%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU215+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n031.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:43:19 EDT 2023 % Result : Theorem 23.35s 3.96s % Output : Proof 78.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU215+1 : TPTP v8.1.2. Released v3.3.0. % 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n031.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Wed Aug 23 22:42:35 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.65 ________ _____ % 0.20/0.65 ___ __ \_________(_)________________________________ % 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.65 % 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.65 (2023-06-19) % 0.20/0.65 % 0.20/0.65 (c) Philipp Rümmer, 2009-2023 % 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.65 Amanda Stjerna. % 0.20/0.65 Free software under BSD-3-Clause. % 0.20/0.65 % 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.65 % 0.20/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.67 Running up to 7 provers in parallel. % 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.13/1.14 Prover 1: Preprocessing ... % 2.91/1.15 Prover 4: Preprocessing ... % 2.91/1.19 Prover 2: Preprocessing ... % 2.91/1.19 Prover 5: Preprocessing ... % 2.91/1.19 Prover 3: Preprocessing ... % 2.91/1.19 Prover 6: Preprocessing ... % 2.91/1.19 Prover 0: Preprocessing ... % 5.87/1.63 Prover 1: Warning: ignoring some quantifiers % 6.65/1.68 Prover 3: Warning: ignoring some quantifiers % 6.65/1.68 Prover 1: Constructing countermodel ... % 6.65/1.68 Prover 5: Proving ... % 6.65/1.69 Prover 3: Constructing countermodel ... % 6.65/1.70 Prover 6: Proving ... % 6.65/1.72 Prover 2: Proving ... % 7.64/1.85 Prover 4: Warning: ignoring some quantifiers % 8.00/1.92 Prover 4: Constructing countermodel ... % 9.88/2.19 Prover 0: Proving ... % 12.10/2.44 Prover 3: gave up % 12.10/2.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.10/2.48 Prover 7: Preprocessing ... % 13.13/2.60 Prover 7: Warning: ignoring some quantifiers % 13.13/2.61 Prover 7: Constructing countermodel ... % 16.04/2.98 Prover 1: gave up % 16.04/2.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.04/3.04 Prover 8: Preprocessing ... % 17.07/3.12 Prover 8: Warning: ignoring some quantifiers % 17.07/3.13 Prover 8: Constructing countermodel ... % 21.15/3.68 Prover 8: gave up % 21.55/3.70 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 21.55/3.74 Prover 9: Preprocessing ... % 23.35/3.96 Prover 0: proved (3281ms) % 23.35/3.96 % 23.35/3.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 23.35/3.96 % 23.35/3.96 Prover 5: stopped % 23.35/3.97 Prover 6: stopped % 23.35/3.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.35/3.98 Prover 2: stopped % 23.35/3.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.35/3.98 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 23.35/3.98 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 23.77/4.00 Prover 9: Warning: ignoring some quantifiers % 23.77/4.00 Prover 9: Constructing countermodel ... % 23.77/4.01 Prover 9: stopped % 23.77/4.01 Prover 11: Preprocessing ... % 23.77/4.02 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 23.77/4.02 Prover 10: Preprocessing ... % 23.77/4.05 Prover 16: Preprocessing ... % 23.77/4.05 Prover 13: Preprocessing ... % 23.77/4.09 Prover 19: Preprocessing ... % 23.77/4.10 Prover 10: Warning: ignoring some quantifiers % 23.77/4.10 Prover 10: Constructing countermodel ... % 23.77/4.11 Prover 16: Warning: ignoring some quantifiers % 23.77/4.11 Prover 16: Constructing countermodel ... % 23.77/4.13 Prover 13: Warning: ignoring some quantifiers % 23.77/4.14 Prover 13: Constructing countermodel ... % 23.77/4.16 Prover 10: gave up % 25.14/4.19 Prover 19: Warning: ignoring some quantifiers % 25.14/4.20 Prover 19: Constructing countermodel ... % 25.64/4.25 Prover 11: Warning: ignoring some quantifiers % 25.64/4.25 Prover 11: Constructing countermodel ... % 31.63/5.03 Prover 19: gave up % 65.98/9.59 Prover 13: stopped % 73.00/10.84 Prover 16: stopped % 76.50/11.90 Prover 11: Found proof (size 319) % 76.50/11.90 Prover 11: proved (7924ms) % 76.50/11.90 Prover 4: stopped % 76.50/11.90 Prover 7: stopped % 76.50/11.90 % 76.50/11.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 76.50/11.90 % 77.33/11.92 % SZS output start Proof for theBenchmark % 77.37/11.92 Assumptions after simplification: % 77.37/11.92 --------------------------------- % 77.37/11.92 % 77.37/11.92 (d4_funct_1) % 77.37/11.96 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 77.37/11.96 [v4: $i] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ % 77.37/11.96 $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v5: int] : ? [v6: any] : ? [v7: int] % 77.37/11.96 : (( ~ (v6 = 0) & function(v0) = v6) | ( ~ (v5 = 0) & relation(v0) = v5) | ( % 77.37/11.96 ~ (v5 = 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, v0) = 0) | ( ~ (v6 = % 77.37/11.96 v3) & apply(v0, v2) = v6 & $i(v6))) & ((v6 = v3 & apply(v0, v2) = % 77.37/11.96 v3) | ( ~ (v7 = 0) & in(v4, v0) = v7))))) & ? [v0: $i] : ! [v1: % 77.37/11.96 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 77.37/11.96 (relation_dom(v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ $i(v1) | ~ % 77.37/11.96 $i(v0) | ? [v5: any] : ? [v6: int] : (( ~ (v6 = 0) & function(v1) = v6) | % 77.37/11.96 ( ~ (v5 = 0) & relation(v1) = v5) | (( ~ (v0 = empty_set) | (v5 = % 77.37/11.96 empty_set & apply(v1, v3) = empty_set)) & (v0 = empty_set | ( ~ (v5 % 77.37/11.96 = v0) & apply(v1, v3) = v5 & $i(v5)))))) & ! [v0: $i] : ! [v1: % 77.37/11.96 $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (relation_dom(v0) = % 77.37/11.96 v1) | ~ (apply(v0, v2) = v3) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? % 77.37/11.97 [v4: int] : ? [v5: int] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & % 77.37/11.97 function(v0) = v5) | ( ~ (v4 = 0) & relation(v0) = v4))) & ! [v0: $i] : % 77.37/11.97 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ % 77.37/11.97 (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | % 77.37/11.97 ? [v4: int] : ? [v5: int] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & % 77.37/11.97 function(v0) = v5) | ( ~ (v4 = 0) & relation(v0) = v4))) & ! [v0: $i] : % 77.37/11.97 ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : (( ~ (v1 = % 77.37/11.97 0) & function(v0) = v1) | (relation_dom(v0) = v2 & $i(v2) & ! [v3: % 77.37/11.97 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ % 77.37/11.97 $i(v4) | ~ $i(v3) | ? [v6: int] : ? [v7: $i] : ? [v8: int] : (( ~ % 77.37/11.97 (v6 = 0) & in(v3, v2) = v6) | (((v8 = 0 & in(v5, v0) = 0) | ( ~ % 77.37/11.97 (v7 = v4) & apply(v0, v3) = v7 & $i(v7))) & ((v7 = v4 & % 77.37/11.97 apply(v0, v3) = v4) | ( ~ (v8 = 0) & in(v5, v0) = v8))))) & ? % 77.37/11.97 [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | % 77.37/11.97 ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : (( ~ (v3 = empty_set) | (v6 = % 77.37/11.97 empty_set & apply(v0, v4) = empty_set)) & (v3 = empty_set | ( ~ % 77.37/11.97 (v6 = v3) & apply(v0, v4) = v6 & $i(v6))))) & ! [v3: $i] : ! % 77.37/11.97 [v4: $i] : (v4 = empty_set | ~ (apply(v0, v3) = v4) | ~ $i(v4) | ~ % 77.37/11.97 $i(v3) | in(v3, v2) = 0) & ! [v3: $i] : ! [v4: $i] : (v4 = empty_set % 77.37/11.97 | ~ (apply(v0, v3) = v4) | ~ $i(v3) | in(v3, v2) = 0)))) & ! [v0: % 77.37/11.97 $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : (( ~ % 77.37/11.97 (v1 = 0) & relation(v0) = v1) | (relation_dom(v0) = v2 & $i(v2) & ! % 77.37/11.97 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v3, v4) = v5) | % 77.37/11.97 ~ $i(v4) | ~ $i(v3) | ? [v6: int] : ? [v7: $i] : ? [v8: int] : (( % 77.37/11.97 ~ (v6 = 0) & in(v3, v2) = v6) | (((v8 = 0 & in(v5, v0) = 0) | ( ~ % 77.37/11.97 (v7 = v4) & apply(v0, v3) = v7 & $i(v7))) & ((v7 = v4 & % 77.37/11.97 apply(v0, v3) = v4) | ( ~ (v8 = 0) & in(v5, v0) = v8))))) & ? % 77.37/11.97 [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | % 77.37/11.97 ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : (( ~ (v3 = empty_set) | (v6 = % 77.37/11.97 empty_set & apply(v0, v4) = empty_set)) & (v3 = empty_set | ( ~ % 77.37/11.97 (v6 = v3) & apply(v0, v4) = v6 & $i(v6))))) & ! [v3: $i] : ! % 77.37/11.97 [v4: $i] : (v4 = empty_set | ~ (apply(v0, v3) = v4) | ~ $i(v4) | ~ % 77.37/11.97 $i(v3) | in(v3, v2) = 0) & ! [v3: $i] : ! [v4: $i] : (v4 = empty_set % 77.37/11.97 | ~ (apply(v0, v3) = v4) | ~ $i(v3) | in(v3, v2) = 0)))) % 77.37/11.97 % 77.37/11.97 (fc1_funct_1) % 77.37/11.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 77.37/11.97 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] : % 77.37/11.97 ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v7 = 0 & % 77.37/11.97 relation(v2) = 0 & function(v2) = 0) | ( ~ (v6 = 0) & function(v1) = v6) % 77.37/11.97 | ( ~ (v5 = 0) & relation(v1) = v5) | ( ~ (v4 = 0) & function(v0) = v4) | % 77.37/11.97 ( ~ (v3 = 0) & relation(v0) = v3))) % 77.37/11.97 % 77.37/11.97 (fc5_relat_1) % 77.37/11.97 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 77.37/11.97 [v2: int] : ? [v3: $i] : ? [v4: int] : (( ~ (v4 = 0) & relation_dom(v0) = % 77.37/11.97 v3 & empty(v3) = v4 & $i(v3)) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! % 77.37/11.97 [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 77.37/11.97 int] : ? [v3: int] : ? [v4: int] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v4 = % 77.37/11.97 0) & empty(v1) = v4) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0: % 77.37/11.97 $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ? % 77.37/11.97 [v3: int] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & relation_dom(v0) = v2 % 77.37/11.97 & empty(v2) = v3 & $i(v2)))) % 77.37/11.97 % 77.37/11.97 (fc7_relat_1) % 77.37/11.97 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 77.37/11.97 int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & relation(v1) = 0 % 77.37/11.97 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0: $i] : ( ~ % 77.37/11.97 (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (relation_dom(v0) = v1 & % 77.37/11.97 relation(v1) = 0 & empty(v1) = 0 & $i(v1))) % 77.37/11.97 % 77.37/11.97 (rc1_funct_1) % 77.37/11.98 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & $i(v0)) % 77.37/11.98 % 77.37/11.98 (t21_funct_1) % 77.80/12.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 77.80/12.02 (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ $i(v3) | ~ $i(v1) | % 77.80/12.02 ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 77.80/12.02 int] : ? [v10: $i] : ? [v11: int] : ? [v12: int] : (( ~ (v6 = 0) & % 77.80/12.02 function(v3) = v6) | ( ~ (v6 = 0) & function(v1) = v6) | ( ~ (v5 = 0) & % 77.80/12.02 relation(v3) = v5) | ( ~ (v5 = 0) & relation(v1) = v5) | (((v12 = 0 & % 77.80/12.02 v11 = 0 & relation_dom(v3) = v10 & in(v4, v2) = 0 & in(v0, v10) = 0 % 77.80/12.02 & $i(v10)) | ( ~ (v9 = 0) & relation_composition(v3, v1) = v7 & % 77.80/12.02 relation_dom(v7) = v8 & in(v0, v8) = v9 & $i(v8) & $i(v7))) & ((v9 = % 77.80/12.02 0 & relation_composition(v3, v1) = v7 & relation_dom(v7) = v8 & % 77.80/12.02 in(v0, v8) = 0 & $i(v8) & $i(v7)) | ( ~ (v12 = 0) & in(v4, v2) = % 77.80/12.02 v12) | ( ~ (v11 = 0) & relation_dom(v3) = v10 & in(v0, v10) = v11 & % 77.80/12.02 $i(v10)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 77.80/12.02 : ! [v4: $i] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) % 77.80/12.02 = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : % 77.80/12.02 ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? % 77.80/12.02 [v12: int] : (( ~ (v6 = 0) & function(v3) = v6) | ( ~ (v6 = 0) & % 77.80/12.02 function(v1) = v6) | ( ~ (v5 = 0) & relation(v3) = v5) | ( ~ (v5 = 0) & % 77.80/12.02 relation(v1) = v5) | (((v12 = 0 & v10 = 0 & relation_dom(v3) = v9 & % 77.80/12.02 apply(v3, v0) = v11 & in(v11, v2) = 0 & in(v0, v9) = 0 & $i(v11) & % 77.80/12.02 $i(v9)) | ( ~ (v8 = 0) & relation_dom(v4) = v7 & in(v0, v7) = v8 & % 77.80/12.02 $i(v7))) & ((v8 = 0 & relation_dom(v4) = v7 & in(v0, v7) = 0 & % 77.80/12.02 $i(v7)) | ( ~ (v12 = 0) & apply(v3, v0) = v11 & in(v11, v2) = v12 & % 77.80/12.02 $i(v11)) | ( ~ (v10 = 0) & relation_dom(v3) = v9 & in(v0, v9) = v10 % 77.80/12.02 & $i(v9)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 77.80/12.02 $i] : ! [v4: $i] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) % 77.80/12.02 | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 77.80/12.02 $i] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ? [v11: $i] : ? [v12: % 77.80/12.02 int] : (( ~ (v6 = 0) & function(v3) = v6) | ( ~ (v6 = 0) & function(v1) = % 77.80/12.02 v6) | ( ~ (v5 = 0) & relation(v3) = v5) | ( ~ (v5 = 0) & relation(v1) = % 77.80/12.02 v5) | (((v12 = 0 & v10 = 0 & apply(v3, v0) = v11 & in(v11, v2) = 0 & % 77.80/12.02 in(v0, v4) = 0 & $i(v11)) | ( ~ (v9 = 0) & relation_composition(v3, % 77.80/12.02 v1) = v7 & relation_dom(v7) = v8 & in(v0, v8) = v9 & $i(v8) & % 77.80/12.02 $i(v7))) & ((v9 = 0 & relation_composition(v3, v1) = v7 & % 77.80/12.02 relation_dom(v7) = v8 & in(v0, v8) = 0 & $i(v8) & $i(v7)) | ( ~ (v12 % 77.80/12.02 = 0) & apply(v3, v0) = v11 & in(v11, v2) = v12 & $i(v11)) | ( ~ % 77.80/12.02 (v10 = 0) & in(v0, v4) = v10))))) & ? [v0: $i] : ! [v1: $i] : ! % 77.80/12.02 [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v1) = v2) | ~ (relation(v3) = 0) | % 77.80/12.02 ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: any] : ? [v6: % 77.80/12.02 $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: % 77.80/12.02 int] : (( ~ (v5 = 0) & function(v1) = v5) | ( ~ (v4 = 0) & relation(v1) = % 77.80/12.02 v4) | ( ~ (v4 = 0) & function(v3) = v4) | (((v11 = 0 & v9 = 0 & % 77.80/12.02 relation_dom(v3) = v8 & apply(v3, v0) = v10 & in(v10, v2) = 0 & % 77.80/12.02 in(v0, v8) = 0 & $i(v10) & $i(v8)) | ( ~ (v7 = 0) & % 77.80/12.02 relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & in(v0, % 77.80/12.02 v6) = v7 & $i(v6) & $i(v5))) & ((v7 = 0 & relation_composition(v3, % 77.80/12.02 v1) = v5 & relation_dom(v5) = v6 & in(v0, v6) = 0 & $i(v6) & % 77.80/12.02 $i(v5)) | ( ~ (v11 = 0) & apply(v3, v0) = v10 & in(v10, v2) = v11 & % 77.80/12.02 $i(v10)) | ( ~ (v9 = 0) & relation_dom(v3) = v8 & in(v0, v8) = v9 & % 77.80/12.02 $i(v8)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 77.80/12.02 : ( ~ (relation_dom(v1) = v2) | ~ (function(v3) = 0) | ~ $i(v3) | ~ $i(v1) % 77.80/12.02 | ~ $i(v0) | ? [v4: int] : ? [v5: any] : ? [v6: $i] : ? [v7: int] : ? % 77.80/12.02 [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: int] : (( ~ (v5 = 0) & % 77.80/12.02 function(v1) = v5) | ( ~ (v4 = 0) & relation(v3) = v4) | ( ~ (v4 = 0) & % 77.80/12.02 relation(v1) = v4) | (((v11 = 0 & v9 = 0 & relation_dom(v3) = v8 & % 77.80/12.02 apply(v3, v0) = v10 & in(v10, v2) = 0 & in(v0, v8) = 0 & $i(v10) & % 77.80/12.02 $i(v8)) | ( ~ (v7 = 0) & relation_composition(v3, v1) = v5 & % 77.80/12.02 relation_dom(v5) = v6 & in(v0, v6) = v7 & $i(v6) & $i(v5))) & ((v7 = % 77.80/12.02 0 & relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & % 77.80/12.02 in(v0, v6) = 0 & $i(v6) & $i(v5)) | ( ~ (v11 = 0) & apply(v3, v0) = % 77.80/12.02 v10 & in(v10, v2) = v11 & $i(v10)) | ( ~ (v9 = 0) & relation_dom(v3) % 77.80/12.02 = v8 & in(v0, v8) = v9 & $i(v8)))))) & ? [v0: $i] : ! [v1: $i] : ( % 77.80/12.02 ~ (relation(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : % 77.80/12.02 (( ~ (v2 = 0) & function(v1) = v2) | (relation_dom(v1) = v3 & $i(v3) & ! % 77.80/12.02 [v4: $i] : ! [v5: $i] : ( ~ (relation_composition(v4, v1) = v5) | ~ % 77.80/12.02 $i(v4) | ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? % 77.80/12.02 [v10: $i] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : (( ~ (v7 = % 77.80/12.02 0) & function(v4) = v7) | ( ~ (v6 = 0) & relation(v4) = v6) | % 77.80/12.02 (((v13 = 0 & v11 = 0 & relation_dom(v4) = v10 & apply(v4, v0) = v12 % 77.80/12.02 & in(v12, v3) = 0 & in(v0, v10) = 0 & $i(v12) & $i(v10)) | ( ~ % 77.80/12.02 (v9 = 0) & relation_dom(v5) = v8 & in(v0, v8) = v9 & $i(v8))) % 77.80/12.02 & ((v9 = 0 & relation_dom(v5) = v8 & in(v0, v8) = 0 & $i(v8)) | ( % 77.80/12.02 ~ (v13 = 0) & apply(v4, v0) = v12 & in(v12, v3) = v13 & % 77.80/12.02 $i(v12)) | ( ~ (v11 = 0) & relation_dom(v4) = v10 & in(v0, % 77.80/12.02 v10) = v11 & $i(v10)))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 77.80/12.02 (relation_dom(v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 77.80/12.02 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : ? [v12: $i] % 77.80/12.02 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 77.80/12.02 relation(v4) = v6) | (((v13 = 0 & v11 = 0 & apply(v4, v0) = v12 & % 77.80/12.02 in(v12, v3) = 0 & in(v0, v5) = 0 & $i(v12)) | ( ~ (v10 = 0) & % 77.80/12.02 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 77.80/12.02 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 77.80/12.02 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 77.80/12.02 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & apply(v4, % 77.80/12.02 v0) = v12 & in(v12, v3) = v13 & $i(v12)) | ( ~ (v11 = 0) & % 77.80/12.02 in(v0, v5) = v11))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 77.80/12.02 (apply(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 77.80/12.02 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] % 77.80/12.02 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 77.80/12.02 relation(v4) = v6) | (((v13 = 0 & v12 = 0 & relation_dom(v4) = v11 % 77.80/12.02 & in(v5, v3) = 0 & in(v0, v11) = 0 & $i(v11)) | ( ~ (v10 = 0) % 77.80/12.02 & relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 77.80/12.02 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 77.80/12.02 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 77.80/12.02 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & in(v5, v3) % 77.80/12.02 = v13) | ( ~ (v12 = 0) & relation_dom(v4) = v11 & in(v0, v11) % 77.80/12.02 = v12 & $i(v11)))))) & ! [v4: $i] : ( ~ (relation(v4) = 0) | % 77.80/12.02 ~ $i(v4) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 77.80/12.02 ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] : (( ~ (v5 = % 77.80/12.02 0) & function(v4) = v5) | (((v12 = 0 & v10 = 0 & % 77.80/12.02 relation_dom(v4) = v9 & apply(v4, v0) = v11 & in(v11, v3) = 0 % 77.80/12.02 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 = 0) & % 77.80/12.02 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 77.80/12.02 in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 77.80/12.02 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 77.80/12.02 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 77.80/12.02 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 77.80/12.02 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9)))))) & ! % 77.80/12.02 [v4: $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: int] : ? [v6: % 77.80/12.02 $i] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? % 