23.32 | | | | (107) $i(all_151_2) & ((all_151_0 = all_65_0 & m_Down(all_151_2) = % 168.34/23.32 | | | | all_65_0) | (all_151_1 = all_65_0 & m_Halt(all_151_2) = % 168.34/23.32 | | | | all_65_0)) % 168.34/23.32 | | | | % 168.34/23.32 | | | | ALPHA: (107) implies: % 168.34/23.32 | | | | (108) $i(all_151_2) % 168.34/23.32 | | | | (109) (all_151_0 = all_65_0 & m_Down(all_151_2) = all_65_0) | % 168.34/23.32 | | | | (all_151_1 = all_65_0 & m_Halt(all_151_2) = all_65_0) % 168.34/23.32 | | | | % 168.34/23.32 | | | | BETA: splitting (67) gives: % 168.34/23.32 | | | | % 168.34/23.32 | | | | Case 1: % 168.34/23.32 | | | | | % 168.34/23.32 | | | | | (110) leq(all_65_5, all_65_15) % 168.34/23.32 | | | | | % 168.34/23.32 | | | | | BETA: splitting (68) gives: % 168.34/23.32 | | | | | % 168.34/23.32 | | | | | Case 1: % 168.34/23.32 | | | | | | % 168.34/23.32 | | | | | | (111) leq(all_65_15, all_65_5) % 168.34/23.32 | | | | | | % 168.34/23.32 | | | | | | GROUND_INST: instantiating (6) with all_65_15, all_65_5, simplifying % 168.34/23.32 | | | | | | with (28), (32), (110), (111) gives: % 168.34/23.32 | | | | | | (112) all_65_5 = all_65_15 % 168.34/23.32 | | | | | | % 168.34/23.32 | | | | | | REDUCE: (19), (112) imply: % 168.34/23.32 | | | | | | (113) $false % 168.34/23.32 | | | | | | % 168.34/23.32 | | | | | | CLOSE: (113) is inconsistent. % 168.34/23.32 | | | | | | % 168.34/23.32 | | | | | Case 2: % 168.34/23.32 | | | | | | % 168.34/23.32 | | | | | | (114) ~ leq(all_65_15, all_65_5) % 168.34/23.32 | | | | | | % 168.34/23.33 | | | | | | REF_CLOSE: (12), (13), (15), (21), (22), (23), (26), (27), (31), % 168.34/23.33 | | | | | | (33), (36), (37), (38), (39), (40), (41), (46), (48), % 168.34/23.33 | | | | | | (49), (50), (51), (52), (54), (56), (57), (58), (71), % 168.34/23.33 | | | | | | (79), (101), (105), (106), (108), (109), (114), % 168.34/23.33 | | | | | | (axiom_17), (axiom_26), (axiom_30) are inconsistent by % 168.34/23.33 | | | | | | sub-proof #1. % 168.34/23.33 | | | | | | % 168.34/23.33 | | | | | End of split % 168.34/23.33 | | | | | % 168.34/23.33 | | | | Case 2: % 168.34/23.33 | | | | | % 168.34/23.33 | | | | | (115) ~ leq(all_65_5, all_65_15) % 168.34/23.33 | | | | | % 168.34/23.33 | | | | | BETA: splitting (68) gives: % 168.34/23.33 | | | | | % 168.34/23.33 | | | | | Case 1: % 168.34/23.33 | | | | | | % 168.34/23.33 | | | | | | (116) leq(all_65_15, all_65_5) % 168.34/23.33 | | | | | | % 168.34/23.33 | | | | | | BETA: splitting (61) gives: % 168.34/23.33 | | | | | | % 168.34/23.33 | | | | | | Case 1: % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | (117) all_65_1 = all_65_6 % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | COMBINE_EQS: (62), (117) imply: % 168.34/23.33 | | | | | | | (118) all_65_6 = all_65_17 % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | SIMP: (118) implies: % 168.34/23.33 | | | | | | | (119) all_65_6 = all_65_17 % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | REDUCE: (40), (119) imply: % 168.34/23.33 | | | | | | | (120) host(all_65_17) = all_65_5 % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | GROUND_INST: instantiating (13) with all_65_15, all_65_5, % 168.34/23.33 | | | | | | | all_65_17, simplifying with (38), (120) gives: % 168.34/23.33 | | | | | | | (121) all_65_5 = all_65_15 % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | REDUCE: (19), (121) imply: % 168.34/23.33 | | | | | | | (122) $false % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | CLOSE: (122) is inconsistent. % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | Case 2: % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | (123) ~ (all_65_1 = all_65_6) % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | REDUCE: (62), (123) imply: % 168.34/23.33 | | | | | | | (124) ~ (all_65_6 = all_65_17) % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | SIMP: (124) implies: % 168.34/23.33 | | | | | | | (125) ~ (all_65_6 = all_65_17) % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | BETA: splitting (60) gives: % 168.34/23.33 | | | | | | | % 168.34/23.33 | | | | | | | Case 1: % 168.34/23.33 | | | | | | | | % 168.34/23.33 | | | | | | | | (126) all_65_1 = all_65_6 % 168.34/23.33 | | | | | | | | % 168.34/23.33 | | | | | | | | COMBINE_EQS: (62), (126) imply: % 168.34/23.33 | | | | | | | | (127) all_65_6 = all_65_17 % 168.34/23.33 | | | | | | | | % 168.34/23.33 | | | | | | | | SIMP: (127) implies: % 168.34/23.33 | | | | | | | | (128) all_65_6 = all_65_17 % 168.34/23.33 | | | | | | | | % 168.34/23.33 | | | | | | | | REDUCE: (125), (128) imply: % 168.34/23.33 | | | | | | | | (129) $false % 168.34/23.33 | | | | | | | | % 168.34/23.33 | | | | | | | | CLOSE: (129) is inconsistent. % 168.34/23.33 | | | | | | | | % 168.34/23.33 | | | | | | | Case 2: % 168.34/23.33 | | | | | | | | % 168.34/23.33 | | | | | | | | % 168.34/23.34 | | | | | | | | GROUND_INST: instantiating (7) with all_65_15, all_65_5, % 168.34/23.34 | | | | | | | | all_65_7, all_82_0, simplifying with (28), (32), % 168.34/23.34 | | | | | | | | (44), (76), (116) gives: % 168.34/23.34 | | | | | | | | (130) leq(all_65_7, all_82_0) % 168.34/23.34 | | | | | | | | % 168.34/23.34 | | | | | | | | BETA: splitting (109) gives: % 168.34/23.34 | | | | | | | | % 168.34/23.34 | | | | | | | | Case 1: % 168.34/23.34 | | | | | | | | | % 168.34/23.34 | | | | | | | | | (131) all_151_0 = all_65_0 & m_Down(all_151_2) = all_65_0 % 168.34/23.34 | | | | | | | | | % 168.34/23.34 | | | | | | | | | ALPHA: (131) implies: % 168.34/23.34 | | | | | | | | | (132) m_Down(all_151_2) = all_65_0 % 168.34/23.34 | | | | | | | | | % 168.34/23.34 | | | | | | | | | GROUND_INST: instantiating (axiom_17) with all_151_2, % 168.34/23.34 | | | | | | | | | all_65_17, all_65_0, simplifying with (26), (79), % 168.34/23.34 | | | | | | | | | (108), (132) gives: % 168.34/23.34 | | | | | | | | | (133) $false % 168.34/23.34 | | | | | | | | | % 168.34/23.34 | | | | | | | | | CLOSE: (133) is inconsistent. % 168.34/23.34 | | | | | | | | | % 168.34/23.34 | | | | | | | | Case 2: % 168.34/23.34 | | | | | | | | | % 168.34/23.34 | | | | | | | | | % 168.34/23.34 | | | | | | | | | GROUND_INST: instantiating (10) with all_65_7, all_65_5, % 168.34/23.34 | | | | | | | | | all_82_0, simplifying with (20), (30), (32), (76), % 168.34/23.34 | | | | | | | | | (130) gives: % 168.34/23.34 | | | | | | | | | (134) all_82_0 = all_65_7 % 168.34/23.34 | | | | | | | | | % 168.34/23.34 | | | | | | | | | REDUCE: (76), (134) imply: % 168.34/23.34 | | | | | | | | | (135) s(all_65_5) = all_65_7 % 168.34/23.34 | | | | | | | | | % 168.34/23.34 | | | | | | | | | GROUND_INST: instantiating (8) with all_65_5, all_65_15, % 168.34/23.34 | | | | | | | | | all_65_7, all_65_7, simplifying with (28), (32), % 168.34/23.34 | | | | | | | | | (44), (64), (115), (135) gives: % 168.34/23.34 | | | | | | | | | (136) $false % 168.34/23.34 | | | | | | | | | % 168.34/23.34 | | | | | | | | | CLOSE: (136) is inconsistent. % 168.34/23.34 | | | | | | | | | % 168.34/23.34 | | | | | | | | End of split % 168.34/23.34 | | | | | | | | % 168.34/23.34 | | | | | | | End of split % 168.34/23.34 | | | | | | | % 168.34/23.34 | | | | | | End of split % 168.34/23.34 | | | | | | % 168.34/23.34 | | | | | Case 2: % 168.34/23.34 | | | | | | % 168.34/23.34 | | | | | | (137) ~ leq(all_65_15, all_65_5) % 168.34/23.34 | | | | | | % 168.34/23.35 | | | | | | REF_CLOSE: (12), (13), (15), (21), (22), (23), (26), (27), (31), % 168.34/23.35 | | | | | | (33), (36), (37), (38), (39), (40), (41), (46), (48), % 168.34/23.35 | | | | | | (49), (50), (51), (52), (54), (56), (57), (58), (71), % 168.34/23.35 | | | | | | (79), (101), (105), (106), (108), (109), (137), % 168.34/23.35 | | | | | | (axiom_17), (axiom_26), (axiom_30) are inconsistent by % 168.34/23.35 | | | | | | sub-proof #1. % 168.34/23.35 | | | | | | % 168.34/23.35 | | | | | End of split % 168.34/23.35 | | | | | % 168.34/23.35 | | | | End of split % 168.34/23.35 | | | | % 168.34/23.35 | | | Case 2: % 168.34/23.35 | | | | % 168.34/23.35 | | | | (138) queue(all_65_15) = all_107_3 & $i(all_107_3) & ~ % 168.34/23.35 | | | | elem(all_65_13, all_107_3) % 168.34/23.35 | | | | % 168.34/23.35 | | | | ALPHA: (138) implies: % 168.34/23.35 | | | | (139) ~ elem(all_65_13, all_107_3) % 168.34/23.35 | | | | (140) queue(all_65_15) = all_107_3 % 168.34/23.35 | | | | % 168.34/23.35 | | | | GROUND_INST: instantiating (12) with all_65_14, all_107_3, all_65_15, % 168.34/23.35 | | | | simplifying with (36), (140) gives: % 168.34/23.35 | | | | (141) all_107_3 = all_65_14 % 168.34/23.35 | | | | % 168.34/23.35 | | | | REDUCE: (139), (141) imply: % 168.34/23.35 | | | | (142) ~ elem(all_65_13, all_65_14) % 168.34/23.35 | | | | % 168.34/23.35 | | | | PRED_UNIFY: (71), (142) imply: % 168.34/23.35 | | | | (143) $false % 168.34/23.35 | | | | % 168.34/23.35 | | | | CLOSE: (143) is inconsistent. % 168.34/23.35 | | | | % 168.34/23.35 | | | End of split % 168.34/23.35 | | | % 168.34/23.35 | | End of split % 168.34/23.35 | | % 168.34/23.35 | Case 2: % 168.34/23.35 | | % 168.34/23.35 | | (144) queue(all_65_3) = all_99_1 & $i(all_99_1) & ~ elem(all_65_0, % 168.34/23.35 | | all_99_1) % 168.34/23.35 | | % 168.34/23.35 | | ALPHA: (144) implies: % 168.34/23.35 | | (145) ~ elem(all_65_0, all_99_1) % 168.34/23.35 | | (146) queue(all_65_3) = all_99_1 % 168.34/23.35 | | % 168.34/23.35 | | GROUND_INST: instantiating (12) with all_65_2, all_99_1, all_65_3, % 168.34/23.35 | | simplifying with (37), (146) gives: % 168.34/23.35 | | (147) all_99_1 = all_65_2 % 168.34/23.35 | | % 168.34/23.35 | | REDUCE: (145), (147) imply: % 168.34/23.35 | | (148) ~ elem(all_65_0, all_65_2) % 168.34/23.35 | | % 168.34/23.35 | | PRED_UNIFY: (21), (148) imply: % 168.34/23.35 | | (149) $false % 168.34/23.35 | | % 168.34/23.35 | | CLOSE: (149) is inconsistent. % 168.34/23.35 | | % 168.34/23.36 | End of split % 168.34/23.36 | % 168.34/23.36 End of proof % 168.34/23.36 % 168.34/23.36 Sub-proof #1 shows that the following formulas are inconsistent: % 168.34/23.36 ---------------------------------------------------------------- % 168.34/23.36 (1) index(status, all_65_15) = elec_1 % 168.34/23.36 (2) $i(all_149_2) % 168.34/23.36 (3) (all_151_0 = all_65_0 & m_Down(all_151_2) = all_65_0) | (all_151_1 = % 168.34/23.36 all_65_0 & m_Halt(all_151_2) = all_65_0) % 168.34/23.36 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v1) = v2) % 168.34/23.36 | ~ (m_Halt(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 