%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU215+3 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n003.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 26.27s 4.29s % Output : Proof 89.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU215+3 : TPTP v8.1.2. Released v3.2.0. % 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n003.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 16:06:52 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.69/1.09 Prover 4: Preprocessing ... % 2.69/1.09 Prover 1: Preprocessing ... % 3.18/1.14 Prover 5: Preprocessing ... % 3.18/1.14 Prover 0: Preprocessing ... % 3.18/1.14 Prover 2: Preprocessing ... % 3.18/1.14 Prover 3: Preprocessing ... % 3.18/1.14 Prover 6: Preprocessing ... % 6.80/1.66 Prover 1: Warning: ignoring some quantifiers % 7.00/1.67 Prover 3: Warning: ignoring some quantifiers % 7.00/1.71 Prover 1: Constructing countermodel ... % 7.00/1.71 Prover 3: Constructing countermodel ... % 7.00/1.72 Prover 5: Proving ... % 7.00/1.72 Prover 2: Proving ... % 7.41/1.74 Prover 6: Proving ... % 8.14/1.85 Prover 4: Warning: ignoring some quantifiers % 8.48/1.90 Prover 4: Constructing countermodel ... % 9.81/2.11 Prover 0: Proving ... % 12.18/2.39 Prover 3: gave up % 12.18/2.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.84/2.47 Prover 7: Preprocessing ... % 13.44/2.56 Prover 7: Warning: ignoring some quantifiers % 13.44/2.58 Prover 7: Constructing countermodel ... % 16.46/2.98 Prover 1: gave up % 16.46/3.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.93/3.05 Prover 8: Preprocessing ... % 17.29/3.14 Prover 8: Warning: ignoring some quantifiers % 17.29/3.14 Prover 8: Constructing countermodel ... % 26.27/4.28 Prover 8: gave up % 26.27/4.28 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 26.27/4.29 Prover 0: proved (3648ms) % 26.27/4.29 % 26.27/4.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 26.27/4.29 % 26.27/4.29 Prover 5: stopped % 26.27/4.29 Prover 6: stopped % 26.27/4.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 26.27/4.29 Prover 2: stopped % 26.27/4.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 26.27/4.30 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 26.27/4.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 26.80/4.35 Prover 9: Preprocessing ... % 26.80/4.35 Prover 13: Preprocessing ... % 26.80/4.35 Prover 11: Preprocessing ... % 27.22/4.37 Prover 10: Preprocessing ... % 27.22/4.37 Prover 16: Preprocessing ... % 27.22/4.42 Prover 13: Warning: ignoring some quantifiers % 27.22/4.43 Prover 13: Constructing countermodel ... % 27.22/4.43 Prover 10: Warning: ignoring some quantifiers % 27.22/4.44 Prover 10: Constructing countermodel ... % 27.90/4.45 Prover 16: Warning: ignoring some quantifiers % 27.90/4.46 Prover 16: Constructing countermodel ... % 28.15/4.52 Prover 10: gave up % 28.15/4.53 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 28.44/4.56 Prover 19: Preprocessing ... % 28.44/4.57 Prover 9: Warning: ignoring some quantifiers % 28.44/4.58 Prover 9: Constructing countermodel ... % 28.44/4.58 Prover 9: stopped % 28.44/4.65 Prover 11: Warning: ignoring some quantifiers % 29.09/4.67 Prover 19: Warning: ignoring some quantifiers % 29.09/4.67 Prover 19: Constructing countermodel ... % 29.09/4.67 Prover 11: Constructing countermodel ... % 33.28/5.21 Prover 19: gave up % 67.55/9.74 Prover 13: stopped % 74.30/10.96 Prover 16: stopped % 87.15/14.33 Prover 11: Found proof (size 431) % 87.15/14.33 Prover 11: proved (10037ms) % 87.15/14.33 Prover 4: stopped % 87.15/14.33 Prover 7: stopped % 87.15/14.33 % 87.15/14.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 87.15/14.33 % 87.47/14.38 % SZS output start Proof for theBenchmark % 87.59/14.38 Assumptions after simplification: % 87.59/14.38 --------------------------------- % 87.59/14.39 % 87.59/14.39 (cc1_funct_1) % 87.69/14.43 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (function(v0) = v1) | ~ $i(v0) | ? % 87.69/14.43 [v2: int] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0: $i] : ( ~ (empty(v0) = % 87.69/14.43 0) | ~ $i(v0) | function(v0) = 0) % 87.69/14.43 % 87.69/14.43 (d4_funct_1) % 87.69/14.46 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 87.69/14.46 [v4: $i] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ % 87.69/14.46 $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v5: int] : ? [v6: any] : ? [v7: int] % 87.69/14.46 : (( ~ (v6 = 0) & function(v0) = v6) | ( ~ (v5 = 0) & relation(v0) = v5) | ( % 87.69/14.46 ~ (v5 = 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, v0) = 0) | ( ~ (v6 = % 87.69/14.46 v3) & apply(v0, v2) = v6 & $i(v6))) & ((v6 = v3 & apply(v0, v2) = % 87.69/14.46 v3) | ( ~ (v7 = 0) & in(v4, v0) = v7))))) & ? [v0: $i] : ! [v1: % 87.69/14.46 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 87.69/14.46 (relation_dom(v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ $i(v1) | ~ % 87.69/14.46 $i(v0) | ? [v5: any] : ? [v6: int] : (( ~ (v6 = 0) & function(v1) = v6) | % 87.69/14.46 ( ~ (v5 = 0) & relation(v1) = v5) | (( ~ (v0 = empty_set) | (v5 = % 87.69/14.46 empty_set & apply(v1, v3) = empty_set)) & (v0 = empty_set | ( ~ (v5 % 87.69/14.46 = v0) & apply(v1, v3) = v5 & $i(v5)))))) & ! [v0: $i] : ! [v1: % 87.69/14.46 $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (relation_dom(v0) = % 87.69/14.46 v1) | ~ (apply(v0, v2) = v3) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? % 87.69/14.46 [v4: int] : ? [v5: int] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & % 87.69/14.46 function(v0) = v5) | ( ~ (v4 = 0) & relation(v0) = v4))) & ! [v0: $i] : % 87.69/14.46 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ % 87.69/14.46 (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | % 87.69/14.46 ? [v4: int] : ? [v5: int] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & % 87.69/14.46 function(v0) = v5) | ( ~ (v4 = 0) & relation(v0) = v4))) & ! [v0: $i] : % 87.69/14.46 ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : (( ~ (v1 = % 87.69/14.46 0) & function(v0) = v1) | (relation_dom(v0) = v2 & $i(v2) & ! [v3: % 87.69/14.46 $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ % 87.69/14.46 $i(v4) | ~ $i(v3) | ? [v6: int] : ? [v7: $i] : ? [v8: int] : (( ~ % 87.69/14.46 (v6 = 0) & in(v3, v2) = v6) | (((v8 = 0 & in(v5, v0) = 0) | ( ~ % 87.69/14.46 (v7 = v4) & apply(v0, v3) = v7 & $i(v7))) & ((v7 = v4 & % 87.69/14.46 apply(v0, v3) = v4) | ( ~ (v8 = 0) & in(v5, v0) = v8))))) & ? % 87.69/14.46 [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | % 87.69/14.46 ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : (( ~ (v3 = empty_set) | (v6 = % 87.69/14.46 empty_set & apply(v0, v4) = empty_set)) & (v3 = empty_set | ( ~ % 87.69/14.46 (v6 = v3) & apply(v0, v4) = v6 & $i(v6))))) & ! [v3: $i] : ! % 87.69/14.46 [v4: $i] : (v4 = empty_set | ~ (apply(v0, v3) = v4) | ~ $i(v4) | ~ % 87.69/14.46 $i(v3) | in(v3, v2) = 0) & ! [v3: $i] : ! [v4: $i] : (v4 = empty_set % 87.69/14.46 | ~ (apply(v0, v3) = v4) | ~ $i(v3) | in(v3, v2) = 0)))) & ! [v0: % 87.69/14.46 $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : (( ~ % 87.69/14.46 (v1 = 0) & relation(v0) = v1) | (relation_dom(v0) = v2 & $i(v2) & ! % 87.69/14.46 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v3, v4) = v5) | % 87.69/14.46 ~ $i(v4) | ~ $i(v3) | ? [v6: int] : ? [v7: $i] : ? [v8: int] : (( % 87.69/14.46 ~ (v6 = 0) & in(v3, v2) = v6) | (((v8 = 0 & in(v5, v0) = 0) | ( ~ % 87.69/14.46 (v7 = v4) & apply(v0, v3) = v7 & $i(v7))) & ((v7 = v4 & % 87.69/14.46 apply(v0, v3) = v4) | ( ~ (v8 = 0) & in(v5, v0) = v8))))) & ? % 87.69/14.46 [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | % 87.69/14.46 ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : (( ~ (v3 = empty_set) | (v6 = % 87.69/14.47 empty_set & apply(v0, v4) = empty_set)) & (v3 = empty_set | ( ~ % 87.69/14.47 (v6 = v3) & apply(v0, v4) = v6 & $i(v6))))) & ! [v3: $i] : ! % 87.69/14.47 [v4: $i] : (v4 = empty_set | ~ (apply(v0, v3) = v4) | ~ $i(v4) | ~ % 87.69/14.47 $i(v3) | in(v3, v2) = 0) & ! [v3: $i] : ! [v4: $i] : (v4 = empty_set % 87.69/14.47 | ~ (apply(v0, v3) = v4) | ~ $i(v3) | in(v3, v2) = 0)))) % 87.69/14.47 % 87.69/14.47 (fc1_funct_1) % 87.69/14.