%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV449+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 : n006.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 22:56:32 EDT 2023 % Result : Theorem 47.95s 7.08s % Output : Proof 55.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV449+1 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n006.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 03:20:51 EDT 2023 % 0.12/0.33 % CPUTime : % 0.47/0.60 ________ _____ % 0.47/0.60 ___ __ \_________(_)________________________________ % 0.47/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.47/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.47/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.47/0.60 % 0.47/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.47/0.60 (2023-06-19) % 0.47/0.60 % 0.47/0.60 (c) Philipp Rümmer, 2009-2023 % 0.47/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.47/0.60 Amanda Stjerna. % 0.47/0.60 Free software under BSD-3-Clause. % 0.47/0.60 % 0.47/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.47/0.60 % 0.47/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.47/0.61 Running up to 7 provers in parallel. % 0.47/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.47/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.47/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.47/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.47/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.47/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.47/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.24/1.24 Prover 4: Preprocessing ... % 3.24/1.24 Prover 1: Preprocessing ... % 4.20/1.29 Prover 5: Preprocessing ... % 4.20/1.29 Prover 3: Preprocessing ... % 4.20/1.29 Prover 2: Preprocessing ... % 4.20/1.29 Prover 0: Preprocessing ... % 4.20/1.31 Prover 6: Preprocessing ... % 10.71/2.19 Prover 3: Constructing countermodel ... % 10.71/2.19 Prover 6: Proving ... % 10.71/2.19 Prover 1: Constructing countermodel ... % 10.71/2.19 Prover 5: Proving ... % 10.71/2.24 Prover 4: Constructing countermodel ... % 11.59/2.31 Prover 2: Proving ... % 11.59/2.38 Prover 0: Proving ... % 16.64/3.06 Prover 3: gave up % 16.64/3.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.67/3.14 Prover 7: Preprocessing ... % 19.42/3.41 Prover 7: Warning: ignoring some quantifiers % 19.90/3.44 Prover 7: Constructing countermodel ... % 34.30/5.30 Prover 1: gave up % 34.30/5.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 34.75/5.35 Prover 8: Preprocessing ... % 35.89/5.53 Prover 8: Warning: ignoring some quantifiers % 36.23/5.55 Prover 8: Constructing countermodel ... % 40.95/6.17 Prover 8: gave up % 40.95/6.18 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 41.60/6.27 Prover 9: Preprocessing ... % 43.25/6.52 Prover 9: Constructing countermodel ... % 47.95/7.08 Prover 2: proved (6422ms) % 47.95/7.08 % 47.95/7.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 47.95/7.08 % 47.95/7.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 47.95/7.08 Prover 0: stopped % 47.95/7.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 47.95/7.08 Prover 5: stopped % 47.95/7.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 47.95/7.08 Prover 9: stopped % 47.95/7.08 Prover 6: stopped % 47.95/7.09 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 47.95/7.09 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 47.95/7.15 Prover 13: Preprocessing ... % 47.95/7.15 Prover 16: Preprocessing ... % 48.66/7.16 Prover 11: Preprocessing ... % 48.66/7.16 Prover 19: Preprocessing ... % 48.66/7.18 Prover 10: Preprocessing ... % 49.33/7.29 Prover 16: Warning: ignoring some quantifiers % 49.33/7.29 Prover 10: Warning: ignoring some quantifiers % 49.33/7.30 Prover 10: Constructing countermodel ... % 49.33/7.30 Prover 16: Constructing countermodel ... % 49.79/7.31 Prover 19: Warning: ignoring some quantifiers % 49.79/7.32 Prover 11: Constructing countermodel ... % 49.79/7.33 Prover 19: Constructing countermodel ... % 49.79/7.36 Prover 13: Warning: ignoring some quantifiers % 49.79/7.37 Prover 13: Constructing countermodel ... % 55.32/8.05 Prover 10: Found proof (size 76) % 55.32/8.05 Prover 10: proved (969ms) % 55.32/8.05 Prover 13: stopped % 55.32/8.05 Prover 16: stopped % 55.32/8.05 Prover 7: stopped % 55.32/8.05 Prover 19: stopped % 55.32/8.05 Prover 11: stopped % 55.32/8.05 Prover 4: stopped % 55.32/8.05 % 55.32/8.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 55.32/8.05 % 55.32/8.06 % SZS output start Proof for theBenchmark % 55.32/8.06 Assumptions after simplification: % 55.32/8.06 --------------------------------- % 55.32/8.06 % 55.32/8.07 (axiom_18) % 55.32/8.