%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV453+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 : n031.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 22:56:33 EDT 2023 % Result : Theorem 32.02s 5.18s % Output : Proof 39.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SWV453+1 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.38 % Computer : n031.cluster.edu % 0.14/0.38 % Model : x86_64 x86_64 % 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.38 % Memory : 8042.1875MB % 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.38 % CPULimit : 300 % 0.14/0.38 % WCLimit : 300 % 0.14/0.38 % DateTime : Tue Aug 29 11:06:26 EDT 2023 % 0.14/0.38 % CPUTime : % 0.24/0.68 ________ _____ % 0.24/0.68 ___ __ \_________(_)________________________________ % 0.24/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.24/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.24/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.24/0.68 % 0.24/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.24/0.68 (2023-06-19) % 0.24/0.68 % 0.24/0.68 (c) Philipp Rümmer, 2009-2023 % 0.24/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.24/0.68 Amanda Stjerna. % 0.24/0.68 Free software under BSD-3-Clause. % 0.24/0.68 % 0.24/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.24/0.68 % 0.24/0.68 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.24/0.69 Running up to 7 provers in parallel. % 0.24/0.72 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.24/0.72 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.24/0.72 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.24/0.72 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.24/0.72 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.24/0.72 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.24/0.72 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.22/1.57 Prover 4: Preprocessing ... % 5.22/1.58 Prover 1: Preprocessing ... % 5.22/1.59 Prover 6: Preprocessing ... % 5.22/1.59 Prover 2: Preprocessing ... % 5.22/1.59 Prover 3: Preprocessing ... % 5.22/1.59 Prover 5: Preprocessing ... % 5.22/1.61 Prover 0: Preprocessing ... % 13.52/2.75 Prover 1: Constructing countermodel ... % 13.52/2.85 Prover 6: Proving ... % 13.52/2.86 Prover 3: Constructing countermodel ... % 15.16/2.93 Prover 5: Proving ... % 15.25/2.96 Prover 4: Constructing countermodel ... % 15.83/3.02 Prover 2: Proving ... % 15.83/3.06 Prover 0: Proving ... % 21.90/3.83 Prover 3: gave up % 21.90/3.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.11/3.91 Prover 7: Preprocessing ... % 24.81/4.23 Prover 7: Warning: ignoring some quantifiers % 25.10/4.27 Prover 7: Constructing countermodel ... % 32.02/5.16 Prover 2: proved (4421ms) % 32.02/5.18 % 32.02/5.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 32.02/5.18 % 32.02/5.18 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 32.02/5.18 Prover 5: stopped % 32.02/5.18 Prover 6: stopped % 32.02/5.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 32.02/5.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 32.02/5.20 Prover 0: stopped % 32.02/5.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 32.50/5.22 Prover 8: Preprocessing ... % 32.50/5.25 Prover 10: Preprocessing ... % 32.50/5.25 Prover 13: Preprocessing ... % 32.87/5.27 Prover 11: Preprocessing ... % 32.87/5.38 Prover 10: Warning: ignoring some quantifiers % 33.61/5.42 Prover 10: Constructing countermodel ... % 33.61/5.44 Prover 8: Warning: ignoring some quantifiers % 33.61/5.44 Prover 8: Constructing countermodel ... % 34.35/5.46 Prover 13: Warning: ignoring some quantifiers % 34.35/5.47 Prover 13: Constructing countermodel ... % 34.70/5.51 Prover 11: Constructing countermodel ... % 38.59/6.11 Prover 10: Found proof (size 71) % 38.59/6.11 Prover 10: proved (918ms) % 38.59/6.11 Prover 7: stopped % 38.59/6.11 Prover 11: stopped % 38.59/6.11 Prover 13: stopped % 38.59/6.11 Prover 1: stopped % 38.59/6.11 Prover 4: stopped % 38.59/6.12 Prover 8: stopped % 38.59/6.12 % 38.59/6.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 38.59/6.12 % 38.59/6.12 % SZS output start Proof for theBenchmark % 39.41/6.12 Assumptions after simplification: % 39.41/6.12 --------------------------------- % 39.41/6.12 % 39.41/6.12 (axiom_46) % 39.42/6.