77.80/12.02 [v11: $i] : ? [v12: int] : (( ~ (v5 = 0) & relation(v4) = v5) | % 77.80/12.02 (((v12 = 0 & v10 = 0 & relation_dom(v4) = v9 & apply(v4, v0) = v11 & % 77.80/12.02 in(v11, v3) = 0 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 % 77.80/12.02 = 0) & relation_composition(v4, v1) = v6 & relation_dom(v6) % 77.80/12.02 = v7 & in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 77.80/12.02 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 77.80/12.02 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 77.80/12.02 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 77.80/12.02 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9))))))))) & ? % 77.80/12.02 [v0: $i] : ! [v1: $i] : ( ~ (function(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 77.80/12.02 [v2: int] : ? [v3: $i] : (( ~ (v2 = 0) & relation(v1) = v2) | % 77.80/12.02 (relation_dom(v1) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ % 77.80/12.02 (relation_composition(v4, v1) = v5) | ~ $i(v4) | ? [v6: int] : ? % 77.80/12.02 [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: int] % 77.80/12.02 : ? [v12: $i] : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | % 77.80/12.02 ( ~ (v6 = 0) & relation(v4) = v6) | (((v13 = 0 & v11 = 0 & % 77.80/12.02 relation_dom(v4) = v10 & apply(v4, v0) = v12 & in(v12, v3) = 0 % 77.80/12.02 & in(v0, v10) = 0 & $i(v12) & $i(v10)) | ( ~ (v9 = 0) & % 77.80/12.02 relation_dom(v5) = v8 & in(v0, v8) = v9 & $i(v8))) & ((v9 = 0 % 77.80/12.02 & relation_dom(v5) = v8 & in(v0, v8) = 0 & $i(v8)) | ( ~ (v13 % 77.80/12.02 = 0) & apply(v4, v0) = v12 & in(v12, v3) = v13 & $i(v12)) | % 77.80/12.02 ( ~ (v11 = 0) & relation_dom(v4) = v10 & in(v0, v10) = v11 & % 77.80/12.02 $i(v10)))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 77.80/12.02 (relation_dom(v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 77.80/12.02 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : ? [v12: $i] % 77.80/12.02 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 77.80/12.02 relation(v4) = v6) | (((v13 = 0 & v11 = 0 & apply(v4, v0) = v12 & % 77.80/12.02 in(v12, v3) = 0 & in(v0, v5) = 0 & $i(v12)) | ( ~ (v10 = 0) & % 77.80/12.02 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 77.80/12.02 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 77.80/12.02 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 77.80/12.02 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & apply(v4, % 77.80/12.02 v0) = v12 & in(v12, v3) = v13 & $i(v12)) | ( ~ (v11 = 0) & % 77.80/12.02 in(v0, v5) = v11))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 77.80/12.02 (apply(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 77.80/12.02 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] % 77.80/12.02 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 77.80/12.02 relation(v4) = v6) | (((v13 = 0 & v12 = 0 & relation_dom(v4) = v11 % 77.80/12.02 & in(v5, v3) = 0 & in(v0, v11) = 0 & $i(v11)) | ( ~ (v10 = 0) % 77.80/12.02 & relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 77.80/12.02 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 77.80/12.02 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 77.80/12.02 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & in(v5, v3) % 77.80/12.02 = v13) | ( ~ (v12 = 0) & relation_dom(v4) = v11 & in(v0, v11) % 77.80/12.02 = v12 & $i(v11)))))) & ! [v4: $i] : ( ~ (relation(v4) = 0) | % 77.80/12.02 ~ $i(v4) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 77.80/12.02 ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] : (( ~ (v5 = % 77.80/12.02 0) & function(v4) = v5) | (((v12 = 0 & v10 = 0 & % 77.80/12.02 relation_dom(v4) = v9 & apply(v4, v0) = v11 & in(v11, v3) = 0 % 77.80/12.02 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 = 0) & % 77.80/12.02 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 77.80/12.02 in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 77.80/12.02 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 77.80/12.02 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 77.80/12.02 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 77.80/12.02 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9)))))) & ! % 77.80/12.02 [v4: $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: int] : ? [v6: % 77.80/12.02 $i] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? % 77.80/12.02 [v11: $i] : ? [v12: int] : (( ~ (v5 = 0) & relation(v4) = v5) | % 77.80/12.02 (((v12 = 0 & v10 = 0 & relation_dom(v4) = v9 & apply(v4, v0) = v11 & % 77.80/12.02 in(v11, v3) = 0 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 % 77.80/12.02 = 0) & relation_composition(v4, v1) = v6 & relation_dom(v6) % 77.80/12.02 = v7 & in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 77.80/12.02 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 77.80/12.02 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 77.80/12.02 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 77.80/12.02 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9))))))))) % 77.80/12.02 % 77.80/12.02 (t22_funct_1) % 77.80/12.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v2, v0) = % 77.80/12.04 v3) | ~ (relation(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 77.80/12.04 int] : ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ? [v9: % 77.80/12.04 $i] : ? [v10: $i] : ((v10 = v9 & relation_composition(v2, v1) = v6 & % 77.80/12.04 apply(v6, v0) = v9 & apply(v1, v3) = v9 & $i(v9) & $i(v6)) | ( ~ (v8 = % 77.80/12.04 0) & relation_composition(v2, v1) = v6 & relation_dom(v6) = v7 & % 77.80/12.04 in(v0, v7) = v8 & $i(v7) & $i(v6)) | ( ~ (v5 = 0) & function(v2) = v5) | % 77.80/12.04 ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & function(v1) = v4))) & % 77.80/12.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v2, v0) = % 77.80/12.04 v3) | ~ (function(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 77.80/12.04 int] : ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ? [v9: % 77.80/12.04 $i] : ? [v10: $i] : ((v10 = v9 & relation_composition(v2, v1) = v6 & % 77.80/12.04 apply(v6, v0) = v9 & apply(v1, v3) = v9 & $i(v9) & $i(v6)) | ( ~ (v8 = % 77.80/12.04 0) & relation_composition(v2, v1) = v6 & relation_dom(v6) = v7 & % 77.80/12.04 in(v0, v7) = v8 & $i(v7) & $i(v6)) | ( ~ (v5 = 0) & function(v2) = v5) | % 77.80/12.04 ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & relation(v1) = v4))) & % 77.80/12.04 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 77.80/12.04 (relation_composition(v2, v1) = v3) | ~ (relation(v1) = 0) | ~ $i(v2) | ~ % 77.80/12.04 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: $i] : ? [v7: % 77.80/12.04 int] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ((v10 = v8 & apply(v3, % 77.80/12.04 v0) = v8 & apply(v2, v0) = v9 & apply(v1, v9) = v8 & $i(v9) & $i(v8)) % 77.80/12.04 | ( ~ (v7 = 0) & relation_dom(v3) = v6 & in(v0, v6) = v7 & $i(v6)) | ( ~ % 77.80/12.04 (v5 = 0) & function(v2) = v5) | ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ % 77.80/12.04 (v4 = 0) & function(v1) = v4))) & ? [v0: $i] : ! [v1: $i] : ! [v2: % 77.80/12.04 $i] : ! [v3: $i] : ( ~ (relation_composition(v2, v1) = v3) | ~ % 77.80/12.04 (function(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? % 77.80/12.04 [v5: int] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: $i] : ? % 77.80/12.04 [v10: $i] : ((v10 = v8 & apply(v3, v0) = v8 & apply(v2, v0) = v9 & apply(v1, % 77.80/12.04 v9) = v8 & $i(v9) & $i(v8)) | ( ~ (v7 = 0) & relation_dom(v3) = v6 & % 77.80/12.04 in(v0, v6) = v7 & $i(v6)) | ( ~ (v5 = 0) & function(v2) = v5) | ( ~ (v4 % 77.80/12.04 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & relation(v1) = v4))) & ? % 77.80/12.04 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation(v2) = 0) | ~ % 77.80/12.04 (relation(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? % 77.80/12.04 [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 77.80/12.04 $i] : ((v9 = v7 & relation_composition(v2, v1) = v4 & apply(v4, v0) = v7 & % 77.80/12.04 apply(v2, v0) = v8 & apply(v1, v8) = v7 & $i(v8) & $i(v7) & $i(v4)) | ( % 77.80/12.04 ~ (v6 = 0) & relation_composition(v2, v1) = v4 & relation_dom(v4) = v5 & % 77.80/12.04 in(v0, v5) = v6 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & function(v2) = v3) | % 77.80/12.04 ( ~ (v3 = 0) & function(v1) = v3))) & ? [v0: $i] : ! [v1: $i] : ! [v2: % 77.80/12.04 $i] : ( ~ (relation(v2) = 0) | ~ (function(v1) = 0) | ~ $i(v2) | ~ $i(v1) % 77.80/12.04 | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? % 77.80/12.04 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((v9 = v7 & relation_composition(v2, % 77.80/12.04 v1) = v4 & apply(v4, v0) = v7 & apply(v2, v0) = v8 & apply(v1, v8) = % 77.80/12.04 v7 & $i(v8) & $i(v7) & $i(v4)) | ( ~ (v6 = 0) & relation_composition(v2, % 77.80/12.04 v1) = v4 & relation_dom(v4) = v5 & in(v0, v5) = v6 & $i(v5) & $i(v4)) % 77.80/12.04 | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v2) = v3))) % 77.80/12.04 & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation(v1) = 0) | ~ % 77.80/12.04 (function(v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? % 77.80/12.04 [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 77.80/12.04 $i] : ((v9 = v7 & relation_composition(v2, v1) = v4 & apply(v4, v0) = v7 & % 77.80/12.04 apply(v2, v0) = v8 & apply(v1, v8) = v7 & $i(v8) & $i(v7) & $i(v4)) | ( % 77.80/12.04 ~ (v6 = 0) & relation_composition(v2, v1) = v4 & relation_dom(v4) = v5 & % 77.80/12.04 in(v0, v5) = v6 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & relation(v2) = v3) | % 77.80/12.04 ( ~ (v3 = 0) & function(v1) = v3))) & ? [v0: $i] : ! [v1: $i] : ! [v2: % 77.80/12.04 $i] : ( ~ (function(v2) = 0) | ~ (function(v1) = 0) | ~ $i(v2) | ~ $i(v1) % 77.80/12.04 | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? % 77.80/12.04 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((v9 = v7 & relation_composition(v2, % 77.80/12.04 v1) = v4 & apply(v4, v0) = v7 & apply(v2, v0) = v8 & apply(v1, v8) = % 77.80/12.04 v7 & $i(v8) & $i(v7) & $i(v4)) | ( ~ (v6 = 0) & relation_composition(v2, % 77.80/12.04 v1) = v4 & relation_dom(v4) = v5 & in(v0, v5) = v6 & $i(v5) & $i(v4)) % 77.80/12.04 | ( ~ (v3 = 0) & relation(v2) = v3) | ( ~ (v3 = 0) & relation(v1) = v3))) % 77.80/12.04 % 77.80/12.04 (t23_funct_1) % 77.80/12.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 77.80/12.04 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & relation_composition(v1, % 77.80/12.04 v4) = v5 & relation_dom(v1) = v2 & apply(v5, v0) = v6 & apply(v4, v3) = v7 % 77.80/12.04 & apply(v1, v0) = v3 & relation(v4) = 0 & relation(v1) = 0 & function(v4) = % 77.80/12.04 0 & function(v1) = 0 & in(v0, v2) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 77.80/12.04 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 77.80/12.04 % 77.80/12.04 (t7_boole) % 77.80/12.05 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 77.80/12.05 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2)) % 77.80/12.05 % 77.80/12.05 (function-axioms) % 77.80/12.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 77.80/12.05 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 77.80/12.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 77.80/12.05 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 77.80/12.05 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 77.80/12.05 ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 77.80/12.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) % 77.80/12.05 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 77.80/12.05 : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 77.80/12.05 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 77.80/12.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = % 77.80/12.05 v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 77.80/12.05 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 77.80/12.05 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 77.80/12.05 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) % 77.80/12.05 | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 77.80/12.05 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: % 77.80/12.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 77.80/12.05 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 77.80/12.05 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) % 77.80/12.05 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 77.80/12.05 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 77.80/12.05 (empty(v2) = v0)) % 77.80/12.05 % 77.80/12.05 Further assumptions not needed in the proof: % 77.80/12.05 -------------------------------------------- % 77.80/12.05 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, commutativity_k2_tarski, % 77.80/12.05 d5_tarski, dt_k1_funct_1, dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0, % 77.80/12.05 dt_k2_tarski, dt_k4_tarski, dt_k5_relat_1, dt_m1_subset_1, % 77.80/12.05 existence_m1_subset_1, fc10_relat_1, fc12_relat_1, fc1_xboole_0, fc1_zfmisc_1, % 77.80/12.05 fc2_subset_1, fc3_subset_1, fc4_relat_1, fc9_relat_1, rc1_relat_1, rc1_xboole_0, % 77.80/12.05 rc2_relat_1, rc2_xboole_0, rc3_relat_1, t1_subset, t2_subset, t6_boole, t8_boole % 77.80/12.05 % 77.80/12.05 Those formulas are unsatisfiable: % 77.80/12.05 --------------------------------- % 77.80/12.05 % 77.80/12.05 Begin of proof % 77.80/12.05 | % 77.80/12.05 | ALPHA: (d4_funct_1) implies: % 77.80/12.06 | (1) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? % 77.80/12.06 | [v2: $i] : (( ~ (v1 = 0) & relation(v0) = v1) | (relation_dom(v0) = % 77.80/12.06 | v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 77.80/12.06 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: % 77.80/12.06 | int] : ? [v7: $i] : ? [v8: int] : (( ~ (v6 = 0) & in(v3, % 77.80/12.06 | v2) = v6) | (((v8 = 0 & in(v5, v0) = 0) | ( ~ (v7 = v4) & % 77.80/12.06 | apply(v0, v3) = v7 & $i(v7))) & ((v7 = v4 & apply(v0, % 77.80/12.06 | v3) = v4) | ( ~ (v8 = 0) & in(v5, v0) = v8))))) & ? % 77.80/12.06 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v2) % 77.80/12.06 | = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : (( ~ (v3 = % 77.80/12.06 | empty_set) | (v6 = empty_set & apply(v0, v4) = % 77.80/12.06 | empty_set)) & (v3 = empty_set | ( ~ (v6 = v3) & apply(v0, % 77.80/12.06 | v4) = v6 & $i(v6))))) & ! [v3: $i] : ! [v4: $i] : (v4 % 77.80/12.06 | = empty_set | ~ (apply(v0, v3) = v4) | ~ $i(v4) | ~ $i(v3) | % 77.80/12.06 | in(v3, v2) = 0) & ! [v3: $i] : ! [v4: $i] : (v4 = empty_set | % 77.80/12.06 | ~ (apply(v0, v3) = v4) | ~ $i(v3) | in(v3, v2) = 0)))) % 77.80/12.06 | (2) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? % 77.80/12.06 | [v2: $i] : (( ~ (v1 = 0) & function(v0) = v1) | (relation_dom(v0) = % 77.80/12.06 | v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 77.80/12.06 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: % 77.80/12.06 | int] : ? [v7: $i] : ? [v8: int] : (( ~ (v6 = 0) & in(v3, % 77.80/12.06 | v2) = v6) | (((v8 = 0 & in(v5, v0) = 0) | ( ~ (v7 = v4) & % 77.80/12.06 | apply(v0, v3) = v7 & $i(v7))) & ((v7 = v4 & apply(v0, % 77.80/12.06 | v3) = v4) | ( ~ (v8 = 0) & in(v5, v0) = v8))))) & ? % 77.80/12.06 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v2) % 77.80/12.06 | = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : (( ~ (v3 = % 77.80/12.06 | empty_set) | (v6 = empty_set & apply(v0, v4) = % 77.80/12.06 | empty_set)) & (v3 = empty_set | ( ~ (v6 = v3) & apply(v0, % 77.80/12.06 | v4) = v6 & $i(v6))))) & ! [v3: $i] : ! [v4: $i] : (v4 % 77.80/12.06 | = empty_set | ~ (apply(v0, v3) = v4) | ~ $i(v4) | ~ $i(v3) | % 77.80/12.06 | in(v3, v2) = 0) & ! [v3: $i] : ! [v4: $i] : (v4 = empty_set | % 77.80/12.06 | ~ (apply(v0, v3) = v4) | ~ $i(v3) | in(v3, v2) = 0)))) % 77.80/12.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set % 77.80/12.06 | | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v2) | % 77.80/12.06 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ((v4 = 0 & in(v2, v1) = 0) | % 77.80/12.06 | ( ~ (v5 = 0) & function(v0) = v5) | ( ~ (v4 = 0) & relation(v0) = % 77.80/12.06 | v4))) % 77.80/12.06 | % 77.80/12.06 | ALPHA: (fc5_relat_1) implies: % 77.80/12.06 | (4) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? % 77.80/12.06 | [v2: $i] : ? [v3: int] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & % 77.80/12.06 | relation_dom(v0) = v2 & empty(v2) = v3 & $i(v2)))) % 77.80/12.06 | % 77.80/12.06 | ALPHA: (fc7_relat_1) implies: % 77.80/12.06 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 77.80/12.06 | ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & % 77.80/12.06 | relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = % 77.80/12.06 | v2))) % 77.80/12.06 | % 77.80/12.06 | ALPHA: (t21_funct_1) implies: % 77.80/12.06 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 77.80/12.06 | ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ $i(v3) | ~ % 77.80/12.06 | $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: $i] : ? % 77.80/12.06 | [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: int] : ? [v12: % 77.80/12.06 | int] : (( ~ (v6 = 0) & function(v3) = v6) | ( ~ (v6 = 0) & % 77.80/12.06 | function(v1) = v6) | ( ~ (v5 = 0) & relation(v3) = v5) | ( ~ (v5 % 77.80/12.06 | = 0) & relation(v1) = v5) | (((v12 = 0 & v11 = 0 & % 77.80/12.06 | relation_dom(v3) = v10 & in(v4, v2) = 0 & in(v0, v10) = 0 & % 77.80/12.06 | $i(v10)) | ( ~ (v9 = 0) & relation_composition(v3, v1) = v7 & % 77.80/12.06 | relation_dom(v7) = v8 & in(v0, v8) = v9 & $i(v8) & $i(v7))) & % 77.80/12.06 | ((v9 = 0 & relation_composition(v3, v1) = v7 & relation_dom(v7) = % 77.80/12.07 | v8 & in(v0, v8) = 0 & $i(v8) & $i(v7)) | ( ~ (v12 = 0) & % 77.80/12.07 | in(v4, v2) = v12) | ( ~ (v11 = 0) & relation_dom(v3) = v10 & % 77.80/12.07 | in(v0, v10) = v11 & $i(v10)))))) % 77.80/12.07 | % 77.80/12.07 | ALPHA: (t22_funct_1) implies: % 77.80/12.07 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v2, % 77.80/12.07 | v0) = v3) | ~ (function(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 77.80/12.07 | $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? % 77.80/12.07 | [v8: int] : ? [v9: $i] : ? [v10: $i] : ((v10 = v9 & % 77.80/12.07 | relation_composition(v2, v1) = v6 & apply(v6, v0) = v9 & % 77.80/12.07 | apply(v1, v3) = v9 & $i(v9) & $i(v6)) | ( ~ (v8 = 0) & % 77.80/12.07 | relation_composition(v2, v1) = v6 & relation_dom(v6) = v7 & % 77.80/12.07 | in(v0, v7) = v8 & $i(v7) & $i(v6)) | ( ~ (v5 = 0) & function(v2) % 77.80/12.07 | = v5) | ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & % 77.80/12.07 | relation(v1) = v4))) % 77.80/12.07 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v2, % 77.80/12.07 | v0) = v3) | ~ (relation(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 77.80/12.07 | $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? % 77.80/12.07 | [v8: int] : ? [v9: $i] : ? [v10: $i] : ((v10 = v9 & % 77.80/12.07 | relation_composition(v2, v1) = v6 & apply(v6, v0) = v9 & % 77.80/12.07 | apply(v1, v3) = v9 & $i(v9) & $i(v6)) | ( ~ (v8 = 0) & % 77.80/12.07 | relation_composition(v2, v1) = v6 & relation_dom(v6) = v7 & % 77.80/12.07 | in(v0, v7) = v8 & $i(v7) & $i(v6)) | ( ~ (v5 = 0) & function(v2) % 77.80/12.07 | = v5) | ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & % 77.80/12.07 | function(v1) = v4))) % 77.80/12.07 | % 77.80/12.07 | ALPHA: (function-axioms) implies: % 77.80/12.07 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 77.80/12.07 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 77.80/12.07 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 77.80/12.07 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 77.80/12.07 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 77.80/12.07 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 77.80/12.07 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 77.80/12.07 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 77.80/12.07 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 77.80/12.07 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 77.80/12.07 | v0)) % 77.80/12.07 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 77.80/12.07 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 77.80/12.07 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 77.80/12.07 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, % 77.80/12.07 | v2) = v0)) % 77.80/12.07 | % 77.80/12.07 | DELTA: instantiating (rc1_funct_1) with fresh symbol all_33_0 gives: % 77.80/12.07 | (16) relation(all_33_0) = 0 & function(all_33_0) = 0 & $i(all_33_0) % 77.80/12.07 | % 77.80/12.07 | ALPHA: (16) implies: % 77.80/12.07 | (17) $i(all_33_0) % 77.80/12.07 | (18) function(all_33_0) = 0 % 77.80/12.07 | (19) relation(all_33_0) = 0 % 77.80/12.07 | % 77.80/12.07 | DELTA: instantiating (t23_funct_1) with fresh symbols all_41_0, all_41_1, % 77.80/12.07 | all_41_2, all_41_3, all_41_4, all_41_5, all_41_6, all_41_7 gives: % 77.80/12.07 | (20) ~ (all_41_0 = all_41_1) & relation_composition(all_41_6, all_41_3) = % 77.80/12.07 | all_41_2 & relation_dom(all_41_6) = all_41_5 & apply(all_41_2, % 77.80/12.07 | all_41_7) = all_41_1 & apply(all_41_3, all_41_4) = all_41_0 & % 77.80/12.07 | apply(all_41_6, all_41_7) = all_41_4 & relation(all_41_3) = 0 & % 77.80/12.07 | relation(all_41_6) = 0 & function(all_41_3) = 0 & function(all_41_6) = % 77.80/12.07 | 0 & in(all_41_7, all_41_5) = 0 & $i(all_41_0) & $i(all_41_1) & % 77.80/12.07 | $i(all_41_2) & $i(all_41_3) & $i(all_41_4) & $i(all_41_5) & % 77.80/12.07 | $i(all_41_6) & $i(all_41_7) % 77.80/12.07 | % 77.80/12.07 | ALPHA: (20) implies: % 77.80/12.07 | (21) ~ (all_41_0 = all_41_1) % 77.80/12.07 | (22) $i(all_41_7) % 77.80/12.07 | (23) $i(all_41_6) % 77.80/12.07 | (24) $i(all_41_5) % 77.80/12.07 | (25) $i(all_41_4) % 77.80/12.07 | (26) $i(all_41_3) % 77.80/12.07 | (27) in(all_41_7, all_41_5) = 0 % 77.80/12.07 | (28) function(all_41_6) = 0 % 77.80/12.08 | (29) function(all_41_3) = 0 % 77.80/12.08 | (30) relation(all_41_6) = 0 % 77.80/12.08 | (31) relation(all_41_3) = 0 % 77.80/12.08 | (32) apply(all_41_6, all_41_7) = all_41_4 % 77.80/12.08 | (33) apply(all_41_3, all_41_4) = all_41_0 % 77.80/12.08 | (34) apply(all_41_2, all_41_7) = all_41_1 % 77.80/12.08 | (35) relation_dom(all_41_6) = all_41_5 % 77.80/12.08 | (36) relation_composition(all_41_6, all_41_3) = all_41_2 % 77.80/12.08 | % 77.80/12.08 | GROUND_INST: instantiating (t7_boole) with all_41_7, all_41_5, simplifying % 77.80/12.08 | with (22), (24), (27) gives: % 77.80/12.08 | (37) ? [v0: int] : ( ~ (v0 = 0) & empty(all_41_5) = v0) % 77.80/12.08 | % 77.80/12.08 | GROUND_INST: instantiating (1) with all_33_0, simplifying with (17), (18) % 77.80/12.08 | gives: % 77.80/12.08 | (38) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & relation(all_33_0) = v0) % 77.80/12.08 | | (relation_dom(all_33_0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 77.80/12.08 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 77.80/12.08 | $i(v2) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (( ~ (v5 = % 77.80/12.08 | 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, all_33_0) = 0) % 77.80/12.08 | | ( ~ (v6 = v3) & apply(all_33_0, v2) = v6 & $i(v6))) & % 77.80/12.08 | ((v6 = v3 & apply(all_33_0, v2) = v3) | ( ~ (v7 = 0) & % 77.80/12.08 | in(v4, all_33_0) = v7))))) & ? [v2: $i] : ! [v3: $i] : % 77.80/12.08 | ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 77.80/12.08 | $i(v2) | ? [v5: $i] : (( ~ (v2 = empty_set) | (v5 = empty_set & % 77.80/12.08 | apply(all_33_0, v3) = empty_set)) & (v2 = empty_set | ( ~ % 77.80/12.08 | (v5 = v2) & apply(all_33_0, v3) = v5 & $i(v5))))) & ! % 77.80/12.08 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_33_0, v2) % 77.80/12.08 | = v3) | ~ $i(v3) | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 77.80/12.08 | : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_33_0, v2) = v3) | % 77.80/12.08 | ~ $i(v2) | in(v2, v1) = 0))) % 77.80/12.08 | % 77.80/12.08 | GROUND_INST: instantiating (1) with all_41_6, simplifying with (23), (28) % 77.80/12.08 | gives: % 77.80/12.08 | (39) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & relation(all_41_6) = v0) % 77.80/12.08 | | (relation_dom(all_41_6) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 77.80/12.08 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 77.80/12.08 | $i(v2) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (( ~ (v5 = % 77.80/12.08 | 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, all_41_6) = 0) % 77.80/12.08 | | ( ~ (v6 = v3) & apply(all_41_6, v2) = v6 & $i(v6))) & % 77.80/12.08 | ((v6 = v3 & apply(all_41_6, v2) = v3) | ( ~ (v7 = 0) & % 77.80/12.08 | in(v4, all_41_6) = v7))))) & ? [v2: $i] : ! [v3: $i] : % 77.80/12.08 | ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 77.80/12.08 | $i(v2) | ? [v5: $i] : (( ~ (v2 = empty_set) | (v5 = empty_set & % 77.80/12.08 | apply(all_41_6, v3) = empty_set)) & (v2 = empty_set | ( ~ % 77.80/12.08 | (v5 = v2) & apply(all_41_6, v3) = v5 & $i(v5))))) & ! % 77.80/12.08 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_41_6, v2) % 77.80/12.08 | = v3) | ~ $i(v3) | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 77.80/12.08 | : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_41_6, v2) = v3) | % 77.80/12.08 | ~ $i(v2) | in(v2, v1) = 0))) % 77.80/12.08 | % 77.80/12.08 | GROUND_INST: instantiating (1) with all_41_3, simplifying with (26), (29) % 77.80/12.08 | gives: % 78.16/12.09 | (40) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & relation(all_41_3) = v0) % 78.16/12.09 | | (relation_dom(all_41_3) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 78.16/12.09 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 78.16/12.09 | $i(v2) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (( ~ (v5 = % 78.16/12.09 | 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, all_41_3) = 0) % 78.16/12.09 | | ( ~ (v6 = v3) & apply(all_41_3, v2) = v6 & $i(v6))) & % 78.16/12.09 | ((v6 = v3 & apply(all_41_3, v2) = v3) | ( ~ (v7 = 0) & % 78.16/12.09 | in(v4, all_41_3) = v7))))) & ? [v2: $i] : ! [v3: $i] : % 78.16/12.09 | ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 78.16/12.09 | $i(v2) | ? [v5: $i] : (( ~ (v2 = empty_set) | (v5 = empty_set & % 78.16/12.09 | apply(all_41_3, v3) = empty_set)) & (v2 = empty_set | ( ~ % 78.16/12.09 | (v5 = v2) & apply(all_41_3, v3) = v5 & $i(v5))))) & ! % 78.16/12.09 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_41_3, v2) % 78.16/12.09 | = v3) | ~ $i(v3) | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 78.16/12.09 | : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_41_3, v2) = v3) | % 78.16/12.09 | ~ $i(v2) | in(v2, v1) = 0))) % 78.16/12.09 | % 78.16/12.09 | GROUND_INST: instantiating (4) with all_41_6, simplifying with (23), (30) % 78.16/12.09 | gives: % 78.16/12.09 | (41) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v0 = 0 & empty(all_41_6) % 78.16/12.09 | = 0) | ( ~ (v2 = 0) & relation_dom(all_41_6) = v1 & empty(v1) = v2 % 78.16/12.09 | & $i(v1))) % 78.16/12.09 | % 78.16/12.09 | GROUND_INST: instantiating (2) with all_41_6, simplifying with (23), (30) % 78.16/12.09 | gives: % 78.16/12.09 | (42) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & function(all_41_6) = v0) % 78.16/12.09 | | (relation_dom(all_41_6) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 78.16/12.09 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 78.16/12.09 | $i(v2) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (( ~ (v5 = % 78.16/12.09 | 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, all_41_6) = 0) % 78.16/12.09 | | ( ~ (v6 = v3) & apply(all_41_6, v2) = v6 & $i(v6))) & % 78.16/12.09 | ((v6 = v3 & apply(all_41_6, v2) = v3) | ( ~ (v7 = 0) & % 78.16/12.09 | in(v4, all_41_6) = v7))))) & ? [v2: $i] : ! [v3: $i] : % 78.16/12.09 | ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 78.16/12.09 | $i(v2) | ? [v5: $i] : (( ~ (v2 = empty_set) | (v5 = empty_set & % 78.16/12.09 | apply(all_41_6, v3) = empty_set)) & (v2 = empty_set | ( ~ % 78.16/12.09 | (v5 = v2) & apply(all_41_6, v3) = v5 & $i(v5))))) & ! % 78.16/12.09 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_41_6, v2) % 78.16/12.09 | = v3) | ~ $i(v3) | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 78.16/12.09 | : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_41_6, v2) = v3) | % 78.16/12.09 | ~ $i(v2) | in(v2, v1) = 0))) % 78.16/12.09 | % 78.16/12.09 | GROUND_INST: instantiating (2) with all_41_3, simplifying with (26), (31) % 78.16/12.09 | gives: % 78.16/12.09 | (43) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & function(all_41_3) = v0) % 78.16/12.09 | | (relation_dom(all_41_3) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 78.16/12.09 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 78.16/12.09 | $i(v2) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (( ~ (v5 = % 78.16/12.09 | 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, all_41_3) = 0) % 78.16/12.09 | | ( ~ (v6 = v3) & apply(all_41_3, v2) = v6 & $i(v6))) & % 78.16/12.09 | ((v6 = v3 & apply(all_41_3, v2) = v3) | ( ~ (v7 = 0) & % 78.16/12.09 | in(v4, all_41_3) = v7))))) & ? [v2: $i] : ! [v3: $i] : % 78.16/12.09 | ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 78.16/12.09 | $i(v2) | ? [v5: $i] : (( ~ (v2 = empty_set) | (v5 = empty_set & % 78.16/12.09 | apply(all_41_3, v3) = empty_set)) & (v2 = empty_set | ( ~ % 78.16/12.09 | (v5 = v2) & apply(all_41_3, v3) = v5 & $i(v5))))) & ! % 78.16/12.09 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_41_3, v2) % 78.16/12.09 | = v3) | ~ $i(v3) | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 78.16/12.09 | : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_41_3, v2) = v3) | % 78.16/12.09 | ~ $i(v2) | in(v2, v1) = 0))) % 78.16/12.09 | % 78.16/12.09 | GROUND_INST: instantiating (8) with all_41_7, all_41_3, all_41_6, all_41_4, % 78.16/12.09 | simplifying with (22), (23), (26), (31), (32) gives: % 78.16/12.09 | (44) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] % 78.16/12.09 | : ? [v5: $i] : ? [v6: $i] : ((v6 = v5 & % 78.16/12.09 | relation_composition(all_41_6, all_41_3) = v2 & apply(v2, % 78.16/12.09 | all_41_7) = v5 & apply(all_41_3, all_41_4) = v5 & $i(v5) & % 78.16/12.09 | $i(v2)) | ( ~ (v4 = 0) & relation_composition(all_41_6, all_41_3) % 78.16/12.09 | = v2 & relation_dom(v2) = v3 & in(all_41_7, v3) = v4 & $i(v3) & % 78.16/12.09 | $i(v2)) | ( ~ (v1 = 0) & function(all_41_6) = v1) | ( ~ (v0 = 0) & % 78.16/12.09 | relation(all_41_6) = v0) | ( ~ (v0 = 0) & function(all_41_3) = % 78.16/12.09 | v0)) % 78.16/12.09 | % 78.16/12.09 | GROUND_INST: instantiating (7) with all_41_7, all_41_3, all_41_6, all_41_4, % 78.16/12.09 | simplifying with (22), (23), (26), (29), (32) gives: % 78.16/12.09 | (45) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] % 78.16/12.09 | : ? [v5: $i] : ? [v6: $i] : ((v6 = v5 & % 78.16/12.09 | relation_composition(all_41_6, all_41_3) = v2 & apply(v2, % 78.16/12.09 | all_41_7) = v5 & apply(all_41_3, all_41_4) = v5 & $i(v5) & % 78.16/12.09 | $i(v2)) | ( ~ (v4 = 0) & relation_composition(all_41_6, all_41_3) % 78.16/12.09 | = v2 & relation_dom(v2) = v3 & in(all_41_7, v3) = v4 & $i(v3) & % 78.16/12.09 | $i(v2)) | ( ~ (v1 = 0) & function(all_41_6) = v1) | ( ~ (v0 = 0) & % 78.16/12.09 | relation(all_41_3) = v0) | ( ~ (v0 = 0) & relation(all_41_6) = % 78.16/12.09 | v0)) % 78.16/12.09 | % 78.16/12.09 | GROUND_INST: instantiating (5) with all_41_6, all_41_5, simplifying with (23), % 78.16/12.09 | (35) gives: % 78.16/12.10 | (46) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0 & % 78.16/12.10 | relation(all_41_5) = 0 & empty(all_41_5) = 0) | ( ~ (v0 = 0) & % 78.16/12.10 | empty(all_41_6) = v0)) % 78.16/12.10 | % 78.16/12.10 | GROUND_INST: instantiating (fc1_funct_1) with all_41_6, all_41_3, all_41_2, % 78.16/12.10 | simplifying with (23), (26), (36) gives: % 78.16/12.10 | (47) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: % 78.16/12.10 | int] : ? [v5: int] : ((v5 = 0 & v4 = 0 & relation(all_41_2) = 0 & % 78.16/12.10 | function(all_41_2) = 0) | ( ~ (v3 = 0) & function(all_41_3) = v3) % 78.16/12.10 | | ( ~ (v2 = 0) & relation(all_41_3) = v2) | ( ~ (v1 = 0) & % 78.16/12.10 | function(all_41_6) = v1) | ( ~ (v0 = 0) & relation(all_41_6) = % 78.16/12.10 | v0)) % 78.16/12.10 | % 78.16/12.10 | DELTA: instantiating (37) with fresh symbol all_75_0 gives: % 78.16/12.10 | (48) ~ (all_75_0 = 0) & empty(all_41_5) = all_75_0 % 78.16/12.10 | % 78.16/12.10 | ALPHA: (48) implies: % 78.16/12.10 | (49) ~ (all_75_0 = 0) % 78.16/12.10 | (50) empty(all_41_5) = all_75_0 % 78.16/12.10 | % 78.16/12.10 | DELTA: instantiating (41) with fresh symbols all_83_0, all_83_1, all_83_2 % 78.16/12.10 | gives: % 78.16/12.10 | (51) (all_83_2 = 0 & empty(all_41_6) = 0) | ( ~ (all_83_0 = 0) & % 78.16/12.10 | relation_dom(all_41_6) = all_83_1 & empty(all_83_1) = all_83_0 & % 78.16/12.10 | $i(all_83_1)) % 78.16/12.10 | % 78.16/12.10 | DELTA: instantiating (46) with fresh symbols all_91_0, all_91_1, all_91_2 % 78.16/12.10 | gives: % 78.16/12.10 | (52) (all_91_0 = 0 & all_91_1 = 0 & relation(all_41_5) = 0 & % 78.16/12.10 | empty(all_41_5) = 0) | ( ~ (all_91_2 = 0) & empty(all_41_6) = % 78.16/12.10 | all_91_2) % 78.16/12.10 | % 78.16/12.10 | DELTA: instantiating (47) with fresh symbols all_95_0, all_95_1, all_95_2, % 78.16/12.10 | all_95_3, all_95_4, all_95_5 gives: % 78.16/12.10 | (53) (all_95_0 = 0 & all_95_1 = 0 & relation(all_41_2) = 0 & % 78.16/12.10 | function(all_41_2) = 0) | ( ~ (all_95_2 = 0) & function(all_41_3) = % 78.16/12.10 | all_95_2) | ( ~ (all_95_3 = 0) & relation(all_41_3) = all_95_3) | ( % 78.16/12.10 | ~ (all_95_4 = 0) & function(all_41_6) = all_95_4) | ( ~ (all_95_5 = % 78.16/12.10 | 0) & relation(all_41_6) = all_95_5) % 78.16/12.10 | % 78.16/12.10 | DELTA: instantiating (45) with fresh symbols all_102_0, all_102_1, all_102_2, % 78.16/12.10 | all_102_3, all_102_4, all_102_5, all_102_6 gives: % 78.16/12.10 | (54) (all_102_0 = all_102_1 & relation_composition(all_41_6, all_41_3) = % 78.16/12.10 | all_102_4 & apply(all_102_4, all_41_7) = all_102_1 & apply(all_41_3, % 78.16/12.10 | all_41_4) = all_102_1 & $i(all_102_1) & $i(all_102_4)) | ( ~ % 78.16/12.10 | (all_102_2 = 0) & relation_composition(all_41_6, all_41_3) = % 78.16/12.10 | all_102_4 & relation_dom(all_102_4) = all_102_3 & in(all_41_7, % 78.16/12.10 | all_102_3) = all_102_2 & $i(all_102_3) & $i(all_102_4)) | ( ~ % 78.16/12.10 | (all_102_5 = 0) & function(all_41_6) = all_102_5) | ( ~ (all_102_6 = % 78.16/12.10 | 0) & relation(all_41_3) = all_102_6) | ( ~ (all_102_6 = 0) & % 78.16/12.10 | relation(all_41_6) = all_102_6) % 78.16/12.10 | % 78.16/12.10 | DELTA: instantiating (44) with fresh symbols all_117_0, all_117_1, all_117_2, % 78.16/12.10 | all_117_3, all_117_4, all_117_5, all_117_6 gives: % 78.16/12.10 | (55) (all_117_0 = all_117_1 & relation_composition(all_41_6, all_41_3) = % 78.16/12.10 | all_117_4 & apply(all_117_4, all_41_7) = all_117_1 & apply(all_41_3, % 78.16/12.10 | all_41_4) = all_117_1 & $i(all_117_1) & $i(all_117_4)) | ( ~ % 78.16/12.10 | (all_117_2 = 0) & relation_composition(all_41_6, all_41_3) = % 78.16/12.10 | all_117_4 & relation_dom(all_117_4) = all_117_3 & in(all_41_7, % 78.16/12.10 | all_117_3) = all_117_2 & $i(all_117_3) & $i(all_117_4)) | ( ~ % 78.16/12.10 | (all_117_5 = 0) & function(all_41_6) = all_117_5) | ( ~ (all_117_6 = % 78.16/12.10 | 0) & relation(all_41_6) = all_117_6) | ( ~ (all_117_6 = 0) & % 78.16/12.10 | function(all_41_3) = all_117_6) % 78.16/12.10 | % 78.16/12.10 | DELTA: instantiating (40) with fresh symbols all_129_0, all_129_1 gives: % 78.16/12.10 | (56) ( ~ (all_129_1 = 0) & relation(all_41_3) = all_129_1) | % 78.16/12.10 | (relation_dom(all_41_3) = all_129_0 & $i(all_129_0) & ! [v0: $i] : ! % 78.16/12.10 | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) % 78.16/12.10 | | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 % 78.16/12.10 | = 0) & in(v0, all_129_0) = v3) | (((v5 = 0 & in(v2, % 78.16/12.10 | all_41_3) = 0) | ( ~ (v4 = v1) & apply(all_41_3, v0) = % 78.16/12.10 | v4 & $i(v4))) & ((v4 = v1 & apply(all_41_3, v0) = v1) | ( % 78.16/12.10 | ~ (v5 = 0) & in(v2, all_41_3) = v5))))) & ? [v0: $i] : ! % 78.16/12.10 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_129_0) = v2) | ~ % 78.16/12.10 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 78.16/12.10 | empty_set & apply(all_41_3, v1) = empty_set)) & (v0 = % 78.16/12.10 | empty_set | ( ~ (v3 = v0) & apply(all_41_3, v1) = v3 & % 78.16/12.10 | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.10 | ~ (apply(all_41_3, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 78.16/12.10 | all_129_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.10 | ~ (apply(all_41_3, v0) = v1) | ~ $i(v0) | in(v0, all_129_0) = 0)) % 78.16/12.10 | % 78.16/12.10 | DELTA: instantiating (39) with fresh symbols all_130_0, all_130_1 gives: % 78.16/12.10 | (57) ( ~ (all_130_1 = 0) & relation(all_41_6) = all_130_1) | % 78.16/12.10 | (relation_dom(all_41_6) = all_130_0 & $i(all_130_0) & ! [v0: $i] : ! % 78.16/12.10 | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) % 78.16/12.10 | | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 % 78.16/12.10 | = 0) & in(v0, all_130_0) = v3) | (((v5 = 0 & in(v2, % 78.16/12.10 | all_41_6) = 0) | ( ~ (v4 = v1) & apply(all_41_6, v0) = % 78.16/12.10 | v4 & $i(v4))) & ((v4 = v1 & apply(all_41_6, v0) = v1) | ( % 78.16/12.10 | ~ (v5 = 0) & in(v2, all_41_6) = v5))))) & ? [v0: $i] : ! % 78.16/12.10 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_130_0) = v2) | ~ % 78.16/12.10 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 78.16/12.10 | empty_set & apply(all_41_6, v1) = empty_set)) & (v0 = % 78.16/12.10 | empty_set | ( ~ (v3 = v0) & apply(all_41_6, v1) = v3 & % 78.16/12.10 | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.10 | ~ (apply(all_41_6, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 78.16/12.10 | all_130_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.10 | ~ (apply(all_41_6, v0) = v1) | ~ $i(v0) | in(v0, all_130_0) = 0)) % 78.16/12.10 | % 78.16/12.10 | DELTA: instantiating (38) with fresh symbols all_131_0, all_131_1 gives: % 78.16/12.11 | (58) ( ~ (all_131_1 = 0) & relation(all_33_0) = all_131_1) | % 78.16/12.11 | (relation_dom(all_33_0) = all_131_0 & $i(all_131_0) & ! [v0: $i] : ! % 78.16/12.11 | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) % 78.16/12.11 | | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 % 78.16/12.11 | = 0) & in(v0, all_131_0) = v3) | (((v5 = 0 & in(v2, % 78.16/12.11 | all_33_0) = 0) | ( ~ (v4 = v1) & apply(all_33_0, v0) = % 78.16/12.11 | v4 & $i(v4))) & ((v4 = v1 & apply(all_33_0, v0) = v1) | ( % 78.16/12.11 | ~ (v5 = 0) & in(v2, all_33_0) = v5))))) & ? [v0: $i] : ! % 78.16/12.11 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_131_0) = v2) | ~ % 78.16/12.11 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 78.16/12.11 | empty_set & apply(all_33_0, v1) = empty_set)) & (v0 = % 78.16/12.11 | empty_set | ( ~ (v3 = v0) & apply(all_33_0, v1) = v3 & % 78.16/12.11 | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.11 | ~ (apply(all_33_0, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 78.16/12.11 | all_131_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.11 | ~ (apply(all_33_0, v0) = v1) | ~ $i(v0) | in(v0, all_131_0) = 0)) % 78.16/12.11 | % 78.16/12.11 | DELTA: instantiating (42) with fresh symbols all_133_0, all_133_1 gives: % 78.16/12.11 | (59) ( ~ (all_133_1 = 0) & function(all_41_6) = all_133_1) | % 78.16/12.11 | (relation_dom(all_41_6) = all_133_0 & $i(all_133_0) & ! [v0: $i] : ! % 78.16/12.11 | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) % 78.16/12.11 | | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 % 78.16/12.11 | = 0) & in(v0, all_133_0) = v3) | (((v5 = 0 & in(v2, % 78.16/12.11 | all_41_6) = 0) | ( ~ (v4 = v1) & apply(all_41_6, v0) = % 78.16/12.11 | v4 & $i(v4))) & ((v4 = v1 & apply(all_41_6, v0) = v1) | ( % 78.16/12.11 | ~ (v5 = 0) & in(v2, all_41_6) = v5))))) & ? [v0: $i] : ! % 78.16/12.11 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_133_0) = v2) | ~ % 78.16/12.11 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 78.16/12.11 | empty_set & apply(all_41_6, v1) = empty_set)) & (v0 = % 78.16/12.11 | empty_set | ( ~ (v3 = v0) & apply(all_41_6, v1) = v3 & % 78.16/12.11 | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.11 | ~ (apply(all_41_6, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 78.16/12.11 | all_133_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.11 | ~ (apply(all_41_6, v0) = v1) | ~ $i(v0) | in(v0, all_133_0) = 0)) % 78.16/12.11 | % 78.16/12.11 | DELTA: instantiating (43) with fresh symbols all_135_0, all_135_1 gives: % 78.16/12.11 | (60) ( ~ (all_135_1 = 0) & function(all_41_3) = all_135_1) | % 78.16/12.11 | (relation_dom(all_41_3) = all_135_0 & $i(all_135_0) & ! [v0: $i] : ! % 78.16/12.11 | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) % 78.16/12.11 | | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 % 78.16/12.11 | = 0) & in(v0, all_135_0) = v3) | (((v5 = 0 & in(v2, % 78.16/12.11 | all_41_3) = 0) | ( ~ (v4 = v1) & apply(all_41_3, v0) = % 78.16/12.11 | v4 & $i(v4))) & ((v4 = v1 & apply(all_41_3, v0) = v1) | ( % 78.16/12.11 | ~ (v5 = 0) & in(v2, all_41_3) = v5))))) & ? [v0: $i] : ! % 78.16/12.11 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_135_0) = v2) | ~ % 78.16/12.11 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 78.16/12.11 | empty_set & apply(all_41_3, v1) = empty_set)) & (v0 = % 78.16/12.11 | empty_set | ( ~ (v3 = v0) & apply(all_41_3, v1) = v3 & % 78.16/12.11 | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.11 | ~ (apply(all_41_3, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 78.16/12.11 | all_135_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.11 | ~ (apply(all_41_3, v0) = v1) | ~ $i(v0) | in(v0, all_135_0) = 0)) % 78.16/12.11 | % 78.16/12.11 | BETA: splitting (57) gives: % 78.16/12.11 | % 78.16/12.11 | Case 1: % 78.16/12.11 | | % 78.16/12.11 | | (61) ~ (all_130_1 = 0) & relation(all_41_6) = all_130_1 % 78.16/12.11 | | % 78.16/12.11 | | ALPHA: (61) implies: % 78.16/12.11 | | (62) ~ (all_130_1 = 0) % 78.16/12.11 | | (63) relation(all_41_6) = all_130_1 % 78.16/12.11 | | % 78.16/12.11 | | GROUND_INST: instantiating (11) with 0, all_130_1, all_41_6, simplifying % 78.16/12.11 | | with (30), (63) gives: % 78.16/12.11 | | (64) all_130_1 = 0 % 78.16/12.11 | | % 78.16/12.11 | | REDUCE: (62), (64) imply: % 78.16/12.11 | | (65) $false % 78.16/12.11 | | % 78.16/12.11 | | CLOSE: (65) is inconsistent. % 78.16/12.11 | | % 78.16/12.11 | Case 2: % 78.16/12.11 | | % 78.16/12.12 | | (66) relation_dom(all_41_6) = all_130_0 & $i(all_130_0) & ! [v0: $i] : % 78.16/12.12 | | ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 78.16/12.12 | | $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : % 78.16/12.12 | | (( ~ (v3 = 0) & in(v0, all_130_0) = v3) | (((v5 = 0 & in(v2, % 78.16/12.12 | | all_41_6) = 0) | ( ~ (v4 = v1) & apply(all_41_6, v0) = % 78.16/12.12 | | v4 & $i(v4))) & ((v4 = v1 & apply(all_41_6, v0) = v1) | ( % 78.16/12.12 | | ~ (v5 = 0) & in(v2, all_41_6) = v5))))) & ? [v0: $i] : ! % 78.16/12.12 | | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_130_0) = v2) | ~ % 78.16/12.12 | | $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 78.16/12.12 | | empty_set & apply(all_41_6, v1) = empty_set)) & (v0 = % 78.16/12.12 | | empty_set | ( ~ (v3 = v0) & apply(all_41_6, v1) = v3 & % 78.16/12.12 | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.12 | | ~ (apply(all_41_6, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 78.16/12.12 | | all_130_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.12 | | ~ (apply(all_41_6, v0) = v1) | ~ $i(v0) | in(v0, all_130_0) = 0) % 78.16/12.12 | | % 78.16/12.12 | | ALPHA: (66) implies: % 78.16/12.12 | | (67) relation_dom(all_41_6) = all_130_0 % 78.16/12.12 | | % 78.16/12.12 | | BETA: splitting (60) gives: % 78.16/12.12 | | % 78.16/12.12 | | Case 1: % 78.16/12.12 | | | % 78.16/12.12 | | | (68) ~ (all_135_1 = 0) & function(all_41_3) = all_135_1 % 78.16/12.12 | | | % 78.16/12.12 | | | ALPHA: (68) implies: % 78.16/12.12 | | | (69) ~ (all_135_1 = 0) % 78.16/12.12 | | | (70) function(all_41_3) = all_135_1 % 78.16/12.12 | | | % 78.16/12.12 | | | GROUND_INST: instantiating (10) with 0, all_135_1, all_41_3, simplifying % 78.16/12.12 | | | with (29), (70) gives: % 78.16/12.12 | | | (71) all_135_1 = 0 % 78.16/12.12 | | | % 78.16/12.12 | | | REDUCE: (69), (71) imply: % 78.16/12.12 | | | (72) $false % 78.16/12.12 | | | % 78.16/12.12 | | | CLOSE: (72) is inconsistent. % 78.16/12.12 | | | % 78.16/12.12 | | Case 2: % 78.16/12.12 | | | % 78.16/12.12 | | | (73) relation_dom(all_41_3) = all_135_0 & $i(all_135_0) & ! [v0: $i] : % 78.16/12.12 | | | ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 78.16/12.12 | | | $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : % 78.16/12.12 | | | (( ~ (v3 = 0) & in(v0, all_135_0) = v3) | (((v5 = 0 & in(v2, % 78.16/12.12 | | | all_41_3) = 0) | ( ~ (v4 = v1) & apply(all_41_3, v0) = % 78.16/12.12 | | | v4 & $i(v4))) & ((v4 = v1 & apply(all_41_3, v0) = v1) | % 78.16/12.12 | | | ( ~ (v5 = 0) & in(v2, all_41_3) = v5))))) & ? [v0: $i] : % 78.16/12.12 | | | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_135_0) = v2) % 78.16/12.12 | | | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | % 78.16/12.12 | | | (v3 = empty_set & apply(all_41_3, v1) = empty_set)) & (v0 = % 78.16/12.12 | | | empty_set | ( ~ (v3 = v0) & apply(all_41_3, v1) = v3 & % 78.16/12.12 | | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 78.16/12.12 | | | ~ (apply(all_41_3, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 78.16/12.12 | | | all_135_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set % 78.16/12.12 | | | | ~ (apply(all_41_3, v0) = v1) | ~ $i(v0) | in(v0, all_135_0) % 78.16/12.12 | | | = 0) % 78.16/12.12 | | | % 78.16/12.12 | | | ALPHA: (73) implies: % 78.16/12.12 | | | (74) relation_dom(all_41_3) = all_135_0 % 78.16/12.12 | | | (75) ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ (apply(all_41_3, % 78.16/12.12 | | | v0) = v1) | ~ $i(v0) | in(v0, all_135_0) = 0) % 78.16/12.12 | | | % 78.16/12.12 | | | GROUND_INST: instantiating (75) with all_41_4, all_41_0, simplifying with % 78.16/12.12 | | | (25), (33) gives: % 78.16/12.12 | | | (76) all_41_0 = empty_set | in(all_41_4, all_135_0) = 0 % 78.16/12.12 | | | % 78.16/12.12 | | | BETA: splitting (55) gives: % 78.16/12.12 | | | % 78.16/12.12 | | | Case 1: % 78.16/12.12 | | | | % 78.16/12.12 | | | | (77) (all_117_0 = all_117_1 & relation_composition(all_41_6, % 78.16/12.12 | | | | all_41_3) = all_117_4 & apply(all_117_4, all_41_7) = % 78.16/12.12 | | | | all_117_1 & apply(all_41_3, all_41_4) = all_117_1 & % 78.16/12.12 | | | | $i(all_117_1) & $i(all_117_4)) | ( ~ (all_117_2 = 0) & % 78.16/12.12 | | | | relation_composition(all_41_6, all_41_3) = all_117_4 & % 78.16/12.12 | | | | relation_dom(all_117_4) = all_117_3 & in(all_41_7, all_117_3) % 78.16/12.12 | | | | = all_117_2 & $i(all_117_3) & $i(all_117_4)) % 78.16/12.12 | | | | % 78.16/12.12 | | | | BETA: splitting (77) gives: % 78.16/12.12 | | | | % 78.16/12.12 | | | | Case 1: % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | (78) all_117_0 = all_117_1 & relation_composition(all_41_6, % 78.16/12.12 | | | | | all_41_3) = all_117_4 & apply(all_117_4, all_41_7) = % 78.16/12.12 | | | | | all_117_1 & apply(all_41_3, all_41_4) = all_117_1 & % 78.16/12.12 | | | | | $i(all_117_1) & $i(all_117_4) % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | ALPHA: (78) implies: % 78.16/12.12 | | | | | (79) apply(all_41_3, all_41_4) = all_117_1 % 78.16/12.12 | | | | | (80) apply(all_117_4, all_41_7) = all_117_1 % 78.16/12.12 | | | | | (81) relation_composition(all_41_6, all_41_3) = all_117_4 % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | GROUND_INST: instantiating (14) with all_41_0, all_117_1, all_41_4, % 78.16/12.12 | | | | | all_41_3, simplifying with (33), (79) gives: % 78.16/12.12 | | | | | (82) all_117_1 = all_41_0 % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | GROUND_INST: instantiating (15) with all_41_2, all_117_4, all_41_3, % 78.16/12.12 | | | | | all_41_6, simplifying with (36), (81) gives: % 78.16/12.12 | | | | | (83) all_117_4 = all_41_2 % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | REDUCE: (80), (82), (83) imply: % 78.16/12.12 | | | | | (84) apply(all_41_2, all_41_7) = all_41_0 % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | GROUND_INST: instantiating (14) with all_41_1, all_41_0, all_41_7, % 78.16/12.12 | | | | | all_41_2, simplifying with (34), (84) gives: % 78.16/12.12 | | | | | (85) all_41_0 = all_41_1 % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | REDUCE: (21), (85) imply: % 78.16/12.12 | | | | | (86) $false % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | CLOSE: (86) is inconsistent. % 78.16/12.12 | | | | | % 78.16/12.12 | | | | Case 2: % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | (87) ~ (all_117_2 = 0) & relation_composition(all_41_6, all_41_3) % 78.16/12.12 | | | | | = all_117_4 & relation_dom(all_117_4) = all_117_3 & % 78.16/12.12 | | | | | in(all_41_7, all_117_3) = all_117_2 & $i(all_117_3) & % 78.16/12.12 | | | | | $i(all_117_4) % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | ALPHA: (87) implies: % 78.16/12.12 | | | | | (88) ~ (all_117_2 = 0) % 78.16/12.12 | | | | | (89) in(all_41_7, all_117_3) = all_117_2 % 78.16/12.12 | | | | | (90) relation_dom(all_117_4) = all_117_3 % 78.16/12.12 | | | | | (91) relation_composition(all_41_6, all_41_3) = all_117_4 % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | BETA: splitting (52) gives: % 78.16/12.12 | | | | | % 78.16/12.12 | | | | | Case 1: % 78.16/12.12 | | | | | | % 78.16/12.12 | | | | | | (92) all_91_0 = 0 & all_91_1 = 0 & relation(all_41_5) = 0 & % 78.16/12.12 | | | | | | empty(all_41_5) = 0 % 78.16/12.12 | | | | | | % 78.16/12.12 | | | | | | ALPHA: (92) implies: % 78.16/12.12 | | | | | | (93) empty(all_41_5) = 0 % 78.16/12.12 | | | | | | % 78.16/12.12 | | | | | | GROUND_INST: instantiating (9) with 0, all_75_0, all_41_5, % 78.16/12.12 | | | | | | simplifying with (50), (93) gives: % 78.16/12.12 | | | | | | (94) all_75_0 = 0 % 78.16/12.12 | | | | | | % 78.16/12.12 | | | | | | REDUCE: (49), (94) imply: % 78.16/12.12 | | | | | | (95) $false % 78.16/12.12 | | | | | | % 78.16/12.12 | | | | | | CLOSE: (95) is inconsistent. % 78.16/12.12 | | | | | | % 78.16/12.12 | | | | | Case 2: % 78.16/12.12 | | | | | | % 78.16/12.12 | | | | | | (96) ~ (all_91_2 = 0) & empty(all_41_6) = all_91_2 % 78.16/12.12 | | | | | | % 78.16/12.12 | | | | | | ALPHA: (96) implies: % 78.16/12.12 | | | | | | (97) ~ (all_91_2 = 0) % 78.16/12.12 | | | | | | (98) empty(all_41_6) = all_91_2 % 78.16/12.12 | | | | | | % 78.16/12.12 | | | | | | BETA: splitting (56) gives: % 78.16/12.12 | | | | | | % 78.16/12.12 | | | | | | Case 1: % 78.16/12.12 | | | | | | | % 78.16/12.12 | | | | | | | (99) ~ (all_129_1 = 0) & relation(all_41_3) = all_129_1 % 78.16/12.12 | | | | | | | % 78.16/12.12 | | | | | | | ALPHA: (99) implies: % 78.16/12.12 | | | | | | | (100) ~ (all_129_1 = 0) % 78.16/12.12 | | | | | | | (101) relation(all_41_3) = all_129_1 % 78.16/12.13 | | | | | | | % 78.16/12.13 | | | | | | | GROUND_INST: instantiating (11) with 0, all_129_1, all_41_3, % 78.16/12.13 | | | | | | | simplifying with (31), (101) gives: % 78.16/12.13 | | | | | | | (102) all_129_1 = 0 % 78.16/12.13 | | | | | | | % 78.16/12.13 | | | | | | | REDUCE: (100), (102) imply: % 78.16/12.13 | | | | | | | (103) $false % 78.16/12.13 | | | | | | | % 78.16/12.13 | | | | | | | CLOSE: (103) is inconsistent. % 78.16/12.13 | | | | | | | % 78.16/12.13 | | | | | | Case 2: % 78.16/12.13 | | | | | | | % 78.16/12.13 | | | | | | | (104) relation_dom(all_41_3) = all_129_0 & $i(all_129_0) & ! % 78.16/12.13 | | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 78.16/12.13 | | | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 78.16/12.13 | | | | | | | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 = % 78.16/12.13 | | | | | | | 0) & in(v0, all_129_0) = v3) | (((v5 = 0 & in(v2, % 78.16/12.13 | | | | | | | all_41_3) = 0) | ( ~ (v4 = v1) & % 78.16/12.13 | | | | | | | apply(all_41_3, v0) = v4 & $i(v4))) & ((v4 = v1 % 78.16/12.13 | | | | | | | & apply(all_41_3, v0) = v1) | ( ~ (v5 = 0) & % 78.16/12.13 | | | | | | | in(v2, all_41_3) = v5))))) & ? [v0: $i] : ! % 78.16/12.13 | | | | | | | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_129_0) % 78.16/12.13 | | | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ % 78.16/12.13 | | | | | | | (v0 = empty_set) | (v3 = empty_set & % 78.16/12.13 | | | | | | | apply(all_41_3, v1) = empty_set)) & (v0 = % 78.16/12.13 | | | | | | | empty_set | ( ~ (v3 = v0) & apply(all_41_3, v1) = % 78.16/12.13 | | | | | | | v3 & $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 % 78.16/12.13 | | | | | | | = empty_set | ~ (apply(all_41_3, v0) = v1) | ~ $i(v1) % 78.16/12.13 | | | | | | | | ~ $i(v0) | in(v0, all_129_0) = 0) & ! [v0: $i] : ! % 78.16/12.13 | | | | | | | [v1: $i] : (v1 = empty_set | ~ (apply(all_41_3, v0) = % 78.16/12.13 | | | | | | | v1) | ~ $i(v0) | in(v0, all_129_0) = 0) % 78.16/12.13 | | | | | | | % 78.16/12.13 | | | | | | | ALPHA: (104) implies: % 78.16/12.13 | | | | | | | (105) relation_dom(all_41_3) = all_129_0 % 78.16/12.13 | | | | | | | % 78.16/12.13 | | | | | | | BETA: splitting (53) gives: % 78.16/12.13 | | | | | | | % 78.16/12.13 | | | | | | | Case 1: % 78.16/12.13 | | | | | | | | % 78.16/12.13 | | | | | | | | (106) (all_95_0 = 0 & all_95_1 = 0 & relation(all_41_2) = 0 & % 78.16/12.13 | | | | | | | | function(all_41_2) = 0) | ( ~ (all_95_2 = 0) & % 78.16/12.13 | | | | | | | | function(all_41_3) = all_95_2) % 78.16/12.13 | | | | | | | | % 78.16/12.13 | | | | | | | | BETA: splitting (106) gives: % 78.16/12.13 | | | | | | | | % 78.16/12.13 | | | | | | | | Case 1: % 78.16/12.13 | | | | | | | | | % 78.16/12.13 | | | | | | | | | (107) all_95_0 = 0 & all_95_1 = 0 & relation(all_41_2) = 0 % 78.16/12.13 | | | | | | | | | & function(all_41_2) = 0 % 78.16/12.13 | | | | | | | | | % 78.16/12.13 | | | | | | | | | ALPHA: (107) implies: % 78.16/12.13 | | | | | | | | | (108) function(all_41_2) = 0 % 78.16/12.13 | | | | | | | | | (109) relation(all_41_2) = 0 % 78.16/12.13 | | | | | | | | | % 78.16/12.13 | | | | | | | | | BETA: splitting (59) gives: % 78.16/12.13 | | | | | | | | | % 78.16/12.13 | | | | | | | | | Case 1: % 78.16/12.13 | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | (110) ~ (all_133_1 = 0) & function(all_41_6) = all_133_1 % 78.16/12.13 | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | ALPHA: (110) implies: % 78.16/12.13 | | | | | | | | | | (111) ~ (all_133_1 = 0) % 78.16/12.13 | | | | | | | | | | (112) function(all_41_6) = all_133_1 % 78.16/12.13 | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_133_1, all_41_6, % 78.16/12.13 | | | | | | | | | | simplifying with (28), (112) gives: % 78.16/12.13 | | | | | | | | | | (113) all_133_1 = 0 % 78.16/12.13 | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | REDUCE: (111), (113) imply: % 78.16/12.13 | | | | | | | | | | (114) $false % 78.16/12.13 | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | CLOSE: (114) is inconsistent. % 78.16/12.13 | | | | | | | | | | % 78.16/12.13 | | | | | | | | | Case 2: % 78.16/12.13 | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | (115) relation_dom(all_41_6) = all_133_0 & $i(all_133_0) % 78.16/12.13 | | | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 78.16/12.13 | | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 78.16/12.13 | | | | | | | | | | $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: % 78.16/12.13 | | | | | | | | | | int] : (( ~ (v3 = 0) & in(v0, all_133_0) = v3) % 78.16/12.13 | | | | | | | | | | | (((v5 = 0 & in(v2, all_41_6) = 0) | ( ~ (v4 = % 78.16/12.13 | | | | | | | | | | v1) & apply(all_41_6, v0) = v4 & % 78.16/12.13 | | | | | | | | | | $i(v4))) & ((v4 = v1 & apply(all_41_6, % 78.16/12.13 | | | | | | | | | | v0) = v1) | ( ~ (v5 = 0) & in(v2, % 78.16/12.13 | | | | | | | | | | all_41_6) = v5))))) & ? [v0: $i] : ! % 78.16/12.13 | | | | | | | | | | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, % 78.16/12.13 | | | | | | | | | | all_133_0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 78.16/12.13 | | | | | | | | | | [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 78.16/12.13 | | | | | | | | | | empty_set & apply(all_41_6, v1) = % 78.16/12.13 | | | | | | | | | | empty_set)) & (v0 = empty_set | ( ~ (v3 = % 78.16/12.13 | | | | | | | | | | v0) & apply(all_41_6, v1) = v3 & % 78.16/12.13 | | | | | | | | | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : % 78.16/12.13 | | | | | | | | | | (v1 = empty_set | ~ (apply(all_41_6, v0) = v1) | % 78.16/12.13 | | | | | | | | | | ~ $i(v1) | ~ $i(v0) | in(v0, all_133_0) = 0) & % 78.16/12.13 | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 78.16/12.13 | | | | | | | | | | (apply(all_41_6, v0) = v1) | ~ $i(v0) | in(v0, % 78.16/12.13 | | | | | | | | | | all_133_0) = 0) % 78.16/12.13 | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | ALPHA: (115) implies: % 78.16/12.13 | | | | | | | | | | (116) relation_dom(all_41_6) = all_133_0 % 78.16/12.13 | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | BETA: splitting (51) gives: % 78.16/12.13 | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | Case 1: % 78.16/12.13 | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | (117) all_83_2 = 0 & empty(all_41_6) = 0 % 78.16/12.13 | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | ALPHA: (117) implies: % 78.16/12.13 | | | | | | | | | | | (118) empty(all_41_6) = 0 % 78.16/12.13 | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_91_2, all_41_6, % 78.16/12.13 | | | | | | | | | | | simplifying with (98), (118) gives: % 78.16/12.13 | | | | | | | | | | | (119) all_91_2 = 0 % 78.16/12.13 | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | REDUCE: (97), (119) imply: % 78.16/12.13 | | | | | | | | | | | (120) $false % 78.16/12.13 | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | CLOSE: (120) is inconsistent. % 78.16/12.13 | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | Case 2: % 78.16/12.13 | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | (121) ~ (all_83_0 = 0) & relation_dom(all_41_6) = % 78.16/12.13 | | | | | | | | | | | all_83_1 & empty(all_83_1) = all_83_0 & % 78.16/12.13 | | | | | | | | | | | $i(all_83_1) % 78.16/12.13 | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | ALPHA: (121) implies: % 78.16/12.13 | | | | | | | | | | | (122) relation_dom(all_41_6) = all_83_1 % 78.16/12.13 | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | BETA: splitting (58) gives: % 78.16/12.13 | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | Case 1: % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | (123) ~ (all_131_1 = 0) & relation(all_33_0) = % 78.16/12.13 | | | | | | | | | | | | all_131_1 % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | ALPHA: (123) implies: % 78.16/12.13 | | | | | | | | | | | | (124) ~ (all_131_1 = 0) % 78.16/12.13 | | | | | | | | | | | | (125) relation(all_33_0) = all_131_1 % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_131_1, all_33_0, % 78.16/12.13 | | | | | | | | | | | | simplifying with (19), (125) gives: % 78.16/12.13 | | | | | | | | | | | | (126) all_131_1 = 0 % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | REDUCE: (124), (126) imply: % 78.16/12.13 | | | | | | | | | | | | (127) $false % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | CLOSE: (127) is inconsistent. % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | Case 2: % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_41_5, all_133_0, % 78.16/12.13 | | | | | | | | | | | | all_41_6, simplifying with (35), (116) gives: % 78.16/12.13 | | | | | | | | | | | | (128) all_133_0 = all_41_5 % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_130_0, all_133_0, % 78.16/12.13 | | | | | | | | | | | | all_41_6, simplifying with (67), (116) gives: % 78.16/12.13 | | | | | | | | | | | | (129) all_133_0 = all_130_0 % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_83_1, all_133_0, % 78.16/12.13 | | | | | | | | | | | | all_41_6, simplifying with (116), (122) gives: % 78.16/12.13 | | | | | | | | | | | | (130) all_133_0 = all_83_1 % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_129_0, all_135_0, % 78.16/12.13 | | | | | | | | | | | | all_41_3, simplifying with (74), (105) gives: % 78.16/12.13 | | | | | | | | | | | | (131) all_135_0 = all_129_0 % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_41_2, all_117_4, % 78.16/12.13 | | | | | | | | | | | | all_41_3, all_41_6, simplifying with (36), (91) % 78.16/12.13 | | | | | | | | | | | | gives: % 78.16/12.13 | | | | | | | | | | | | (132) all_117_4 = all_41_2 % 78.16/12.13 | | | | | | | | | | | | % 78.16/12.13 | | | | | | | | | | | | COMBINE_EQS: (128), (129) imply: % 78.16/12.14 | | | | | | | | | | | | (133) all_130_0 = all_41_5 % 78.16/12.14 | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | COMBINE_EQS: (129), (130) imply: % 78.16/12.14 | | | | | | | | | | | | (134) all_130_0 = all_83_1 % 78.16/12.14 | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | COMBINE_EQS: (133), (134) imply: % 78.16/12.14 | | | | | | | | | | | | (135) all_83_1 = all_41_5 % 78.16/12.14 | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | REDUCE: (90), (132) imply: % 78.16/12.14 | | | | | | | | | | | | (136) relation_dom(all_41_2) = all_117_3 % 78.16/12.14 | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | BETA: splitting (54) gives: % 78.16/12.14 | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | Case 1: % 78.16/12.14 | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | (137) (all_102_0 = all_102_1 & % 78.16/12.14 | | | | | | | | | | | | | relation_composition(all_41_6, all_41_3) = % 78.16/12.14 | | | | | | | | | | | | | all_102_4 & apply(all_102_4, all_41_7) = % 78.16/12.14 | | | | | | | | | | | | | all_102_1 & apply(all_41_3, all_41_4) = % 78.16/12.14 | | | | | | | | | | | | | all_102_1 & $i(all_102_1) & $i(all_102_4)) | ( ~ % 78.16/12.14 | | | | | | | | | | | | | (all_102_2 = 0) & relation_composition(all_41_6, % 78.16/12.14 | | | | | | | | | | | | | all_41_3) = all_102_4 & % 78.16/12.14 | | | | | | | | | | | | | relation_dom(all_102_4) = all_102_3 & % 78.16/12.14 | | | | | | | | | | | | | in(all_41_7, all_102_3) = all_102_2 & % 78.16/12.14 | | | | | | | | | | | | | $i(all_102_3) & $i(all_102_4)) % 78.16/12.14 | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | BETA: splitting (137) gives: % 78.16/12.14 | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | Case 1: % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | (138) all_102_0 = all_102_1 & % 78.16/12.14 | | | | | | | | | | | | | | relation_composition(all_41_6, all_41_3) = % 78.16/12.14 | | | | | | | | | | | | | | all_102_4 & apply(all_102_4, all_41_7) = all_102_1 % 78.16/12.14 | | | | | | | | | | | | | | & apply(all_41_3, all_41_4) = all_102_1 & % 78.16/12.14 | | | | | | | | | | | | | | $i(all_102_1) & $i(all_102_4) % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | ALPHA: (138) implies: % 78.16/12.14 | | | | | | | | | | | | | | (139) apply(all_41_3, all_41_4) = all_102_1 % 78.16/12.14 | | | | | | | | | | | | | | (140) apply(all_102_4, all_41_7) = all_102_1 % 78.16/12.14 | | | | | | | | | | | | | | (141) relation_composition(all_41_6, all_41_3) = % 78.16/12.14 | | | | | | | | | | | | | | all_102_4 % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_41_0, all_102_1, % 78.16/12.14 | | | | | | | | | | | | | | all_41_4, all_41_3, simplifying with (33), (139) % 78.16/12.14 | | | | | | | | | | | | | | gives: % 78.16/12.14 | | | | | | | | | | | | | | (142) all_102_1 = all_41_0 % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_41_2, all_102_4, % 78.16/12.14 | | | | | | | | | | | | | | all_41_3, all_41_6, simplifying with (36), (141) % 78.16/12.14 | | | | | | | | | | | | | | gives: % 78.16/12.14 | | | | | | | | | | | | | | (143) all_102_4 = all_41_2 % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | REDUCE: (140), (142), (143) imply: % 78.16/12.14 | | | | | | | | | | | | | | (144) apply(all_41_2, all_41_7) = all_41_0 % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_41_1, all_41_0, % 78.16/12.14 | | | | | | | | | | | | | | all_41_7, all_41_2, simplifying with (34), (144) % 78.16/12.14 | | | | | | | | | | | | | | gives: % 78.16/12.14 | | | | | | | | | | | | | | (145) all_41_0 = all_41_1 % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | REDUCE: (21), (145) imply: % 78.16/12.14 | | | | | | | | | | | | | | (146) $false % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | CLOSE: (146) is inconsistent. % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | Case 2: % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | (147) ~ (all_102_2 = 0) & % 78.16/12.14 | | | | | | | | | | | | | | relation_composition(all_41_6, all_41_3) = % 78.16/12.14 | | | | | | | | | | | | | | all_102_4 & relation_dom(all_102_4) = all_102_3 & % 78.16/12.14 | | | | | | | | | | | | | | in(all_41_7, all_102_3) = all_102_2 & % 78.16/12.14 | | | | | | | | | | | | | | $i(all_102_3) & $i(all_102_4) % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | ALPHA: (147) implies: % 78.16/12.14 | | | | | | | | | | | | | | (148) $i(all_102_4) % 78.16/12.14 | | | | | | | | | | | | | | (149) in(all_41_7, all_102_3) = all_102_2 % 78.16/12.14 | | | | | | | | | | | | | | (150) relation_dom(all_102_4) = all_102_3 % 78.16/12.14 | | | | | | | | | | | | | | (151) relation_composition(all_41_6, all_41_3) = % 78.16/12.14 | | | | | | | | | | | | | | all_102_4 % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_41_2, all_102_4, % 78.16/12.14 | | | | | | | | | | | | | | all_41_3, all_41_6, simplifying with (36), (151) % 78.16/12.14 | | | | | | | | | | | | | | gives: % 78.16/12.14 | | | | | | | | | | | | | | (152) all_102_4 = all_41_2 % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | REDUCE: (150), (152) imply: % 78.16/12.14 | | | | | | | | | | | | | | (153) relation_dom(all_41_2) = all_102_3 % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | REDUCE: (148), (152) imply: % 78.16/12.14 | | | | | | | | | | | | | | (154) $i(all_41_2) % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_117_3, all_102_3, % 78.16/12.14 | | | | | | | | | | | | | | all_41_2, simplifying with (136), (153) gives: % 78.16/12.14 | | | | | | | | | | | | | | (155) all_117_3 = all_102_3 % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | REDUCE: (89), (155) imply: % 78.16/12.14 | | | | | | | | | | | | | | (156) in(all_41_7, all_102_3) = all_117_2 % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_102_2, all_117_2, % 78.16/12.14 | | | | | | | | | | | | | | all_102_3, all_41_7, simplifying with (149), (156) % 78.16/12.14 | | | | | | | | | | | | | | gives: % 78.16/12.14 | | | | | | | | | | | | | | (157) all_117_2 = all_102_2 % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | REDUCE: (88), (157) imply: % 78.16/12.14 | | | | | | | | | | | | | | (158) ~ (all_102_2 = 0) % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_41_2, simplifying with % 78.16/12.14 | | | | | | | | | | | | | | (108), (154) gives: % 78.16/12.14 | | | | | | | | | | | | | | (159) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & % 78.16/12.14 | | | | | | | | | | | | | | relation(all_41_2) = v0) | % 78.16/12.14 | | | | | | | | | | | | | | (relation_dom(all_41_2) = v1 & $i(v1) & ! [v2: % 78.16/12.14 | | | | | | | | | | | | | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 78.16/12.14 | | | | | | | | | | | | | | (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 78.16/12.14 | | | | | | | | | | | | | | $i(v2) | ? [v5: int] : ? [v6: $i] : ? % 78.16/12.14 | | | | | | | | | | | | | | [v7: int] : (( ~ (v5 = 0) & in(v2, v1) = v5) % 78.16/12.14 | | | | | | | | | | | | | | | (((v7 = 0 & in(v4, all_41_2) = 0) | ( ~ % 78.16/12.14 | | | | | | | | | | | | | | (v6 = v3) & apply(all_41_2, v2) = v6 % 78.16/12.14 | | | | | | | | | | | | | | & $i(v6))) & ((v6 = v3 & % 78.16/12.14 | | | | | | | | | | | | | | apply(all_41_2, v2) = v3) | ( ~ (v7 % 78.16/12.14 | | | | | | | | | | | | | | = 0) & in(v4, all_41_2) = v7))))) % 78.16/12.14 | | | | | | | | | | | | | | & ? [v2: $i] : ! [v3: $i] : ! [v4: int] : % 78.16/12.14 | | | | | | | | | | | | | | (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | % 78.16/12.14 | | | | | | | | | | | | | | ~ $i(v2) | ? [v5: $i] : (( ~ (v2 = % 78.16/12.14 | | | | | | | | | | | | | | empty_set) | (v5 = empty_set & % 78.16/12.14 | | | | | | | | | | | | | | apply(all_41_2, v3) = empty_set)) & % 78.16/12.14 | | | | | | | | | | | | | | (v2 = empty_set | ( ~ (v5 = v2) & % 78.16/12.14 | | | | | | | | | | | | | | apply(all_41_2, v3) = v5 & $i(v5))))) % 78.16/12.14 | | | | | | | | | | | | | | & ! [v2: $i] : ! [v3: $i] : (v3 = empty_set % 78.16/12.14 | | | | | | | | | | | | | | | ~ (apply(all_41_2, v2) = v3) | ~ $i(v3) % 78.16/12.14 | | | | | | | | | | | | | | | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 78.16/12.14 | | | | | | | | | | | | | | : ! [v3: $i] : (v3 = empty_set | ~ % 78.16/12.14 | | | | | | | | | | | | | | (apply(all_41_2, v2) = v3) | ~ $i(v2) | % 78.16/12.14 | | | | | | | | | | | | | | in(v2, v1) = 0))) % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_41_2, simplifying with % 78.16/12.14 | | | | | | | | | | | | | | (109), (154) gives: % 78.16/12.14 | | | | | | | | | | | | | | (160) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & % 78.16/12.14 | | | | | | | | | | | | | | function(all_41_2) = v0) | % 78.16/12.14 | | | | | | | | | | | | | | (relation_dom(all_41_2) = v1 & $i(v1) & ! [v2: % 78.16/12.14 | | | | | | | | | | | | | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 78.16/12.14 | | | | | | | | | | | | | | (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 78.16/12.14 | | | | | | | | | | | | | | $i(v2) | ? [v5: int] : ? [v6: $i] : ? % 78.16/12.14 | | | | | | | | | | | | | | [v7: int] : (( ~ (v5 = 0) & in(v2, v1) = v5) % 78.16/12.14 | | | | | | | | | | | | | | | (((v7 = 0 & in(v4, all_41_2) = 0) | ( ~ % 78.16/12.14 | | | | | | | | | | | | | | (v6 = v3) & apply(all_41_2, v2) = v6 % 78.16/12.14 | | | | | | | | | | | | | | & $i(v6))) & ((v6 = v3 & % 78.16/12.14 | | | | | | | | | | | | | | apply(all_41_2, v2) = v3) | ( ~ (v7 % 78.16/12.14 | | | | | | | | | | | | | | = 0) & in(v4, all_41_2) = v7))))) % 78.16/12.14 | | | | | | | | | | | | | | & ? [v2: $i] : ! [v3: $i] : ! [v4: int] : % 78.16/12.14 | | | | | | | | | | | | | | (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | % 78.16/12.14 | | | | | | | | | | | | | | ~ $i(v2) | ? [v5: $i] : (( ~ (v2 = % 78.16/12.14 | | | | | | | | | | | | | | empty_set) | (v5 = empty_set & % 78.16/12.14 | | | | | | | | | | | | | | apply(all_41_2, v3) = empty_set)) & % 78.16/12.14 | | | | | | | | | | | | | | (v2 = empty_set | ( ~ (v5 = v2) & % 78.16/12.14 | | | | | | | | | | | | | | apply(all_41_2, v3) = v5 & $i(v5))))) % 78.16/12.14 | | | | | | | | | | | | | | & ! [v2: $i] : ! [v3: $i] : (v3 = empty_set % 78.16/12.14 | | | | | | | | | | | | | | | ~ (apply(all_41_2, v2) = v3) | ~ $i(v3) % 78.16/12.14 | | | | | | | | | | | | | | | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 78.16/12.14 | | | | | | | | | | | | | | : ! [v3: $i] : (v3 = empty_set | ~ % 78.16/12.14 | | | | | | | | | | | | | | (apply(all_41_2, v2) = v3) | ~ $i(v2) | % 78.16/12.14 | | | | | | | | | | | | | | in(v2, v1) = 0))) % 78.16/12.14 | | | | | | | | | | | | | | % 78.16/12.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_41_7, all_41_3, % 78.16/12.14 | | | | | | | | | | | | | | all_129_0, all_41_2, all_41_1, simplifying with % 78.16/12.14 | | | | | | | | | | | | | | (22), (26), (34), (105), (154) gives: % 78.16/12.15 | | | | | | | | | | | | | | (161) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? % 78.16/12.15 | | | | | | | | | | | | | | [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: % 78.16/12.15 | | | | | | | | | | | | | | int] : ? [v7: int] : (( ~ (v1 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | function(all_41_2) = v1) | ( ~ (v1 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | function(all_41_3) = v1) | ( ~ (v0 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | relation(all_41_2) = v0) | ( ~ (v0 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | relation(all_41_3) = v0) | (((v7 = 0 & v6 = 0 % 78.16/12.15 | | | | | | | | | | | | | | & relation_dom(all_41_2) = v5 & % 78.16/12.15 | | | | | | | | | | | | | | in(all_41_1, all_129_0) = 0 & in(all_41_7, % 78.16/12.15 | | | | | | | | | | | | | | v5) = 0 & $i(v5)) | ( ~ (v4 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | relation_composition(all_41_2, all_41_3) = % 78.16/12.15 | | | | | | | | | | | | | | v2 & relation_dom(v2) = v3 & in(all_41_7, % 78.16/12.15 | | | | | | | | | | | | | | v3) = v4 & $i(v3) & $i(v2))) & ((v4 = 0 % 78.16/12.15 | | | | | | | | | | | | | | & relation_composition(all_41_2, all_41_3) % 78.16/12.15 | | | | | | | | | | | | | | = v2 & relation_dom(v2) = v3 & % 78.16/12.15 | | | | | | | | | | | | | | in(all_41_7, v3) = 0 & $i(v3) & $i(v2)) | % 78.16/12.15 | | | | | | | | | | | | | | ( ~ (v7 = 0) & in(all_41_1, all_129_0) = v7) % 78.16/12.15 | | | | | | | | | | | | | | | ( ~ (v6 = 0) & relation_dom(all_41_2) = v5 % 78.16/12.15 | | | | | | | | | | | | | | & in(all_41_7, v5) = v6 & $i(v5))))) % 78.16/12.15 | | | | | | | | | | | | | | % 78.16/12.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_41_7, all_41_3, % 78.16/12.15 | | | | | | | | | | | | | | all_129_0, all_41_6, all_41_4, simplifying with % 78.16/12.15 | | | | | | | | | | | | | | (22), (23), (26), (32), (105) gives: % 78.16/12.15 | | | | | | | | | | | | | | (162) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? % 78.16/12.15 | | | | | | | | | | | | | | [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: % 78.16/12.15 | | | | | | | | | | | | | | int] : ? [v7: int] : (( ~ (v1 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | function(all_41_3) = v1) | ( ~ (v1 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | function(all_41_6) = v1) | ( ~ (v0 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | relation(all_41_3) = v0) | ( ~ (v0 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | relation(all_41_6) = v0) | (((v7 = 0 & v6 = 0 % 78.16/12.15 | | | | | | | | | | | | | | & relation_dom(all_41_6) = v5 & % 78.16/12.15 | | | | | | | | | | | | | | in(all_41_4, all_129_0) = 0 & in(all_41_7, % 78.16/12.15 | | | | | | | | | | | | | | v5) = 0 & $i(v5)) | ( ~ (v4 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | relation_composition(all_41_6, all_41_3) = % 78.16/12.15 | | | | | | | | | | | | | | v2 & relation_dom(v2) = v3 & in(all_41_7, % 78.16/12.15 | | | | | | | | | | | | | | v3) = v4 & $i(v3) & $i(v2))) & ((v4 = 0 % 78.16/12.15 | | | | | | | | | | | | | | & relation_composition(all_41_6, all_41_3) % 78.16/12.15 | | | | | | | | | | | | | | = v2 & relation_dom(v2) = v3 & % 78.16/12.15 | | | | | | | | | | | | | | in(all_41_7, v3) = 0 & $i(v3) & $i(v2)) | % 78.16/12.15 | | | | | | | | | | | | | | ( ~ (v7 = 0) & in(all_41_4, all_129_0) = v7) % 78.16/12.15 | | | | | | | | | | | | | | | ( ~ (v6 = 0) & relation_dom(all_41_6) = v5 % 78.16/12.15 | | | | | | | | | | | | | | & in(all_41_7, v5) = v6 & $i(v5))))) % 78.16/12.15 | | | | | | | | | | | | | | % 78.16/12.