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Ldr(v1) = v2) | ~ % 55.32/8.09 (m_Down(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 55.32/8.09 % 55.32/8.09 (axiom_46) % 55.32/8.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 55.32/8.09 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) | % 55.32/8.09 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 55.32/8.09 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 55.32/8.09 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) % 55.32/8.09 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2)) % 55.32/8.09 % 55.32/8.09 (axiom_47) % 55.32/8.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 55.32/8.09 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) | % 55.32/8.09 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 55.32/8.09 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 55.32/8.09 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (snoc(v1, v0) % 55.32/8.09 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2)) % 55.32/8.09 % 55.32/8.09 (conj) % 55.32/8.10 $i(acks) & $i(pendack) & $i(status) & $i(elid) & $i(alive) & $i(elec_2) & % 55.32/8.10 $i(nbr_proc) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 55.32/8.10 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 55.32/8.10 ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? % 55.32/8.10 [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ( ~ % 55.32/8.10 (v15 = v4) & index(acks, v4) = v8 & index(pendack, v4) = v7 & index(status, % 55.32/8.10 v4) = elec_2 & index(elid, v4) = v1 & snoc(v0, v9) = v10 & cons(v6, v0) = % 55.32/8.10 v5 & m_Ldr(v2) = v9 & m_Down(v18) = v19 & m_Down(v13) = v16 & m_Ack(v1, v3) % 55.32/8.10 = v6 & host(v18) = v15 & host(v14) = v15 & host(v13) = v4 & host(v12) = v4 & % 55.32/8.10 host(v11) = v4 & host(v3) = v7 & host(v2) = v4 & queue(v15) = v17 & % 55.32/8.10 queue(v4) = v5 & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 55.32/8.10 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 55.32/8.10 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(nbr_proc, v7) & % 55.32/8.10 setIn(v14, alive) & setIn(v12, alive) & setIn(v2, alive) & elem(v19, v10) & % 55.32/8.10 elem(v16, v17) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : % 55.32/8.10 ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : (v25 = v24 | ~ % 55.32/8.10 (m_Down(v23) = v26) | ~ (m_Down(v21) = v27) | ~ (host(v22) = v24) | ~ % 55.32/8.10 (host(v20) = v25) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ % 55.32/8.10 setIn(v22, alive) | ~ setIn(v20, alive) | ? [v28: $i] : ? [v29: $i] : % 55.32/8.10 ? [v30: $i] : ? [v31: $i] : (( ~ (v29 = v24) & host(v23) = v29 & $i(v29)) % 55.32/8.10 | ( ~ (v28 = v25) & host(v21) = v28 & $i(v28)) | (queue(v25) = v30 & % 55.32/8.10 $i(v30) & ~ elem(v26, v30)) | (queue(v24) = v31 & $i(v31) & ~ % 55.32/8.10 elem(v27, v31)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! % 55.32/8.10 [v23: $i] : ! [v24: $i] : ( ~ (m_Ack(v22, v20) = v23) | ~ (host(v21) = % 55.32/8.10 v24) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ? [v25: $i] : ? [v26: % 55.32/8.10 $i] : ? [v27: $i] : ((host(v22) = v27 & host(v20) = v26 & $i(v27) & % 55.32/8.10 $i(v26) & ~ leq(v26, v27)) | (queue(v24) = v25 & $i(v25) & ~ % 55.32/8.10 elem(v23, v25)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! % 55.32/8.10 [v23: $i] : ( ~ (m_Down(v21) = v22) | ~ (host(v20) = v23) | ~ $i(v21) | ~ % 55.32/8.10 $i(v20) | ~ setIn(v21, alive) | ? [v24: $i] : (queue(v23) = v24 & % 55.32/8.10 $i(v24) & ~ elem(v22, v24))) & ! [v20: $i] : ! [v21: $i] : ! [v22: % 55.32/8.10 $i] : ! [v23: $i] : ( ~ (m_Down(v21) = v22) | ~ (host(v20) = v23) | ~ % 55.32/8.10 $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25: $i] : (( ~ (v25 = v23) & % 55.32/8.10 host(v21) = v25 & $i(v25)) | (queue(v23) = v24 & $i(v24) & ~ % 55.32/8.10 elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! % 55.32/8.10 [v23: $i] : ( ~ (m_Halt(v21) = v22) | ~ (host(v20) = v23) | ~ $i(v21) | ~ % 55.32/8.10 $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) = v25 & $i(v25) & ~ % 55.32/8.10 leq(v23, v25)) | (queue(v23) = v24 & $i(v24) & ~ elem(v22, v24)))) & % 55.32/8.10 ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : (v21 = v20 | ~ (host(v21) = % 55.32/8.10 v22) | ~ (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, % 55.32/8.10 alive) | ~ setIn(v20, alive)) & ! [v20: $i] : ! [v21: $i] : ! [v22: % 55.32/8.10 $i] : ( ~ (host(v21) = v22) | ~ (host(v20) = v22) | ~ $i(v21) | ~ % 55.32/8.10 $i(v20) | ~ leq(v21, v20) | ~ setIn(v21, alive) | setIn(v20, alive)) & % 55.32/8.10 (v7 = v4 | setIn(v4, v8))) % 55.32/8.10 % 55.32/8.10 (function-axioms) % 55.73/8.