%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU003+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 : n013.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 17:42:15 EDT 2023 % Result : Theorem 24.03s 4.08s % Output : Proof 104.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.15 % Problem : SEU003+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n013.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Wed Aug 23 12:38:32 EDT 2023 % 0.14/0.35 % CPUTime : % 0.19/0.64 ________ _____ % 0.19/0.64 ___ __ \_________(_)________________________________ % 0.19/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.64 % 0.19/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.64 (2023-06-19) % 0.19/0.64 % 0.19/0.64 (c) Philipp Rümmer, 2009-2023 % 0.19/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.64 Amanda Stjerna. % 0.19/0.64 Free software under BSD-3-Clause. % 0.19/0.64 % 0.19/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.64 % 0.19/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.66 Running up to 7 provers in parallel. % 0.19/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.69/1.16 Prover 4: Preprocessing ... % 2.69/1.16 Prover 1: Preprocessing ... % 3.29/1.20 Prover 0: Preprocessing ... % 3.29/1.20 Prover 3: Preprocessing ... % 3.29/1.20 Prover 6: Preprocessing ... % 3.29/1.20 Prover 2: Preprocessing ... % 3.29/1.20 Prover 5: Preprocessing ... % 6.87/1.72 Prover 1: Warning: ignoring some quantifiers % 6.87/1.74 Prover 3: Warning: ignoring some quantifiers % 7.27/1.76 Prover 1: Constructing countermodel ... % 7.27/1.76 Prover 3: Constructing countermodel ... % 7.27/1.77 Prover 5: Proving ... % 7.27/1.80 Prover 6: Proving ... % 7.27/1.83 Prover 2: Proving ... % 8.53/1.97 Prover 4: Warning: ignoring some quantifiers % 8.53/2.01 Prover 4: Constructing countermodel ... % 9.71/2.16 Prover 0: Proving ... % 10.84/2.31 Prover 3: gave up % 11.18/2.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.35/2.38 Prover 7: Preprocessing ... % 11.97/2.47 Prover 7: Warning: ignoring some quantifiers % 12.36/2.50 Prover 7: Constructing countermodel ... % 17.55/3.19 Prover 1: gave up % 17.55/3.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.86/3.25 Prover 8: Preprocessing ... % 17.86/3.32 Prover 8: Warning: ignoring some quantifiers % 17.86/3.32 Prover 8: Constructing countermodel ... % 20.99/3.72 Prover 7: gave up % 21.69/3.74 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 21.69/3.77 Prover 9: Preprocessing ... % 22.13/3.83 Prover 8: gave up % 22.13/3.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.70/3.88 Prover 10: Preprocessing ... % 22.70/3.94 Prover 10: Warning: ignoring some quantifiers % 22.70/3.96 Prover 10: Constructing countermodel ... % 22.70/3.98 Prover 9: Warning: ignoring some quantifiers % 22.70/3.98 Prover 9: Constructing countermodel ... % 23.26/4.04 Prover 10: gave up % 23.26/4.04 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 24.03/4.07 Prover 11: Preprocessing ... % 24.03/4.08 Prover 0: proved (3407ms) % 24.03/4.08 % 24.03/4.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 24.03/4.08 % 24.03/4.08 Prover 9: stopped % 24.03/4.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.03/4.08 Prover 2: stopped % 24.03/4.08 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 24.03/4.08 Prover 5: stopped % 24.03/4.08 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 24.03/4.08 Prover 6: stopped % 24.03/4.11 Prover 19: Preprocessing ... % 24.03/4.12 Prover 16: Preprocessing ... % 24.03/4.12 Prover 13: Preprocessing ... % 24.75/4.15 Prover 16: Warning: ignoring some quantifiers % 24.75/4.18 Prover 16: Constructing countermodel ... % 25.12/4.19 Prover 13: Warning: ignoring some quantifiers % 25.12/4.20 Prover 13: Constructing countermodel ... % 25.12/4.21 Prover 19: Warning: ignoring some quantifiers % 25.12/4.22 Prover 19: Constructing countermodel ... % 25.12/4.24 Prover 11: Warning: ignoring some quantifiers % 25.12/4.24 Prover 11: Constructing countermodel ... % 27.93/4.62 Prover 19: gave up % 66.75/10.34 Prover 13: stopped % 73.25/12.02 Prover 16: stopped % 102.81/23.46 Prover 11: Found proof (size 444) % 102.81/23.46 Prover 11: proved (19418ms) % 102.81/23.46 Prover 4: stopped % 102.81/23.46 % 102.81/23.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 102.81/23.46 % 103.07/23.50 % SZS output start Proof for theBenchmark % 103.07/23.50 Assumptions after simplification: % 103.07/23.50 --------------------------------- % 103.07/23.50 % 103.07/23.50 (cc1_funct_1) % 103.17/23.55 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (function(v0) = v1) | ~ $i(v0) | ? % 103.17/23.55 [v2: int] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0: $i] : ( ~ (empty(v0) = % 103.17/23.55 0) | ~ $i(v0) | function(v0) = 0) % 103.17/23.55 % 103.17/23.55 (d3_tarski) % 103.17/23.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 103.17/23.56 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 103.17/23.56 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 103.17/23.56 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 103.17/23.56 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 103.17/23.56 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 103.17/23.56 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 103.17/23.56 $i(v0) | in(v2, v1) = 0) % 103.17/23.56 % 103.17/23.56 (d5_funct_1) % 103.17/23.60 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 103.17/23.60 int] : ? [v3: int] : ? [v4: $i] : (( ~ (v3 = 0) & function(v0) = v3) | ( % 103.17/23.60 ~ (v2 = 0) & relation(v0) = v2) | (relation_dom(v0) = v4 & $i(v4) & ! % 103.17/23.60 [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ (apply(v0, v7) = % 103.17/23.60 v5) | ~ (in(v5, v1) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v1) | ? % 103.17/23.60 [v8: int] : ( ~ (v8 = 0) & in(v7, v4) = v8)) & ! [v5: $i] : ! [v6: % 103.17/23.60 int] : ! [v7: $i] : (v6 = 0 | ~ (in(v7, v4) = 0) | ~ (in(v5, v1) = % 103.17/23.60 v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v1) | ? [v8: $i] : ( ~ (v8 = % 103.17/23.60 v5) & apply(v0, v7) = v8 & $i(v8))) & ! [v5: $i] : ( ~ (in(v5, % 103.17/23.60 v1) = 0) | ~ $i(v5) | ~ $i(v1) | ? [v6: $i] : (apply(v0, v6) = % 103.17/23.60 v5 & in(v6, v4) = 0 & $i(v6))) & ? [v5: $i] : (v5 = v1 | ~ $i(v5) % 103.17/23.60 | ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: % 103.17/23.60 $i] : ($i(v8) & $i(v6) & ((v10 = v6 & v9 = 0 & apply(v0, v8) = v6 & % 103.17/23.60 in(v8, v4) = 0) | (v7 = 0 & in(v6, v5) = 0)) & (( ~ (v7 = 0) & % 103.17/23.60 in(v6, v5) = v7) | ( ! [v11: $i] : ( ~ (apply(v0, v11) = v6) | % 103.17/23.60 ~ $i(v11) | ? [v12: int] : ( ~ (v12 = 0) & in(v11, v4) = % 103.17/23.60 v12)) & ! [v11: $i] : ( ~ (in(v11, v4) = 0) | ~ $i(v11) | % 103.17/23.60 ? [v12: $i] : ( ~ (v12 = v6) & apply(v0, v11) = v12 & % 103.17/23.60 $i(v12)))))))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 103.17/23.60 (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ? [v4: % 103.17/23.60 $i] : (( ~ (v3 = 0) & function(v0) = v3) | ( ~ (v2 = 0) & relation(v0) = % 103.17/23.60 v2) | (relation_rng(v0) = v4 & $i(v4) & ! [v5: $i] : ! [v6: int] : ! % 103.17/23.60 [v7: $i] : (v6 = 0 | ~ (apply(v0, v7) = v5) | ~ (in(v5, v4) = v6) | ~ % 103.17/23.60 $i(v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & in(v7, v1) = v8)) & % 103.17/23.60 ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ (in(v7, v1) = 0) % 103.17/23.60 | ~ (in(v5, v4) = v6) | ~ $i(v7) | ~ $i(v5) | ? [v8: $i] : ( ~ (v8 % 103.17/23.60 = v5) & apply(v0, v7) = v8 & $i(v8))) & ! [v5: $i] : ( ~ (in(v5, % 103.17/23.60 v4) = 0) | ~ $i(v5) | ? [v6: $i] : (apply(v0, v6) = v5 & in(v6, % 103.17/23.60 v1) = 0 & $i(v6))) & ? [v5: $i] : (v5 = v4 | ~ $i(v5) | ? [v6: % 103.17/23.60 $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : % 103.17/23.60 ($i(v8) & $i(v6) & ((v10 = v6 & v9 = 0 & apply(v0, v8) = v6 & in(v8, % 103.17/23.60 v1) = 0) | (v7 = 0 & in(v6, v5) = 0)) & (( ~ (v7 = 0) & in(v6, % 103.17/23.60 v5) = v7) | ( ! [v11: $i] : ( ~ (apply(v0, v11) = v6) | ~ % 103.17/23.60 $i(v11) | ? [v12: int] : ( ~ (v12 = 0) & in(v11, v1) = v12)) % 103.17/23.60 & ! [v11: $i] : ( ~ (in(v11, v1) = 0) | ~ $i(v11) | ? [v12: % 103.17/23.60 $i] : ( ~ (v12 = v6) & apply(v0, v11) = v12 & % 103.17/23.60 $i(v12)))))))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ % 103.17/23.61 $i(v0) | ? [v1: int] : ? [v2: $i] : ? [v3: $i] : (( ~ (v1 = 0) & % 103.17/23.61 function(v0) = v1) | (relation_rng(v0) = v2 & relation_dom(v0) = v3 & % 103.17/23.61 $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | % 103.17/23.61 ~ (apply(v0, v6) = v4) | ~ (in(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) % 103.17/23.61 | ? [v7: int] : ( ~ (v7 = 0) & in(v6, v3) = v7)) & ! [v4: $i] : ! % 103.17/23.61 [v5: int] : ! [v6: $i] : (v5 = 0 | ~ (in(v6, v3) = 0) | ~ (in(v4, v2) % 103.17/23.61 = v5) | ~ $i(v6) | ~ $i(v4) | ? [v7: $i] : ( ~ (v7 = v4) & % 103.17/23.61 apply(v0, v6) = v7 & $i(v7))) & ! [v4: $i] : ( ~ (in(v4, v2) = 0) | % 103.17/23.61 ~ $i(v4) | ? [v5: $i] : (apply(v0, v5) = v4 & in(v5, v3) = 0 & % 103.17/23.61 $i(v5))) & ? [v4: $i] : (v4 = v2 | ~ $i(v4) | ? [v5: $i] : ? % 103.17/23.61 [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ($i(v7) & % 103.17/23.61 $i(v5) & ((v9 = v5 & v8 = 0 & apply(v0, v7) = v5 & in(v7, v3) = 0) | % 103.17/23.61 (v6 = 0 & in(v5, v4) = 0)) & (( ~ (v6 = 0) & in(v5, v4) = v6) | ( % 103.17/23.61 ! [v10: $i] : ( ~ (apply(v0, v10) = v5) | ~ $i(v10) | ? [v11: % 103.17/23.61 int] : ( ~ (v11 = 0) & in(v10, v3) = v11)) & ! [v10: $i] : % 103.17/23.61 ( ~ (in(v10, v3) = 0) | ~ $i(v10) | ? [v11: $i] : ( ~ (v11 = % 103.17/23.61 v5) & apply(v0, v10) = v11 & $i(v11)))))))))) & ! [v0: % 103.17/23.61 $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ? % 103.17/23.61 [v3: $i] : (( ~ (v1 = 0) & relation(v0) = v1) | (relation_rng(v0) = v2 & % 103.17/23.61 relation_dom(v0) = v3 & $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: int] : % 103.17/23.61 ! [v6: $i] : (v5 = 0 | ~ (apply(v0, v6) = v4) | ~ (in(v4, v2) = v5) | % 103.17/23.61 ~ $i(v6) | ~ $i(v4) | ? [v7: int] : ( ~ (v7 = 0) & in(v6, v3) = v7)) % 103.17/23.61 & ! [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ (in(v6, v3) = % 103.17/23.61 0) | ~ (in(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) | ? [v7: $i] : ( % 103.17/23.61 ~ (v7 = v4) & apply(v0, v6) = v7 & $i(v7))) & ! [v4: $i] : ( ~ % 103.17/23.61 (in(v4, v2) = 0) | ~ $i(v4) | ? [v5: $i] : (apply(v0, v5) = v4 & % 103.17/23.61 in(v5, v3) = 0 & $i(v5))) & ? [v4: $i] : (v4 = v2 | ~ $i(v4) | ? % 103.17/23.61 [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : % 103.17/23.61 ($i(v7) & $i(v5) & ((v9 = v5 & v8 = 0 & apply(v0, v7) = v5 & in(v7, % 103.17/23.61 v3) = 0) | (v6 = 0 & in(v5, v4) = 0)) & (( ~ (v6 = 0) & in(v5, % 103.17/23.61 v4) = v6) | ( ! [v10: $i] : ( ~ (apply(v0, v10) = v5) | ~ % 103.17/23.61 $i(v10) | ? [v11: int] : ( ~ (v11 = 0) & in(v10, v3) = v11)) % 103.17/23.61 & ! [v10: $i] : ( ~ (in(v10, v3) = 0) | ~ $i(v10) | ? [v11: % 103.17/23.61 $i] : ( ~ (v11 = v5) & apply(v0, v10) = v11 & % 103.17/23.61 $i(v11)))))))))) % 103.17/23.61 % 103.17/23.61 (fc10_relat_1) % 103.17/23.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v1, v0) = % 103.17/23.61 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] : % 103.17/23.61 ? [v6: int] : ((v6 = 0 & v5 = 0 & relation(v2) = 0 & empty(v2) = 0) | ( ~ % 103.17/23.61 (v4 = 0) & relation(v1) = v4) | ( ~ (v3 = 0) & empty(v0) = v3))) % 103.17/23.61 % 103.17/23.61 (fc4_relat_1) % 103.17/23.61 relation(empty_set) = 0 & empty(empty_set) = 0 & $i(empty_set) % 103.17/23.61 % 103.17/23.61 (fc5_relat_1) % 103.17/23.61 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 103.17/23.61 [v2: int] : ? [v3: $i] : ? [v4: int] : (( ~ (v4 = 0) & relation_dom(v0) = % 103.17/23.61 v3 & empty(v3) = v4 & $i(v3)) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! % 103.17/23.61 [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 103.17/23.61 int] : ? [v3: int] : ? [v4: int] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v4 = % 103.17/23.61 0) & empty(v1) = v4) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0: % 103.17/23.61 $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ? % 103.17/23.61 [v3: int] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & relation_dom(v0) = v2 % 103.17/23.61 & empty(v2) = v3 & $i(v2)))) % 103.17/23.61 % 103.17/23.61 (fc6_relat_1) % 103.17/23.62 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 103.17/23.62 [v2: int] : ? [v3: $i] : ? [v4: int] : (( ~ (v4 = 0) & relation_rng(v0) = % 103.17/23.62 v3 & empty(v3) = v4 & $i(v3)) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! % 103.17/23.62 [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 103.17/23.62 int] : ? [v3: int] : ? [v4: int] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v4 = % 103.17/23.62 0) & empty(v1) = v4) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0: % 103.17/23.62 $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ? % 103.17/23.62 [v3: int] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & relation_rng(v0) = v2 % 103.17/23.62 & empty(v2) = v3 & $i(v2)))) % 103.17/23.62 % 103.17/23.62 (fc7_relat_1) % 103.17/23.62 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 103.17/23.62 int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & relation(v1) = 0 % 103.17/23.62 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0: $i] : ( ~ % 103.17/23.62 (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (relation_dom(v0) = v1 & % 103.17/23.62 relation(v1) = 0 & empty(v1) = 0 & $i(v1))) % 103.17/23.62 % 103.17/23.62 (fc8_relat_1) % 103.17/23.62 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 103.17/23.62 int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & relation(v1) = 0 % 103.17/23.62 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0: $i] : ( ~ % 103.17/23.62 (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (relation_rng(v0) = v1 & % 103.17/23.62 relation(v1) = 0 & empty(v1) = 0 & $i(v1))) % 103.17/23.62 % 103.17/23.62 (rc1_relat_1) % 103.17/23.62 ? [v0: $i] : (relation(v0) = 0 & empty(v0) = 0 & $i(v0)) % 103.17/23.62 % 103.17/23.62 (rc1_subset_1) % 103.17/23.62 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 103.17/23.62 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v0) = v2 & % 103.17/23.62 element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) & $i(v2))) & ! [v0: $i] : % 103.17/23.62 ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] % 103.17/23.62 : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & % 103.17/23.62 element(v3, v1) = 0 & empty(v3) = v5) | (v2 = 0 & empty(v0) = 0)))) % 103.17/23.62 % 103.17/23.62 (rc1_xboole_0) % 103.17/23.62 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 103.17/23.62 % 103.17/23.62 (rc2_relat_1) % 103.17/23.62 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1 % 103.17/23.62 & $i(v0)) % 103.17/23.62 % 103.17/23.62 (rc2_subset_1) % 103.17/23.63 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 103.17/23.63 : (element(v2, v1) = 0 & empty(v2) = 0 & $i(v2))) % 103.17/23.63 % 103.17/23.63 (rc2_xboole_0) % 103.17/23.63 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 103.17/23.63 % 103.17/23.63 (rc3_relat_1) % 103.17/23.63 ? [v0: $i] : (relation_empty_yielding(v0) = 0 & relation(v0) = 0 & $i(v0)) % 103.17/23.63 % 103.17/23.63 (t21_funct_1) % 103.47/23.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 103.47/23.67 (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ $i(v3) | ~ $i(v1) | % 103.47/23.67 ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 103.47/23.67 int] : ? [v10: $i] : ? [v11: int] : ? [v12: int] : (( ~ (v6 = 0) & % 103.47/23.67 function(v3) = v6) | ( ~ (v6 = 0) & function(v1) = v6) | ( ~ (v5 = 0) & % 103.47/23.67 relation(v3) = v5) | ( ~ (v5 = 0) & relation(v1) = v5) | (((v12 = 0 & % 103.47/23.67 v11 = 0 & relation_dom(v3) = v10 & in(v4, v2) = 0 & in(v0, v10) = 0 % 103.47/23.67 & $i(v10)) | ( ~ (v9 = 0) & relation_composition(v3, v1) = v7 & % 103.47/23.67 relation_dom(v7) = v8 & in(v0, v8) = v9 & $i(v8) & $i(v7))) & ((v9 = % 103.47/23.67 0 & relation_composition(v3, v1) = v7 & relation_dom(v7) = v8 & % 103.47/23.67 in(v0, v8) = 0 & $i(v8) & $i(v7)) | ( ~ (v12 = 0) & in(v4, v2) = % 103.47/23.67 v12) | ( ~ (v11 = 0) & relation_dom(v3) = v10 & in(v0, v10) = v11 & % 103.47/23.67 $i(v10)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 103.47/23.67 : ! [v4: $i] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) % 103.47/23.67 = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : % 103.47/23.67 ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? % 103.47/23.67 [v12: int] : (( ~ (v6 = 0) & function(v3) = v6) | ( ~ (v6 = 0) & % 103.47/23.67 function(v1) = v6) | ( ~ (v5 = 0) & relation(v3) = v5) | ( ~ (v5 = 0) & % 103.47/23.67 relation(v1) = v5) | (((v12 = 0 & v10 = 0 & relation_dom(v3) = v9 & % 103.47/23.67 apply(v3, v0) = v11 & in(v11, v2) = 0 & in(v0, v9) = 0 & $i(v11) & % 103.47/23.67 $i(v9)) | ( ~ (v8 = 0) & relation_dom(v4) = v7 & in(v0, v7) = v8 & % 103.47/23.67 $i(v7))) & ((v8 = 0 & relation_dom(v4) = v7 & in(v0, v7) = 0 & % 103.47/23.67 $i(v7)) | ( ~ (v12 = 0) & apply(v3, v0) = v11 & in(v11, v2) = v12 & % 103.47/23.67 $i(v11)) | ( ~ (v10 = 0) & relation_dom(v3) = v9 & in(v0, v9) = v10 % 103.47/23.67 & $i(v9)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 103.47/23.67 $i] : ! [v4: $i] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) % 103.47/23.67 | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 103.47/23.67 $i] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ? [v11: $i] : ? [v12: % 103.47/23.67 int] : (( ~ (v6 = 0) & function(v3) = v6) | ( ~ (v6 = 0) & function(v1) = % 103.47/23.67 v6) | ( ~ (v5 = 0) & relation(v3) = v5) | ( ~ (v5 = 0) & relation(v1) = % 103.47/23.67 v5) | (((v12 = 0 & v10 = 0 & apply(v3, v0) = v11 & in(v11, v2) = 0 & % 103.47/23.67 in(v0, v4) = 0 & $i(v11)) | ( ~ (v9 = 0) & relation_composition(v3, % 103.47/23.67 v1) = v7 & relation_dom(v7) = v8 & in(v0, v8) = v9 & $i(v8) & % 103.47/23.67 $i(v7))) & ((v9 = 0 & relation_composition(v3, v1) = v7 & % 103.47/23.67 relation_dom(v7) = v8 & in(v0, v8) = 0 & $i(v8) & $i(v7)) | ( ~ (v12 % 103.47/23.67 = 0) & apply(v3, v0) = v11 & in(v11, v2) = v12 & $i(v11)) | ( ~ % 103.47/23.67 (v10 = 0) & in(v0, v4) = v10))))) & ? [v0: $i] : ! [v1: $i] : ! % 103.47/23.67 [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v1) = v2) | ~ (relation(v3) = 0) | % 103.47/23.67 ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: any] : ? [v6: % 103.47/23.67 $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: % 103.47/23.67 int] : (( ~ (v5 = 0) & function(v1) = v5) | ( ~ (v4 = 0) & relation(v1) = % 103.47/23.67 v4) | ( ~ (v4 = 0) & function(v3) = v4) | (((v11 = 0 & v9 = 0 & % 103.47/23.67 relation_dom(v3) = v8 & apply(v3, v0) = v10 & in(v10, v2) = 0 & % 103.47/23.67 in(v0, v8) = 0 & $i(v10) & $i(v8)) | ( ~ (v7 = 0) & % 103.47/23.67 relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & in(v0, % 103.47/23.67 v6) = v7 & $i(v6) & $i(v5))) & ((v7 = 0 & relation_composition(v3, % 103.47/23.67 v1) = v5 & relation_dom(v5) = v6 & in(v0, v6) = 0 & $i(v6) & % 103.47/23.67 $i(v5)) | ( ~ (v11 = 0) & apply(v3, v0) = v10 & in(v10, v2) = v11 & % 103.47/23.67 $i(v10)) | ( ~ (v9 = 0) & relation_dom(v3) = v8 & in(v0, v8) = v9 & % 103.47/23.67 $i(v8)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 103.47/23.67 : ( ~ (relation_dom(v1) = v2) | ~ (function(v3) = 0) | ~ $i(v3) | ~ $i(v1) % 103.47/23.67 | ~ $i(v0) | ? [v4: int] : ? [v5: any] : ? [v6: $i] : ? [v7: int] : ? % 103.47/23.67 [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: int] : (( ~ (v5 = 0) & % 103.47/23.68 function(v1) = v5) | ( ~ (v4 = 0) & relation(v3) = v4) | ( ~ (v4 = 0) & % 103.47/23.68 relation(v1) = v4) | (((v11 = 0 & v9 = 0 & relation_dom(v3) = v8 & % 103.47/23.68 apply(v3, v0) = v10 & in(v10, v2) = 0 & in(v0, v8) = 0 & $i(v10) & % 103.47/23.68 $i(v8)) | ( ~ (v7 = 0) & relation_composition(v3, v1) = v5 & % 103.47/23.68 relation_dom(v5) = v6 & in(v0, v6) = v7 & $i(v6) & $i(v5))) & ((v7 = % 103.47/23.68 0 & relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & % 103.47/23.68 in(v0, v6) = 0 & $i(v6) & $i(v5)) | ( ~ (v11 = 0) & apply(v3, v0) = % 103.47/23.68 v10 & in(v10, v2) = v11 & $i(v10)) | ( ~ (v9 = 0) & relation_dom(v3) % 103.47/23.68 = v8 & in(v0, v8) = v9 & $i(v8)))))) & ? [v0: $i] : ! [v1: $i] : ( % 103.47/23.68 ~ (relation(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : % 103.47/23.68 (( ~ (v2 = 0) & function(v1) = v2) | (relation_dom(v1) = v3 & $i(v3) & ! % 103.47/23.68 [v4: $i] : ! [v5: $i] : ( ~ (relation_composition(v4, v1) = v5) | ~ % 103.47/23.68 $i(v4) | ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? % 103.47/23.68 [v10: $i] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : (( ~ (v7 = % 103.47/23.68 0) & function(v4) = v7) | ( ~ (v6 = 0) & relation(v4) = v6) | % 103.47/23.68 (((v13 = 0 & v11 = 0 & relation_dom(v4) = v10 & apply(v4, v0) = v12 % 103.47/23.68 & in(v12, v3) = 0 & in(v0, v10) = 0 & $i(v12) & $i(v10)) | ( ~ % 103.47/23.68 (v9 = 0) & relation_dom(v5) = v8 & in(v0, v8) = v9 & $i(v8))) % 103.47/23.68 & ((v9 = 0 & relation_dom(v5) = v8 & in(v0, v8) = 0 & $i(v8)) | ( % 103.47/23.68 ~ (v13 = 0) & apply(v4, v0) = v12 & in(v12, v3) = v13 & % 103.47/23.68 $i(v12)) | ( ~ (v11 = 0) & relation_dom(v4) = v10 & in(v0, % 103.47/23.68 v10) = v11 & $i(v10)))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 103.47/23.68 (relation_dom(v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 103.47/23.68 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : ? [v12: $i] % 103.47/23.68 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 103.47/23.68 relation(v4) = v6) | (((v13 = 0 & v11 = 0 & apply(v4, v0) = v12 & % 103.47/23.68 in(v12, v3) = 0 & in(v0, v5) = 0 & $i(v12)) | ( ~ (v10 = 0) & % 103.47/23.68 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 103.47/23.68 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 103.47/23.68 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 103.47/23.68 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & apply(v4, % 103.47/23.68 v0) = v12 & in(v12, v3) = v13 & $i(v12)) | ( ~ (v11 = 0) & % 103.47/23.68 in(v0, v5) = v11))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 103.47/23.68 (apply(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 103.47/23.68 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] % 103.47/23.68 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 103.47/23.68 relation(v4) = v6) | (((v13 = 0 & v12 = 0 & relation_dom(v4) = v11 % 103.47/23.68 & in(v5, v3) = 0 & in(v0, v11) = 0 & $i(v11)) | ( ~ (v10 = 0) % 103.47/23.68 & relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 103.47/23.68 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 103.47/23.68 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 103.47/23.68 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & in(v5, v3) % 103.47/23.68 = v13) | ( ~ (v12 = 0) & relation_dom(v4) = v11 & in(v0, v11) % 103.47/23.68 = v12 & $i(v11)))))) & ! [v4: $i] : ( ~ (relation(v4) = 0) | % 103.47/23.68 ~ $i(v4) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 103.47/23.68 ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] : (( ~ (v5 = % 103.47/23.68 0) & function(v4) = v5) | (((v12 = 0 & v10 = 0 & % 103.47/23.68 relation_dom(v4) = v9 & apply(v4, v0) = v11 & in(v11, v3) = 0 % 103.47/23.68 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 = 0) & % 103.47/23.68 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 103.47/23.68 in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 103.47/23.68 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 103.47/23.68 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 103.47/23.68 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 103.47/23.68 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9)))))) & ! % 103.47/23.68 [v4: $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: int] : ? [v6: % 103.47/23.68 $i] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? % 103.47/23.68 [v11: $i] : ? [v12: int] : (( ~ (v5 = 0) & relation(v4) = v5) | % 