168.34/23.36 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1) | % 168.34/23.36 ~ (host(v2) = v0)) % 168.34/23.36 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 168.34/23.36 [v5: $i] : ( ~ (m_Down(v1) = v5) | ~ (host(v2) = v3) | ~ (host(v0) = % 168.34/23.36 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v0, alive) | % 168.34/23.36 leq(v3, v4) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 168.34/23.36 ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ($i(v12) & (( ~ (v12 = v7) % 168.34/23.36 & index(down, v3) = v6 & host(v1) = v7 & $i(v7) & $i(v6) & % 168.34/23.36 leq(all_65_20, v12) & ~ leq(v3, v12) & ~ setIn(v12, v6)) | ( ~ % 168.34/23.36 (v11 = norm) & index(status, v4) = v11 & $i(v11)) | ( ~ (v10 = % 168.34/23.36 v4) & index(ldr, v4) = v10 & $i(v10)) | ( ~ (v9 = elec_1) & % 168.34/23.36 index(status, v3) = v9 & $i(v9)) | (queue(v3) = v8 & $i(v8) & ~ % 168.34/23.36 elem(v5, v8))))) % 168.34/23.36 (7) host(all_65_16) = all_65_12 % 168.34/23.36 (8) $i(all_65_6) % 168.34/23.36 (9) (all_149_0 = all_65_13 & m_Down(all_149_2) = all_65_13) | (all_149_1 = % 168.34/23.36 all_65_13 & m_Halt(all_149_2) = all_65_13) % 168.34/23.36 (10) index(down, all_65_15) = all_65_8 % 168.34/23.36 (11) ! [v0: any] : (v0 = all_65_12 | ~ $i(v0) | ~ leq(all_65_20, v0) | % 168.34/23.36 leq(all_65_15, v0) | setIn(v0, all_65_8)) % 168.34/23.36 (12) $i(all_65_17) % 168.34/23.36 (13) index(ldr, all_65_5) = all_65_5 % 168.34/23.36 (14) leq(all_65_15, all_65_15) % 168.34/23.37 (15) host(all_65_4) = all_65_3 % 168.34/23.37 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) % 168.34/23.37 | ~ (queue(v2) = v0)) % 168.34/23.37 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v1) = % 168.34/23.37 v2) | ~ (m_Down(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 168.34/23.37 (18) host(all_65_6) = all_65_5 % 168.34/23.37 (19) setIn(all_65_17, alive) % 168.34/23.37 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~ % 168.34/23.37 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 168.34/23.37 (21) elem(all_65_0, all_65_2) % 168.34/23.37 (22) m_Down(all_65_16) = all_65_13 % 168.34/23.37 (23) $i(all_65_4) % 168.34/23.37 (24) m_Halt(all_65_17) = all_65_0 % 168.34/23.37 (25) index(status, all_65_5) = norm % 168.34/23.37 (26) $i(all_65_16) % 168.34/23.37 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 168.34/23.37 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) % 168.34/23.37 (28) host(all_65_17) = all_65_15 % 168.34/23.37 (29) $i(all_151_2) % 168.34/23.37 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Halt(v1) % 168.34/23.37 = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 168.34/23.37 ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3) = % 168.34/23.37 v4 & $i(v4) & ~ elem(v2, v4)))) % 168.34/23.37 (31) queue(all_65_15) = all_65_14 % 168.34/23.37 (32) elem(all_65_13, all_65_14) % 168.34/23.37 (33) ~ leq(all_65_15, all_65_5) % 168.34/23.37 (34) queue(all_65_3) = all_65_2 % 168.34/23.37 (35) setIn(all_65_6, alive) % 168.34/23.37 (36) all_65_20 = all_59_0 % 168.34/23.37 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 168.34/23.37 [v5: $i] : ( ~ (m_Down(v1) = v3) | ~ (host(v2) = v4) | ~ (host(v0) = % 168.34/23.37 v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ % 168.34/23.37 setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 168.34/23.37 $i] : (( ~ (v9 = norm) & index(status, v5) = v9 & $i(v9)) | ( ~ (v8 % 168.34/23.37 = v5) & index(ldr, v5) = v8 & $i(v8)) | ( ~ (v7 = v5) & host(v1) % 168.34/23.37 = v7 & $i(v7)) | (queue(v4) = v6 & $i(v6) & ~ elem(v3, v6)))) % 168.34/23.37 % 168.34/23.37 Begin of proof % 168.34/23.37 | % 168.34/23.37 | BETA: splitting (9) gives: % 168.34/23.37 | % 168.34/23.37 | Case 1: % 168.34/23.37 | | % 168.34/23.38 | | (38) all_149_0 = all_65_13 & m_Down(all_149_2) = all_65_13 % 168.34/23.38 | | % 168.34/23.38 | | ALPHA: (38) implies: % 168.34/23.38 | | (39) m_Down(all_149_2) = all_65_13 % 168.34/23.38 | | % 168.34/23.38 | | BETA: splitting (3) gives: % 168.34/23.38 | | % 168.34/23.38 | | Case 1: % 168.34/23.38 | | | % 168.34/23.38 | | | (40) all_151_0 = all_65_0 & m_Down(all_151_2) = all_65_0 % 168.34/23.38 | | | % 168.34/23.38 | | | ALPHA: (40) implies: % 168.34/23.38 | | | (41) m_Down(all_151_2) = all_65_0 % 168.34/23.38 | | | % 168.34/23.38 | | | GROUND_INST: instantiating (20) with all_151_2, all_65_17, all_65_0, % 168.34/23.38 | | | simplifying with (12), (24), (29), (41) gives: % 168.34/23.38 | | | (42) $false % 168.34/23.38 | | | % 168.34/23.38 | | | CLOSE: (42) is inconsistent. % 168.34/23.38 | | | % 168.34/23.38 | | Case 2: % 168.34/23.38 | | | % 168.34/23.38 | | | (43) all_151_1 = all_65_0 & m_Halt(all_151_2) = all_65_0 % 168.34/23.38 | | | % 168.34/23.38 | | | ALPHA: (43) implies: % 168.34/23.38 | | | (44) m_Halt(all_151_2) = all_65_0 % 168.34/23.38 | | | % 168.34/23.38 | | | GROUND_INST: instantiating (30) with all_65_4, all_151_2, all_65_0, % 168.34/23.38 | | | all_65_3, simplifying with (15), (23), (29), (44) gives: % 168.34/23.38 | | | (45) ? [v0: $i] : ? [v1: $i] : ((host(all_151_2) = v1 & $i(v1) & ~ % 168.34/23.38 | | | leq(all_65_3, v1)) | (queue(all_65_3) = v0 & $i(v0) & ~ % 168.34/23.38 | | | elem(all_65_0, v0))) % 168.34/23.38 | | | % 168.34/23.38 | | | GROUND_INST: instantiating (30) with all_65_17, all_151_2, all_65_0, % 168.34/23.38 | | | all_65_15, simplifying with (12), (28), (29), (44) gives: % 168.34/23.38 | | | (46) ? [v0: $i] : ? [v1: $i] : ((host(all_151_2) = v1 & $i(v1) & ~ % 168.34/23.38 | | | leq(all_65_15, v1)) | (queue(all_65_15) = v0 & $i(v0) & ~ % 168.34/23.38 | | | elem(all_65_0, v0))) % 168.34/23.38 | | | % 168.34/23.38 | | | GROUND_INST: instantiating (4) with all_65_17, all_151_2, all_65_0, % 168.34/23.38 | | | simplifying with (12), (24), (29), (44) gives: % 168.34/23.38 | | | (47) all_151_2 = all_65_17 % 168.34/23.38 | | | % 168.34/23.38 | | | GROUND_INST: instantiating (6) with all_65_6, all_149_2, all_65_17, % 168.34/23.38 | | | all_65_15, all_65_5, all_65_13, simplifying with (2), (8), % 168.34/23.38 | | | (12), (18), (28), (33), (35), (39) gives: % 168.34/23.38 | | | (48) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 168.34/23.38 | | | any] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & (( ~ (v6 = v1) & % 168.34/23.38 | | | index(down, all_65_15) = v0 & host(all_149_2) = v1 & $i(v1) % 168.34/23.38 | | | & $i(v0) & leq(all_65_20, v6) & ~ leq(all_65_15, v6) & ~ % 168.34/23.38 | | | setIn(v6, v0)) | ( ~ (v5 = norm) & index(status, all_65_5) = % 168.34/23.38 | | | v5 & $i(v5)) | ( ~ (v4 = all_65_5) & index(ldr, all_65_5) = % 168.34/23.38 | | | v4 & $i(v4)) | ( ~ (v3 = elec_1) & index(status, all_65_15) % 168.34/23.38 | | | = v3 & $i(v3)) | (queue(all_65_15) = v2 & $i(v2) & ~ % 168.34/23.38 | | | elem(all_65_13, v2)))) % 168.34/23.38 | | | % 168.81/23.39 | | | GROUND_INST: instantiating (37) with all_65_6, all_149_2, all_65_17, % 168.81/23.39 | | | all_65_13, all_65_15, all_65_5, simplifying with (2), (8), % 168.81/23.39 | | | (12), (18), (19), (28), (35), (39) gives: % 168.81/23.39 | | | (49) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : (( ~ (v3 % 168.81/23.39 | | | = norm) & index(status, all_65_5) = v3 & $i(v3)) | ( ~ (v2 = % 168.81/23.39 | | | all_65_5) & index(ldr, all_65_5) = v2 & $i(v2)) | ( ~ (v1 = % 168.81/23.39 | | | all_65_5) & host(all_149_2) = v1 & $i(v1)) | % 168.81/23.39 | | | (queue(all_65_15) = v0 & $i(v0) & ~ elem(all_65_13, v0))) % 168.81/23.39 | | | % 168.81/23.39 | | | GROUND_INST: instantiating (17) with all_65_16, all_149_2, all_65_13, % 168.81/23.39 | | | simplifying with (2), (22), (26), (39) gives: % 168.81/23.39 | | | (50) all_149_2 = all_65_16 % 168.81/23.39 | | | % 168.81/23.39 | | | DELTA: instantiating (45) with fresh symbols all_509_0, all_509_1 gives: % 168.81/23.39 | | | (51) (host(all_151_2) = all_509_0 & $i(all_509_0) & ~ leq(all_65_3, % 168.81/23.39 | | | all_509_0)) | (queue(all_65_3) = all_509_1 & $i(all_509_1) & % 168.81/23.39 | | | ~ elem(all_65_0, all_509_1)) % 168.81/23.39 | | | % 168.81/23.39 | | | DELTA: instantiating (46) with fresh symbols all_510_0, all_510_1 gives: % 168.81/23.39 | | | (52) (host(all_151_2) = all_510_0 & $i(all_510_0) & ~ leq(all_65_15, % 168.81/23.39 | | | all_510_0)) | (queue(all_65_15) = all_510_1 & $i(all_510_1) & % 168.81/23.39 | | | ~ elem(all_65_0, all_510_1)) % 168.81/23.39 | | | % 168.81/23.39 | | | DELTA: instantiating (49) with fresh symbols all_512_0, all_512_1, % 168.81/23.39 | | | all_512_2, all_512_3 gives: % 168.81/23.39 | | | (53) ( ~ (all_512_0 = norm) & index(status, all_65_5) = all_512_0 & % 168.81/23.39 | | | $i(all_512_0)) | ( ~ (all_512_1 = all_65_5) & index(ldr, % 168.81/23.39 | | | all_65_5) = all_512_1 & $i(all_512_1)) | ( ~ (all_512_2 = % 168.81/23.39 | | | all_65_5) & host(all_149_2) = all_512_2 & $i(all_512_2)) | % 168.81/23.39 | | | (queue(all_65_15) = all_512_3 & $i(all_512_3) & ~ elem(all_65_13, % 168.81/23.39 | | | all_512_3)) % 168.81/23.39 | | | % 168.81/23.39 | | | DELTA: instantiating (48) with fresh symbols all_516_0, all_516_1, % 168.81/23.39 | | | all_516_2, all_516_3, all_516_4, all_516_5, all_516_6 gives: % 168.85/23.39 | | | (54) $i(all_516_0) & (( ~ (all_516_0 = all_516_5) & index(down, % 168.85/23.39 | | | all_65_15) = all_516_6 & host(all_149_2) = all_516_5 & % 168.85/23.39 | | | $i(all_516_5) & $i(all_516_6) & leq(all_65_20, all_516_0) & ~ % 168.85/23.39 | | | leq(all_65_15, all_516_0) & ~ setIn(all_516_0, all_516_6)) | % 168.85/23.39 | | | ( ~ (all_516_1 = norm) & index(status, all_65_5) = all_516_1 & % 168.85/23.39 | | | $i(all_516_1)) | ( ~ (all_516_2 = all_65_5) & index(ldr, % 168.85/23.39 | | | all_65_5) = all_516_2 & $i(all_516_2)) | ( ~ (all_516_3 = % 168.85/23.39 | | | elec_1) & index(status, all_65_15) = all_516_3 & % 168.85/23.39 | | | $i(all_516_3)) | (queue(all_65_15) = all_516_4 & $i(all_516_4) % 168.85/23.39 | | | & ~ elem(all_65_13, all_516_4))) % 168.85/23.39 | | | % 168.85/23.39 | | | ALPHA: (54) implies: % 168.85/23.39 | | | (55) $i(all_516_0) % 168.85/23.39 | | | (56) ( ~ (all_516_0 = all_516_5) & index(down, all_65_15) = all_516_6 & % 168.85/23.39 | | | host(all_149_2) = all_516_5 & $i(all_516_5) & $i(all_516_6) & % 168.85/23.39 | | | leq(all_65_20, all_516_0) & ~ leq(all_65_15, all_516_0) & ~ % 168.85/23.39 | | | setIn(all_516_0, all_516_6)) | ( ~ (all_516_1 = norm) & % 168.85/23.39 | | | index(status, all_65_5) = all_516_1 & $i(all_516_1)) | ( ~ % 168.85/23.39 | | | (all_516_2 = all_65_5) & index(ldr, all_65_5) = all_516_2 & % 168.85/23.39 | | | $i(all_516_2)) | ( ~ (all_516_3 = elec_1) & index(status, % 168.85/23.39 | | | all_65_15) = all_516_3 & $i(all_516_3)) | (queue(all_65_15) = % 168.85/23.39 | | | all_516_4 & $i(all_516_4) & ~ elem(all_65_13, all_516_4)) % 168.85/23.39 | | | % 168.85/23.39 | | | BETA: splitting (53) gives: % 168.85/23.39 | | | % 168.85/23.39 | | | Case 1: % 168.85/23.39 | | | | % 168.85/23.39 | | | | (57) ( ~ (all_512_0 = norm) & index(status, all_65_5) = all_512_0 & % 168.85/23.39 | | | | $i(all_512_0)) | ( ~ (all_512_1 = all_65_5) & index(ldr, % 168.85/23.39 | | | | all_65_5) = all_512_1 & $i(all_512_1)) % 168.85/23.40 | | | | % 168.85/23.40 | | | | BETA: splitting (57) gives: % 168.85/23.40 | | | | % 168.85/23.40 | | | | Case 1: % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | (58) ~ (all_512_0 = norm) & index(status, all_65_5) = all_512_0 & % 168.85/23.40 | | | | | $i(all_512_0) % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | ALPHA: (58) implies: % 168.85/23.40 | | | | | (59) ~ (all_512_0 = norm) % 168.85/23.40 | | | | | (60) index(status, all_65_5) = all_512_0 % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | GROUND_INST: instantiating (27) with norm, all_512_0, all_65_5, % 168.85/23.40 | | | | | status, simplifying with (25), (60) gives: % 168.85/23.40 | | | | | (61) all_512_0 = norm % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | REDUCE: (59), (61) imply: % 168.85/23.40 | | | | | (62) $false % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | CLOSE: (62) is inconsistent. % 168.85/23.40 | | | | | % 168.85/23.40 | | | | Case 2: % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | (63) ~ (all_512_1 = all_65_5) & index(ldr, all_65_5) = all_512_1 & % 168.85/23.40 | | | | | $i(all_512_1) % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | ALPHA: (63) implies: % 168.85/23.40 | | | | | (64) ~ (all_512_1 = all_65_5) % 168.85/23.40 | | | | | (65) index(ldr, all_65_5) = all_512_1 % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | GROUND_INST: instantiating (27) with all_65_5, all_512_1, all_65_5, % 168.85/23.40 | | | | | ldr, simplifying with (13), (65) gives: % 168.85/23.40 | | | | | (66) all_512_1 = all_65_5 % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | REDUCE: (64), (66) imply: % 168.85/23.40 | | | | | (67) $false % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | CLOSE: (67) is inconsistent. % 168.85/23.40 | | | | | % 168.85/23.40 | | | | End of split % 168.85/23.40 | | | | % 168.85/23.40 | | | Case 2: % 168.85/23.40 | | | | % 168.85/23.40 | | | | (68) ( ~ (all_512_2 = all_65_5) & host(all_149_2) = all_512_2 & % 168.85/23.40 | | | | $i(all_512_2)) | (queue(all_65_15) = all_512_3 & $i(all_512_3) % 168.85/23.40 | | | | & ~ elem(all_65_13, all_512_3)) % 168.85/23.40 | | | | % 168.85/23.40 | | | | BETA: splitting (68) gives: % 168.85/23.40 | | | | % 168.85/23.40 | | | | Case 1: % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | (69) ~ (all_512_2 = all_65_5) & host(all_149_2) = all_512_2 & % 168.85/23.40 | | | | | $i(all_512_2) % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | ALPHA: (69) implies: % 168.85/23.40 | | | | | (70) host(all_149_2) = all_512_2 % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | REDUCE: (50), (70) imply: % 168.85/23.40 | | | | | (71) host(all_65_16) = all_512_2 % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | BETA: splitting (56) gives: % 168.85/23.40 | | | | | % 168.85/23.40 | | | | | Case 1: % 168.85/23.40 | | | | | | % 168.85/23.40 | | | | | | (72) ( ~ (all_516_0 = all_516_5) & index(down, all_65_15) = % 168.85/23.40 | | | | | | all_516_6 & host(all_149_2) = all_516_5 & $i(all_516_5) & % 168.85/23.40 | | | | | | $i(all_516_6) & leq(all_65_20, all_516_0) & ~ % 168.85/23.40 | | | | | | leq(all_65_15, all_516_0) & ~ setIn(all_516_0, % 168.85/23.40 | | | | | | all_516_6)) | ( ~ (all_516_1 = norm) & index(status, % 168.85/23.40 | | | | | | all_65_5) = all_516_1 & $i(all_516_1)) % 168.85/23.40 | | | | | | % 168.85/23.40 | | | | | | BETA: splitting (72) gives: % 168.85/23.40 | | | | | | % 168.85/23.40 | | | | | | Case 1: % 168.85/23.40 | | | | | | | % 168.85/23.40 | | | | | | | (73) ~ (all_516_0 = all_516_5) & index(down, all_65_15) = % 168.85/23.40 | | | | | | | all_516_6 & host(all_149_2) = all_516_5 & $i(all_516_5) & % 168.85/23.40 | | | | | | | $i(all_516_6) & leq(all_65_20, all_516_0) & ~ % 168.85/23.40 | | | | | | | leq(all_65_15, all_516_0) & ~ setIn(all_516_0, all_516_6) % 168.85/23.40 | | | | | | | % 168.85/23.40 | | | | | | | ALPHA: (73) implies: % 168.85/23.40 | | | | | | | (74) ~ (all_516_0 = all_516_5) % 168.85/23.40 | | | | | | | (75) ~ setIn(all_516_0, all_516_6) % 168.85/23.40 | | | | | | | (76) ~ leq(all_65_15, all_516_0) % 168.85/23.40 | | | | | | | (77) leq(all_65_20, all_516_0) % 168.85/23.40 | | | | | | | (78) host(all_149_2) = all_516_5 % 168.85/23.40 | | | | | | | (79) index(down, all_65_15) = all_516_6 % 168.85/23.40 | | | | | | | % 168.85/23.40 | | | | | | | REDUCE: (50), (78) imply: % 168.85/23.40 | | | | | | | (80) host(all_65_16) = all_516_5 % 168.85/23.40 | | | | | | | % 