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_41_2, all_102_3, % 78.16/12.15 | | | | | | | | | | | | | | all_41_7, all_41_1, simplifying with (22), (34), % 78.16/12.15 | | | | | | | | | | | | | | (153), (154) gives: % 78.16/12.15 | | | | | | | | | | | | | | (163) all_41_1 = empty_set | ? [v0: int] : ? [v1: int] % 78.16/12.15 | | | | | | | | | | | | | | : ((v0 = 0 & in(all_41_7, all_102_3) = 0) | ( ~ % 78.16/12.15 | | | | | | | | | | | | | | (v1 = 0) & function(all_41_2) = v1) | ( ~ (v0 % 78.16/12.15 | | | | | | | | | | | | | | = 0) & relation(all_41_2) = v0)) % 78.16/12.15 | | | | | | | | | | | | | | % 78.16/12.15 | | | | | | | | | | | | | | DELTA: instantiating (162) with fresh symbols all_311_0, % 78.16/12.15 | | | | | | | | | | | | | | all_311_1, all_311_2, all_311_3, all_311_4, % 78.16/12.15 | | | | | | | | | | | | | | all_311_5, all_311_6, all_311_7 gives: % 78.16/12.15 | | | | | | | | | | | | | | (164) ( ~ (all_311_6 = 0) & function(all_41_3) = % 78.16/12.15 | | | | | | | | | | | | | | all_311_6) | ( ~ (all_311_6 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | function(all_41_6) = all_311_6) | ( ~ (all_311_7 % 78.16/12.15 | | | | | | | | | | | | | | = 0) & relation(all_41_3) = all_311_7) | ( ~ % 78.16/12.15 | | | | | | | | | | | | | | (all_311_7 = 0) & relation(all_41_6) = % 78.16/12.15 | | | | | | | | | | | | | | all_311_7) | (((all_311_0 = 0 & all_311_1 = 0 & % 78.16/12.15 | | | | | | | | | | | | | | relation_dom(all_41_6) = all_311_2 & % 78.16/12.15 | | | | | | | | | | | | | | in(all_41_4, all_129_0) = 0 & in(all_41_7, % 78.16/12.15 | | | | | | | | | | | | | | all_311_2) = 0 & $i(all_311_2)) | ( ~ % 78.16/12.15 | | | | | | | | | | | | | | (all_311_3 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | relation_composition(all_41_6, all_41_3) = % 78.16/12.15 | | | | | | | | | | | | | | all_311_5 & relation_dom(all_311_5) = % 78.16/12.15 | | | | | | | | | | | | | | all_311_4 & in(all_41_7, all_311_4) = % 78.16/12.15 | | | | | | | | | | | | | | all_311_3 & $i(all_311_4) & $i(all_311_5))) % 78.16/12.15 | | | | | | | | | | | | | | & ((all_311_3 = 0 & % 78.16/12.15 | | | | | | | | | | | | | | relation_composition(all_41_6, all_41_3) = % 78.16/12.15 | | | | | | | | | | | | | | all_311_5 & relation_dom(all_311_5) = % 78.16/12.15 | | | | | | | | | | | | | | all_311_4 & in(all_41_7, all_311_4) = 0 & % 78.16/12.15 | | | | | | | | | | | | | | $i(all_311_4) & $i(all_311_5)) | ( ~ % 78.16/12.15 | | | | | | | | | | | | | | (all_311_0 = 0) & in(all_41_4, all_129_0) = % 78.16/12.15 | | | | | | | | | | | | | | all_311_0) | ( ~ (all_311_1 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | relation_dom(all_41_6) = all_311_2 & % 78.16/12.15 | | | | | | | | | | | | | | in(all_41_7, all_311_2) = all_311_1 & % 78.16/12.15 | | | | | | | | | | | | | | $i(all_311_2)))) % 78.16/12.15 | | | | | | | | | | | | | | % 78.16/12.15 | | | | | | | | | | | | | | DELTA: instantiating (161) with fresh symbols all_317_0, % 78.16/12.15 | | | | | | | | | | | | | | all_317_1, all_317_2, all_317_3, all_317_4, % 78.16/12.15 | | | | | | | | | | | | | | all_317_5, all_317_6, all_317_7 gives: % 78.16/12.15 | | | | | | | | | | | | | | (165) ( ~ (all_317_6 = 0) & function(all_41_2) = % 78.16/12.15 | | | | | | | | | | | | | | all_317_6) | ( ~ (all_317_6 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | function(all_41_3) = all_317_6) | ( ~ (all_317_7 % 78.16/12.15 | | | | | | | | | | | | | | = 0) & relation(all_41_2) = all_317_7) | ( ~ % 78.16/12.15 | | | | | | | | | | | | | | (all_317_7 = 0) & relation(all_41_3) = % 78.16/12.15 | | | | | | | | | | | | | | all_317_7) | (((all_317_0 = 0 & all_317_1 = 0 & % 78.16/12.15 | | | | | | | | | | | | | | relation_dom(all_41_2) = all_317_2 & % 78.16/12.15 | | | | | | | | | | | | | | in(all_41_1, all_129_0) = 0 & in(all_41_7, % 78.16/12.15 | | | | | | | | | | | | | | all_317_2) = 0 & $i(all_317_2)) | ( ~ % 78.16/12.15 | | | | | | | | | | | | | | (all_317_3 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | relation_composition(all_41_2, all_41_3) = % 78.16/12.15 | | | | | | | | | | | | | | all_317_5 & relation_dom(all_317_5) = % 78.16/12.15 | | | | | | | | | | | | | | all_317_4 & in(all_41_7, all_317_4) = % 78.16/12.15 | | | | | | | | | | | | | | all_317_3 & $i(all_317_4) & $i(all_317_5))) % 78.16/12.15 | | | | | | | | | | | | | | & ((all_317_3 = 0 & % 78.16/12.15 | | | | | | | | | | | | | | relation_composition(all_41_2, all_41_3) = % 78.16/12.15 | | | | | | | | | | | | | | all_317_5 & relation_dom(all_317_5) = % 78.16/12.15 | | | | | | | | | | | | | | all_317_4 & in(all_41_7, all_317_4) = 0 & % 78.16/12.15 | | | | | | | | | | | | | | $i(all_317_4) & $i(all_317_5)) | ( ~ % 78.16/12.15 | | | | | | | | | | | | | | (all_317_0 = 0) & in(all_41_1, all_129_0) = % 78.16/12.15 | | | | | | | | | | | | | | all_317_0) | ( ~ (all_317_1 = 0) & % 78.16/12.15 | | | | | | | | | | | | | | relation_dom(all_41_2) = all_317_2 & % 78.16/12.15 | | | | | | | | | | | | | | in(all_41_7, all_317_2) = all_317_1 & % 78.16/12.15 | | | | | | | | | | | | | | $i(all_317_2)))) % 78.16/12.15 | | | | | | | | | | | | | | % 78.16/12.15 | | | | | | | | | | | | | | DELTA: instantiating (160) with fresh symbols all_321_0, % 78.16/12.15 | | | | | | | | | | | | | | all_321_1 gives: % 78.16/12.15 | | | | | | | | | | | | | | (166) ( ~ (all_321_1 = 0) & function(all_41_2) = % 78.16/12.15 | | | | | | | | | | | | | | all_321_1) | (relation_dom(all_41_2) = all_321_0 % 78.16/12.15 | | | | | | | | | | | | | | & $i(all_321_0) & ! [v0: $i] : ! [v1: $i] : ! % 78.16/12.15 | | | | | | | | | | | | | | [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 78.16/12.15 | | | | | | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 78.16/12.15 | | | | | | | | | | | | | | $i] : ? [v5: int] : (( ~ (v3 = 0) & in(v0, % 78.16/12.15 | | | | | | | | | | | | | | all_321_0) = v3) | (((v5 = 0 & in(v2, % 78.16/12.15 | | | | | | | | | | | | | | all_41_2) = 0) | ( ~ (v4 = v1) & % 78.16/12.15 | | | | | | | | | | | | | | apply(all_41_2, v0) = v4 & $i(v4))) & % 78.16/12.15 | | | | | | | | | | | | | | ((v4 = v1 & apply(all_41_2, v0) = v1) | ( % 78.16/12.15 | | | | | | | | | | | | | | ~ (v5 = 0) & in(v2, all_41_2) = % 78.16/12.15 | | | | | | | | | | | | | | v5))))) & ? [v0: $i] : ! [v1: $i] : % 78.16/12.15 | | | | | | | | | | | | | | ! [v2: int] : (v2 = 0 | ~ (in(v1, all_321_0) = % 78.16/12.15 | | | | | | | | | | | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 78.16/12.15 | | | | | | | | | | | | | | (( ~ (v0 = empty_set) | (v3 = empty_set & % 78.16/12.15 | | | | | | | | | | | | | | apply(all_41_2, v1) = empty_set)) & (v0 % 78.16/12.15 | | | | | | | | | | | | | | = empty_set | ( ~ (v3 = v0) & % 78.16/12.15 | | | | | | | | | | | | | | apply(all_41_2, v1) = v3 & $i(v3))))) & % 78.16/12.15 | | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 78.16/12.15 | | | | | | | | | | | | | | (apply(all_41_2, v0) = v1) | ~ $i(v1) | ~ % 78.16/12.15 | | | | | | | | | | | | | | $i(v0) | in(v0, all_321_0) = 0) & ! [v0: $i] % 78.16/12.15 | | | | | | | | | | | | | | : ! [v1: $i] : (v1 = empty_set | ~ % 78.16/12.15 | | | | | | | | | | | | | | (apply(all_41_2, v0) = v1) | ~ $i(v0) | % 78.16/12.15 | | | | | | | | | | | | | | in(v0, all_321_0) = 0)) % 78.16/12.15 | | | | | | | | | | | | | | % 78.16/12.15 | | | | | | | | | | | | | | DELTA: instantiating (159) with fresh symbols all_323_0, % 78.16/12.15 | | | | | | | | | | | | | | all_323_1 gives: % 78.16/12.16 | | | | | | | | | | | | | | (167) ( ~ (all_323_1 = 0) & relation(all_41_2) = % 78.16/12.16 | | | | | | | | | | | | | | all_323_1) | (relation_dom(all_41_2) = all_323_0 % 78.16/12.16 | | | | | | | | | | | | | | & $i(all_323_0) & ! [v0: $i] : ! [v1: $i] : ! % 78.16/12.16 | | | | | | | | | | | | | | [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 78.16/12.16 | | | | | | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 78.16/12.16 | | | | | | | | | | | | | | $i] : ? [v5: int] : (( ~ (v3 = 0) & in(v0, % 78.16/12.16 | | | | | | | | | | | | | | all_323_0) = v3) | (((v5 = 0 & in(v2, % 78.16/12.16 | | | | | | | | | | | | | | all_41_2) = 0) | ( ~ (v4 = v1) & % 78.16/12.16 | | | | | | | | | | | | | | apply(all_41_2, v0) = v4 & $i(v4))) & % 78.16/12.16 | | | | | | | | | | | | | | ((v4 = v1 & apply(all_41_2, v0) = v1) | ( % 78.16/12.16 | | | | | | | | | | | | | | ~ (v5 = 0) & in(v2, all_41_2) = % 78.16/12.16 | | | | | | | | | | | | | | v5))))) & ? [v0: $i] : ! [v1: $i] : % 78.16/12.16 | | | | | | | | | | | | | | ! [v2: int] : (v2 = 0 | ~ (in(v1, all_323_0) = % 78.16/12.16 | | | | | | | | | | | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 78.16/12.16 | | | | | | | | | | | | | | (( ~ (v0 = empty_set) | (v3 = empty_set & % 78.16/12.16 | | | | | | | | | | | | | | apply(all_41_2, v1) = empty_set)) & (v0 % 78.16/12.16 | | | | | | | | | | | | | | = empty_set | ( ~ (v3 = v0) & % 78.16/12.16 | | | | | | | | | | | | | | apply(all_41_2, v1) = v3 & $i(v3))))) & % 78.16/12.16 | | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 78.16/12.16 | | | | | | | | | | | | | | (apply(all_41_2, v0) = v1) | ~ $i(v1) | ~ % 78.16/12.16 | | | | | | | | | | | | | | $i(v0) | in(v0, all_323_0) = 0) & ! [v0: $i] % 78.16/12.16 | | | | | | | | | | | | | | : ! [v1: $i] : (v1 = empty_set | ~ % 78.16/12.16 | | | | | | | | | | | | | | (apply(all_41_2, v0) = v1) | ~ $i(v0) | % 78.16/12.16 | | | | | | | | | | | | | | in(v0, all_323_0) = 0)) % 78.16/12.16 | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | BETA: splitting (167) gives: % 78.16/12.16 | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | Case 1: % 78.16/12.16 | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | (168) ~ (all_323_1 = 0) & relation(all_41_2) = % 78.16/12.16 | | | | | | | | | | | | | | | all_323_1 % 78.16/12.16 | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | ALPHA: (168) implies: % 78.16/12.16 | | | | | | | | | | | | | | | (169) ~ (all_323_1 = 0) % 78.16/12.16 | | | | | | | | | | | | | | | (170) relation(all_41_2) = all_323_1 % 78.16/12.16 | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_323_1, all_41_2, % 78.16/12.16 | | | | | | | | | | | | | | | simplifying with (109), (170) gives: % 78.16/12.16 | | | | | | | | | | | | | | | (171) all_323_1 = 0 % 78.16/12.16 | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | REDUCE: (169), (171) imply: % 78.16/12.16 | | | | | | | | | | | | | | | (172) $false % 78.16/12.16 | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent. % 78.16/12.16 | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | Case 2: % 78.16/12.16 | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | (173) relation_dom(all_41_2) = all_323_0 & $i(all_323_0) % 78.16/12.16 | | | | | | | | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 78.16/12.16 | | | | | | | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 78.16/12.16 | | | | | | | | | | | | | | | $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: % 78.16/12.16 | | | | | | | | | | | | | | | int] : (( ~ (v3 = 0) & in(v0, all_323_0) = v3) % 78.16/12.16 | | | | | | | | | | | | | | | | (((v5 = 0 & in(v2, all_41_2) = 0) | ( ~ (v4 % 78.16/12.16 | | | | | | | | | | | | | | | = v1) & apply(all_41_2, v0) = v4 & % 78.16/12.16 | | | | | | | | | | | | | | | $i(v4))) & ((v4 = v1 & apply(all_41_2, % 78.16/12.16 | | | | | | | | | | | | | | | v0) = v1) | ( ~ (v5 = 0) & in(v2, % 78.16/12.16 | | | | | | | | | | | | | | | all_41_2) = v5))))) & ? [v0: $i] : ! % 78.16/12.16 | | | | | | | | | | | | | | | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, % 78.16/12.16 | | | | | | | | | | | | | | | all_323_0) = v2) | ~ $i(v1) | ~ $i(v0) | % 78.16/12.16 | | | | | | | | | | | | | | | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 78.16/12.16 | | | | | | | | | | | | | | | empty_set & apply(all_41_2, v1) = % 78.16/12.16 | | | | | | | | | | | | | | | empty_set)) & (v0 = empty_set | ( ~ (v3 = % 78.16/12.16 | | | | | | | | | | | | | | | v0) & apply(all_41_2, v1) = v3 & % 78.16/12.16 | | | | | | | | | | | | | | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : % 78.16/12.16 | | | | | | | | | | | | | | | (v1 = empty_set | ~ (apply(all_41_2, v0) = v1) | % 78.16/12.16 | | | | | | | | | | | | | | | ~ $i(v1) | ~ $i(v0) | in(v0, all_323_0) = 0) & % 78.16/12.16 | | | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 78.16/12.16 | | | | | | | | | | | | | | | (apply(all_41_2, v0) = v1) | ~ $i(v0) | in(v0, % 78.16/12.16 | | | | | | | | | | | | | | | all_323_0) = 0) % 78.16/12.16 | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | ALPHA: (173) implies: % 78.16/12.16 | | | | | | | | | | | | | | | (174) relation_dom(all_41_2) = all_323_0 % 78.16/12.16 | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | BETA: splitting (166) gives: % 78.16/12.16 | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | Case 1: % 78.16/12.16 | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | (175) ~ (all_321_1 = 0) & function(all_41_2) = % 78.16/12.16 | | | | | | | | | | | | | | | | all_321_1 % 78.16/12.16 | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | ALPHA: (175) implies: % 78.16/12.16 | | | | | | | | | | | | | | | | (176) ~ (all_321_1 = 0) % 78.16/12.16 | | | | | | | | | | | | | | | | (177) function(all_41_2) = all_321_1 % 78.16/12.16 | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_321_1, all_41_2, % 78.16/12.16 | | | | | | | | | | | | | | | | simplifying with (108), (177) gives: % 78.16/12.16 | | | | | | | | | | | | | | | | (178) all_321_1 = 0 % 78.16/12.16 | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | REDUCE: (176), (178) imply: % 78.16/12.16 | | | | | | | | | | | | | | | | (179) $false % 78.16/12.16 | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 78.16/12.16 | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | Case 2: % 78.16/12.16 | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | (180) relation_dom(all_41_2) = all_321_0 & $i(all_321_0) % 78.16/12.16 | | | | | | | | | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 78.16/12.16 | | | | | | | | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 78.16/12.16 | | | | | | | | | | | | | | | | $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: % 78.16/12.16 | | | | | | | | | | | | | | | | int] : (( ~ (v3 = 0) & in(v0, all_321_0) = v3) % 78.16/12.16 | | | | | | | | | | | | | | | | | (((v5 = 0 & in(v2, all_41_2) = 0) | ( ~ (v4 % 78.16/12.16 | | | | | | | | | | | | | | | | = v1) & apply(all_41_2, v0) = v4 & % 78.16/12.16 | | | | | | | | | | | | | | | | $i(v4))) & ((v4 = v1 & apply(all_41_2, % 78.16/12.16 | | | | | | | | | | | | | | | | v0) = v1) | ( ~ (v5 = 0) & in(v2, % 78.16/12.16 | | | | | | | | | | | | | | | | all_41_2) = v5))))) & ? [v0: $i] : ! % 78.16/12.16 | | | | | | | | | | | | | | | | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, % 78.16/12.16 | | | | | | | | | | | | | | | | all_321_0) = v2) | ~ $i(v1) | ~ $i(v0) | % 78.16/12.16 | | | | | | | | | | | | | | | | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 78.16/12.16 | | | | | | | | | | | | | | | | empty_set & apply(all_41_2, v1) = % 78.16/12.16 | | | | | | | | | | | | | | | | empty_set)) & (v0 = empty_set | ( ~ (v3 = % 78.16/12.16 | | | | | | | | | | | | | | | | v0) & apply(all_41_2, v1) = v3 & % 78.16/12.16 | | | | | | | | | | | | | | | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : % 78.16/12.16 | | | | | | | | | | | | | | | | (v1 = empty_set | ~ (apply(all_41_2, v0) = v1) | % 78.16/12.16 | | | | | | | | | | | | | | | | ~ $i(v1) | ~ $i(v0) | in(v0, all_321_0) = 0) & % 78.16/12.16 | | | | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 78.16/12.16 | | | | | | | | | | | | | | | | (apply(all_41_2, v0) = v1) | ~ $i(v0) | in(v0, % 78.16/12.16 | | | | | | | | | | | | | | | | all_321_0) = 0) % 78.16/12.16 | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | ALPHA: (180) implies: % 78.16/12.16 | | | | | | | | | | | | | | | | (181) relation_dom(all_41_2) = all_321_0 % 78.16/12.16 | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | BETA: splitting (163) gives: % 78.16/12.16 | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | Case 1: % 78.16/12.16 | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | (182) all_41_1 = empty_set % 78.16/12.16 | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | REDUCE: (21), (182) imply: % 78.16/12.16 | | | | | | | | | | | | | | | | | (183) ~ (all_41_0 = empty_set) % 78.16/12.16 | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 78.16/12.16 | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | Case 1: % 78.16/12.16 | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | (184) in(all_41_4, all_135_0) = 0 % 78.16/12.16 | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | REDUCE: (131), (184) imply: % 78.16/12.16 | | | | | | | | | | | | | | | | | | (185) in(all_41_4, all_129_0) = 0 % 78.16/12.16 | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 78.16/12.16 | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | Case 1: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | (186) ( ~ (all_311_6 = 0) & function(all_41_3) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | all_311_6) | ( ~ (all_311_6 = 0) & % 78.16/12.16 | | | | | | | | | | | | | | | | | | | function(all_41_6) = all_311_6) % 78.16/12.16 | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | Case 1: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | (187) ~ (all_311_6 = 0) & function(all_41_3) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | all_311_6 % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | (188) ~ (all_311_6 = 0) % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | (189) function(all_41_3) = all_311_6 % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_311_6, all_41_3, % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | simplifying with (29), (189) gives: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | (190) all_311_6 = 0 % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (190) imply: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | (191) $false % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | CLOSE: (191) is inconsistent. % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | Case 2: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | (192) ~ (all_311_6 = 0) & function(all_41_6) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | all_311_6 % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | (193) ~ (all_311_6 = 0) % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | (194) function(all_41_6) = all_311_6 % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_311_6, all_41_6, % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | simplifying with (28), (194) gives: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | (195) all_311_6 = 0 % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (195) imply: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | (196) $false % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | End of split % 78.16/12.16 | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | Case 2: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | (197) ( ~ (all_311_7 = 