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 87.69/14.47 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] : % 87.69/14.47 ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v7 = 0 & % 87.69/14.47 relation(v2) = 0 & function(v2) = 0) | ( ~ (v6 = 0) & function(v1) = v6) % 87.69/14.47 | ( ~ (v5 = 0) & relation(v1) = v5) | ( ~ (v4 = 0) & function(v0) = v4) | % 87.69/14.47 ( ~ (v3 = 0) & relation(v0) = v3))) % 87.69/14.47 % 87.69/14.47 (fc4_relat_1) % 87.69/14.47 relation(empty_set) = 0 & empty(empty_set) = 0 & $i(empty_set) % 87.69/14.47 % 87.69/14.47 (fc5_relat_1) % 87.69/14.48 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 87.69/14.48 [v2: int] : ? [v3: $i] : ? [v4: int] : (( ~ (v4 = 0) & relation_dom(v0) = % 87.69/14.48 v3 & empty(v3) = v4 & $i(v3)) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! % 87.69/14.48 [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 87.69/14.48 int] : ? [v3: int] : ? [v4: int] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v4 = % 87.69/14.48 0) & empty(v1) = v4) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0: % 87.69/14.48 $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ? % 87.69/14.48 [v3: int] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & relation_dom(v0) = v2 % 87.69/14.48 & empty(v2) = v3 & $i(v2)))) % 87.69/14.48 % 87.69/14.48 (fc7_relat_1) % 87.69/14.48 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 87.69/14.48 int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & relation(v1) = 0 % 87.69/14.48 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0: $i] : ( ~ % 87.69/14.48 (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (relation_dom(v0) = v1 & % 87.69/14.48 relation(v1) = 0 & empty(v1) = 0 & $i(v1))) % 87.69/14.48 % 87.69/14.48 (rc1_relat_1) % 87.69/14.48 ? [v0: $i] : (relation(v0) = 0 & empty(v0) = 0 & $i(v0)) % 87.69/14.48 % 87.69/14.48 (rc1_subset_1) % 87.69/14.48 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 87.69/14.48 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v0) = v2 & % 87.69/14.48 element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) & $i(v2))) & ! [v0: $i] : % 87.69/14.48 ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] % 87.69/14.48 : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & % 87.69/14.48 element(v3, v1) = 0 & empty(v3) = v5) | (v2 = 0 & empty(v0) = 0)))) % 87.69/14.48 % 87.69/14.48 (rc1_xboole_0) % 87.69/14.48 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 87.69/14.48 % 87.69/14.48 (rc2_relat_1) % 87.69/14.48 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1 % 87.69/14.48 & $i(v0)) % 87.69/14.48 % 87.69/14.48 (rc2_xboole_0) % 87.69/14.48 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 87.69/14.48 % 87.69/14.49 (t21_funct_1) % 87.69/14.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 87.69/14.54 (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ $i(v3) | ~ $i(v1) | % 87.69/14.54 ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 87.69/14.54 int] : ? [v10: $i] : ? [v11: int] : ? [v12: int] : (( ~ (v6 = 0) & % 87.69/14.54 function(v3) = v6) | ( ~ (v6 = 0) & function(v1) = v6) | ( ~ (v5 = 0) & % 87.69/14.54 relation(v3) = v5) | ( ~ (v5 = 0) & relation(v1) = v5) | (((v12 = 0 & % 87.69/14.54 v11 = 0 & relation_dom(v3) = v10 & in(v4, v2) = 0 & in(v0, v10) = 0 % 87.69/14.54 & $i(v10)) | ( ~ (v9 = 0) & relation_composition(v3, v1) = v7 & % 87.69/14.54 relation_dom(v7) = v8 & in(v0, v8) = v9 & $i(v8) & $i(v7))) & ((v9 = % 87.69/14.54 0 & relation_composition(v3, v1) = v7 & relation_dom(v7) = v8 & % 87.69/14.54 in(v0, v8) = 0 & $i(v8) & $i(v7)) | ( ~ (v12 = 0) & in(v4, v2) = % 87.69/14.54 v12) | ( ~ (v11 = 0) & relation_dom(v3) = v10 & in(v0, v10) = v11 & % 87.69/14.54 $i(v10)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 87.69/14.54 : ! [v4: $i] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) % 87.69/14.54 = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : % 87.69/14.54 ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? % 87.69/14.54 [v12: int] : (( ~ (v6 = 0) & function(v3) = v6) | ( ~ (v6 = 0) & % 87.69/14.54 function(v1) = v6) | ( ~ (v5 = 0) & relation(v3) = v5) | ( ~ (v5 = 0) & % 87.69/14.54 relation(v1) = v5) | (((v12 = 0 & v10 = 0 & relation_dom(v3) = v9 & % 87.69/14.54 apply(v3, v0) = v11 & in(v11, v2) = 0 & in(v0, v9) = 0 & $i(v11) & % 87.69/14.54 $i(v9)) | ( ~ (v8 = 0) & relation_dom(v4) = v7 & in(v0, v7) = v8 & % 87.69/14.54 $i(v7))) & ((v8 = 0 & relation_dom(v4) = v7 & in(v0, v7) = 0 & % 87.69/14.54 $i(v7)) | ( ~ (v12 = 0) & apply(v3, v0) = v11 & in(v11, v2) = v12 & % 87.69/14.54 $i(v11)) | ( ~ (v10 = 0) & relation_dom(v3) = v9 & in(v0, v9) = v10 % 87.69/14.54 & $i(v9)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 87.69/14.54 $i] : ! [v4: $i] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) % 87.69/14.54 | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 87.69/14.54 $i] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ? [v11: $i] : ? [v12: % 87.69/14.54 int] : (( ~ (v6 = 0) & function(v3) = v6) | ( ~ (v6 = 0) & function(v1) = % 87.69/14.54 v6) | ( ~ (v5 = 0) & relation(v3) = v5) | ( ~ (v5 = 0) & relation(v1) = % 87.69/14.54 v5) | (((v12 = 0 & v10 = 0 & apply(v3, v0) = v11 & in(v11, v2) = 0 & % 87.69/14.54 in(v0, v4) = 0 & $i(v11)) | ( ~ (v9 = 0) & relation_composition(v3, % 87.69/14.54 v1) = v7 & relation_dom(v7) = v8 & in(v0, v8) = v9 & $i(v8) & % 87.69/14.54 $i(v7))) & ((v9 = 0 & relation_composition(v3, v1) = v7 & % 87.69/14.54 relation_dom(v7) = v8 & in(v0, v8) = 0 & $i(v8) & $i(v7)) | ( ~ (v12 % 87.69/14.54 = 0) & apply(v3, v0) = v11 & in(v11, v2) = v12 & $i(v11)) | ( ~ % 87.69/14.54 (v10 = 0) & in(v0, v4) = v10))))) & ? [v0: $i] : ! [v1: $i] : ! % 87.69/14.54 [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v1) = v2) | ~ (relation(v3) = 0) | % 87.69/14.54 ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: any] : ? [v6: % 87.69/14.54 $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: % 87.69/14.54 int] : (( ~ (v5 = 0) & function(v1) = v5) | ( ~ (v4 = 0) & relation(v1) = % 87.69/14.54 v4) | ( ~ (v4 = 0) & function(v3) = v4) | (((v11 = 0 & v9 = 0 & % 87.69/14.54 relation_dom(v3) = v8 & apply(v3, v0) = v10 & in(v10, v2) = 0 & % 87.69/14.54 in(v0, v8) = 0 & $i(v10) & $i(v8)) | ( ~ (v7 = 0) & % 87.69/14.54 relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & in(v0, % 87.69/14.54 v6) = v7 & $i(v6) & $i(v5))) & ((v7 = 0 & relation_composition(v3, % 87.69/14.54 v1) = v5 & relation_dom(v5) = v6 & in(v0, v6) = 0 & $i(v6) & % 87.69/14.54 $i(v5)) | ( ~ (v11 = 0) & apply(v3, v0) = v10 & in(v10, v2) = v11 & % 87.69/14.54 $i(v10)) | ( ~ (v9 = 0) & relation_dom(v3) = v8 & in(v0, v8) = v9 & % 87.69/14.54 $i(v8)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 87.69/14.54 : ( ~ (relation_dom(v1) = v2) | ~ (function(v3) = 0) | ~ $i(v3) | ~ $i(v1) % 87.69/14.54 | ~ $i(v0) | ? [v4: int] : ? [v5: any] : ? [v6: $i] : ? [v7: int] : ? % 87.69/14.54 [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: int] : (( ~ (v5 = 0) & % 87.69/14.54 function(v1) = v5) | ( ~ (v4 = 0) & relation(v3) = v4) | ( ~ (v4 = 0) & % 87.69/14.54 relation(v1) = v4) | (((v11 = 0 & v9 = 0 & relation_dom(v3) = v8 & % 87.69/14.54 apply(v3, v0) = v10 & in(v10, v2) = 0 & in(v0, v8) = 0 & $i(v10) & % 87.69/14.54 $i(v8)) | ( ~ (v7 = 0) & relation_composition(v3, v1) = v5 & % 87.69/14.54 relation_dom(v5) = v6 & in(v0, v6) = v7 & $i(v6) & $i(v5))) & ((v7 = % 87.69/14.54 0 & relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & % 87.69/14.54 in(v0, v6) = 0 & $i(v6) & $i(v5)) | ( ~ (v11 = 0) & apply(v3, v0) = % 87.69/14.54 v10 & in(v10, v2) = v11 & $i(v10)) | ( ~ (v9 = 0) & relation_dom(v3) % 87.69/14.54 = v8 & in(v0, v8) = v9 & $i(v8)))))) & ? [v0: $i] : ! [v1: $i] : ( % 87.69/14.54 ~ (relation(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : % 87.69/14.54 (( ~ (v2 = 0) & function(v1) = v2) | (relation_dom(v1) = v3 & $i(v3) & ! % 87.69/14.54 [v4: $i] : ! [v5: $i] : ( ~ (relation_composition(v4, v1) = v5) | ~ % 87.69/14.54 $i(v4) | ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? % 87.69/14.54 [v10: $i] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : (( ~ (v7 = % 87.69/14.54 0) & function(v4) = v7) | ( ~ (v6 = 0) & relation(v4) = v6) | % 87.69/14.54 (((v13 = 0 & v11 = 0 & relation_dom(v4) = v10 & apply(v4, v0) = v12 % 87.69/14.54 & in(v12, v3) = 0 & in(v0, v10) = 0 & $i(v12) & $i(v10)) | ( ~ % 87.69/14.54 (v9 = 0) & relation_dom(v5) = v8 & in(v0, v8) = v9 & $i(v8))) % 87.69/14.54 & ((v9 = 0 & relation_dom(v5) = v8 & in(v0, v8) = 0 & $i(v8)) | ( % 87.69/14.54 ~ (v13 = 0) & apply(v4, v0) = v12 & in(v12, v3) = v13 & % 87.69/14.54 $i(v12)) | ( ~ (v11 = 0) & relation_dom(v4) = v10 & in(v0, % 87.69/14.54 v10) = v11 & $i(v10)))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 87.69/14.54 (relation_dom(v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 87.69/14.54 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : ? [v12: $i] % 87.69/14.54 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 87.69/14.54 relation(v4) = v6) | (((v13 = 0 & v11 = 0 & apply(v4, v0) = v12 & % 87.69/14.54 in(v12, v3) = 0 & in(v0, v5) = 0 & $i(v12)) | ( ~ (v10 = 0) & % 87.69/14.54 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 87.69/14.54 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 87.69/14.54 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 87.69/14.54 