168.85/23.40 | | | | | | | REDUCE: (36), (77) imply: % 168.85/23.40 | | | | | | | (81) leq(all_59_0, all_516_0) % 168.85/23.40 | | | | | | | % 168.85/23.40 | | | | | | | BETA: splitting (51) gives: % 168.85/23.40 | | | | | | | % 168.85/23.40 | | | | | | | Case 1: % 168.85/23.40 | | | | | | | | % 168.91/23.40 | | | | | | | | (82) host(all_151_2) = all_509_0 & $i(all_509_0) & ~ % 168.91/23.40 | | | | | | | | leq(all_65_3, all_509_0) % 168.91/23.40 | | | | | | | | % 168.91/23.40 | | | | | | | | ALPHA: (82) implies: % 168.91/23.40 | | | | | | | | (83) host(all_151_2) = all_509_0 % 168.91/23.40 | | | | | | | | % 168.91/23.40 | | | | | | | | REDUCE: (47), (83) imply: % 168.91/23.40 | | | | | | | | (84) host(all_65_17) = all_509_0 % 168.91/23.40 | | | | | | | | % 168.91/23.40 | | | | | | | | GROUND_INST: instantiating (5) with all_65_15, all_509_0, % 168.91/23.40 | | | | | | | | all_65_17, simplifying with (28), (84) gives: % 168.91/23.40 | | | | | | | | (85) all_509_0 = all_65_15 % 168.91/23.40 | | | | | | | | % 168.91/23.41 | | | | | | | | GROUND_INST: instantiating (5) with all_65_12, all_516_5, % 168.91/23.41 | | | | | | | | all_65_16, simplifying with (7), (80) gives: % 168.91/23.41 | | | | | | | | (86) all_516_5 = all_65_12 % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | GROUND_INST: instantiating (5) with all_512_2, all_516_5, % 168.91/23.41 | | | | | | | | all_65_16, simplifying with (71), (80) gives: % 168.91/23.41 | | | | | | | | (87) all_516_5 = all_512_2 % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | GROUND_INST: instantiating (27) with all_65_8, all_516_6, % 168.91/23.41 | | | | | | | | all_65_15, down, simplifying with (10), (79) gives: % 168.91/23.41 | | | | | | | | (88) all_516_6 = all_65_8 % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | COMBINE_EQS: (86), (87) imply: % 168.91/23.41 | | | | | | | | (89) all_512_2 = all_65_12 % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | REDUCE: (74), (86) imply: % 168.91/23.41 | | | | | | | | (90) ~ (all_516_0 = all_65_12) % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | REDUCE: (75), (88) imply: % 168.91/23.41 | | | | | | | | (91) ~ setIn(all_516_0, all_65_8) % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | BETA: splitting (52) gives: % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | Case 1: % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | (92) host(all_151_2) = all_510_0 & $i(all_510_0) & ~ % 168.91/23.41 | | | | | | | | | leq(all_65_15, all_510_0) % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | ALPHA: (92) implies: % 168.91/23.41 | | | | | | | | | (93) ~ leq(all_65_15, all_510_0) % 168.91/23.41 | | | | | | | | | (94) host(all_151_2) = all_510_0 % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | REDUCE: (47), (94) imply: % 168.91/23.41 | | | | | | | | | (95) host(all_65_17) = all_510_0 % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | GROUND_INST: instantiating (5) with all_65_15, all_510_0, % 168.91/23.41 | | | | | | | | | all_65_17, simplifying with (28), (95) gives: % 168.91/23.41 | | | | | | | | | (96) all_510_0 = all_65_15 % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | GROUND_INST: instantiating (5) with all_509_0, all_510_0, % 168.91/23.41 | | | | | | | | | all_65_17, simplifying with (84), (95) gives: % 168.91/23.41 | | | | | | | | | (97) all_510_0 = all_509_0 % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | REDUCE: (93), (96) imply: % 168.91/23.41 | | | | | | | | | (98) ~ leq(all_65_15, all_65_15) % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | PRED_UNIFY: (14), (98) imply: % 168.91/23.41 | | | | | | | | | (99) $false % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | CLOSE: (99) is inconsistent. % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | Case 2: % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | GROUND_INST: instantiating (11) with all_516_0, simplifying % 168.91/23.41 | | | | | | | | | with (55), (76), (91) gives: % 168.91/23.41 | | | | | | | | | (100) all_516_0 = all_65_12 | ~ leq(all_65_20, all_516_0) % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | BETA: splitting (100) gives: % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | | Case 1: % 168.91/23.41 | | | | | | | | | | % 168.91/23.41 | | | | | | | | | | (101) ~ leq(all_65_20, all_516_0) % 168.91/23.41 | | | | | | | | | | % 168.91/23.41 | | | | | | | | | | REDUCE: (36), (101) imply: % 168.91/23.41 | | | | | | | | | | (102) ~ leq(all_59_0, all_516_0) % 168.91/23.41 | | | | | | | | | | % 168.91/23.41 | | | | | | | | | | PRED_UNIFY: (81), (102) imply: % 168.91/23.41 | | | | | | | | | | (103) $false % 168.91/23.41 | | | | | | | | | | % 168.91/23.41 | | | | | | | | | | CLOSE: (103) is inconsistent. % 168.91/23.41 | | | | | | | | | | % 168.91/23.41 | | | | | | | | | Case 2: % 168.91/23.41 | | | | | | | | | | % 168.91/23.41 | | | | | | | | | | (104) all_516_0 = all_65_12 % 168.91/23.41 | | | | | | | | | | % 168.91/23.41 | | | | | | | | | | REDUCE: (90), (104) imply: % 168.91/23.41 | | | | | | | | | | (105) $false % 168.91/23.41 | | | | | | | | | | % 168.91/23.41 | | | | | | | | | | CLOSE: (105) is inconsistent. % 168.91/23.41 | | | | | | | | | | % 168.91/23.41 | | | | | | | | | End