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 39.42/6.15 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) | % 39.42/6.15 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 39.42/6.15 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 39.42/6.15 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) % 39.42/6.15 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2)) % 39.42/6.15 % 39.42/6.15 (conj) % 39.42/6.16 $i(elid) & $i(status) & $i(ldr) & $i(alive) & $i(norm) & $i(wait) & $i(zero) & % 39.42/6.16 $i(pids) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 39.42/6.16 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 39.42/6.16 [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? % 39.42/6.16 [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? % 39.42/6.16 [v20: $i] : ( ~ (v14 = v5) & ~ (v5 = v0) & index(status, v5) = v10 & cons(v7, % 39.42/6.16 v1) = v6 & m_Down(v19) = v20 & m_Down(v16) = v18 & m_Down(v4) = v7 & % 39.42/6.16 s(zero) = v0 & host(v19) = v5 & host(v17) = v5 & host(v16) = v14 & host(v13) % 39.42/6.16 = v14 & host(v4) = v8 & host(v3) = v5 & host(v2) = v5 & queue(v14) = v15 & % 39.42/6.16 queue(v5) = v6 & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & % 39.42/6.16 $i(v14) & $i(v13) & $i(v10) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 39.42/6.16 $i(v3) & $i(v2) & $i(v1) & $i(v0) & setIn(v3, alive) & elem(v20, v15) & % 39.42/6.16 elem(v18, v1) & ~ leq(v5, v8) & ~ setIn(v2, pids) & ! [v21: $i] : ! % 39.42/6.16 [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! % 39.42/6.16 [v27: $i] : ! [v28: $i] : (v26 = v25 | ~ (m_Down(v24) = v27) | ~ % 39.42/6.16 (m_Down(v22) = v28) | ~ (host(v23) = v25) | ~ (host(v21) = v26) | ~ % 39.42/6.16 $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v23, alive) | ~ % 39.42/6.16 setIn(v21, alive) | ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: % 39.42/6.16 $i] : (( ~ (v30 = v25) & host(v24) = v30 & $i(v30)) | ( ~ (v29 = v26) & % 39.42/6.16 host(v22) = v29 & $i(v29)) | (queue(v26) = v31 & $i(v31) & ~ % 39.42/6.16 elem(v27, v31)) | (queue(v25) = v32 & $i(v32) & ~ elem(v28, v32)))) & % 39.42/6.16 ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( % 39.42/6.16 ~ (m_Ack(v23, v21) = v24) | ~ (host(v22) = v25) | ~ $i(v23) | ~ $i(v22) % 39.42/6.16 | ~ $i(v21) | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ((host(v23) = % 39.42/6.16 v28 & host(v21) = v27 & $i(v28) & $i(v27) & ~ leq(v27, v28)) | % 39.42/6.16 (queue(v25) = v26 & $i(v26) & ~ elem(v24, v26)))) & ! [v21: $i] : ! % 39.42/6.16 [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (m_Down(v22) = v23) | ~ % 39.42/6.16 (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v22, alive) | ? % 39.42/6.16 [v25: $i] : (queue(v24) = v25 & $i(v25) & ~ elem(v23, v25))) & ! [v21: % 39.42/6.16 $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (m_Down(v22) = v23) % 39.42/6.16 | ~ (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ? [v25: $i] : ? [v26: % 39.42/6.16 $i] : (( ~ (v26 = v24) & host(v22) = v26 & $i(v26)) | (queue(v24) = v25 % 39.42/6.16 & $i(v25) & ~ elem(v23, v25)))) & ! [v21: $i] : ! [v22: $i] : ! % 39.42/6.16 [v23: $i] : ! [v24: $i] : ( ~ (m_Halt(v22) = v23) | ~ (host(v21) = v24) | % 39.42/6.16 ~ $i(v22) | ~ $i(v21) | ? [v25: $i] : ? [v26: $i] : ((host(v22) = v26 & % 39.42/6.16 $i(v26) & ~ leq(v24, v26)) | (queue(v24) = v25 & $i(v25) & ~ % 39.42/6.16 elem(v23, v25)))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : (v22 % 39.42/6.16 = v21 | ~ (host(v22) = v23) | ~ (host(v21) = v23) | ~ $i(v22) | ~ % 39.42/6.16 $i(v21) | ~ setIn(v22, alive) | ~ setIn(v21, alive)) & ! [v21: $i] : ! % 39.42/6.16 [v22: $i] : ! [v23: $i] : ( ~ (host(v22) = v23) | ~ (host(v21) = v23) | ~ % 39.42/6.16 $i(v22) | ~ $i(v21) | ~ leq(v22, v21) | ~ setIn(v22, alive) | % 39.42/6.16 setIn(v21, alive)) & ! [v21: $i] : ( ~ (host(v21) = v5) | ~ $i(v21) | % 39.42/6.16 leq(v21, v2)) & (v17 = v2 | ( ~ (v17 = v3) & setIn(v17, alive))) & (v13 = % 39.42/6.16 v2 | ( ~ (v13 = v3) & setIn(v13, alive))) & ((v12 = v8 & v10 = wait & % 39.42/6.16 index(elid, v5) = v11 & host(v11) = v8 & $i(v11)) | (v10 = norm & v9 = % 39.42/6.16 v8 & index(ldr, v5) = v8))) % 39.42/6.16 % 39.42/6.16 (function-axioms) % 39.42/6.