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 55.73/8.11 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 55.73/8.11 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3, % 55.73/8.11 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 55.73/8.11 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! % 55.73/8.11 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~ % 55.73/8.11 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 55.73/8.11 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 55.73/8.11 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i] % 55.73/8.11 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) = % 55.73/8.11 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) = % 55.73/8.11 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 55.73/8.11 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 55.73/8.11 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & ! % 55.73/8.11 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~ % 55.73/8.11 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 55.73/8.11 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 55.73/8.11 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & ! % 55.73/8.11 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~ % 55.73/8.11 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 55.73/8.11 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 55.73/8.11 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1: % 55.73/8.11 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0)) % 55.73/8.11 % 55.73/8.11 Further assumptions not needed in the proof: % 55.73/8.11 -------------------------------------------- % 55.73/8.11 axiom, axiom_01, axiom_02, axiom_03, axiom_04, axiom_05, axiom_06, axiom_07, % 55.73/8.11 axiom_08, axiom_09, axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15, % 55.73/8.11 axiom_16, axiom_17, axiom_19, axiom_20, axiom_21, axiom_22, axiom_23, axiom_24, % 55.73/8.11 axiom_25, axiom_26, axiom_27, axiom_28, axiom_29, axiom_30, axiom_31, axiom_32, % 55.73/8.11 axiom_33, axiom_34, axiom_35, axiom_36, axiom_37, axiom_38, axiom_39, axiom_40, % 55.73/8.11 axiom_41, axiom_42, axiom_43, axiom_44, axiom_45, axiom_48, axiom_49, axiom_50, % 55.73/8.11 axiom_51, axiom_52, axiom_53, axiom_54, axiom_55, axiom_56, axiom_57, axiom_58, % 55.73/8.11 axiom_59, axiom_60, axiom_61, axiom_62, axiom_63, axiom_64, axiom_65 % 55.73/8.11 % 55.73/8.11 Those formulas are unsatisfiable: % 55.73/8.11 --------------------------------- % 55.73/8.11 % 55.73/8.11 Begin of proof % 55.73/8.11 | % 55.73/8.11 | ALPHA: (axiom_46) implies: % 55.73/8.11 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, % 55.73/8.11 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) | % 55.73/8.11 | elem(v0, v3)) % 55.73/8.11 | % 55.73/8.11 | ALPHA: (axiom_47) implies: % 55.73/8.11 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 55.73/8.11 | (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, % 55.73/8.11 | v3) | elem(v0, v2)) % 55.73/8.11 | % 55.73/8.11 | ALPHA: (conj) implies: % 55.73/8.12 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 55.73/8.12 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 55.73/8.12 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 55.73/8.12 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 55.73/8.12 | $i] : ( ~ (v15 = v4) & index(acks, v4) = v8 & index(pendack, v4) = v7 % 55.73/8.12 | & index(status, v4) = elec_2 & index(elid, v4) = v1 & snoc(v0, v9) = % 55.73/8.12 | v10 & cons(v6, v0) = v5 & m_Ldr(v2) = v9 & m_Down(v18) = v19 & % 55.73/8.12 | m_Down(v13) = v16 & m_Ack(v1, v3) = v6 & host(v18) = v15 & host(v14) % 55.73/8.12 | = v15 & host(v13) = v4 & host(v12) = v4 & host(v11) = v4 & host(v3) = % 55.73/8.12 | v7 & host(v2) = v4 & queue(v15) = v17 & queue(v4) = v5 & $i(v19) & % 55.73/8.12 | $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 55.73/8.12 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 55.73/8.12 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(nbr_proc, v7) & % 55.73/8.12 | setIn(v14, alive) & setIn(v12, alive) & setIn(v2, alive) & elem(v19, % 55.73/8.12 | v10) & elem(v16, v17) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] % 55.73/8.12 | : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! % 55.73/8.12 | [v27: $i] : (v25 = v24 | ~ (m_Down(v23) = v26) | ~ (m_Down(v21) = % 55.73/8.12 | v27) | ~ (host(v22) = v24) | ~ (host(v20) = v25) | ~ $i(v23) | % 55.73/8.12 | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~ % 55.73/8.12 | setIn(v20, alive) | ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? % 55.73/8.12 | [v31: $i] : (( ~ (v29 = v24) & host(v23) = v29 & $i(v29)) | ( ~ % 55.73/8.12 | (v28 = v25) & host(v21) = v28 & $i(v28)) | (queue(v25) = v30 & % 55.73/8.12 | $i(v30) & ~ elem(v26, v30)) | (queue(v24) = v31 & $i(v31) & ~ % 55.73/8.12 | elem(v27, v31)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] % 55.73/8.12 | : ! [v23: $i] : ! [v24: $i] : ( ~ (m_Ack(v22, v20) = v23) | ~ % 55.73/8.12 | (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ? [v25: % 55.73/8.12 | $i] : ? [v26: $i] : ? [v27: $i] : ((host(v22) = v27 & host(v20) % 55.73/8.12 | = v26 & $i(v27) & $i(v26) & ~ leq(v26, v27)) | (queue(v24) = % 55.73/8.12 | v25 & $i(v25) & ~ elem(v23, v25)))) & ! [v20: $i] : ! [v21: % 55.73/8.12 | $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (m_Down(v21) = v22) | ~ % 55.73/8.12 | (host(v20) = v23) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) % 55.73/8.12 | | ? [v24: $i] : (queue(v23) = v24 & $i(v24) & ~ elem(v22, v24))) % 55.73/8.12 | & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ % 55.73/8.12 | (m_Down(v21) = v22) | ~ (host(v20) = v23) | ~ $i(v21) | ~ % 55.73/8.12 | $i(v20) | ? [v24: $i] : ? [v25: $i] : (( ~ (v25 = v23) & % 55.73/8.12 | host(v21) = v25 & $i(v25)) | (queue(v23) = v24 & $i(v24) & ~ % 55.73/8.12 | elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] % 55.73/8.12 | : ! [v23: $i] : ( ~ (m_Halt(v21) = v22) | ~ (host(v20) = v23) | ~ % 55.73/8.12 | $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) = % 55.73/8.12 | v25 & $i(v25) & ~ leq(v23, v25)) | (queue(v23) = v24 & $i(v24) % 55.73/8.12 | & ~ elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: % 55.73/8.12 | $i] : (v21 = v20 | ~ (host(v21) = v22) | ~ (host(v20) = v22) | ~ % 55.73/8.12 | $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) | ~ setIn(v20, alive)) % 55.73/8.12 | & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ (host(v21) = v22) % 55.73/8.12 | | ~ (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ leq(v21, v20) % 55.73/8.12 | | ~ setIn(v21, alive) | setIn(v20, alive)) & (v7 = v4 | setIn(v4, % 55.73/8.12 | v8))) % 55.73/8.12 | % 55.73/8.12 | ALPHA: (function-axioms) implies: % 55.73/8.12 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = % 55.73/8.12 | v1) | ~ (queue(v2) = v0)) % 55.73/8.12 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1) % 55.73/8.12 | | ~ (host(v2) = v0)) % 55.73/8.12 | % 55.73/8.12 | DELTA: instantiating (3) with fresh symbols all_65_0, all_65_1, all_65_2, % 55.73/8.12 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9, % 55.73/8.12 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15, % 55.73/8.12 | all_65_16, all_65_17, all_65_18, all_65_19 gives: % 55.73/8.13 | (6) ~ (all_65_4 = all_65_15) & index(acks, all_65_15) = all_65_11 & % 55.73/8.13 | index(pendack, all_65_15) = all_65_12 & index(status, all_65_15) = % 55.73/8.13 | elec_2 & index(elid, all_65_15) = all_65_18 & snoc(all_65_19, % 55.73/8.13 | all_65_10) = all_65_9 & cons(all_65_13, all_65_19) = all_65_14 & % 55.73/8.13 | m_Ldr(all_65_17) = all_65_10 & m_Down(all_65_1) = all_65_0 & % 55.73/8.13 | m_Down(all_65_6) = all_65_3 & m_Ack(all_65_18, all_65_16) = all_65_13 & % 55.73/8.13 | host(all_65_1) = all_65_4 & host(all_65_5) = all_65_4 & host(all_65_6) % 55.73/8.13 | = all_65_15 & host(all_65_7) = all_65_15 & host(all_65_8) = all_65_15 & % 55.73/8.13 | host(all_65_16) = all_65_12 & host(all_65_17) = all_65_15 & % 55.73/8.13 | queue(all_65_4) = all_65_2 & queue(all_65_15) = all_65_14 & % 55.73/8.13 | $i(all_65_0) & $i(all_65_1) & $i(all_65_2) & $i(all_65_3) & % 55.73/8.13 | $i(all_65_4) & $i(all_65_5) & $i(all_65_6) & $i(all_65_7) & % 55.73/8.13 | $i(all_65_8) & $i(all_65_9) & $i(all_65_10) & $i(all_65_11) & % 55.73/8.13 | $i(all_65_12) & $i(all_65_13) & $i(all_65_14) & $i(all_65_15) & % 55.73/8.13 | $i(all_65_16) & $i(all_65_17) & $i(all_65_18) & $i(all_65_19) & % 55.73/8.13 | leq(nbr_proc, all_65_12) & setIn(all_65_5, alive) & setIn(all_65_7, % 55.73/8.13 | alive) & setIn(all_65_17, alive) & elem(all_65_0, all_65_9) & % 55.73/8.13 | elem(all_65_3, all_65_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 55.73/8.13 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v5 % 55.73/8.13 | = v4 | ~ (m_Down(v3) = v6) | ~ (m_Down(v1) = v7) | ~ (host(v2) = % 55.73/8.13 | v4) | ~ (host(v0) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 