%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU044+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n014.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 17:42:23 EDT 2023 % Result : Theorem 45.76s 7.10s % Output : Proof 100.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SEU044+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.32 % Computer : n014.cluster.edu % 0.10/0.32 % Model : x86_64 x86_64 % 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.32 % Memory : 8042.1875MB % 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.32 % CPULimit : 300 % 0.10/0.32 % WCLimit : 300 % 0.10/0.32 % DateTime : Wed Aug 23 12:26:49 EDT 2023 % 0.10/0.32 % CPUTime : % 0.16/0.60 ________ _____ % 0.16/0.60 ___ __ \_________(_)________________________________ % 0.16/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.60 % 0.16/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.60 (2023-06-19) % 0.16/0.60 % 0.16/0.60 (c) Philipp Rümmer, 2009-2023 % 0.16/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.60 Amanda Stjerna. % 0.16/0.60 Free software under BSD-3-Clause. % 0.16/0.60 % 0.16/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.60 % 0.16/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.62 Running up to 7 provers in parallel. % 0.16/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.90/1.23 Prover 1: Preprocessing ... % 2.90/1.23 Prover 4: Preprocessing ... % 3.06/1.31 Prover 5: Preprocessing ... % 3.06/1.31 Prover 2: Preprocessing ... % 3.06/1.32 Prover 3: Preprocessing ... % 3.06/1.32 Prover 6: Preprocessing ... % 3.06/1.32 Prover 0: Preprocessing ... % 7.62/1.96 Prover 1: Warning: ignoring some quantifiers % 7.62/1.98 Prover 3: Warning: ignoring some quantifiers % 7.62/2.00 Prover 3: Constructing countermodel ... % 7.62/2.00 Prover 5: Proving ... % 7.62/2.01 Prover 6: Proving ... % 7.62/2.01 Prover 1: Constructing countermodel ... % 8.83/2.26 Prover 2: Proving ... % 13.15/2.88 Prover 4: Warning: ignoring some quantifiers % 13.15/2.94 Prover 4: Constructing countermodel ... % 15.46/3.10 Prover 0: Proving ... % 17.37/3.33 Prover 3: gave up % 17.37/3.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.73/3.40 Prover 7: Preprocessing ... % 19.18/3.63 Prover 7: Warning: ignoring some quantifiers % 19.18/3.66 Prover 7: Constructing countermodel ... % 20.83/3.78 Prover 1: gave up % 20.83/3.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.21/3.82 Prover 8: Preprocessing ... % 22.28/3.97 Prover 8: Warning: ignoring some quantifiers % 22.28/3.99 Prover 8: Constructing countermodel ... % 26.34/4.60 Prover 8: gave up % 26.34/4.62 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 27.02/4.69 Prover 9: Preprocessing ... % 32.91/5.45 Prover 9: Warning: ignoring some quantifiers % 32.91/5.46 Prover 9: Constructing countermodel ... % 45.76/7.10 Prover 2: proved (6441ms) % 45.76/7.10 % 45.76/7.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 45.76/7.10 % 45.76/7.11 Prover 5: stopped % 45.76/7.11 Prover 6: stopped % 45.76/7.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 45.76/7.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 45.76/7.13 Prover 9: stopped % 45.76/7.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 45.76/7.14 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 46.15/7.16 Prover 11: Preprocessing ... % 46.15/7.16 Prover 10: Preprocessing ... % 46.15/7.19 Prover 13: Preprocessing ... % 46.15/7.19 Prover 0: stopped % 46.15/7.20 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 46.15/7.20 Prover 16: Preprocessing ... % 46.15/7.20 Prover 10: Warning: ignoring some quantifiers % 46.15/7.20 Prover 10: Constructing countermodel ... % 46.15/7.23 Prover 19: Preprocessing ... % 46.15/7.35 Prover 16: Warning: ignoring some quantifiers % 46.15/7.35 Prover 16: Constructing countermodel ... % 46.15/7.38 Prover 13: Warning: ignoring some quantifiers % 46.15/7.39 Prover 13: Constructing countermodel ... % 47.40/7.45 Prover 19: Warning: ignoring some quantifiers % 47.40/7.46 Prover 19: Constructing countermodel ... % 47.40/7.46 Prover 10: gave up % 48.64/7.57 Prover 11: Warning: ignoring some quantifiers % 48.64/7.58 Prover 11: Constructing countermodel ... % 51.82/8.02 Prover 19: gave up % 79.72/11.66 Prover 13: stopped % 88.51/12.92 Prover 16: stopped % 97.85/15.04 Prover 4: Found proof (size 199) % 97.85/15.04 Prover 4: proved (14406ms) % 97.85/15.04 Prover 7: stopped % 97.85/15.06 Prover 11: stopped % 97.85/15.06 % 97.85/15.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 97.85/15.06 % 98.54/15.09 % SZS output start Proof for theBenchmark % 98.54/15.10 Assumptions after simplification: % 98.54/15.10 --------------------------------- % 98.54/15.10 % 98.54/15.10 (cc2_funct_1) % 99.01/15.14 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2: % 99.01/15.14 any] : ? [v3: any] : ? [v4: any] : (function(v0) = v4 & empty(v0) = v3 & % 99.01/15.14 relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) & % 99.01/15.14 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] % 99.01/15.14 : ? [v3: any] : (one_to_one(v0) = v3 & empty(v0) = v2 & relation(v0) = v1 & % 99.01/15.14 ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) % 99.01/15.14 | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = % 99.01/15.14 v3 & function(v0) = v2 & relation(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 99.01/15.14 v3 = 0))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: % 99.01/15.14 any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = % 99.01/15.14 v2 & empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 99.01/15.14 % 99.01/15.14 (dt_k8_relat_1) % 99.01/15.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0, % 99.01/15.15 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 99.01/15.15 (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 99.01/15.15 % 99.01/15.15 (fc5_funct_1) % 99.01/15.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0, % 99.01/15.15 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 99.01/15.15 [v5: any] : ? [v6: any] : (function(v2) = v6 & function(v1) = v4 & % 99.01/15.15 relation(v2) = v5 & relation(v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = % 99.01/15.15 0 & v5 = 0)))) % 99.01/15.15 % 99.01/15.15 (fc5_relat_1) % 99.01/15.15 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 99.01/15.15 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 & empty(v3) % 99.01/15.15 = v4 & relation(v0) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! % 99.01/15.15 [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 99.01/15.15 any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & empty(v0) = v2 & % 99.01/15.15 relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0: $i] : % 99.01/15.15 ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any] % 99.01/15.15 : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & $i(v2) & ( ~ % 99.01/15.15 (v3 = 0) | v1 = 0))) % 99.01/15.15 % 99.01/15.15 (t85_funct_1) % 99.72/15.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 99.72/15.29 (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ % 99.72/15.29 $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] % 99.72/15.29 : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: int] : ? [v12: $i] : % 99.72/15.29 ? [v13: $i] : ? [v14: $i] : ? [v15: any] : ? [v16: any] : ? [v17: $i] : % 99.72/15.29 ? [v18: any] : ($i(v14) & $i(v10) & ((relation_dom(v3) = v9 & function(v3) % 99.72/15.29 = v8 & relation(v3) = v7 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ % 99.72/15.29 (v4 = v1) | ( ! [v19: $i] : ! [v20: int] : (v20 = 0 | ~ % 99.72/15.29 (in(v19, v2) = v20) | ~ $i(v19) | ? [v21: any] : ? [v22: % 99.72/15.29 $i] : ? [v23: any] : (apply(v3, v19) = v22 & in(v22, v0) % 99.72/15.29 = v23 & in(v19, v9) = v21 & $i(v22) & ( ~ (v23 = 0) | ~ % 99.72/15.29 (v21 = 0)))) & ! [v19: $i] : ! [v20: $i] : ( ~ % 99.72/15.29 (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ? % 99.72/15.29 [v22: any] : ? [v23: any] : (in(v20, v0) = v23 & in(v19, % 99.72/15.29 v9) = v22 & in(v19, v2) = v21 & ( ~ (v21 = 0) | (v23 = 0 % 99.72/15.29 & v22 = 0)))) & ! [v19: $i] : ! [v20: $i] : ( ~ % 99.72/15.29 (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ? % 99.72/15.29 [v22: any] : ? [v23: any] : (in(v20, v0) = v22 & in(v19, % 99.72/15.29 v9) = v21 & in(v19, v2) = v23 & ( ~ (v22 = 0) | ~ (v21 % 99.72/15.29 = 0) | v23 = 0))) & ! [v19: $i] : ! [v20: $i] : ( ~ % 99.72/15.29 (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ? % 99.72/15.29 [v22: $i] : (apply(v1, v19) = v22 & in(v19, v2) = v21 & % 99.72/15.29 $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19: $i] : ! % 99.72/15.29 [v20: $i] : ( ~ (apply(v1, v19) = v20) | ~ $i(v19) | ? [v21: % 99.72/15.29 any] : ? [v22: $i] : (apply(v3, v19) = v22 & in(v19, v2) % 99.72/15.29 = v21 & $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19: % 99.72/15.29 $i] : ! [v20: any] : ( ~ (in(v19, v9) = v20) | ~ $i(v19) | % 99.72/15.29 ? [v21: any] : ? [v22: $i] : ? [v23: any] : (apply(v3, % 99.72/15.29 v19) = v22 & in(v22, v0) = v23 & in(v19, v2) = v21 & % 99.72/15.29 $i(v22) & ( ~ (v21 = 0) | (v23 = 0 & v20 = 0)))) & ! % 99.72/15.29 [v19: $i] : ( ~ (in(v19, v9) = 0) | ~ $i(v19) | ? [v20: $i] % 99.72/15.29 : ? [v21: any] : ? [v22: any] : (apply(v3, v19) = v20 & % 99.72/15.29 in(v20, v0) = v21 & in(v19, v2) = v22 & $i(v20) & ( ~ (v21 % 99.72/15.29 = 0) | v22 = 0))) & ! [v19: $i] : ( ~ (in(v19, v2) = % 99.72/15.29 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3, v19) = v20 & % 99.72/15.29 apply(v1, v19) = v20 & $i(v20))) & ! [v19: $i] : ( ~ % 99.72/15.29 (in(v19, v2) = 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3, % 99.72/15.29 v19) = v20 & in(v20, v0) = 0 & in(v19, v9) = 0 & % 99.72/15.29 $i(v20))))) & (v4 = v1 | (v11 = 0 & ~ (v13 = v12) & % 99.72/15.29 apply(v3, v10) = v13 & apply(v1, v10) = v12 & in(v10, v2) = 0 % 99.72/15.29 & $i(v13) & $i(v12)) | (apply(v3, v14) = v17 & in(v17, v0) = % 99.72/15.29 v18 & in(v14, v9) = v16 & in(v14, v2) = v15 & $i(v17) & ( ~ % 99.72/15.29 (v18 = 0) | ~ (v16 = 0) | ~ (v15 = 0)) & (v15 = 0 | (v18 = % 99.72/15.29 0 & v16 = 0))))))) | (function(v1) = v6 & relation(v1) = % 99.72/15.29 v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))))) & ? [v0: $i] : ! [v1: $i] : ! % 99.72/15.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (relation_dom(v3) = v4) | ~ % 99.72/15.29 (relation_dom(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : % 99.72/15.29 ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? % 99.72/15.29 [v11: int] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: any] : ? % 99.72/15.29 [v16: any] : ? [v17: $i] : ? [v18: any] : ($i(v14) & $i(v10) & % 99.72/15.29 ((relation_rng_restriction(v0, v3) = v9 & function(v3) = v8 & relation(v3) % 99.72/15.29 = v7 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = v1) | ( ! % 99.72/15.29 [v19: $i] : ! [v20: int] : (v20 = 0 | ~ (in(v19, v2) = v20) % 99.72/15.29 | ~ $i(v19) | ? [v21: any] : ? [v22: $i] : ? [v23: any] % 99.72/15.29 : (apply(v3, v19) = v22 & in(v22, v0) = v23 & in(v19, v4) = % 99.72/15.29 v21 & $i(v22) & ( ~ (v23 = 0) | ~ (v21 = 0)))) & ! [v19: % 99.72/15.29 $i] : ! [v20: $i] : ( ~ (apply(v3, v19) = v20) | ~ $i(v19) % 99.72/15.29 | ? [v21: any] : ? [v22: any] : ? [v23: any] : (in(v20, % 99.72/15.29 v0) = v23 & in(v19, v4) = v22 & in(v19, v2) = v21 & ( ~ % 99.72/15.29 (v21 = 0) | (v23 = 0 & v22 = 0)))) & ! [v19: $i] : ! % 99.72/15.29 [v20: $i] : ( ~ (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: % 99.72/15.29 any] : ? [v22: any] : ? [v23: any] : (in(v20, v0) = v22 % 99.72/15.29 & in(v19, v4) = v21 & in(v19, v2) = v23 & ( ~ (v22 = 0) | % 99.72/15.29 ~ (v21 = 0) | v23 = 0))) & ! [v19: $i] : ! [v20: $i] : % 99.72/15.29 ( ~ (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : ? % 99.72/15.29 [v22: $i] : (apply(v1, v19) = v22 & in(v19, v2) = v21 & % 99.72/15.29 $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19: $i] : ! % 99.72/15.29 [v20: $i] : ( ~ (apply(v1, v19) = v20) | ~ $i(v19) | ? [v21: % 99.72/15.29 any] : ? [v22: $i] : (apply(v3, v19) = v22 & in(v19, v2) % 99.72/15.29 = v21 & $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! [v19: % 99.72/15.29 $i] : ! [v20: any] : ( ~ (in(v19, v4) = v20) | ~ $i(v19) | % 99.72/15.29 ? [v21: any] : ? [v22: $i] : ? [v23: any] : (apply(v3, % 99.72/15.29 v19) = v22 & in(v22, v0) = v23 & in(v19, v2) = v21 & % 99.72/15.29 $i(v22) & ( ~ (v21 = 0) | (v23 = 0 & v20 = 0)))) & ! % 99.72/15.29 [v19: $i] : ( ~ (in(v19, v4) = 0) | ~ $i(v19) | ? [v20: $i] % 99.72/15.30 : ? [v21: any] : ? [v22: any] : (apply(v3, v19) = v20 & % 99.72/15.30 in(v20, v0) = v21 & in(v19, v2) = v22 & $i(v20) & ( ~ (v21 % 99.72/15.30 = 0) | v22 = 0))) & ! [v19: $i] : ( ~ (in(v19, v2) = % 99.72/15.30 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3, v19) = v20 & % 99.72/15.30 apply(v1, v19) = v20 & $i(v20))) & ! [v19: $i] : ( ~ % 99.72/15.30 (in(v19, v2) = 0) | ~ $i(v19) | ? [v20: $i] : (apply(v3, % 99.72/15.30 v19) = v20 & in(v20, v0) = 0 & in(v19, v4) = 0 & % 99.72/15.30 $i(v20))))) & (v9 = v1 | (v11 = 0 & ~ (v13 = v12) & % 99.72/15.30 apply(v3, v10) = v13 & apply(v1, v10) = v12 & in(v10, v2) = 0 % 99.72/15.30 & $i(v13) & $i(v12)) | (apply(v3, v14) = v17 & in(v17, v0) = % 99.72/15.30 v18 & in(v14, v4) = v16 & in(v14, v2) = v15 & $i(v17) & ( ~ % 99.72/15.30 (v18 = 0) | ~ (v16 = 0) | ~ (v15 = 0)) & (v15 = 0 | (v18 = % 99.72/15.30 0 & v16 = 0))))))) | (function(v1) = v6 & relation(v1) = % 99.72/15.30 v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))))) & ? [v0: $i] : ! [v1: $i] : ! % 99.72/15.30 [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v1) = v2) | ~ (function(v3) = 0) | % 99.72/15.30 ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 99.72/15.30 any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: % 99.72/15.30 $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15: any] : ? % 99.72/15.30 [v16: $i] : ? [v17: any] : ($i(v13) & $i(v9) & % 99.72/15.30 ((relation_rng_restriction(v0, v3) = v7 & relation_dom(v3) = v8 & % 99.72/15.30 relation(v3) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 = v1) | % 99.72/15.30 ( ! [v18: $i] : ! [v19: int] : (v19 = 0 | ~ (in(v18, v2) = % 99.72/15.30 v19) | ~ $i(v18) | ? [v20: any] : ? [v21: $i] : ? % 99.72/15.30 [v22: any] : (apply(v3, v18) = v21 & in(v21, v0) = v22 & % 99.72/15.30 in(v18, v8) = v20 & $i(v21) & ( ~ (v22 = 0) | ~ (v20 = % 99.72/15.30 0)))) & ! [v18: $i] : ! [v19: $i] : ( ~ (apply(v3, % 99.72/15.30 v18) = v19) | ~ $i(v18) | ? [v20: any] : ? [v21: any] % 99.72/15.30 : ? [v22: any] : (in(v19, v0) = v22 & in(v18, v8) = v21 & % 99.72/15.30 in(v18, v2) = v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) % 99.72/15.30 & ! [v18: $i] : ! [v19: $i] : ( ~ (apply(v3, v18) = v19) | % 99.72/15.30 ~ $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] : % 99.72/15.30 (in(v19, v0) = v21 & in(v18, v8) = v20 & in(v18, v2) = v22 & % 99.72/15.30 ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! [v18: $i] : % 99.72/15.30 ! [v19: $i] : ( ~ (apply(v3, v18) = v19) | ~ $i(v18) | ? % 99.72/15.30 [v20: any] : ? [v21: $i] : (apply(v1, v18) = v21 & in(v18, % 99.72/15.30 v2) = v20 & $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! % 99.72/15.30 [v18: $i] : ! [v19: $i] : ( ~ (apply(v1, v18) = v19) | ~ % 99.72/15.30 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v3, v18) = % 99.72/15.30 v21 & in(v18, v2) = v20 & $i(v21) & ( ~ (v20 = 0) | v21 = % 99.72/15.30 v19))) & ! [v18: $i] : ! [v19: any] : ( ~ (in(v18, v8) % 99.72/15.30 = v19) | ~ $i(v18) | ? [v20: any] : ? [v21: $i] : ? % 99.72/15.30 [v22: any] : (apply(v3, v18) = v21 & in(v21, v0) = v22 & % 99.72/15.30 in(v18, v2) = v20 & $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & % 99.72/15.30 v19 = 0)))) & ! [v18: $i] : ( ~ (in(v18, v8) = 0) | % 99.72/15.30 ~ $i(v18) | ? [v19: $i] : ? [v20: any] : ? [v21: any] : % 99.72/15.30 (apply(v3, v18) = v19 & in(v19, v0) = v20 & in(v18, v2) = % 99.72/15.30 v21 & $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] % 