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & apply(v4, % 87.69/14.54 v0) = v12 & in(v12, v3) = v13 & $i(v12)) | ( ~ (v11 = 0) & % 87.69/14.54 in(v0, v5) = v11))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 87.69/14.54 (apply(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 87.69/14.54 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] % 87.69/14.54 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 87.69/14.54 relation(v4) = v6) | (((v13 = 0 & v12 = 0 & relation_dom(v4) = v11 % 87.69/14.54 & in(v5, v3) = 0 & in(v0, v11) = 0 & $i(v11)) | ( ~ (v10 = 0) % 87.69/14.54 & relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 87.69/14.54 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 87.69/14.54 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 87.69/14.54 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & in(v5, v3) % 87.69/14.54 = v13) | ( ~ (v12 = 0) & relation_dom(v4) = v11 & in(v0, v11) % 87.69/14.54 = v12 & $i(v11)))))) & ! [v4: $i] : ( ~ (relation(v4) = 0) | % 87.69/14.54 ~ $i(v4) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 87.69/14.54 ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] : (( ~ (v5 = % 87.69/14.54 0) & function(v4) = v5) | (((v12 = 0 & v10 = 0 & % 87.69/14.54 relation_dom(v4) = v9 & apply(v4, v0) = v11 & in(v11, v3) = 0 % 87.69/14.54 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 = 0) & % 87.69/14.54 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 87.69/14.54 in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 87.69/14.54 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 87.69/14.54 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 87.69/14.54 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 87.69/14.54 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9)))))) & ! % 87.69/14.54 [v4: $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: int] : ? [v6: % 87.69/14.54 $i] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? % 87.69/14.54 [v11: $i] : ? [v12: int] : (( ~ (v5 = 0) & relation(v4) = v5) | % 87.69/14.54 (((v12 = 0 & v10 = 0 & relation_dom(v4) = v9 & apply(v4, v0) = v11 & % 87.69/14.54 in(v11, v3) = 0 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 % 87.69/14.54 = 0) & relation_composition(v4, v1) = v6 & relation_dom(v6) % 87.69/14.54 = v7 & in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 87.69/14.54 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 87.69/14.54 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 87.69/14.54 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 87.69/14.54 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9))))))))) & ? % 87.69/14.54 [v0: $i] : ! [v1: $i] : ( ~ (function(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 87.69/14.54 [v2: int] : ? [v3: $i] : (( ~ (v2 = 0) & relation(v1) = v2) | % 87.69/14.54 (relation_dom(v1) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ % 87.69/14.54 (relation_composition(v4, v1) = v5) | ~ $i(v4) | ? [v6: int] : ? % 87.69/14.54 [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: int] % 87.69/14.54 : ? [v12: $i] : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | % 87.69/14.54 ( ~ (v6 = 0) & relation(v4) = v6) | (((v13 = 0 & v11 = 0 & % 87.69/14.54 relation_dom(v4) = v10 & apply(v4, v0) = v12 & in(v12, v3) = 0 % 87.69/14.54 & in(v0, v10) = 0 & $i(v12) & $i(v10)) | ( ~ (v9 = 0) & % 87.69/14.54 relation_dom(v5) = v8 & in(v0, v8) = v9 & $i(v8))) & ((v9 = 0 % 87.69/14.54 & relation_dom(v5) = v8 & in(v0, v8) = 0 & $i(v8)) | ( ~ (v13 % 87.69/14.54 = 0) & apply(v4, v0) = v12 & in(v12, v3) = v13 & $i(v12)) | % 87.69/14.54 ( ~ (v11 = 0) & relation_dom(v4) = v10 & in(v0, v10) = v11 & % 87.69/14.54 $i(v10)))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 87.69/14.54 (relation_dom(v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 87.69/14.54 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : ? [v12: $i] % 87.69/14.54 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 87.69/14.54 relation(v4) = v6) | (((v13 = 0 & v11 = 0 & apply(v4, v0) = v12 & % 87.69/14.54 in(v12, v3) = 0 & in(v0, v5) = 0 & $i(v12)) | ( ~ (v10 = 0) & % 87.69/14.54 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 87.69/14.54 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 87.69/14.54 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 87.69/14.54 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & apply(v4, % 87.69/14.54 v0) = v12 & in(v12, v3) = v13 & $i(v12)) | ( ~ (v11 = 0) & % 87.69/14.54 in(v0, v5) = v11))))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 87.69/14.54 (apply(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ? % 87.69/14.54 [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] % 87.69/14.54 : ? [v13: int] : (( ~ (v7 = 0) & function(v4) = v7) | ( ~ (v6 = 0) & % 87.69/14.54 relation(v4) = v6) | (((v13 = 0 & v12 = 0 & relation_dom(v4) = v11 % 87.69/14.54 & in(v5, v3) = 0 & in(v0, v11) = 0 & $i(v11)) | ( ~ (v10 = 0) % 87.69/14.54 & relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 87.69/14.54 in(v0, v9) = v10 & $i(v9) & $i(v8))) & ((v10 = 0 & % 87.69/14.54 relation_composition(v4, v1) = v8 & relation_dom(v8) = v9 & % 87.69/14.54 in(v0, v9) = 0 & $i(v9) & $i(v8)) | ( ~ (v13 = 0) & in(v5, v3) % 87.69/14.54 = v13) | ( ~ (v12 = 0) & relation_dom(v4) = v11 & in(v0, v11) % 87.69/14.54 = v12 & $i(v11)))))) & ! [v4: $i] : ( ~ (relation(v4) = 0) | % 87.69/14.54 ~ $i(v4) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 87.69/14.54 ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] : (( ~ (v5 = % 87.69/14.54 0) & function(v4) = v5) | (((v12 = 0 & v10 = 0 & % 87.69/14.54 relation_dom(v4) = v9 & apply(v4, v0) = v11 & in(v11, v3) = 0 % 87.69/14.54 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 = 0) & % 87.69/14.54 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 87.69/14.54 in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 87.69/14.54 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 87.69/14.54 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 87.69/14.54 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 87.69/14.54 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9)))))) & ! % 87.69/14.54 [v4: $i] : ( ~ (function(v4) = 0) | ~ $i(v4) | ? [v5: int] : ? [v6: % 87.69/14.54 $i] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? % 87.69/14.54 [v11: $i] : ? [v12: int] : (( ~ (v5 = 0) & relation(v4) = v5) | % 87.69/14.54 (((v12 = 0 & v10 = 0 & relation_dom(v4) = v9 & apply(v4, v0) = v11 & % 87.69/14.54 in(v11, v3) = 0 & in(v0, v9) = 0 & $i(v11) & $i(v9)) | ( ~ (v8 % 87.69/14.54 = 0) & relation_composition(v4, v1) = v6 & relation_dom(v6) % 87.69/14.54 = v7 & in(v0, v7) = v8 & $i(v7) & $i(v6))) & ((v8 = 0 & % 87.69/14.54 relation_composition(v4, v1) = v6 & relation_dom(v6) = v7 & % 87.69/14.54 in(v0, v7) = 0 & $i(v7) & $i(v6)) | ( ~ (v12 = 0) & apply(v4, % 87.69/14.54 v0) = v11 & in(v11, v3) = v12 & $i(v11)) | ( ~ (v10 = 0) & % 87.69/14.54 relation_dom(v4) = v9 & in(v0, v9) = v10 & $i(v9))))))))) % 87.69/14.54 % 87.69/14.54 (t22_funct_1) % 87.69/14.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v2, v0) = % 87.69/14.56 v3) | ~ (relation(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 87.69/14.56 int] : ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ? [v9: % 87.69/14.56 $i] : ? [v10: $i] : ((v10 = v9 & relation_composition(v2, v1) = v6 & % 87.69/14.56 apply(v6, v0) = v9 & apply(v1, v3) = v9 & $i(v9) & $i(v6)) | ( ~ (v8 = % 87.69/14.56 0) & relation_composition(v2, v1) = v6 & relation_dom(v6) = v7 & % 87.69/14.56 in(v0, v7) = v8 & $i(v7) & $i(v6)) | ( ~ (v5 = 0) & function(v2) = v5) | % 87.69/14.56 ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & function(v1) = v4))) & % 87.69/14.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v2, v0) = % 87.69/14.56 v3) | ~ (function(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 87.69/14.56 int] : ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ? [v9: % 87.69/14.56 $i] : ? [v10: $i] : ((v10 = v9 & relation_composition(v2, v1) = v6 & % 87.69/14.56 apply(v6, v0) = v9 & apply(v1, v3) = v9 & $i(v9) & $i(v6)) | ( ~ (v8 = % 87.69/14.56 0) & relation_composition(v2, v1) = v6 & relation_dom(v6) = v7 & % 87.69/14.56 in(v0, v7) = v8 & $i(v7) & $i(v6)) | ( ~ (v5 = 0) & function(v2) = v5) | % 87.69/14.56 ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & relation(v1) = v4))) & % 87.69/14.56 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 87.69/14.56 (relation_composition(v2, v1) = v3) | ~ (relation(v1) = 0) | ~ $i(v2) | ~ % 87.69/14.56 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: $i] : ? [v7: % 87.69/14.56 int] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ((v10 = v8 & apply(v3, % 87.69/14.56 v0) = v8 & apply(v2, v0) = v9 & apply(v1, v9) = v8 & $i(v9) & $i(v8)) % 87.69/14.56 | ( ~ (v7 = 0) & relation_dom(v3) = v6 & in(v0, v6) = v7 & $i(v6)) | ( ~ % 87.69/14.56 (v5 = 0) & function(v2) = v5) | ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ % 87.69/14.56 (v4 = 0) & function(v1) = v4))) & ? [v0: $i] : ! [v1: $i] : ! [v2: % 87.69/14.56 $i] : ! [v3: $i] : ( ~ (relation_composition(v2, v1) = v3) | ~ % 87.69/14.56 (function(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? % 87.69/14.56 [v5: int] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: $i] : ? % 87.69/14.56 [v10: $i] : ((v10 = v8 & apply(v3, v0) = v8 & apply(v2, v0) = v9 & apply(v1, % 87.69/14.56 v9) = v8 & $i(v9) & $i(v8)) | ( ~ (v7 = 0) & relation_dom(v3) = v6 & % 87.69/14.56 in(v0, v6) = v7 & $i(v6)) | ( ~ (v5 = 0) & function(v2) = v5) | ( ~ (v4 % 87.69/14.56 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & relation(v1) = v4))) & ? % 87.69/14.