103.47/23.68 (((v12 = 0 & v10 = 0 & relation_dom(v4) = v9 & apply(v4, v0) = v11 & % 103.47/23.68 in(v11, v3) = 0 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 % 103.47/23.68 = 0) & relation_composition(v4, v1) = v6 & relation_dom(v6) % 103.47/23.68 = v7 & in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 103.47/23.68 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 103.47/23.68 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 103.47/23.68 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 103.47/23.68 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9))))))))) & ? % 103.47/23.68 [v0: $i] : ! [v1: $i] : ( ~ (function(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 103.47/23.68 [v2: int] : ? [v3: $i] : (( ~ (v2 = 0) & relation(v1) = v2) | % 103.47/23.68 (relation_dom(v1) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ % 103.47/23.68 (relation_composition(v4, v1) = v5) | ~ $i(v4) | ? [v6: int] : ? % 103.47/23.68 [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: int] % 103.47/23.68 : ? [v12: $i] : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | % 103.47/23.68 ( ~ (v6 = 0) & relation(v4) = v6) | (((v13 = 0 & v11 = 0 & % 103.47/23.68 relation_dom(v4) = v10 & apply(v4, v0) = v12 & in(v12, v3) = 0 % 103.47/23.68 & in(v0, v10) = 0 & $i(v12) & $i(v10)) | ( ~ (v9 = 0) & % 103.47/23.68 relation_dom(v5) = v8 & in(v0, v8) = v9 & $i(v8))) & ((v9 = 0 % 103.47/23.68 & relation_dom(v5) = v8 & in(v0, v8) = 0 & $i(v8)) | ( ~ (v13 % 103.47/23.68 = 0) & apply(v4, v0) = v12 & in(v12, v3) = v13 & $i(v12)) | % 103.47/23.68 ( ~ (v11 = 0) & relation_dom(v4) = v10 & in(v0, v10) = v11 & % 103.47/23.68 $i(v10)))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 103.47/23.68 (relation_dom(v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 103.47/23.68 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : ? [v12: $i] % 103.47/23.68 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 103.47/23.68 relation(v4) = v6) | (((v13 = 0 & v11 = 0 & apply(v4, v0) = v12 & % 103.47/23.68 in(v12, v3) = 0 & in(v0, v5) = 0 & $i(v12)) | ( ~ (v10 = 0) & % 103.47/23.68 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 103.47/23.68 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 103.47/23.68 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 103.47/23.68 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & apply(v4, % 103.47/23.68 v0) = v12 & in(v12, v3) = v13 & $i(v12)) | ( ~ (v11 = 0) & % 103.47/23.68 in(v0, v5) = v11))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 103.47/23.68 (apply(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 103.47/23.68 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] % 103.47/23.68 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 103.47/23.68 relation(v4) = v6) | (((v13 = 0 & v12 = 0 & relation_dom(v4) = v11 % 103.47/23.68 & in(v5, v3) = 0 & in(v0, v11) = 0 & $i(v11)) | ( ~ (v10 = 0) % 103.47/23.68 & relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 103.47/23.68 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 103.47/23.68 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 103.47/23.68 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & in(v5, v3) % 103.47/23.68 = v13) | ( ~ (v12 = 0) & relation_dom(v4) = v11 & in(v0, v11) % 103.47/23.68 = v12 & $i(v11)))))) & ! [v4: $i] : ( ~ (relation(v4) = 0) | % 103.47/23.68 ~ $i(v4) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 103.47/23.68 ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] : (( ~ (v5 = % 103.47/23.68 0) & function(v4) = v5) | (((v12 = 0 & v10 = 0 & % 103.47/23.68 relation_dom(v4) = v9 & apply(v4, v0) = v11 & in(v11, v3) = 0 % 103.47/23.68 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 = 0) & % 103.47/23.68 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 103.47/23.68 in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 103.47/23.68 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 103.47/23.68 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 103.47/23.68 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 103.47/23.68 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9)))))) & ! % 103.47/23.68 [v4: $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: int] : ? [v6: % 103.47/23.68 $i] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? % 103.47/23.68 [v11: $i] : ? [v12: int] : (( ~ (v5 = 0) & relation(v4) = v5) | % 103.47/23.68 (((v12 = 0 & v10 = 0 & relation_dom(v4) = v9 & apply(v4, v0) = v11 & % 103.47/23.68 in(v11, v3) = 0 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 % 103.47/23.68 = 0) & relation_composition(v4, v1) = v6 & relation_dom(v6) % 103.47/23.68 = v7 & in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 103.47/23.68 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 103.47/23.68 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 103.47/23.68 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 103.47/23.68 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9))))))))) % 103.47/23.68 % 103.47/23.68 (t27_funct_1) % 103.47/23.69 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 103.47/23.69 $i] : ? [v6: int] : ( ~ (v6 = 0) & relation_composition(v2, v0) = v3 & % 103.47/23.69 relation_rng(v2) = v5 & relation_dom(v3) = v4 & relation_dom(v2) = v4 & % 103.47/23.69 relation_dom(v0) = v1 & subset(v5, v1) = v6 & relation(v2) = 0 & % 103.47/23.69 relation(v0) = 0 & function(v2) = 0 & function(v0) = 0 & $i(v5) & $i(v4) & % 103.47/23.69 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 103.47/23.69 % 103.47/23.69 (t2_subset) % 103.47/23.69 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ % 103.47/23.69 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & empty(v1) = 0) % 103.47/23.69 | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 103.47/23.69 (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] % 103.47/23.69 : ((v3 = 0 & in(v0, v1) = 0) | (v2 = 0 & empty(v1) = 0))) % 103.47/23.69 % 103.47/23.69 (t3_subset) % 103.47/23.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 103.47/23.69 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 103.47/23.69 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] % 103.47/23.69 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 103.47/23.69 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, % 103.47/23.69 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 103.47/23.69 (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | % 103.47/23.69 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | % 103.47/23.69 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = % 103.47/23.69 0 & $i(v2))) % 103.47/23.69 % 103.47/23.69 (t4_subset) % 103.47/23.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 103.47/23.69 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = % 103.47/23.69 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 103.47/23.69 in(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] % 103.47/23.69 : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ % 103.47/23.69 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 103.47/23.69 powerset(v2) = v4 & element(v1, v4) = v5 & $i(v4))) & ! [v0: $i] : ! % 103.47/23.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = v3) | ~ % 103.47/23.69 (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 103.47/23.69 $i(v0) | element(v0, v2) = 0) % 103.47/23.69 % 103.47/23.69 (t6_boole) % 103.47/23.69 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 103.47/23.69 $i(v0)) % 103.47/23.69 % 103.47/23.69 (t7_boole) % 103.47/23.69 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 103.47/23.69 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2)) % 103.47/23.69 % 103.47/23.69 (t8_boole) % 103.47/23.69 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 103.47/23.69 | ~ $i(v1) | ~ $i(v0)) % 103.47/23.69 % 103.47/23.69 (function-axioms) % 103.47/23.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 103.47/23.70 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 103.47/23.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 103.47/23.70 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 103.47/23.70 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 103.47/23.70 ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: % 103.47/23.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 103.47/23.70 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 103.47/23.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 103.47/23.70 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 103.47/23.70 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 103.47/23.70 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 103.47/23.70 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ % 103.47/23.70 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 103.47/23.70 $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & % 103.47/23.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) % 103.47/23.70 | ~ (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 103.47/23.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 103.47/23.70 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 103.47/23.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 103.47/23.70 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 103.47/23.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 103.47/23.70 (empty(v2) = v0)) % 103.47/23.70 % 103.47/23.70 Further assumptions not needed in the proof: % 103.47/23.70 -------------------------------------------- % 103.47/23.70 antisymmetry_r2_hidden, cc1_relat_1, dt_k5_relat_1, existence_m1_subset_1, % 103.47/23.70 fc12_relat_1, fc1_funct_1, fc1_subset_1, fc1_xboole_0, fc9_relat_1, rc1_funct_1, % 103.47/23.70 reflexivity_r1_tarski, t1_subset, t5_subset % 103.47/23.70 % 103.47/23.70 Those formulas are unsatisfiable: % 103.47/23.70 --------------------------------- % 103.47/23.70 % 103.47/23.70 Begin of proof % 103.47/23.70 | % 103.47/23.70 | ALPHA: (cc1_funct_1) implies: % 103.47/23.70 | (1) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | function(v0) = 0) % 103.47/23.70 | % 103.47/23.70 | ALPHA: (d3_tarski) implies: % 103.47/23.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 103.47/23.70 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 103.47/23.70 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 103.47/23.70 | % 103.47/23.70 | ALPHA: (d5_funct_1) implies: % 103.47/23.71 | (3) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? % 103.47/23.71 | [v2: $i] : ? [v3: $i] : (( ~ (v1 = 0) & relation(v0) = v1) | % 103.47/23.71 | (relation_rng(v0) = v2 & relation_dom(v0) = v3 & $i(v3) & $i(v2) & % 103.47/23.71 | ! [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ (apply(v0, % 103.47/23.71 | v6) = v4) | ~ (in(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) | % 103.47/23.71 | ? [v7: int] : ( ~ (v7 = 0) & in(v6, v3) = v7)) & ! [v4: $i] : % 103.47/23.71 | ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ (in(v6, v3) = 0) | ~ % 103.47/23.71 | (in(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) | ? [v7: $i] : ( ~ % 103.47/23.71 | (v7 = v4) & apply(v0, v6) = v7 & $i(v7))) & ! [v4: $i] : ( ~ % 103.47/23.71 | (in(v4, v2) = 0) | ~ $i(v4) | ? [v5: $i] : (apply(v0, v5) = % 103.47/23.71 | v4 & in(v5, v3) = 0 & $i(v5))) & ? [v4: $i] : (v4 = v2 | ~ % 103.47/23.71 | $i(v4) | ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: % 103.47/23.71 | int] : ? [v9: $i] : ($i(v7) & $i(v5) & ((v9 = v5 & v8 = 0 & % 103.47/23.71 | apply(v0, v7) = v5 & in(v7, v3) = 0) | (v6 = 0 & in(v5, % 103.47/23.71 | v4) = 0)) & (( ~ (v6 = 0) & in(v5, v4) = v6) | ( ! % 103.47/23.71 | [v10: $i] : ( ~ (apply(v0, v10) = v5) | ~ $i(v10) | ? % 103.47/23.71 | [v11: int] : ( ~ (v11 = 0) & in(v10, v3) = v11)) & ! % 103.47/23.71 | [v10: $i] : ( ~ (in(v10, v3) = 0) | ~ $i(v10) | ? [v11: % 103.47/23.71 | $i] : ( ~ (v11 = v5) & apply(v0, v10) = v11 & % 103.47/23.71 | $i(v11)))))))))) % 103.47/23.71 | (4) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? % 103.47/23.71 | [v2: $i] : ? [v3: $i] : (( ~ (v1 = 0) & function(v0) = v1) | % 103.47/23.71 | (relation_rng(v0) = v2 & relation_dom(v0) = v3 & $i(v3) & $i(v2) & % 103.47/23.71 | ! [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ (apply(v0, % 103.47/23.71 | v6) = v4) | ~ (in(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) | % 103.47/23.71 | ? [v7: int] : ( ~ (v7 = 0) & in(v6, v3) = v7)) & ! [v4: $i] : % 103.47/23.71 | ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ (in(v6, v3) = 0) | ~ % 103.47/23.71 | (in(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) | ? [v7: $i] : ( ~ % 103.47/23.71 | (v7 = v4) & apply(v0, v6) = v7 & $i(v7))) & ! [v4: $i] : ( ~ % 103.47/23.71 | (in(v4, v2) = 0) | ~ $i(v4) | ? [v5: $i] : (apply(v0, v5) = % 103.47/23.71 | v4 & in(v5, v3) = 0 & $i(v5))) & ? [v4: $i] : (v4 = v2 | ~ % 103.47/23.71 | $i(v4) | ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: % 103.47/23.71 | int] : ? [v9: $i] : ($i(v7) & $i(v5) & ((v9 = v5 & v8 = 0 & % 103.47/23.71 | apply(v0, v7) = v5 & in(v7, v3) = 0) | (v6 = 0 & in(v5, % 103.47/23.71 | v4) = 0)) & (( ~ (v6 = 0) & in(v5, v4) = v6) | ( ! % 103.47/23.71 | [v10: $i] : ( ~ (apply(v0, v10) = v5) | ~ $i(v10) | ? % 103.47/23.71 | [v11: int] : ( ~ (v11 = 0) & in(v10, v3) = v11)) & ! % 103.47/23.71 | [v10: $i] : ( ~ (in(v10, v3) = 0) | ~ $i(v10) | ? [v11: % 103.47/23.71 | $i] : ( ~ (v11 = v5) & apply(v0, v10) = v11 & % 103.47/23.71 | $i(v11)))))))))) % 103.47/23.71 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 103.47/23.71 | ? [v2: int] : ? [v3: int] : ? [v4: $i] : (( ~ (v3 = 0) & % 103.47/23.71 | function(v0) = v3) | ( ~ (v2 = 0) & relation(v0) = v2) | % 103.47/23.71 | (relation_rng(v0) = v4 & $i(v4) & ! [v5: $i] : ! [v6: int] : ! % 103.47/23.71 | [v7: $i] : (v6 = 0 | ~ (apply(v0, v7) = v5) | ~ (in(v5, v4) = % 103.47/23.71 | v6) | ~ $i(v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 103.47/23.71 | in(v7, v1) = v8)) & ! [v5: $i] : ! [v6: int] : ! [v7: $i] % 103.47/23.71 | : (v6 = 0 | ~ (in(v7, v1) = 0) | ~ (in(v5, v4) = v6) | ~ % 103.47/23.71 | $i(v7) | ~ $i(v5) | ? [v8: $i] : ( ~ (v8 = v5) & apply(v0, % 103.47/23.71 | v7) = v8 & $i(v8))) & ! [v5: $i] : ( ~ (in(v5, v4) = 0) | % 103.47/23.71 | ~ $i(v5) | ? [v6: $i] : (apply(v0, v6) = v5 & in(v6, v1) = 0 & % 103.47/23.71 | $i(v6))) & ? [v5: $i] : (v5 = v4 | ~ $i(v5) | ? [v6: $i] : % 103.47/23.71 | ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : % 103.47/23.71 | ($i(v8) & $i(v6) & ((v10 = v6 & v9 = 0 & apply(v0, v8) = v6 & % 103.47/23.71 | in(v8, v1) = 0) | (v7 = 0 & in(v6, v5) = 0)) & (( ~ (v7 = % 103.47/23.71 | 0) & in(v6, v5) = v7) | ( ! [v11: $i] : ( ~ (apply(v0, % 103.47/23.71 | v11) = v6) | ~ $i(v11) | ? [v12: int] : ( ~ (v12 % 103.47/23.71 | = 0) & in(v11, v1) = v12)) & ! [v11: $i] : ( ~ % 103.47/23.71 | (in(v11, v1) = 0) | ~ $i(v11) | ? [v12: $i] : ( ~ % 103.47/23.71 | (v12 = v6) & apply(v0, v11) = v12 & $i(v12)))))))))) % 103.47/23.72 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 103.47/23.72 | ? [v2: int] : ? [v3: int] : ? [v4: $i] : (( ~ (v3 = 0) & % 103.47/23.72 | function(v0) = v3) | ( ~ (v2 = 0) & relation(v0) = v2) | % 103.47/23.72 | (relation_dom(v0) = v4 & $i(v4) & ! [v5: $i] : ! [v6: int] : ! % 103.47/23.72 | [v7: $i] : (v6 = 0 | ~ (apply(v0, v7) = v5) | ~ (in(v5, v1) = % 103.47/23.72 | v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v1) | ? [v8: int] : ( ~ % 103.47/23.72 | (v8 = 0) & in(v7, v4) = v8)) & ! [v5: $i] : ! [v6: int] : % 103.47/23.72 | ! [v7: $i] : (v6 = 0 | ~ (in(v7, v4) = 0) | ~ (in(v5, v1) = v6) % 103.47/23.72 | | ~ $i(v7) | ~ $i(v5) | ~ $i(v1) | ? [v8: $i] : ( ~ (v8 = % 103.47/23.72 | v5) & apply(v0, v7) = v8 & $i(v8))) & ! [v5: $i] : ( ~ % 103.47/23.72 | (in(v5, v1) = 0) | ~ $i(v5) | ~ $i(v1) | ? [v6: $i] : % 103.47/23.72 | (apply(v0, v6) = v5 & in(v6, v4) = 0 & $i(v6))) & ? [v5: $i] : % 103.47/23.72 | (v5 = v1 | ~ $i(v5) | ? [v6: $i] : ? [v7: int] : ? [v8: $i] : % 103.47/23.72 | ? [v9: int] : ? [v10: $i] : ($i(v8) & $i(v6) & ((v10 = v6 & % 103.47/23.72 | v9 = 0 & apply(v0, v8) = v6 & in(v8, v4) = 0) | (v7 = 0 & % 103.47/23.72 | in(v6, v5) = 0)) & (( ~ (v7 = 0) & in(v6, v5) = v7) | ( ! % 103.47/23.72 | [v11: $i] : ( ~ (apply(v0, v11) = v6) | ~ $i(v11) | ? % 103.47/23.72 | [v12: int] : ( ~ (v12 = 0) & in(v11, v4) = v12)) & ! % 103.47/23.72 | [v11: $i] : ( ~ (in(v11, v4) = 0) | ~ $i(v11) | ? [v12: % 103.47/23.72 | $i] : ( ~ (v12 = v6) & apply(v0, v11) = v12 & % 103.47/23.72 | $i(v12)))))))))) % 103.47/23.72 | % 103.47/23.72 | ALPHA: (fc4_relat_1) implies: % 103.47/23.72 | (7) empty(empty_set) = 0 % 103.47/23.72 | (8) relation(empty_set) = 0 % 103.47/23.72 | % 103.47/23.72 | ALPHA: (fc5_relat_1) implies: % 103.47/23.72 | (9) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? % 103.47/23.72 | [v2: $i] : ? [v3: int] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & % 103.47/23.72 | relation_dom(v0) = v2 & empty(v2) = v3 & $i(v2)))) % 103.47/23.72 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 103.47/23.72 | ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v2 = 0 & empty(v0) = % 103.47/23.72 | 0) | ( ~ (v4 = 0) & empty(v1) = v4) | ( ~ (v3 = 0) & % 103.47/23.72 | relation(v0) = v3))) % 103.47/23.72 | % 103.47/23.72 | ALPHA: (fc6_relat_1) implies: % 103.47/23.72 | (11) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? % 103.47/23.72 | [v2: $i] : ? [v3: int] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & % 103.47/23.72 | relation_rng(v0) = v2 & empty(v2) = v3 & $i(v2)))) % 103.47/23.72 | % 103.47/23.72 | ALPHA: (fc7_relat_1) implies: % 103.47/23.72 | (12) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 103.47/23.72 | (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0 & $i(v1))) % 103.47/23.72 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 103.47/23.72 | ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & % 103.47/23.72 | relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = % 103.47/23.72 | v2))) % 103.47/23.72 | % 103.47/23.72 | ALPHA: (fc8_relat_1) implies: % 103.47/23.72 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 103.47/23.72 | ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & % 103.47/23.72 | relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = % 103.47/23.72 | v2))) % 103.47/23.72 | % 103.47/23.72 | ALPHA: (rc1_subset_1) implies: % 103.47/23.72 | (15) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) % 103.47/23.72 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 103.47/23.72 | powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) % 103.47/23.72 | & $i(v2))) % 103.47/23.72 | % 103.47/23.72 | ALPHA: (t21_funct_1) implies: % 103.47/23.73 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 103.47/23.73 | ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ $i(v3) | ~ % 103.47/23.73 | $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: $i] : ? % 103.47/23.73 | [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: int] : ? [v12: % 103.47/23.73 | int] : (( ~ (v6 = 0) & function(v3) = v6) | ( ~ (v6 = 0) & % 103.47/23.73 | function(v1) = v6) | ( ~ (v5 = 0) & relation(v3) = v5) | ( ~ (v5 % 103.47/23.73 | = 0) & relation(v1) = v5) | (((v12 = 0 & v11 = 0 & % 103.47/23.73 | relation_dom(v3) = v10 & in(v4, v2) = 0 & in(v0, v10) = 0 & % 103.47/23.73 | $i(v10)) | ( ~ (v9 = 0) & relation_composition(v3, v1) = v7 % 103.47/23.73 | & relation_dom(v7) = v8 & in(v0, v8) = v9 & $i(v8) & % 103.47/23.73 | $i(v7))) & ((v9 = 0 & relation_composition(v3, v1) = v7 & % 103.47/23.73 | relation_dom(v7) = v8 & in(v0, v8) = 0 & $i(v8) & $i(v7)) | % 103.47/23.73 | ( ~ (v12 = 0) & in(v4, v2) = v12) | ( ~ (v11 = 0) & % 103.47/23.73 | relation_dom(v3) = v10 & in(v0, v10) = v11 & $i(v10)))))) % 103.47/23.73 | % 103.47/23.73 | ALPHA: (t2_subset) implies: % 103.47/23.73 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = % 103.47/23.73 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = % 103.47/23.73 | 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) % 103.47/23.73 | % 103.47/23.73 | ALPHA: (t3_subset) implies: % 103.47/23.73 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, % 103.47/23.73 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 103.47/23.73 | ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4 & $i(v3))) % 103.47/23.73 | % 103.47/23.73 | ALPHA: (t4_subset) implies: % 103.47/23.73 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 103.47/23.73 | (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ % 103.47/23.73 | (element(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 103.47/23.73 | int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) % 103.47/23.73 | % 103.47/23.73 | ALPHA: (t6_boole) implies: % 103.47/23.73 | (20) $i(empty_set) % 103.47/23.73 | (21) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 103.47/23.73 | % 103.47/23.73 | ALPHA: (function-axioms) implies: % 103.47/23.73 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 103.47/23.73 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 103.47/23.73 | (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 103.47/23.73 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 103.47/23.73 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 103.47/23.73 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 103.47/23.73 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 103.47/23.73 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 103.47/23.73 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 103.47/23.73 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 103.47/23.73 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 103.47/23.73 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 103.47/23.73 | v0)) % 103.47/23.73 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 103.47/23.73 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, % 103.47/23.73 | v2) = v0)) % 103.47/23.73 | % 103.47/23.73 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_30_0 gives: % 103.47/23.73 | (29) empty(all_30_0) = 0 & $i(all_30_0) % 103.47/23.73 | % 103.47/23.73 | ALPHA: (29) implies: % 103.47/23.73 | (30) $i(all_30_0) % 103.47/23.73 | (31) empty(all_30_0) = 0 % 103.47/23.73 | % 103.47/23.73 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_34_0 gives: % 103.47/23.73 | (32) relation(all_34_0) = 0 & empty(all_34_0) = 0 & $i(all_34_0) % 103.47/23.73 | % 103.47/23.73 | ALPHA: (32) implies: % 103.47/23.73 | (33) $i(all_34_0) % 103.47/23.73 | (34) empty(all_34_0) = 0 % 103.47/23.73 | (35) relation(all_34_0) = 0 % 103.47/23.73 | % 103.47/23.73 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_37_0, all_37_1 % 103.47/23.73 | gives: % 103.47/23.73 | (36) ~ (all_37_0 = 0) & empty(all_37_1) = all_37_0 & $i(all_37_1) % 103.47/23.73 | % 103.47/23.73 | ALPHA: (36) implies: % 103.47/23.73 | (37) ~ (all_37_0 = 0) % 103.47/23.73 | (38) $i(all_37_1) % 103.47/23.73 | (39) empty(all_37_1) = all_37_0 % 103.47/23.73 | % 103.47/23.73 | DELTA: instantiating (rc3_relat_1) with fresh symbol all_39_0 gives: % 103.47/23.73 | (40) relation_empty_yielding(all_39_0) = 0 & relation(all_39_0) = 0 & % 103.47/23.73 | $i(all_39_0) % 103.47/23.73 | % 103.47/23.73 | ALPHA: (40) implies: % 103.47/23.73 | (41) $i(all_39_0) % 103.47/23.73 | (42) relation(all_39_0) = 0 % 103.47/23.73 | % 103.47/23.73 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_41_0, all_41_1 % 103.47/23.73 | gives: % 103.47/23.74 | (43) ~ (all_41_0 = 0) & relation(all_41_1) = 0 & empty(all_41_1) = % 103.47/23.74 | all_41_0 & $i(all_41_1) % 103.47/23.74 | % 103.47/23.74 | ALPHA: (43) implies: % 103.47/23.74 | (44) ~ (all_41_0 = 0) % 103.47/23.74 | (45) $i(all_41_1) % 103.47/23.74 | (46) empty(all_41_1) = all_41_0 % 103.47/23.74 | % 103.47/23.74 | DELTA: instantiating (t27_funct_1) with fresh symbols all_43_0, all_43_1, % 103.47/23.74 | all_43_2, all_43_3, all_43_4, all_43_5, all_43_6 gives: % 103.47/23.74 | (47) ~ (all_43_0 = 0) & relation_composition(all_43_4, all_43_6) = % 103.47/23.74 | all_43_3 & relation_rng(all_43_4) = all_43_1 & relation_dom(all_43_3) % 103.47/23.74 | = all_43_2 & relation_dom(all_43_4) = all_43_2 & % 103.47/23.74 | relation_dom(all_43_6) = all_43_5 & subset(all_43_1, all_43_5) = % 103.47/23.74 | all_43_0 & relation(all_43_4) = 0 & relation(all_43_6) = 0 & % 103.47/23.74 | function(all_43_4) = 0 & function(all_43_6) = 0 & $i(all_43_1) & % 103.47/23.74 | $i(all_43_2) & $i(all_43_3) & $i(all_43_4) & $i(all_43_5) & % 103.47/23.74 | $i(all_43_6) % 103.47/23.74 | % 103.47/23.74 | ALPHA: (47) implies: % 103.47/23.74 | (48) ~ (all_43_0 = 0) % 104.27/23.74 | (49) $i(all_43_6) % 104.27/23.74 | (50) $i(all_43_5) % 104.27/23.74 | (51) $i(all_43_4) % 104.27/23.74 | (52) $i(all_43_3) % 104.27/23.74 | (53) $i(all_43_1) % 104.27/23.74 | (54) function(all_43_6) = 0 % 104.27/23.74 | (55) function(all_43_4) = 0 % 104.27/23.74 | (56) relation(all_43_6) = 0 % 104.27/23.74 | (57) relation(all_43_4) = 0 % 104.27/23.74 | (58) subset(all_43_1, all_43_5) = all_43_0 % 104.27/23.74 | (59) relation_dom(all_43_6) = all_43_5 % 104.27/23.74 | (60) relation_dom(all_43_4) = all_43_2 % 104.27/23.74 | (61) relation_dom(all_43_3) = all_43_2 % 104.27/23.74 | (62) relation_rng(all_43_4) = all_43_1 % 104.27/23.74 | (63) relation_composition(all_43_4, all_43_6) = all_43_3 % 104.27/23.74 | % 104.27/23.74 | GROUND_INST: instantiating (12) with empty_set, simplifying with (7), (20) % 104.27/23.74 | gives: % 104.27/23.74 | (64) ? [v0: $i] : (relation_dom(empty_set) = v0 & relation(v0) = 0 & % 104.27/23.74 | empty(v0) = 0 & $i(v0)) % 104.27/23.74 | % 104.27/23.74 | GROUND_INST: instantiating (1) with all_30_0, simplifying with (30), (31) % 104.27/23.74 | gives: % 104.27/23.74 | (65) function(all_30_0) = 0 % 104.27/23.74 | % 104.27/23.74 | GROUND_INST: instantiating (12) with all_30_0, simplifying with (30), (31) % 104.27/23.74 | gives: % 104.27/23.74 | (66) ? [v0: $i] : (relation_dom(all_30_0) = v0 & relation(v0) = 0 & % 104.27/23.74 | empty(v0) = 0 & $i(v0)) % 104.27/23.74 | % 104.27/23.74 | GROUND_INST: instantiating (t8_boole) with all_30_0, all_34_0, simplifying % 104.27/23.74 | with (30), (31), (33), (34) gives: % 104.27/23.74 | (67) all_34_0 = all_30_0 % 104.27/23.74 | % 104.27/23.74 | GROUND_INST: instantiating (21) with all_34_0, simplifying with (33), (34) % 104.27/23.74 | gives: % 104.27/23.74 | (68) all_34_0 = empty_set % 104.27/23.74 | % 104.27/23.74 | GROUND_INST: instantiating (12) with all_34_0, simplifying with (33), (34) % 104.27/23.74 | gives: % 104.27/23.74 | (69) ? [v0: $i] : (relation_dom(all_34_0) = v0 & relation(v0) = 0 & % 104.27/23.74 | empty(v0) = 0 & $i(v0)) % 104.27/23.74 | % 104.27/23.74 | GROUND_INST: instantiating (15) with all_37_1, all_37_0, simplifying with % 104.27/23.74 | (38), (39) gives: % 104.27/23.74 | (70) all_37_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 104.27/23.74 | & powerset(all_37_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2 & % 104.27/23.74 | $i(v1) & $i(v0)) % 104.27/23.74 | % 104.27/23.74 | GROUND_INST: instantiating (15) with all_41_1, all_41_0, simplifying with % 104.27/23.74 | (45), (46) gives: % 104.27/23.74 | (71) all_41_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 104.27/23.74 | & powerset(all_41_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2 & % 104.27/23.74 | $i(v1) & $i(v0)) % 104.27/23.74 | % 104.27/23.74 | GROUND_INST: instantiating (3) with all_43_6, simplifying with (49), (54) % 104.27/23.74 | gives: % 104.27/23.75 | (72) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : (( ~ (v0 = 0) & % 104.27/23.75 | relation(all_43_6) = v0) | (relation_rng(all_43_6) = v1 & % 104.27/23.75 | relation_dom(all_43_6) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! % 104.27/23.75 | [v4: int] : ! [v5: $i] : (v4 = 0 | ~ (apply(all_43_6, v5) = v3) % 104.27/23.75 | | ~ (in(v3, v1) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: int] : % 104.27/23.75 | ( ~ (v6 = 0) & in(v5, v2) = v6)) & ! [v3: $i] : ! [v4: int] : % 104.27/23.75 | ! [v5: $i] : (v4 = 0 | ~ (in(v5, v2) = 0) | ~ (in(v3, v1) = v4) % 104.27/23.75 | | ~ $i(v5) | ~ $i(v3) | ? [v6: $i] : ( ~ (v6 = v3) & % 104.27/23.75 | apply(all_43_6, v5) = v6 & $i(v6))) & ! [v3: $i] : ( ~ % 104.27/23.75 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_43_6, % 104.27/23.75 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 = % 104.27/23.75 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ? % 104.27/23.75 | [v7: int] : ? [v8: $i] : ($i(v6) & $i(v4) & ((v8 = v4 & v7 = 0 % 104.27/23.75 | & apply(all_43_6, v6) = v4 & in(v6, v2) = 0) | (v5 = 0 & % 104.27/23.75 | in(v4, v3) = 0)) & (( ~ (v5 = 0) & in(v4, v3) = v5) | ( ! % 104.27/23.75 | [v9: $i] : ( ~ (apply(all_43_6, v9) = v4) | ~ $i(v9) | ? % 104.27/23.75 | [v10: int] : ( ~ (v10 = 0) & in(v9, v2) = v10)) & ! % 104.27/23.75 | [v9: $i] : ( ~ (in(v9, v2) = 0) | ~ $i(v9) | ? [v10: $i] % 104.27/23.75 | : ( ~ (v10 = v4) & apply(all_43_6, v9) = v10 & % 104.27/23.75 | $i(v10))))))))) % 104.27/23.75 | % 104.27/23.75 | GROUND_INST: instantiating (3) with all_43_4, simplifying with (51), (55) % 104.27/23.75 | gives: % 104.27/23.75 | (73) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : (( ~ (v0 = 0) & % 104.27/23.75 | relation(all_43_4) = v0) | (relation_rng(all_43_4) = v1 & % 104.27/23.75 | relation_dom(all_43_4) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! % 104.27/23.75 | [v4: int] : ! [v5: $i] : (v4 = 0 | ~ (apply(all_43_4, v5) = v3) % 104.27/23.75 | | ~ (in(v3, v1) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: int] : % 104.27/23.75 | ( ~ (v6 = 0) & in(v5, v2) = v6)) & ! [v3: $i] : ! [v4: int] : % 104.27/23.75 | ! [v5: $i] : (v4 = 0 | ~ (in(v5, v2) = 0) | ~ (in(v3, v1) = v4) % 104.27/23.75 | | ~ $i(v5) | ~ $i(v3) | ? [v6: $i] : ( ~ (v6 = v3) & % 104.27/23.75 | apply(all_43_4, v5) = v6 & $i(v6))) & ! [v3: $i] : ( ~ % 104.27/23.75 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_43_4, % 104.27/23.75 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 = % 104.27/23.75 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ? % 104.27/23.75 | [v7: int] : ? [v8: $i] : ($i(v6) & $i(v4) & ((v8 = v4 & v7 = 0 % 104.27/23.75 | & apply(all_43_4, v6) = v4 & in(v6, v2) = 0) | (v5 = 0 & % 104.27/23.75 | in(v4, v3) = 0)) & (( ~ (v5 = 0) & in(v4, v3) = v5) | ( ! % 104.27/23.75 | [v9: $i] : ( ~ (apply(all_43_4, v9) = v4) | ~ $i(v9) | ? % 104.27/23.75 | [v10: int] : ( ~ (v10 = 0) & in(v9, v2) = v10)) & ! % 104.27/23.75 | [v9: $i] : ( ~ (in(v9, v2) = 0) | ~ $i(v9) | ? [v10: $i] % 104.27/23.75 | : ( ~ (v10 = v4) & apply(all_43_4, v9) = v10 & % 104.27/23.75 | $i(v10))))))))) % 104.27/23.75 | % 104.27/23.75 | GROUND_INST: instantiating (4) with empty_set, simplifying with (8), (20) % 104.27/23.75 | gives: % 104.27/23.75 | (74) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : (( ~ (v0 = 0) & % 104.27/23.75 | function(empty_set) = v0) | (relation_rng(empty_set) = v1 & % 104.27/23.75 | relation_dom(empty_set) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! % 104.27/23.75 | [v4: int] : ! [v5: $i] : (v4 = 0 | ~ (apply(empty_set, v5) = v3) % 104.27/23.75 | | ~ (in(v3, v1) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: int] : % 104.27/23.75 | ( ~ (v6 = 0) & in(v5, v2) = v6)) & ! [v3: $i] : ! [v4: int] : % 104.27/23.75 | ! [v5: $i] : (v4 = 0 | ~ (in(v5, v2) = 0) | ~ (in(v3, v1) = v4) % 104.27/23.75 | | ~ $i(v5) | ~ $i(v3) | ? [v6: $i] : ( ~ (v6 = v3) & % 104.27/23.75 | apply(empty_set, v5) = v6 & $i(v6))) & ! [v3: $i] : ( ~ % 104.27/23.75 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(empty_set, % 104.27/23.75 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 = % 104.27/23.75 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ? % 104.27/23.75 | [v7: int] : ? [v8: $i] : ($i(v6) & $i(v4) & ((v8 = v4 & v7 = 0 % 104.27/23.75 | & apply(empty_set, v6) = v4 & in(v6, v2) = 0) | (v5 = 0 & % 104.27/23.75 | in(v4, v3) = 0)) & (( ~ (v5 = 0) & in(v4, v3) = v5) | ( ! % 104.27/23.75 | [v9: $i] : ( ~ (apply(empty_set, v9) = v4) | ~ $i(v9) | % 104.27/23.75 | ? [v10: int] : ( ~ (v10 = 0) & in(v9, v2) = v10)) & ! % 104.27/23.75 | [v9: $i] : ( ~ (in(v9, v2) = 0) | ~ $i(v9) | ? [v10: $i] % 104.27/23.75 | : ( ~ (v10 = v4) & apply(empty_set, v9) = v10 & % 104.27/23.75 | $i(v10))))))))) % 104.27/23.75 | % 104.27/23.75 | GROUND_INST: instantiating (9) with all_34_0, simplifying with (33), (35) % 104.27/23.75 | gives: % 104.27/23.75 | (75) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v0 = 0 & empty(all_34_0) % 104.27/23.75 | = 0) | ( ~ (v2 = 0) & relation_dom(all_34_0) = v1 & empty(v1) = v2 % 104.27/23.75 | & $i(v1))) % 104.27/23.75 | % 104.27/23.75 | GROUND_INST: instantiating (4) with all_34_0, simplifying with (33), (35) % 104.27/23.75 | gives: % 104.27/23.76 | (76) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : (( ~ (v0 = 0) & % 104.27/23.76 | function(all_34_0) = v0) | (relation_rng(all_34_0) = v1 & % 104.27/23.76 | relation_dom(all_34_0) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! % 104.27/23.76 | [v4: int] : ! [v5: $i] : (v4 = 0 | ~ (apply(all_34_0, v5) = v3) % 104.27/23.76 | | ~ (in(v3, v1) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: int] : % 104.27/23.76 | ( ~ (v6 = 0) & in(v5, v2) = v6)) & ! [v3: $i] : ! [v4: int] : % 104.27/23.76 | ! [v5: $i] : (v4 = 0 | ~ (in(v5, v2) = 0) | ~ (in(v3, v1) = v4) % 104.27/23.76 | | ~ $i(v5) | ~ $i(v3) | ? [v6: $i] : ( ~ (v6 = v3) & % 104.27/23.76 | apply(all_34_0, v5) = v6 & $i(v6))) & ! [v3: $i] : ( ~ % 104.27/23.76 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_34_0, % 104.27/23.76 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 = % 104.27/23.76 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ? % 104.27/23.76 | [v7: int] : ? [v8: $i] : ($i(v6) & $i(v4) & ((v8 = v4 & v7 = 0 % 104.27/23.76 | & apply(all_34_0, v6) = v4 & in(v6, v2) = 0) | (v5 = 0 & % 104.27/23.76 | in(v4, v3) = 0)) & (( ~ (v5 = 0) & in(v4, v3) = v5) | ( ! % 104.27/23.76 | [v9: $i] : ( ~ (apply(all_34_0, v9) = v4) | ~ $i(v9) | ? % 104.27/23.76 | [v10: int] : ( ~ (v10 = 0) & in(v9, v2) = v10)) & ! % 104.27/23.76 | [v9: $i] : ( ~ (in(v9, v2) = 0) | ~ $i(v9) | ? [v10: $i] % 104.27/23.76 | : ( ~ (v10 = v4) & apply(all_34_0, v9) = v10 & % 104.27/23.76 | $i(v10))))))))) % 104.27/23.76 | % 104.27/23.76 | GROUND_INST: instantiating (11) with all_39_0, simplifying with (41), (42) % 104.27/23.76 | gives: % 104.27/23.76 | (77) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v0 = 0 & empty(all_39_0) % 104.27/23.76 | = 0) | ( ~ (v2 = 0) & relation_rng(all_39_0) = v1 & empty(v1) = v2 % 104.27/23.76 | & $i(v1))) % 104.27/23.76 | % 104.27/23.76 | GROUND_INST: instantiating (9) with all_39_0, simplifying with (41), (42) % 104.27/23.76 | gives: % 104.27/23.76 | (78) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v0 = 0 & empty(all_39_0) % 104.27/23.76 | = 0) | ( ~ (v2 = 0) & relation_dom(all_39_0) = v1 & empty(v1) = v2 % 104.27/23.76 | & $i(v1))) % 104.27/23.76 | % 104.27/23.76 | GROUND_INST: instantiating (4) with all_39_0, simplifying with (41), (42) % 104.27/23.76 | gives: % 104.27/23.76 | (79) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : (( ~ (v0 = 0) & % 104.27/23.76 | function(all_39_0) = v0) | (relation_rng(all_39_0) = v1 & % 104.27/23.76 | relation_dom(all_39_0) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! % 104.27/23.76 | [v4: int] : ! [v5: $i] : (v4 = 0 | ~ (apply(all_39_0, v5) = v3) % 104.27/23.76 | | ~ (in(v3, v1) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: int] : % 104.27/23.76 | ( ~ (v6 = 0) & in(v5, v2) = v6)) & ! [v3: $i] : ! [v4: int] : % 104.27/23.76 | ! [v5: $i] : (v4 = 0 | ~ (in(v5, v2) = 0) | ~ (in(v3, v1) = v4) % 104.27/23.76 | | ~ $i(v5) | ~ $i(v3) | ? [v6: $i] : ( ~ (v6 = v3) & % 104.27/23.76 | apply(all_39_0, v5) = v6 & $i(v6))) & ! [v3: $i] : ( ~ % 104.27/23.76 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_39_0, % 104.27/23.76 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 = % 104.27/23.76 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ? % 104.27/23.76 | [v7: int] : ? [v8: $i] : ($i(v6) & $i(v4) & ((v8 = v4 & v7 = 0 % 104.27/23.76 | & apply(all_39_0, v6) = v4 & in(v6, v2) = 0) | (v5 = 0 & % 104.27/23.76 | in(v4, v3) = 0)) & (( ~ (v5 = 0) & in(v4, v3) = v5) | ( ! % 104.27/23.76 | [v9: $i] : ( ~ (apply(all_39_0, v9) = v4) | ~ $i(v9) | ? % 104.27/23.76 | [v10: int] : ( ~ (v10 = 0) & in(v9, v2) = v10)) & ! % 104.27/23.76 | [v9: $i] : ( ~ (in(v9, v2) = 0) | ~ $i(v9) | ? [v10: $i] % 104.27/23.76 | : ( ~ (v10 = v4) & apply(all_39_0, v9) = v10 & % 104.27/23.76 | $i(v10))))))))) % 104.27/23.76 | % 104.27/23.76 | GROUND_INST: instantiating (4) with all_43_6, simplifying with (49), (56) % 104.27/23.76 | gives: % 104.27/23.76 | (80) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : (( ~ (v0 = 0) & % 104.27/23.76 | function(all_43_6) = v0) | (relation_rng(all_43_6) = v1 & % 104.27/23.76 | relation_dom(all_43_6) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! % 104.27/23.76 | [v4: int] : ! [v5: $i] : (v4 = 0 | ~ (apply(all_43_6, v5) = v3) % 104.27/23.76 | | ~ (in(v3, v1) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: int] : % 104.27/23.76 | ( ~ (v6 = 0) & in(v5, v2) = v6)) & ! [v3: $i] : ! [v4: int] : % 104.27/23.76 | ! [v5: $i] : (v4 = 0 | ~ (in(v5, v2) = 0) | ~ (in(v3, v1) = v4) % 104.27/23.76 | | ~ $i(v5) | ~ $i(v3) | ? [v6: $i] : ( ~ (v6 = v3) & % 104.27/23.76 | apply(all_43_6, v5) = v6 & $i(v6))) & ! [v3: $i] : ( ~ % 104.27/23.76 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_43_6, % 104.27/23.76 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 = % 104.27/23.76 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ? % 104.27/23.76 | [v7: int] : ? [v8: $i] : ($i(v6) & $i(v4) & ((v8 = v4 & v7 = 0 % 104.27/23.76 | & apply(all_43_6, v6) = v4 & in(v6, v2) = 0) | (v5 = 0 & % 104.27/23.76 | in(v4, v3) = 0)) & (( ~ (v5 = 0) & in(v4, v3) = v5) | ( ! % 104.27/23.76 | [v9: $i] : ( ~ (apply(all_43_6, v9) = v4) | ~ $i(v9) | ? % 104.27/23.76 | [v10: int] : ( ~ (v10 = 0) & in(v9, v2) = v10)) & ! % 104.27/23.76 | [v9: $i] : ( ~ (in(v9, v2) = 0) | ~ $i(v9) | ? [v10: $i] % 104.27/23.76 | : ( ~ (v10 = v4) & apply(all_43_6, v9) = v10 & % 104.27/23.76 | $i(v10))))))))) % 104.27/23.76 | % 104.27/23.76 | GROUND_INST: instantiating (4) with all_43_4, simplifying with (51), (57) % 104.27/23.76 | gives: % 104.27/23.77 | (81) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : (( ~ (v0 = 0) & % 104.27/23.77 | function(all_43_4) = v0) | (relation_rng(all_43_4) = v1 & % 104.27/23.77 | relation_dom(all_43_4) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! % 104.27/23.77 | [v4: int] : ! [v5: $i] : (v4 = 0 | ~ (apply(all_43_4, v5) = v3) % 104.27/23.77 | | ~ (in(v3, v1) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: int] : % 104.27/23.77 | ( ~ (v6 = 0) & in(v5, v2) = v6)) & ! [v3: $i] : ! [v4: int] : % 104.27/23.77 | ! [v5: $i] : (v4 = 0 | ~ (in(v5, v2) = 0) | ~ (in(v3, v1) = v4) % 104.27/23.77 | | ~ $i(v5) | ~ $i(v3) | ? [v6: $i] : ( ~ (v6 = v3) & % 104.27/23.77 | apply(all_43_4, v5) = v6 & $i(v6))) & ! [v3: $i] : ( ~ % 104.27/23.77 | (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(all_43_4, % 104.27/23.77 | v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 = % 104.27/23.77 | v1 | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ? % 104.27/23.77 | [v7: int] : ? [v8: $i] : ($i(v6) & $i(v4) & ((v8 = v4 & v7 = 0 % 104.27/23.77 | & apply(all_43_4, v6) = v4 & in(v6, v2) = 0) | (v5 = 0 & % 104.27/23.77 | in(v4, v3) = 0)) & (( ~ (v5 = 0) & in(v4, v3) = v5) | ( ! % 104.27/23.77 | [v9: $i] : ( ~ (apply(all_43_4, v9) = v4) | ~ $i(v9) | ? % 104.27/23.77 | [v10: int] : ( ~ (v10 = 0) & in(v9, v2) = v10)) & ! % 104.27/23.77 | [v9: $i] : ( ~ (in(v9, v2) = 0) | ~ $i(v9) | ? [v10: $i] % 104.27/23.77 | : ( ~ (v10 = v4) & apply(all_43_4, v9) = v10 & % 104.27/23.77 | $i(v10))))))))) % 104.27/23.77 | % 104.27/23.77 | GROUND_INST: instantiating (18) with all_43_1, all_43_5, all_43_0, simplifying % 104.27/23.77 | with (50), (53), (58) gives: % 104.27/23.77 | (82) all_43_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 104.27/23.77 | powerset(all_43_5) = v0 & element(all_43_1, v0) = v1 & $i(v0)) % 104.27/23.77 | % 104.27/23.77 | GROUND_INST: instantiating (2) with all_43_1, all_43_5, all_43_0, simplifying % 104.27/23.77 | with (50), (53), (58) gives: % 104.27/23.77 | (83) all_43_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 104.27/23.77 | all_43_1) = 0 & in(v0, all_43_5) = v1 & $i(v0)) % 104.27/23.77 | % 104.27/23.77 | GROUND_INST: instantiating (10) with all_43_6, all_43_5, simplifying with % 104.27/23.77 | (49), (59) gives: % 104.27/23.77 | (84) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v0 = 0 & % 104.27/23.77 | empty(all_43_6) = 0) | ( ~ (v2 = 0) & empty(all_43_5) = v2) | ( ~ % 104.27/23.77 | (v1 = 0) & relation(all_43_6) = v1)) % 104.27/23.77 | % 104.27/23.77 | GROUND_INST: instantiating (10) with all_43_4, all_43_2, simplifying with % 104.27/23.77 | (51), (60) gives: % 104.27/23.77 | (85) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v0 = 0 & % 104.27/23.77 | empty(all_43_4) = 0) | ( ~ (v2 = 0) & empty(all_43_2) = v2) | ( ~ % 104.27/23.77 | (v1 = 0) & relation(all_43_4) = v1)) % 104.27/23.77 | % 104.27/23.77 | GROUND_INST: instantiating (5) with all_43_4, all_43_2, simplifying with (51), % 104.27/23.77 | (60) gives: % 104.27/23.77 | (86) ? [v0: int] : ? [v1: int] : ? [v2: $i] : (( ~ (v1 = 0) & % 104.27/23.77 | function(all_43_4) = v1) | ( ~ (v0 = 0) & relation(all_43_4) = v0) % 104.27/23.77 | | (relation_rng(all_43_4) = v2 & $i(v2) & ! [v3: $i] : ! [v4: int] % 104.27/23.77 | : ! [v5: $i] : (v4 = 0 | ~ (apply(all_43_4, v5) = v3) | ~ % 104.27/23.77 | (in(v3, v2) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: int] : ( ~ % 104.27/23.77 | (v6 = 0) & in(v5, all_43_2) = v6)) & ! [v3: $i] : ! [v4: % 104.27/23.77 | int] : ! [v5: $i] : (v4 = 0 | ~ (in(v5, all_43_2) = 0) | ~ % 104.27/23.77 | (in(v3, v2) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: $i] : ( ~ % 104.27/23.77 | (v6 = v3) & apply(all_43_4, v5) = v6 & $i(v6))) & ! [v3: $i] % 104.27/23.77 | : ( ~ (in(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] : % 104.27/23.77 | (apply(all_43_4, v4) = v3 & in(v4, all_43_2) = 0 & $i(v4))) & ? % 104.27/23.77 | [v3: $i] : (v3 = v2 | ~ $i(v3) | ? [v4: $i] : ? [v5: int] : ? % 104.27/23.77 | [v6: $i] : ? [v7: int] : ? [v8: $i] : ($i(v6) & $i(v4) & ((v8 % 104.27/23.77 | = v4 & v7 = 0 & apply(all_43_4, v6) = v4 & in(v6, % 104.27/23.77 | all_43_2) = 0) | (v5 = 0 & in(v4, v3) = 0)) & (( ~ (v5 = % 104.27/23.77 | 0) & in(v4, v3) = v5) | ( ! [v9: $i] : ( ~ % 104.27/23.77 | (apply(all_43_4, v9) = v4) | ~ $i(v9) | ? [v10: int] : % 104.27/23.77 | ( ~ (v10 = 0) & in(v9, all_43_2) = v10)) & ! [v9: $i] : % 104.27/23.77 | ( ~ (in(v9, all_43_2) = 0) | ~ $i(v9) | ? [v10: $i] : ( % 104.27/23.77 | ~ (v10 = v4) & apply(all_43_4, v9) = v10 & % 104.27/23.77 | $i(v10))))))))) % 104.27/23.77 | % 104.27/23.77 | GROUND_INST: instantiating (13) with all_43_3, all_43_2, simplifying with % 104.27/23.77 | (52), (61) gives: % 104.27/23.77 | (87) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0 & % 104.27/23.77 | relation(all_43_2) = 0 & empty(all_43_2) = 0) | ( ~ (v0 = 0) & % 104.27/23.77 | empty(all_43_3) = v0)) % 104.27/23.77 | % 104.27/23.77 | GROUND_INST: instantiating (14) with all_43_4, all_43_1, simplifying with % 104.27/23.77 | (51), (62) gives: % 104.27/23.77 | (88) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0 & % 104.27/23.77 | relation(all_43_1) = 0 & empty(all_43_1) = 0) | ( ~ (v0 = 0) & % 104.27/23.77 | empty(all_43_4) = v0)) % 104.27/23.77 | % 104.27/23.77 | GROUND_INST: instantiating (6) with all_43_4, all_43_1, simplifying with (51), % 104.27/23.77 | (62) gives: % 104.27/23.78 | (89) ? [v0: int] : ? [v1: int] : ? [v2: $i] : (( ~ (v1 = 0) & % 104.27/23.78 | function(all_43_4) = v1) | ( ~ (v0 = 0) & relation(all_43_4) = v0) % 104.27/23.78 | | (relation_dom(all_43_4) = v2 & $i(v2) & ! [v3: $i] : ! [v4: int] % 104.27/23.78 | : ! [v5: $i] : (v4 = 0 | ~ (apply(all_43_4, v5) = v3) | ~ % 104.27/23.78 | (in(v3, all_43_1) = v4) | ~ $i(v5) | ~ $i(v3) | ~ % 104.27/23.78 | $i(all_43_1) | ? [v6: int] : ( ~ (v6 = 0) & in(v5, v2) = v6)) & % 104.27/23.78 | ! [v3: $i] : ! [v4: int] : ! [v5: $i] : (v4 = 0 | ~ (in(v5, % 104.27/23.78 | v2) = 0) | ~ (in(v3, all_43_1) = v4) | ~ $i(v5) | ~ % 104.27/23.78 | $i(v3) | ~ $i(all_43_1) | ? [v6: $i] : ( ~ (v6 = v3) & % 104.27/23.78 | apply(all_43_4, v5) = v6 & $i(v6))) & ! [v3: $i] : ( ~ % 104.27/23.78 | (in(v3, all_43_1) = 0) | ~ $i(v3) | ~ $i(all_43_1) | ? [v4: % 104.27/23.78 | $i] : (apply(all_43_4, v4) = v3 & in(v4, v2) = 0 & $i(v4))) & % 104.27/23.78 | ? [v3: any] : (v3 = all_43_1 | ~ $i(v3) | ? [v4: $i] : ? [v5: % 104.27/23.78 | int] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ($i(v6) & % 104.27/23.78 | $i(v4) & ((v8 = v4 & v7 = 0 & apply(all_43_4, v6) = v4 & % 104.27/23.78 | in(v6, v2) = 0) | (v5 = 0 & in(v4, v3) = 0)) & (( ~ (v5 = % 104.27/23.78 | 0) & in(v4, v3) = v5) | ( ! [v9: $i] : ( ~ % 104.27/23.78 | (apply(all_43_4, v9) = v4) | ~ $i(v9) | ? [v10: int] : % 104.27/23.78 | ( ~ (v10 = 0) & in(v9, v2) = v10)) & ! [v9: $i] : ( ~ % 104.27/23.78 | (in(v9, v2) = 0) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = % 104.27/23.78 | v4) & apply(all_43_4, v9) = v10 & $i(v10))))))))) % 104.27/23.78 | % 104.27/23.78 | GROUND_INST: instantiating (fc10_relat_1) with all_43_6, all_43_4, all_43_3, % 104.27/23.78 | simplifying with (49), (51), (63) gives: % 104.27/23.78 | (90) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 104.27/23.78 | v2 = 0 & relation(all_43_3) = 0 & empty(all_43_3) = 0) | ( ~ (v1 = % 104.27/23.78 | 0) & relation(all_43_4) = v1) | ( ~ (v0 = 0) & empty(all_43_6) = % 104.27/23.78 | v0)) % 104.27/23.78 | % 104.27/23.78 | COMBINE_EQS: (67), (68) imply: % 104.27/23.78 | (91) all_30_0 = empty_set % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (66) with fresh symbol all_63_0 gives: % 104.27/23.78 | (92) relation_dom(all_30_0) = all_63_0 & relation(all_63_0) = 0 & % 104.27/23.78 | empty(all_63_0) = 0 & $i(all_63_0) % 104.27/23.78 | % 104.27/23.78 | ALPHA: (92) implies: % 104.27/23.78 | (93) relation_dom(all_30_0) = all_63_0 % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (64) with fresh symbol all_65_0 gives: % 104.27/23.78 | (94) relation_dom(empty_set) = all_65_0 & relation(all_65_0) = 0 & % 104.27/23.78 | empty(all_65_0) = 0 & $i(all_65_0) % 104.27/23.78 | % 104.27/23.78 | ALPHA: (94) implies: % 104.27/23.78 | (95) empty(all_65_0) = 0 % 104.27/23.78 | (96) relation_dom(empty_set) = all_65_0 % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (69) with fresh symbol all_69_0 gives: % 104.27/23.78 | (97) relation_dom(all_34_0) = all_69_0 & relation(all_69_0) = 0 & % 104.27/23.78 | empty(all_69_0) = 0 & $i(all_69_0) % 104.27/23.78 | % 104.27/23.78 | ALPHA: (97) implies: % 104.27/23.78 | (98) relation_dom(all_34_0) = all_69_0 % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (87) with fresh symbols all_77_0, all_77_1, all_77_2 % 104.27/23.78 | gives: % 104.27/23.78 | (99) (all_77_0 = 0 & all_77_1 = 0 & relation(all_43_2) = 0 & % 104.27/23.78 | empty(all_43_2) = 0) | ( ~ (all_77_2 = 0) & empty(all_43_3) = % 104.27/23.78 | all_77_2) % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (88) with fresh symbols all_79_0, all_79_1, all_79_2 % 104.27/23.78 | gives: % 104.27/23.78 | (100) (all_79_0 = 0 & all_79_1 = 0 & relation(all_43_1) = 0 & % 104.27/23.78 | empty(all_43_1) = 0) | ( ~ (all_79_2 = 0) & empty(all_43_4) = % 104.27/23.78 | all_79_2) % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (85) with fresh symbols all_80_0, all_80_1, all_80_2 % 104.27/23.78 | gives: % 104.27/23.78 | (101) (all_80_2 = 0 & empty(all_43_4) = 0) | ( ~ (all_80_0 = 0) & % 104.27/23.78 | empty(all_43_2) = all_80_0) | ( ~ (all_80_1 = 0) & % 104.27/23.78 | relation(all_43_4) = all_80_1) % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (84) with fresh symbols all_85_0, all_85_1, all_85_2 % 104.27/23.78 | gives: % 104.27/23.78 | (102) (all_85_2 = 0 & empty(all_43_6) = 0) | ( ~ (all_85_0 = 0) & % 104.27/23.78 | empty(all_43_5) = all_85_0) | ( ~ (all_85_1 = 0) & % 104.27/23.78 | relation(all_43_6) = all_85_1) % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (78) with fresh symbols all_92_0, all_92_1, all_92_2 % 104.27/23.78 | gives: % 104.27/23.78 | (103) (all_92_2 = 0 & empty(all_39_0) = 0) | ( ~ (all_92_0 = 0) & % 104.27/23.78 | relation_dom(all_39_0) = all_92_1 & empty(all_92_1) = all_92_0 & % 104.27/23.78 | $i(all_92_1)) % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (77) with fresh symbols all_94_0, all_94_1, all_94_2 % 104.27/23.78 | gives: % 104.27/23.78 | (104) (all_94_2 = 0 & empty(all_39_0) = 0) | ( ~ (all_94_0 = 0) & % 104.27/23.78 | relation_rng(all_39_0) = all_94_1 & empty(all_94_1) = all_94_0 & % 104.27/23.78 | $i(all_94_1)) % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (75) with fresh symbols all_97_0, all_97_1, all_97_2 % 104.27/23.78 | gives: % 104.27/23.78 | (105) (all_97_2 = 0 & empty(all_34_0) = 0) | ( ~ (all_97_0 = 0) & % 104.27/23.78 | relation_dom(all_34_0) = all_97_1 & empty(all_97_1) = all_97_0 & % 104.27/23.78 | $i(all_97_1)) % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (90) with fresh symbols all_98_0, all_98_1, all_98_2, % 104.27/23.78 | all_98_3 gives: % 104.27/23.78 | (106) (all_98_0 = 0 & all_98_1 = 0 & relation(all_43_3) = 0 & % 104.27/23.78 | empty(all_43_3) = 0) | ( ~ (all_98_2 = 0) & relation(all_43_4) = % 104.27/23.78 | all_98_2) | ( ~ (all_98_3 = 0) & empty(all_43_6) = all_98_3) % 104.27/23.78 | % 104.27/23.78 | DELTA: instantiating (80) with fresh symbols all_102_0, all_102_1, all_102_2 % 104.27/23.78 | gives: % 104.27/23.79 | (107) ( ~ (all_102_2 = 0) & function(all_43_6) = all_102_2) | % 104.27/23.79 | (relation_rng(all_43_6) = all_102_1 & relation_dom(all_43_6) = % 104.27/23.79 | all_102_0 & $i(all_102_0) & $i(all_102_1) & ! [v0: $i] : ! [v1: % 104.27/23.79 | int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_43_6, v2) = v0) | ~ % 104.27/23.79 | (in(v0, all_102_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : % 104.27/23.79 | ( ~ (v3 = 0) & in(v2, all_102_0) = v3)) & ! [v0: $i] : ! [v1: % 104.27/23.79 | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_102_0) = 0) | ~ % 104.27/23.79 | (in(v0, all_102_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : % 104.27/23.79 | ( ~ (v3 = v0) & apply(all_43_6, v2) = v3 & $i(v3))) & ! [v0: $i] % 104.27/23.79 | : ( ~ (in(v0, all_102_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.27/23.79 | (apply(all_43_6, v1) = v0 & in(v1, all_102_0) = 0 & $i(v1))) & ? % 104.27/23.79 | [v0: any] : (v0 = all_102_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 104.27/23.79 | int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & % 104.27/23.79 | $i(v1) & ((v5 = v1 & v4 = 0 & apply(all_43_6, v3) = v1 & in(v3, % 104.27/23.79 | all_102_0) = 0) | (v2 = 0 & in(v1, v0) = 0)) & (( ~ (v2 = % 104.27/23.79 | 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( ~ % 104.27/23.79 | (apply(all_43_6, v6) = v1) | ~ $i(v6) | ? [v7: int] : ( % 104.27/23.79 | ~ (v7 = 0) & in(v6, all_102_0) = v7)) & ! [v6: $i] : ( % 104.27/23.79 | ~ (in(v6, all_102_0) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ % 104.27/23.79 | (v7 = v1) & apply(all_43_6, v6) = v7 & $i(v7)))))))) % 104.27/23.79 | % 104.27/23.79 | DELTA: instantiating (72) with fresh symbols all_103_0, all_103_1, all_103_2 % 104.27/23.79 | gives: % 104.27/23.79 | (108) ( ~ (all_103_2 = 0) & relation(all_43_6) = all_103_2) | % 104.27/23.79 | (relation_rng(all_43_6) = all_103_1 & relation_dom(all_43_6) = % 104.27/23.79 | all_103_0 & $i(all_103_0) & $i(all_103_1) & ! [v0: $i] : ! [v1: % 104.27/23.79 | int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_43_6, v2) = v0) | ~ % 104.27/23.79 | (in(v0, all_103_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : % 104.27/23.79 | ( ~ (v3 = 0) & in(v2, all_103_0) = v3)) & ! [v0: $i] : ! [v1: % 104.27/23.79 | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_103_0) = 0) | ~ % 104.27/23.79 | (in(v0, all_103_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : % 104.27/23.79 | ( ~ (v3 = v0) & apply(all_43_6, v2) = v3 & $i(v3))) & ! [v0: $i] % 104.27/23.79 | : ( ~ (in(v0, all_103_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.27/23.79 | (apply(all_43_6, v1) = v0 & in(v1, all_103_0) = 0 & $i(v1))) & ? % 104.27/23.79 | [v0: any] : (v0 = all_103_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 104.27/23.79 | int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & % 104.27/23.79 | $i(v1) & ((v5 = v1 & v4 = 0 & apply(all_43_6, v3) = v1 & in(v3, % 104.27/23.79 | all_103_0) = 0) | (v2 = 0 & in(v1, v0) = 0)) & (( ~ (v2 = % 104.27/23.79 | 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( ~ % 104.27/23.79 | (apply(all_43_6, v6) = v1) | ~ $i(v6) | ? [v7: int] : ( % 104.27/23.79 | ~ (v7 = 0) & in(v6, all_103_0) = v7)) & ! [v6: $i] : ( % 104.27/23.79 | ~ (in(v6, all_103_0) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ % 104.27/23.79 | (v7 = v1) & apply(all_43_6, v6) = v7 & $i(v7)))))))) % 104.27/23.79 | % 104.27/23.79 | DELTA: instantiating (86) with fresh symbols all_104_0, all_104_1, all_104_2 % 104.27/23.79 | gives: % 104.27/23.79 | (109) ( ~ (all_104_1 = 0) & function(all_43_4) = all_104_1) | ( ~ % 104.27/23.79 | (all_104_2 = 0) & relation(all_43_4) = all_104_2) | % 104.27/23.79 | (relation_rng(all_43_4) = all_104_0 & $i(all_104_0) & ! [v0: $i] : % 104.27/23.79 | ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_43_4, v2) = v0) % 104.27/23.79 | | ~ (in(v0, all_104_0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: % 104.27/23.79 | int] : ( ~ (v3 = 0) & in(v2, all_43_2) = v3)) & ! [v0: $i] : % 104.27/23.79 | ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_43_2) = 0) | % 104.27/23.79 | ~ (in(v0, all_104_0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] % 104.27/23.79 | : ( ~ (v3 = v0) & apply(all_43_4, v2) = v3 & $i(v3))) & ! [v0: % 104.27/23.79 | $i] : ( ~ (in(v0, all_104_0) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.27/23.79 | (apply(all_43_4, v1) = v0 & in(v1, all_43_2) = 0 & $i(v1))) & ? % 104.27/23.79 | [v0: any] : (v0 = all_104_0 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 104.27/23.79 | int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & % 104.27/23.79 | $i(v1) & ((v5 = v1 & v4 = 0 & apply(all_43_4, v3) = v1 & in(v3, % 104.27/23.79 | all_43_2) = 0) | (v2 = 0 & in(v1, v0) = 0)) & (( ~ (v2 = % 104.27/23.79 | 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( ~ % 104.27/23.79 | (apply(all_43_4, v6) = v1) | ~ $i(v6) | ? [v7: int] : ( % 104.27/23.79 | ~ (v7 = 0) & in(v6, all_43_2) = v7)) & ! [v6: $i] : ( % 104.27/23.79 | ~ (in(v6, all_43_2) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ % 104.27/23.79 | (v7 = v1) & apply(all_43_4, v6) = v7 & $i(v7)))))))) % 104.27/23.79 | % 104.27/23.79 | DELTA: instantiating (79) with fresh symbols all_108_0, all_108_1, all_108_2 % 104.27/23.79 | gives: % 104.27/23.80 | (110) ( ~ (all_108_2 = 0) & function(all_39_0) = all_108_2) | % 104.27/23.80 | (relation_rng(all_39_0) = all_108_1 & relation_dom(all_39_0) = % 104.27/23.80 | all_108_0 & $i(all_108_0) & $i(all_108_1) & ! [v0: $i] : ! [v1: % 104.27/23.80 | int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_39_0, v2) = v0) | ~ % 104.27/23.80 | (in(v0, all_108_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : % 104.27/23.80 | ( ~ (v3 = 0) & in(v2, all_108_0) = v3)) & ! [v0: $i] : ! [v1: % 104.27/23.80 | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_108_0) = 0) | ~ % 104.27/23.80 | (in(v0, all_108_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : % 104.27/23.80 | ( ~ (v3 = v0) & apply(all_39_0, v2) = v3 & $i(v3))) & ! [v0: $i] % 104.27/23.80 | : ( ~ (in(v0, all_108_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.27/23.80 | (apply(all_39_0, v1) = v0 & in(v1, all_108_0) = 0 & $i(v1))) & ? % 104.27/23.80 | [v0: any] : (v0 = all_108_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 104.27/23.80 | int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & % 104.27/23.80 | $i(v1) & ((v5 = v1 & v4 = 0 & apply(all_39_0, v3) = v1 & in(v3, % 104.27/23.80 | all_108_0) = 0) | (v2 = 0 & in(v1, v0) = 0)) & (( ~ (v2 = % 104.27/23.80 | 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( ~ % 104.27/23.80 | (apply(all_39_0, v6) = v1) | ~ $i(v6) | ? [v7: int] : ( % 104.27/23.80 | ~ (v7 = 0) & in(v6, all_108_0) = v7)) & ! [v6: $i] : ( % 104.27/23.80 | ~ (in(v6, all_108_0) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ % 104.27/23.80 | (v7 = v1) & apply(all_39_0, v6) = v7 & $i(v7)))))))) % 104.27/23.80 | % 104.27/23.80 | DELTA: instantiating (81) with fresh symbols all_109_0, all_109_1, all_109_2 % 104.27/23.80 | gives: % 104.27/23.80 | (111) ( ~ (all_109_2 = 0) & function(all_43_4) = all_109_2) | % 104.27/23.80 | (relation_rng(all_43_4) = all_109_1 & relation_dom(all_43_4) = % 104.27/23.80 | all_109_0 & $i(all_109_0) & $i(all_109_1) & ! [v0: $i] : ! [v1: % 104.27/23.80 | int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_43_4, v2) = v0) | ~ % 104.27/23.80 | (in(v0, all_109_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : % 104.27/23.80 | ( ~ (v3 = 0) & in(v2, all_109_0) = v3)) & ! [v0: $i] : ! [v1: % 104.27/23.80 | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_109_0) = 0) | ~ % 104.27/23.80 | (in(v0, all_109_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : % 104.27/23.80 | ( ~ (v3 = v0) & apply(all_43_4, v2) = v3 & $i(v3))) & ! [v0: $i] % 104.27/23.80 | : ( ~ (in(v0, all_109_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.27/23.80 | (apply(all_43_4, v1) = v0 & in(v1, all_109_0) = 0 & $i(v1))) & ? % 104.27/23.80 | [v0: any] : (v0 = all_109_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 104.27/23.80 | int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & % 104.27/23.80 | $i(v1) & ((v5 = v1 & v4 = 0 & apply(all_43_4, v3) = v1 & in(v3, % 104.27/23.80 | all_109_0) = 0) | (v2 = 0 & in(v1, v0) = 0)) & (( ~ (v2 = % 104.27/23.80 | 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( ~ % 104.27/23.80 | (apply(all_43_4, v6) = v1) | ~ $i(v6) | ? [v7: int] : ( % 104.27/23.80 | ~ (v7 = 0) & in(v6, all_109_0) = v7)) & ! [v6: $i] : ( % 104.27/23.80 | ~ (in(v6, all_109_0) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ % 104.27/23.80 | (v7 = v1) & apply(all_43_4, v6) = v7 & $i(v7)))))))) % 104.27/23.80 | % 104.27/23.80 | DELTA: instantiating (73) with fresh symbols all_110_0, all_110_1, all_110_2 % 104.27/23.80 | gives: % 104.27/23.80 | (112) ( ~ (all_110_2 = 0) & relation(all_43_4) = all_110_2) | % 104.27/23.80 | (relation_rng(all_43_4) = all_110_1 & relation_dom(all_43_4) = % 104.27/23.80 | all_110_0 & $i(all_110_0) & $i(all_110_1) & ! [v0: $i] : ! [v1: % 104.27/23.80 | int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_43_4, v2) = v0) | ~ % 104.27/23.80 | (in(v0, all_110_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : % 104.27/23.80 | ( ~ (v3 = 0) & in(v2, all_110_0) = v3)) & ! [v0: $i] : ! [v1: % 104.27/23.80 | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_110_0) = 0) | ~ % 104.27/23.80 | (in(v0, all_110_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : % 104.27/23.80 | ( ~ (v3 = v0) & apply(all_43_4, v2) = v3 & $i(v3))) & ! [v0: $i] % 104.27/23.80 | : ( ~ (in(v0, all_110_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.27/23.80 | (apply(all_43_4, v1) = v0 & in(v1, all_110_0) = 0 & $i(v1))) & ? % 104.27/23.80 | [v0: any] : (v0 = all_110_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 104.27/23.80 | int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & % 104.27/23.80 | $i(v1) & ((v5 = v1 & v4 = 0 & apply(all_43_4, v3) = v1 & in(v3, % 104.27/23.80 | all_110_0) = 0) | (v2 = 0 & in(v1, v0) = 0)) & (( ~ (v2 = % 104.27/23.80 | 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( ~ % 104.27/23.80 | (apply(all_43_4, v6) = v1) | ~ $i(v6) | ? [v7: int] : ( % 104.27/23.80 | ~ (v7 = 0) & in(v6, all_110_0) = v7)) & ! [v6: $i] : ( % 104.27/23.80 | ~ (in(v6, all_110_0) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ % 104.27/23.80 | (v7 = v1) & apply(all_43_4, v6) = v7 & $i(v7)))))))) % 104.27/23.80 | % 104.27/23.80 | DELTA: instantiating (74) with fresh symbols all_112_0, all_112_1, all_112_2 % 104.27/23.80 | gives: % 104.27/23.80 | (113) ( ~ (all_112_2 = 0) & function(empty_set) = all_112_2) | % 104.27/23.80 | (relation_rng(empty_set) = all_112_1 & relation_dom(empty_set) = % 104.27/23.80 | all_112_0 & $i(all_112_0) & $i(all_112_1) & ! [v0: $i] : ! [v1: % 104.27/23.80 | int] : ! [v2: $i] : (v1 = 0 | ~ (apply(empty_set, v2) = v0) | % 104.27/23.80 | ~ (in(v0, all_112_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] % 104.27/23.80 | : ( ~ (v3 = 0) & in(v2, all_112_0) = v3)) & ! [v0: $i] : ! [v1: % 104.27/23.80 | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_112_0) = 0) | ~ % 104.27/23.80 | (in(v0, all_112_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : % 104.27/23.80 | ( ~ (v3 = v0) & apply(empty_set, v2) = v3 & $i(v3))) & ! [v0: % 104.27/23.80 | $i] : ( ~ (in(v0, all_112_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.27/23.80 | (apply(empty_set, v1) = v0 & in(v1, all_112_0) = 0 & $i(v1))) & % 104.27/23.80 | ? [v0: any] : (v0 = all_112_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 104.27/23.80 | int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & % 104.27/23.80 | $i(v1) & ((v5 = v1 & v4 = 0 & apply(empty_set, v3) = v1 & % 104.27/23.80 | in(v3, all_112_0) = 0) | (v2 = 0 & in(v1, v0) = 0)) & (( ~ % 104.27/23.80 | (v2 = 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( ~ % 104.27/23.80 | (apply(empty_set, v6) = v1) | ~ $i(v6) | ? [v7: int] : % 104.27/23.80 | ( ~ (v7 = 0) & in(v6, all_112_0) = v7)) & ! [v6: $i] : ( % 104.27/23.80 | ~ (in(v6, all_112_0) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ % 104.27/23.80 | (v7 = v1) & apply(empty_set, v6) = v7 & $i(v7)))))))) % 104.27/23.80 | % 104.27/23.80 | DELTA: instantiating (76) with fresh symbols all_113_0, all_113_1, all_113_2 % 104.27/23.80 | gives: % 104.27/23.81 | (114) ( ~ (all_113_2 = 0) & function(all_34_0) = all_113_2) | % 104.27/23.81 | (relation_rng(all_34_0) = all_113_1 & relation_dom(all_34_0) = % 104.27/23.81 | all_113_0 & $i(all_113_0) & $i(all_113_1) & ! [v0: $i] : ! [v1: % 104.27/23.81 | int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_34_0, v2) = v0) | ~ % 104.27/23.81 | (in(v0, all_113_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : % 104.27/23.81 | ( ~ (v3 = 0) & in(v2, all_113_0) = v3)) & ! [v0: $i] : ! [v1: % 104.27/23.81 | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_113_0) = 0) | ~ % 104.27/23.81 | (in(v0, all_113_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : % 104.27/23.81 | ( ~ (v3 = v0) & apply(all_34_0, v2) = v3 & $i(v3))) & ! [v0: $i] % 104.27/23.81 | : ( ~ (in(v0, all_113_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.27/23.81 | (apply(all_34_0, v1) = v0 & in(v1, all_113_0) = 0 & $i(v1))) & ? % 104.27/23.81 | [v0: any] : (v0 = all_113_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 104.27/23.81 | int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & % 104.27/23.81 | $i(v1) & ((v5 = v1 & v4 = 0 & apply(all_34_0, v3) = v1 & in(v3, % 104.27/23.81 | all_113_0) = 0) | (v2 = 0 & in(v1, v0) = 0)) & (( ~ (v2 = % 104.27/23.81 | 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( ~ % 104.27/23.81 | (apply(all_34_0, v6) = v1) | ~ $i(v6) | ? [v7: int] : ( % 104.27/23.81 | ~ (v7 = 0) & in(v6, all_113_0) = v7)) & ! [v6: $i] : ( % 104.27/23.81 | ~ (in(v6, all_113_0) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ % 104.27/23.81 | (v7 = v1) & apply(all_34_0, v6) = v7 & $i(v7)))))))) % 104.27/23.81 | % 104.27/23.81 | DELTA: instantiating (89) with fresh symbols all_114_0, all_114_1, all_114_2 % 104.27/23.81 | gives: % 104.27/23.81 | (115) ( ~ (all_114_1 = 0) & function(all_43_4) = all_114_1) | ( ~ % 104.27/23.81 | (all_114_2 = 0) & relation(all_43_4) = all_114_2) | % 104.27/23.81 | (relation_dom(all_43_4) = all_114_0 & $i(all_114_0) & ! [v0: $i] : % 104.27/23.81 | ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_43_4, v2) = v0) % 104.27/23.81 | | ~ (in(v0, all_43_1) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 104.27/23.81 | $i(all_43_1) | ? [v3: int] : ( ~ (v3 = 0) & in(v2, all_114_0) = % 104.27/23.81 | v3)) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ % 104.27/23.81 | (in(v2, all_114_0) = 0) | ~ (in(v0, all_43_1) = v1) | ~ $i(v2) % 104.27/23.81 | | ~ $i(v0) | ~ $i(all_43_1) | ? [v3: $i] : ( ~ (v3 = v0) & % 104.27/23.81 | apply(all_43_4, v2) = v3 & $i(v3))) & ! [v0: $i] : ( ~ (in(v0, % 104.27/23.81 | all_43_1) = 0) | ~ $i(v0) | ~ $i(all_43_1) | ? [v1: $i] : % 104.27/23.81 | (apply(all_43_4, v1) = v0 & in(v1, all_114_0) = 0 & $i(v1))) & ? % 104.27/23.81 | [v0: any] : (v0 = all_43_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: int] % 104.27/23.81 | : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & $i(v1) & % 104.27/23.81 | ((v5 = v1 & v4 = 0 & apply(all_43_4, v3) = v1 & in(v3, % 104.27/23.81 | all_114_0) = 0) | (v2 = 0 & in(v1, v0) = 0)) & (( ~ (v2 = % 104.27/23.81 | 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( ~ % 104.27/23.81 | (apply(all_43_4, v6) = v1) | ~ $i(v6) | ? [v7: int] : ( % 104.27/23.81 | ~ (v7 = 0) & in(v6, all_114_0) = v7)) & ! [v6: $i] : ( % 104.27/23.81 | ~ (in(v6, all_114_0) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ % 104.27/23.81 | (v7 = v1) & apply(all_43_4, v6) = v7 & $i(v7)))))))) % 104.27/23.81 | % 104.27/23.81 | REDUCE: (68), (98) imply: % 104.27/23.81 | (116) relation_dom(empty_set) = all_69_0 % 104.27/23.81 | % 104.27/23.81 | REDUCE: (91), (93) imply: % 104.27/23.81 | (117) relation_dom(empty_set) = all_63_0 % 104.27/23.81 | % 104.27/23.81 | REDUCE: (65), (91) imply: % 104.27/23.81 | (118) function(empty_set) = 0 % 104.27/23.81 | % 104.27/23.81 | BETA: splitting (70) gives: % 104.27/23.81 | % 104.27/23.81 | Case 1: % 104.27/23.81 | | % 104.27/23.81 | | (119) all_37_0 = 0 % 104.27/23.81 | | % 104.27/23.81 | | REDUCE: (37), (119) imply: % 104.27/23.81 | | (120) $false % 104.27/23.81 | | % 104.27/23.81 | | CLOSE: (120) is inconsistent. % 104.27/23.81 | | % 104.27/23.81 | Case 2: % 104.27/23.81 | | % 104.27/23.81 | | (121) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 104.27/23.81 | | powerset(all_37_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2 & % 104.27/23.81 | | $i(v1) & $i(v0)) % 104.27/23.81 | | % 104.27/23.81 | | DELTA: instantiating (121) with fresh symbols all_136_0, all_136_1, % 104.27/23.81 | | all_136_2 gives: % 104.27/23.81 | | (122) ~ (all_136_0 = 0) & powerset(all_37_1) = all_136_2 & % 104.27/23.81 | | element(all_136_1, all_136_2) = 0 & empty(all_136_1) = all_136_0 & % 104.27/23.81 | | $i(all_136_1) & $i(all_136_2) % 104.27/23.81 | | % 104.27/23.81 | | ALPHA: (122) implies: % 104.27/23.81 | | (123) powerset(all_37_1) = all_136_2 % 104.27/23.81 | | % 104.27/23.81 | | BETA: splitting (115) gives: % 104.27/23.81 | | % 104.27/23.81 | | Case 1: % 104.27/23.81 | | | % 104.27/23.81 | | | (124) ~ (all_114_1 = 0) & function(all_43_4) = all_114_1 % 104.27/23.81 | | | % 104.27/23.81 | | | ALPHA: (124) implies: % 104.27/23.81 | | | (125) ~ (all_114_1 = 0) % 104.27/23.81 | | | (126) function(all_43_4) = all_114_1 % 104.27/23.81 | | | % 104.27/23.81 | | | GROUND_INST: instantiating (23) with 0, all_114_1, all_43_4, simplifying % 104.27/23.81 | | | with (55), (126) gives: % 104.27/23.81 | | | (127) all_114_1 = 0 % 104.27/23.81 | | | % 104.27/23.81 | | | REDUCE: (125), (127) imply: % 104.60/23.81 | | | (128) $false % 104.60/23.81 | | | % 104.60/23.81 | | | CLOSE: (128) is inconsistent. % 104.60/23.81 | | | % 104.60/23.81 | | Case 2: % 104.60/23.81 | | | % 104.60/23.82 | | | (129) ( ~ (all_114_2 = 0) & relation(all_43_4) = all_114_2) | % 104.60/23.82 | | | (relation_dom(all_43_4) = all_114_0 & $i(all_114_0) & ! [v0: $i] % 104.60/23.82 | | | : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_43_4, % 104.60/23.82 | | | v2) = v0) | ~ (in(v0, all_43_1) = v1) | ~ $i(v2) | ~ % 104.60/23.82 | | | $i(v0) | ~ $i(all_43_1) | ? [v3: int] : ( ~ (v3 = 0) & % 104.60/23.82 | | | in(v2, all_114_0) = v3)) & ! [v0: $i] : ! [v1: int] : ! % 104.60/23.82 | | | [v2: $i] : (v1 = 0 | ~ (in(v2, all_114_0) = 0) | ~ (in(v0, % 104.60/23.82 | | | all_43_1) = v1) | ~ $i(v2) | ~ $i(v0) | ~ $i(all_43_1) % 104.60/23.82 | | | | ? [v3: $i] : ( ~ (v3 = v0) & apply(all_43_4, v2) = v3 & % 104.60/23.82 | | | $i(v3))) & ! [v0: $i] : ( ~ (in(v0, all_43_1) = 0) | ~ % 104.60/23.82 | | | $i(v0) | ~ $i(all_43_1) | ? [v1: $i] : (apply(all_43_4, v1) % 104.60/23.82 | | | = v0 & in(v1, all_114_0) = 0 & $i(v1))) & ? [v0: any] : % 104.60/23.82 | | | (v0 = all_43_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: int] : ? % 104.60/23.82 | | | [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & $i(v1) & % 104.60/23.82 | | | ((v5 = v1 & v4 = 0 & apply(all_43_4, v3) = v1 & in(v3, % 104.60/23.82 | | | all_114_0) = 0) | (v2 = 0 & in(v1, v0) = 0)) & (( ~ % 104.60/23.82 | | | (v2 = 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( ~ % 104.60/23.82 | | | (apply(all_43_4, v6) = v1) | ~ $i(v6) | ? [v7: int] % 104.60/23.82 | | | : ( ~ (v7 = 0) & in(v6, all_114_0) = v7)) & ! [v6: % 104.60/23.82 | | | $i] : ( ~ (in(v6, all_114_0) = 0) | ~ $i(v6) | ? % 104.60/23.82 | | | [v7: $i] : ( ~ (v7 = v1) & apply(all_43_4, v6) = v7 & % 104.60/23.82 | | | $i(v7)))))))) % 104.60/23.82 | | | % 104.60/23.82 | | | BETA: splitting (129) gives: % 104.60/23.82 | | | % 104.60/23.82 | | | Case 1: % 104.60/23.82 | | | | % 104.60/23.82 | | | | (130) ~ (all_114_2 = 0) & relation(all_43_4) = all_114_2 % 104.60/23.82 | | | | % 104.60/23.82 | | | | ALPHA: (130) implies: % 104.60/23.82 | | | | (131) ~ (all_114_2 = 0) % 104.60/23.82 | | | | (132) relation(all_43_4) = all_114_2 % 104.60/23.82 | | | | % 104.60/23.82 | | | | GROUND_INST: instantiating (24) with 0, all_114_2, all_43_4, simplifying % 104.60/23.82 | | | | with (57), (132) gives: % 104.60/23.82 | | | | (133) all_114_2 = 0 % 104.60/23.82 | | | | % 104.60/23.82 | | | | REDUCE: (131), (133) imply: % 104.60/23.82 | | | | (134) $false % 104.60/23.82 | | | | % 104.60/23.82 | | | | CLOSE: (134) is inconsistent. % 104.60/23.82 | | | | % 104.60/23.82 | | | Case 2: % 104.60/23.82 | | | | % 104.60/23.82 | | | | (135) relation_dom(all_43_4) = all_114_0 & $i(all_114_0) & ! [v0: % 104.60/23.82 | | | | $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ % 104.60/23.82 | | | | (apply(all_43_4, v2) = v0) | ~ (in(v0, all_43_1) = v1) | ~ % 104.60/23.82 | | | | $i(v2) | ~ $i(v0) | ~ $i(all_43_1) | ? [v3: int] : ( ~ (v3 % 104.60/23.82 | | | | = 0) & in(v2, all_114_0) = v3)) & ! [v0: $i] : ! [v1: % 104.60/23.82 | | | | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_114_0) = 0) | % 104.60/23.82 | | | | ~ (in(v0, all_43_1) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 104.60/23.82 | | | | $i(all_43_1) | ? [v3: $i] : ( ~ (v3 = v0) & apply(all_43_4, % 104.60/23.82 | | | | v2) = v3 & $i(v3))) & ! [v0: $i] : ( ~ (in(v0, all_43_1) % 104.60/23.82 | | | | = 0) | ~ $i(v0) | ~ $i(all_43_1) | ? [v1: $i] : % 104.60/23.82 | | | | (apply(all_43_4, v1) = v0 & in(v1, all_114_0) = 0 & $i(v1))) % 104.60/23.82 | | | | & ? [v0: any] : (v0 = all_43_1 | ~ $i(v0) | ? [v1: $i] : ? % 104.60/23.82 | | | | [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : % 104.60/23.82 | | | | ($i(v3) & $i(v1) & ((v5 = v1 & v4 = 0 & apply(all_43_4, v3) = % 104.60/23.82 | | | | v1 & in(v3, all_114_0) = 0) | (v2 = 0 & in(v1, v0) = % 104.60/23.82 | | | | 0)) & (( ~ (v2 = 0) & in(v1, v0) = v2) | ( ! [v6: $i] : % 104.60/23.82 | | | | ( ~ (apply(all_43_4, v6) = v1) | ~ $i(v6) | ? [v7: % 104.60/23.82 | | | | int] : ( ~ (v7 = 0) & in(v6, all_114_0) = v7)) & ! % 104.60/23.82 | | | | [v6: $i] : ( ~ (in(v6, all_114_0) = 0) | ~ $i(v6) | ? % 104.60/23.82 | | | | [v7: $i] : ( ~ (v7 = v1) & apply(all_43_4, v6) = v7 & % 104.60/23.82 | | | | $i(v7))))))) % 104.60/23.82 | | | | % 104.60/23.82 | | | | ALPHA: (135) implies: % 104.60/23.82 | | | | (136) relation_dom(all_43_4) = all_114_0 % 104.60/23.82 | | | | (137) ! [v0: $i] : ( ~ (in(v0, all_43_1) = 0) | ~ $i(v0) | ~ % 104.60/23.82 | | | | $i(all_43_1) | ? [v1: $i] : (apply(all_43_4, v1) = v0 & % 104.60/23.82 | | | | in(v1, all_114_0) = 0 & $i(v1))) % 104.60/23.82 | | | | % 104.60/23.82 | | | | BETA: splitting (71) gives: % 104.60/23.82 | | | | % 104.60/23.82 | | | | Case 1: % 104.60/23.82 | | | | | % 104.60/23.82 | | | | | (138) all_41_0 = 0 % 104.60/23.82 | | | | | % 104.60/23.82 | | | | | REDUCE: (44), (138) imply: % 104.60/23.82 | | | | | (139) $false % 104.60/23.82 | | | | | % 104.60/23.82 | | | | | CLOSE: (139) is inconsistent. % 104.60/23.82 | | | | | % 104.60/23.82 | | | | Case 2: % 104.60/23.82 | | | | | % 104.60/23.82 | | | | | (140) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 104.60/23.82 | | | | | powerset(all_41_1) = v0 & element(v1, v0) = 0 & empty(v1) = % 104.60/23.82 | | | | | v2 & $i(v1) & $i(v0)) % 104.60/23.82 | | | | | % 104.60/23.82 | | | | | DELTA: instantiating (140) with fresh symbols all_147_0, all_147_1, % 104.60/23.82 | | | | | all_147_2 gives: % 104.60/23.82 | | | | | (141) ~ (all_147_0 = 0) & powerset(all_41_1) = all_147_2 & % 104.60/23.82 | | | | | element(all_147_1, all_147_2) = 0 & empty(all_147_1) = % 104.60/23.82 | | | | | all_147_0 & $i(all_147_1) & $i(all_147_2) % 104.60/23.82 | | | | | % 104.60/23.82 | | | | | ALPHA: (141) implies: % 104.60/23.82 | | | | | (142) powerset(all_41_1) = all_147_2 % 104.60/23.82 | | | | | % 104.60/23.82 | | | | | BETA: splitting (107) gives: % 104.60/23.82 | | | | | % 104.60/23.82 | | | | | Case 1: % 104.60/23.82 | | | | | | % 104.60/23.82 | | | | | | (143) ~ (all_102_2 = 0) & function(all_43_6) = all_102_2 % 104.60/23.82 | | | | | | % 104.60/23.82 | | | | | | ALPHA: (143) implies: % 104.60/23.82 | | | | | | (144) ~ (all_102_2 = 0) % 104.60/23.82 | | | | | | (145) function(all_43_6) = all_102_2 % 104.60/23.82 | | | | | | % 104.60/23.82 | | | | | | GROUND_INST: instantiating (23) with 0, all_102_2, all_43_6, % 104.60/23.82 | | | | | | simplifying with (54), (145) gives: % 104.60/23.82 | | | | | | (146) all_102_2 = 0 % 104.60/23.82 | | | | | | % 104.60/23.82 | | | | | | REDUCE: (144), (146) imply: % 104.60/23.82 | | | | | | (147) $false % 104.60/23.82 | | | | | | % 104.60/23.82 | | | | | | CLOSE: (147) is inconsistent. % 104.60/23.82 | | | | | | % 104.60/23.82 | | | | | Case 2: % 104.60/23.82 | | | | | | % 104.60/23.83 | | | | | | (148) relation_rng(all_43_6) = all_102_1 & relation_dom(all_43_6) % 104.60/23.83 | | | | | | = all_102_0 & $i(all_102_0) & $i(all_102_1) & ! [v0: $i] : % 104.60/23.83 | | | | | | ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_43_6, % 104.60/23.83 | | | | | | v2) = v0) | ~ (in(v0, all_102_1) = v1) | ~ $i(v2) | % 104.60/23.83 | | | | | | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v2, % 104.60/23.83 | | | | | | all_102_0) = v3)) & ! [v0: $i] : ! [v1: int] : ! % 104.60/23.83 | | | | | | [v2: $i] : (v1 = 0 | ~ (in(v2, all_102_0) = 0) | ~ % 104.60/23.83 | | | | | | (in(v0, all_102_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? % 104.60/23.83 | | | | | | [v3: $i] : ( ~ (v3 = v0) & apply(all_43_6, v2) = v3 & % 104.60/23.83 | | | | | | $i(v3))) & ! [v0: $i] : ( ~ (in(v0, all_102_1) = 0) | % 104.60/23.83 | | | | | | ~ $i(v0) | ? [v1: $i] : (apply(all_43_6, v1) = v0 & % 104.60/23.83 | | | | | | in(v1, all_102_0) = 0 & $i(v1))) & ? [v0: any] : (v0 = % 104.60/23.83 | | | | | | all_102_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: int] : ? % 104.60/23.83 | | | | | | [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) & $i(v1) % 104.60/23.83 | | | | | | & ((v5 = v1 & v4 = 0 & apply(all_43_6, v3) = v1 & % 104.60/23.83 | | | | | | in(v3, all_102_0) = 0) | (v2 = 0 & in(v1, v0) = 0)) % 104.60/23.83 | | | | | | & (( ~ (v2 = 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( ~ % 104.60/23.83 | | | | | | (apply(all_43_6, v6) = v1) | ~ $i(v6) | ? [v7: % 104.60/23.83 | | | | | | int] : ( ~ (v7 = 0) & in(v6, all_102_0) = v7)) % 104.60/23.83 | | | | | | & ! [v6: $i] : ( ~ (in(v6, all_102_0) = 0) | ~ % 104.60/23.83 | | | | | | $i(v6) | ? [v7: $i] : ( ~ (v7 = v1) & % 104.60/23.83 | | | | | | apply(all_43_6, v6) = v7 & $i(v7))))))) % 104.60/23.83 | | | | | | % 104.60/23.83 | | | | | | ALPHA: (148) implies: % 104.60/23.83 | | | | | | (149) $i(all_102_0) % 104.60/23.83 | | | | | | (150) relation_dom(all_43_6) = all_102_0 % 104.60/23.83 | | | | | | % 104.60/23.83 | | | | | | BETA: splitting (109) gives: % 104.60/23.83 | | | | | | % 104.60/23.83 | | | | | | Case 1: % 104.60/23.83 | | | | | | | % 104.60/23.83 | | | | | | | (151) ~ (all_104_1 = 0) & function(all_43_4) = all_104_1 % 104.60/23.83 | | | | | | | % 104.60/23.83 | | | | | | | ALPHA: (151) implies: % 104.60/23.83 | | | | | | | (152) ~ (all_104_1 = 0) % 104.60/23.83 | | | | | | | (153) function(all_43_4) = all_104_1 % 104.60/23.83 | | | | | | | % 104.60/23.83 | | | | | | | GROUND_INST: instantiating (23) with 0, all_104_1, all_43_4, % 104.60/23.83 | | | | | | | simplifying with (55), (153) gives: % 104.60/23.83 | | | | | | | (154) all_104_1 = 0 % 104.60/23.83 | | | | | | | % 104.60/23.83 | | | | | | | REDUCE: (152), (154) imply: % 104.60/23.83 | | | | | | | (155) $false % 104.60/23.83 | | | | | | | % 104.60/23.83 | | | | | | | CLOSE: (155) is inconsistent. % 104.60/23.83 | | | | | | | % 104.60/23.83 | | | | | | Case 2: % 104.60/23.83 | | | | | | | % 104.60/23.83 | | | | | | | (156) ( ~ (all_104_2 = 0) & relation(all_43_4) = all_104_2) | % 104.60/23.83 | | | | | | | (relation_rng(all_43_4) = all_104_0 & $i(all_104_0) & ! % 104.60/23.83 | | | | | | | [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ % 104.60/23.83 | | | | | | | (apply(all_43_4, v2) = v0) | ~ (in(v0, all_104_0) = % 104.60/23.83 | | | | | | | v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : ( ~ % 104.60/23.83 | | | | | | | (v3 = 0) & in(v2, all_43_2) = v3)) & ! [v0: $i] : % 104.60/23.83 | | | | | | | ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, % 104.60/23.83 | | | | | | | all_43_2) = 0) | ~ (in(v0, all_104_0) = v1) | ~ % 104.60/23.83 | | | | | | | $i(v2) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v0) & % 104.60/23.83 | | | | | | | apply(all_43_4, v2) = v3 & $i(v3))) & ! [v0: $i] : % 104.60/23.83 | | | | | | | ( ~ (in(v0, all_104_0) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.60/23.83 | | | | | | | (apply(all_43_4, v1) = v0 & in(v1, all_43_2) = 0 & % 104.60/23.83 | | | | | | | $i(v1))) & ? [v0: any] : (v0 = all_104_0 | ~ % 104.60/23.83 | | | | | | | $i(v0) | ? [v1: $i] : ? [v2: int] : ? [v3: $i] : % 104.60/23.83 | | | | | | | ? [v4: int] : ? [v5: $i] : ($i(v3) & $i(v1) & ((v5 = % 104.60/23.83 | | | | | | | v1 & v4 = 0 & apply(all_43_4, v3) = v1 & in(v3, % 104.60/23.83 | | | | | | | all_43_2) = 0) | (v2 = 0 & in(v1, v0) = 0)) & % 104.60/23.83 | | | | | | | (( ~ (v2 = 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( % 104.60/23.83 | | | | | | | ~ (apply(all_43_4, v6) = v1) | ~ $i(v6) | ? % 104.60/23.83 | | | | | | | [v7: int] : ( ~ (v7 = 0) & in(v6, all_43_2) = % 104.60/23.83 | | | | | | | v7)) & ! [v6: $i] : ( ~ (in(v6, all_43_2) % 104.60/23.83 | | | | | | | = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = % 104.60/23.83 | | | | | | | v1) & apply(all_43_4, v6) = v7 & % 104.60/23.83 | | | | | | | $i(v7)))))))) % 104.60/23.83 | | | | | | | % 104.60/23.83 | | | | | | | BETA: splitting (156) gives: % 104.60/23.83 | | | | | | | % 104.60/23.83 | | | | | | | Case 1: % 104.60/23.83 | | | | | | | | % 104.60/23.83 | | | | | | | | (157) ~ (all_104_2 = 0) & relation(all_43_4) = all_104_2 % 104.60/23.83 | | | | | | | | % 104.60/23.83 | | | | | | | | ALPHA: (157) implies: % 104.60/23.83 | | | | | | | | (158) ~ (all_104_2 = 0) % 104.60/23.83 | | | | | | | | (159) relation(all_43_4) = all_104_2 % 104.60/23.83 | | | | | | | | % 104.60/23.83 | | | | | | | | GROUND_INST: instantiating (24) with 0, all_104_2, all_43_4, % 104.60/23.83 | | | | | | | | simplifying with (57), (159) gives: % 104.60/23.83 | | | | | | | | (160) all_104_2 = 0 % 104.60/23.83 | | | | | | | | % 104.60/23.83 | | | | | | | | REDUCE: (158), (160) imply: % 104.60/23.83 | | | | | | | | (161) $false % 104.60/23.83 | | | | | | | | % 104.60/23.83 | | | | | | | | CLOSE: (161) is inconsistent. % 104.60/23.83 | | | | | | | | % 104.60/23.83 | | | | | | | Case 2: % 104.60/23.83 | | | | | | | | % 104.60/23.83 | | | | | | | | (162) relation_rng(all_43_4) = all_104_0 & $i(all_104_0) & ! % 104.60/23.83 | | | | | | | | [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ % 104.60/23.83 | | | | | | | | (apply(all_43_4, v2) = v0) | ~ (in(v0, all_104_0) = % 104.60/23.83 | | | | | | | | v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : ( ~ % 104.60/23.83 | | | | | | | | (v3 = 0) & in(v2, all_43_2) = v3)) & ! [v0: $i] : % 104.60/23.83 | | | | | | | | ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, % 104.60/23.83 | | | | | | | | all_43_2) = 0) | ~ (in(v0, all_104_0) = v1) | ~ % 104.60/23.83 | | | | | | | | $i(v2) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v0) & % 104.60/23.83 | | | | | | | | apply(all_43_4, v2) = v3 & $i(v3))) & ! [v0: $i] : % 104.60/23.83 | | | | | | | | ( ~ (in(v0, all_104_0) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.60/23.83 | | | | | | | | (apply(all_43_4, v1) = v0 & in(v1, all_43_2) = 0 & % 104.60/23.83 | | | | | | | | $i(v1))) & ? [v0: any] : (v0 = all_104_0 | ~ % 104.60/23.83 | | | | | | | | $i(v0) | ? [v1: $i] : ? [v2: int] : ? [v3: $i] : % 104.60/23.83 | | | | | | | | ? [v4: int] : ? [v5: $i] : ($i(v3) & $i(v1) & ((v5 = % 104.60/23.83 | | | | | | | | v1 & v4 = 0 & apply(all_43_4, v3) = v1 & in(v3, % 104.60/23.83 | | | | | | | | all_43_2) = 0) | (v2 = 0 & in(v1, v0) = 0)) & % 104.60/23.83 | | | | | | | | (( ~ (v2 = 0) & in(v1, v0) = v2) | ( ! [v6: $i] : ( % 104.60/23.83 | | | | | | | | ~ (apply(all_43_4, v6) = v1) | ~ $i(v6) | ? % 104.60/23.83 | | | | | | | | [v7: int] : ( ~ (v7 = 0) & in(v6, all_43_2) = % 104.60/23.83 | | | | | | | | v7)) & ! [v6: $i] : ( ~ (in(v6, all_43_2) % 104.60/23.83 | | | | | | | | = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = % 104.60/23.83 | | | | | | | | v1) & apply(all_43_4, v6) = v7 & % 104.60/23.83 | | | | | | | | $i(v7))))))) % 104.60/23.83 | | | | | | | | % 104.60/23.83 | | | | | | | | ALPHA: (162) implies: % 104.60/23.83 | | | | | | | | (163) $i(all_104_0) % 104.60/23.83 | | | | | | | | (164) relation_rng(all_43_4) = all_104_0 % 104.60/23.83 | | | | | | | | % 104.60/23.83 | | | | | | | | BETA: splitting (114) gives: % 104.60/23.83 | | | | | | | | % 104.60/23.83 | | | | | | | | Case 1: % 104.60/23.83 | | | | | | | | | % 104.60/23.83 | | | | | | | | | (165) ~ (all_113_2 = 0) & function(all_34_0) = all_113_2 % 104.60/23.83 | | | | | | | | | % 104.60/23.83 | | | | | | | | | ALPHA: (165) implies: % 104.60/23.83 | | | | | | | | | (166) ~ (all_113_2 = 0) % 104.60/23.83 | | | | | | | | | (167) function(all_34_0) = all_113_2 % 104.60/23.83 | | | | | | | | | % 104.60/23.84 | | | | | | | | | REDUCE: (68), (167) imply: % 104.60/23.84 | | | | | | | | | (168) function(empty_set) = all_113_2 % 104.60/23.84 | | | | | | | | | % 104.60/23.84 | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_113_2, empty_set, % 104.60/23.84 | | | | | | | | | simplifying with (118), (168) gives: % 104.60/23.84 | | | | | | | | | (169) all_113_2 = 0 % 104.60/23.84 | | | | | | | | | % 104.60/23.84 | | | | | | | | | REDUCE: (166), (169) imply: % 104.60/23.84 | | | | | | | | | (170) $false % 104.60/23.84 | | | | | | | | | % 104.60/23.84 | | | | | | | | | CLOSE: (170) is inconsistent. % 104.60/23.84 | | | | | | | | | % 104.60/23.84 | | | | | | | | Case 2: % 104.60/23.84 | | | | | | | | | % 104.60/23.84 | | | | | | | | | (171) relation_rng(all_34_0) = all_113_1 & % 104.60/23.84 | | | | | | | | | relation_dom(all_34_0) = all_113_0 & $i(all_113_0) & % 104.60/23.84 | | | | | | | | | $i(all_113_1) & ! [v0: $i] : ! [v1: int] : ! [v2: % 104.60/23.84 | | | | | | | | | $i] : (v1 = 0 | ~ (apply(all_34_0, v2) = v0) | ~ % 104.60/23.84 | | | | | | | | | (in(v0, all_113_1) = v1) | ~ $i(v2) | ~ $i(v0) | % 104.60/23.84 | | | | | | | | | ? [v3: int] : ( ~ (v3 = 0) & in(v2, all_113_0) = % 104.60/23.84 | | | | | | | | | v3)) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : % 104.60/23.84 | | | | | | | | | (v1 = 0 | ~ (in(v2, all_113_0) = 0) | ~ (in(v0, % 104.60/23.84 | | | | | | | | | all_113_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? % 104.60/23.84 | | | | | | | | | [v3: $i] : ( ~ (v3 = v0) & apply(all_34_0, v2) = v3 % 104.60/23.84 | | | | | | | | | & $i(v3))) & ! [v0: $i] : ( ~ (in(v0, all_113_1) % 104.60/23.84 | | | | | | | | | = 0) | ~ $i(v0) | ? [v1: $i] : (apply(all_34_0, % 104.60/23.84 | | | | | | | | | v1) = v0 & in(v1, all_113_0) = 0 & $i(v1))) & % 104.60/23.84 | | | | | | | | | ? [v0: any] : (v0 = all_113_1 | ~ $i(v0) | ? [v1: % 104.60/23.84 | | | | | | | | | $i] : ? [v2: int] : ? [v3: $i] : ? [v4: int] : % 104.60/23.84 | | | | | | | | | ? [v5: $i] : ($i(v3) & $i(v1) & ((v5 = v1 & v4 = 0 % 104.60/23.84 | | | | | | | | | & apply(all_34_0, v3) = v1 & in(v3, % 104.60/23.84 | | | | | | | | | all_113_0) = 0) | (v2 = 0 & in(v1, v0) = % 104.60/23.84 | | | | | | | | | 0)) & (( ~ (v2 = 0) & in(v1, v0) = v2) | ( ! % 104.60/23.84 | | | | | | | | | [v6: $i] : ( ~ (apply(all_34_0, v6) = v1) | % 104.60/23.84 | | | | | | | | | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & % 104.60/23.84 | | | | | | | | | in(v6, all_113_0) = v7)) & ! [v6: $i] : % 104.60/23.84 | | | | | | | | | ( ~ (in(v6, all_113_0) = 0) | ~ $i(v6) | ? % 104.60/23.84 | | | | | | | | | [v7: $i] : ( ~ (v7 = v1) & apply(all_34_0, % 104.60/23.84 | | | | | | | | | v6) = v7 & $i(v7))))))) % 104.60/23.84 | | | | | | | | | % 104.60/23.84 | | | | | | | | | ALPHA: (171) implies: % 104.60/23.84 | | | | | | | | | (172) relation_dom(all_34_0) = all_113_0 % 104.60/23.84 | | | | | | | | | % 104.60/23.84 | | | | | | | | | REDUCE: (68), (172) imply: % 104.60/23.84 | | | | | | | | | (173) relation_dom(empty_set) = all_113_0 % 104.60/23.84 | | | | | | | | | % 104.60/23.84 | | | | | | | | | BETA: splitting (108) gives: % 104.60/23.84 | | | | | | | | | % 104.60/23.84 | | | | | | | | | Case 1: % 104.60/23.84 | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | (174) ~ (all_103_2 = 0) & relation(all_43_6) = all_103_2 % 104.60/23.84 | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | ALPHA: (174) implies: % 104.60/23.84 | | | | | | | | | | (175) ~ (all_103_2 = 0) % 104.60/23.84 | | | | | | | | | | (176) relation(all_43_6) = all_103_2 % 104.60/23.84 | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_103_2, all_43_6, % 104.60/23.84 | | | | | | | | | | simplifying with (56), (176) gives: % 104.60/23.84 | | | | | | | | | | (177) all_103_2 = 0 % 104.60/23.84 | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | REDUCE: (175), (177) imply: % 104.60/23.84 | | | | | | | | | | (178) $false % 104.60/23.84 | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | CLOSE: (178) is inconsistent. % 104.60/23.84 | | | | | | | | | | % 104.60/23.84 | | | | | | | | | Case 2: % 104.60/23.84 | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | (179) relation_rng(all_43_6) = all_103_1 & % 104.60/23.84 | | | | | | | | | | relation_dom(all_43_6) = all_103_0 & $i(all_103_0) % 104.60/23.84 | | | | | | | | | | & $i(all_103_1) & ! [v0: $i] : ! [v1: int] : ! % 104.60/23.84 | | | | | | | | | | [v2: $i] : (v1 = 0 | ~ (apply(all_43_6, v2) = v0) % 104.60/23.84 | | | | | | | | | | | ~ (in(v0, all_103_1) = v1) | ~ $i(v2) | ~ % 104.60/23.84 | | | | | | | | | | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v2, % 104.60/23.84 | | | | | | | | | | all_103_0) = v3)) & ! [v0: $i] : ! [v1: % 104.60/23.84 | | | | | | | | | | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, % 104.60/23.84 | | | | | | | | | | all_103_0) = 0) | ~ (in(v0, all_103_1) = v1) % 104.60/23.84 | | | | | | | | | | | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = % 104.60/23.84 | | | | | | | | | | v0) & apply(all_43_6, v2) = v3 & $i(v3))) & % 104.60/23.84 | | | | | | | | | | ! [v0: $i] : ( ~ (in(v0, all_103_1) = 0) | ~ % 104.60/23.84 | | | | | | | | | | $i(v0) | ? [v1: $i] : (apply(all_43_6, v1) = v0 % 104.60/23.84 | | | | | | | | | | & in(v1, all_103_0) = 0 & $i(v1))) & ? [v0: % 104.60/23.84 | | | | | | | | | | any] : (v0 = all_103_1 | ~ $i(v0) | ? [v1: $i] % 104.60/23.84 | | | | | | | | | | : ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? % 104.60/23.84 | | | | | | | | | | [v5: $i] : ($i(v3) & $i(v1) & ((v5 = v1 & v4 = 0 % 104.60/23.84 | | | | | | | | | | & apply(all_43_6, v3) = v1 & in(v3, % 104.60/23.84 | | | | | | | | | | all_103_0) = 0) | (v2 = 0 & in(v1, v0) = % 104.60/23.84 | | | | | | | | | | 0)) & (( ~ (v2 = 0) & in(v1, v0) = v2) | ( % 104.60/23.84 | | | | | | | | | | ! [v6: $i] : ( ~ (apply(all_43_6, v6) = v1) % 104.60/23.84 | | | | | | | | | | | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) % 104.60/23.84 | | | | | | | | | | & in(v6, all_103_0) = v7)) & ! [v6: % 104.60/23.84 | | | | | | | | | | $i] : ( ~ (in(v6, all_103_0) = 0) | ~ % 104.60/23.84 | | | | | | | | | | $i(v6) | ? [v7: $i] : ( ~ (v7 = v1) & % 104.60/23.84 | | | | | | | | | | apply(all_43_6, v6) = v7 & $i(v7))))))) % 104.60/23.84 | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | ALPHA: (179) implies: % 104.60/23.84 | | | | | | | | | | (180) relation_dom(all_43_6) = all_103_0 % 104.60/23.84 | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | BETA: splitting (83) gives: % 104.60/23.84 | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | Case 1: % 104.60/23.84 | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | (181) all_43_0 = 0 % 104.60/23.84 | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | REDUCE: (48), (181) imply: % 104.60/23.84 | | | | | | | | | | | (182) $false % 104.60/23.84 | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | CLOSE: (182) is inconsistent. % 104.60/23.84 | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | Case 2: % 104.60/23.84 | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | (183) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 104.60/23.84 | | | | | | | | | | | all_43_1) = 0 & in(v0, all_43_5) = v1 & % 104.60/23.84 | | | | | | | | | | | $i(v0)) % 104.60/23.84 | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | DELTA: instantiating (183) with fresh symbols all_192_0, % 104.60/23.84 | | | | | | | | | | | all_192_1 gives: % 104.60/23.84 | | | | | | | | | | | (184) ~ (all_192_0 = 0) & in(all_192_1, all_43_1) = 0 & % 104.60/23.84 | | | | | | | | | | | in(all_192_1, all_43_5) = all_192_0 & % 104.60/23.84 | | | | | | | | | | | $i(all_192_1) % 104.60/23.84 | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | ALPHA: (184) implies: % 104.60/23.84 | | | | | | | | | | | (185) ~ (all_192_0 = 0) % 104.60/23.84 | | | | | | | | | | | (186) $i(all_192_1) % 104.60/23.84 | | | | | | | | | | | (187) in(all_192_1, all_43_5) = all_192_0 % 104.60/23.84 | | | | | | | | | | | (188) in(all_192_1, all_43_1) = 0 % 104.60/23.84 | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | BETA: splitting (82) gives: % 104.60/23.84 | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | Case 1: % 104.60/23.84 | | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | | (189) all_43_0 = 0 % 104.60/23.84 | | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | | REDUCE: (48), (189) imply: % 104.60/23.84 | | | | | | | | | | | | (190) $false % 104.60/23.84 | | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | | CLOSE: (190) is inconsistent. % 104.60/23.84 | | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | Case 2: % 104.60/23.84 | | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | | (191) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 104.60/23.84 | | | | | | | | | | | | powerset(all_43_5) = v0 & element(all_43_1, v0) % 104.60/23.84 | | | | | | | | | | | | = v1 & $i(v0)) % 104.60/23.84 | | | | | | | | | | | | % 104.60/23.84 | | | | | | | | | | | | DELTA: instantiating (191) with fresh symbols all_197_0, % 104.60/23.84 | | | | | | | | | | | | all_197_1 gives: % 104.60/23.85 | | | | | | | | | | | | (192) ~ (all_197_0 = 0) & powerset(all_43_5) = % 104.60/23.85 | | | | | | | | | | | | all_197_1 & element(all_43_1, all_197_1) = % 104.60/23.85 | | | | | | | | | | | | all_197_0 & $i(all_197_1) % 104.60/23.85 | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | ALPHA: (192) implies: % 104.60/23.85 | | | | | | | | | | | | (193) powerset(all_43_5) = all_197_1 % 104.60/23.85 | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | BETA: splitting (111) gives: % 104.60/23.85 | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | Case 1: % 104.60/23.85 | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | (194) ~ (all_109_2 = 0) & function(all_43_4) = % 104.60/23.85 | | | | | | | | | | | | | all_109_2 % 104.60/23.85 | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | ALPHA: (194) implies: % 104.60/23.85 | | | | | | | | | | | | | (195) ~ (all_109_2 = 0) % 104.60/23.85 | | | | | | | | | | | | | (196) function(all_43_4) = all_109_2 % 104.60/23.85 | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_109_2, all_43_4, % 104.60/23.85 | | | | | | | | | | | | | simplifying with (55), (196) gives: % 104.60/23.85 | | | | | | | | | | | | | (197) all_109_2 = 0 % 104.60/23.85 | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | REDUCE: (195), (197) imply: % 104.60/23.85 | | | | | | | | | | | | | (198) $false % 104.60/23.85 | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | CLOSE: (198) is inconsistent. % 104.60/23.85 | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | Case 2: % 104.60/23.85 | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | (199) relation_rng(all_43_4) = all_109_1 & % 104.60/23.85 | | | | | | | | | | | | | relation_dom(all_43_4) = all_109_0 & $i(all_109_0) % 104.60/23.85 | | | | | | | | | | | | | & $i(all_109_1) & ! [v0: $i] : ! [v1: int] : ! % 104.60/23.85 | | | | | | | | | | | | | [v2: $i] : (v1 = 0 | ~ (apply(all_43_4, v2) = v0) % 104.60/23.85 | | | | | | | | | | | | | | ~ (in(v0, all_109_1) = v1) | ~ $i(v2) | ~ % 104.60/23.85 | | | | | | | | | | | | | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v2, % 104.60/23.85 | | | | | | | | | | | | | all_109_0) = v3)) & ! [v0: $i] : ! [v1: % 104.60/23.85 | | | | | | | | | | | | | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, % 104.60/23.85 | | | | | | | | | | | | | all_109_0) = 0) | ~ (in(v0, all_109_1) = % 104.60/23.85 | | | | | | | | | | | | | v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ( % 104.60/23.85 | | | | | | | | | | | | | ~ (v3 = v0) & apply(all_43_4, v2) = v3 & % 104.60/23.85 | | | | | | | | | | | | | $i(v3))) & ! [v0: $i] : ( ~ (in(v0, % 104.60/23.85 | | | | | | | | | | | | | all_109_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.60/23.85 | | | | | | | | | | | | | (apply(all_43_4, v1) = v0 & in(v1, all_109_0) = % 104.60/23.85 | | | | | | | | | | | | | 0 & $i(v1))) & ? [v0: any] : (v0 = all_109_1 % 104.60/23.85 | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: int] : ? % 104.60/23.85 | | | | | | | | | | | | | [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) % 104.60/23.85 | | | | | | | | | | | | | & $i(v1) & ((v5 = v1 & v4 = 0 & % 104.60/23.85 | | | | | | | | | | | | | apply(all_43_4, v3) = v1 & in(v3, % 104.60/23.85 | | | | | | | | | | | | | all_109_0) = 0) | (v2 = 0 & in(v1, v0) = % 104.60/23.85 | | | | | | | | | | | | | 0)) & (( ~ (v2 = 0) & in(v1, v0) = v2) | ( % 104.60/23.85 | | | | | | | | | | | | | ! [v6: $i] : ( ~ (apply(all_43_4, v6) = % 104.60/23.85 | | | | | | | | | | | | | v1) | ~ $i(v6) | ? [v7: int] : ( ~ % 104.60/23.85 | | | | | | | | | | | | | (v7 = 0) & in(v6, all_109_0) = v7)) & % 104.60/23.85 | | | | | | | | | | | | | ! [v6: $i] : ( ~ (in(v6, all_109_0) = 0) | % 104.60/23.85 | | | | | | | | | | | | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v1) % 104.60/23.85 | | | | | | | | | | | | | & apply(all_43_4, v6) = v7 & % 104.60/23.85 | | | | | | | | | | | | | $i(v7))))))) % 104.60/23.85 | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | ALPHA: (199) implies: % 104.60/23.85 | | | | | | | | | | | | | (200) relation_rng(all_43_4) = all_109_1 % 104.60/23.85 | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | BETA: splitting (112) gives: % 104.60/23.85 | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | Case 1: % 104.60/23.85 | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | (201) ~ (all_110_2 = 0) & relation(all_43_4) = % 104.60/23.85 | | | | | | | | | | | | | | all_110_2 % 104.60/23.85 | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | ALPHA: (201) implies: % 104.60/23.85 | | | | | | | | | | | | | | (202) ~ (all_110_2 = 0) % 104.60/23.85 | | | | | | | | | | | | | | (203) relation(all_43_4) = all_110_2 % 104.60/23.85 | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_110_2, all_43_4, % 104.60/23.85 | | | | | | | | | | | | | | simplifying with (57), (203) gives: % 104.60/23.85 | | | | | | | | | | | | | | (204) all_110_2 = 0 % 104.60/23.85 | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | REDUCE: (202), (204) imply: % 104.60/23.85 | | | | | | | | | | | | | | (205) $false % 104.60/23.85 | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 104.60/23.85 | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | Case 2: % 104.60/23.85 | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | (206) relation_rng(all_43_4) = all_110_1 & % 104.60/23.85 | | | | | | | | | | | | | | relation_dom(all_43_4) = all_110_0 & $i(all_110_0) % 104.60/23.85 | | | | | | | | | | | | | | & $i(all_110_1) & ! [v0: $i] : ! [v1: int] : ! % 104.60/23.85 | | | | | | | | | | | | | | [v2: $i] : (v1 = 0 | ~ (apply(all_43_4, v2) = v0) % 104.60/23.85 | | | | | | | | | | | | | | | ~ (in(v0, all_110_1) = v1) | ~ $i(v2) | ~ % 104.60/23.85 | | | | | | | | | | | | | | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v2, % 104.60/23.85 | | | | | | | | | | | | | | all_110_0) = v3)) & ! [v0: $i] : ! [v1: % 104.60/23.85 | | | | | | | | | | | | | | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, % 104.60/23.85 | | | | | | | | | | | | | | all_110_0) = 0) | ~ (in(v0, all_110_1) = % 104.60/23.85 | | | | | | | | | | | | | | v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ( % 104.60/23.85 | | | | | | | | | | | | | | ~ (v3 = v0) & apply(all_43_4, v2) = v3 & % 104.60/23.85 | | | | | | | | | | | | | | $i(v3))) & ! [v0: $i] : ( ~ (in(v0, % 104.60/23.85 | | | | | | | | | | | | | | all_110_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.60/23.85 | | | | | | | | | | | | | | (apply(all_43_4, v1) = v0 & in(v1, all_110_0) = % 104.60/23.85 | | | | | | | | | | | | | | 0 & $i(v1))) & ? [v0: any] : (v0 = all_110_1 % 104.60/23.85 | | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: int] : ? % 104.60/23.85 | | | | | | | | | | | | | | [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) % 104.60/23.85 | | | | | | | | | | | | | | & $i(v1) & ((v5 = v1 & v4 = 0 & % 104.60/23.85 | | | | | | | | | | | | | | apply(all_43_4, v3) = v1 & in(v3, % 104.60/23.85 | | | | | | | | | | | | | | all_110_0) = 0) | (v2 = 0 & in(v1, v0) = % 104.60/23.85 | | | | | | | | | | | | | | 0)) & (( ~ (v2 = 0) & in(v1, v0) = v2) | ( % 104.60/23.85 | | | | | | | | | | | | | | ! [v6: $i] : ( ~ (apply(all_43_4, v6) = % 104.60/23.85 | | | | | | | | | | | | | | v1) | ~ $i(v6) | ? [v7: int] : ( ~ % 104.60/23.85 | | | | | | | | | | | | | | (v7 = 0) & in(v6, all_110_0) = v7)) & % 104.60/23.85 | | | | | | | | | | | | | | ! [v6: $i] : ( ~ (in(v6, all_110_0) = 0) | % 104.60/23.85 | | | | | | | | | | | | | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v1) % 104.60/23.85 | | | | | | | | | | | | | | & apply(all_43_4, v6) = v7 & % 104.60/23.85 | | | | | | | | | | | | | | $i(v7))))))) % 104.60/23.85 | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | ALPHA: (206) implies: % 104.60/23.85 | | | | | | | | | | | | | | (207) relation_rng(all_43_4) = all_110_1 % 104.60/23.85 | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | BETA: splitting (113) gives: % 104.60/23.85 | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | Case 1: % 104.60/23.85 | | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | | (208) ~ (all_112_2 = 0) & function(empty_set) = % 104.60/23.85 | | | | | | | | | | | | | | | all_112_2 % 104.60/23.85 | | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | | ALPHA: (208) implies: % 104.60/23.85 | | | | | | | | | | | | | | | (209) ~ (all_112_2 = 0) % 104.60/23.85 | | | | | | | | | | | | | | | (210) function(empty_set) = all_112_2 % 104.60/23.85 | | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_112_2, empty_set, % 104.60/23.85 | | | | | | | | | | | | | | | simplifying with (118), (210) gives: % 104.60/23.85 | | | | | | | | | | | | | | | (211) all_112_2 = 0 % 104.60/23.85 | | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | | REDUCE: (209), (211) imply: % 104.60/23.85 | | | | | | | | | | | | | | | (212) $false % 104.60/23.85 | | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | | CLOSE: (212) is inconsistent. % 104.60/23.85 | | | | | | | | | | | | | | | % 104.60/23.85 | | | | | | | | | | | | | | Case 2: % 104.60/23.85 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | (213) relation_rng(empty_set) = all_112_1 & % 104.60/23.86 | | | | | | | | | | | | | | | relation_dom(empty_set) = all_112_0 & % 104.60/23.86 | | | | | | | | | | | | | | | $i(all_112_0) & $i(all_112_1) & ! [v0: $i] : ! % 104.60/23.86 | | | | | | | | | | | | | | | [v1: int] : ! [v2: $i] : (v1 = 0 | ~ % 104.60/23.86 | | | | | | | | | | | | | | | (apply(empty_set, v2) = v0) | ~ (in(v0, % 104.60/23.86 | | | | | | | | | | | | | | | all_112_1) = v1) | ~ $i(v2) | ~ $i(v0) | % 104.60/23.86 | | | | | | | | | | | | | | | ? [v3: int] : ( ~ (v3 = 0) & in(v2, all_112_0) = % 104.60/23.86 | | | | | | | | | | | | | | | v3)) & ! [v0: $i] : ! [v1: int] : ! [v2: % 104.60/23.86 | | | | | | | | | | | | | | | $i] : (v1 = 0 | ~ (in(v2, all_112_0) = 0) | ~ % 104.60/23.86 | | | | | | | | | | | | | | | (in(v0, all_112_1) = v1) | ~ $i(v2) | ~ $i(v0) % 104.60/23.86 | | | | | | | | | | | | | | | | ? [v3: $i] : ( ~ (v3 = v0) & apply(empty_set, % 104.60/23.86 | | | | | | | | | | | | | | | v2) = v3 & $i(v3))) & ! [v0: $i] : ( ~ % 104.60/23.86 | | | | | | | | | | | | | | | (in(v0, all_112_1) = 0) | ~ $i(v0) | ? [v1: % 104.60/23.86 | | | | | | | | | | | | | | | $i] : (apply(empty_set, v1) = v0 & in(v1, % 104.60/23.86 | | | | | | | | | | | | | | | all_112_0) = 0 & $i(v1))) & ? [v0: any] : % 104.60/23.86 | | | | | | | | | | | | | | | (v0 = all_112_1 | ~ $i(v0) | ? [v1: $i] : ? % 104.60/23.86 | | | | | | | | | | | | | | | [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: % 104.60/23.86 | | | | | | | | | | | | | | | $i] : ($i(v3) & $i(v1) & ((v5 = v1 & v4 = 0 & % 104.60/23.86 | | | | | | | | | | | | | | | apply(empty_set, v3) = v1 & in(v3, % 104.60/23.86 | | | | | | | | | | | | | | | all_112_0) = 0) | (v2 = 0 & in(v1, v0) = % 104.60/23.86 | | | | | | | | | | | | | | | 0)) & (( ~ (v2 = 0) & in(v1, v0) = v2) | ( % 104.60/23.86 | | | | | | | | | | | | | | | ! [v6: $i] : ( ~ (apply(empty_set, v6) = % 104.60/23.86 | | | | | | | | | | | | | | | v1) | ~ $i(v6) | ? [v7: int] : ( ~ % 104.60/23.86 | | | | | | | | | | | | | | | (v7 = 0) & in(v6, all_112_0) = v7)) & % 104.60/23.86 | | | | | | | | | | | | | | | ! [v6: $i] : ( ~ (in(v6, all_112_0) = 0) | % 104.60/23.86 | | | | | | | | | | | | | | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v1) % 104.60/23.86 | | | | | | | | | | | | | | | & apply(empty_set, v6) = v7 & % 104.60/23.86 | | | | | | | | | | | | | | | $i(v7))))))) % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | ALPHA: (213) implies: % 104.60/23.86 | | | | | | | | | | | | | | | (214) relation_dom(empty_set) = all_112_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_65_0, all_69_0, % 104.60/23.86 | | | | | | | | | | | | | | | empty_set, simplifying with (96), (116) gives: % 104.60/23.86 | | | | | | | | | | | | | | | (215) all_69_0 = all_65_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_69_0, all_112_0, % 104.60/23.86 | | | | | | | | | | | | | | | empty_set, simplifying with (116), (214) gives: % 104.60/23.86 | | | | | | | | | | | | | | | (216) all_112_0 = all_69_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_112_0, all_113_0, % 104.60/23.86 | | | | | | | | | | | | | | | empty_set, simplifying with (173), (214) gives: % 104.60/23.86 | | | | | | | | | | | | | | | (217) all_113_0 = all_112_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_63_0, all_113_0, % 104.60/23.86 | | | | | | | | | | | | | | | empty_set, simplifying with (117), (173) gives: % 104.60/23.86 | | | | | | | | | | | | | | | (218) all_113_0 = all_63_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_43_5, all_103_0, % 104.60/23.86 | | | | | | | | | | | | | | | all_43_6, simplifying with (59), (180) gives: % 104.60/23.86 | | | | | | | | | | | | | | | (219) all_103_0 = all_43_5 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_102_0, all_103_0, % 104.60/23.86 | | | | | | | | | | | | | | | all_43_6, simplifying with (150), (180) gives: % 104.60/23.86 | | | | | | | | | | | | | | | (220) all_103_0 = all_102_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_43_2, all_114_0, % 104.60/23.86 | | | | | | | | | | | | | | | all_43_4, simplifying with (60), (136) gives: % 104.60/23.86 | | | | | | | | | | | | | | | (221) all_114_0 = all_43_2 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_43_1, all_109_1, % 104.60/23.86 | | | | | | | | | | | | | | | all_43_4, simplifying with (62), (200) gives: % 104.60/23.86 | | | | | | | | | | | | | | | (222) all_109_1 = all_43_1 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_109_1, all_110_1, % 104.60/23.86 | | | | | | | | | | | | | | | all_43_4, simplifying with (200), (207) gives: % 104.60/23.86 | | | | | | | | | | | | | | | (223) all_110_1 = all_109_1 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_104_0, all_110_1, % 104.60/23.86 | | | | | | | | | | | | | | | all_43_4, simplifying with (164), (207) gives: % 104.60/23.86 | | | | | | | | | | | | | | | (224) all_110_1 = all_104_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | COMBINE_EQS: (217), (218) imply: % 104.60/23.86 | | | | | | | | | | | | | | | (225) all_112_0 = all_63_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | SIMP: (225) implies: % 104.60/23.86 | | | | | | | | | | | | | | | (226) all_112_0 = all_63_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | COMBINE_EQS: (216), (226) imply: % 104.60/23.86 | | | | | | | | | | | | | | | (227) all_69_0 = all_63_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | SIMP: (227) implies: % 104.60/23.86 | | | | | | | | | | | | | | | (228) all_69_0 = all_63_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | COMBINE_EQS: (223), (224) imply: % 104.60/23.86 | | | | | | | | | | | | | | | (229) all_109_1 = all_104_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | SIMP: (229) implies: % 104.60/23.86 | | | | | | | | | | | | | | | (230) all_109_1 = all_104_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | COMBINE_EQS: (222), (230) imply: % 104.60/23.86 | | | | | | | | | | | | | | | (231) all_104_0 = all_43_1 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | COMBINE_EQS: (219), (220) imply: % 104.60/23.86 | | | | | | | | | | | | | | | (232) all_102_0 = all_43_5 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | COMBINE_EQS: (215), (228) imply: % 104.60/23.86 | | | | | | | | | | | | | | | (233) all_65_0 = all_63_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | SIMP: (233) implies: % 104.60/23.86 | | | | | | | | | | | | | | | (234) all_65_0 = all_63_0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | REDUCE: (95), (234) imply: % 104.60/23.86 | | | | | | | | | | | | | | | (235) empty(all_63_0) = 0 % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | BETA: splitting (105) gives: % 104.60/23.86 | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | Case 1: % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_192_1, all_43_5, % 104.60/23.86 | | | | | | | | | | | | | | | | all_192_0, simplifying with (50), (186), (187) % 104.60/23.86 | | | | | | | | | | | | | | | | gives: % 104.60/23.86 | | | | | | | | | | | | | | | | (236) all_192_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 % 104.60/23.86 | | | | | | | | | | | | | | | | = 0 & empty(all_43_5) = 0) | ( ~ (v0 = 0) & % 104.60/23.86 | | | | | | | | | | | | | | | | element(all_192_1, all_43_5) = v0)) % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (137) with all_192_1, simplifying % 104.60/23.86 | | | | | | | | | | | | | | | | with (53), (186), (188) gives: % 104.60/23.86 | | | | | | | | | | | | | | | | (237) ? [v0: $i] : (apply(all_43_4, v0) = all_192_1 & % 104.60/23.86 | | | | | | | | | | | | | | | | in(v0, all_114_0) = 0 & $i(v0)) % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t7_boole) with all_192_1, all_43_1, % 104.60/23.86 | | | | | | | | | | | | | | | | simplifying with (53), (186), (188) gives: % 104.60/23.86 | | | | | | | | | | | | | | | | (238) ? [v0: int] : ( ~ (v0 = 0) & empty(all_43_1) = % 104.60/23.86 | | | | | | | | | | | | | | | | v0) % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_37_1, % 104.60/23.86 | | | | | | | | | | | | | | | | all_136_2, simplifying with (38), (123) gives: % 104.60/23.86 | | | | | | | | | | | | | | | | (239) ? [v0: $i] : (element(v0, all_136_2) = 0 & % 104.60/23.86 | | | | | | | | | | | | | | | | empty(v0) = 0 & $i(v0)) % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_41_1, % 104.60/23.86 | | | | | | | | | | | | | | | | all_147_2, simplifying with (45), (142) gives: % 104.60/23.86 | | | | | | | | | | | | | | | | (240) ? [v0: $i] : (element(v0, all_147_2) = 0 & % 104.60/23.86 | | | | | | | | | | | | | | | | empty(v0) = 0 & $i(v0)) % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_43_5, % 104.60/23.86 | | | | | | | | | | | | | | | | all_197_1, simplifying with (50), (193) gives: % 104.60/23.86 | | | | | | | | | | | | | | | | (241) ? [v0: $i] : (element(v0, all_197_1) = 0 & % 104.60/23.86 | | | | | | | | | | | | | | | | empty(v0) = 0 & $i(v0)) % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | DELTA: instantiating (238) with fresh symbol all_273_0 % 104.60/23.86 | | | | | | | | | | | | | | | | gives: % 104.60/23.86 | | | | | | | | | | | | | | | | (242) ~ (all_273_0 = 0) & empty(all_43_1) = all_273_0 % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | ALPHA: (242) implies: % 104.60/23.86 | | | | | | | | | | | | | | | | (243) ~ (all_273_0 = 0) % 104.60/23.86 | | | | | | | | | | | | | | | | (244) empty(all_43_1) = all_273_0 % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | DELTA: instantiating (240) with fresh symbol all_279_0 % 104.60/23.86 | | | | | | | | | | | | | | | | gives: % 104.60/23.86 | | | | | | | | | | | | | | | | (245) element(all_279_0, all_147_2) = 0 & % 104.60/23.86 | | | | | | | | | | | | | | | | empty(all_279_0) = 0 & $i(all_279_0) % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | ALPHA: (245) implies: % 104.60/23.86 | | | | | | | | | | | | | | | | (246) $i(all_279_0) % 104.60/23.86 | | | | | | | | | | | | | | | | (247) empty(all_279_0) = 0 % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | DELTA: instantiating (237) with fresh symbol all_281_0 % 104.60/23.86 | | | | | | | | | | | | | | | | gives: % 104.60/23.86 | | | | | | | | | | | | | | | | (248) apply(all_43_4, all_281_0) = all_192_1 & % 104.60/23.86 | | | | | | | | | | | | | | | | in(all_281_0, all_114_0) = 0 & $i(all_281_0) % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | ALPHA: (248) implies: % 104.60/23.86 | | | | | | | | | | | | | | | | (249) $i(all_281_0) % 104.60/23.86 | | | | | | | | | | | | | | | | (250) in(all_281_0, all_114_0) = 0 % 104.60/23.86 | | | | | | | | | | | | | | | | (251) apply(all_43_4, all_281_0) = all_192_1 % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | DELTA: instantiating (239) with fresh symbol all_283_0 % 104.60/23.86 | | | | | | | | | | | | | | | | gives: % 104.60/23.86 | | | | | | | | | | | | | | | | (252) element(all_283_0, all_136_2) = 0 & % 104.60/23.86 | | | | | | | | | | | | | | | | empty(all_283_0) = 0 & $i(all_283_0) % 104.60/23.86 | | | | | | | | | | | | | | | | % 104.60/23.86 | | | | | | | | | | | | | | | | ALPHA: (252) implies: % 104.60/23.86 | | | | | | | | | | | | | | | | (253) $i(all_283_0) % 104.60/23.87 | | | | | | | | | | | | | | | | (254) empty(all_283_0) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | DELTA: instantiating (241) with fresh symbol all_285_0 % 104.60/23.87 | | | | | | | | | | | | | | | | gives: % 104.60/23.87 | | | | | | | | | | | | | | | | (255) element(all_285_0, all_197_1) = 0 & % 104.60/23.87 | | | | | | | | | | | | | | | | empty(all_285_0) = 0 & $i(all_285_0) % 104.60/23.87 | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | ALPHA: (255) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | (256) $i(all_285_0) % 104.60/23.87 | | | | | | | | | | | | | | | | (257) empty(all_285_0) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | (258) element(all_285_0, all_197_1) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | REDUCE: (221), (250) imply: % 104.60/23.87 | | | | | | | | | | | | | | | | (259) in(all_281_0, all_43_2) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | Case 1: % 104.60/23.87 | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | (260) all_192_0 = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | REDUCE: (185), (260) imply: % 104.60/23.87 | | | | | | | | | | | | | | | | | (261) $false % 104.60/23.87 | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | CLOSE: (261) is inconsistent. % 104.60/23.87 | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | Case 2: % 104.60/23.87 | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | (262) ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 104.60/23.87 | | | | | | | | | | | | | | | | | empty(all_43_5) = 0) | ( ~ (v0 = 0) & % 104.60/23.87 | | | | | | | | | | | | | | | | | element(all_192_1, all_43_5) = v0)) % 104.60/23.87 | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | DELTA: instantiating (262) with fresh symbols all_345_0, % 104.60/23.87 | | | | | | | | | | | | | | | | | all_345_1 gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | (263) (all_345_0 = 0 & empty(all_43_5) = 0) | ( ~ % 104.60/23.87 | | | | | | | | | | | | | | | | | (all_345_1 = 0) & element(all_192_1, all_43_5) = % 104.60/23.87 | | | | | | | | | | | | | | | | | all_345_1) % 104.60/23.87 | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | Case 1: % 104.60/23.87 | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | (264) all_79_0 = 0 & all_79_1 = 0 & relation(all_43_1) = % 104.60/23.87 | | | | | | | | | | | | | | | | | | 0 & empty(all_43_1) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | ALPHA: (264) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | (265) empty(all_43_1) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_273_0, all_43_1, % 104.60/23.87 | | | | | | | | | | | | | | | | | | simplifying with (244), (265) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | (266) all_273_0 = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | REDUCE: (243), (266) imply: % 104.60/23.87 | | | | | | | | | | | | | | | | | | (267) $false % 104.60/23.87 | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | CLOSE: (267) is inconsistent. % 104.60/23.87 | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | Case 2: % 104.60/23.87 | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | (268) ~ (all_79_2 = 0) & empty(all_43_4) = all_79_2 % 104.60/23.87 | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | ALPHA: (268) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | (269) ~ (all_79_2 = 0) % 104.60/23.87 | | | | | | | | | | | | | | | | | | (270) empty(all_43_4) = all_79_2 % 104.60/23.87 | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | Case 1: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | (271) all_80_2 = 0 & empty(all_43_4) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | (272) empty(all_43_4) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_79_2, all_43_4, % 104.60/23.87 | | | | | | | | | | | | | | | | | | | simplifying with (270), (272) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | (273) all_79_2 = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | REDUCE: (269), (273) imply: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | (274) $false % 104.60/23.87 | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | CLOSE: (274) is inconsistent. % 104.60/23.87 | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | Case 2: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | (275) ( ~ (all_80_0 = 0) & empty(all_43_2) = all_80_0) | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | ( ~ (all_80_1 = 0) & relation(all_43_4) = % 104.60/23.87 | | | | | | | | | | | | | | | | | | | all_80_1) % 104.60/23.87 | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | Case 1: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | (276) ~ (all_80_0 = 0) & empty(all_43_2) = all_80_0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | (277) ~ (all_80_0 = 0) % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | (278) empty(all_43_2) = all_80_0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | Case 1: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | (279) all_77_0 = 0 & all_77_1 = 0 & relation(all_43_2) = % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | 0 & empty(all_43_2) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | (280) empty(all_43_2) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_80_0, all_43_2, % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | simplifying with (278), (280) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | (281) all_80_0 = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | REDUCE: (277), (281) imply: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | (282) $false % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | CLOSE: (282) is inconsistent. % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | Case 2: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | (283) ~ (all_77_2 = 0) & empty(all_43_3) = all_77_2 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (283) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | (284) ~ (all_77_2 = 0) % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | (285) empty(all_43_3) = all_77_2 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | (286) all_98_0 = 0 & all_98_1 = 0 & relation(all_43_3) = % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | 0 & empty(all_43_3) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | (287) empty(all_43_3) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_77_2, all_43_3, % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | simplifying with (285), (287) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | (288) all_77_2 = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (284), (288) imply: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | (289) $false % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (289) is inconsistent. % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | (290) ( ~ (all_98_2 = 0) & relation(all_43_4) = % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | all_98_2) | ( ~ (all_98_3 = 0) & empty(all_43_6) % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | = all_98_3) % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | (291) ~ (all_98_2 = 0) & relation(all_43_4) = all_98_2 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (291) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | (292) ~ (all_98_2 = 0) % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | (293) relation(all_43_4) = all_98_2 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_98_2, all_43_4, % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (57), (293) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | (294) all_98_2 = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (292), (294) imply: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | (295) $false % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent. % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | (296) ~ (all_98_3 = 0) & empty(all_43_6) = all_98_3 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | (297) ~ (all_98_3 = 0) % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | (298) empty(all_43_6) = all_98_3 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (299) all_85_2 = 0 & empty(all_43_6) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (300) empty(all_43_6) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_98_3, all_43_6, % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (298), (300) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (301) all_98_3 = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (297), (301) imply: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (302) $false % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (302) is inconsistent. % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (303) ( ~ (all_85_0 = 0) & empty(all_43_5) = all_85_0) | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_85_1 = 0) & relation(all_43_6) = % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | all_85_1) % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | (304) ~ (all_85_0 = 0) & empty(all_43_5) = all_85_0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (304) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | (305) ~ (all_85_0 = 0) % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | (306) empty(all_43_5) = all_85_0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_345_0 = 0 & empty(all_43_5) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (308) empty(all_43_5) = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_85_0, all_43_5, % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (306), (308) gives: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_85_0 = 0 % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (305), (309) imply: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (310) $false % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (310) is inconsistent. % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.60/23.