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 39.42/6.16 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 39.42/6.16 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3, % 39.42/6.16 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 39.42/6.16 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! % 39.42/6.16 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~ % 39.42/6.16 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 39.42/6.16 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 39.42/6.16 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i] % 39.42/6.16 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) = % 39.42/6.16 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) = % 39.42/6.16 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 39.42/6.16 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 39.42/6.16 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & ! % 39.42/6.16 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~ % 39.42/6.16 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 39.42/6.16 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 39.42/6.16 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & ! % 39.42/6.16 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~ % 39.42/6.16 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 39.42/6.16 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 39.42/6.16 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1: % 39.42/6.16 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0)) % 39.42/6.16 % 39.42/6.16 Further assumptions not needed in the proof: % 39.42/6.16 -------------------------------------------- % 39.42/6.16 axiom, axiom_01, axiom_02, axiom_03, axiom_04, axiom_05, axiom_06, axiom_07, % 39.42/6.16 axiom_08, axiom_09, axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15, % 39.42/6.16 axiom_16, axiom_17, axiom_18, axiom_19, axiom_20, axiom_21, axiom_22, axiom_23, % 39.42/6.16 axiom_24, axiom_25, axiom_26, axiom_27, axiom_28, axiom_29, axiom_30, axiom_31, % 39.42/6.16 axiom_32, axiom_33, axiom_34, axiom_35, axiom_36, axiom_37, axiom_38, axiom_39, % 39.42/6.16 axiom_40, axiom_41, axiom_42, axiom_43, axiom_44, axiom_45, axiom_47, axiom_48, % 39.42/6.16 axiom_49, axiom_50, axiom_51, axiom_52, axiom_53, axiom_54, axiom_55, axiom_56, % 39.42/6.16 axiom_57, axiom_58, axiom_59, axiom_60, axiom_61, axiom_62, axiom_63, axiom_64, % 39.42/6.16 axiom_65 % 39.42/6.16 % 39.42/6.16 Those formulas are unsatisfiable: % 39.42/6.16 --------------------------------- % 39.42/6.16 % 39.42/6.16 Begin of proof % 39.42/6.17 | % 39.42/6.17 | ALPHA: (axiom_46) implies: % 39.42/6.17 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, % 39.42/6.17 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 39.42/6.17 | elem(v0, v3)) % 39.42/6.17 | % 39.42/6.17 | ALPHA: (conj) implies: % 39.42/6.17 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 39.42/6.17 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 39.42/6.17 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 39.42/6.17 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 39.42/6.17 | $i] : ? [v20: $i] : ( ~ (v14 = v5) & ~ (v5 = v0) & index(status, % 39.42/6.17 | v5) = v10 & cons(v7, v1) = v6 & m_Down(v19) = v20 & m_Down(v16) = % 39.42/6.17 | v18 & m_Down(v4) = v7 & s(zero) = v0 & host(v19) = v5 & host(v17) = % 39.42/6.17 | v5 & host(v16) = v14 & host(v13) = v14 & host(v4) = v8 & host(v3) = % 39.42/6.17 | v5 & host(v2) = v5 & queue(v14) = v15 & queue(v5) = v6 & $i(v20) & % 39.42/6.17 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & % 39.42/6.17 | $i(v10) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 39.42/6.17 | $i(v2) & $i(v1) & $i(v0) & setIn(v3, alive) & elem(v20, v15) & % 39.42/6.17 | elem(v18, v1) & ~ leq(v5, v8) & ~ setIn(v2, pids) & ! [v21: $i] : % 39.42/6.17 | ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: % 39.42/6.17 | $i] : ! [v27: $i] : ! [v28: $i] : (v26 = v25 | ~ (m_Down(v24) = % 39.42/6.17 | v27) | ~ (m_Down(v22) = v28) | ~ (host(v23) = v25) | ~ % 39.42/6.17 | (host(v21) = v26) | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ % 39.42/6.17 | $i(v21) | ~ setIn(v23, alive) | ~ setIn(v21, alive) | ? [v29: % 39.42/6.17 | $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : (( ~ (v30 = % 39.42/6.17 | v25) & host(v24) = v30 & $i(v30)) | ( ~ (v29 = v26) & % 39.42/6.17 | host(v22) = v29 & $i(v29)) | (queue(v26) = v31 & $i(v31) & ~ % 39.42/6.17 | elem(v27, v31)) | (queue(v25) = v32 & $i(v32) & ~ elem(v28, % 39.42/6.17 | v32)))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! % 39.42/6.17 | [v24: $i] : ! [v25: $i] : ( ~ (m_Ack(v23, v21) = v24) | ~ % 39.42/6.17 | (host(v22) = v25) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ? [v26: % 39.42/6.17 | $i] : ? [v27: $i] : ? [v28: $i] : ((host(v23) = v28 & host(v21) % 39.42/6.17 | = v27 & $i(v28) & $i(v27) & ~ leq(v27, v28)) | (queue(v25) = % 39.42/6.17 | v26 & $i(v26) & ~ elem(v24, v26)))) & ! [v21: $i] : ! [v22: % 39.42/6.17 | $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (m_Down(v22) = v23) | ~ % 39.42/6.17 | (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ~ setIn(v22, alive) % 39.42/6.17 | | ? [v25: $i] : (queue(v24) = v25 & $i(v25) & ~ elem(v23, v25))) % 39.42/6.17 | & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ % 39.42/6.17 | (m_Down(v22) = v23) | ~ (host(v21) = v24) | ~ $i(v22) | ~ % 39.42/6.17 | $i(v21) | ? [v25: $i] : ? [v26: $i] : (( ~ (v26 = v24) & % 39.42/6.17 | host(v22) = v26 & $i(v26)) | (queue(v24) = v25 & $i(v25) & ~ % 39.42/6.17 | elem(v23, v25)))) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] % 39.42/6.17 | : ! [v24: $i] : ( ~ (m_Halt(v22) = v23) | ~ (host(v21) = v24) | ~ % 39.42/6.17 | $i(v22) | ~ $i(v21) | ? [v25: $i] : ? [v26: $i] : ((host(v22) = % 39.42/6.17 | v26 & $i(v26) & ~ leq(v24, v26)) | (queue(v24) = v25 & $i(v25) % 39.42/6.17 | & ~ elem(v23, v25)))) & ! [v21: $i] : ! [v22: $i] : ! [v23: % 39.42/6.17 | $i] : (v22 = v21 | ~ (host(v22) = v23) | ~ (host(v21) = v23) | ~ % 39.42/6.17 | $i(v22) | ~ $i(v21) | ~ setIn(v22, alive) | ~ setIn(v21, alive)) % 39.42/6.17 | & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (host(v22) = v23) % 39.42/6.17 | | ~ (host(v21) = v23) | ~ $i(v22) | ~ $i(v21) | ~ leq(v22, v21) % 39.42/6.17 | | ~ setIn(v22, alive) | setIn(v21, alive)) & ! [v21: $i] : ( ~ % 39.42/6.17 | (host(v21) = v5) | ~ $i(v21) | leq(v21, v2)) & (v17 = v2 | ( ~ % 39.42/6.17 | (v17 = v3) & setIn(v17, alive))) & (v13 = v2 | ( ~ (v13 = v3) & % 39.42/6.17 | setIn(v13, alive))) & ((v12 = v8 & v10 = wait & index(elid, v5) = % 39.42/6.17 | v11 & host(v11) = v8 & $i(v11)) | (v10 = norm & v9 = v8 & % 39.42/6.17 | index(ldr, v5) = v8))) % 39.42/6.17 | % 39.42/6.17 | ALPHA: (function-axioms) implies: % 39.42/6.17 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = % 39.42/6.17 | v1) | ~ (queue(v2) = v0)) % 39.42/6.18 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1) % 39.42/6.18 | | ~ (host(v2) = v0)) % 39.42/6.18 | % 39.42/6.18 | DELTA: instantiating (2) with fresh symbols all_65_0, all_65_1, all_65_2, % 39.42/6.18 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9, % 39.42/6.18 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15, % 39.42/6.18 | all_65_16, all_65_17, all_65_18, all_65_19, all_65_20 gives: % 39.42/6.18 | (5) ~ (all_65_6 = all_65_15) & ~ (all_65_15 = all_65_20) & index(status, % 39.42/6.18 | all_65_15) = all_65_10 & cons(all_65_13, all_65_19) = all_65_14 & % 39.42/6.18 | m_Down(all_65_1) = all_65_0 & m_Down(all_65_4) = all_65_2 & % 39.42/6.18 | m_Down(all_65_16) = all_65_13 & s(zero) = all_65_20 & host(all_65_1) = % 39.42/6.18 | all_65_15 & host(all_65_3) = all_65_15 & host(all_65_4) = all_65_6 & % 39.42/6.18 | host(all_65_7) = all_65_6 & host(all_65_16) = all_65_12 & % 39.42/6.18 | host(all_65_17) = all_65_15 & host(all_65_18) = all_65_15 & % 39.42/6.18 | queue(all_65_6) = all_65_5 & queue(all_65_15) = all_65_14 & % 39.42/6.18 | $i(all_65_0) & $i(all_65_1) & $i(all_65_2) & $i(all_65_3) & % 39.42/6.18 | $i(all_65_4) & $i(all_65_5) & $i(all_65_6) & $i(all_65_7) & % 39.42/6.18 | $i(all_65_10) & $i(all_65_12) & $i(all_65_13) & $i(all_65_14) & % 39.42/6.18 | $i(all_65_15) & $i(all_65_16) & $i(all_65_17) & $i(all_65_18) & % 39.42/6.18 | $i(all_65_19) & $i(all_65_20) & setIn(all_65_17, alive) & % 39.42/6.18 | elem(all_65_0, all_65_5) & elem(all_65_2, all_65_19) & ~ % 39.42/6.18 | leq(all_65_15, all_65_12) & ~ setIn(all_65_18, pids) & ! [v0: $i] : % 39.42/6.18 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 39.42/6.18 | [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ (m_Down(v3) = v6) | ~ % 39.42/6.18 | (m_Down(v1) = v7) | ~ (host(v2) = v4) | ~ (host(v0) = v5) | ~ % 39.42/6.18 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ % 39.42/6.18 | setIn(v0, alive) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? % 