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation(v2) = 0) | ~ % 87.69/14.56 (relation(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? % 87.69/14.56 [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 87.69/14.56 $i] : ((v9 = v7 & relation_composition(v2, v1) = v4 & apply(v4, v0) = v7 & % 87.69/14.56 apply(v2, v0) = v8 & apply(v1, v8) = v7 & $i(v8) & $i(v7) & $i(v4)) | ( % 87.69/14.56 ~ (v6 = 0) & relation_composition(v2, v1) = v4 & relation_dom(v4) = v5 & % 87.69/14.56 in(v0, v5) = v6 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & function(v2) = v3) | % 87.69/14.56 ( ~ (v3 = 0) & function(v1) = v3))) & ? [v0: $i] : ! [v1: $i] : ! [v2: % 87.69/14.56 $i] : ( ~ (relation(v2) = 0) | ~ (function(v1) = 0) | ~ $i(v2) | ~ $i(v1) % 87.69/14.56 | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? % 87.69/14.56 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((v9 = v7 & relation_composition(v2, % 87.69/14.56 v1) = v4 & apply(v4, v0) = v7 & apply(v2, v0) = v8 & apply(v1, v8) = % 87.69/14.56 v7 & $i(v8) & $i(v7) & $i(v4)) | ( ~ (v6 = 0) & relation_composition(v2, % 87.69/14.56 v1) = v4 & relation_dom(v4) = v5 & in(v0, v5) = v6 & $i(v5) & $i(v4)) % 87.69/14.56 | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v2) = v3))) % 87.69/14.56 & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation(v1) = 0) | ~ % 87.69/14.57 (function(v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? % 87.69/14.57 [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 87.69/14.57 $i] : ((v9 = v7 & relation_composition(v2, v1) = v4 & apply(v4, v0) = v7 & % 87.69/14.57 apply(v2, v0) = v8 & apply(v1, v8) = v7 & $i(v8) & $i(v7) & $i(v4)) | ( % 87.69/14.57 ~ (v6 = 0) & relation_composition(v2, v1) = v4 & relation_dom(v4) = v5 & % 87.69/14.57 in(v0, v5) = v6 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & relation(v2) = v3) | % 87.69/14.57 ( ~ (v3 = 0) & function(v1) = v3))) & ? [v0: $i] : ! [v1: $i] : ! [v2: % 87.69/14.57 $i] : ( ~ (function(v2) = 0) | ~ (function(v1) = 0) | ~ $i(v2) | ~ $i(v1) % 87.69/14.57 | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? % 87.69/14.57 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((v9 = v7 & relation_composition(v2, % 87.69/14.57 v1) = v4 & apply(v4, v0) = v7 & apply(v2, v0) = v8 & apply(v1, v8) = % 87.69/14.57 v7 & $i(v8) & $i(v7) & $i(v4)) | ( ~ (v6 = 0) & relation_composition(v2, % 87.69/14.57 v1) = v4 & relation_dom(v4) = v5 & in(v0, v5) = v6 & $i(v5) & $i(v4)) % 87.69/14.57 | ( ~ (v3 = 0) & relation(v2) = v3) | ( ~ (v3 = 0) & relation(v1) = v3))) % 87.69/14.57 % 87.69/14.57 (t23_funct_1) % 87.69/14.57 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 87.69/14.57 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & relation_composition(v1, % 87.69/14.57 v4) = v5 & relation_dom(v1) = v2 & apply(v5, v0) = v6 & apply(v4, v3) = v7 % 87.69/14.57 & apply(v1, v0) = v3 & relation(v4) = 0 & relation(v1) = 0 & function(v4) = % 87.69/14.57 0 & function(v1) = 0 & in(v0, v2) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 87.69/14.57 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 87.69/14.57 % 87.69/14.57 (t6_boole) % 87.69/14.57 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 87.69/14.57 $i(v0)) % 87.69/14.57 % 87.69/14.57 (t7_boole) % 87.69/14.57 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 87.69/14.57 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2)) % 87.69/14.57 % 87.69/14.57 (t8_boole) % 87.69/14.57 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 87.69/14.57 | ~ $i(v1) | ~ $i(v0)) % 87.69/14.57 % 87.69/14.57 (function-axioms) % 87.69/14.57 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 87.69/14.57 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 87.69/14.57 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 87.69/14.57 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! % 87.69/14.58 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 87.69/14.58 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 87.69/14.58 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 87.69/14.58 ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 87.69/14.58 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) % 87.69/14.58 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 87.69/14.58 : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 87.69/14.58 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 87.69/14.58 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = % 87.69/14.58 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 87.69/14.58 (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: % 87.69/14.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 87.69/14.58 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = % 87.69/14.58 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 87.69/14.58 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 87.69/14.58 : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = % 87.69/14.58 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 87.69/14.58 $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: % 87.69/14.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 87.69/14.58 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] % 87.69/14.58 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | % 87.69/14.58 ~ (empty(v2) = v0)) % 87.69/14.58 % 87.69/14.58 Further assumptions not needed in the proof: % 87.69/14.58 -------------------------------------------- % 87.69/14.58 antisymmetry_r2_hidden, cc1_relat_1, commutativity_k2_tarski, d5_tarski, % 87.69/14.58 dt_k5_relat_1, existence_m1_subset_1, fc10_relat_1, fc12_relat_1, fc1_subset_1, % 87.69/14.58 fc1_xboole_0, fc1_zfmisc_1, fc2_subset_1, fc3_subset_1, fc9_relat_1, % 87.69/14.58 rc1_funct_1, rc2_subset_1, rc3_relat_1, reflexivity_r1_tarski, t1_subset, % 87.69/14.58 t2_subset, t3_subset, t4_subset, t5_subset % 87.69/14.58 % 87.69/14.58 Those formulas are unsatisfiable: % 87.69/14.58 --------------------------------- % 87.69/14.58 % 87.69/14.58 Begin of proof % 87.69/14.58 | % 87.69/14.58 | ALPHA: (cc1_funct_1) implies: % 87.69/14.58 | (1) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | function(v0) = 0) % 87.69/14.58 | % 87.69/14.58 | ALPHA: (d4_funct_1) implies: % 87.69/14.58 | (2) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? % 87.69/14.58 | [v2: $i] : (( ~ (v1 = 0) & relation(v0) = v1) | (relation_dom(v0) = % 87.69/14.58 | v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 87.69/14.58 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: % 87.69/14.58 | int] : ? [v7: $i] : ? [v8: int] : (( ~ (v6 = 0) & in(v3, % 87.69/14.58 | v2) = v6) | (((v8 = 0 & in(v5, v0) = 0) | ( ~ (v7 = v4) & % 87.69/14.58 | apply(v0, v3) = v7 & $i(v7))) & ((v7 = v4 & apply(v0, % 87.69/14.58 | v3) = v4) | ( ~ (v8 = 0) & in(v5, v0) = v8))))) & ? % 87.69/14.58 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v2) % 87.69/14.58 | = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : (( ~ (v3 = % 87.69/14.58 | empty_set) | (v6 = empty_set & apply(v0, v4) = % 87.69/14.58 | empty_set)) & (v3 = empty_set | ( ~ (v6 = v3) & apply(v0, % 87.69/14.58 | v4) = v6 & $i(v6))))) & ! [v3: $i] : ! [v4: $i] : (v4 % 87.69/14.58 | = empty_set | ~ (apply(v0, v3) = v4) | ~ $i(v4) | ~ $i(v3) | % 87.69/14.58 | in(v3, v2) = 0) & ! [v3: $i] : ! [v4: $i] : (v4 = empty_set | % 87.69/14.58 | ~ (apply(v0, v3) = v4) | ~ $i(v3) | in(v3, v2) = 0)))) % 87.69/14.59 | (3) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? % 87.69/14.59 | [v2: $i] : (( ~ (v1 = 0) & function(v0) = v1) | (relation_dom(v0) = % 87.69/14.59 | v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 87.69/14.59 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: % 87.69/14.59 | int] : ? [v7: $i] : ? [v8: int] : (( ~ (v6 = 0) & in(v3, % 87.69/14.59 | v2) = v6) | (((v8 = 0 & in(v5, v0) = 0) | ( ~ (v7 = v4) & % 87.69/14.59 | apply(v0, v3) = v7 & $i(v7))) & ((v7 = v4 & apply(v0, % 