of split % 168.91/23.41 | | | | | | | | | % 168.91/23.41 | | | | | | | | End of split % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | Case 2: % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | (106) queue(all_65_3) = all_509_1 & $i(all_509_1) & ~ % 168.91/23.41 | | | | | | | | elem(all_65_0, all_509_1) % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | ALPHA: (106) implies: % 168.91/23.41 | | | | | | | | (107) ~ elem(all_65_0, all_509_1) % 168.91/23.41 | | | | | | | | (108) queue(all_65_3) = all_509_1 % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | GROUND_INST: instantiating (16) with all_65_2, all_509_1, % 168.91/23.41 | | | | | | | | all_65_3, simplifying with (34), (108) gives: % 168.91/23.41 | | | | | | | | (109) all_509_1 = all_65_2 % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | REDUCE: (107), (109) imply: % 168.91/23.41 | | | | | | | | (110) ~ elem(all_65_0, all_65_2) % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | PRED_UNIFY: (21), (110) imply: % 168.91/23.41 | | | | | | | | (111) $false % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | | CLOSE: (111) is inconsistent. % 168.91/23.41 | | | | | | | | % 168.91/23.41 | | | | | | | End of split % 168.91/23.41 | | | | | | | % 168.91/23.41 | | | | | | Case 2: % 168.91/23.41 | | | | | | | % 168.91/23.41 | | | | | | | (112) ~ (all_516_1 = norm) & index(status, all_65_5) = % 168.91/23.41 | | | | | | | all_516_1 & $i(all_516_1) % 168.91/23.41 | | | | | | | % 168.91/23.41 | | | | | | | ALPHA: (112) implies: % 168.91/23.41 | | | | | | | (113) ~ (all_516_1 = norm) % 168.91/23.41 | | | | | | | (114) index(status, all_65_5) = all_516_1 % 168.91/23.41 | | | | | | | % 168.91/23.41 | | | | | | | GROUND_INST: instantiating (27) with norm, all_516_1, all_65_5, % 168.91/23.41 | | | | | | | status, simplifying with (25), (114) gives: % 168.91/23.41 | | | | | | | (115) all_516_1 = norm % 168.91/23.41 | | | | | | | % 168.91/23.41 | | | | | | | REDUCE: (113), (115) imply: % 168.91/23.41 | | | | | | | (116) $false % 168.91/23.41 | | | | | | | % 168.91/23.41 | | | | | | | CLOSE: (116) is inconsistent. % 168.91/23.41 | | | | | | | % 168.91/23.41 | | | | | | End of split % 168.91/23.41 | | | | | | % 168.91/23.41 | | | | | Case 2: % 168.91/23.41 | | | | | | % 168.91/23.42 | | | | | | (117) ( ~ (all_516_2 = all_65_5) & index(ldr, all_65_5) = % 168.91/23.42 | | | | | | all_516_2 & $i(all_516_2)) | ( ~ (all_516_3 = elec_1) & % 168.91/23.42 | | | | | | index(status, all_65_15) = all_516_3 & $i(all_516_3)) | % 168.91/23.42 | | | | | | (queue(all_65_15) = all_516_4 & $i(all_516_4) & ~ % 168.91/23.42 | | | | | | elem(all_65_13, all_516_4)) % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | | BETA: splitting (117) gives: % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | | Case 1: % 168.91/23.42 | | | | | | | % 168.91/23.42 | | | | | | | (118) ~ (all_516_2 = all_65_5) & index(ldr, all_65_5) = % 168.91/23.42 | | | | | | | all_516_2 & $i(all_516_2) % 168.91/23.42 | | | | | | | % 168.91/23.42 | | | | | | | ALPHA: (118) implies: % 168.91/23.42 | | | | | | | (119) ~ (all_516_2 = all_65_5) % 168.91/23.42 | | | | | | | (120) index(ldr, all_65_5) = all_516_2 % 168.91/23.42 | | | | | | | % 168.91/23.42 | | | | | | | GROUND_INST: instantiating (27) with all_65_5, all_516_2, % 168.91/23.42 | | | | | | | all_65_5, ldr, simplifying with (13), (120) gives: % 168.91/23.42 | | | | | | | (121) all_516_2 = all_65_5 % 168.91/23.42 | | | | | | | % 168.91/23.42 | | | | | | | REDUCE: (119), (121) imply: % 168.91/23.42 | | | | | | | (122) $false % 168.91/23.42 | | | | | | | % 168.91/23.42 | | | | | | | CLOSE: (122) is inconsistent. % 168.91/23.42 | | | | | | | % 168.91/23.42 | | | | | | Case 2: % 168.91/23.42 | | | | | | | % 168.91/23.42 | | | | | | | (123) ( ~ (all_516_3 = elec_1) & index(status, all_65_15) = % 168.91/23.42 | | | | | | | all_516_3 & $i(all_516_3)) | (queue(all_65_15) = % 168.91/23.42 | | | | | | | all_516_4 & $i(all_516_4) & ~ elem(all_65_13, % 168.91/23.42 | | | | | | | all_516_4)) % 168.91/23.42 | | | | | | | % 168.91/23.42 | | | | | | | BETA: splitting (123) gives: % 168.91/23.42 | | | | | | | % 168.91/23.42 | | | | | | | Case 1: % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | | (124) ~ (all_516_3 = elec_1) & index(status, all_65_15) = % 168.91/23.42 | | | | | | | | all_516_3 & $i(all_516_3) % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | | ALPHA: (124) implies: % 168.91/23.42 | | | | | | | | (125) ~ (all_516_3 = elec_1) % 168.91/23.42 | | | | | | | | (126) index(status, all_65_15) = all_516_3 % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | | GROUND_INST: instantiating (27) with elec_1, all_516_3, % 168.91/23.42 | | | | | | | | all_65_15, status, simplifying with (1), (126) % 168.91/23.42 | | | | | | | | gives: % 168.91/23.42 | | | | | | | | (127) all_516_3 = elec_1 % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | | REDUCE: (125), (127) imply: % 168.91/23.42 | | | | | | | | (128) $false % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | | CLOSE: (128) is inconsistent. % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | Case 2: % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | | (129) queue(all_65_15) = all_516_4 & $i(all_516_4) & ~ % 168.91/23.42 | | | | | | | | elem(all_65_13, all_516_4) % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | | ALPHA: (129) implies: % 168.91/23.42 | | | | | | | | (130) ~ elem(all_65_13, all_516_4) % 168.91/23.42 | | | | | | | | (131) queue(all_65_15) = all_516_4 % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | | GROUND_INST: instantiating (16) with all_65_14, all_516_4, % 168.91/23.42 | | | | | | | | all_65_15, simplifying with (31), (131) gives: % 168.91/23.42 | | | | | | | | (132) all_516_4 = all_65_14 % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | | REDUCE: (130), (132) imply: % 168.91/23.42 | | | | | | | | (133) ~ elem(all_65_13, all_65_14) % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | | PRED_UNIFY: (32), (133) imply: % 168.91/23.42 | | | | | | | | (134) $false % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | | CLOSE: (134) is inconsistent. % 168.91/23.42 | | | | | | | | % 168.91/23.42 | | | | | | | End of split % 168.91/23.42 | | | | | | | % 168.91/23.42 | | | | | | End of split % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | End of split % 168.91/23.42 | | | | | % 168.91/23.42 | | | | Case 2: % 168.91/23.42 | | | | | % 168.91/23.42 | | | | | (135) queue(all_65_15) = all_512_3 & $i(all_512_3) & ~ % 168.91/23.42 | | | | | elem(all_65_13, all_512_3) % 168.91/23.42 | | | | | % 168.91/23.42 | | | | | ALPHA: (135) implies: % 168.91/23.42 | | | | | (136) ~ elem(all_65_13, all_512_3) % 168.91/23.42 | | | | | (137) queue(all_65_15) = all_512_3 % 168.91/23.42 | | | | | % 168.91/23.42 | | | | | BETA: splitting (52) gives: % 168.91/23.42 | | | | | % 168.91/23.42 | | | | | Case 1: % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | | (138) host(all_151_2) = all_510_0 & $i(all_510_0) & ~ % 168.91/23.42 | | | | | | leq(all_65_15, all_510_0) % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | | ALPHA: (138) implies: % 168.91/23.42 | | | | | | (139) ~ leq(all_65_15, all_510_0) % 168.91/23.42 | | | | | | (140) host(all_151_2) = all_510_0 % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | | REDUCE: (47), (140) imply: % 168.91/23.42 | | | | | | (141) host(all_65_17) = all_510_0 % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | | GROUND_INST: instantiating (5) with all_65_15, all_510_0, all_65_17, % 168.91/23.42 | | | | | | simplifying with (28), (141) gives: % 168.91/23.42 | | | | | | (142) all_510_0 = all_65_15 % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | | REDUCE: (139), (142) imply: % 168.91/23.42 | | | | | | (143) ~ leq(all_65_15, all_65_15) % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | | PRED_UNIFY: (14), (143) imply: % 168.91/23.42 | | | | | | (144) $false % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | | CLOSE: (144) is inconsistent. % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | Case 2: % 168.91/23.42 | | | | | | % 168.91/23.42 | | | | | | (145) queue(all_65_15) = all_510_1 & $i(all_510_1) & ~ % 168.91/23.42 | | | | | | elem(all_65_0, all_510_1) % 168.91/23.42 | | | | | | % 168.91/23.43 | | | | | | ALPHA: (145) implies: % 168.91/23.43 | | | | | | (146) queue(all_65_15) = all_510_1 % 168.91/23.43 | | | | | | % 168.91/23.43 | | | | | | GROUND_INST: instantiating (16) with all_65_14, all_512_3, % 168.91/23.43 | | | | | | all_65_15, simplifying with (31), (137) gives: % 168.91/23.43 | | | | | | (147) all_512_3 = all_65_14 % 168.91/23.43 | | | | | | % 168.91/23.43 | | | | | | GROUND_INST: instantiating (16) with all_510_1, all_512_3, % 168.91/23.43 | | | | | | all_65_15, simplifying with (137), (146) gives: % 168.91/23.43 | | | | | | (148) all_512_3 = all_510_1 % 168.91/23.43 | | | | | | % 168.91/23.43 | | | | | | COMBINE_EQS: (147), (148) imply: % 168.91/23.43 | | | | | | (149) all_510_1 = all_65_14 % 168.91/23.43 | | | | | | % 168.91/23.43 | | | | | | REDUCE: (136), (147) imply: % 168.91/23.43 | | | | | | (150) ~ elem(all_65_13, all_65_14) % 168.91/23.43 | | | | | | % 168.91/23.43 | | | | | | PRED_UNIFY: (32), (150) imply: % 168.91/23.43 | | | | | | (151) $false % 168.91/23.43 | | | | | | % 168.91/23.43 | | | | | | CLOSE: (151) is inconsistent. % 168.91/23.43 | | | | | | % 168.91/23.43 | | | | | End of split % 168.91/23.43 | | | | | % 168.91/23.43 | | | | End of split % 168.91/23.43 | | | | % 168.91/23.43 | | | End of split % 168.91/23.43 | | | % 168.91/23.43 | | End of split % 168.91/23.43 | | % 168.91/23.43 | Case 2: % 168.91/23.43 | | % 168.91/23.43 | | (152) all_149_1 = all_65_13 & m_Halt(all_149_2) = all_65_13 % 168.91/23.43 | | % 168.91/23.43 | | ALPHA: (152) implies: % 168.91/23.43 | | (153) m_Halt(all_149_2) = all_65_13 % 168.91/23.43 | | % 168.91/23.43 | | GROUND_INST: instantiating (20) with all_65_16, all_149_2, all_65_13, % 168.91/23.43 | | simplifying with (2), (22), (26), (153) gives: % 168.91/23.43 | | (154) $false % 168.91/23.43 | | % 168.91/23.43 | | CLOSE: (154) is inconsistent. % 168.91/23.43 | | % 168.91/23.43 | End of split % 168.91/23.43 | % 168.91/23.43 End of proof % 168.91/23.43 % SZS output end Proof for theBenchmark % 168.91/23.43 % 168.91/23.43 22833ms %------------------------------------------------------------------------------