0) & relation(all_41_3) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | all_311_7) | ( ~ (all_311_7 = 0) & % 78.16/12.16 | | | | | | | | | | | | | | | | | | | relation(all_41_6) = all_311_7) | (((all_311_0 = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | 0 & all_311_1 = 0 & relation_dom(all_41_6) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | all_311_2 & in(all_41_4, all_129_0) = 0 & % 78.16/12.16 | | | | | | | | | | | | | | | | | | | in(all_41_7, all_311_2) = 0 & $i(all_311_2)) % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | ( ~ (all_311_3 = 0) & % 78.16/12.16 | | | | | | | | | | | | | | | | | | | relation_composition(all_41_6, all_41_3) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | all_311_5 & relation_dom(all_311_5) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | all_311_4 & in(all_41_7, all_311_4) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | all_311_3 & $i(all_311_4) & $i(all_311_5))) % 78.16/12.16 | | | | | | | | | | | | | | | | | | | & ((all_311_3 = 0 & % 78.16/12.16 | | | | | | | | | | | | | | | | | | | relation_composition(all_41_6, all_41_3) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | all_311_5 & relation_dom(all_311_5) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | all_311_4 & in(all_41_7, all_311_4) = 0 & % 78.16/12.16 | | | | | | | | | | | | | | | | | | | $i(all_311_4) & $i(all_311_5)) | ( ~ % 78.16/12.16 | | | | | | | | | | | | | | | | | | | (all_311_0 = 0) & in(all_41_4, all_129_0) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | all_311_0) | ( ~ (all_311_1 = 0) & % 78.16/12.16 | | | | | | | | | | | | | | | | | | | relation_dom(all_41_6) = all_311_2 & % 78.16/12.16 | | | | | | | | | | | | | | | | | | | in(all_41_7, all_311_2) = all_311_1 & % 78.16/12.16 | | | | | | | | | | | | | | | | | | | $i(all_311_2)))) % 78.16/12.16 | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | Case 1: % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | (198) ~ (all_311_7 = 0) & relation(all_41_3) = % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | all_311_7 % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | % 78.16/12.16 | | | | | | | | | | | | | | | | | | | | ALPHA: (198) implies: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | (199) ~ (all_311_7 = 0) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | (200) relation(all_41_3) = all_311_7 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_311_7, all_41_3, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | simplifying with (31), (200) gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | (201) all_311_7 = 0 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (201) imply: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | (202) $false % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent. % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | Case 2: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | (203) ( ~ (all_311_7 = 0) & relation(all_41_6) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | all_311_7) | (((all_311_0 = 0 & all_311_1 = 0 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | relation_dom(all_41_6) = all_311_2 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | in(all_41_4, all_129_0) = 0 & in(all_41_7, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | all_311_2) = 0 & $i(all_311_2)) | ( ~ % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | (all_311_3 = 0) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | relation_composition(all_41_6, all_41_3) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | all_311_5 & relation_dom(all_311_5) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | all_311_4 & in(all_41_7, all_311_4) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | all_311_3 & $i(all_311_4) & $i(all_311_5))) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | & ((all_311_3 = 0 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | relation_composition(all_41_6, all_41_3) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | all_311_5 & relation_dom(all_311_5) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | all_311_4 & in(all_41_7, all_311_4) = 0 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | $i(all_311_4) & $i(all_311_5)) | ( ~ % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | (all_311_0 = 0) & in(all_41_4, all_129_0) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | all_311_0) | ( ~ (all_311_1 = 0) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | relation_dom(all_41_6) = all_311_2 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | in(all_41_7, all_311_2) = all_311_1 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | $i(all_311_2)))) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | Case 1: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | (204) ~ (all_311_7 = 0) & relation(all_41_6) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | all_311_7 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | (205) ~ (all_311_7 = 0) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | (206) relation(all_41_6) = all_311_7 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_311_7, all_41_6, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | simplifying with (30), (206) gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | (207) all_311_7 = 0 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (207) imply: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | (208) $false % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | CLOSE: (208) is inconsistent. % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | Case 2: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | (209) ((all_311_0 = 0 & all_311_1 = 0 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | relation_dom(all_41_6) = all_311_2 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | in(all_41_4, all_129_0) = 0 & in(all_41_7, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | all_311_2) = 0 & $i(all_311_2)) | ( ~ % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | (all_311_3 = 0) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | relation_composition(all_41_6, all_41_3) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | all_311_5 & relation_dom(all_311_5) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | all_311_4 & in(all_41_7, all_311_4) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | all_311_3 & $i(all_311_4) & $i(all_311_5))) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | ((all_311_3 = 0 & relation_composition(all_41_6, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | all_41_3) = all_311_5 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | relation_dom(all_311_5) = all_311_4 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | in(all_41_7, all_311_4) = 0 & $i(all_311_4) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | $i(all_311_5)) | ( ~ (all_311_0 = 0) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | in(all_41_4, all_129_0) = all_311_0) | ( ~ % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | (all_311_1 = 0) & relation_dom(all_41_6) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | all_311_2 & in(all_41_7, all_311_2) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | all_311_1 & $i(all_311_2))) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | (210) (all_311_3 = 0 & relation_composition(all_41_6, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | all_41_3) = all_311_5 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | relation_dom(all_311_5) = all_311_4 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | in(all_41_7, all_311_4) = 0 & $i(all_311_4) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | $i(all_311_5)) | ( ~ (all_311_0 = 0) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | in(all_41_4, all_129_0) = all_311_0) | ( ~ % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | (all_311_1 = 0) & relation_dom(all_41_6) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | all_311_2 & in(all_41_7, all_311_2) = all_311_1 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | & $i(all_311_2)) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | Case 1: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | (211) all_311_3 = 0 & relation_composition(all_41_6, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | all_41_3) = all_311_5 & relation_dom(all_311_5) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | = all_311_4 & in(all_41_7, all_311_4) = 0 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | $i(all_311_4) & $i(all_311_5) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | (212) in(all_41_7, all_311_4) = 0 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | (213) relation_dom(all_311_5) = all_311_4 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | (214) relation_composition(all_41_6, all_41_3) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | all_311_5 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_102_3, all_323_0, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | all_41_2, simplifying with (153), (174) gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | (215) all_323_0 = all_102_3 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_321_0, all_323_0, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | all_41_2, simplifying with (174), (181) gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | (216) all_323_0 = all_321_0 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_41_2, all_311_5, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | all_41_3, all_41_6, simplifying with (36), (214) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | (217) all_311_5 = all_41_2 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (216) imply: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | (218) all_321_0 = all_102_3 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (213), (217) imply: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | (219) relation_dom(all_41_2) = all_311_4 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | (220) ( ~ (all_317_6 = 0) & function(all_41_2) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | all_317_6) | ( ~ (all_317_6 = 0) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | function(all_41_3) = all_317_6) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (221) ~ (all_317_6 = 0) & function(all_41_2) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | all_317_6 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (222) ~ (all_317_6 = 0) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (223) function(all_41_2) = all_317_6 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_317_6, all_41_2, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (108), (223) gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (224) all_317_6 = 0 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (222), (224) imply: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (225) $false % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent. % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (226) ~ (all_317_6 = 0) & function(all_41_3) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | all_317_6 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (227) ~ (all_317_6 = 0) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (228) function(all_41_3) = all_317_6 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_317_6, all_41_3, % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (29), (228) gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (229) all_317_6 = 0 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (227), (229) imply: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (230) $false % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent. % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | End of split % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | (231) ( ~ (all_317_7 = 0) & relation(all_41_2) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | all_317_7) | ( ~ (all_317_7 = 0) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | relation(all_41_3) = all_317_7) | (((all_317_0 = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | 0 & all_317_1 = 0 & relation_dom(all_41_2) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | all_317_2 & in(all_41_1, all_129_0) = 0 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | in(all_41_7, all_317_2) = 0 & $i(all_317_2)) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_317_3 = 0) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_41_2, all_41_3) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | all_317_5 & relation_dom(all_317_5) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | all_317_4 & in(all_41_7, all_317_4) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | all_317_3 & $i(all_317_4) & $i(all_317_5))) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | & ((all_317_3 = 0 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_41_2, all_41_3) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | all_317_5 & relation_dom(all_317_5) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | all_317_4 & in(all_41_7, all_317_4) = 0 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | $i(all_317_4) & $i(all_317_5)) | ( ~ % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | (all_317_0 = 0) & in(all_41_1, all_129_0) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | all_317_0) | ( ~ (all_317_1 = 0) & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_41_2) = all_317_2 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | in(all_41_7, all_317_2) = all_317_1 & % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | $i(all_317_2)))) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (232) ~ (all_317_7 = 0) & relation(all_41_2) = % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | all_317_7 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies: % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (233) ~ (all_317_7 = 0) % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (234) relation(all_41_2) = all_317_7 % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.16/12.17 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_317_7, all_41_2, % 78.56/12.17 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (109), (234) gives: % 78.56/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (235) all_317_7 = 0 % 78.56/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.17 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (233), (235) imply: % 78.56/12.17 | | | | | | | | | | | | | | | | | | | | | | | | (236) $false % 78.56/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.17 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent. % 78.56/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.17 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 78.56/12.17 | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | (237) ( ~ (all_317_7 = 0) & relation(all_41_3) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | all_317_7) | (((all_317_0 = 0 & all_317_1 = 0 & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_41_2) = all_317_2 & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | in(all_41_1, all_129_0) = 0 & in(all_41_7, % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | all_317_2) = 0 & $i(all_317_2)) | ( ~ % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_317_3 = 0) & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_41_2, all_41_3) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | all_317_5 & relation_dom(all_317_5) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | all_317_4 & in(all_41_7, all_317_4) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | all_317_3 & $i(all_317_4) & $i(all_317_5))) % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | & ((all_317_3 = 0 & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_41_2, all_41_3) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | all_317_5 & relation_dom(all_317_5) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | all_317_4 & in(all_41_7, all_317_4) = 0 & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_317_4) & $i(all_317_5)) | ( ~ % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_317_0 = 0) & in(all_41_1, all_129_0) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | all_317_0) | ( ~ (all_317_1 = 0) & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_41_2) = all_317_2 & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | in(all_41_7, all_317_2) = all_317_1 & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_317_2)))) % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | (238) ~ (all_317_7 = 0) & relation(all_41_3) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | all_317_7 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | (239) ~ (all_317_7 = 0) % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | (240) relation(all_41_3) = all_317_7 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_317_7, all_41_3, % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (31), (240) gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_317_7 = 0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (239), (241) imply: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | (242) $false % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent. % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_102_3, all_311_4, % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | all_41_2, simplifying with (153), (219) gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_311_4 = all_102_3 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (212), (243) imply: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | (244) in(all_41_7, all_102_3) = 0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (149), (158), (244) are inconsistent by % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | Case 2: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | (245) ( ~ (all_311_0 = 0) & in(all_41_4, all_129_0) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | all_311_0) | ( ~ (all_311_1 = 0) & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_41_6) = all_311_2 & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | in(all_41_7, all_311_2) = all_311_1 & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_311_2)) % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (246) ~ (all_311_0 = 0) & in(all_41_4, all_129_0) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | all_311_0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (247) ~ (all_311_0 = 0) % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (248) in(all_41_4, all_129_0) = all_311_0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_311_0, all_129_0, % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | all_41_4, simplifying with (185), (248) gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (249) all_311_0 = 0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (247), (249) imply: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (250) $false % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (250) is inconsistent. % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (251) ~ (all_311_1 = 0) & relation_dom(all_41_6) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | all_311_2 & in(all_41_7, all_311_2) = all_311_1 & % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_311_2) % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (252) ~ (all_311_1 = 0) % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (253) in(all_41_7, all_311_2) = all_311_1 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (254) relation_dom(all_41_6) = all_311_2 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_41_5, all_311_2, % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | all_41_6, simplifying with (35), (254) gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (255) all_311_2 = all_41_5 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (253), (255) imply: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (256) in(all_41_7, all_41_5) = all_311_1 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_311_1, all_41_5, % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | all_41_7, simplifying with (27), (256) gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (257) all_311_1 = 0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (252), (257) imply: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | (258) $false % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (258) is inconsistent. % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | Case 2: % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | (259) all_41_0 = empty_set % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | REDUCE: (183), (259) imply: % 78.56/12.18 | | | | | | | | | | | | | | | | | | (260) $false % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | CLOSE: (260) is inconsistent. % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | Case 2: % 78.56/12.18 | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | (261) ? [v0: int] : ? [v1: int] : ((v0 = 0 & % 78.56/12.18 | | | | | | | | | | | | | | | | | in(all_41_7, all_102_3) = 0) | ( ~ (v1 = 0) & % 78.56/12.18 | | | | | | | | | | | | | | | | | function(all_41_2) = v1) | ( ~ (v0 = 0) & % 78.56/12.18 | | | | | | | | | | | | | | | | | relation(all_41_2) = v0)) % 78.56/12.18 | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | DELTA: instantiating (261) with fresh symbols all_363_0, % 78.56/12.18 | | | | | | | | | | | | | | | | | all_363_1 gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | (262) (all_363_1 = 0 & in(all_41_7, all_102_3) = 0) | ( % 78.56/12.18 | | | | | | | | | | | | | | | | | ~ (all_363_0 = 0) & function(all_41_2) = % 78.56/12.18 | | | | | | | | | | | | | | | | | all_363_0) | ( ~ (all_363_1 = 0) & % 78.56/12.18 | | | | | | | | | | | | | | | | | relation(all_41_2) = all_363_1) % 78.56/12.18 | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | BETA: splitting (262) gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | Case 1: % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | (263) all_363_1 = 0 & in(all_41_7, all_102_3) = 0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | ALPHA: (263) implies: % 78.56/12.18 | | | | | | | | | | | | | | | | | | (264) in(all_41_7, all_102_3) = 0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (149), (158), (264) are inconsistent by % 78.56/12.18 | | | | | | | | | | | | | | | | | | sub-proof #1. % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | Case 2: % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | (265) ( ~ (all_363_0 = 0) & function(all_41_2) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | all_363_0) | ( ~ (all_363_1 = 0) & % 78.56/12.18 | | | | | | | | | | | | | | | | | | relation(all_41_2) = all_363_1) % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | Case 1: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | (266) ~ (all_363_0 = 0) & function(all_41_2) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | all_363_0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | (267) ~ (all_363_0 = 0) % 78.56/12.18 | | | | | | | | | | | | | | | | | | | (268) function(all_41_2) = all_363_0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_363_0, all_41_2, % 78.56/12.18 | | | | | | | | | | | | | | | | | | | simplifying with (108), (268) gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | (269) all_363_0 = 0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | REDUCE: (267), (269) imply: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | (270) $false % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | CLOSE: (270) is inconsistent. % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | Case 2: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | (271) ~ (all_363_1 = 0) & relation(all_41_2) = % 78.56/12.18 | | | | | | | | | | | | | | | | | | | all_363_1 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | (272) ~ (all_363_1 = 0) % 78.56/12.18 | | | | | | | | | | | | | | | | | | | (273) relation(all_41_2) = all_363_1 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_363_1, all_41_2, % 78.56/12.18 | | | | | | | | | | | | | | | | | | | simplifying with (109), (273) gives: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | (274) all_363_1 = 0 % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | REDUCE: (272), (274) imply: % 78.56/12.18 | | | | | | | | | | | | | | | | | | | (275) $false % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | | CLOSE: (275) is inconsistent. % 78.56/12.18 | | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | End of split % 78.56/12.18 | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | Case 2: % 78.56/12.18 | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | (276) ( ~ (all_102_5 = 0) & function(all_41_6) = % 78.56/12.18 | | | | | | | | | | | | | all_102_5) | ( ~ (all_102_6 = 0) & % 78.56/12.18 | | | | | | | | | | | | | relation(all_41_3) = all_102_6) | ( ~ (all_102_6 % 78.56/12.18 | | | | | | | | | | | | | = 0) & relation(all_41_6) = all_102_6) % 78.56/12.18 | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | BETA: splitting (276) gives: % 78.56/12.18 | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | Case 1: % 78.56/12.18 | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | (277) ~ (all_102_5 = 0) & function(all_41_6) = % 78.56/12.18 | | | | | | | | | | | | | | all_102_5 % 78.56/12.18 | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | ALPHA: (277) implies: % 78.56/12.18 | | | | | | | | | | | | | | (278) ~ (all_102_5 = 0) % 78.56/12.18 | | | | | | | | | | | | | | (279) function(all_41_6) = all_102_5 % 78.56/12.18 | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_102_5, all_41_6, % 78.56/12.18 | | | | | | | | | | | | | | simplifying with (28), (279) gives: % 78.56/12.18 | | | | | | | | | | | | | | (280) all_102_5 = 0 % 78.56/12.18 | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | REDUCE: (278), (280) imply: % 78.56/12.18 | | | | | | | | | | | | | | (281) $false % 78.56/12.18 | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | CLOSE: (281) is inconsistent. % 78.56/12.18 | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | Case 2: % 78.56/12.18 | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | (282) ( ~ (all_102_6 = 0) & relation(all_41_3) = % 78.56/12.18 | | | | | | | | | | | | | | all_102_6) | ( ~ (all_102_6 = 0) & % 78.56/12.18 | | | | | | | | | | | | | | relation(all_41_6) = all_102_6) % 78.56/12.18 | | | | | | | | | | | | | | % 78.56/12.18 | | | | | | | | | | | | | | BETA: splitting (282) gives: % 78.56/12.18 | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | Case 1: % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | | (283) ~ (all_102_6 = 0) & relation(all_41_3) = % 78.56/12.19 | | | | | | | | | | | | | | | all_102_6 % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | | ALPHA: (283) implies: % 78.56/12.19 | | | | | | | | | | | | | | | (284) ~ (all_102_6 = 0) % 78.56/12.19 | | | | | | | | | | | | | | | (285) relation(all_41_3) = all_102_6 % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_102_6, all_41_3, % 78.56/12.19 | | | | | | | | | | | | | | | simplifying with (31), (285) gives: % 78.56/12.19 | | | | | | | | | | | | | | | (286) all_102_6 = 0 % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | | REDUCE: (284), (286) imply: % 78.56/12.19 | | | | | | | | | | | | | | | (287) $false % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | | CLOSE: (287) is inconsistent. % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | Case 2: % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | | (288) ~ (all_102_6 = 0) & relation(all_41_6) = % 78.56/12.19 | | | | | | | | | | | | | | | all_102_6 % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | | ALPHA: (288) implies: % 78.56/12.19 | | | | | | | | | | | | | | | (289) ~ (all_102_6 = 0) % 78.56/12.19 | | | | | | | | | | | | | | | (290) relation(all_41_6) = all_102_6 % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_102_6, all_41_6, % 78.56/12.19 | | | | | | | | | | | | | | | simplifying with (30), (290) gives: % 78.56/12.19 | | | | | | | | | | | | | | | (291) all_102_6 = 0 % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | | REDUCE: (289), (291) imply: % 78.56/12.19 | | | | | | | | | | | | | | | (292) $false % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent. % 78.56/12.19 | | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | | End of split % 78.56/12.19 | | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | | End of split % 78.56/12.19 | | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | | End of split % 78.56/12.19 | | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | | End of split % 78.56/12.19 | | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | End of split % 78.56/12.19 | | | | | | | | | | % 78.56/12.19 | | | | | | | | | End of split % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | Case 2: % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | (293) ~ (all_95_2 = 0) & function(all_41_3) = all_95_2 % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | ALPHA: (293) implies: % 78.56/12.19 | | | | | | | | | (294) ~ (all_95_2 = 0) % 78.56/12.19 | | | | | | | | | (295) function(all_41_3) = all_95_2 % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_95_2, all_41_3, % 78.56/12.19 | | | | | | | | | simplifying with (29), (295) gives: % 78.56/12.19 | | | | | | | | | (296) all_95_2 = 0 % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | REDUCE: (294), (296) imply: % 78.56/12.19 | | | | | | | | | (297) $false % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | CLOSE: (297) is inconsistent. % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | End of split % 78.56/12.19 | | | | | | | | % 78.56/12.19 | | | | | | | Case 2: % 78.56/12.19 | | | | | | | | % 78.56/12.19 | | | | | | | | (298) ( ~ (all_95_3 = 0) & relation(all_41_3) = all_95_3) | ( % 78.56/12.19 | | | | | | | | ~ (all_95_4 = 0) & function(all_41_6) = all_95_4) | ( % 78.56/12.19 | | | | | | | | ~ (all_95_5 = 0) & relation(all_41_6) = all_95_5) % 78.56/12.19 | | | | | | | | % 78.56/12.19 | | | | | | | | BETA: splitting (298) gives: % 78.56/12.19 | | | | | | | | % 78.56/12.19 | | | | | | | | Case 1: % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | (299) ~ (all_95_3 = 0) & relation(all_41_3) = all_95_3 % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | ALPHA: (299) implies: % 78.56/12.19 | | | | | | | | | (300) ~ (all_95_3 = 0) % 78.56/12.19 | | | | | | | | | (301) relation(all_41_3) = all_95_3 % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_95_3, all_41_3, % 78.56/12.19 | | | | | | | | | simplifying with (31), (301) gives: % 78.56/12.19 | | | | | | | | | (302) all_95_3 = 0 % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | REDUCE: (300), (302) imply: % 78.56/12.19 | | | | | | | | | (303) $false % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | CLOSE: (303) is inconsistent. % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | Case 2: % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | (304) ( ~ (all_95_4 = 0) & function(all_41_6) = all_95_4) | % 78.56/12.19 | | | | | | | | | ( ~ (all_95_5 = 0) & relation(all_41_6) = all_95_5) % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | BETA: splitting (304) gives: % 78.56/12.19 | | | | | | | | | % 78.56/12.19 | | | | | | | | | Case 1: % 78.56/12.19 | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | (305) ~ (all_95_4 = 0) & function(all_41_6) = all_95_4 % 78.56/12.19 | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | ALPHA: (305) implies: % 78.56/12.19 | | | | | | | | | | (306) ~ (all_95_4 = 0) % 78.56/12.19 | | | | | | | | | | (307) function(all_41_6) = all_95_4 % 78.56/12.19 | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_95_4, all_41_6, % 78.56/12.19 | | | | | | | | | | simplifying with (28), (307) gives: % 78.56/12.19 | | | | | | | | | | (308) all_95_4 = 0 % 78.56/12.19 | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | REDUCE: (306), (308) imply: % 78.56/12.19 | | | | | | | | | | (309) $false % 78.56/12.19 | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | CLOSE: (309) is inconsistent. % 78.56/12.19 | | | | | | | | | | % 78.56/12.19 | | | | | | | | | Case 2: % 78.56/12.19 | | | | | | | | | | % 78.56/12.19 | | | | | | | | | | (310) ~ (all_95_5 = 0) & relation(all_41_6) = all_95_5 % 78.63/12.19 | | | | | | | | | | % 78.63/12.19 | | | | | | | | | | ALPHA: (310) implies: % 78.63/12.19 | | | | | | | | | | (311) ~ (all_95_5 = 0) % 78.63/12.19 | | | | | | | | | | (312) relation(all_41_6) = all_95_5 % 78.63/12.19 | | | | | | | | | | % 78.63/12.19 | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_95_5, all_41_6, % 78.63/12.19 | | | | | | | | | | simplifying with (30), (312) gives: % 78.63/12.19 | | | | | | | | | | (313) all_95_5 = 0 % 78.63/12.19 | | | | | | | | | | % 78.63/12.19 | | | | | | | | | | REDUCE: (311), (313) imply: % 78.63/12.19 | | | | | | | | | | (314) $false % 78.63/12.19 | | | | | | | | | | % 78.63/12.19 | | | | | | | | | | CLOSE: (314) is inconsistent. % 78.63/12.19 | | | | | | | | | | % 78.63/12.19 | | | | | | | | | End of split % 78.63/12.19 | | | | | | | | | % 78.63/12.19 | | | | | | | | End of split % 78.63/12.19 | | | | | | | | % 78.63/12.19 | | | | | | | End of split % 78.63/12.19 | | | | | | | % 78.63/12.19 | | | | | | End of split % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | End of split % 78.63/12.19 | | | | | % 78.63/12.19 | | | | End of split % 78.63/12.19 | | | | % 78.63/12.19 | | | Case 2: % 78.63/12.19 | | | | % 78.63/12.19 | | | | (315) ( ~ (all_117_5 = 0) & function(all_41_6) = all_117_5) | ( ~ % 78.63/12.19 | | | | (all_117_6 = 0) & relation(all_41_6) = all_117_6) | ( ~ % 78.63/12.19 | | | | (all_117_6 = 0) & function(all_41_3) = all_117_6) % 78.63/12.19 | | | | % 78.63/12.19 | | | | BETA: splitting (315) gives: % 78.63/12.19 | | | | % 78.63/12.19 | | | | Case 1: % 78.63/12.19 | | | | | % 78.63/12.19 | | | | | (316) ~ (all_117_5 = 0) & function(all_41_6) = all_117_5 % 78.63/12.19 | | | | | % 78.63/12.19 | | | | | ALPHA: (316) implies: % 78.63/12.19 | | | | | (317) ~ (all_117_5 = 0) % 78.63/12.19 | | | | | (318) function(all_41_6) = all_117_5 % 78.63/12.19 | | | | | % 78.63/12.19 | | | | | GROUND_INST: instantiating (10) with 0, all_117_5, all_41_6, % 78.63/12.19 | | | | | simplifying with (28), (318) gives: % 78.63/12.19 | | | | | (319) all_117_5 = 0 % 78.63/12.19 | | | | | % 78.63/12.19 | | | | | REDUCE: (317), (319) imply: % 78.63/12.19 | | | | | (320) $false % 78.63/12.19 | | | | | % 78.63/12.19 | | | | | CLOSE: (320) is inconsistent. % 78.63/12.19 | | | | | % 78.63/12.19 | | | | Case 2: % 78.63/12.19 | | | | | % 78.63/12.19 | | | | | (321) ( ~ (all_117_6 = 0) & relation(all_41_6) = all_117_6) | ( ~ % 78.63/12.19 | | | | | (all_117_6 = 0) & function(all_41_3) = all_117_6) % 78.63/12.19 | | | | | % 78.63/12.19 | | | | | BETA: splitting (321) gives: % 78.63/12.19 | | | | | % 78.63/12.19 | | | | | Case 1: % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | | (322) ~ (all_117_6 = 0) & relation(all_41_6) = all_117_6 % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | | ALPHA: (322) implies: % 78.63/12.19 | | | | | | (323) ~ (all_117_6 = 0) % 78.63/12.19 | | | | | | (324) relation(all_41_6) = all_117_6 % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | | GROUND_INST: instantiating (11) with 0, all_117_6, all_41_6, % 78.63/12.19 | | | | | | simplifying with (30), (324) gives: % 78.63/12.19 | | | | | | (325) all_117_6 = 0 % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | | REDUCE: (323), (325) imply: % 78.63/12.19 | | | | | | (326) $false % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | | CLOSE: (326) is inconsistent. % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | Case 2: % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | | (327) ~ (all_117_6 = 0) & function(all_41_3) = all_117_6 % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | | ALPHA: (327) implies: % 78.63/12.19 | | | | | | (328) ~ (all_117_6 = 0) % 78.63/12.19 | | | | | | (329) function(all_41_3) = all_117_6 % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | | GROUND_INST: instantiating (10) with 0, all_117_6, all_41_3, % 78.63/12.19 | | | | | | simplifying with (29), (329) gives: % 78.63/12.19 | | | | | | (330) all_117_6 = 0 % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | | REDUCE: (328), (330) imply: % 78.63/12.19 | | | | | | (331) $false % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | | CLOSE: (331) is inconsistent. % 78.63/12.19 | | | | | | % 78.63/12.19 | | | | | End of split % 78.63/12.19 | | | | | % 78.63/12.19 | | | | End of split % 78.63/12.19 | | | | % 78.63/12.19 | | | End of split % 78.63/12.19 | | | % 78.63/12.19 | | End of split % 78.63/12.19 | | % 78.63/12.19 | End of split % 78.63/12.19 | % 78.63/12.19 End of proof % 78.63/12.19 % 78.63/12.19 Sub-proof #1 shows that the following formulas are inconsistent: % 78.63/12.19 ---------------------------------------------------------------- % 78.63/12.19 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 78.63/12.19 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 78.63/12.19 (2) in(all_41_7, all_102_3) = all_102_2 % 78.63/12.19 (3) in(all_41_7, all_102_3) = 0 % 78.63/12.19 (4) ~ (all_102_2 = 0) % 78.63/12.19 % 78.63/12.19 Begin of proof % 78.63/12.19 | % 78.63/12.19 | GROUND_INST: instantiating (1) with all_102_2, 0, all_102_3, all_41_7, % 78.63/12.19 | simplifying with (2), (3) gives: % 78.63/12.19 | (5) all_102_2 = 0 % 78.63/12.19 | % 78.63/12.19 | REDUCE: (4), (5) imply: % 78.63/12.19 | (6) $false % 78.63/12.19 | % 78.63/12.19 | CLOSE: (6) is inconsistent. % 78.63/12.19 | % 78.63/12.19 End of proof % 78.63/12.19 % SZS output end Proof for theBenchmark % 78.63/12.19 % 78.63/12.19 11544ms %------------------------------------------------------------------------------