99.72/15.30 : ( ~ (in(v18, v2) = 0) | ~ $i(v18) | ? [v19: $i] : % 99.72/15.30 (apply(v3, v18) = v19 & apply(v1, v18) = v19 & $i(v19))) & % 99.72/15.30 ! [v18: $i] : ( ~ (in(v18, v2) = 0) | ~ $i(v18) | ? [v19: % 99.72/15.30 $i] : (apply(v3, v18) = v19 & in(v19, v0) = 0 & in(v18, % 99.72/15.30 v8) = 0 & $i(v19))))) & (v7 = v1 | (v10 = 0 & ~ (v12 = % 99.72/15.30 v11) & apply(v3, v9) = v12 & apply(v1, v9) = v11 & in(v9, % 99.72/15.30 v2) = 0 & $i(v12) & $i(v11)) | (apply(v3, v13) = v16 & % 99.72/15.30 in(v16, v0) = v17 & in(v13, v8) = v15 & in(v13, v2) = v14 & % 99.72/15.30 $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 = 0)) & (v14 % 99.72/15.30 = 0 | (v17 = 0 & v15 = 0))))))) | (function(v1) = v5 & % 99.72/15.30 relation(v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))) & ? [v0: $i] : ! % 99.72/15.30 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v1) = v2) | ~ % 99.72/15.30 (relation(v3) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 99.72/15.30 [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 99.72/15.30 [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? % 99.72/15.30 [v15: any] : ? [v16: $i] : ? [v17: any] : ($i(v13) & $i(v9) & % 99.72/15.30 ((relation_rng_restriction(v0, v3) = v7 & relation_dom(v3) = v8 & % 99.72/15.30 function(v3) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 = v1) | % 99.72/15.30 ( ! [v18: $i] : ! [v19: int] : (v19 = 0 | ~ (in(v18, v2) = % 99.72/15.30 v19) | ~ $i(v18) | ? [v20: any] : ? [v21: $i] : ? % 99.72/15.30 [v22: any] : (apply(v3, v18) = v21 & in(v21, v0) = v22 & % 99.72/15.30 in(v18, v8) = v20 & $i(v21) & ( ~ (v22 = 0) | ~ (v20 = % 99.72/15.30 0)))) & ! [v18: $i] : ! [v19: $i] : ( ~ (apply(v3, % 99.72/15.30 v18) = v19) | ~ $i(v18) | ? [v20: any] : ? [v21: any] % 99.72/15.30 : ? [v22: any] : (in(v19, v0) = v22 & in(v18, v8) = v21 & % 99.72/15.30 in(v18, v2) = v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) % 99.72/15.30 & ! [v18: $i] : ! [v19: $i] : ( ~ (apply(v3, v18) = v19) | % 99.72/15.30 ~ $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] : % 99.72/15.30 (in(v19, v0) = v21 & in(v18, v8) = v20 & in(v18, v2) = v22 & % 99.72/15.30 ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! [v18: $i] : % 99.72/15.30 ! [v19: $i] : ( ~ (apply(v3, v18) = v19) | ~ $i(v18) | ? % 99.72/15.30 [v20: any] : ? [v21: $i] : (apply(v1, v18) = v21 & in(v18, % 99.72/15.30 v2) = v20 & $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! % 99.72/15.30 [v18: $i] : ! [v19: $i] : ( ~ (apply(v1, v18) = v19) | ~ % 99.72/15.30 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v3, v18) = % 99.72/15.30 v21 & in(v18, v2) = v20 & $i(v21) & ( ~ (v20 = 0) | v21 = % 99.72/15.30 v19))) & ! [v18: $i] : ! [v19: any] : ( ~ (in(v18, v8) % 99.72/15.30 = v19) | ~ $i(v18) | ? [v20: any] : ? [v21: $i] : ? % 99.72/15.30 [v22: any] : (apply(v3, v18) = v21 & in(v21, v0) = v22 & % 99.72/15.30 in(v18, v2) = v20 & $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & % 99.72/15.30 v19 = 0)))) & ! [v18: $i] : ( ~ (in(v18, v8) = 0) | % 99.72/15.30 ~ $i(v18) | ? [v19: $i] : ? [v20: any] : ? [v21: any] : % 99.72/15.30 (apply(v3, v18) = v19 & in(v19, v0) = v20 & in(v18, v2) = % 99.72/15.30 v21 & $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] % 99.72/15.31 : ( ~ (in(v18, v2) = 0) | ~ $i(v18) | ? [v19: $i] : % 99.72/15.31 (apply(v3, v18) = v19 & apply(v1, v18) = v19 & $i(v19))) & % 99.72/15.31 ! [v18: $i] : ( ~ (in(v18, v2) = 0) | ~ $i(v18) | ? [v19: % 99.72/15.31 $i] : (apply(v3, v18) = v19 & in(v19, v0) = 0 & in(v18, % 99.72/15.31 v8) = 0 & $i(v19))))) & (v7 = v1 | (v10 = 0 & ~ (v12 = % 99.72/15.31 v11) & apply(v3, v9) = v12 & apply(v1, v9) = v11 & in(v9, % 99.72/15.31 v2) = 0 & $i(v12) & $i(v11)) | (apply(v3, v13) = v16 & % 99.72/15.31 in(v16, v0) = v17 & in(v13, v8) = v15 & in(v13, v2) = v14 & % 99.72/15.31 $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 = 0)) & (v14 % 99.72/15.31 = 0 | (v17 = 0 & v15 = 0))))))) | (function(v1) = v5 & % 99.72/15.31 relation(v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))) & ? [v0: $i] : ! % 99.72/15.31 [v1: $i] : ( ~ (function(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? % 99.72/15.31 [v3: $i] : (relation_dom(v1) = v3 & relation(v1) = v2 & $i(v3) & ( ~ (v2 = % 99.72/15.31 0) | ( ! [v4: $i] : ! [v5: $i] : ( ~ (relation_rng_restriction(v0, % 99.72/15.31 v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : ? [v8: % 99.72/15.31 $i] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: $i] : % 99.72/15.31 ? [v13: $i] : ? [v14: any] : ? [v15: any] : ? [v16: $i] : ? % 99.72/15.31 [v17: any] : (relation_dom(v4) = v8 & function(v4) = v7 & % 99.72/15.31 relation(v4) = v6 & $i(v13) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ % 99.72/15.31 (v6 = 0) | (( ~ (v5 = v1) | ( ! [v18: $i] : ! [v19: int] : (v19 % 99.72/15.31 = 0 | ~ (in(v18, v3) = v19) | ~ $i(v18) | ? [v20: % 99.72/15.31 any] : ? [v21: $i] : ? [v22: any] : (apply(v4, v18) % 99.72/15.31 = v21 & in(v21, v0) = v22 & in(v18, v8) = v20 & % 99.72/15.31 $i(v21) & ( ~ (v22 = 0) | ~ (v20 = 0)))) & ! [v18: % 99.72/15.31 $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] % 99.72/15.31 : (in(v19, v0) = v22 & in(v18, v8) = v21 & in(v18, v3) = % 99.72/15.31 v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & ! % 99.72/15.31 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] % 99.72/15.31 : (in(v19, v0) = v21 & in(v18, v8) = v20 & in(v18, v3) = % 99.72/15.31 v22 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! % 99.72/15.31 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18) % 99.72/15.31 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) | % 99.72/15.31 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~ % 99.72/15.31 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ? % 99.72/15.31 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 & % 99.72/15.31 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i] % 99.72/15.31 : ! [v19: any] : ( ~ (in(v18, v8) = v19) | ~ $i(v18) | % 99.72/15.31 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4, % 99.72/15.31 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 & % 99.72/15.31 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & ! % 99.72/15.31 [v18: $i] : ( ~ (in(v18, v8) = 0) | ~ $i(v18) | ? [v19: % 99.72/15.31 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18) % 99.72/15.31 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 & % 99.72/15.31 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] : % 99.72/15.31 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] : % 99.72/15.31 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19))) % 99.72/15.31 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? % 99.72/15.31 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 & % 99.72/15.31 in(v18, v8) = 0 & $i(v19))))) & (v5 = v1 | (v10 = 0 & % 99.72/15.31 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11 % 99.72/15.31 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) = % 99.72/15.31 v16 & in(v16, v0) = v17 & in(v13, v8) = v15 & in(v13, v3) % 99.72/15.31 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 = % 99.72/15.31 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4: % 99.72/15.31 $i] : ! [v5: $i] : ( ~ (relation_dom(v4) = v5) | ~ $i(v4) | ? % 99.72/15.31 [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] % 99.72/15.31 : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? % 99.72/15.31 [v15: any] : ? [v16: $i] : ? [v17: any] : % 99.72/15.31 (relation_rng_restriction(v0, v4) = v8 & function(v4) = v7 & % 99.72/15.31 relation(v4) = v6 & $i(v13) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ % 99.72/15.31 (v6 = 0) | (( ~ (v8 = v1) | ( ! [v18: $i] : ! [v19: int] : (v19 % 99.72/15.31 = 0 | ~ (in(v18, v3) = v19) | ~ $i(v18) | ? [v20: % 99.72/15.31 any] : ? [v21: $i] : ? [v22: any] : (apply(v4, v18) % 99.72/15.31 = v21 & in(v21, v0) = v22 & in(v18, v5) = v20 & % 99.72/15.31 $i(v21) & ( ~ (v22 = 0) | ~ (v20 = 0)))) & ! [v18: % 99.72/15.31 $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] % 99.72/15.31 : (in(v19, v0) = v22 & in(v18, v5) = v21 & in(v18, v3) = % 99.72/15.31 v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & ! % 99.72/15.31 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] % 99.72/15.31 : (in(v19, v0) = v21 & in(v18, v5) = v20 & in(v18, v3) = % 99.72/15.31 v22 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! % 99.72/15.31 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.31 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18) % 99.72/15.31 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) | % 99.72/15.31 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~ % 99.72/15.31 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ? % 99.72/15.31 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 & % 99.72/15.31 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i] % 99.72/15.31 : ! [v19: any] : ( ~ (in(v18, v5) = v19) | ~ $i(v18) | % 99.72/15.31 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4, % 99.72/15.31 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 & % 99.72/15.31 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & ! % 99.72/15.31 [v18: $i] : ( ~ (in(v18, v5) = 0) | ~ $i(v18) | ? [v19: % 99.72/15.31 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18) % 99.72/15.31 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 & % 99.72/15.31 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] : % 99.72/15.31 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] : % 99.72/15.31 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19))) % 99.72/15.31 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? % 99.72/15.31 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 & % 99.72/15.31 in(v18, v5) = 0 & $i(v19))))) & (v8 = v1 | (v10 = 0 & % 99.72/15.31 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11 % 99.72/15.31 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) = % 99.72/15.31 v16 & in(v16, v0) = v17 & in(v13, v5) = v15 & in(v13, v3) % 99.72/15.31 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 = % 99.72/15.31 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4: % 99.72/15.31 $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: % 99.72/15.31 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? % 99.72/15.31 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15: % 99.72/15.31 $i] : ? [v16: any] : (relation_rng_restriction(v0, v4) = v6 & % 99.72/15.31 relation_dom(v4) = v7 & relation(v4) = v5 & $i(v12) & $i(v8) & % 99.72/15.31 $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1) | ( ! [v17: $i] : % 99.72/15.31 ! [v18: int] : (v18 = 0 | ~ (in(v17, v3) = v18) | ~ % 99.72/15.31 $i(v17) | ? [v19: any] : ? [v20: $i] : ? [v21: any] : % 99.72/15.31 (apply(v4, v17) = v20 & in(v20, v0) = v21 & in(v17, v7) % 99.72/15.31 = v19 & $i(v20) & ( ~ (v21 = 0) | ~ (v19 = 0)))) & ! % 99.72/15.31 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.31 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any] % 99.72/15.31 : (in(v18, v0) = v21 & in(v17, v7) = v20 & in(v17, v3) = % 99.72/15.31 v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & ! % 99.72/15.31 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.31 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any] % 99.72/15.31 : (in(v18, v0) = v20 & in(v17, v7) = v19 & in(v17, v3) = % 99.72/15.31 v21 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & ! % 99.72/15.31 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.31 $i(v17) | ? [v19: any] : ? [v20: $i] : (apply(v1, v17) % 99.72/15.31 = v20 & in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) | % 99.72/15.31 v20 = v18))) & ! [v17: $i] : ! [v18: $i] : ( ~ % 99.72/15.31 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ? % 99.72/15.31 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 & % 99.72/15.31 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i] % 99.72/15.31 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) | % 99.72/15.31 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4, % 99.72/15.31 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 & % 99.72/15.31 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & ! % 99.72/15.31 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18: % 99.72/15.31 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17) % 99.72/15.31 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 & % 99.72/15.31 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] : % 99.72/15.31 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] : % 99.72/15.31 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18))) % 99.72/15.31 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? % 99.72/15.31 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 & % 99.72/15.31 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 & % 99.72/15.31 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10 % 99.72/15.31 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) = % 99.72/15.31 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3) % 99.72/15.31 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 = % 99.72/15.31 0)) & (v13 = 0 | (v16 = 0 & v14 = 0)))))))) & ! [v4: % 99.72/15.31 $i] : ( ~ (relation(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: % 99.72/15.31 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? % 99.72/15.31 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15: % 99.72/15.31 $i] : ? [v16: any] : (relation_rng_restriction(v0, v4) = v6 & % 99.72/15.31 relation_dom(v4) = v7 & function(v4) = v5 & $i(v12) & $i(v8) & % 99.72/15.32 $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1) | ( ! [v17: $i] : % 99.72/15.32 ! [v18: int] : (v18 = 0 | ~ (in(v17, v3) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : ? [v21: any] : % 99.72/15.32 (apply(v4, v17) = v20 & in(v20, v0) = v21 & in(v17, v7) % 99.72/15.32 = v19 & $i(v20) & ( ~ (v21 = 0) | ~ (v19 = 0)))) & ! % 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any] % 99.72/15.32 : (in(v18, v0) = v21 & in(v17, v7) = v20 & in(v17, v3) = % 99.72/15.32 v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & ! % 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any] % 99.72/15.32 : (in(v18, v0) = v20 & in(v17, v7) = v19 & in(v17, v3) = % 99.72/15.32 v21 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & ! % 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : (apply(v1, v17) % 99.72/15.32 = v20 & in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) | % 99.72/15.32 v20 = v18))) & ! [v17: $i] : ! [v18: $i] : ( ~ % 99.72/15.32 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ? % 99.72/15.32 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 & % 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i] % 99.72/15.32 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) | % 99.72/15.32 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4, % 99.72/15.32 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 & % 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & ! % 99.72/15.32 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18: % 99.72/15.32 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17) % 99.72/15.32 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 & % 99.72/15.32 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] : % 99.72/15.32 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] : % 99.72/15.32 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18))) % 99.72/15.32 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? % 99.72/15.32 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 & % 99.72/15.32 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 & % 99.72/15.32 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10 % 99.72/15.32 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) = % 99.72/15.32 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3) % 99.72/15.32 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 = % 99.72/15.32 0)) & (v13 = 0 | (v16 = 0 & v14 = 0)))))))))))) & ? % 99.72/15.32 [v0: $i] : ! [v1: $i] : ( ~ (relation(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 99.72/15.32 [v2: any] : ? [v3: $i] : (relation_dom(v1) = v3 & function(v1) = v2 & % 99.72/15.32 $i(v3) & ( ~ (v2 = 0) | ( ! [v4: $i] : ! [v5: $i] : ( ~ % 99.72/15.32 (relation_rng_restriction(v0, v4) = v5) | ~ $i(v4) | ? [v6: any] : % 99.72/15.32 ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: % 99.72/15.32 $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15: any] % 99.72/15.32 : ? [v16: $i] : ? [v17: any] : (relation_dom(v4) = v8 & % 99.72/15.32 function(v4) = v7 & relation(v4) = v6 & $i(v13) & $i(v9) & $i(v8) % 99.72/15.32 & ( ~ (v7 = 0) | ~ (v6 = 0) | (( ~ (v5 = v1) | ( ! [v18: $i] : ! % 99.72/15.32 [v19: int] : (v19 = 0 | ~ (in(v18, v3) = v19) | ~ % 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: $i] : ? [v22: any] : % 99.72/15.32 (apply(v4, v18) = v21 & in(v21, v0) = v22 & in(v18, v8) % 99.72/15.32 = v20 & $i(v21) & ( ~ (v22 = 0) | ~ (v20 = 0)))) & ! % 99.72/15.32 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] % 99.72/15.32 : (in(v19, v0) = v22 & in(v18, v8) = v21 & in(v18, v3) = % 99.72/15.32 v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & ! % 99.72/15.32 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] % 99.72/15.32 : (in(v19, v0) = v21 & in(v18, v8) = v20 & in(v18, v3) = % 99.72/15.32 v22 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! % 99.72/15.32 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18) % 99.72/15.32 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) | % 99.72/15.32 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~ % 99.72/15.32 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ? % 99.72/15.32 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 & % 99.72/15.32 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i] % 99.72/15.32 : ! [v19: any] : ( ~ (in(v18, v8) = v19) | ~ $i(v18) | % 99.72/15.32 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4, % 99.72/15.32 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 & % 99.72/15.32 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & ! % 99.72/15.32 [v18: $i] : ( ~ (in(v18, v8) = 0) | ~ $i(v18) | ? [v19: % 99.72/15.32 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18) % 99.72/15.32 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 & % 99.72/15.32 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] : % 99.72/15.32 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] : % 99.72/15.32 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19))) % 99.72/15.32 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? % 99.72/15.32 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 & % 99.72/15.32 in(v18, v8) = 0 & $i(v19))))) & (v5 = v1 | (v10 = 0 & % 99.72/15.32 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11 % 99.72/15.32 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) = % 99.72/15.32 v16 & in(v16, v0) = v17 & in(v13, v8) = v15 & in(v13, v3) % 99.72/15.32 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 = % 99.72/15.32 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4: % 99.72/15.32 $i] : ! [v5: $i] : ( ~ (relation_dom(v4) = v5) | ~ $i(v4) | ? % 99.72/15.32 [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] % 99.72/15.32 : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? % 99.72/15.32 [v15: any] : ? [v16: $i] : ? [v17: any] : % 99.72/15.32 (relation_rng_restriction(v0, v4) = v8 & function(v4) = v7 & % 99.72/15.32 relation(v4) = v6 & $i(v13) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ % 99.72/15.32 (v6 = 0) | (( ~ (v8 = v1) | ( ! [v18: $i] : ! [v19: int] : (v19 % 99.72/15.32 = 0 | ~ (in(v18, v3) = v19) | ~ $i(v18) | ? [v20: % 99.72/15.32 any] : ? [v21: $i] : ? [v22: any] : (apply(v4, v18) % 99.72/15.32 = v21 & in(v21, v0) = v22 & in(v18, v5) = v20 & % 99.72/15.32 $i(v21) & ( ~ (v22 = 0) | ~ (v20 = 0)))) & ! [v18: % 99.72/15.32 $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] % 99.72/15.32 : (in(v19, v0) = v22 & in(v18, v5) = v21 & in(v18, v3) = % 99.72/15.32 v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & ! % 99.72/15.32 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: any] : ? [v22: any] % 99.72/15.32 : (in(v19, v0) = v21 & in(v18, v5) = v20 & in(v18, v3) = % 99.72/15.32 v22 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! % 99.72/15.32 [v18: $i] : ! [v19: $i] : ( ~ (apply(v4, v18) = v19) | ~ % 99.72/15.32 $i(v18) | ? [v20: any] : ? [v21: $i] : (apply(v1, v18) % 99.72/15.32 = v21 & in(v18, v3) = v20 & $i(v21) & ( ~ (v20 = 0) | % 99.72/15.32 v21 = v19))) & ! [v18: $i] : ! [v19: $i] : ( ~ % 99.72/15.32 (apply(v1, v18) = v19) | ~ $i(v18) | ? [v20: any] : ? % 99.72/15.32 [v21: $i] : (apply(v4, v18) = v21 & in(v18, v3) = v20 & % 99.72/15.32 $i(v21) & ( ~ (v20 = 0) | v21 = v19))) & ! [v18: $i] % 99.72/15.32 : ! [v19: any] : ( ~ (in(v18, v5) = v19) | ~ $i(v18) | % 99.72/15.32 ? [v20: any] : ? [v21: $i] : ? [v22: any] : (apply(v4, % 99.72/15.32 v18) = v21 & in(v21, v0) = v22 & in(v18, v3) = v20 & % 99.72/15.32 $i(v21) & ( ~ (v20 = 0) | (v22 = 0 & v19 = 0)))) & ! % 99.72/15.32 [v18: $i] : ( ~ (in(v18, v5) = 0) | ~ $i(v18) | ? [v19: % 99.72/15.32 $i] : ? [v20: any] : ? [v21: any] : (apply(v4, v18) % 99.72/15.32 = v19 & in(v19, v0) = v20 & in(v18, v3) = v21 & % 99.72/15.32 $i(v19) & ( ~ (v20 = 0) | v21 = 0))) & ! [v18: $i] : % 99.72/15.32 ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? [v19: $i] : % 99.72/15.32 (apply(v4, v18) = v19 & apply(v1, v18) = v19 & $i(v19))) % 99.72/15.32 & ! [v18: $i] : ( ~ (in(v18, v3) = 0) | ~ $i(v18) | ? % 99.72/15.32 [v19: $i] : (apply(v4, v18) = v19 & in(v19, v0) = 0 & % 99.72/15.32 in(v18, v5) = 0 & $i(v19))))) & (v8 = v1 | (v10 = 0 & % 99.72/15.32 ~ (v12 = v11) & apply(v4, v9) = v12 & apply(v1, v9) = v11 % 99.72/15.32 & in(v9, v3) = 0 & $i(v12) & $i(v11)) | (apply(v4, v13) = % 99.72/15.32 v16 & in(v16, v0) = v17 & in(v13, v5) = v15 & in(v13, v3) % 99.72/15.32 = v14 & $i(v16) & ( ~ (v17 = 0) | ~ (v15 = 0) | ~ (v14 = % 99.72/15.32 0)) & (v14 = 0 | (v17 = 0 & v15 = 0)))))))) & ! [v4: % 99.72/15.32 $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: % 99.72/15.32 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? % 99.72/15.32 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15: % 99.72/15.32 $i] : ? [v16: any] : (relation_rng_restriction(v0, v4) = v6 & % 99.72/15.32 relation_dom(v4) = v7 & relation(v4) = v5 & $i(v12) & $i(v8) & % 99.72/15.32 $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1) | ( ! [v17: $i] : % 99.72/15.32 ! [v18: int] : (v18 = 0 | ~ (in(v17, v3) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : ? [v21: any] : % 99.72/15.32 (apply(v4, v17) = v20 & in(v20, v0) = v21 & in(v17, v7) % 99.72/15.32 = v19 & $i(v20) & ( ~ (v21 = 0) | ~ (v19 = 0)))) & ! % 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any] % 99.72/15.32 : (in(v18, v0) = v21 & in(v17, v7) = v20 & in(v17, v3) = % 99.72/15.32 v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & ! % 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any] % 99.72/15.32 : (in(v18, v0) = v20 & in(v17, v7) = v19 & in(v17, v3) = % 99.72/15.32 v21 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & ! % 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : (apply(v1, v17) % 99.72/15.32 = v20 & in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) | % 99.72/15.32 v20 = v18))) & ! [v17: $i] : ! [v18: $i] : ( ~ % 99.72/15.32 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ? % 99.72/15.32 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 & % 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i] % 99.72/15.32 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) | % 99.72/15.32 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4, % 99.72/15.32 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 & % 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & ! % 99.72/15.32 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18: % 99.72/15.32 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17) % 99.72/15.32 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 & % 99.72/15.32 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] : % 99.72/15.32 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] : % 99.72/15.32 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18))) % 99.72/15.32 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? % 99.72/15.32 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 & % 99.72/15.32 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 & % 99.72/15.32 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10 % 99.72/15.32 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) = % 99.72/15.32 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3) % 99.72/15.32 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 = % 99.72/15.32 0)) & (v13 = 0 | (v16 = 0 & v14 = 0)))))))) & ! [v4: % 99.72/15.32 $i] : ( ~ (relation(v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: % 99.72/15.32 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? % 99.72/15.32 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: any] : ? [v15: % 99.72/15.32 $i] : ? [v16: any] : (relation_rng_restriction(v0, v4) = v6 & % 99.72/15.32 relation_dom(v4) = v7 & function(v4) = v5 & $i(v12) & $i(v8) & % 99.72/15.32 $i(v7) & $i(v6) & ( ~ (v5 = 0) | (( ~ (v6 = v1) | ( ! [v17: $i] : % 99.72/15.32 ! [v18: int] : (v18 = 0 | ~ (in(v17, v3) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : ? [v21: any] : % 99.72/15.32 (apply(v4, v17) = v20 & in(v20, v0) = v21 & in(v17, v7) % 99.72/15.32 = v19 & $i(v20) & ( ~ (v21 = 0) | ~ (v19 = 0)))) & ! % 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any] % 99.72/15.32 : (in(v18, v0) = v21 & in(v17, v7) = v20 & in(v17, v3) = % 99.72/15.32 v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & ! % 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: any] : ? [v21: any] % 99.72/15.32 : (in(v18, v0) = v20 & in(v17, v7) = v19 & in(v17, v3) = % 99.72/15.32 v21 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & ! % 99.72/15.32 [v17: $i] : ! [v18: $i] : ( ~ (apply(v4, v17) = v18) | ~ % 99.72/15.32 $i(v17) | ? [v19: any] : ? [v20: $i] : (apply(v1, v17) % 99.72/15.32 = v20 & in(v17, v3) = v19 & $i(v20) & ( ~ (v19 = 0) | % 99.72/15.32 v20 = v18))) & ! [v17: $i] : ! [v18: $i] : ( ~ % 99.72/15.32 (apply(v1, v17) = v18) | ~ $i(v17) | ? [v19: any] : ? % 99.72/15.32 [v20: $i] : (apply(v4, v17) = v20 & in(v17, v3) = v19 & % 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | v20 = v18))) & ! [v17: $i] % 99.72/15.32 : ! [v18: any] : ( ~ (in(v17, v7) = v18) | ~ $i(v17) | % 99.72/15.32 ? [v19: any] : ? [v20: $i] : ? [v21: any] : (apply(v4, % 99.72/15.32 v17) = v20 & in(v20, v0) = v21 & in(v17, v3) = v19 & % 99.72/15.32 $i(v20) & ( ~ (v19 = 0) | (v21 = 0 & v18 = 0)))) & ! % 99.72/15.32 [v17: $i] : ( ~ (in(v17, v7) = 0) | ~ $i(v17) | ? [v18: % 99.72/15.32 $i] : ? [v19: any] : ? [v20: any] : (apply(v4, v17) % 99.72/15.32 = v18 & in(v18, v0) = v19 & in(v17, v3) = v20 & % 99.72/15.32 $i(v18) & ( ~ (v19 = 0) | v20 = 0))) & ! [v17: $i] : % 99.72/15.32 ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? [v18: $i] : % 99.72/15.32 (apply(v4, v17) = v18 & apply(v1, v17) = v18 & $i(v18))) % 99.72/15.32 & ! [v17: $i] : ( ~ (in(v17, v3) = 0) | ~ $i(v17) | ? % 99.72/15.32 [v18: $i] : (apply(v4, v17) = v18 & in(v18, v0) = 0 & % 99.72/15.32 in(v17, v7) = 0 & $i(v18))))) & (v6 = v1 | (v9 = 0 & % 99.72/15.32 ~ (v11 = v10) & apply(v4, v8) = v11 & apply(v1, v8) = v10 % 99.72/15.32 & in(v8, v3) = 0 & $i(v11) & $i(v10)) | (apply(v4, v12) = % 99.72/15.33 v15 & in(v15, v0) = v16 & in(v12, v7) = v14 & in(v12, v3) % 99.72/15.33 = v13 & $i(v15) & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 = % 99.72/15.33 0)) & (v13 = 0 | (v16 = 0 & v14 = 0)))))))))))) % 99.72/15.33 % 99.72/15.33 (t86_funct_1) % 99.72/15.33 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 99.72/15.33 any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (apply(v2, % 99.72/15.33 v1) = v8 & relation_rng_restriction(v0, v2) = v3 & in(v8, v0) = v9 & % 99.72/15.33 in(v1, v6) = v7 & in(v1, v4) = v5 & relation_dom(v3) = v4 & relation_dom(v2) % 99.72/15.33 = v6 & function(v2) = 0 & relation(v2) = 0 & $i(v8) & $i(v6) & $i(v4) & % 99.72/15.33 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v9 = 0 & v7 = 0 & ~ (v5 = 0)) | (v5 = % 99.72/15.33 0 & ( ~ (v9 = 0) | ~ (v7 = 0))))) % 99.72/15.33 % 99.72/15.33 (function-axioms) % 99.72/15.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 99.72/15.33 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 99.72/15.33 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) % 99.72/15.33 = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0: % 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 99.72/15.33 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 99.72/15.33 : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: % 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 99.72/15.33 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 99.72/15.33 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 99.72/15.33 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 99.72/15.33 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: % 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 99.72/15.33 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: % 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 99.72/15.33 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] % 99.72/15.33 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 99.72/15.33 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 99.72/15.33 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 99.72/15.33 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: % 99.72/15.