55.73/8.13 | $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? [v8: $i] : ? % 55.73/8.13 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v9 = v4) & host(v3) = % 55.73/8.13 | v9 & $i(v9)) | ( ~ (v8 = v5) & host(v1) = v8 & $i(v8)) | % 55.73/8.13 | (queue(v5) = v10 & $i(v10) & ~ elem(v6, v10)) | (queue(v4) = v11 & % 55.73/8.13 | $i(v11) & ~ elem(v7, v11)))) & ! [v0: $i] : ! [v1: $i] : ! % 55.73/8.13 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (m_Ack(v2, v0) = v3) | ~ % 55.73/8.13 | (host(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : % 55.73/8.13 | ? [v6: $i] : ? [v7: $i] : ((host(v2) = v7 & host(v0) = v6 & $i(v7) & % 55.73/8.13 | $i(v6) & ~ leq(v6, v7)) | (queue(v4) = v5 & $i(v5) & ~ elem(v3, % 55.73/8.13 | v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 55.73/8.13 | : ( ~ (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | % 55.73/8.13 | ~ setIn(v1, alive) | ? [v4: $i] : (queue(v3) = v4 & $i(v4) & ~ % 55.73/8.13 | elem(v2, v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 55.73/8.13 | $i] : ( ~ (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ % 55.73/8.13 | $i(v0) | ? [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 & % 55.73/8.13 | $i(v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) & ! [v0: % 55.73/8.13 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Halt(v1) = v2) % 55.73/8.13 | | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: % 55.73/8.13 | $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3) = v4 % 55.73/8.13 | & $i(v4) & ~ elem(v2, v4)))) & ! [v0: $i] : ! [v1: $i] : ! % 55.73/8.13 | [v2: $i] : (v1 = v0 | ~ (host(v1) = v2) | ~ (host(v0) = v2) | ~ % 55.73/8.13 | $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive)) & ! % 55.73/8.13 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~ % 55.73/8.13 | (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) | ~ % 55.73/8.13 | setIn(v1, alive) | setIn(v0, alive)) & (all_65_12 = all_65_15 | % 55.73/8.13 | setIn(all_65_15, all_65_11)) % 55.73/8.13 | % 55.73/8.13 | ALPHA: (6) implies: % 55.73/8.13 | (7) ~ (all_65_4 = all_65_15) % 55.73/8.13 | (8) elem(all_65_3, all_65_2) % 55.73/8.13 | (9) elem(all_65_0, all_65_9) % 55.73/8.13 | (10) setIn(all_65_17, alive) % 55.73/8.13 | (11) setIn(all_65_7, alive) % 55.73/8.13 | (12) setIn(all_65_5, alive) % 55.73/8.13 | (13) $i(all_65_19) % 55.73/8.13 | (14) $i(all_65_17) % 55.73/8.13 | (15) $i(all_65_13) % 55.73/8.13 | (16) $i(all_65_10) % 55.73/8.13 | (17) $i(all_65_7) % 55.73/8.13 | (18) $i(all_65_6) % 55.73/8.13 | (19) $i(all_65_5) % 55.73/8.13 | (20) $i(all_65_1) % 55.73/8.13 | (21) $i(all_65_0) % 55.73/8.13 | (22) queue(all_65_15) = all_65_14 % 55.73/8.13 | (23) queue(all_65_4) = all_65_2 % 55.73/8.13 | (24) host(all_65_17) = all_65_15 % 55.73/8.13 | (25) host(all_65_7) = all_65_15 % 55.73/8.13 | (26) host(all_65_6) = all_65_15 % 55.73/8.13 | (27) host(all_65_5) = all_65_4 % 55.73/8.14 | (28) host(all_65_1) = all_65_4 % 55.73/8.14 | (29) m_Down(all_65_6) = all_65_3 % 55.73/8.14 | (30) m_Down(all_65_1) = all_65_0 % 55.73/8.14 | (31) m_Ldr(all_65_17) = all_65_10 % 55.73/8.14 | (32) cons(all_65_13, all_65_19) = all_65_14 % 55.73/8.14 | (33) snoc(all_65_19, all_65_10) = all_65_9 % 55.73/8.14 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v1) = % 55.73/8.14 | v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, % 55.73/8.14 | alive) | ~ setIn(v0, alive)) % 55.73/8.14 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 55.73/8.14 | (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 55.73/8.14 | [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 & $i(v5)) | % 55.73/8.14 | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) % 55.73/8.14 | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 55.73/8.14 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ (m_Down(v3) = % 55.73/8.14 | v6) | ~ (m_Down(v1) = v7) | ~ (host(v2) = v4) | ~ (host(v0) = % 55.73/8.14 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, % 55.73/8.14 | alive) | ~ setIn(v0, alive) | ? [v8: $i] : ? [v9: $i] : ? % 55.73/8.14 | [v10: $i] : ? [v11: $i] : (( ~ (v9 = v4) & host(v3) = v9 & $i(v9)) % 55.73/8.14 | | ( ~ (v8 = v5) & host(v1) = v8 & $i(v8)) | (queue(v5) = v10 & % 55.73/8.14 | $i(v10) & ~ elem(v6, v10)) | (queue(v4) = v11 & $i(v11) & ~ % 55.73/8.14 | elem(v7, v11)))) % 55.73/8.14 | % 55.73/8.14 | GROUND_INST: instantiating (34) with all_65_17, all_65_7, all_65_15, % 55.73/8.14 | simplifying with (10), (11), (14), (17), (24), (25) gives: % 55.73/8.14 | (37) all_65_7 = all_65_17 % 55.73/8.14 | % 55.73/8.14 | GROUND_INST: instantiating (35) with all_65_17, all_65_6, all_65_3, all_65_15, % 55.73/8.14 | simplifying with (14), (18), (24), (29) gives: % 55.73/8.14 | (38) ? [v0: $i] : ? [v1: any] : (( ~ (v1 = all_65_15) & host(all_65_6) = % 55.73/8.14 | v1 & $i(v1)) | (queue(all_65_15) = v0 & $i(v0) & ~ elem(all_65_3, % 55.73/8.14 | v0))) % 55.73/8.14 | % 55.73/8.14 | GROUND_INST: instantiating (36) with all_65_17, all_65_1, all_65_5, all_65_1, % 55.73/8.14 | all_65_4, all_65_15, all_65_0, all_65_0, simplifying with (10), % 55.73/8.14 | (12), (14), (19), (20), (24), (27), (30) gives: % 55.73/8.14 | (39) all_65_4 = all_65_15 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 55.73/8.14 | [v3: $i] : (( ~ (v1 = all_65_4) & host(all_65_1) = v1 & $i(v1)) | ( ~ % 55.73/8.14 | (v0 = all_65_15) & host(all_65_1) = v0 & $i(v0)) | % 55.73/8.14 | (queue(all_65_4) = v3 & $i(v3) & ~ elem(all_65_0, v3)) | % 55.73/8.14 | (queue(all_65_15) = v2 & $i(v2) & ~ elem(all_65_0, v2))) % 55.73/8.14 | % 55.73/8.14 | GROUND_INST: instantiating (36) with all_65_17, all_65_6, all_65_5, all_65_1, % 55.73/8.14 | all_65_4, all_65_15, all_65_0, all_65_3, simplifying with (10), % 55.73/8.14 | (12), (14), (18), (19), (20), (24), (27), (29), (30) gives: % 55.73/8.15 | (40) all_65_4 = all_65_15 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 55.73/8.15 | [v3: $i] : (( ~ (v1 = all_65_4) & host(all_65_1) = v1 & $i(v1)) | ( ~ % 55.73/8.15 | (v0 = all_65_15) & host(all_65_6) = v0 & $i(v0)) | % 55.73/8.15 | (queue(all_65_4) = v3 & $i(v3) & ~ elem(all_65_3, v3)) | % 55.73/8.15 | (queue(all_65_15) = v2 & $i(v2) & ~ elem(all_65_0, v2))) % 55.73/8.15 | % 55.73/8.15 | GROUND_INST: instantiating (35) with all_65_5, all_65_1, all_65_0, all_65_4, % 55.73/8.15 | simplifying with (19), (20), (27), (30) gives: % 55.73/8.15 | (41) ? [v0: $i] : ? [v1: any] : (( ~ (v1 = all_65_4) & host(all_65_1) = % 55.73/8.15 | v1 & $i(v1)) | (queue(all_65_4) = v0 & $i(v0) & ~ elem(all_65_0, % 55.73/8.15 | v0))) % 55.73/8.15 | % 55.73/8.15 | GROUND_INST: instantiating (2) with all_65_0, all_65_10, all_65_19, all_65_9, % 55.73/8.15 | simplifying with (9), (13), (16), (21), (33) gives: % 55.73/8.15 | (42) all_65_0 = all_65_10 | elem(all_65_0, all_65_19) % 55.73/8.15 | % 55.73/8.15 | DELTA: instantiating (41) with fresh symbols all_85_0, all_85_1 gives: % 55.73/8.15 | (43) ( ~ (all_85_0 = all_65_4) & host(all_65_1) = all_85_0 & $i(all_85_0)) % 55.73/8.15 | | (queue(all_65_4) = all_85_1 & $i(all_85_1) & ~ elem(all_65_0, % 55.73/8.15 | all_85_1)) % 55.73/8.15 | % 55.73/8.15 | DELTA: instantiating (38) with fresh symbols all_87_0, all_87_1 gives: % 55.73/8.15 | (44) ( ~ (all_87_0 = all_65_15) & host(all_65_6) = all_87_0 & $i(all_87_0)) % 55.73/8.15 | | (queue(all_65_15) = all_87_1 & $i(all_87_1) & ~ elem(all_65_3, % 55.73/8.15 | all_87_1)) % 55.73/8.15 | % 55.73/8.15 | BETA: splitting (43) gives: % 55.73/8.15 | % 55.73/8.15 | Case 1: % 55.73/8.15 | | % 55.73/8.15 | | (45) ~ (all_85_0 = all_65_4) & host(all_65_1) = all_85_0 & $i(all_85_0) % 55.73/8.15 | | % 55.73/8.15 | | ALPHA: (45) implies: % 55.73/8.15 | | (46) ~ (all_85_0 = all_65_4) % 55.73/8.15 | | (47) host(all_65_1) = all_85_0 % 55.73/8.15 | | % 55.73/8.15 | | GROUND_INST: instantiating (5) with all_65_4, all_85_0, all_65_1, % 55.73/8.15 | | simplifying with (28), (47) gives: % 55.73/8.15 | | (48) all_85_0 = all_65_4 % 55.73/8.15 | | % 55.73/8.15 | | REDUCE: (46), (48) imply: % 55.73/8.15 | | (49) $false % 55.73/8.15 | | % 55.73/8.15 | | CLOSE: (49) is inconsistent. % 55.73/8.15 | | % 55.73/8.15 | Case 2: % 55.73/8.15 | | % 55.73/8.15 | | (50) queue(all_65_4) = all_85_1 & $i(all_85_1) & ~ elem(all_65_0, % 55.73/8.15 | | all_85_1) % 55.73/8.15 | | % 55.73/8.15 | | ALPHA: (50) implies: % 55.73/8.15 | | (51) queue(all_65_4) = all_85_1 % 55.73/8.15 | | % 55.73/8.15 | | BETA: splitting (44) gives: % 55.73/8.15 | | % 55.73/8.15 | | Case 1: % 55.73/8.15 | | | % 55.73/8.15 | | | (52) ~ (all_87_0 = all_65_15) & host(all_65_6) = all_87_0 & % 55.73/8.15 | | | $i(all_87_0) % 55.73/8.15 | | | % 55.73/8.15 | | | ALPHA: (52) implies: % 55.73/8.15 | | | (53) ~ (all_87_0 = all_65_15) % 55.73/8.15 | | | (54) host(all_65_6) = all_87_0 % 55.73/8.15 | | | % 55.73/8.15 | | | GROUND_INST: instantiating (5) with all_65_15, all_87_0, all_65_6, % 55.73/8.15 | | | simplifying with (26), (54) gives: % 55.73/8.15 | | | (55) all_87_0 = all_65_15 % 55.73/8.15 | | | % 55.73/8.15 | | | REDUCE: (53), (55) imply: % 55.73/8.15 | | | (56) $false % 55.73/8.15 | | | % 55.73/8.15 | | | CLOSE: (56) is inconsistent. % 55.73/8.15 | | | % 55.73/8.15 | | Case 2: % 55.73/8.15 | | | % 55.73/8.15 | | | (57) queue(all_65_15) = all_87_1 & $i(all_87_1) & ~ elem(all_65_3, % 55.73/8.15 | | | all_87_1) % 55.73/8.15 | | | % 55.73/8.15 | | | ALPHA: (57) implies: % 55.73/8.15 | | | (58) queue(all_65_15) = all_87_1 % 55.73/8.15 | | | % 55.73/8.15 | | | BETA: splitting (40) gives: % 55.73/8.15 | | | % 55.73/8.15 | | | Case 1: % 55.73/8.15 | | | | % 55.73/8.15 | | | | (59) all_65_4 = all_65_15 % 55.73/8.15 | | | | % 55.73/8.15 | | | | REDUCE: (7), (59) imply: % 55.73/8.15 | | | | (60) $false % 55.73/8.15 | | | | % 55.73/8.15 | | | | CLOSE: (60) is inconsistent. % 55.73/8.15 | | | | % 55.73/8.15 | | | Case 2: % 55.73/8.15 | | | | % 55.73/8.15 | | | | (61) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : (( ~ % 55.73/8.15 | | | | (v1 = all_65_4) & host(all_65_1) = v1 & $i(v1)) | ( ~ (v0 = % 55.73/8.15 | | | | all_65_15) & host(all_65_6) = v0 & $i(v0)) | % 55.73/8.15 | | | | (queue(all_65_4) = v3 & $i(v3) & ~ elem(all_65_3, v3)) | % 55.73/8.15 | | | | (queue(all_65_15) = v2 & $i(v2) & ~ elem(all_65_0, v2))) % 55.73/8.15 | | | | % 55.73/8.15 | | | | DELTA: instantiating (61) with fresh symbols all_116_0, all_116_1, % 55.73/8.15 | | | | all_116_2, all_116_3 gives: % 55.73/8.15 | | | | (62) ( ~ (all_116_2 = all_65_4) & host(all_65_1) = all_116_2 & % 55.73/8.15 | | | | $i(all_116_2)) | ( ~ (all_116_3 = all_65_15) & host(all_65_6) % 55.73/8.15 | | | | = all_116_3 & $i(all_116_3)) | (queue(all_65_4) = all_116_0 & % 55.73/8.15 | | | | $i(all_116_0) & ~ elem(all_65_3, all_116_0)) | % 55.73/8.15 | | | | (queue(all_65_15) = all_116_1 & $i(all_116_1) & ~ % 55.73/8.15 | | | | elem(all_65_0, all_116_1)) % 55.73/8.15 | | | | % 55.73/8.15 | | | | BETA: splitting (62) gives: % 55.73/8.15 | | | | % 55.73/8.15 | | | | Case 1: % 55.73/8.15 | | | | | % 55.73/8.15 | | | | | (63) ( ~ (all_116_2 = all_65_4) & host(all_65_1) = all_116_2 & % 55.73/8.15 | | | | | $i(all_116_2)) | ( ~ (all_116_3 = all_65_15) & % 55.73/8.15 | | | | | host(all_65_6) = all_116_3 & $i(all_116_3)) % 55.73/8.15 | | | | | % 55.73/8.15 | | | | | BETA: splitting (63) gives: % 55.73/8.15 | | | | | % 55.73/8.15 | | | | | Case 1: % 55.73/8.15 | | | | | | % 55.73/8.15 | | | | | | (64) ~ (all_116_2 = all_65_4) & host(all_65_1) = all_116_2 & % 55.73/8.15 | | | | | | $i(all_116_2) % 55.73/8.15 | | | | | | % 55.73/8.15 | | | | | | ALPHA: (64) implies: % 55.73/8.15 | | | | | | (65) ~ (all_116_2 = all_65_4) % 55.73/8.16 | | | | | | (66) host(all_65_1) = all_116_2 % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | GROUND_INST: instantiating (5) with all_65_4, all_116_2, all_65_1, % 55.73/8.16 | | | | | | simplifying with (28), (66) gives: % 55.73/8.16 | | | | | | (67) all_116_2 = all_65_4 % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | REDUCE: (65), (67) imply: % 55.73/8.16 | | | | | | (68) $false % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | CLOSE: (68) is inconsistent. % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | Case 2: % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | (69) ~ (all_116_3 = all_65_15) & host(all_65_6) = all_116_3 & % 55.73/8.16 | | | | | | $i(all_116_3) % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | ALPHA: (69) implies: % 55.73/8.16 | | | | | | (70) ~ (all_116_3 = all_65_15) % 55.73/8.16 | | | | | | (71) host(all_65_6) = all_116_3 % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | GROUND_INST: instantiating (5) with all_65_15, all_116_3, all_65_6, % 55.73/8.16 | | | | | | simplifying with (26), (71) gives: % 55.73/8.16 | | | | | | (72) all_116_3 = all_65_15 % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | REDUCE: (70), (72) imply: % 55.73/8.16 | | | | | | (73) $false % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | CLOSE: (73) is inconsistent. % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | End of split % 55.73/8.16 | | | | | % 55.73/8.16 | | | | Case 2: % 55.73/8.16 | | | | | % 55.73/8.16 | | | | | (74) (queue(all_65_4) = all_116_0 & $i(all_116_0) & ~ % 55.73/8.16 | | | | | elem(all_65_3, all_116_0)) | (queue(all_65_15) = all_116_1 & % 55.73/8.16 | | | | | $i(all_116_1) & ~ elem(all_65_0, all_116_1)) % 55.73/8.16 | | | | | % 55.73/8.16 | | | | | BETA: splitting (74) gives: % 55.73/8.16 | | | | | % 55.73/8.16 | | | | | Case 1: % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | (75) queue(all_65_4) = all_116_0 & $i(all_116_0) & ~ % 55.73/8.16 | | | | | | elem(all_65_3, all_116_0) % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | ALPHA: (75) implies: % 55.73/8.16 | | | | | | (76) ~ elem(all_65_3, all_116_0) % 55.73/8.16 | | | | | | (77) queue(all_65_4) = all_116_0 % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | GROUND_INST: instantiating (4) with all_65_2, all_116_0, all_65_4, % 55.73/8.16 | | | | | | simplifying with (23), (77) gives: % 55.73/8.16 | | | | | | (78) all_116_0 = all_65_2 % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | GROUND_INST: instantiating (4) with all_85_1, all_116_0, all_65_4, % 55.73/8.16 | | | | | | simplifying with (51), (77) gives: % 55.73/8.16 | | | | | | (79) all_116_0 = all_85_1 % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | COMBINE_EQS: (78), (79) imply: % 55.73/8.16 | | | | | | (80) all_85_1 = all_65_2 % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | REDUCE: (76), (78) imply: % 55.73/8.16 | | | | | | (81) ~ elem(all_65_3, all_65_2) % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | PRED_UNIFY: (8), (81) imply: % 55.73/8.16 | | | | | | (82) $false % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | CLOSE: (82) is inconsistent. % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | Case 2: % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | (83) queue(all_65_15) = all_116_1 & $i(all_116_1) & ~ % 55.73/8.16 | | | | | | elem(all_65_0, all_116_1) % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | ALPHA: (83) implies: % 55.73/8.16 | | | | | | (84) ~ elem(all_65_0, all_116_1) % 55.73/8.16 | | | | | | (85) queue(all_65_15) = all_116_1 % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | BETA: splitting (39) gives: % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | | Case 1: % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | | (86) all_65_4 = all_65_15 % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | | REDUCE: (7), (86) imply: % 55.73/8.16 | | | | | | | (87) $false % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | | CLOSE: (87) is inconsistent. % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | Case 2: % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | | GROUND_INST: instantiating (4) with all_65_14, all_116_1, % 55.73/8.16 | | | | | | | all_65_15, simplifying with (22), (85) gives: % 55.73/8.16 | | | | | | | (88) all_116_1 = all_65_14 % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | | GROUND_INST: instantiating (4) with all_87_1, all_116_1, % 55.73/8.16 | | | | | | | all_65_15, simplifying with (58), (85) gives: % 55.73/8.16 | | | | | | | (89) all_116_1 = all_87_1 % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | | COMBINE_EQS: (88), (89) imply: % 55.73/8.16 | | | | | | | (90) all_87_1 = all_65_14 % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | | REDUCE: (84), (88) imply: % 55.73/8.16 | | | | | | | (91) ~ elem(all_65_0, all_65_14) % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | | BETA: splitting (42) gives: % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | | Case 1: % 55.73/8.16 | | | | | | | | % 55.73/8.16 | | | | | | | | (92) elem(all_65_0, all_65_19) % 55.73/8.16 | | | | | | | | % 55.73/8.16 | | | | | | | | GROUND_INST: instantiating (1) with all_65_0, all_65_13, % 55.73/8.16 | | | | | | | | all_65_19, all_65_14, simplifying with (13), (15), % 55.73/8.16 | | | | | | | | (21), (32), (91), (92) gives: % 55.73/8.16 | | | | | | | | (93) $false % 55.73/8.16 | | | | | | | | % 55.73/8.16 | | | | | | | | CLOSE: (93) is inconsistent. % 55.73/8.16 | | | | | | | | % 55.73/8.16 | | | | | | | Case 2: % 55.73/8.16 | | | | | | | | % 55.73/8.16 | | | | | | | | (94) all_65_0 = all_65_10 % 55.73/8.16 | | | | | | | | % 55.73/8.16 | | | | | | | | REDUCE: (30), (94) imply: % 55.73/8.16 | | | | | | | | (95) m_Down(all_65_1) = all_65_10 % 55.73/8.16 | | | | | | | | % 55.73/8.16 | | | | | | | | GROUND_INST: instantiating (axiom_18) with all_65_1, all_65_17, % 55.73/8.16 | | | | | | | | all_65_10, simplifying with (14), (20), (31), (95) % 55.73/8.16 | | | | | | | | gives: % 55.73/8.16 | | | | | | | | (96) $false % 55.73/8.16 | | | | | | | | % 55.73/8.16 | | | | | | | | CLOSE: (96) is inconsistent. % 55.73/8.16 | | | | | | | | % 55.73/8.16 | | | | | | | End of split % 55.73/8.16 | | | | | | | % 55.73/8.16 | | | | | | End of split % 55.73/8.16 | | | | | | % 55.73/8.16 | | | | | End of split % 55.73/8.16 | | | | | % 55.73/8.16 | | | | End of split % 55.73/8.16 | | | | % 55.73/8.16 | | | End of split % 55.73/8.16 | | | % 55.73/8.16 | | End of split % 55.73/8.16 | | % 55.73/8.16 | End of split % 55.73/8.16 | % 55.73/8.16 End of proof % 55.73/8.16 % SZS output end Proof for theBenchmark % 55.73/8.16 % 55.73/8.16 7562ms %------------------------------------------------------------------------------