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (311) ~ (all_345_1 = 0) & element(all_192_1, all_43_5) % 104.60/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_345_1 % 104.60/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.60/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (312) ~ (all_345_1 = 0) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (313) element(all_192_1, all_43_5) = all_345_1 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_281_0, all_43_6, % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_5, all_43_4, all_192_1, simplifying with % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (49), (51), (59), (249), (251) gives: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | int] : ? [v7: int] : (( ~ (v1 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | function(all_43_4) = v1) | ( ~ (v1 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | function(all_43_6) = v1) | ( ~ (v0 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | relation(all_43_4) = v0) | ( ~ (v0 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | relation(all_43_6) = v0) | (((v7 = 0 & v6 = 0 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | & relation_dom(all_43_4) = v5 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, v5) = 0 & in(all_192_1, % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_5) = 0 & $i(v5)) | ( ~ (v4 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | v2 & relation_dom(v2) = v3 & in(all_281_0, % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | v3) = v4 & $i(v3) & $i(v2))) & ((v4 = 0 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | & relation_composition(all_43_4, all_43_6) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | = v2 & relation_dom(v2) = v3 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, v3) = 0 & $i(v3) & $i(v2)) | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v7 = 0) & in(all_192_1, all_43_5) = v7) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v6 = 0) & relation_dom(all_43_4) = v5 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | & in(all_281_0, v5) = v6 & $i(v5))))) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_192_1, all_285_0, % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_5, all_197_1, all_345_1, simplifying with % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (50), (186), (193), (256), (258), (313) gives: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_345_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_192_1, all_285_0) = v0) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (314) with fresh symbols all_1118_0, % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_1, all_1118_2, all_1118_3, all_1118_4, % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5, all_1118_6, all_1118_7 gives: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) ( ~ (all_1118_6 = 0) & function(all_43_4) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_6) | ( ~ (all_1118_6 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | function(all_43_6) = all_1118_6) | ( ~ % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1118_7 = 0) & relation(all_43_4) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_7) | ( ~ (all_1118_7 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | relation(all_43_6) = all_1118_7) | (((all_1118_0 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0 & all_1118_1 = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1118_2 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1118_2) = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_192_1, all_43_5) = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_2)) | ( ~ (all_1118_3 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5 & relation_dom(all_1118_5) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_4 & in(all_281_0, all_1118_4) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_3 & $i(all_1118_4) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_5))) & ((all_1118_3 = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5 & relation_dom(all_1118_5) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_4 & in(all_281_0, all_1118_4) = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_4) & $i(all_1118_5)) | ( ~ % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1118_0 = 0) & in(all_192_1, all_43_5) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_0) | ( ~ (all_1118_1 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1118_2 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1118_2) = all_1118_1 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_2)))) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) ( ~ (all_1118_6 = 0) & function(all_43_4) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_6) | ( ~ (all_1118_6 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | function(all_43_6) = all_1118_6) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) ~ (all_1118_6 = 0) & function(all_43_4) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_6 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) ~ (all_1118_6 = 0) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) function(all_43_4) = all_1118_6 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_1118_6, all_43_4, % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (55), (320) gives: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_1118_6 = 0 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (319), (321) imply: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) $false % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (322) is inconsistent. % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) ~ (all_1118_6 = 0) & function(all_43_6) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_6 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) ~ (all_1118_6 = 0) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) function(all_43_6) = all_1118_6 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_1118_6, all_43_6, % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (54), (325) gives: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_1118_6 = 0 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (324), (326) imply: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) $false % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (327) is inconsistent. % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) ( ~ (all_1118_7 = 0) & relation(all_43_4) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_7) | ( ~ (all_1118_7 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation(all_43_6) = all_1118_7) | (((all_1118_0 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0 & all_1118_1 = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1118_2 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1118_2) = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_192_1, all_43_5) = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_2)) | ( ~ (all_1118_3 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5 & relation_dom(all_1118_5) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_4 & in(all_281_0, all_1118_4) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_3 & $i(all_1118_4) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_5))) & ((all_1118_3 = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5 & relation_dom(all_1118_5) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_4 & in(all_281_0, all_1118_4) = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_4) & $i(all_1118_5)) | ( ~ % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1118_0 = 0) & in(all_192_1, all_43_5) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_0) | ( ~ (all_1118_1 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1118_2 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1118_2) = all_1118_1 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_2)))) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) ~ (all_1118_7 = 0) & relation(all_43_4) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_7 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) ~ (all_1118_7 = 0) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) relation(all_43_4) = all_1118_7 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_1118_7, all_43_4, % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (57), (331) gives: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_1118_7 = 0 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (332) imply: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) $false % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (333) is inconsistent. % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) ( ~ (all_1118_7 = 0) & relation(all_43_6) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_7) | (((all_1118_0 = 0 & all_1118_1 = 0 % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & relation_dom(all_43_4) = all_1118_2 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1118_2) = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_192_1, all_43_5) = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_2)) | ( ~ (all_1118_3 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5 & relation_dom(all_1118_5) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_4 & in(all_281_0, all_1118_4) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_3 & $i(all_1118_4) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_5))) & ((all_1118_3 = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5 & relation_dom(all_1118_5) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_4 & in(all_281_0, all_1118_4) = 0 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_4) & $i(all_1118_5)) | ( ~ % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1118_0 = 0) & in(all_192_1, all_43_5) = % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_0) | ( ~ (all_1118_1 = 0) & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1118_2 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1118_2) = all_1118_1 & % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_2)))) % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) ~ (all_1118_7 = 0) & relation(all_43_6) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_7 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (335) implies: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) ~ (all_1118_7 = 0) % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) relation(all_43_6) = all_1118_7 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_1118_7, all_43_6, % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (56), (337) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_1118_7 = 0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (336), (338) imply: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) $false % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (339) is inconsistent. % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) ((all_1118_0 = 0 & all_1118_1 = 0 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1118_2 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1118_2) = 0 & in(all_192_1, % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_5) = 0 & $i(all_1118_2)) | ( ~ % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1118_3 = 0) & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5 & relation_dom(all_1118_5) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_4 & in(all_281_0, all_1118_4) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_3 & $i(all_1118_4) & $i(all_1118_5))) % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ((all_1118_3 = 0 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5 & relation_dom(all_1118_5) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_4 & in(all_281_0, all_1118_4) = 0 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_4) & $i(all_1118_5)) | ( ~ % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1118_0 = 0) & in(all_192_1, all_43_5) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_0) | ( ~ (all_1118_1 = 0) & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1118_2 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1118_2) = all_1118_1 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_2))) % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (340) implies: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) (all_1118_0 = 0 & all_1118_1 = 0 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1118_2 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1118_2) = 0 & in(all_192_1, % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_5) = 0 & $i(all_1118_2)) | ( ~ % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1118_3 = 0) & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5 & relation_dom(all_1118_5) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_4 & in(all_281_0, all_1118_4) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_3 & $i(all_1118_4) & $i(all_1118_5)) % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_1118_0 = 0 & all_1118_1 = 0 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1118_2 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1118_2) = 0 & in(all_192_1, % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_5) = 0 & $i(all_1118_2) % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) in(all_192_1, all_43_5) = 0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (185), (187), (343) are inconsistent by % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) ~ (all_1118_3 = 0) & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5 & relation_dom(all_1118_5) = all_1118_4 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & in(all_281_0, all_1118_4) = all_1118_3 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1118_4) & $i(all_1118_5) % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) ~ (all_1118_3 = 0) % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) in(all_281_0, all_1118_4) = all_1118_3 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) relation_dom(all_1118_5) = all_1118_4 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) relation_composition(all_43_4, all_43_6) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1118_5 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_345_1 = 0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (312), (349) imply: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) $false % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (350) is inconsistent. % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_43_3, all_1118_5, % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_6, all_43_4, simplifying with (63), (348) % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_1118_5 = all_43_3 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (351) imply: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) relation_dom(all_43_3) = all_1118_4 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_43_2, all_1118_4, % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_3, simplifying with (61), (352) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_1118_4 = all_43_2 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (353) imply: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) in(all_281_0, all_43_2) = all_1118_3 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_1118_3, all_43_2, % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_281_0, simplifying with (259), (354) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_1118_3 = 0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (345), (355) imply: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) $false % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (356) is inconsistent. % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) ~ (all_92_0 = 0) & relation_dom(all_39_0) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_92_1 & empty(all_92_1) = all_92_0 & % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_92_1) % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (357) implies: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) ~ (all_92_0 = 0) % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) empty(all_92_1) = all_92_0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) relation_dom(all_39_0) = all_92_1 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_94_2 = 0 & empty(all_39_0) = 0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (361) implies: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) empty(all_39_0) = 0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) ~ (all_108_2 = 0) & function(all_39_0) = % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_108_2 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (363) implies: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) ~ (all_108_2 = 0) % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) function(all_39_0) = all_108_2 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_39_0, simplifying with % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (41), (362) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) function(all_39_0) = 0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_39_0, all_279_0, % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (41), (246), (247), (362) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_279_0 = all_39_0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_279_0, % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_283_0, simplifying with (246), (247), (253), % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_283_0 = all_279_0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_283_0, % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_285_0, simplifying with (253), (254), (256), % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_285_0 = all_283_0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_285_0, simplifying % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (256), (257) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_285_0 = empty_set % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (369), (370) imply: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_283_0 = empty_set % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (371) implies: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_283_0 = empty_set % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (368), (372) imply: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_279_0 = empty_set % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (373) implies: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_279_0 = empty_set % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (374) imply: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_39_0 = empty_set % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (375) implies: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_39_0 = empty_set % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (376) imply: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) function(empty_set) = all_108_2 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_108_2, empty_set, % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (118), (377) gives: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_108_2 = 0 % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (378) imply: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) $false % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (379) is inconsistent. % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) relation_rng(all_39_0) = all_108_1 & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_39_0) = all_108_0 & $i(all_108_0) % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_108_1) & ! [v0: $i] : ! [v1: int] : ! % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: $i] : (v1 = 0 | ~ (apply(all_39_0, v2) = v0) % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (in(v0, all_108_1) = v1) | ~ $i(v2) | ~ % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v2, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_108_0) = v3)) & ! [v0: $i] : ! [v1: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_108_0) = 0) | ~ (in(v0, all_108_1) = % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ( % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v3 = v0) & apply(all_39_0, v2) = v3 & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v3))) & ! [v0: $i] : ( ~ (in(v0, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_108_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (apply(all_39_0, v1) = v0 & in(v1, all_108_0) = % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & $i(v1))) & ? [v0: any] : (v0 = all_108_1 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: int] : ? % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: int] : ? [v5: $i] : ($i(v3) % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(v1) & ((v5 = v1 & v4 = 0 & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | apply(all_39_0, v3) = v1 & in(v3, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_108_0) = 0) | (v2 = 0 & in(v1, v0) = % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0)) & (( ~ (v2 = 0) & in(v1, v0) = v2) | ( % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ! [v6: $i] : ( ~ (apply(all_39_0, v6) = % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1) | ~ $i(v6) | ? [v7: int] : ( ~ % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v7 = 0) & in(v6, all_108_0) = v7)) & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ! [v6: $i] : ( ~ (in(v6, all_108_0) = 0) | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v1) % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & apply(all_39_0, v6) = v7 & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v7))))))) % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) relation_dom(all_39_0) = all_108_0 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_92_1, all_108_0, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_39_0, simplifying with (360), (381) gives: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_108_0 = all_92_1 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_39_0, all_279_0, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (41), (246), (247), (362) gives: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_279_0 = all_39_0 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_279_0, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_283_0, simplifying with (246), (247), (253), % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) gives: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_283_0 = all_279_0 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_283_0, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_285_0, simplifying with (253), (254), (256), % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) gives: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_285_0 = all_283_0 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_285_0, simplifying % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (256), (257) gives: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_285_0 = empty_set % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_39_0, all_92_1, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (41), (360) gives: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0 & v1 = 0 & relation(all_92_1) = 0 & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | empty(all_92_1) = 0) | ( ~ (v0 = 0) & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | empty(all_39_0) = v0)) % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (386) imply: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_283_0 = empty_set % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (388) implies: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_283_0 = empty_set % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (384), (389) imply: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_279_0 = empty_set % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (390) implies: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_279_0 = empty_set % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (383), (391) imply: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_39_0 = empty_set % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (392) implies: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_39_0 = empty_set % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (387) with fresh symbols all_1082_0, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1082_1, all_1082_2 gives: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) (all_1082_0 = 0 & all_1082_1 = 0 & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation(all_92_1) = 0 & empty(all_92_1) = 0) | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_1082_2 = 0) & empty(all_39_0) = % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1082_2) % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (394) gives: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_1082_0 = 0 & all_1082_1 = 0 & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation(all_92_1) = 0 & empty(all_92_1) = 0 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (395) implies: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) empty(all_92_1) = 0 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_92_0, 0, all_92_1, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (359), (396) gives: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_92_0 = 0 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (397) imply: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) $false % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (398) is inconsistent. % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) ~ (all_1082_2 = 0) & empty(all_39_0) = all_1082_2 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (399) implies: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) ~ (all_1082_2 = 0) % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) empty(all_39_0) = all_1082_2 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (401) imply: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) empty(empty_set) = all_1082_2 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_1082_2, empty_set, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (7), (402) gives: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_1082_2 = 0 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (400), (403) imply: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) $false % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (404) is inconsistent. % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_281_0, all_43_6, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_5, all_43_4, all_192_1, simplifying with % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (49), (51), (59), (249), (251) gives: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | int] : ? [v7: int] : (( ~ (v1 = 0) & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | function(all_43_4) = v1) | ( ~ (v1 = 0) & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | function(all_43_6) = v1) | ( ~ (v0 = 0) & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation(all_43_4) = v0) | ( ~ (v0 = 0) & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation(all_43_6) = v0) | (((v7 = 0 & v6 = 0 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & relation_dom(all_43_4) = v5 & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, v5) = 0 & in(all_192_1, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_5) = 0 & $i(v5)) | ( ~ (v4 = 0) & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v2 & relation_dom(v2) = v3 & in(all_281_0, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v3) = v4 & $i(v3) & $i(v2))) & ((v4 = 0 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & relation_composition(all_43_4, all_43_6) % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v2 & relation_dom(v2) = v3 & % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, v3) = 0 & $i(v3) & $i(v2)) | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v7 = 0) & in(all_192_1, all_43_5) = v7) % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v6 = 0) & relation_dom(all_43_4) = v5 % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & in(all_281_0, v5) = v6 & $i(v5))))) % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (405) with fresh symbols all_1109_0, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_1, all_1109_2, all_1109_3, all_1109_4, % 104.87/23.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5, all_1109_6, all_1109_7 gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) ( ~ (all_1109_6 = 0) & function(all_43_4) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_6) | ( ~ (all_1109_6 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | function(all_43_6) = all_1109_6) | ( ~ % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1109_7 = 0) & relation(all_43_4) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_7) | ( ~ (all_1109_7 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation(all_43_6) = all_1109_7) | (((all_1109_0 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0 & all_1109_1 = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1109_2 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1109_2) = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_192_1, all_43_5) = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_2)) | ( ~ (all_1109_3 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5 & relation_dom(all_1109_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_4 & in(all_281_0, all_1109_4) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_3 & $i(all_1109_4) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_5))) & ((all_1109_3 = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5 & relation_dom(all_1109_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_4 & in(all_281_0, all_1109_4) = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_4) & $i(all_1109_5)) | ( ~ % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1109_0 = 0) & in(all_192_1, all_43_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_0) | ( ~ (all_1109_1 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1109_2 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1109_2) = all_1109_1 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_2)))) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (406) gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) ( ~ (all_1109_6 = 0) & function(all_43_4) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_6) | ( ~ (all_1109_6 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | function(all_43_6) = all_1109_6) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (407) gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) ~ (all_1109_6 = 0) & function(all_43_4) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_6 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (408) implies: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) ~ (all_1109_6 = 0) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) function(all_43_4) = all_1109_6 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_1109_6, all_43_4, % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (55), (410) gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_1109_6 = 0 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (409), (411) imply: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) $false % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (412) is inconsistent. % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) ~ (all_1109_6 = 0) & function(all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_6 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (413) implies: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) ~ (all_1109_6 = 0) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) function(all_43_6) = all_1109_6 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_1109_6, all_43_6, % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (54), (415) gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_1109_6 = 0 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (414), (416) imply: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) $false % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (417) is inconsistent. % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) ( ~ (all_1109_7 = 0) & relation(all_43_4) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_7) | ( ~ (all_1109_7 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation(all_43_6) = all_1109_7) | (((all_1109_0 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0 & all_1109_1 = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1109_2 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1109_2) = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_192_1, all_43_5) = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_2)) | ( ~ (all_1109_3 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5 & relation_dom(all_1109_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_4 & in(all_281_0, all_1109_4) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_3 & $i(all_1109_4) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_5))) & ((all_1109_3 = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5 & relation_dom(all_1109_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_4 & in(all_281_0, all_1109_4) = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_4) & $i(all_1109_5)) | ( ~ % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1109_0 = 0) & in(all_192_1, all_43_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_0) | ( ~ (all_1109_1 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1109_2 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1109_2) = all_1109_1 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_2)))) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (418) gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) ~ (all_1109_7 = 0) & relation(all_43_4) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_7 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (419) implies: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) ~ (all_1109_7 = 0) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) relation(all_43_4) = all_1109_7 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_1109_7, all_43_4, % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (57), (421) gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_1109_7 = 0 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (420), (422) imply: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) $false % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (423) is inconsistent. % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) ( ~ (all_1109_7 = 0) & relation(all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_7) | (((all_1109_0 = 0 & all_1109_1 = 0 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & relation_dom(all_43_4) = all_1109_2 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1109_2) = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_192_1, all_43_5) = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_2)) | ( ~ (all_1109_3 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5 & relation_dom(all_1109_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_4 & in(all_281_0, all_1109_4) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_3 & $i(all_1109_4) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_5))) & ((all_1109_3 = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5 & relation_dom(all_1109_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_4 & in(all_281_0, all_1109_4) = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_4) & $i(all_1109_5)) | ( ~ % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1109_0 = 0) & in(all_192_1, all_43_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_0) | ( ~ (all_1109_1 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1109_2 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1109_2) = all_1109_1 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_2)))) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (424) gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) ~ (all_1109_7 = 0) & relation(all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_7 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (425) implies: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) ~ (all_1109_7 = 0) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) relation(all_43_6) = all_1109_7 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_1109_7, all_43_6, % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (56), (427) gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_1109_7 = 0 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (426), (428) imply: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) $false % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (429) is inconsistent. % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) ((all_1109_0 = 0 & all_1109_1 = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1109_2 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1109_2) = 0 & in(all_192_1, % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_5) = 0 & $i(all_1109_2)) | ( ~ % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1109_3 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5 & relation_dom(all_1109_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_4 & in(all_281_0, all_1109_4) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_3 & $i(all_1109_4) & $i(all_1109_5))) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ((all_1109_3 = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5 & relation_dom(all_1109_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_4 & in(all_281_0, all_1109_4) = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_4) & $i(all_1109_5)) | ( ~ % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1109_0 = 0) & in(all_192_1, all_43_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_0) | ( ~ (all_1109_1 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1109_2 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1109_2) = all_1109_1 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_2))) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (430) implies: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) (all_1109_0 = 0 & all_1109_1 = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1109_2 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1109_2) = 0 & in(all_192_1, % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_5) = 0 & $i(all_1109_2)) | ( ~ % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1109_3 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5 & relation_dom(all_1109_5) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_4 & in(all_281_0, all_1109_4) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_3 & $i(all_1109_4) & $i(all_1109_5)) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (431) gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) all_1109_0 = 0 & all_1109_1 = 0 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_43_4) = all_1109_2 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_281_0, all_1109_2) = 0 & in(all_192_1, % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_5) = 0 & $i(all_1109_2) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (432) implies: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) in(all_192_1, all_43_5) = 0 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (185), (187), (433) are inconsistent by % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) ~ (all_1109_3 = 0) & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_43_4, all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5 & relation_dom(all_1109_5) = all_1109_4 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & in(all_281_0, all_1109_4) = all_1109_3 & % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_1109_4) & $i(all_1109_5) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (434) implies: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) ~ (all_1109_3 = 0) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) in(all_281_0, all_1109_4) = all_1109_3 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) relation_dom(all_1109_5) = all_1109_4 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) relation_composition(all_43_4, all_43_6) = % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1109_5 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_43_3, all_1109_5, % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_6, all_43_4, simplifying with (63), (438) % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) all_1109_5 = all_43_3 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (437), (439) imply: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) relation_dom(all_43_3) = all_1109_4 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_43_2, all_1109_4, % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_43_3, simplifying with (61), (440) gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_1109_4 = all_43_2 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (436), (441) imply: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) in(all_281_0, all_43_2) = all_1109_3 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_1109_3, all_43_2, % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_281_0, simplifying with (259), (442) gives: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) all_1109_3 = 0 % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (435), (443) imply: % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) $false % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (444) is inconsistent. % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | (445) ~ (all_85_1 = 0) & relation(all_43_6) = all_85_1 % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies: % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | (446) ~ (all_85_1 = 0) % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | (447) relation(all_43_6) = all_85_1 % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_85_1, all_43_6, % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (56), (447) gives: % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_85_1 = 0 % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (446), (448) imply: % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | (449) $false % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (449) is inconsistent. % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | Case 2: % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | (450) ~ (all_80_1 = 0) & relation(all_43_4) = all_80_1 % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | ALPHA: (450) implies: % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | (451) ~ (all_80_1 = 0) % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | (452) relation(all_43_4) = all_80_1 % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_80_1, all_43_4, % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | simplifying with (57), (452) gives: % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | (453) all_80_1 = 0 % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | REDUCE: (451), (453) imply: % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | (454) $false % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | CLOSE: (454) is inconsistent. % 104.87/23.92 | | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | Case 2: % 104.87/23.92 | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | (455) ~ (all_97_0 = 0) & relation_dom(all_34_0) = % 104.87/23.92 | | | | | | | | | | | | | | | | all_97_1 & empty(all_97_1) = all_97_0 & % 104.87/23.92 | | | | | | | | | | | | | | | | $i(all_97_1) % 104.87/23.92 | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | ALPHA: (455) implies: % 104.87/23.92 | | | | | | | | | | | | | | | | (456) ~ (all_97_0 = 0) % 104.87/23.92 | | | | | | | | | | | | | | | | (457) empty(all_97_1) = all_97_0 % 104.87/23.92 | | | | | | | | | | | | | | | | (458) relation_dom(all_34_0) = all_97_1 % 104.87/23.92 | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | REDUCE: (68), (458) imply: % 104.87/23.92 | | | | | | | | | | | | | | | | (459) relation_dom(empty_set) = all_97_1 % 104.87/23.92 | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_63_0, all_97_1, % 104.87/23.92 | | | | | | | | | | | | | | | | empty_set, simplifying with (117), (459) gives: % 104.87/23.92 | | | | | | | | | | | | | | | | (460) all_97_1 = all_63_0 % 104.87/23.92 | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | REDUCE: (457), (460) imply: % 104.87/23.92 | | | | | | | | | | | | | | | | (461) empty(all_63_0) = all_97_0 % 104.87/23.92 | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_97_0, all_63_0, % 104.87/23.92 | | | | | | | | | | | | | | | | simplifying with (235), (461) gives: % 104.87/23.92 | | | | | | | | | | | | | | | | (462) all_97_0 = 0 % 104.87/23.92 | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | REDUCE: (456), (462) imply: % 104.87/23.92 | | | | | | | | | | | | | | | | (463) $false % 104.87/23.92 | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | | CLOSE: (463) is inconsistent. % 104.87/23.92 | | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | | % 104.87/23.92 | | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | | % 104.87/23.92 | | | | | | | | | End of split % 104.87/23.92 | | | | | | | | | % 104.87/23.92 | | | | | | | | End of split % 104.87/23.92 | | | | | | | | % 104.87/23.92 | | | | | | | End of split % 104.87/23.92 | | | | | | | % 104.87/23.92 | | | | | | End of split % 104.87/23.92 | | | | | | % 104.87/23.92 | | | | | End of split % 104.87/23.92 | | | | | % 104.87/23.92 | | | | End of split % 104.87/23.92 | | | | % 104.87/23.92 | | | End of split % 104.87/23.92 | | | % 104.87/23.92 | | End of split % 104.87/23.92 | | % 104.87/23.92 | End of split % 104.87/23.92 | % 104.87/23.92 End of proof % 104.87/23.92 % 104.87/23.92 Sub-proof #1 shows that the following formulas are inconsistent: % 104.87/23.92 ---------------------------------------------------------------- % 104.87/23.92 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 104.87/23.92 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 104.87/23.92 (2) in(all_192_1, all_43_5) = all_192_0 % 104.87/23.92 (3) in(all_192_1, all_43_5) = 0 % 104.87/23.92 (4) ~ (all_192_0 = 0) % 104.87/23.92 % 104.87/23.92 Begin of proof % 104.87/23.92 | % 104.87/23.92 | GROUND_INST: instantiating (1) with all_192_0, 0, all_43_5, all_192_1, % 104.87/23.92 | simplifying with (2), (3) gives: % 104.87/23.92 | (5) all_192_0 = 0 % 104.87/23.92 | % 104.87/23.92 | REDUCE: (4), (5) imply: % 104.87/23.92 | (6) $false % 104.87/23.92 | % 104.87/23.92 | CLOSE: (6) is inconsistent. % 104.87/23.92 | % 104.87/23.92 End of proof % 104.87/23.92 % SZS output end Proof for theBenchmark % 104.87/23.92 % 104.87/23.92 23275ms %------------------------------------------------------------------------------