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 99.72/15.33 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 99.72/15.33 % 99.72/15.33 Further assumptions not needed in the proof: % 99.72/15.33 -------------------------------------------- % 99.72/15.33 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, existence_m1_subset_1, % 99.72/15.33 fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, fc7_relat_1, rc1_funct_1, % 99.72/15.34 rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_subset_1, % 99.72/15.34 rc2_xboole_0, rc3_funct_1, rc3_relat_1, reflexivity_r1_tarski, t1_subset, % 99.72/15.34 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 99.72/15.34 % 99.72/15.34 Those formulas are unsatisfiable: % 99.72/15.34 --------------------------------- % 99.72/15.34 % 99.72/15.34 Begin of proof % 99.72/15.34 | % 99.72/15.34 | ALPHA: (cc2_funct_1) implies: % 99.72/15.34 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 99.72/15.34 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & % 99.72/15.34 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 99.72/15.34 | (2) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 99.72/15.34 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & empty(v0) = v2 & % 99.72/15.34 | relation(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 99.72/15.34 | % 99.72/15.34 | ALPHA: (fc5_relat_1) implies: % 99.72/15.34 | (3) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 99.72/15.34 | [v2: $i] : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 & % 99.72/15.34 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0))) % 99.72/15.34 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 99.72/15.34 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & % 99.72/15.34 | empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | % 99.72/15.34 | v2 = 0))) % 99.72/15.34 | % 99.72/15.34 | ALPHA: (t85_funct_1) implies: % 99.72/15.35 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 99.72/15.35 | ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) = % 99.72/15.35 | v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 99.72/15.35 | any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : % 99.72/15.36 | ? [v11: int] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: % 99.72/15.36 | any] : ? [v16: any] : ? [v17: $i] : ? [v18: any] : ($i(v14) & % 99.72/15.36 | $i(v10) & ((relation_dom(v3) = v9 & function(v3) = v8 & % 99.72/15.36 | relation(v3) = v7 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ % 99.72/15.36 | (v4 = v1) | ( ! [v19: $i] : ! [v20: int] : (v20 = 0 | ~ % 99.72/15.36 | (in(v19, v2) = v20) | ~ $i(v19) | ? [v21: any] : ? % 99.72/15.36 | [v22: $i] : ? [v23: any] : (apply(v3, v19) = v22 & % 99.72/15.36 | in(v22, v0) = v23 & in(v19, v9) = v21 & $i(v22) & ( % 99.72/15.36 | ~ (v23 = 0) | ~ (v21 = 0)))) & ! [v19: $i] : ! % 99.72/15.36 | [v20: $i] : ( ~ (apply(v3, v19) = v20) | ~ $i(v19) | % 99.72/15.36 | ? [v21: any] : ? [v22: any] : ? [v23: any] : % 99.72/15.36 | (in(v20, v0) = v23 & in(v19, v9) = v22 & in(v19, v2) % 99.72/15.36 | = v21 & ( ~ (v21 = 0) | (v23 = 0 & v22 = 0)))) & ! % 99.72/15.36 | [v19: $i] : ! [v20: $i] : ( ~ (apply(v3, v19) = v20) | % 99.72/15.36 | ~ $i(v19) | ? [v21: any] : ? [v22: any] : ? [v23: % 99.72/15.36 | any] : (in(v20, v0) = v22 & in(v19, v9) = v21 & % 99.72/15.36 | in(v19, v2) = v23 & ( ~ (v22 = 0) | ~ (v21 = 0) | % 99.72/15.36 | v23 = 0))) & ! [v19: $i] : ! [v20: $i] : ( ~ % 99.72/15.36 | (apply(v3, v19) = v20) | ~ $i(v19) | ? [v21: any] : % 99.72/15.36 | ? [v22: $i] : (apply(v1, v19) = v22 & in(v19, v2) = % 99.72/15.36 | v21 & $i(v22) & ( ~ (v21 = 0) | v22 = v20))) & ! % 99.72/15.36 | [v19: $i] : ! [v20: $i] : ( ~ (apply(v1, v19) = v20) | % 99.72/15.36 | ~ $i(v19) | ? [v21: any] : ? [v22: $i] : % 99.72/15.36 | (apply(v3, v19) = v22 & in(v19, v2) = v21 & $i(v22) & % 99.72/15.36 | ( ~ (v21 = 0) | v22 = v20))) & ! [v19: $i] : ! % 99.72/15.36 | [v20: any] : ( ~ (in(v19, v9) = v20) | ~ $i(v19) | ? % 99.72/15.36 | [v21: any] : ? [v22: $i] : ? [v23: any] : % 99.72/15.36 | (apply(v3, v19) = v22 & in(v22, v0) = v23 & in(v19, % 99.72/15.36 | v2) = v21 & $i(v22) & ( ~ (v21 = 0) | (v23 = 0 & % 99.72/15.36 | v20 = 0)))) & ! [v19: $i] : ( ~ (in(v19, v9) = % 99.72/15.36 | 0) | ~ $i(v19) | ? [v20: $i] : ? [v21: any] : ? % 99.72/15.36 | [v22: any] : (apply(v3, v19) = v20 & in(v20, v0) = % 99.72/15.36 | v21 & in(v19, v2) = v22 & $i(v20) & ( ~ (v21 = 0) | % 99.72/15.36 | v22 = 0))) & ! [v19: $i] : ( ~ (in(v19, v2) = 0) % 99.72/15.36 | | ~ $i(v19) | ? [v20: $i] : (apply(v3, v19) = v20 & % 99.72/15.36 | apply(v1, v19) = v20 & $i(v20))) & ! [v19: $i] : ( % 99.72/15.36 | ~ (in(v19, v2) = 0) | ~ $i(v19) | ? [v20: $i] : % 99.72/15.36 | (apply(v3, v19) = v20 & in(v20, v0) = 0 & in(v19, v9) % 99.72/15.36 | = 0 & $i(v20))))) & (v4 = v1 | (v11 = 0 & ~ (v13 = % 99.72/15.36 | v12) & apply(v3, v10) = v13 & apply(v1, v10) = v12 & % 99.72/15.36 | in(v10, v2) = 0 & $i(v13) & $i(v12)) | (apply(v3, v14) % 99.72/15.36 | = v17 & in(v17, v0) = v18 & in(v14, v9) = v16 & in(v14, % 99.72/15.36 | v2) = v15 & $i(v17) & ( ~ (v18 = 0) | ~ (v16 = 0) | % 99.72/15.36 | ~ (v15 = 0)) & (v15 = 0 | (v18 = 0 & v16 = 0))))))) | % 99.72/15.36 | (function(v1) = v6 & relation(v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 99.72/15.36 | 0)))))) % 99.72/15.36 | % 99.72/15.36 | ALPHA: (function-axioms) implies: % 99.72/15.36 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 99.72/15.36 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 99.72/15.36 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 99.72/15.36 | (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 99.72/15.36 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 99.72/15.36 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 99.72/15.36 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 99.72/15.36 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 99.72/15.36 | % 99.72/15.36 | DELTA: instantiating (t86_funct_1) with fresh symbols all_42_0, all_42_1, % 99.72/15.36 | all_42_2, all_42_3, all_42_4, all_42_5, all_42_6, all_42_7, all_42_8, % 99.72/15.36 | all_42_9 gives: % 99.72/15.36 | (10) apply(all_42_7, all_42_8) = all_42_1 & % 99.72/15.36 | relation_rng_restriction(all_42_9, all_42_7) = all_42_6 & in(all_42_1, % 99.72/15.36 | all_42_9) = all_42_0 & in(all_42_8, all_42_3) = all_42_2 & % 99.72/15.36 | in(all_42_8, all_42_5) = all_42_4 & relation_dom(all_42_6) = all_42_5 % 99.72/15.36 | & relation_dom(all_42_7) = all_42_3 & function(all_42_7) = 0 & % 99.72/15.36 | relation(all_42_7) = 0 & $i(all_42_1) & $i(all_42_3) & $i(all_42_5) & % 99.72/15.36 | $i(all_42_6) & $i(all_42_7) & $i(all_42_8) & $i(all_42_9) & ((all_42_0 % 99.72/15.36 | = 0 & all_42_2 = 0 & ~ (all_42_4 = 0)) | (all_42_4 = 0 & ( ~ % 99.72/15.36 | (all_42_0 = 0) | ~ (all_42_2 = 0)))) % 99.72/15.36 | % 99.72/15.36 | ALPHA: (10) implies: % 99.72/15.36 | (11) $i(all_42_9) % 99.72/15.36 | (12) $i(all_42_8) % 99.72/15.36 | (13) $i(all_42_7) % 99.72/15.36 | (14) $i(all_42_6) % 99.72/15.36 | (15) relation(all_42_7) = 0 % 99.72/15.36 | (16) function(all_42_7) = 0 % 99.72/15.36 | (17) relation_dom(all_42_7) = all_42_3 % 99.72/15.36 | (18) relation_dom(all_42_6) = all_42_5 % 99.72/15.36 | (19) in(all_42_8, all_42_5) = all_42_4 % 99.72/15.36 | (20) in(all_42_8, all_42_3) = all_42_2 % 99.72/15.36 | (21) in(all_42_1, all_42_9) = all_42_0 % 99.72/15.36 | (22) relation_rng_restriction(all_42_9, all_42_7) = all_42_6 % 99.72/15.36 | (23) apply(all_42_7, all_42_8) = all_42_1 % 99.72/15.36 | (24) (all_42_0 = 0 & all_42_2 = 0 & ~ (all_42_4 = 0)) | (all_42_4 = 0 & ( % 99.72/15.36 | ~ (all_42_0 = 0) | ~ (all_42_2 = 0))) % 99.72/15.36 | % 99.72/15.37 | GROUND_INST: instantiating (3) with all_42_7, simplifying with (13), (15) % 99.72/15.37 | gives: % 99.72/15.37 | (25) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_42_7) = % 99.72/15.37 | v1 & empty(v1) = v2 & empty(all_42_7) = v0 & $i(v1) & ( ~ (v2 = 0) | % 99.72/15.37 | v0 = 0)) % 99.72/15.37 | % 99.72/15.37 | GROUND_INST: instantiating (1) with all_42_7, simplifying with (13), (15) % 99.72/15.37 | gives: % 99.72/15.37 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_42_7) = % 99.72/15.37 | v2 & function(all_42_7) = v1 & empty(all_42_7) = v0 & ( ~ (v1 = 0) | % 99.72/15.37 | ~ (v0 = 0) | v2 = 0)) % 99.72/15.37 | % 99.72/15.37 | GROUND_INST: instantiating (2) with all_42_7, simplifying with (13), (16) % 99.72/15.37 | gives: % 99.72/15.37 | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_42_7) = % 99.72/15.37 | v2 & empty(all_42_7) = v1 & relation(all_42_7) = v0 & ( ~ (v1 = 0) | % 99.72/15.37 | ~ (v0 = 0) | v2 = 0)) % 99.72/15.37 | % 99.72/15.37 | GROUND_INST: instantiating (4) with all_42_7, all_42_3, simplifying with (13), % 99.72/15.37 | (17) gives: % 99.72/15.37 | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_42_3) = v2 & % 99.72/15.37 | empty(all_42_7) = v0 & relation(all_42_7) = v1 & ( ~ (v2 = 0) | ~ % 99.72/15.37 | (v1 = 0) | v0 = 0)) % 99.72/15.37 | % 99.72/15.37 | GROUND_INST: instantiating (4) with all_42_6, all_42_5, simplifying with (14), % 99.72/15.37 | (18) gives: % 99.72/15.37 | (29) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_42_5) = v2 & % 99.72/15.37 | empty(all_42_6) = v0 & relation(all_42_6) = v1 & ( ~ (v2 = 0) | ~ % 99.72/15.37 | (v1 = 0) | v0 = 0)) % 99.72/15.37 | % 99.72/15.37 | GROUND_INST: instantiating (5) with all_42_9, all_42_6, all_42_5, all_42_7, % 99.72/15.37 | all_42_6, simplifying with (11), (13), (14), (18), (22) gives: % 100.16/15.38 | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 100.16/15.38 | $i] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & % 100.16/15.38 | ((relation_dom(all_42_7) = v4 & function(all_42_7) = v3 & % 100.16/15.38 | relation(all_42_7) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | % 100.16/15.38 | ( ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (in(v7, all_42_5) = % 100.16/15.38 | v8) | ~ $i(v7) | ? [v9: any] : ? [v10: $i] : ? [v11: % 100.16/15.38 | any] : (apply(all_42_7, v7) = v10 & in(v10, all_42_9) = % 100.16/15.38 | v11 & in(v7, v4) = v9 & $i(v10) & ( ~ (v11 = 0) | ~ (v9 % 100.16/15.38 | = 0)))) & ! [v7: $i] : ! [v8: $i] : ( ~ % 100.16/15.38 | (apply(all_42_6, v7) = v8) | ~ $i(v7) | ? [v9: any] : ? % 100.16/15.38 | [v10: $i] : (apply(all_42_7, v7) = v10 & in(v7, all_42_5) % 100.16/15.38 | = v9 & $i(v10) & ( ~ (v9 = 0) | v10 = v8))) & ! [v7: % 100.16/15.38 | $i] : ! [v8: $i] : ( ~ (apply(all_42_7, v7) = v8) | ~ % 100.16/15.38 | $i(v7) | ? [v9: any] : ? [v10: any] : ? [v11: any] : % 100.16/15.38 | (in(v8, all_42_9) = v11 & in(v7, v4) = v10 & in(v7, % 100.16/15.38 | all_42_5) = v9 & ( ~ (v9 = 0) | (v11 = 0 & v10 = 0)))) % 100.16/15.38 | & ! [v7: $i] : ! [v8: $i] : ( ~ (apply(all_42_7, v7) = v8) % 100.16/15.38 | | ~ $i(v7) | ? [v9: any] : ? [v10: any] : ? [v11: any] % 100.16/15.38 | : (in(v8, all_42_9) = v10 & in(v7, v4) = v9 & in(v7, % 100.16/15.38 | all_42_5) = v11 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = % 100.16/15.38 | 0))) & ! [v7: $i] : ! [v8: $i] : ( ~ % 100.16/15.38 | (apply(all_42_7, v7) = v8) | ~ $i(v7) | ? [v9: any] : ? % 100.16/15.38 | [v10: $i] : (apply(all_42_6, v7) = v10 & in(v7, all_42_5) % 100.16/15.38 | = v9 & $i(v10) & ( ~ (v9 = 0) | v10 = v8))) & ! [v7: % 100.16/15.38 | $i] : ! [v8: any] : ( ~ (in(v7, v4) = v8) | ~ $i(v7) | % 100.16/15.38 | ? [v9: any] : ? [v10: $i] : ? [v11: any] : % 100.16/15.38 | (apply(all_42_7, v7) = v10 & in(v10, all_42_9) = v11 & % 100.16/15.38 | in(v7, all_42_5) = v9 & $i(v10) & ( ~ (v9 = 0) | (v11 = % 100.16/15.38 | 0 & v8 = 0)))) & ! [v7: $i] : ( ~ (in(v7, v4) = 0) % 100.16/15.38 | | ~ $i(v7) | ? [v8: $i] : ? [v9: any] : ? [v10: any] : % 100.16/15.38 | (apply(all_42_7, v7) = v8 & in(v8, all_42_9) = v9 & in(v7, % 100.16/15.38 | all_42_5) = v10 & $i(v8) & ( ~ (v9 = 0) | v10 = 0))) & % 100.16/15.38 | ! [v7: $i] : ( ~ (in(v7, all_42_5) = 0) | ~ $i(v7) | ? % 100.16/15.38 | [v8: $i] : (apply(all_42_6, v7) = v8 & apply(all_42_7, v7) % 100.16/15.38 | = v8 & $i(v8))) & ! [v7: $i] : ( ~ (in(v7, all_42_5) = % 100.16/15.38 | 0) | ~ $i(v7) | ? [v8: $i] : (apply(all_42_7, v7) = v8 % 100.16/15.38 | & in(v8, all_42_9) = 0 & in(v7, v4) = 0 & $i(v8)))))) | % 100.16/15.38 | (function(all_42_6) = v1 & relation(all_42_6) = v0 & ( ~ (v1 = 0) % 100.16/15.38 | | ~ (v0 = 0))))) % 100.16/15.38 | % 100.16/15.38 | GROUND_INST: instantiating (5) with all_42_9, all_42_7, all_42_3, all_42_7, % 100.16/15.38 | all_42_6, simplifying with (11), (13), (17), (22) gives: % 100.16/15.39 | (31) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 100.16/15.39 | $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? % 100.16/15.39 | [v9: $i] : ? [v10: any] : ? [v11: any] : ? [v12: $i] : ? [v13: % 100.16/15.39 | any] : ($i(v9) & $i(v5) & ((relation_dom(all_42_7) = v4 & % 100.16/15.39 | function(all_42_7) = v3 & relation(all_42_7) = v2 & $i(v4) & ( ~ % 100.16/15.39 | (v3 = 0) | ~ (v2 = 0) | (( ~ (all_42_6 = all_42_7) | ( ! % 100.16/15.39 | [v14: $i] : ! [v15: int] : (v15 = 0 | ~ (in(v14, % 100.16/15.39 | all_42_3) = v15) | ~ $i(v14) | ? [v16: any] : ? % 100.16/15.39 | [v17: $i] : ? [v18: any] : (apply(all_42_7, v14) = % 100.16/15.39 | v17 & in(v17, all_42_9) = v18 & in(v14, v4) = v16 & % 100.16/15.39 | $i(v17) & ( ~ (v18 = 0) | ~ (v16 = 0)))) & ! [v14: % 100.16/15.39 | $i] : ! [v15: $i] : ( ~ (apply(all_42_7, v14) = v15) % 100.16/15.39 | | ~ $i(v14) | ? [v16: any] : ? [v17: any] : ? % 100.16/15.39 | [v18: any] : (in(v15, all_42_9) = v18 & in(v14, v4) = % 100.16/15.39 | v17 & in(v14, all_42_3) = v16 & ( ~ (v16 = 0) | (v18 % 100.16/15.39 | = 0 & v17 = 0)))) & ! [v14: $i] : ! [v15: $i] % 100.16/15.39 | : ( ~ (apply(all_42_7, v14) = v15) | ~ $i(v14) | ? % 100.16/15.39 | [v16: any] : ? [v17: any] : ? [v18: any] : (in(v15, % 100.16/15.39 | all_42_9) = v17 & in(v14, v4) = v16 & in(v14, % 100.16/15.39 | all_42_3) = v18 & ( ~ (v17 = 0) | ~ (v16 = 0) | % 100.16/15.39 | v18 = 0))) & ! [v14: $i] : ! [v15: $i] : ( ~ % 100.16/15.39 | (apply(all_42_7, v14) = v15) | ~ $i(v14) | ? [v16: % 100.16/15.39 | any] : ? [v17: $i] : (apply(all_42_7, v14) = v17 & % 100.16/15.39 | in(v14, all_42_3) = v16 & $i(v17) & ( ~ (v16 = 0) | % 100.16/15.39 | v17 = v15))) & ! [v14: $i] : ! [v15: any] : ( ~ % 100.16/15.39 | (in(v14, v4) = v15) | ~ $i(v14) | ? [v16: any] : ? % 100.16/15.39 | [v17: $i] : ? [v18: any] : (apply(all_42_7, v14) = % 100.16/15.39 | v17 & in(v17, all_42_9) = v18 & in(v14, all_42_3) = % 100.16/15.39 | v16 & $i(v17) & ( ~ (v16 = 0) | (v18 = 0 & v15 = % 100.16/15.39 | 0)))) & ! [v14: $i] : ( ~ (in(v14, v4) = 0) | % 100.16/15.39 | ~ $i(v14) | ? [v15: $i] : ? [v16: any] : ? [v17: % 100.16/15.39 | any] : (apply(all_42_7, v14) = v15 & in(v15, % 100.16/15.39 | all_42_9) = v16 & in(v14, all_42_3) = v17 & % 100.16/15.39 | $i(v15) & ( ~ (v16 = 0) | v17 = 0))) & ! [v14: $i] % 100.16/15.39 | : ( ~ (in(v14, all_42_3) = 0) | ~ $i(v14) | ? [v15: % 100.16/15.39 | $i] : (apply(all_42_7, v14) = v15 & in(v15, % 100.16/15.39 | all_42_9) = 0 & in(v14, v4) = 0 & $i(v15))) & ! % 100.16/15.39 | [v14: $i] : ( ~ (in(v14, all_42_3) = 0) | ~ $i(v14) | % 100.16/15.39 | ? [v15: $i] : (apply(all_42_7, v14) = v15 & % 100.16/15.39 | $i(v15))))) & (all_42_6 = all_42_7 | (v6 = 0 & ~ % 100.16/15.39 | (v8 = v7) & apply(all_42_7, v5) = v8 & apply(all_42_7, % 100.16/15.39 | v5) = v7 & in(v5, all_42_3) = 0 & $i(v8) & $i(v7)) | % 100.16/15.39 | (apply(all_42_7, v9) = v12 & in(v12, all_42_9) = v13 & % 100.16/15.39 | in(v9, v4) = v11 & in(v9, all_42_3) = v10 & $i(v12) & ( % 100.16/15.39 | ~ (v13 = 0) | ~ (v11 = 0) | ~ (v10 = 0)) & (v10 = 0 % 100.16/15.39 | | (v13 = 0 & v11 = 0))))))) | (function(all_42_7) = v1 % 100.16/15.39 | & relation(all_42_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))) % 100.16/15.39 | % 100.16/15.39 | GROUND_INST: instantiating (fc5_funct_1) with all_42_9, all_42_7, all_42_6, % 100.16/15.39 | simplifying with (11), (13), (22) gives: % 100.16/15.39 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 100.16/15.39 | (function(all_42_6) = v3 & function(all_42_7) = v1 & % 100.16/15.39 | relation(all_42_6) = v2 & relation(all_42_7) = v0 & ( ~ (v1 = 0) | % 100.16/15.39 | ~ (v0 = 0) | (v3 = 0 & v2 = 0))) % 100.16/15.39 | % 100.16/15.39 | GROUND_INST: instantiating (dt_k8_relat_1) with all_42_9, all_42_7, all_42_6, % 100.16/15.39 | simplifying with (11), (13), (22) gives: % 100.16/15.39 | (33) ? [v0: any] : ? [v1: any] : (relation(all_42_6) = v1 & % 100.16/15.39 | relation(all_42_7) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 100.16/15.39 | % 100.16/15.39 | DELTA: instantiating (33) with fresh symbols all_62_0, all_62_1 gives: % 100.16/15.39 | (34) relation(all_42_6) = all_62_0 & relation(all_42_7) = all_62_1 & ( ~ % 100.16/15.39 | (all_62_1 = 0) | all_62_0 = 0) % 100.16/15.39 | % 100.16/15.39 | ALPHA: (34) implies: % 100.16/15.39 | (35) relation(all_42_7) = all_62_1 % 100.16/15.39 | (36) relation(all_42_6) = all_62_0 % 100.16/15.39 | (37) ~ (all_62_1 = 0) | all_62_0 = 0 % 100.16/15.39 | % 100.16/15.39 | DELTA: instantiating (29) with fresh symbols all_72_0, all_72_1, all_72_2 % 100.16/15.39 | gives: % 100.16/15.39 | (38) empty(all_42_5) = all_72_0 & empty(all_42_6) = all_72_2 & % 100.16/15.39 | relation(all_42_6) = all_72_1 & ( ~ (all_72_0 = 0) | ~ (all_72_1 = 0) % 100.16/15.39 | | all_72_2 = 0) % 100.16/15.39 | % 100.16/15.39 | ALPHA: (38) implies: % 100.16/15.39 | (39) relation(all_42_6) = all_72_1 % 100.16/15.39 | % 100.16/15.39 | DELTA: instantiating (27) with fresh symbols all_78_0, all_78_1, all_78_2 % 100.16/15.39 | gives: % 100.16/15.39 | (40) one_to_one(all_42_7) = all_78_0 & empty(all_42_7) = all_78_1 & % 100.16/15.39 | relation(all_42_7) = all_78_2 & ( ~ (all_78_1 = 0) | ~ (all_78_2 = 0) % 100.16/15.39 | | all_78_0 = 0) % 100.16/15.39 | % 100.16/15.39 | ALPHA: (40) implies: % 100.16/15.39 | (41) relation(all_42_7) = all_78_2 % 100.16/15.39 | % 100.16/15.39 | DELTA: instantiating (26) with fresh symbols all_88_0, all_88_1, all_88_2 % 100.16/15.39 | gives: % 100.24/15.39 | (42) one_to_one(all_42_7) = all_88_0 & function(all_42_7) = all_88_1 & % 100.24/15.39 | empty(all_42_7) = all_88_2 & ( ~ (all_88_1 = 0) | ~ (all_88_2 = 0) | % 100.24/15.39 | all_88_0 = 0) % 100.24/15.39 | % 100.24/15.39 | ALPHA: (42) implies: % 100.24/15.39 | (43) function(all_42_7) = all_88_1 % 100.24/15.39 | % 100.24/15.39 | DELTA: instantiating (25) with fresh symbols all_90_0, all_90_1, all_90_2 % 100.24/15.39 | gives: % 100.24/15.40 | (44) relation_dom(all_42_7) = all_90_1 & empty(all_90_1) = all_90_0 & % 100.24/15.40 | empty(all_42_7) = all_90_2 & $i(all_90_1) & ( ~ (all_90_0 = 0) | % 100.24/15.40 | all_90_2 = 0) % 100.24/15.40 | % 100.24/15.40 | ALPHA: (44) implies: % 100.24/15.40 | (45) relation_dom(all_42_7) = all_90_1 % 100.24/15.40 | % 100.24/15.40 | DELTA: instantiating (28) with fresh symbols all_92_0, all_92_1, all_92_2 % 100.24/15.40 | gives: % 100.24/15.40 | (46) empty(all_42_3) = all_92_0 & empty(all_42_7) = all_92_2 & % 100.24/15.40 | relation(all_42_7) = all_92_1 & ( ~ (all_92_0 = 0) | ~ (all_92_1 = 0) % 100.24/15.40 | | all_92_2 = 0) % 100.24/15.40 | % 100.24/15.40 | ALPHA: (46) implies: % 100.24/15.40 | (47) relation(all_42_7) = all_92_1 % 100.24/15.40 | % 100.24/15.40 | DELTA: instantiating (32) with fresh symbols all_128_0, all_128_1, all_128_2, % 100.24/15.40 | all_128_3 gives: % 100.24/15.40 | (48) function(all_42_6) = all_128_0 & function(all_42_7) = all_128_2 & % 100.24/15.40 | relation(all_42_6) = all_128_1 & relation(all_42_7) = all_128_3 & ( ~ % 100.24/15.40 | (all_128_2 = 0) | ~ (all_128_3 = 0) | (all_128_0 = 0 & all_128_1 = % 100.24/15.40 | 0)) % 100.24/15.40 | % 100.24/15.40 | ALPHA: (48) implies: % 100.24/15.40 | (49) relation(all_42_7) = all_128_3 % 100.24/15.40 | (50) relation(all_42_6) = all_128_1 % 100.24/15.40 | (51) function(all_42_7) = all_128_2 % 100.24/15.40 | (52) function(all_42_6) = all_128_0 % 100.24/15.40 | (53) ~ (all_128_2 = 0) | ~ (all_128_3 = 0) | (all_128_0 = 0 & all_128_1 = % 100.24/15.40 | 0) % 100.24/15.40 | % 100.24/15.40 | DELTA: instantiating (30) with fresh symbols all_130_0, all_130_1, all_130_2, % 100.24/15.40 | all_130_3, all_130_4, all_130_5, all_130_6 gives: % 100.24/15.41 | (54) $i(all_130_0) & $i(all_130_1) & ((relation_dom(all_42_7) = all_130_2 & % 100.24/15.41 | function(all_42_7) = all_130_3 & relation(all_42_7) = all_130_4 & % 100.24/15.41 | $i(all_130_2) & ( ~ (all_130_3 = 0) | ~ (all_130_4 = 0) | ( ! % 100.24/15.41 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_42_5) = v1) % 100.24/15.41 | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 100.24/15.41 | (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 & in(v0, % 100.24/15.41 | all_130_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0)))) % 100.24/15.41 | & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_6, v0) = v1) | % 100.24/15.41 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (apply(all_42_7, % 100.24/15.41 | v0) = v3 & in(v0, all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) % 100.24/15.41 | | v3 = v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.24/15.41 | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.24/15.41 | [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v4 & in(v0, % 100.24/15.41 | all_130_2) = v3 & in(v0, all_42_5) = v2 & ( ~ (v2 = 0) | % 100.24/15.41 | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.24/15.41 | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.24/15.41 | [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v3 & in(v0, % 100.24/15.41 | all_130_2) = v2 & in(v0, all_42_5) = v4 & ( ~ (v3 = 0) | % 100.24/15.41 | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( % 100.24/15.41 | ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.24/15.41 | [v3: $i] : (apply(all_42_6, v0) = v3 & in(v0, all_42_5) = v2 % 100.24/15.41 | & $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] : ! % 100.24/15.41 | [v1: any] : ( ~ (in(v0, all_130_2) = v1) | ~ $i(v0) | ? [v2: % 100.24/15.41 | any] : ? [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = % 100.24/15.41 | v3 & in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 & % 100.24/15.41 | $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i] % 100.24/15.41 | : ( ~ (in(v0, all_130_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 100.24/15.41 | [v2: any] : ? [v3: any] : (apply(all_42_7, v0) = v1 & % 100.24/15.41 | in(v1, all_42_9) = v2 & in(v0, all_42_5) = v3 & $i(v1) & ( % 100.24/15.41 | ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0, % 100.24/15.41 | all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] : % 100.24/15.41 | (apply(all_42_6, v0) = v1 & apply(all_42_7, v0) = v1 & % 100.24/15.41 | $i(v1))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = 0) | ~ % 100.24/15.41 | $i(v0) | ? [v1: $i] : (apply(all_42_7, v0) = v1 & in(v1, % 100.24/15.41 | all_42_9) = 0 & in(v0, all_130_2) = 0 & $i(v1)))))) | % 100.24/15.41 | (function(all_42_6) = all_130_5 & relation(all_42_6) = all_130_6 & ( % 100.24/15.41 | ~ (all_130_5 = 0) | ~ (all_130_6 = 0)))) % 100.24/15.41 | % 100.24/15.41 | ALPHA: (54) implies: % 100.33/15.42 | (55) (relation_dom(all_42_7) = all_130_2 & function(all_42_7) = all_130_3 & % 100.33/15.42 | relation(all_42_7) = all_130_4 & $i(all_130_2) & ( ~ (all_130_3 = 0) % 100.33/15.42 | | ~ (all_130_4 = 0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 100.33/15.42 | (in(v0, all_42_5) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 100.33/15.42 | $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & in(v3, % 100.33/15.42 | all_42_9) = v4 & in(v0, all_130_2) = v2 & $i(v3) & ( ~ (v4 % 100.33/15.42 | = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.33/15.42 | (apply(all_42_6, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.33/15.42 | [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0, all_42_5) = v2 & % 100.33/15.42 | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] : ! [v1: % 100.33/15.42 | $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: % 100.33/15.42 | any] : ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v4 % 100.33/15.42 | & in(v0, all_130_2) = v3 & in(v0, all_42_5) = v2 & ( ~ (v2 = % 100.33/15.42 | 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 100.33/15.42 | ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.33/15.42 | [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v3 & in(v0, % 100.33/15.42 | all_130_2) = v2 & in(v0, all_42_5) = v4 & ( ~ (v3 = 0) | % 100.33/15.42 | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.33/15.42 | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.33/15.42 | [v3: $i] : (apply(all_42_6, v0) = v3 & in(v0, all_42_5) = v2 & % 100.33/15.42 | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] : ! [v1: % 100.33/15.42 | any] : ( ~ (in(v0, all_130_2) = v1) | ~ $i(v0) | ? [v2: any] % 100.33/15.42 | : ? [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & % 100.33/15.42 | in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 & $i(v3) & ( ~ % 100.33/15.42 | (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~ % 100.33/15.42 | (in(v0, all_130_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 100.33/15.42 | any] : ? [v3: any] : (apply(all_42_7, v0) = v1 & in(v1, % 100.33/15.42 | all_42_9) = v2 & in(v0, all_42_5) = v3 & $i(v1) & ( ~ (v2 % 100.33/15.42 | = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = % 100.33/15.42 | 0) | ~ $i(v0) | ? [v1: $i] : (apply(all_42_6, v0) = v1 & % 100.33/15.42 | apply(all_42_7, v0) = v1 & $i(v1))) & ! [v0: $i] : ( ~ % 100.33/15.42 | (in(v0, all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] : % 100.33/15.42 | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 & in(v0, % 100.33/15.42 | all_130_2) = 0 & $i(v1)))))) | (function(all_42_6) = % 100.33/15.42 | all_130_5 & relation(all_42_6) = all_130_6 & ( ~ (all_130_5 = 0) | % 100.33/15.42 | ~ (all_130_6 = 0))) % 100.33/15.42 | % 100.33/15.42 | DELTA: instantiating (31) with fresh symbols all_132_0, all_132_1, all_132_2, % 100.33/15.42 | all_132_3, all_132_4, all_132_5, all_132_6, all_132_7, all_132_8, % 100.33/15.42 | all_132_9, all_132_10, all_132_11, all_132_12, all_132_13 gives: % 100.34/15.42 | (56) $i(all_132_4) & $i(all_132_8) & ((relation_dom(all_42_7) = all_132_9 & % 100.34/15.42 | function(all_42_7) = all_132_10 & relation(all_42_7) = all_132_11 % 100.34/15.42 | & $i(all_132_9) & ( ~ (all_132_10 = 0) | ~ (all_132_11 = 0) | (( % 100.34/15.42 | ~ (all_42_6 = all_42_7) | ( ! [v0: $i] : ! [v1: int] : (v1 % 100.34/15.42 | = 0 | ~ (in(v0, all_42_3) = v1) | ~ $i(v0) | ? [v2: % 100.34/15.42 | any] : ? [v3: $i] : ? [v4: any] : (apply(all_42_7, % 100.34/15.42 | v0) = v3 & in(v3, all_42_9) = v4 & in(v0, all_132_9) % 100.34/15.42 | = v2 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! % 100.34/15.42 | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | % 100.34/15.42 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 100.34/15.42 | (in(v1, all_42_9) = v4 & in(v0, all_132_9) = v3 & in(v0, % 100.34/15.42 | all_42_3) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 100.34/15.42 | & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = % 100.34/15.42 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? % 100.34/15.42 | [v4: any] : (in(v1, all_42_9) = v3 & in(v0, all_132_9) = % 100.34/15.42 | v2 & in(v0, all_42_3) = v4 & ( ~ (v3 = 0) | ~ (v2 = % 100.34/15.42 | 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.34/15.42 | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 100.34/15.42 | ? [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0, % 100.34/15.42 | all_42_3) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1))) % 100.34/15.42 | & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_132_9) = % 100.34/15.42 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: % 100.34/15.42 | any] : (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = % 100.34/15.42 | v4 & in(v0, all_42_3) = v2 & $i(v3) & ( ~ (v2 = 0) | % 100.34/15.42 | (v4 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~ (in(v0, % 100.34/15.42 | all_132_9) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 100.34/15.42 | any] : ? [v3: any] : (apply(all_42_7, v0) = v1 & % 100.34/15.42 | in(v1, all_42_9) = v2 & in(v0, all_42_3) = v3 & $i(v1) % 100.34/15.42 | & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0, % 100.34/15.42 | all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] : % 100.34/15.42 | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 & % 100.34/15.42 | in(v0, all_132_9) = 0 & $i(v1))) & ! [v0: $i] : ( ~ % 100.34/15.42 | (in(v0, all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] : % 100.34/15.42 | (apply(all_42_7, v0) = v1 & $i(v1))))) & (all_42_6 = % 100.34/15.42 | all_42_7 | (all_132_7 = 0 & ~ (all_132_5 = all_132_6) & % 100.34/15.42 | apply(all_42_7, all_132_8) = all_132_5 & apply(all_42_7, % 100.34/15.42 | all_132_8) = all_132_6 & in(all_132_8, all_42_3) = 0 & % 100.34/15.42 | $i(all_132_5) & $i(all_132_6)) | (apply(all_42_7, % 100.34/15.42 | all_132_4) = all_132_1 & in(all_132_1, all_42_9) = % 100.34/15.42 | all_132_0 & in(all_132_4, all_132_9) = all_132_2 & % 100.34/15.42 | in(all_132_4, all_42_3) = all_132_3 & $i(all_132_1) & ( ~ % 100.34/15.42 | (all_132_0 = 0) | ~ (all_132_2 = 0) | ~ (all_132_3 = % 100.34/15.42 | 0)) & (all_132_3 = 0 | (all_132_0 = 0 & all_132_2 = % 100.34/15.42 | 0))))))) | (function(all_42_7) = all_132_12 & % 100.34/15.42 | relation(all_42_7) = all_132_13 & ( ~ (all_132_12 = 0) | ~ % 100.34/15.42 | (all_132_13 = 0)))) % 100.34/15.42 | % 100.34/15.42 | ALPHA: (56) implies: % 100.34/15.43 | (57) (relation_dom(all_42_7) = all_132_9 & function(all_42_7) = all_132_10 % 100.34/15.43 | & relation(all_42_7) = all_132_11 & $i(all_132_9) & ( ~ (all_132_10 % 100.34/15.43 | = 0) | ~ (all_132_11 = 0) | (( ~ (all_42_6 = all_42_7) | ( ! % 100.34/15.43 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_42_3) = % 100.34/15.43 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: % 100.34/15.43 | any] : (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 % 100.34/15.43 | & in(v0, all_132_9) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ % 100.34/15.43 | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.34/15.43 | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.34/15.43 | [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v4 & in(v0, % 100.34/15.43 | all_132_9) = v3 & in(v0, all_42_3) = v2 & ( ~ (v2 = 0) % 100.34/15.43 | | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( % 100.34/15.43 | ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 100.34/15.43 | ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v3 & % 100.34/15.43 | in(v0, all_132_9) = v2 & in(v0, all_42_3) = v4 & ( ~ (v3 % 100.34/15.43 | = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ! % 100.34/15.43 | [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? % 100.34/15.43 | [v2: any] : ? [v3: $i] : (apply(all_42_7, v0) = v3 & % 100.34/15.43 | in(v0, all_42_3) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = % 100.34/15.43 | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, % 100.34/15.43 | all_132_9) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 100.34/15.43 | $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & in(v3, % 100.34/15.43 | all_42_9) = v4 & in(v0, all_42_3) = v2 & $i(v3) & ( ~ % 100.34/15.43 | (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~ % 100.34/15.43 | (in(v0, all_132_9) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 100.34/15.43 | [v2: any] : ? [v3: any] : (apply(all_42_7, v0) = v1 & % 100.34/15.43 | in(v1, all_42_9) = v2 & in(v0, all_42_3) = v3 & $i(v1) & % 100.34/15.43 | ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0, % 100.34/15.43 | all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] : % 100.34/15.43 | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 & in(v0, % 100.34/15.43 | all_132_9) = 0 & $i(v1))) & ! [v0: $i] : ( ~ (in(v0, % 100.34/15.43 | all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] : % 100.34/15.43 | (apply(all_42_7, v0) = v1 & $i(v1))))) & (all_42_6 = % 100.34/15.43 | all_42_7 | (all_132_7 = 0 & ~ (all_132_5 = all_132_6) & % 100.34/15.43 | apply(all_42_7, all_132_8) = all_132_5 & apply(all_42_7, % 100.34/15.43 | all_132_8) = all_132_6 & in(all_132_8, all_42_3) = 0 & % 100.34/15.43 | $i(all_132_5) & $i(all_132_6)) | (apply(all_42_7, all_132_4) % 100.34/15.43 | = all_132_1 & in(all_132_1, all_42_9) = all_132_0 & % 100.34/15.43 | in(all_132_4, all_132_9) = all_132_2 & in(all_132_4, % 100.34/15.43 | all_42_3) = all_132_3 & $i(all_132_1) & ( ~ (all_132_0 = % 100.34/15.43 | 0) | ~ (all_132_2 = 0) | ~ (all_132_3 = 0)) & % 100.34/15.43 | (all_132_3 = 0 | (all_132_0 = 0 & all_132_2 = 0))))))) | % 100.34/15.43 | (function(all_42_7) = all_132_12 & relation(all_42_7) = all_132_13 & ( % 100.34/15.43 | ~ (all_132_12 = 0) | ~ (all_132_13 = 0))) % 100.34/15.43 | % 100.34/15.44 | GROUND_INST: instantiating (6) with 0, all_128_3, all_42_7, simplifying with % 100.34/15.44 | (15), (49) gives: % 100.34/15.44 | (58) all_128_3 = 0 % 100.34/15.44 | % 100.34/15.44 | GROUND_INST: instantiating (6) with all_92_1, all_128_3, all_42_7, simplifying % 100.34/15.44 | with (47), (49) gives: % 100.34/15.44 | (59) all_128_3 = all_92_1 % 100.34/15.44 | % 100.34/15.44 | GROUND_INST: instantiating (6) with all_78_2, all_128_3, all_42_7, simplifying % 100.34/15.44 | with (41), (49) gives: % 100.34/15.44 | (60) all_128_3 = all_78_2 % 100.34/15.44 | % 100.34/15.44 | GROUND_INST: instantiating (6) with all_62_1, all_128_3, all_42_7, simplifying % 100.34/15.44 | with (35), (49) gives: % 100.34/15.44 | (61) all_128_3 = all_62_1 % 100.34/15.44 | % 100.34/15.44 | GROUND_INST: instantiating (6) with all_72_1, all_128_1, all_42_6, simplifying % 100.34/15.44 | with (39), (50) gives: % 100.34/15.44 | (62) all_128_1 = all_72_1 % 100.34/15.44 | % 100.34/15.44 | GROUND_INST: instantiating (6) with all_62_0, all_128_1, all_42_6, simplifying % 100.34/15.44 | with (36), (50) gives: % 100.34/15.44 | (63) all_128_1 = all_62_0 % 100.34/15.44 | % 100.34/15.44 | GROUND_INST: instantiating (7) with 0, all_128_2, all_42_7, simplifying with % 100.34/15.44 | (16), (51) gives: % 100.34/15.44 | (64) all_128_2 = 0 % 100.34/15.44 | % 100.34/15.44 | GROUND_INST: instantiating (7) with all_88_1, all_128_2, all_42_7, simplifying % 100.34/15.44 | with (43), (51) gives: % 100.34/15.44 | (65) all_128_2 = all_88_1 % 100.34/15.44 | % 100.34/15.44 | GROUND_INST: instantiating (8) with all_42_3, all_90_1, all_42_7, simplifying % 100.34/15.44 | with (17), (45) gives: % 100.34/15.44 | (66) all_90_1 = all_42_3 % 100.34/15.44 | % 100.34/15.44 | COMBINE_EQS: (62), (63) imply: % 100.34/15.44 | (67) all_72_1 = all_62_0 % 100.34/15.44 | % 100.34/15.44 | COMBINE_EQS: (64), (65) imply: % 100.34/15.44 | (68) all_88_1 = 0 % 100.34/15.44 | % 100.34/15.44 | SIMP: (68) implies: % 100.34/15.44 | (69) all_88_1 = 0 % 100.34/15.44 | % 100.34/15.44 | COMBINE_EQS: (58), (59) imply: % 100.34/15.44 | (70) all_92_1 = 0 % 100.34/15.44 | % 100.34/15.44 | COMBINE_EQS: (59), (61) imply: % 100.34/15.44 | (71) all_92_1 = all_62_1 % 100.34/15.44 | % 100.34/15.44 | COMBINE_EQS: (59), (60) imply: % 100.34/15.44 | (72) all_92_1 = all_78_2 % 100.34/15.44 | % 100.34/15.44 | COMBINE_EQS: (70), (72) imply: % 100.34/15.44 | (73) all_78_2 = 0 % 100.34/15.44 | % 100.34/15.45 | COMBINE_EQS: (71), (72) imply: % 100.34/15.45 | (74) all_78_2 = all_62_1 % 100.34/15.45 | % 100.34/15.45 | COMBINE_EQS: (73), (74) imply: % 100.34/15.45 | (75) all_62_1 = 0 % 100.34/15.45 | % 100.34/15.45 | SIMP: (75) implies: % 100.34/15.45 | (76) all_62_1 = 0 % 100.34/15.45 | % 100.34/15.45 | BETA: splitting (57) gives: % 100.34/15.45 | % 100.34/15.45 | Case 1: % 100.34/15.45 | | % 100.34/15.45 | | (77) relation_dom(all_42_7) = all_132_9 & function(all_42_7) = all_132_10 % 100.34/15.45 | | & relation(all_42_7) = all_132_11 & $i(all_132_9) & ( ~ (all_132_10 % 100.34/15.45 | | = 0) | ~ (all_132_11 = 0) | (( ~ (all_42_6 = all_42_7) | ( ! % 100.34/15.45 | | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_42_3) = % 100.34/15.45 | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: % 100.34/15.45 | | any] : (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 % 100.34/15.45 | | & in(v0, all_132_9) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ % 100.34/15.45 | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.34/15.45 | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.34/15.45 | | [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v4 & in(v0, % 100.34/15.45 | | all_132_9) = v3 & in(v0, all_42_3) = v2 & ( ~ (v2 = 0) % 100.34/15.45 | | | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( % 100.34/15.45 | | ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 100.34/15.45 | | ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v3 & % 100.34/15.46 | | in(v0, all_132_9) = v2 & in(v0, all_42_3) = v4 & ( ~ (v3 % 100.34/15.46 | | = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ! % 100.34/15.46 | | [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? % 100.34/15.46 | | [v2: any] : ? [v3: $i] : (apply(all_42_7, v0) = v3 & % 100.34/15.46 | | in(v0, all_42_3) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = % 100.34/15.46 | | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, % 100.34/15.46 | | all_132_9) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 100.34/15.46 | | $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & in(v3, % 100.34/15.46 | | all_42_9) = v4 & in(v0, all_42_3) = v2 & $i(v3) & ( ~ % 100.34/15.46 | | (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~ % 100.34/15.46 | | (in(v0, all_132_9) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 100.34/15.46 | | [v2: any] : ? [v3: any] : (apply(all_42_7, v0) = v1 & % 100.34/15.46 | | in(v1, all_42_9) = v2 & in(v0, all_42_3) = v3 & $i(v1) & % 100.34/15.46 | | ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0, % 100.34/15.46 | | all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] : % 100.34/15.46 | | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 & in(v0, % 100.34/15.46 | | all_132_9) = 0 & $i(v1))) & ! [v0: $i] : ( ~ (in(v0, % 100.34/15.46 | | all_42_3) = 0) | ~ $i(v0) | ? [v1: $i] : % 100.34/15.46 | | (apply(all_42_7, v0) = v1 & $i(v1))))) & (all_42_6 = % 100.34/15.46 | | all_42_7 | (all_132_7 = 0 & ~ (all_132_5 = all_132_6) & % 100.34/15.46 | | apply(all_42_7, all_132_8) = all_132_5 & apply(all_42_7, % 100.34/15.46 | | all_132_8) = all_132_6 & in(all_132_8, all_42_3) = 0 & % 100.34/15.46 | | $i(all_132_5) & $i(all_132_6)) | (apply(all_42_7, all_132_4) % 100.34/15.46 | | = all_132_1 & in(all_132_1, all_42_9) = all_132_0 & % 100.34/15.46 | | in(all_132_4, all_132_9) = all_132_2 & in(all_132_4, % 100.34/15.46 | | all_42_3) = all_132_3 & $i(all_132_1) & ( ~ (all_132_0 = % 100.34/15.46 | | 0) | ~ (all_132_2 = 0) | ~ (all_132_3 = 0)) & % 100.34/15.46 | | (all_132_3 = 0 | (all_132_0 = 0 & all_132_2 = 0)))))) % 100.34/15.46 | | % 100.34/15.46 | | ALPHA: (77) implies: % 100.34/15.46 | | (78) relation(all_42_7) = all_132_11 % 100.34/15.46 | | (79) function(all_42_7) = all_132_10 % 100.34/15.46 | | (80) relation_dom(all_42_7) = all_132_9 % 100.34/15.46 | | % 100.34/15.46 | | BETA: splitting (37) gives: % 100.34/15.46 | | % 100.34/15.46 | | Case 1: % 100.34/15.46 | | | % 100.34/15.46 | | | (81) ~ (all_62_1 = 0) % 100.34/15.46 | | | % 100.34/15.46 | | | REDUCE: (76), (81) imply: % 100.34/15.46 | | | (82) $false % 100.34/15.46 | | | % 100.34/15.46 | | | CLOSE: (82) is inconsistent. % 100.34/15.46 | | | % 100.34/15.46 | | Case 2: % 100.34/15.46 | | | % 100.34/15.46 | | | (83) all_62_0 = 0 % 100.34/15.46 | | | % 100.34/15.46 | | | REDUCE: (36), (83) imply: % 100.34/15.46 | | | (84) relation(all_42_6) = 0 % 100.34/15.46 | | | % 100.34/15.46 | | | BETA: splitting (53) gives: % 100.34/15.46 | | | % 100.34/15.46 | | | Case 1: % 100.34/15.46 | | | | % 100.34/15.46 | | | | (85) ~ (all_128_2 = 0) % 100.34/15.46 | | | | % 100.34/15.46 | | | | REDUCE: (64), (85) imply: % 100.34/15.46 | | | | (86) $false % 100.34/15.46 | | | | % 100.34/15.46 | | | | CLOSE: (86) is inconsistent. % 100.34/15.46 | | | | % 100.34/15.46 | | | Case 2: % 100.34/15.46 | | | | % 100.34/15.46 | | | | (87) ~ (all_128_3 = 0) | (all_128_0 = 0 & all_128_1 = 0) % 100.34/15.46 | | | | % 100.34/15.46 | | | | BETA: splitting (87) gives: % 100.34/15.46 | | | | % 100.34/15.46 | | | | Case 1: % 100.34/15.46 | | | | | % 100.34/15.46 | | | | | (88) ~ (all_128_3 = 0) % 100.34/15.46 | | | | | % 100.34/15.46 | | | | | REDUCE: (58), (88) imply: % 100.34/15.46 | | | | | (89) $false % 100.34/15.46 | | | | | % 100.34/15.46 | | | | | CLOSE: (89) is inconsistent. % 100.34/15.46 | | | | | % 100.34/15.46 | | | | Case 2: % 100.34/15.46 | | | | | % 100.34/15.46 | | | | | (90) all_128_0 = 0 & all_128_1 = 0 % 100.34/15.46 | | | | | % 100.34/15.46 | | | | | ALPHA: (90) implies: % 100.34/15.46 | | | | | (91) all_128_0 = 0 % 100.34/15.46 | | | | | % 100.34/15.46 | | | | | REDUCE: (52), (91) imply: % 100.34/15.46 | | | | | (92) function(all_42_6) = 0 % 100.34/15.46 | | | | | % 100.34/15.46 | | | | | BETA: splitting (55) gives: % 100.34/15.46 | | | | | % 100.34/15.46 | | | | | Case 1: % 100.34/15.46 | | | | | | % 100.34/15.47 | | | | | | (93) relation_dom(all_42_7) = all_130_2 & function(all_42_7) = % 100.34/15.47 | | | | | | all_130_3 & relation(all_42_7) = all_130_4 & $i(all_130_2) & % 100.34/15.47 | | | | | | ( ~ (all_130_3 = 0) | ~ (all_130_4 = 0) | ( ! [v0: $i] : ! % 100.34/15.47 | | | | | | [v1: int] : (v1 = 0 | ~ (in(v0, all_42_5) = v1) | ~ % 100.34/15.47 | | | | | | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 100.34/15.47 | | | | | | (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 & % 100.34/15.47 | | | | | | in(v0, all_130_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ % 100.34/15.47 | | | | | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.34/15.47 | | | | | | (apply(all_42_6, v0) = v1) | ~ $i(v0) | ? [v2: any] % 100.34/15.47 | | | | | | : ? [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0, % 100.34/15.47 | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = % 100.34/15.47 | | | | | | v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.34/15.47 | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] % 100.34/15.47 | | | | | | : ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v4 % 100.34/15.47 | | | | | | & in(v0, all_130_2) = v3 & in(v0, all_42_5) = v2 & ( % 100.34/15.47 | | | | | | ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : % 100.34/15.47 | | | | | | ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) % 100.34/15.47 | | | | | | | ? [v2: any] : ? [v3: any] : ? [v4: any] : (in(v1, % 100.34/15.47 | | | | | | all_42_9) = v3 & in(v0, all_130_2) = v2 & in(v0, % 100.34/15.47 | | | | | | all_42_5) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = % 100.34/15.47 | | | | | | 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.34/15.47 | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] % 100.34/15.47 | | | | | | : ? [v3: $i] : (apply(all_42_6, v0) = v3 & in(v0, % 100.34/15.47 | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = % 100.34/15.47 | | | | | | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, % 100.34/15.47 | | | | | | all_130_2) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.34/15.47 | | | | | | [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & % 100.34/15.47 | | | | | | in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 & % 100.34/15.47 | | | | | | $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! % 100.34/15.47 | | | | | | [v0: $i] : ( ~ (in(v0, all_130_2) = 0) | ~ $i(v0) | ? % 100.34/15.47 | | | | | | [v1: $i] : ? [v2: any] : ? [v3: any] : % 100.34/15.47 | | | | | | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = v2 & % 100.34/15.47 | | | | | | in(v0, all_42_5) = v3 & $i(v1) & ( ~ (v2 = 0) | v3 = % 100.34/15.47 | | | | | | 0))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = 0) | % 100.34/15.47 | | | | | | ~ $i(v0) | ? [v1: $i] : (apply(all_42_6, v0) = v1 & % 100.34/15.47 | | | | | | apply(all_42_7, v0) = v1 & $i(v1))) & ! [v0: $i] : % 100.34/15.47 | | | | | | ( ~ (in(v0, all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] : % 100.34/15.47 | | | | | | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 & % 100.34/15.47 | | | | | | in(v0, all_130_2) = 0 & $i(v1))))) % 100.34/15.47 | | | | | | % 100.34/15.47 | | | | | | ALPHA: (93) implies: % 100.34/15.47 | | | | | | (94) relation(all_42_7) = all_130_4 % 100.34/15.47 | | | | | | (95) function(all_42_7) = all_130_3 % 100.34/15.47 | | | | | | (96) relation_dom(all_42_7) = all_130_2 % 100.34/15.48 | | | | | | (97) ~ (all_130_3 = 0) | ~ (all_130_4 = 0) | ( ! [v0: $i] : ! % 100.34/15.48 | | | | | | [v1: int] : (v1 = 0 | ~ (in(v0, all_42_5) = v1) | ~ % 100.34/15.48 | | | | | | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 100.34/15.48 | | | | | | (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 & % 100.34/15.48 | | | | | | in(v0, all_130_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ % 100.34/15.48 | | | | | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.34/15.48 | | | | | | (apply(all_42_6, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 100.34/15.48 | | | | | | ? [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0, % 100.34/15.48 | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v1))) % 100.34/15.48 | | | | | | & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = % 100.34/15.48 | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? % 100.34/15.48 | | | | | | [v4: any] : (in(v1, all_42_9) = v4 & in(v0, all_130_2) = % 100.34/15.48 | | | | | | v3 & in(v0, all_42_5) = v2 & ( ~ (v2 = 0) | (v4 = 0 & % 100.34/15.48 | | | | | | v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.34/15.48 | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 100.34/15.48 | | | | | | ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = v3 & % 100.34/15.48 | | | | | | in(v0, all_130_2) = v2 & in(v0, all_42_5) = v4 & ( ~ % 100.34/15.48 | | | | | | (v3 = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : % 100.34/15.48 | | | | | | ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) | % 100.34/15.48 | | | | | | ? [v2: any] : ? [v3: $i] : (apply(all_42_6, v0) = v3 & % 100.34/15.48 | | | | | | in(v0, all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = % 100.34/15.48 | | | | | | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, % 100.34/15.48 | | | | | | all_130_2) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.34/15.48 | | | | | | [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & % 100.34/15.48 | | | | | | in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 & $i(v3) % 100.34/15.48 | | | | | | & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! [v0: $i] : % 100.34/15.48 | | | | | | ( ~ (in(v0, all_130_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 100.34/15.48 | | | | | | [v2: any] : ? [v3: any] : (apply(all_42_7, v0) = v1 & % 100.34/15.48 | | | | | | in(v1, all_42_9) = v2 & in(v0, all_42_5) = v3 & $i(v1) % 100.34/15.48 | | | | | | & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0, % 100.34/15.48 | | | | | | all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] : % 100.34/15.48 | | | | | | (apply(all_42_6, v0) = v1 & apply(all_42_7, v0) = v1 & % 100.34/15.48 | | | | | | $i(v1))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = 0) | % 100.34/15.48 | | | | | | ~ $i(v0) | ? [v1: $i] : (apply(all_42_7, v0) = v1 & % 100.34/15.48 | | | | | | in(v1, all_42_9) = 0 & in(v0, all_130_2) = 0 & % 100.34/15.48 | | | | | | $i(v1)))) % 100.34/15.48 | | | | | | % 100.34/15.48 | | | | | | GROUND_INST: instantiating (6) with 0, all_132_11, all_42_7, % 100.34/15.48 | | | | | | simplifying with (15), (78) gives: % 100.34/15.48 | | | | | | (98) all_132_11 = 0 % 100.34/15.48 | | | | | | % 100.34/15.48 | | | | | | GROUND_INST: instantiating (6) with all_130_4, all_132_11, all_42_7, % 100.34/15.48 | | | | | | simplifying with (78), (94) gives: % 100.34/15.48 | | | | | | (99) all_132_11 = all_130_4 % 100.34/15.48 | | | | | | % 100.34/15.48 | | | | | | GROUND_INST: instantiating (7) with 0, all_132_10, all_42_7, % 100.34/15.48 | | | | | | simplifying with (16), (79) gives: % 100.34/15.48 | | | | | | (100) all_132_10 = 0 % 100.34/15.48 | | | | | | % 100.34/15.48 | | | | | | GROUND_INST: instantiating (7) with all_130_3, all_132_10, all_42_7, % 100.34/15.48 | | | | | | simplifying with (79), (95) gives: % 100.34/15.49 | | | | | | (101) all_132_10 = all_130_3 % 100.34/15.49 | | | | | | % 100.34/15.49 | | | | | | GROUND_INST: instantiating (8) with all_42_3, all_132_9, all_42_7, % 100.34/15.49 | | | | | | simplifying with (17), (80) gives: % 100.34/15.49 | | | | | | (102) all_132_9 = all_42_3 % 100.34/15.49 | | | | | | % 100.34/15.49 | | | | | | GROUND_INST: instantiating (8) with all_130_2, all_132_9, all_42_7, % 100.34/15.49 | | | | | | simplifying with (80), (96) gives: % 100.34/15.49 | | | | | | (103) all_132_9 = all_130_2 % 100.34/15.49 | | | | | | % 100.34/15.49 | | | | | | COMBINE_EQS: (102), (103) imply: % 100.34/15.49 | | | | | | (104) all_130_2 = all_42_3 % 100.34/15.49 | | | | | | % 100.34/15.49 | | | | | | COMBINE_EQS: (100), (101) imply: % 100.34/15.49 | | | | | | (105) all_130_3 = 0 % 100.34/15.49 | | | | | | % 100.34/15.49 | | | | | | COMBINE_EQS: (98), (99) imply: % 100.34/15.49 | | | | | | (106) all_130_4 = 0 % 100.34/15.49 | | | | | | % 100.34/15.49 | | | | | | SIMP: (106) implies: % 100.34/15.49 | | | | | | (107) all_130_4 = 0 % 100.34/15.49 | | | | | | % 100.34/15.49 | | | | | | BETA: splitting (97) gives: % 100.34/15.49 | | | | | | % 100.34/15.49 | | | | | | Case 1: % 100.34/15.49 | | | | | | | % 100.34/15.49 | | | | | | | (108) ~ (all_130_3 = 0) % 100.34/15.49 | | | | | | | % 100.34/15.49 | | | | | | | REDUCE: (105), (108) imply: % 100.34/15.49 | | | | | | | (109) $false % 100.34/15.49 | | | | | | | % 100.34/15.49 | | | | | | | CLOSE: (109) is inconsistent. % 100.34/15.49 | | | | | | | % 100.34/15.49 | | | | | | Case 2: % 100.34/15.49 | | | | | | | % 100.34/15.49 | | | | | | | (110) ~ (all_130_4 = 0) | ( ! [v0: $i] : ! [v1: int] : (v1 = % 100.34/15.49 | | | | | | | 0 | ~ (in(v0, all_42_5) = v1) | ~ $i(v0) | ? [v2: % 100.34/15.49 | | | | | | | any] : ? [v3: $i] : ? [v4: any] : % 100.34/15.49 | | | | | | | (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 & % 100.34/15.49 | | | | | | | in(v0, all_130_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ % 100.34/15.49 | | | | | | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.34/15.49 | | | | | | | (apply(all_42_6, v0) = v1) | ~ $i(v0) | ? [v2: any] % 100.34/15.49 | | | | | | | : ? [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0, % 100.34/15.49 | | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = % 100.34/15.49 | | | | | | | v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.34/15.49 | | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] % 100.34/15.49 | | | | | | | : ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = % 100.34/15.49 | | | | | | | v4 & in(v0, all_130_2) = v3 & in(v0, all_42_5) = v2 % 100.34/15.49 | | | | | | | & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] % 100.34/15.49 | | | | | | | : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ % 100.34/15.49 | | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 100.34/15.49 | | | | | | | (in(v1, all_42_9) = v3 & in(v0, all_130_2) = v2 & % 100.34/15.49 | | | | | | | in(v0, all_42_5) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) % 100.34/15.49 | | | | | | | | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.34/15.49 | | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] % 100.34/15.49 | | | | | | | : ? [v3: $i] : (apply(all_42_6, v0) = v3 & in(v0, % 100.34/15.49 | | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = % 100.34/15.49 | | | | | | | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, % 100.34/15.49 | | | | | | | all_130_2) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.34/15.49 | | | | | | | [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & % 100.34/15.49 | | | | | | | in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 & % 100.34/15.49 | | | | | | | $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! % 100.34/15.49 | | | | | | | [v0: $i] : ( ~ (in(v0, all_130_2) = 0) | ~ $i(v0) | ? % 100.34/15.49 | | | | | | | [v1: $i] : ? [v2: any] : ? [v3: any] : % 100.34/15.49 | | | | | | | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = v2 & % 100.34/15.49 | | | | | | | in(v0, all_42_5) = v3 & $i(v1) & ( ~ (v2 = 0) | v3 % 100.34/15.49 | | | | | | | = 0))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = 0) % 100.34/15.49 | | | | | | | | ~ $i(v0) | ? [v1: $i] : (apply(all_42_6, v0) = v1 % 100.34/15.49 | | | | | | | & apply(all_42_7, v0) = v1 & $i(v1))) & ! [v0: $i] % 100.34/15.49 | | | | | | | : ( ~ (in(v0, all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] % 100.34/15.49 | | | | | | | : (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 & % 100.34/15.49 | | | | | | | in(v0, all_130_2) = 0 & $i(v1)))) % 100.34/15.49 | | | | | | | % 100.34/15.49 | | | | | | | BETA: splitting (110) gives: % 100.34/15.49 | | | | | | | % 100.34/15.49 | | | | | | | Case 1: % 100.34/15.49 | | | | | | | | % 100.34/15.49 | | | | | | | | (111) ~ (all_130_4 = 0) % 100.34/15.49 | | | | | | | | % 100.34/15.49 | | | | | | | | REDUCE: (107), (111) imply: % 100.34/15.49 | | | | | | | | (112) $false % 100.34/15.49 | | | | | | | | % 100.34/15.49 | | | | | | | | CLOSE: (112) is inconsistent. % 100.34/15.49 | | | | | | | | % 100.34/15.49 | | | | | | | Case 2: % 100.34/15.49 | | | | | | | | % 100.66/15.50 | | | | | | | | (113) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 100.66/15.50 | | | | | | | | all_42_5) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.66/15.50 | | | | | | | | [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & % 100.66/15.50 | | | | | | | | in(v3, all_42_9) = v4 & in(v0, all_130_2) = v2 & % 100.66/15.50 | | | | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! [v0: % 100.66/15.50 | | | | | | | | $i] : ! [v1: $i] : ( ~ (apply(all_42_6, v0) = v1) | % 100.66/15.50 | | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 100.66/15.50 | | | | | | | | (apply(all_42_7, v0) = v3 & in(v0, all_42_5) = v2 & % 100.66/15.50 | | | | | | | | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] : % 100.66/15.50 | | | | | | | | ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ $i(v0) % 100.66/15.50 | | | | | | | | | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 100.66/15.50 | | | | | | | | (in(v1, all_42_9) = v4 & in(v0, all_130_2) = v3 & % 100.66/15.50 | | | | | | | | in(v0, all_42_5) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 % 100.66/15.50 | | | | | | | | = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.66/15.50 | | | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] % 100.66/15.50 | | | | | | | | : ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = % 100.66/15.50 | | | | | | | | v3 & in(v0, all_130_2) = v2 & in(v0, all_42_5) = v4 % 100.66/15.50 | | | | | | | | & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0))) & ! [v0: % 100.66/15.50 | | | | | | | | $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | % 100.66/15.50 | | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 100.66/15.50 | | | | | | | | (apply(all_42_6, v0) = v3 & in(v0, all_42_5) = v2 & % 100.66/15.50 | | | | | | | | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) & ! [v0: $i] : % 100.66/15.50 | | | | | | | | ! [v1: any] : ( ~ (in(v0, all_130_2) = v1) | ~ $i(v0) % 100.66/15.50 | | | | | | | | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 100.66/15.50 | | | | | | | | (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 & % 100.66/15.50 | | | | | | | | in(v0, all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | (v4 % 100.66/15.50 | | | | | | | | = 0 & v1 = 0)))) & ! [v0: $i] : ( ~ (in(v0, % 100.66/15.50 | | | | | | | | all_130_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 100.66/15.50 | | | | | | | | [v2: any] : ? [v3: any] : (apply(all_42_7, v0) = v1 % 100.66/15.50 | | | | | | | | & in(v1, all_42_9) = v2 & in(v0, all_42_5) = v3 & % 100.66/15.50 | | | | | | | | $i(v1) & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( % 100.66/15.50 | | | | | | | | ~ (in(v0, all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] : % 100.66/15.50 | | | | | | | | (apply(all_42_6, v0) = v1 & apply(all_42_7, v0) = v1 % 100.66/15.50 | | | | | | | | & $i(v1))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = % 100.66/15.50 | | | | | | | | 0) | ~ $i(v0) | ? [v1: $i] : (apply(all_42_7, v0) % 100.66/15.50 | | | | | | | | = v1 & in(v1, all_42_9) = 0 & in(v0, all_130_2) = 0 % 100.66/15.50 | | | | | | | | & $i(v1))) % 100.66/15.50 | | | | | | | | % 100.66/15.50 | | | | | | | | ALPHA: (113) implies: % 100.66/15.50 | | | | | | | | (114) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = % 100.66/15.50 | | | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 100.66/15.50 | | | | | | | | (apply(all_42_6, v0) = v3 & in(v0, all_42_5) = v2 & % 100.66/15.50 | | | | | | | | $i(v3) & ( ~ (v2 = 0) | v3 = v1))) % 100.66/15.51 | | | | | | | | (115) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = % 100.66/15.51 | | | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? % 100.66/15.51 | | | | | | | | [v4: any] : (in(v1, all_42_9) = v3 & in(v0, % 100.66/15.51 | | | | | | | | all_130_2) = v2 & in(v0, all_42_5) = v4 & ( ~ (v3 % 100.66/15.51 | | | | | | | | = 0) | ~ (v2 = 0) | v4 = 0))) % 100.66/15.51 | | | | | | | | (116) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = % 100.66/15.51 | | | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? % 100.66/15.51 | | | | | | | | [v4: any] : (in(v1, all_42_9) = v4 & in(v0, % 100.66/15.51 | | | | | | | | all_130_2) = v3 & in(v0, all_42_5) = v2 & ( ~ (v2 % 100.66/15.51 | | | | | | | | = 0) | (v4 = 0 & v3 = 0)))) % 100.66/15.51 | | | | | | | | % 100.66/15.51 | | | | | | | | GROUND_INST: instantiating (116) with all_42_8, all_42_1, % 100.66/15.51 | | | | | | | | simplifying with (12), (23) gives: % 100.66/15.51 | | | | | | | | (117) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 100.66/15.51 | | | | | | | | (in(all_42_1, all_42_9) = v2 & in(all_42_8, all_130_2) % 100.66/15.51 | | | | | | | | = v1 & in(all_42_8, all_42_5) = v0 & ( ~ (v0 = 0) | % 100.66/15.51 | | | | | | | | (v2 = 0 & v1 = 0))) % 100.66/15.51 | | | | | | | | % 100.66/15.51 | | | | | | | | GROUND_INST: instantiating (115) with all_42_8, all_42_1, % 100.66/15.51 | | | | | | | | simplifying with (12), (23) gives: % 100.66/15.51 | | | | | | | | (118) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 100.66/15.51 | | | | | | | | (in(all_42_1, all_42_9) = v1 & in(all_42_8, all_130_2) % 100.66/15.51 | | | | | | | | = v0 & in(all_42_8, all_42_5) = v2 & ( ~ (v1 = 0) | % 100.66/15.51 | | | | | | | | ~ (v0 = 0) | v2 = 0)) % 100.66/15.51 | | | | | | | | % 100.66/15.51 | | | | | | | | GROUND_INST: instantiating (114) with all_42_8, all_42_1, % 100.66/15.51 | | | | | | | | simplifying with (12), (23) gives: % 100.66/15.51 | | | | | | | | (119) ? [v0: any] : ? [v1: $i] : (apply(all_42_6, all_42_8) % 100.66/15.51 | | | | | | | | = v1 & in(all_42_8, all_42_5) = v0 & $i(v1) & ( ~ (v0 % 100.66/15.51 | | | | | | | | = 0) | v1 = all_42_1)) % 100.66/15.51 | | | | | | | | % 100.66/15.51 | | | | | | | | DELTA: instantiating (119) with fresh symbols all_213_0, % 100.66/15.51 | | | | | | | | all_213_1 gives: % 100.66/15.51 | | | | | | | | (120) apply(all_42_6, all_42_8) = all_213_0 & in(all_42_8, % 100.66/15.51 | | | | | | | | all_42_5) = all_213_1 & $i(all_213_0) & ( ~ % 100.66/15.51 | | | | | | | | (all_213_1 = 0) | all_213_0 = all_42_1) % 100.66/15.51 | | | | | | | | % 100.66/15.51 | | | | | | | | ALPHA: (120) implies: % 100.66/15.51 | | | | | | | | (121) in(all_42_8, all_42_5) = all_213_1 % 100.66/15.51 | | | | | | | | % 100.66/15.51 | | | | | | | | DELTA: instantiating (118) with fresh symbols all_215_0, % 100.66/15.51 | | | | | | | | all_215_1, all_215_2 gives: % 100.66/15.51 | | | | | | | | (122) in(all_42_1, all_42_9) = all_215_1 & in(all_42_8, % 100.66/15.51 | | | | | | | | all_130_2) = all_215_2 & in(all_42_8, all_42_5) = % 100.66/15.51 | | | | | | | | all_215_0 & ( ~ (all_215_1 = 0) | ~ (all_215_2 = 0) | % 100.66/15.51 | | | | | | | | all_215_0 = 0) % 100.66/15.51 | | | | | | | | % 100.66/15.51 | | | | | | | | ALPHA: (122) implies: % 100.66/15.51 | | | | | | | | (123) in(all_42_8, all_42_5) = all_215_0 % 100.66/15.51 | | | | | | | | (124) in(all_42_8, all_130_2) = all_215_2 % 100.66/15.51 | | | | | | | | (125) in(all_42_1, all_42_9) = all_215_1 % 100.66/15.51 | | | | | | | | (126) ~ (all_215_1 = 0) | ~ (all_215_2 = 0) | all_215_0 = 0 % 100.66/15.51 | | | | | | | | % 100.66/15.51 | | | | | | | | DELTA: instantiating (117) with fresh symbols all_217_0, % 100.66/15.51 | | | | | | | | all_217_1, all_217_2 gives: % 100.66/15.52 | | | | | | | | (127) in(all_42_1, all_42_9) = all_217_0 & in(all_42_8, % 100.66/15.52 | | | | | | | | all_130_2) = all_217_1 & in(all_42_8, all_42_5) = % 100.66/15.52 | | | | | | | | all_217_2 & ( ~ (all_217_2 = 0) | (all_217_0 = 0 & % 100.66/15.52 | | | | | | | | all_217_1 = 0)) % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | ALPHA: (127) implies: % 100.66/15.52 | | | | | | | | (128) in(all_42_8, all_42_5) = all_217_2 % 100.66/15.52 | | | | | | | | (129) in(all_42_8, all_130_2) = all_217_1 % 100.66/15.52 | | | | | | | | (130) in(all_42_1, all_42_9) = all_217_0 % 100.66/15.52 | | | | | | | | (131) ~ (all_217_2 = 0) | (all_217_0 = 0 & all_217_1 = 0) % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | REDUCE: (104), (129) imply: % 100.66/15.52 | | | | | | | | (132) in(all_42_8, all_42_3) = all_217_1 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | REDUCE: (104), (124) imply: % 100.66/15.52 | | | | | | | | (133) in(all_42_8, all_42_3) = all_215_2 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_42_4, all_215_0, % 100.66/15.52 | | | | | | | | all_42_5, all_42_8, simplifying with (19), (123) % 100.66/15.52 | | | | | | | | gives: % 100.66/15.52 | | | | | | | | (134) all_215_0 = all_42_4 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_215_0, all_217_2, % 100.66/15.52 | | | | | | | | all_42_5, all_42_8, simplifying with (123), (128) % 100.66/15.52 | | | | | | | | gives: % 100.66/15.52 | | | | | | | | (135) all_217_2 = all_215_0 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_213_1, all_217_2, % 100.66/15.52 | | | | | | | | all_42_5, all_42_8, simplifying with (121), (128) % 100.66/15.52 | | | | | | | | gives: % 100.66/15.52 | | | | | | | | (136) all_217_2 = all_213_1 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_42_2, all_217_1, % 100.66/15.52 | | | | | | | | all_42_3, all_42_8, simplifying with (20), (132) % 100.66/15.52 | | | | | | | | gives: % 100.66/15.52 | | | | | | | | (137) all_217_1 = all_42_2 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_215_2, all_217_1, % 100.66/15.52 | | | | | | | | all_42_3, all_42_8, simplifying with (132), (133) % 100.66/15.52 | | | | | | | | gives: % 100.66/15.52 | | | | | | | | (138) all_217_1 = all_215_2 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_42_0, all_217_0, % 100.66/15.52 | | | | | | | | all_42_9, all_42_1, simplifying with (21), (130) % 100.66/15.52 | | | | | | | | gives: % 100.66/15.52 | | | | | | | | (139) all_217_0 = all_42_0 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | GROUND_INST: instantiating (9) with all_215_1, all_217_0, % 100.66/15.52 | | | | | | | | all_42_9, all_42_1, simplifying with (125), (130) % 100.66/15.52 | | | | | | | | gives: % 100.66/15.52 | | | | | | | | (140) all_217_0 = all_215_1 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | COMBINE_EQS: (139), (140) imply: % 100.66/15.52 | | | | | | | | (141) all_215_1 = all_42_0 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | COMBINE_EQS: (137), (138) imply: % 100.66/15.52 | | | | | | | | (142) all_215_2 = all_42_2 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | COMBINE_EQS: (135), (136) imply: % 100.66/15.52 | | | | | | | | (143) all_215_0 = all_213_1 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | SIMP: (143) implies: % 100.66/15.52 | | | | | | | | (144) all_215_0 = all_213_1 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | COMBINE_EQS: (134), (144) imply: % 100.66/15.52 | | | | | | | | (145) all_213_1 = all_42_4 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | COMBINE_EQS: (136), (145) imply: % 100.66/15.52 | | | | | | | | (146) all_217_2 = all_42_4 % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | BETA: splitting (24) gives: % 100.66/15.52 | | | | | | | | % 100.66/15.52 | | | | | | | | Case 1: % 100.66/15.52 | | | | | | | | | % 100.66/15.52 | | | | | | | | | (147) all_42_0 = 0 & all_42_2 = 0 & ~ (all_42_4 = 0) % 100.66/15.52 | | | | | | | | | % 100.66/15.52 | | | | | | | | | ALPHA: (147) implies: % 100.66/15.52 | | | | | | | | | (148) all_42_2 = 0 % 100.66/15.52 | | | | | | | | | (149) all_42_0 = 0 % 100.66/15.52 | | | | | | | | | (150) ~ (all_42_4 = 0) % 100.66/15.52 | | | | | | | | | % 100.66/15.52 | | | | | | | | | COMBINE_EQS: (142), (148) imply: % 100.66/15.52 | | | | | | | | | (151) all_215_2 = 0 % 100.66/15.52 | | | | | | | | | % 100.66/15.52 | | | | | | | | | COMBINE_EQS: (141), (149) imply: % 100.66/15.52 | | | | | | | | | (152) all_215_1 = 0 % 100.66/15.52 | | | | | | | | | % 100.66/15.52 | | | | | | | | | BETA: splitting (126) gives: % 100.66/15.52 | | | | | | | | | % 100.66/15.52 | | | | | | | | | Case 1: % 100.66/15.52 | | | | | | | | | | % 100.66/15.52 | | | | | | | | | | (153) ~ (all_215_1 = 0) % 100.66/15.52 | | | | | | | | | | % 100.66/15.52 | | | | | | | | | | REDUCE: (152), (153) imply: % 100.66/15.52 | | | | | | | | | | (154) $false % 100.66/15.52 | | | | | | | | | | % 100.66/15.52 | | | | | | | | | | CLOSE: (154) is inconsistent. % 100.66/15.52 | | | | | | | | | | % 100.66/15.52 | | | | | | | | | Case 2: % 100.66/15.52 | | | | | | | | | | % 100.66/15.52 | | | | | | | | | | (155) ~ (all_215_2 = 0) | all_215_0 = 0 % 100.66/15.52 | | | | | | | | | | % 100.66/15.52 | | | | | | | | | | BETA: splitting (155) gives: % 100.66/15.52 | | | | | | | | | | % 100.66/15.52 | | | | | | | | | | Case 1: % 100.66/15.52 | | | | | | | | | | | % 100.66/15.52 | | | | | | | | | | | (156) ~ (all_215_2 = 0) % 100.66/15.52 | | | | | | | | | | | % 100.66/15.52 | | | | | | | | | | | REDUCE: (151), (156) imply: % 100.66/15.52 | | | | | | | | | | | (157) $false % 100.66/15.52 | | | | | | | | | | | % 100.66/15.52 | | | | | | | | | | | CLOSE: (157) is inconsistent. % 100.66/15.52 | | | | | | | | | | | % 100.66/15.52 | | | | | | | | | | Case 2: % 100.66/15.52 | | | | | | | | | | | % 100.66/15.52 | | | | | | | | | | | (158) all_215_0 = 0 % 100.66/15.52 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | | COMBINE_EQS: (134), (158) imply: % 100.66/15.53 | | | | | | | | | | | (159) all_42_4 = 0 % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | | SIMP: (159) implies: % 100.66/15.53 | | | | | | | | | | | (160) all_42_4 = 0 % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | | REDUCE: (150), (160) imply: % 100.66/15.53 | | | | | | | | | | | (161) $false % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | | CLOSE: (161) is inconsistent. % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | End of split % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | End of split % 100.66/15.53 | | | | | | | | | % 100.66/15.53 | | | | | | | | Case 2: % 100.66/15.53 | | | | | | | | | % 100.66/15.53 | | | | | | | | | (162) all_42_4 = 0 & ( ~ (all_42_0 = 0) | ~ (all_42_2 = % 100.66/15.53 | | | | | | | | | 0)) % 100.66/15.53 | | | | | | | | | % 100.66/15.53 | | | | | | | | | ALPHA: (162) implies: % 100.66/15.53 | | | | | | | | | (163) all_42_4 = 0 % 100.66/15.53 | | | | | | | | | (164) ~ (all_42_0 = 0) | ~ (all_42_2 = 0) % 100.66/15.53 | | | | | | | | | % 100.66/15.53 | | | | | | | | | COMBINE_EQS: (146), (163) imply: % 100.66/15.53 | | | | | | | | | (165) all_217_2 = 0 % 100.66/15.53 | | | | | | | | | % 100.66/15.53 | | | | | | | | | BETA: splitting (131) gives: % 100.66/15.53 | | | | | | | | | % 100.66/15.53 | | | | | | | | | Case 1: % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | (166) ~ (all_217_2 = 0) % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | REDUCE: (165), (166) imply: % 100.66/15.53 | | | | | | | | | | (167) $false % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | CLOSE: (167) is inconsistent. % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | Case 2: % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | (168) all_217_0 = 0 & all_217_1 = 0 % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | ALPHA: (168) implies: % 100.66/15.53 | | | | | | | | | | (169) all_217_1 = 0 % 100.66/15.53 | | | | | | | | | | (170) all_217_0 = 0 % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | COMBINE_EQS: (139), (170) imply: % 100.66/15.53 | | | | | | | | | | (171) all_42_0 = 0 % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | COMBINE_EQS: (137), (169) imply: % 100.66/15.53 | | | | | | | | | | (172) all_42_2 = 0 % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | SIMP: (172) implies: % 100.66/15.53 | | | | | | | | | | (173) all_42_2 = 0 % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | BETA: splitting (164) gives: % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | Case 1: % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | | (174) ~ (all_42_0 = 0) % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | | REDUCE: (171), (174) imply: % 100.66/15.53 | | | | | | | | | | | (175) $false % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | | CLOSE: (175) is inconsistent. % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | Case 2: % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | | (176) ~ (all_42_2 = 0) % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | | REDUCE: (173), (176) imply: % 100.66/15.53 | | | | | | | | | | | (177) $false % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | | CLOSE: (177) is inconsistent. % 100.66/15.53 | | | | | | | | | | | % 100.66/15.53 | | | | | | | | | | End of split % 100.66/15.53 | | | | | | | | | | % 100.66/15.53 | | | | | | | | | End of split % 100.66/15.53 | | | | | | | | | % 100.66/15.53 | | | | | | | | End of split % 100.66/15.53 | | | | | | | | % 100.66/15.53 | | | | | | | End of split % 100.66/15.53 | | | | | | | % 100.66/15.53 | | | | | | End of split % 100.66/15.53 | | | | | | % 100.66/15.53 | | | | | Case 2: % 100.66/15.53 | | | | | | % 100.66/15.53 | | | | | | (178) function(all_42_6) = all_130_5 & relation(all_42_6) = % 100.66/15.53 | | | | | | all_130_6 & ( ~ (all_130_5 = 0) | ~ (all_130_6 = 0)) % 100.66/15.53 | | | | | | % 100.66/15.53 | | | | | | ALPHA: (178) implies: % 100.66/15.53 | | | | | | (179) relation(all_42_6) = all_130_6 % 100.66/15.53 | | | | | | (180) function(all_42_6) = all_130_5 % 100.66/15.53 | | | | | | (181) ~ (all_130_5 = 0) | ~ (all_130_6 = 0) % 100.66/15.53 | | | | | | % 100.66/15.53 | | | | | | REF_CLOSE: (6), (7), (84), (92), (179), (180), (181) are % 100.66/15.53 | | | | | | inconsistent by sub-proof #1. % 100.66/15.53 | | | | | | % 100.66/15.53 | | | | | End of split % 100.66/15.53 | | | | | % 100.66/15.53 | | | | End of split % 100.66/15.53 | | | | % 100.66/15.53 | | | End of split % 100.66/15.53 | | | % 100.66/15.53 | | End of split % 100.66/15.53 | | % 100.66/15.53 | Case 2: % 100.66/15.53 | | % 100.66/15.53 | | (182) function(all_42_7) = all_132_12 & relation(all_42_7) = all_132_13 & % 100.66/15.53 | | ( ~ (all_132_12 = 0) | ~ (all_132_13 = 0)) % 100.66/15.53 | | % 100.66/15.53 | | ALPHA: (182) implies: % 100.66/15.53 | | (183) relation(all_42_7) = all_132_13 % 100.66/15.53 | | (184) function(all_42_7) = all_132_12 % 100.66/15.53 | | (185) ~ (all_132_12 = 0) | ~ (all_132_13 = 0) % 100.66/15.53 | | % 100.66/15.53 | | BETA: splitting (37) gives: % 100.66/15.53 | | % 100.66/15.53 | | Case 1: % 100.66/15.53 | | | % 100.66/15.53 | | | (186) ~ (all_62_1 = 0) % 100.66/15.53 | | | % 100.66/15.53 | | | REDUCE: (76), (186) imply: % 100.66/15.53 | | | (187) $false % 100.66/15.53 | | | % 100.66/15.53 | | | CLOSE: (187) is inconsistent. % 100.66/15.53 | | | % 100.66/15.53 | | Case 2: % 100.66/15.53 | | | % 100.66/15.53 | | | (188) all_62_0 = 0 % 100.66/15.53 | | | % 100.66/15.53 | | | REDUCE: (36), (188) imply: % 100.66/15.53 | | | (189) relation(all_42_6) = 0 % 100.66/15.53 | | | % 100.66/15.53 | | | BETA: splitting (53) gives: % 100.66/15.53 | | | % 100.66/15.53 | | | Case 1: % 100.66/15.53 | | | | % 100.66/15.53 | | | | (190) ~ (all_128_2 = 0) % 100.66/15.53 | | | | % 100.66/15.53 | | | | REDUCE: (64), (190) imply: % 100.66/15.53 | | | | (191) $false % 100.66/15.53 | | | | % 100.66/15.53 | | | | CLOSE: (191) is inconsistent. % 100.66/15.53 | | | | % 100.66/15.53 | | | Case 2: % 100.66/15.53 | | | | % 100.66/15.53 | | | | (192) ~ (all_128_3 = 0) | (all_128_0 = 0 & all_128_1 = 0) % 100.66/15.53 | | | | % 100.66/15.53 | | | | BETA: splitting (192) gives: % 100.66/15.53 | | | | % 100.66/15.53 | | | | Case 1: % 100.66/15.53 | | | | | % 100.66/15.53 | | | | | (193) ~ (all_128_3 = 0) % 100.66/15.53 | | | | | % 100.66/15.53 | | | | | REDUCE: (58), (193) imply: % 100.66/15.53 | | | | | (194) $false % 100.66/15.53 | | | | | % 100.66/15.53 | | | | | CLOSE: (194) is inconsistent. % 100.66/15.53 | | | | | % 100.66/15.53 | | | | Case 2: % 100.66/15.53 | | | | | % 100.66/15.53 | | | | | (195) all_128_0 = 0 & all_128_1 = 0 % 100.66/15.53 | | | | | % 100.66/15.53 | | | | | ALPHA: (195) implies: % 100.66/15.53 | | | | | (196) all_128_0 = 0 % 100.66/15.53 | | | | | % 100.66/15.53 | | | | | REDUCE: (52), (196) imply: % 100.66/15.53 | | | | | (197) function(all_42_6) = 0 % 100.66/15.53 | | | | | % 100.66/15.53 | | | | | BETA: splitting (55) gives: % 100.66/15.53 | | | | | % 100.66/15.53 | | | | | Case 1: % 100.66/15.53 | | | | | | % 100.66/15.54 | | | | | | (198) relation_dom(all_42_7) = all_130_2 & function(all_42_7) = % 100.66/15.54 | | | | | | all_130_3 & relation(all_42_7) = all_130_4 & $i(all_130_2) % 100.66/15.54 | | | | | | & ( ~ (all_130_3 = 0) | ~ (all_130_4 = 0) | ( ! [v0: $i] : % 100.66/15.54 | | | | | | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_42_5) = v1) | % 100.66/15.54 | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] % 100.66/15.54 | | | | | | : (apply(all_42_7, v0) = v3 & in(v3, all_42_9) = v4 & % 100.66/15.54 | | | | | | in(v0, all_130_2) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ % 100.66/15.54 | | | | | | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.66/15.54 | | | | | | (apply(all_42_6, v0) = v1) | ~ $i(v0) | ? [v2: any] % 100.66/15.54 | | | | | | : ? [v3: $i] : (apply(all_42_7, v0) = v3 & in(v0, % 100.66/15.54 | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = % 100.66/15.54 | | | | | | v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.66/15.54 | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] % 100.66/15.54 | | | | | | : ? [v3: any] : ? [v4: any] : (in(v1, all_42_9) = % 100.66/15.54 | | | | | | v4 & in(v0, all_130_2) = v3 & in(v0, all_42_5) = v2 % 100.66/15.54 | | | | | | & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] % 100.66/15.54 | | | | | | : ! [v1: $i] : ( ~ (apply(all_42_7, v0) = v1) | ~ % 100.66/15.54 | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 100.66/15.54 | | | | | | (in(v1, all_42_9) = v3 & in(v0, all_130_2) = v2 & % 100.66/15.54 | | | | | | in(v0, all_42_5) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) % 100.66/15.54 | | | | | | | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 100.66/15.54 | | | | | | (apply(all_42_7, v0) = v1) | ~ $i(v0) | ? [v2: any] % 100.66/15.54 | | | | | | : ? [v3: $i] : (apply(all_42_6, v0) = v3 & in(v0, % 100.66/15.54 | | | | | | all_42_5) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = % 100.66/15.54 | | | | | | v1))) & ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, % 100.66/15.54 | | | | | | all_130_2) = v1) | ~ $i(v0) | ? [v2: any] : ? % 100.66/15.54 | | | | | | [v3: $i] : ? [v4: any] : (apply(all_42_7, v0) = v3 & % 100.66/15.54 | | | | | | in(v3, all_42_9) = v4 & in(v0, all_42_5) = v2 & % 100.66/15.54 | | | | | | $i(v3) & ( ~ (v2 = 0) | (v4 = 0 & v1 = 0)))) & ! % 100.66/15.54 | | | | | | [v0: $i] : ( ~ (in(v0, all_130_2) = 0) | ~ $i(v0) | ? % 100.66/15.54 | | | | | | [v1: $i] : ? [v2: any] : ? [v3: any] : % 100.66/15.54 | | | | | | (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = v2 & % 100.66/15.54 | | | | | | in(v0, all_42_5) = v3 & $i(v1) & ( ~ (v2 = 0) | v3 % 100.66/15.54 | | | | | | = 0))) & ! [v0: $i] : ( ~ (in(v0, all_42_5) = 0) % 100.66/15.54 | | | | | | | ~ $i(v0) | ? [v1: $i] : (apply(all_42_6, v0) = v1 % 100.66/15.54 | | | | | | & apply(all_42_7, v0) = v1 & $i(v1))) & ! [v0: $i] % 100.66/15.54 | | | | | | : ( ~ (in(v0, all_42_5) = 0) | ~ $i(v0) | ? [v1: $i] % 100.66/15.54 | | | | | | : (apply(all_42_7, v0) = v1 & in(v1, all_42_9) = 0 & % 100.66/15.54 | | | | | | in(v0, all_130_2) = 0 & $i(v1))))) % 100.66/15.54 | | | | | | % 100.66/15.54 | | | | | | ALPHA: (198) implies: % 100.66/15.54 | | | | | | (199) relation(all_42_7) = all_130_4 % 100.66/15.54 | | | | | | (200) function(all_42_7) = all_130_3 % 100.66/15.54 | | | | | | % 100.66/15.54 | | | | | | GROUND_INST: instantiating (6) with 0, all_132_13, all_42_7, % 100.66/15.54 | | | | | | simplifying with (15), (183) gives: % 100.66/15.54 | | | | | | (201) all_132_13 = 0 % 100.66/15.54 | | | | | | % 100.66/15.54 | | | | | | GROUND_INST: instantiating (6) with all_130_4, all_132_13, all_42_7, % 100.66/15.54 | | | | | | simplifying with (183), (199) gives: % 100.66/15.54 | | | | | | (202) all_132_13 = all_130_4 % 100.66/15.54 | | | | | | % 100.66/15.54 | | | | | | GROUND_INST: instantiating (7) with 0, all_132_12, all_42_7, % 100.66/15.54 | | | | | | simplifying with (16), (184) gives: % 100.66/15.54 | | | | | | (203) all_132_12 = 0 % 100.66/15.54 | | | | | | % 100.66/15.54 | | | | | | GROUND_INST: instantiating (7) with all_130_3, all_132_12, all_42_7, % 100.66/15.54 | | | | | | simplifying with (184), (200) gives: % 100.66/15.54 | | | | | | (204) all_132_12 = all_130_3 % 100.66/15.54 | | | | | | % 100.66/15.54 | | | | | | COMBINE_EQS: (203), (204) imply: % 100.66/15.54 | | | | | | (205) all_130_3 = 0 % 100.66/15.54 | | | | | | % 100.66/15.54 | | | | | | COMBINE_EQS: (201), (202) imply: % 100.66/15.54 | | | | | | (206) all_130_4 = 0 % 100.66/15.54 | | | | | | % 100.66/15.54 | | | | | | BETA: splitting (185) gives: % 100.66/15.54 | | | | | | % 100.66/15.54 | | | | | | Case 1: % 100.66/15.54 | | | | | | | % 100.66/15.54 | | | | | | | (207) ~ (all_132_12 = 0) % 100.66/15.54 | | | | | | | % 100.66/15.54 | | | | | | | REDUCE: (203), (207) imply: % 100.66/15.54 | | | | | | | (208) $false % 100.66/15.54 | | | | | | | % 100.66/15.54 | | | | | | | CLOSE: (208) is inconsistent. % 100.66/15.54 | | | | | | | % 100.66/15.54 | | | | | | Case 2: % 100.66/15.54 | | | | | | | % 100.66/15.54 | | | | | | | (209) ~ (all_132_13 = 0) % 100.66/15.54 | | | | | | | % 100.66/15.54 | | | | | | | REDUCE: (201), (209) imply: % 100.66/15.54 | | | | | | | (210) $false % 100.66/15.54 | | | | | | | % 100.66/15.54 | | | | | | | CLOSE: (210) is inconsistent. % 100.66/15.54 | | | | | | | % 100.66/15.54 | | | | | | End of split % 100.66/15.54 | | | | | | % 100.66/15.54 | | | | | Case 2: % 100.66/15.54 | | | | | | % 100.66/15.55 | | | | | | (211) function(all_42_6) = all_130_5 & relation(all_42_6) = % 100.66/15.55 | | | | | | all_130_6 & ( ~ (all_130_5 = 0) | ~ (all_130_6 = 0)) % 100.66/15.55 | | | | | | % 100.66/15.55 | | | | | | ALPHA: (211) implies: % 100.66/15.55 | | | | | | (212) relation(all_42_6) = all_130_6 % 100.66/15.55 | | | | | | (213) function(all_42_6) = all_130_5 % 100.66/15.55 | | | | | | (214) ~ (all_130_5 = 0) | ~ (all_130_6 = 0) % 100.66/15.55 | | | | | | % 100.66/15.55 | | | | | | REF_CLOSE: (6), (7), (189), (197), (212), (213), (214) are % 100.66/15.55 | | | | | | inconsistent by sub-proof #1. % 100.66/15.55 | | | | | | % 100.66/15.55 | | | | | End of split % 100.66/15.55 | | | | | % 100.66/15.55 | | | | End of split % 100.66/15.55 | | | | % 100.66/15.55 | | | End of split % 100.66/15.55 | | | % 100.66/15.55 | | End of split % 100.66/15.55 | | % 100.66/15.55 | End of split % 100.66/15.55 | % 100.66/15.55 End of proof % 100.66/15.55 % 100.66/15.55 Sub-proof #1 shows that the following formulas are inconsistent: % 100.66/15.55 ---------------------------------------------------------------- % 100.66/15.55 (1) ~ (all_130_5 = 0) | ~ (all_130_6 = 0) % 100.66/15.55 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 100.66/15.55 (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 100.66/15.55 (3) function(all_42_6) = 0 % 100.66/15.55 (4) relation(all_42_6) = all_130_6 % 100.66/15.55 (5) function(all_42_6) = all_130_5 % 100.66/15.55 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 100.66/15.55 (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 100.66/15.55 (7) relation(all_42_6) = 0 % 100.66/15.55 % 100.66/15.55 Begin of proof % 100.66/15.55 | % 100.66/15.55 | GROUND_INST: instantiating (6) with 0, all_130_6, all_42_6, simplifying with % 100.66/15.55 | (4), (7) gives: % 100.66/15.55 | (8) all_130_6 = 0 % 100.66/15.55 | % 100.66/15.55 | GROUND_INST: instantiating (2) with 0, all_130_5, all_42_6, simplifying with % 100.66/15.55 | (3), (5) gives: % 100.66/15.55 | (9) all_130_5 = 0 % 100.66/15.55 | % 100.66/15.55 | BETA: splitting (1) gives: % 100.66/15.55 | % 100.66/15.55 | Case 1: % 100.66/15.55 | | % 100.66/15.55 | | (10) ~ (all_130_5 = 0) % 100.66/15.55 | | % 100.66/15.55 | | REDUCE: (9), (10) imply: % 100.66/15.55 | | (11) $false % 100.66/15.55 | | % 100.66/15.55 | | CLOSE: (11) is inconsistent. % 100.66/15.55 | | % 100.66/15.55 | Case 2: % 100.66/15.55 | | % 100.66/15.55 | | (12) ~ (all_130_6 = 0) % 100.66/15.55 | | % 100.66/15.55 | | REDUCE: (8), (12) imply: % 100.66/15.55 | | (13) $false % 100.66/15.55 | | % 100.66/15.55 | | CLOSE: (13) is inconsistent. % 100.66/15.55 | | % 100.66/15.55 | End of split % 100.66/15.55 | % 100.66/15.55 End of proof % 100.66/15.55 % SZS output end Proof for theBenchmark % 100.66/15.55 % 100.66/15.55 14949ms %------------------------------------------------------------------------------