87.69/14.59 | v3) = v4) | ( ~ (v8 = 0) & in(v5, v0) = v8))))) & ? % 87.69/14.59 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v2) % 87.69/14.59 | = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : (( ~ (v3 = % 87.69/14.59 | empty_set) | (v6 = empty_set & apply(v0, v4) = % 87.69/14.59 | empty_set)) & (v3 = empty_set | ( ~ (v6 = v3) & apply(v0, % 87.69/14.59 | v4) = v6 & $i(v6))))) & ! [v3: $i] : ! [v4: $i] : (v4 % 87.69/14.59 | = empty_set | ~ (apply(v0, v3) = v4) | ~ $i(v4) | ~ $i(v3) | % 87.69/14.59 | in(v3, v2) = 0) & ! [v3: $i] : ! [v4: $i] : (v4 = empty_set | % 87.69/14.59 | ~ (apply(v0, v3) = v4) | ~ $i(v3) | in(v3, v2) = 0)))) % 87.69/14.59 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set % 87.69/14.59 | | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v2) | % 87.69/14.59 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ((v4 = 0 & in(v2, v1) = 0) | % 87.69/14.59 | ( ~ (v5 = 0) & function(v0) = v5) | ( ~ (v4 = 0) & relation(v0) = % 87.69/14.59 | v4))) % 87.69/14.59 | % 87.69/14.59 | ALPHA: (fc4_relat_1) implies: % 87.69/14.59 | (5) empty(empty_set) = 0 % 87.69/14.59 | (6) relation(empty_set) = 0 % 87.69/14.59 | % 87.69/14.59 | ALPHA: (fc5_relat_1) implies: % 87.69/14.59 | (7) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? % 87.69/14.59 | [v2: $i] : ? [v3: int] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & % 87.69/14.59 | relation_dom(v0) = v2 & empty(v2) = v3 & $i(v2)))) % 87.69/14.59 | % 87.69/14.59 | ALPHA: (fc7_relat_1) implies: % 88.25/14.59 | (8) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 88.25/14.59 | (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0 & $i(v1))) % 88.25/14.60 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 88.25/14.60 | ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & % 88.25/14.60 | relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = % 88.25/14.60 | v2))) % 88.25/14.60 | % 88.25/14.60 | ALPHA: (rc1_subset_1) implies: % 88.25/14.60 | (10) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) % 88.25/14.60 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 88.25/14.60 | powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) % 88.25/14.60 | & $i(v2))) % 88.25/14.60 | % 88.25/14.60 | ALPHA: (t21_funct_1) implies: % 88.25/14.60 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 88.25/14.60 | ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ $i(v3) | ~ % 88.25/14.60 | $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: $i] : ? % 88.25/14.60 | [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: int] : ? [v12: % 88.25/14.60 | int] : (( ~ (v6 = 0) & function(v3) = v6) | ( ~ (v6 = 0) & % 88.25/14.60 | function(v1) = v6) | ( ~ (v5 = 0) & relation(v3) = v5) | ( ~ (v5 % 88.25/14.60 | = 0) & relation(v1) = v5) | (((v12 = 0 & v11 = 0 & % 88.25/14.60 | relation_dom(v3) = v10 & in(v4, v2) = 0 & in(v0, v10) = 0 & % 88.25/14.60 | $i(v10)) | ( ~ (v9 = 0) & relation_composition(v3, v1) = v7 % 88.25/14.60 | & relation_dom(v7) = v8 & in(v0, v8) = v9 & $i(v8) & % 88.25/14.60 | $i(v7))) & ((v9 = 0 & relation_composition(v3, v1) = v7 & % 88.25/14.60 | relation_dom(v7) = v8 & in(v0, v8) = 0 & $i(v8) & $i(v7)) | % 88.25/14.60 | ( ~ (v12 = 0) & in(v4, v2) = v12) | ( ~ (v11 = 0) & % 88.25/14.60 | relation_dom(v3) = v10 & in(v0, v10) = v11 & $i(v10)))))) % 88.25/14.60 | % 88.25/14.60 | ALPHA: (t22_funct_1) implies: % 88.25/14.60 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v2, % 88.25/14.60 | v0) = v3) | ~ (function(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 88.25/14.60 | $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: $i] : ? [v7: $i] : % 88.25/14.60 | ? [v8: int] : ? [v9: $i] : ? [v10: $i] : ((v10 = v9 & % 88.25/14.60 | relation_composition(v2, v1) = v6 & apply(v6, v0) = v9 & % 88.25/14.60 | apply(v1, v3) = v9 & $i(v9) & $i(v6)) | ( ~ (v8 = 0) & % 88.25/14.60 | relation_composition(v2, v1) = v6 & relation_dom(v6) = v7 & % 88.25/14.60 | in(v0, v7) = v8 & $i(v7) & $i(v6)) | ( ~ (v5 = 0) & function(v2) % 88.25/14.60 | = v5) | ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & % 88.25/14.60 | relation(v1) = v4))) % 88.25/14.61 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v2, % 88.25/14.61 | v0) = v3) | ~ (relation(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 88.25/14.61 | $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: $i] : ? [v7: $i] : % 88.25/14.61 | ? [v8: int] : ? [v9: $i] : ? [v10: $i] : ((v10 = v9 & % 88.25/14.61 | relation_composition(v2, v1) = v6 & apply(v6, v0) = v9 & % 88.25/14.61 | apply(v1, v3) = v9 & $i(v9) & $i(v6)) | ( ~ (v8 = 0) & % 88.25/14.61 | relation_composition(v2, v1) = v6 & relation_dom(v6) = v7 & % 88.25/14.61 | in(v0, v7) = v8 & $i(v7) & $i(v6)) | ( ~ (v5 = 0) & function(v2) % 88.25/14.61 | = v5) | ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & % 88.25/14.61 | function(v1) = v4))) % 88.25/14.61 | % 88.25/14.61 | ALPHA: (t6_boole) implies: % 88.25/14.61 | (14) $i(empty_set) % 88.25/14.61 | (15) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 88.25/14.61 | % 88.25/14.61 | ALPHA: (function-axioms) implies: % 88.25/14.61 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 88.25/14.61 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 88.25/14.61 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 88.25/14.61 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 88.25/14.61 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 88.25/14.61 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 88.25/14.61 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 88.25/14.61 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 88.25/14.61 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 88.25/14.61 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 88.25/14.61 | v0)) % 88.25/14.61 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.25/14.61 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 88.25/14.61 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 88.25/14.61 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, % 88.25/14.61 | v2) = v0)) % 88.25/14.61 | % 88.25/14.61 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_33_0 gives: % 88.25/14.61 | (23) empty(all_33_0) = 0 & $i(all_33_0) % 88.25/14.61 | % 88.25/14.61 | ALPHA: (23) implies: % 88.25/14.61 | (24) $i(all_33_0) % 88.25/14.61 | (25) empty(all_33_0) = 0 % 88.25/14.61 | % 88.25/14.61 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_35_0 gives: % 88.25/14.61 | (26) relation(all_35_0) = 0 & empty(all_35_0) = 0 & $i(all_35_0) % 88.25/14.61 | % 88.25/14.61 | ALPHA: (26) implies: % 88.25/14.61 | (27) $i(all_35_0) % 88.25/14.61 | (28) empty(all_35_0) = 0 % 88.25/14.61 | (29) relation(all_35_0) = 0 % 88.25/14.61 | % 88.25/14.61 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_38_0, all_38_1 % 88.25/14.61 | gives: % 88.25/14.61 | (30) ~ (all_38_0 = 0) & empty(all_38_1) = all_38_0 & $i(all_38_1) % 88.25/14.61 | % 88.25/14.61 | ALPHA: (30) implies: % 88.25/14.61 | (31) ~ (all_38_0 = 0) % 88.25/14.61 | (32) $i(all_38_1) % 88.25/14.61 | (33) empty(all_38_1) = all_38_0 % 88.25/14.61 | % 88.25/14.61 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_44_0, all_44_1 % 88.25/14.61 | gives: % 88.25/14.61 | (34) ~ (all_44_0 = 0) & relation(all_44_1) = 0 & empty(all_44_1) = % 88.25/14.61 | all_44_0 & $i(all_44_1) % 88.25/14.61 | % 88.25/14.61 | ALPHA: (34) implies: % 88.25/14.61 | (35) ~ (all_44_0 = 0) % 88.25/14.61 | (36) $i(all_44_1) % 88.25/14.61 | (37) empty(all_44_1) = all_44_0 % 88.25/14.61 | (38) relation(all_44_1) = 0 % 88.25/14.61 | % 88.25/14.61 | DELTA: instantiating (t23_funct_1) with fresh symbols all_48_0, all_48_1, % 88.25/14.61 | all_48_2, all_48_3, all_48_4, all_48_5, all_48_6, all_48_7 gives: % 88.25/14.61 | (39) ~ (all_48_0 = all_48_1) & relation_composition(all_48_6, all_48_3) = % 88.25/14.61 | all_48_2 & relation_dom(all_48_6) = all_48_5 & apply(all_48_2, % 88.25/14.61 | all_48_7) = all_48_1 & apply(all_48_3, all_48_4) = all_48_0 & % 88.25/14.61 | apply(all_48_6, all_48_7) = all_48_4 & relation(all_48_3) = 0 & % 88.25/14.61 | relation(all_48_6) = 0 & function(all_48_3) = 0 & function(all_48_6) = % 88.25/14.61 | 0 & in(all_48_7, all_48_5) = 0 & $i(all_48_0) & $i(all_48_1) & % 88.25/14.61 | $i(all_48_2) & $i(all_48_3) & $i(all_48_4) & $i(all_48_5) & % 88.25/14.61 | $i(all_48_6) & $i(all_48_7) % 88.25/14.61 | % 88.25/14.61 | ALPHA: (39) implies: % 88.25/14.61 | (40) ~ (all_48_0 = all_48_1) % 88.25/14.62 | (41) $i(all_48_7) % 88.25/14.62 | (42) $i(all_48_6) % 88.25/14.62 | (43) $i(all_48_5) % 88.25/14.62 | (44) $i(all_48_4) % 88.25/14.62 | (45) $i(all_48_3) % 88.25/14.62 | (46) in(all_48_7, all_48_5) = 0 % 88.25/14.62 | (47) function(all_48_6) = 0 % 88.25/14.62 | (48) function(all_48_3) = 0 % 88.25/14.62 | (49) relation(all_48_6) = 