39.42/6.18 | [v11: $i] : (( ~ (v9 = v4) & host(v3) = v9 & $i(v9)) | ( ~ (v8 = v5) % 39.42/6.18 | & host(v1) = v8 & $i(v8)) | (queue(v5) = v10 & $i(v10) & ~ % 39.42/6.18 | elem(v6, v10)) | (queue(v4) = v11 & $i(v11) & ~ elem(v7, v11)))) % 39.42/6.18 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 39.42/6.18 | ( ~ (m_Ack(v2, v0) = v3) | ~ (host(v1) = v4) | ~ $i(v2) | ~ $i(v1) | % 39.42/6.18 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((host(v2) = v7 % 39.42/6.18 | & host(v0) = v6 & $i(v7) & $i(v6) & ~ leq(v6, v7)) | (queue(v4) % 39.42/6.18 | = v5 & $i(v5) & ~ elem(v3, v5)))) & ! [v0: $i] : ! [v1: $i] : % 39.42/6.18 | ! [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v1) = v2) | ~ (host(v0) = v3) | % 39.42/6.18 | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ? [v4: $i] : % 39.42/6.18 | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4))) & ! [v0: $i] : ! [v1: % 39.42/6.18 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v1) = v2) | ~ % 39.42/6.18 | (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : % 39.42/6.18 | (( ~ (v5 = v3) & host(v1) = v5 & $i(v5)) | (queue(v3) = v4 & $i(v4) & % 39.42/6.18 | ~ elem(v2, v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 39.42/6.18 | [v3: $i] : ( ~ (m_Halt(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ % 39.42/6.18 | $i(v0) | ? [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ % 39.42/6.18 | leq(v3, v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) & ! % 39.42/6.18 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v1) = v2) | % 39.42/6.18 | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ % 39.42/6.18 | setIn(v0, alive)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 39.42/6.18 | (host(v1) = v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 39.42/6.18 | leq(v1, v0) | ~ setIn(v1, alive) | setIn(v0, alive)) & ! [v0: $i] : % 39.42/6.18 | ( ~ (host(v0) = all_65_15) | ~ $i(v0) | leq(v0, all_65_18)) & % 39.42/6.18 | (all_65_3 = all_65_18 | ( ~ (all_65_3 = all_65_17) & setIn(all_65_3, % 39.42/6.18 | alive))) & (all_65_7 = all_65_18 | ( ~ (all_65_7 = all_65_17) & % 39.42/6.18 | setIn(all_65_7, alive))) & ((all_65_8 = all_65_12 & all_65_10 = % 39.42/6.18 | wait & index(elid, all_65_15) = all_65_9 & host(all_65_9) = % 39.42/6.18 | all_65_12 & $i(all_65_9)) | (all_65_10 = norm & all_65_11 = % 39.42/6.18 | all_65_12 & index(ldr, all_65_15) = all_65_12)) % 39.42/6.18 | % 39.42/6.18 | ALPHA: (5) implies: % 39.42/6.18 | (6) elem(all_65_2, all_65_19) % 39.42/6.18 | (7) elem(all_65_0, all_65_5) % 39.42/6.18 | (8) setIn(all_65_17, alive) % 39.42/6.18 | (9) $i(all_65_19) % 39.42/6.18 | (10) $i(all_65_18) % 39.42/6.18 | (11) $i(all_65_17) % 39.42/6.18 | (12) $i(all_65_13) % 39.42/6.18 | (13) $i(all_65_7) % 39.42/6.18 | (14) $i(all_65_4) % 39.42/6.18 | (15) $i(all_65_3) % 39.42/6.18 | (16) $i(all_65_2) % 39.42/6.18 | (17) $i(all_65_1) % 39.42/6.18 | (18) queue(all_65_15) = all_65_14 % 39.42/6.18 | (19) queue(all_65_6) = all_65_5 % 39.42/6.18 | (20) host(all_65_18) = all_65_15 % 39.42/6.18 | (21) host(all_65_17) = all_65_15 % 39.42/6.18 | (22) host(all_65_7) = all_65_6 % 39.42/6.19 | (23) host(all_65_4) = all_65_6 % 39.42/6.19 | (24) host(all_65_3) = all_65_15 % 39.42/6.19 | (25) host(all_65_1) = all_65_15 % 39.42/6.19 | (26) m_Down(all_65_4) = all_65_2 % 39.42/6.19 | (27) m_Down(all_65_1) = all_65_0 % 39.42/6.19 | (28) cons(all_65_13, all_65_19) = all_65_14 % 39.42/6.19 | (29) all_65_7 = all_65_18 | ( ~ (all_65_7 = all_65_17) & setIn(all_65_7, % 39.42/6.19 | alive)) % 39.42/6.19 | (30) all_65_3 = all_65_18 | ( ~ (all_65_3 = all_65_17) & setIn(all_65_3, % 39.42/6.19 | alive)) % 39.42/6.19 | (31) ! [v0: $i] : ( ~ (host(v0) = all_65_15) | ~ $i(v0) | leq(v0, % 39.42/6.19 | all_65_18)) % 39.42/6.19 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~ % 39.42/6.19 | (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) | ~ % 39.42/6.19 | setIn(v1, alive) | setIn(v0, alive)) % 39.42/6.19 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v1) = % 39.42/6.19 | v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 39.42/6.19 | alive) | ~ setIn(v0, alive)) % 39.42/6.19 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 39.42/6.19 | (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 39.42/6.19 | [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 & $i(v5)) | % 39.42/6.19 | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) % 39.42/6.19 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 39.42/6.19 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ (m_Down(v3) = % 39.42/6.19 | v6) | ~ (m_Down(v1) = v7) | ~ (host(v2) = v4) | ~ (host(v0) = % 39.42/6.19 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, % 39.42/6.19 | alive) | ~ setIn(v0, alive) | ? [v8: $i] : ? [v9: $i] : ? % 39.42/6.19 | [v10: $i] : ? [v11: $i] : (( ~ (v9 = v4) & host(v3) = v9 & $i(v9)) % 39.42/6.19 | | ( ~ (v8 = v5) & host(v1) = v8 & $i(v8)) | (queue(v5) = v10 & % 39.42/6.19 | $i(v10) & ~ elem(v6, v10)) | (queue(v4) = v11 & $i(v11) & ~ % 39.42/6.19 | elem(v7, v11)))) % 39.42/6.19 | % 39.42/6.19 | GROUND_INST: instantiating (31) with all_65_17, simplifying with (11), (21) % 39.42/6.19 | gives: % 39.42/6.19 | (36) leq(all_65_17, all_65_18) % 39.42/6.19 | % 39.42/6.19 | GROUND_INST: instantiating (34) with all_65_18, all_65_4, all_65_2, all_65_15, % 39.42/6.19 | simplifying with (10), (14), (20), (26) gives: % 39.42/6.19 | (37) ? [v0: $i] : ? [v1: any] : (( ~ (v1 = all_65_15) & host(all_65_4) = % 39.42/6.19 | v1 & $i(v1)) | (queue(all_65_15) = v0 & $i(v0) & ~ elem(all_65_2, % 39.42/6.19 | v0))) % 39.42/6.19 | % 39.42/6.19 | GROUND_INST: instantiating (1) with all_65_2, all_65_13, all_65_19, all_65_14, % 39.42/6.19 | simplifying with (6), (9), (12), (16), (28) gives: % 39.42/6.19 | (38) elem(all_65_2, all_65_14) % 39.42/6.19 | % 39.42/6.19 | DELTA: instantiating (37) with fresh symbols all_89_0, all_89_1 gives: % 39.42/6.19 | (39) ( ~ (all_89_0 = all_65_15) & host(all_65_4) = all_89_0 & $i(all_89_0)) % 39.42/6.19 | | (queue(all_65_15) = all_89_1 & $i(all_89_1) & ~ elem(all_65_2, % 39.42/6.19 | all_89_1)) % 39.42/6.19 | % 39.42/6.19 | BETA: splitting (39) gives: % 39.42/6.19 | % 39.42/6.19 | Case 1: % 39.42/6.19 | | % 39.42/6.19 | | (40) ~ (all_89_0 = all_65_15) & host(all_65_4) = all_89_0 & $i(all_89_0) % 39.42/6.19 | | % 39.42/6.19 | | ALPHA: (40) implies: % 39.42/6.19 | | (41) ~ (all_89_0 = all_65_15) % 39.42/6.19 | | (42) host(all_65_4) = all_89_0 % 39.42/6.19 | | % 39.42/6.19 | | GROUND_INST: instantiating (4) with all_65_6, all_89_0, all_65_4, % 39.42/6.19 | | simplifying with (23), (42) gives: % 39.42/6.19 | | (43) all_89_0 = all_65_6 % 39.42/6.19 | | % 39.42/6.19 | | REDUCE: (41), (43) imply: % 39.42/6.19 | | (44) ~ (all_65_6 = all_65_15) % 39.42/6.19 | | % 39.42/6.20 | | GROUND_INST: instantiating (32) with all_65_18, all_65_17, all_65_15, % 39.42/6.20 | | simplifying with (8), (10), (11), (20), (21), (36) gives: % 39.42/6.20 | | (45) setIn(all_65_18, alive) % 39.42/6.20 | | % 39.42/6.20 | | GROUND_INST: instantiating (33) with all_65_18, all_65_17, all_65_15, % 39.42/6.20 | | simplifying with (8), (10), (11), (20), (21), (45) gives: % 39.42/6.20 | | (46) all_65_17 = all_65_18 % 39.42/6.20 | | % 39.42/6.20 | | BETA: splitting (29) gives: % 39.42/6.20 | | % 39.42/6.20 | | Case 1: % 39.42/6.20 | | | % 39.42/6.20 | | | (47) all_65_7 = all_65_18 % 39.42/6.20 | | | % 39.42/6.20 | | | REDUCE: (22), (47) imply: % 39.42/6.20 | | | (48) host(all_65_18) = all_65_6 % 39.42/6.20 | | | % 39.42/6.20 | | | GROUND_INST: instantiating (4) with all_65_15, all_65_6, all_65_18, % 39.42/6.20 | | | simplifying with (20), (48) gives: % 39.42/6.20 | | | (49) all_65_6 = all_65_15 % 39.42/6.20 | | | % 39.42/6.20 | | | REDUCE: (44), (49) imply: % 39.42/6.20 | | | (50) $false % 39.42/6.20 | | | % 39.42/6.20 | | | CLOSE: (50) is inconsistent. % 39.42/6.20 | | | % 39.42/6.20 | | Case 2: % 39.42/6.20 | | | % 39.42/6.20 | | | (51) ~ (all_65_7 = all_65_17) & setIn(all_65_7, alive) % 39.42/6.20 | | | % 39.42/6.20 | | | ALPHA: (51) implies: % 39.79/6.20 | | | (52) setIn(all_65_7, alive) % 39.79/6.20 | | | % 39.79/6.20 | | | BETA: splitting (30) gives: % 39.79/6.20 | | | % 39.79/6.20 | | | Case 1: % 39.79/6.20 | | | | % 39.79/6.20 | | | | (53) all_65_3 = all_65_18 % 39.79/6.20 | | | | % 39.79/6.20 | | | | GROUND_INST: instantiating (35) with all_65_18, all_65_1, all_65_7, % 39.79/6.20 | | | | all_65_4, all_65_6, all_65_15, all_65_2, all_65_0, % 39.79/6.20 | | | | simplifying with (10), (13), (14), (17), (20), (22), (26), % 39.79/6.20 | | | | (27), (45), (52) gives: % 39.79/6.20 | | | | (54) all_65_6 = all_65_15 | ? [v0: any] : ? [v1: any] : ? [v2: $i] % 39.79/6.20 | | | | : ? [v3: $i] : (( ~ (v1 = all_65_6) & host(all_65_4) = v1 & % 39.79/6.20 | | | | $i(v1)) | ( ~ (v0 = all_65_15) & host(all_65_1) = v0 & % 39.79/6.20 | | | | $i(v0)) | (queue(all_65_6) = v3 & $i(v3) & ~ elem(all_65_0, % 39.79/6.20 | | | | v3)) | (queue(all_65_15) = v2 & $i(v2) & ~ elem(all_65_2, % 39.79/6.20 | | | | v2))) % 39.79/6.20 | | | | % 39.79/6.20 | | | | BETA: splitting (54) gives: % 39.79/6.20 | | | | % 39.79/6.20 | | | | Case 1: % 39.79/6.20 | | | | | % 39.79/6.20 | | | | | (55) all_65_6 = all_65_15 % 39.79/6.20 | | | | | % 39.79/6.20 | | | | | REDUCE: (44), (55) imply: % 39.79/6.20 | | | | | (56) $false % 39.79/6.20 | | | | | % 39.79/6.20 | | | | | CLOSE: (56) is inconsistent. % 39.79/6.20 | | | | | % 39.79/6.20 | | | | Case 2: % 39.79/6.20 | | | | | % 39.79/6.20 | | | | | (57) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : (( ~ % 39.79/6.20 | | | | | (v1 = all_65_6) & host(all_65_4) = v1 & $i(v1)) | ( ~ (v0 % 39.79/6.20 | | | | | = all_65_15) & host(all_65_1) = v0 & $i(v0)) | % 39.79/6.20 | | | | | (queue(all_65_6) = v3 & $i(v3) & ~ elem(all_65_0, v3)) | % 39.79/6.20 | | | | | (queue(all_65_15) = v2 & $i(v2) & ~ elem(all_65_2, v2))) % 39.79/6.20 | | | | | % 39.79/6.20 | | | | | DELTA: instantiating (57) with fresh symbols all_254_0, all_254_1, % 39.79/6.20 | | | | | all_254_2, all_254_3 gives: % 39.79/6.20 | | | | | (58) ( ~ (all_254_2 = all_65_6) & host(all_65_4) = all_254_2 & % 39.79/6.20 | | | | | $i(all_254_2)) | ( ~ (all_254_3 = all_65_15) & % 39.79/6.20 | | | | | host(all_65_1) = all_254_3 & $i(all_254_3)) | % 39.79/6.20 | | | | | (queue(all_65_6) = all_254_0 & $i(all_254_0) & ~ % 39.79/6.20 | | | | | elem(all_65_0, all_254_0)) | (queue(all_65_15) = all_254_1 & % 39.79/6.20 | | | | | $i(all_254_1) & ~ elem(all_65_2, all_254_1)) % 39.79/6.20 | | | | | % 39.79/6.20 | | | | | BETA: splitting (58) gives: % 39.79/6.20 | | | | | % 39.79/6.20 | | | | | Case 1: % 39.79/6.20 | | | | | | % 39.79/6.20 | | | | | | (59) ( ~ (all_254_2 = all_65_6) & host(all_65_4) = all_254_2 & % 39.79/6.20 | | | | | | $i(all_254_2)) | ( ~ (all_254_3 = all_65_15) & % 39.79/6.20 | | | | | | host(all_65_1) = all_254_3 & $i(all_254_3)) % 39.79/6.20 | | | | | | % 39.79/6.20 | | | | | | BETA: splitting (59) gives: % 39.79/6.20 | | | | | | % 39.79/6.20 | | | | | | Case 1: % 39.79/6.20 | | | | | | | % 39.79/6.20 | | | | | | | (60) ~ (all_254_2 = all_65_6) & host(all_65_4) = all_254_2 & % 39.79/6.20 | | | | | | | $i(all_254_2) % 39.79/6.20 | | | | | | | % 39.79/6.20 | | | | | | | ALPHA: (60) implies: % 39.79/6.20 | | | | | | | (61) ~ (all_254_2 = all_65_6) % 39.79/6.20 | | | | | | | (62) host(all_65_4) = all_254_2 % 39.79/6.20 | | | | | | | % 39.79/6.21 | | | | | | | GROUND_INST: instantiating (4) with all_65_6, all_254_2, all_65_4, % 39.79/6.21 | | | | | | | simplifying with (23), (62) gives: % 39.79/6.21 | | | | | | | (63) all_254_2 = all_65_6 % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | REDUCE: (61), (63) imply: % 39.79/6.21 | | | | | | | (64) $false % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | CLOSE: (64) is inconsistent. % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | Case 2: % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | (65) ~ (all_254_3 = all_65_15) & host(all_65_1) = all_254_3 & % 39.79/6.21 | | | | | | | $i(all_254_3) % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | ALPHA: (65) implies: % 39.79/6.21 | | | | | | | (66) ~ (all_254_3 = all_65_15) % 39.79/6.21 | | | | | | | (67) host(all_65_1) = all_254_3 % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | GROUND_INST: instantiating (4) with all_65_15, all_254_3, % 39.79/6.21 | | | | | | | all_65_1, simplifying with (25), (67) gives: % 39.79/6.21 | | | | | | | (68) all_254_3 = all_65_15 % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | REDUCE: (66), (68) imply: % 39.79/6.21 | | | | | | | (69) $false % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | CLOSE: (69) is inconsistent. % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | End of split % 39.79/6.21 | | | | | | % 39.79/6.21 | | | | | Case 2: % 39.79/6.21 | | | | | | % 39.79/6.21 | | | | | | (70) (queue(all_65_6) = all_254_0 & $i(all_254_0) & ~ % 39.79/6.21 | | | | | | elem(all_65_0, all_254_0)) | (queue(all_65_15) = all_254_1 % 39.79/6.21 | | | | | | & $i(all_254_1) & ~ elem(all_65_2, all_254_1)) % 39.79/6.21 | | | | | | % 39.79/6.21 | | | | | | BETA: splitting (70) gives: % 39.79/6.21 | | | | | | % 39.79/6.21 | | | | | | Case 1: % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | (71) queue(all_65_6) = all_254_0 & $i(all_254_0) & ~ % 39.79/6.21 | | | | | | | elem(all_65_0, all_254_0) % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | ALPHA: (71) implies: % 39.79/6.21 | | | | | | | (72) ~ elem(all_65_0, all_254_0) % 39.79/6.21 | | | | | | | (73) queue(all_65_6) = all_254_0 % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | GROUND_INST: instantiating (3) with all_65_5, all_254_0, all_65_6, % 39.79/6.21 | | | | | | | simplifying with (19), (73) gives: % 39.79/6.21 | | | | | | | (74) all_254_0 = all_65_5 % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | REDUCE: (72), (74) imply: % 39.79/6.21 | | | | | | | (75) ~ elem(all_65_0, all_65_5) % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | PRED_UNIFY: (7), (75) imply: % 39.79/6.21 | | | | | | | (76) $false % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | CLOSE: (76) is inconsistent. % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | Case 2: % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | (77) queue(all_65_15) = all_254_1 & $i(all_254_1) & ~ % 39.79/6.21 | | | | | | | elem(all_65_2, all_254_1) % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | ALPHA: (77) implies: % 39.79/6.21 | | | | | | | (78) ~ elem(all_65_2, all_254_1) % 39.79/6.21 | | | | | | | (79) queue(all_65_15) = all_254_1 % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | GROUND_INST: instantiating (3) with all_65_14, all_254_1, % 39.79/6.21 | | | | | | | all_65_15, simplifying with (18), (79) gives: % 39.79/6.21 | | | | | | | (80) all_254_1 = all_65_14 % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | REDUCE: (78), (80) imply: % 39.79/6.21 | | | | | | | (81) ~ elem(all_65_2, all_65_14) % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | PRED_UNIFY: (38), (81) imply: % 39.79/6.21 | | | | | | | (82) $false % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | | CLOSE: (82) is inconsistent. % 39.79/6.21 | | | | | | | % 39.79/6.21 | | | | | | End of split % 39.79/6.21 | | | | | | % 39.79/6.21 | | | | | End of split % 39.79/6.21 | | | | | % 39.79/6.21 | | | | End of split % 39.79/6.21 | | | | % 39.79/6.21 | | | Case 2: % 39.79/6.21 | | | | % 39.79/6.21 | | | | (83) ~ (all_65_3 = all_65_17) & setIn(all_65_3, alive) % 39.79/6.21 | | | | % 39.79/6.21 | | | | ALPHA: (83) implies: % 39.79/6.21 | | | | (84) ~ (all_65_3 = all_65_17) % 39.79/6.21 | | | | (85) setIn(all_65_3, alive) % 39.79/6.21 | | | | % 39.79/6.21 | | | | REDUCE: (46), (84) imply: % 39.79/6.21 | | | | (86) ~ (all_65_3 = all_65_18) % 39.79/6.21 | | | | % 39.79/6.21 | | | | GROUND_INST: instantiating (33) with all_65_18, all_65_3, all_65_15, % 39.79/6.21 | | | | simplifying with (10), (15), (20), (24), (45), (85) gives: % 39.79/6.21 | | | | (87) all_65_3 = all_65_18 % 39.79/6.21 | | | | % 39.79/6.21 | | | | REDUCE: (86), (87) imply: % 39.79/6.21 | | | | (88) $false % 39.79/6.21 | | | | % 39.79/6.21 | | | | CLOSE: (88) is inconsistent. % 39.79/6.21 | | | | % 39.79/6.21 | | | End of split % 39.79/6.21 | | | % 39.79/6.21 | | End of split % 39.79/6.21 | | % 39.79/6.21 | Case 2: % 39.79/6.21 | | % 39.79/6.21 | | (89) queue(all_65_15) = all_89_1 & $i(all_89_1) & ~ elem(all_65_2, % 39.79/6.21 | | all_89_1) % 39.79/6.21 | | % 39.79/6.21 | | ALPHA: (89) implies: % 39.79/6.21 | | (90) ~ elem(all_65_2, all_89_1) % 39.79/6.21 | | (91) queue(all_65_15) = all_89_1 % 39.79/6.21 | | % 39.79/6.21 | | GROUND_INST: instantiating (3) with all_65_14, all_89_1, all_65_15, % 39.79/6.21 | | simplifying with (18), (91) gives: % 39.79/6.21 | | (92) all_89_1 = all_65_14 % 39.79/6.21 | | % 39.79/6.21 | | REDUCE: (90), (92) imply: % 39.79/6.21 | | (93) ~ elem(all_65_2, all_65_14) % 39.79/6.21 | | % 39.79/6.21 | | PRED_UNIFY: (38), (93) imply: % 39.79/6.21 | | (94) $false % 39.79/6.21 | | % 39.79/6.21 | | CLOSE: (94) is inconsistent. % 39.79/6.21 | | % 39.79/6.21 | End of split % 39.79/6.21 | % 39.79/6.21 End of proof % 39.79/6.21 % SZS output end Proof for theBenchmark % 39.79/6.21 % 39.79/6.21 5534ms %------------------------------------------------------------------------------