0 % 88.25/14.62 | (50) relation(all_48_3) = 0 % 88.25/14.62 | (51) apply(all_48_6, all_48_7) = all_48_4 % 88.25/14.62 | (52) apply(all_48_3, all_48_4) = all_48_0 % 88.25/14.62 | (53) apply(all_48_2, all_48_7) = all_48_1 % 88.25/14.62 | (54) relation_dom(all_48_6) = all_48_5 % 88.25/14.62 | (55) relation_composition(all_48_6, all_48_3) = all_48_2 % 88.25/14.62 | % 88.25/14.62 | GROUND_INST: instantiating (t7_boole) with all_48_7, all_48_5, simplifying % 88.25/14.62 | with (41), (43), (46) gives: % 88.25/14.62 | (56) ? [v0: int] : ( ~ (v0 = 0) & empty(all_48_5) = v0) % 88.25/14.62 | % 88.25/14.62 | GROUND_INST: instantiating (8) with empty_set, simplifying with (5), (14) % 88.25/14.62 | gives: % 88.25/14.62 | (57) ? [v0: $i] : (relation_dom(empty_set) = v0 & relation(v0) = 0 & % 88.25/14.62 | empty(v0) = 0 & $i(v0)) % 88.25/14.62 | % 88.25/14.62 | GROUND_INST: instantiating (1) with all_33_0, simplifying with (24), (25) % 88.25/14.62 | gives: % 88.25/14.62 | (58) function(all_33_0) = 0 % 88.25/14.62 | % 88.25/14.62 | GROUND_INST: instantiating (8) with all_33_0, simplifying with (24), (25) % 88.25/14.62 | gives: % 88.25/14.62 | (59) ? [v0: $i] : (relation_dom(all_33_0) = v0 & relation(v0) = 0 & % 88.25/14.62 | empty(v0) = 0 & $i(v0)) % 88.25/14.62 | % 88.25/14.62 | GROUND_INST: instantiating (t8_boole) with all_33_0, all_35_0, simplifying % 88.25/14.62 | with (24), (25), (27), (28) gives: % 88.25/14.62 | (60) all_35_0 = all_33_0 % 88.25/14.62 | % 88.25/14.62 | GROUND_INST: instantiating (15) with all_35_0, simplifying with (27), (28) % 88.25/14.62 | gives: % 88.25/14.62 | (61) all_35_0 = empty_set % 88.25/14.62 | % 88.25/14.62 | GROUND_INST: instantiating (8) with all_35_0, simplifying with (27), (28) % 88.25/14.62 | gives: % 88.25/14.62 | (62) ? [v0: $i] : (relation_dom(all_35_0) = v0 & relation(v0) = 0 & % 88.25/14.62 | empty(v0) = 0 & $i(v0)) % 88.25/14.62 | % 88.25/14.62 | GROUND_INST: instantiating (10) with all_38_1, all_38_0, simplifying with % 88.25/14.62 | (32), (33) gives: % 88.25/14.62 | (63) all_38_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 88.25/14.62 | & powerset(all_38_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2 & % 88.25/14.62 | $i(v1) & $i(v0)) % 88.25/14.62 | % 88.25/14.62 | GROUND_INST: instantiating (2) with all_48_6, simplifying with (42), (47) % 88.25/14.62 | gives: % 88.25/14.63 | (64) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & relation(all_48_6) = v0) % 88.25/14.63 | | (relation_dom(all_48_6) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 88.25/14.63 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 88.25/14.63 | $i(v2) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (( ~ (v5 = % 88.25/14.63 | 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, all_48_6) = 0) % 88.25/14.63 | | ( ~ (v6 = v3) & apply(all_48_6, v2) = v6 & $i(v6))) & % 88.25/14.63 | ((v6 = v3 & apply(all_48_6, v2) = v3) | ( ~ (v7 = 0) & % 88.25/14.63 | in(v4, all_48_6) = v7))))) & ? [v2: $i] : ! [v3: $i] : % 88.25/14.63 | ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 88.25/14.63 | $i(v2) | ? [v5: $i] : (( ~ (v2 = empty_set) | (v5 = empty_set & % 88.25/14.63 | apply(all_48_6, v3) = empty_set)) & (v2 = empty_set | ( ~ % 88.25/14.63 | (v5 = v2) & apply(all_48_6, v3) = v5 & $i(v5))))) & ! % 88.25/14.63 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_48_6, v2) % 88.25/14.63 | = v3) | ~ $i(v3) | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 88.25/14.63 | : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_48_6, v2) = v3) | % 88.25/14.63 | ~ $i(v2) | in(v2, v1) = 0))) % 88.25/14.63 | % 88.25/14.63 | GROUND_INST: instantiating (2) with all_48_3, simplifying with (45), (48) % 88.25/14.63 | gives: % 88.25/14.63 | (65) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & relation(all_48_3) = v0) % 88.25/14.63 | | (relation_dom(all_48_3) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 88.25/14.63 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 88.25/14.63 | $i(v2) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (( ~ (v5 = % 88.25/14.63 | 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, all_48_3) = 0) % 88.25/14.63 | | ( ~ (v6 = v3) & apply(all_48_3, v2) = v6 & $i(v6))) & % 88.25/14.63 | ((v6 = v3 & apply(all_48_3, v2) = v3) | ( ~ (v7 = 0) & % 88.25/14.63 | in(v4, all_48_3) = v7))))) & ? [v2: $i] : ! [v3: $i] : % 88.25/14.63 | ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 88.25/14.63 | $i(v2) | ? [v5: $i] : (( ~ (v2 = empty_set) | (v5 = empty_set & % 88.25/14.63 | apply(all_48_3, v3) = empty_set)) & (v2 = empty_set | ( ~ % 88.25/14.63 | (v5 = v2) & apply(all_48_3, v3) = v5 & $i(v5))))) & ! % 88.25/14.63 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_48_3, v2) % 88.25/14.63 | = v3) | ~ $i(v3) | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 88.25/14.63 | : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_48_3, v2) = v3) | % 88.25/14.63 | ~ $i(v2) | in(v2, v1) = 0))) % 88.25/14.63 | % 88.25/14.63 | GROUND_INST: instantiating (3) with empty_set, simplifying with (6), (14) % 88.25/14.63 | gives: % 88.25/14.63 | (66) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & function(empty_set) = v0) % 88.25/14.63 | | (relation_dom(empty_set) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 88.25/14.63 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 88.25/14.63 | $i(v2) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (( ~ (v5 = % 88.25/14.63 | 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, empty_set) = 0) % 88.25/14.63 | | ( ~ (v6 = v3) & apply(empty_set, v2) = v6 & $i(v6))) & % 88.25/14.63 | ((v6 = v3 & apply(empty_set, v2) = v3) | ( ~ (v7 = 0) & % 88.25/14.63 | in(v4, empty_set) = v7))))) & ? [v2: $i] : ! [v3: $i] % 88.25/14.63 | : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 88.25/14.63 | $i(v2) | ? [v5: $i] : (( ~ (v2 = empty_set) | (v5 = empty_set & % 88.25/14.63 | apply(empty_set, v3) = empty_set)) & (v2 = empty_set | ( ~ % 88.25/14.63 | (v5 = v2) & apply(empty_set, v3) = v5 & $i(v5))))) & ! % 88.25/14.63 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(empty_set, % 88.25/14.63 | v2) = v3) | ~ $i(v3) | ~ $i(v2) | in(v2, v1) = 0) & ! % 88.25/14.63 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(empty_set, % 88.25/14.63 | v2) = v3) | ~ $i(v2) | in(v2, v1) = 0))) % 88.25/14.63 | % 88.25/14.63 | GROUND_INST: instantiating (3) with all_35_0, simplifying with (27), (29) % 88.25/14.63 | gives: % 88.25/14.63 | (67) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & function(all_35_0) = v0) % 88.25/14.63 | | (relation_dom(all_35_0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 88.25/14.63 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 88.25/14.63 | $i(v2) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (( ~ (v5 = % 88.25/14.63 | 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, all_35_0) = 0) % 88.25/14.63 | | ( ~ (v6 = v3) & apply(all_35_0, v2) = v6 & $i(v6))) & % 88.25/14.63 | ((v6 = v3 & apply(all_35_0, v2) = v3) | ( ~ (v7 = 0) & % 88.25/14.63 | in(v4, all_35_0) = v7))))) & ? [v2: $i] : ! [v3: $i] : % 88.25/14.63 | ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 88.25/14.63 | $i(v2) | ? [v5: $i] : (( ~ (v2 = empty_set) | (v5 = empty_set & % 88.25/14.63 | apply(all_35_0, v3) = empty_set)) & (v2 = empty_set | ( ~ % 88.25/14.63 | (v5 = v2) & apply(all_35_0, v3) = v5 & $i(v5))))) & ! % 88.25/14.64 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_35_0, v2) % 88.25/14.64 | = v3) | ~ $i(v3) | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 88.25/14.64 | : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_35_0, v2) = v3) | % 88.25/14.64 | ~ $i(v2) | in(v2, v1) = 0))) % 88.25/14.64 | % 88.25/14.64 | GROUND_INST: instantiating (7) with all_44_1, simplifying with (36), (38) % 88.25/14.64 | gives: % 88.25/14.64 | (68) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v0 = 0 & empty(all_44_1) % 88.25/14.64 | = 0) | ( ~ (v2 = 0) & relation_dom(all_44_1) = v1 & empty(v1) = v2 % 88.25/14.64 | & $i(v1))) % 88.25/14.64 | % 88.25/14.64 | GROUND_INST: instantiating (7) with all_48_6, simplifying with (42), (49) % 88.25/14.64 | gives: % 88.25/14.64 | (69) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v0 = 0 & empty(all_48_6) % 88.25/14.64 | = 0) | ( ~ (v2 = 0) & relation_dom(all_48_6) = v1 & empty(v1) = v2 % 88.25/14.64 | & $i(v1))) % 88.25/14.64 | % 88.25/14.64 | GROUND_INST: instantiating (3) with all_48_6, simplifying with (42), (49) % 88.25/14.64 | gives: % 88.25/14.64 | (70) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & function(all_48_6) = v0) % 88.25/14.64 | | (relation_dom(all_48_6) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 88.25/14.64 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 88.25/14.64 | $i(v2) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (( ~ (v5 = % 88.25/14.64 | 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, all_48_6) = 0) % 88.25/14.64 | | ( ~ (v6 = v3) & apply(all_48_6, v2) = v6 & $i(v6))) & % 88.25/14.64 | ((v6 = v3 & apply(all_48_6, v2) = v3) | ( ~ (v7 = 0) & % 88.25/14.64 | in(v4, all_48_6) = v7))))) & ? [v2: $i] : ! [v3: $i] : % 88.25/14.64 | ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 88.25/14.64 | $i(v2) | ? [v5: $i] : (( ~ (v2 = empty_set) | (v5 = empty_set & % 88.25/14.64 | apply(all_48_6, v3) = empty_set)) & (v2 = empty_set | ( ~ % 88.25/14.64 | (v5 = v2) & apply(all_48_6, v3) = v5 & $i(v5))))) & ! % 88.25/14.64 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_48_6, v2) % 88.25/14.64 | = v3) | ~ $i(v3) | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 88.25/14.64 | : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_48_6, v2) = v3) | % 88.25/14.64 | ~ $i(v2) | in(v2, v1) = 0))) % 88.25/14.64 | % 88.25/14.64 | GROUND_INST: instantiating (3) with all_48_3, simplifying with (45), (50) % 88.25/14.64 | gives: % 88.25/14.64 | (71) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & function(all_48_3) = v0) % 88.25/14.64 | | (relation_dom(all_48_3) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 88.25/14.64 | : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 88.25/14.64 | $i(v2) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : (( ~ (v5 = % 88.25/14.64 | 0) & in(v2, v1) = v5) | (((v7 = 0 & in(v4, all_48_3) = 0) % 88.25/14.64 | | ( ~ (v6 = v3) & apply(all_48_3, v2) = v6 & $i(v6))) & % 88.25/14.64 | ((v6 = v3 & apply(all_48_3, v2) = v3) | ( ~ (v7 = 0) & % 88.25/14.64 | in(v4, all_48_3) = v7))))) & ? [v2: $i] : ! [v3: $i] : % 88.25/14.64 | ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 88.25/14.64 | $i(v2) | ? [v5: $i] : (( ~ (v2 = empty_set) | (v5 = empty_set & % 88.25/14.64 | apply(all_48_3, v3) = empty_set)) & (v2 = empty_set | ( ~ % 88.25/14.64 | (v5 = v2) & apply(all_48_3, v3) = v5 & $i(v5))))) & ! % 88.25/14.64 | [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_48_3, v2) % 88.25/14.64 | = v3) | ~ $i(v3) | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 88.25/14.64 | : ! [v3: $i] : (v3 = empty_set | ~ (apply(all_48_3, v2) = v3) | % 88.25/14.64 | ~ $i(v2) | in(v2, v1) = 0))) % 88.25/14.64 | % 88.25/14.64 | GROUND_INST: instantiating (13) with all_48_7, all_48_3, all_48_6, all_48_4, % 88.25/14.64 | simplifying with (41), (42), (45), (50), (51) gives: % 88.25/14.64 | (72) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] % 88.25/14.64 | : ? [v5: $i] : ? [v6: $i] : ((v6 = v5 & % 88.25/14.64 | relation_composition(all_48_6, all_48_3) = v2 & apply(v2, % 88.25/14.64 | all_48_7) = v5 & apply(all_48_3, all_48_4) = v5 & $i(v5) & % 88.25/14.64 | $i(v2)) | ( ~ (v4 = 0) & relation_composition(all_48_6, all_48_3) % 88.25/14.64 | = v2 & relation_dom(v2) = v3 & in(all_48_7, v3) = v4 & $i(v3) & % 88.25/14.64 | $i(v2)) | ( ~ (v1 = 0) & function(all_48_6) = v1) | ( ~ (v0 = 0) & % 88.25/14.64 | relation(all_48_6) = v0) | ( ~ (v0 = 0) & function(all_48_3) = % 88.25/14.64 | v0)) % 88.25/14.64 | % 88.25/14.64 | GROUND_INST: instantiating (12) with all_48_7, all_48_3, all_48_6, all_48_4, % 88.25/14.64 | simplifying with (41), (42), (45), (48), (51) gives: % 88.25/14.64 | (73) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] % 88.25/14.64 | : ? [v5: $i] : ? [v6: $i] : ((v6 = v5 & % 88.25/14.64 | relation_composition(all_48_6, all_48_3) = v2 & apply(v2, % 88.25/14.64 | all_48_7) = v5 & apply(all_48_3, all_48_4) = v5 & $i(v5) & % 88.25/14.64 | $i(v2)) | ( ~ (v4 = 0) & relation_composition(all_48_6, all_48_3) % 88.25/14.64 | = v2 & relation_dom(v2) = v3 & in(all_48_7, v3) = v4 & $i(v3) & % 88.25/14.64 | $i(v2)) | ( ~ (v1 = 0) & function(all_48_6) = v1) | ( ~ (v0 = 0) & % 88.25/14.64 | relation(all_48_3) = v0) | ( ~ (v0 = 0) & relation(all_48_6) = % 88.25/14.64 | v0)) % 88.25/14.64 | % 88.25/14.64 | GROUND_INST: instantiating (9) with all_48_6, all_48_5, simplifying with (42), % 88.25/14.64 | (54) gives: % 88.25/14.65 | (74) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0 & % 88.25/14.65 | relation(all_48_5) = 0 & empty(all_48_5) = 0) | ( ~ (v0 = 0) & % 88.25/14.65 | empty(all_48_6) = v0)) % 88.25/14.65 | % 88.25/14.65 | GROUND_INST: instantiating (fc1_funct_1) with all_48_6, all_48_3, all_48_2, % 88.25/14.65 | simplifying with (42), (45), (55) gives: % 88.25/14.65 | (75) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: % 88.25/14.65 | int] : ? [v5: int] : ((v5 = 0 & v4 = 0 & relation(all_48_2) = 0 & % 88.25/14.65 | function(all_48_2) = 0) | ( ~ (v3 = 0) & function(all_48_3) = v3) % 88.25/14.65 | | ( ~ (v2 = 0) & relation(all_48_3) = v2) | ( ~ (v1 = 0) & % 88.25/14.65 | function(all_48_6) = v1) | ( ~ (v0 = 0) & relation(all_48_6) = % 88.25/14.65 | v0)) % 88.25/14.65 | % 88.25/14.65 | COMBINE_EQS: (60), (61) imply: % 88.25/14.65 | (76) all_33_0 = empty_set % 88.25/14.65 | % 88.25/14.65 | SIMP: (76) implies: % 88.25/14.65 | (77) all_33_0 = empty_set % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (56) with fresh symbol all_80_0 gives: % 88.25/14.65 | (78) ~ (all_80_0 = 0) & empty(all_48_5) = all_80_0 % 88.25/14.65 | % 88.25/14.65 | ALPHA: (78) implies: % 88.25/14.65 | (79) ~ (all_80_0 = 0) % 88.25/14.65 | (80) empty(all_48_5) = all_80_0 % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (62) with fresh symbol all_88_0 gives: % 88.25/14.65 | (81) relation_dom(all_35_0) = all_88_0 & relation(all_88_0) = 0 & % 88.25/14.65 | empty(all_88_0) = 0 & $i(all_88_0) % 88.25/14.65 | % 88.25/14.65 | ALPHA: (81) implies: % 88.25/14.65 | (82) relation_dom(all_35_0) = all_88_0 % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (59) with fresh symbol all_92_0 gives: % 88.25/14.65 | (83) relation_dom(all_33_0) = all_92_0 & relation(all_92_0) = 0 & % 88.25/14.65 | empty(all_92_0) = 0 & $i(all_92_0) % 88.25/14.65 | % 88.25/14.65 | ALPHA: (83) implies: % 88.25/14.65 | (84) $i(all_92_0) % 88.25/14.65 | (85) empty(all_92_0) = 0 % 88.25/14.65 | (86) relation(all_92_0) = 0 % 88.25/14.65 | (87) relation_dom(all_33_0) = all_92_0 % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (57) with fresh symbol all_94_0 gives: % 88.25/14.65 | (88) relation_dom(empty_set) = all_94_0 & relation(all_94_0) = 0 & % 88.25/14.65 | empty(all_94_0) = 0 & $i(all_94_0) % 88.25/14.65 | % 88.25/14.65 | ALPHA: (88) implies: % 88.25/14.65 | (89) relation_dom(empty_set) = all_94_0 % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (69) with fresh symbols all_96_0, all_96_1, all_96_2 % 88.25/14.65 | gives: % 88.25/14.65 | (90) (all_96_2 = 0 & empty(all_48_6) = 0) | ( ~ (all_96_0 = 0) & % 88.25/14.65 | relation_dom(all_48_6) = all_96_1 & empty(all_96_1) = all_96_0 & % 88.25/14.65 | $i(all_96_1)) % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (68) with fresh symbols all_99_0, all_99_1, all_99_2 % 88.25/14.65 | gives: % 88.25/14.65 | (91) (all_99_2 = 0 & empty(all_44_1) = 0) | ( ~ (all_99_0 = 0) & % 88.25/14.65 | relation_dom(all_44_1) = all_99_1 & empty(all_99_1) = all_99_0 & % 88.25/14.65 | $i(all_99_1)) % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (74) with fresh symbols all_105_0, all_105_1, all_105_2 % 88.25/14.65 | gives: % 88.25/14.65 | (92) (all_105_0 = 0 & all_105_1 = 0 & relation(all_48_5) = 0 & % 88.25/14.65 | empty(all_48_5) = 0) | ( ~ (all_105_2 = 0) & empty(all_48_6) = % 88.25/14.65 | all_105_2) % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (75) with fresh symbols all_108_0, all_108_1, all_108_2, % 88.25/14.65 | all_108_3, all_108_4, all_108_5 gives: % 88.25/14.65 | (93) (all_108_0 = 0 & all_108_1 = 0 & relation(all_48_2) = 0 & % 88.25/14.65 | function(all_48_2) = 0) | ( ~ (all_108_2 = 0) & function(all_48_3) = % 88.25/14.65 | all_108_2) | ( ~ (all_108_3 = 0) & relation(all_48_3) = all_108_3) | % 88.25/14.65 | ( ~ (all_108_4 = 0) & function(all_48_6) = all_108_4) | ( ~ (all_108_5 % 88.25/14.65 | = 0) & relation(all_48_6) = all_108_5) % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (72) with fresh symbols all_118_0, all_118_1, all_118_2, % 88.25/14.65 | all_118_3, all_118_4, all_118_5, all_118_6 gives: % 88.25/14.65 | (94) (all_118_0 = all_118_1 & relation_composition(all_48_6, all_48_3) = % 88.25/14.65 | all_118_4 & apply(all_118_4, all_48_7) = all_118_1 & apply(all_48_3, % 88.25/14.65 | all_48_4) = all_118_1 & $i(all_118_1) & $i(all_118_4)) | ( ~ % 88.25/14.65 | (all_118_2 = 0) & relation_composition(all_48_6, all_48_3) = % 88.25/14.65 | all_118_4 & relation_dom(all_118_4) = all_118_3 & in(all_48_7, % 88.25/14.65 | all_118_3) = all_118_2 & $i(all_118_3) & $i(all_118_4)) | ( ~ % 88.25/14.65 | (all_118_5 = 0) & function(all_48_6) = all_118_5) | ( ~ (all_118_6 = % 88.25/14.65 | 0) & relation(all_48_6) = all_118_6) | ( ~ (all_118_6 = 0) & % 88.25/14.65 | function(all_48_3) = all_118_6) % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (73) with fresh symbols all_131_0, all_131_1, all_131_2, % 88.25/14.65 | all_131_3, all_131_4, all_131_5, all_131_6 gives: % 88.25/14.65 | (95) (all_131_0 = all_131_1 & relation_composition(all_48_6, all_48_3) = % 88.25/14.65 | all_131_4 & apply(all_131_4, all_48_7) = all_131_1 & apply(all_48_3, % 88.25/14.65 | all_48_4) = all_131_1 & $i(all_131_1) & $i(all_131_4)) | ( ~ % 88.25/14.65 | (all_131_2 = 0) & relation_composition(all_48_6, all_48_3) = % 88.25/14.65 | all_131_4 & relation_dom(all_131_4) = all_131_3 & in(all_48_7, % 88.25/14.65 | all_131_3) = all_131_2 & $i(all_131_3) & $i(all_131_4)) | ( ~ % 88.25/14.65 | (all_131_5 = 0) & function(all_48_6) = all_131_5) | ( ~ (all_131_6 = % 88.25/14.65 | 0) & relation(all_48_3) = all_131_6) | ( ~ (all_131_6 = 0) & % 88.25/14.65 | relation(all_48_6) = all_131_6) % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (70) with fresh symbols all_142_0, all_142_1 gives: % 88.25/14.65 | (96) ( ~ (all_142_1 = 0) & function(all_48_6) = all_142_1) | % 88.25/14.65 | (relation_dom(all_48_6) = all_142_0 & $i(all_142_0) & ! [v0: $i] : ! % 88.25/14.65 | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) % 88.25/14.65 | | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 % 88.25/14.65 | = 0) & in(v0, all_142_0) = v3) | (((v5 = 0 & in(v2, % 88.25/14.65 | all_48_6) = 0) | ( ~ (v4 = v1) & apply(all_48_6, v0) = % 88.25/14.65 | v4 & $i(v4))) & ((v4 = v1 & apply(all_48_6, v0) = v1) | ( % 88.25/14.65 | ~ (v5 = 0) & in(v2, all_48_6) = v5))))) & ? [v0: $i] : ! % 88.25/14.65 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_142_0) = v2) | ~ % 88.25/14.65 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 88.25/14.65 | empty_set & apply(all_48_6, v1) = empty_set)) & (v0 = % 88.25/14.65 | empty_set | ( ~ (v3 = v0) & apply(all_48_6, v1) = v3 & % 88.25/14.65 | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.25/14.65 | ~ (apply(all_48_6, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 88.25/14.65 | all_142_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.25/14.65 | ~ (apply(all_48_6, v0) = v1) | ~ $i(v0) | in(v0, all_142_0) = 0)) % 88.25/14.65 | % 88.25/14.65 | DELTA: instantiating (64) with fresh symbols all_144_0, all_144_1 gives: % 88.25/14.66 | (97) ( ~ (all_144_1 = 0) & relation(all_48_6) = all_144_1) | % 88.25/14.66 | (relation_dom(all_48_6) = all_144_0 & $i(all_144_0) & ! [v0: $i] : ! % 88.25/14.66 | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) % 88.25/14.66 | | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 % 88.25/14.66 | = 0) & in(v0, all_144_0) = v3) | (((v5 = 0 & in(v2, % 88.25/14.66 | all_48_6) = 0) | ( ~ (v4 = v1) & apply(all_48_6, v0) = % 88.25/14.66 | v4 & $i(v4))) & ((v4 = v1 & apply(all_48_6, v0) = v1) | ( % 88.25/14.66 | ~ (v5 = 0) & in(v2, all_48_6) = v5))))) & ? [v0: $i] : ! % 88.25/14.66 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_144_0) = v2) | ~ % 88.25/14.66 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 88.25/14.66 | empty_set & apply(all_48_6, v1) = empty_set)) & (v0 = % 88.25/14.66 | empty_set | ( ~ (v3 = v0) & apply(all_48_6, v1) = v3 & % 88.25/14.66 | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.25/14.66 | ~ (apply(all_48_6, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 88.25/14.66 | all_144_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.25/14.66 | ~ (apply(all_48_6, v0) = v1) | ~ $i(v0) | in(v0, all_144_0) = 0)) % 88.25/14.66 | % 88.25/14.66 | DELTA: instantiating (65) with fresh symbols all_146_0, all_146_1 gives: % 88.25/14.66 | (98) ( ~ (all_146_1 = 0) & relation(all_48_3) = all_146_1) | % 88.25/14.66 | (relation_dom(all_48_3) = all_146_0 & $i(all_146_0) & ! [v0: $i] : ! % 88.25/14.66 | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) % 88.25/14.66 | | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 % 88.25/14.66 | = 0) & in(v0, all_146_0) = v3) | (((v5 = 0 & in(v2, % 88.25/14.66 | all_48_3) = 0) | ( ~ (v4 = v1) & apply(all_48_3, v0) = % 88.25/14.66 | v4 & $i(v4))) & ((v4 = v1 & apply(all_48_3, v0) = v1) | ( % 88.25/14.66 | ~ (v5 = 0) & in(v2, all_48_3) = v5))))) & ? [v0: $i] : ! % 88.25/14.66 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_146_0) = v2) | ~ % 88.25/14.66 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 88.25/14.66 | empty_set & apply(all_48_3, v1) = empty_set)) & (v0 = % 88.25/14.66 | empty_set | ( ~ (v3 = v0) & apply(all_48_3, v1) = v3 & % 88.25/14.66 | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.25/14.66 | ~ (apply(all_48_3, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 88.25/14.66 | all_146_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.25/14.66 | ~ (apply(all_48_3, v0) = v1) | ~ $i(v0) | in(v0, all_146_0) = 0)) % 88.25/14.66 | % 88.25/14.66 | DELTA: instantiating (71) with fresh symbols all_147_0, all_147_1 gives: % 88.25/14.66 | (99) ( ~ (all_147_1 = 0) & function(all_48_3) = all_147_1) | % 88.25/14.66 | (relation_dom(all_48_3) = all_147_0 & $i(all_147_0) & ! [v0: $i] : ! % 88.25/14.66 | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) % 88.25/14.66 | | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 % 88.25/14.66 | = 0) & in(v0, all_147_0) = v3) | (((v5 = 0 & in(v2, % 88.25/14.66 | all_48_3) = 0) | ( ~ (v4 = v1) & apply(all_48_3, v0) = % 88.25/14.66 | v4 & $i(v4))) & ((v4 = v1 & apply(all_48_3, v0) = v1) | ( % 88.25/14.66 | ~ (v5 = 0) & in(v2, all_48_3) = v5))))) & ? [v0: $i] : ! % 88.25/14.66 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_147_0) = v2) | ~ % 88.25/14.66 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 88.25/14.66 | empty_set & apply(all_48_3, v1) = empty_set)) & (v0 = % 88.25/14.66 | empty_set | ( ~ (v3 = v0) & apply(all_48_3, v1) = v3 & % 88.25/14.66 | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.25/14.66 | ~ (apply(all_48_3, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 88.25/14.66 | all_147_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.25/14.66 | ~ (apply(all_48_3, v0) = v1) | ~ $i(v0) | in(v0, all_147_0) = 0)) % 88.25/14.66 | % 88.25/14.66 | DELTA: instantiating (67) with fresh symbols all_150_0, all_150_1 gives: % 88.79/14.66 | (100) ( ~ (all_150_1 = 0) & function(all_35_0) = all_150_1) | % 88.79/14.66 | (relation_dom(all_35_0) = all_150_0 & $i(all_150_0) & ! [v0: $i] : % 88.79/14.66 | ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 88.79/14.66 | $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : % 88.79/14.66 | (( ~ (v3 = 0) & in(v0, all_150_0) = v3) | (((v5 = 0 & in(v2, % 88.79/14.66 | all_35_0) = 0) | ( ~ (v4 = v1) & apply(all_35_0, v0) = % 88.79/14.66 | v4 & $i(v4))) & ((v4 = v1 & apply(all_35_0, v0) = v1) | ( % 88.79/14.66 | ~ (v5 = 0) & in(v2, all_35_0) = v5))))) & ? [v0: $i] : % 88.79/14.66 | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_150_0) = v2) | % 88.79/14.66 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 % 88.79/14.66 | = empty_set & apply(all_35_0, v1) = empty_set)) & (v0 = % 88.79/14.66 | empty_set | ( ~ (v3 = v0) & apply(all_35_0, v1) = v3 & % 88.79/14.66 | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.79/14.66 | ~ (apply(all_35_0, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 88.79/14.66 | all_150_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.79/14.66 | ~ (apply(all_35_0, v0) = v1) | ~ $i(v0) | in(v0, all_150_0) = % 88.79/14.66 | 0)) % 88.79/14.66 | % 88.79/14.66 | DELTA: instantiating (66) with fresh symbols all_151_0, all_151_1 gives: % 88.79/14.67 | (101) ( ~ (all_151_1 = 0) & function(empty_set) = all_151_1) | % 88.79/14.67 | (relation_dom(empty_set) = all_151_0 & $i(all_151_0) & ! [v0: $i] : % 88.79/14.67 | ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 88.79/14.67 | $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : % 88.79/14.67 | (( ~ (v3 = 0) & in(v0, all_151_0) = v3) | (((v5 = 0 & in(v2, % 88.79/14.67 | empty_set) = 0) | ( ~ (v4 = v1) & apply(empty_set, v0) % 88.79/14.67 | = v4 & $i(v4))) & ((v4 = v1 & apply(empty_set, v0) = v1) % 88.79/14.67 | | ( ~ (v5 = 0) & in(v2, empty_set) = v5))))) & ? [v0: $i] % 88.79/14.67 | : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_151_0) = % 88.79/14.67 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = % 88.79/14.67 | empty_set) | (v3 = empty_set & apply(empty_set, v1) = % 88.79/14.67 | empty_set)) & (v0 = empty_set | ( ~ (v3 = v0) & % 88.79/14.67 | apply(empty_set, v1) = v3 & $i(v3))))) & ! [v0: $i] : ! % 88.79/14.67 | [v1: $i] : (v1 = empty_set | ~ (apply(empty_set, v0) = v1) | ~ % 88.79/14.67 | $i(v1) | ~ $i(v0) | in(v0, all_151_0) = 0) & ! [v0: $i] : ! % 88.79/14.67 | [v1: $i] : (v1 = empty_set | ~ (apply(empty_set, v0) = v1) | ~ % 88.79/14.67 | $i(v0) | in(v0, all_151_0) = 0)) % 88.79/14.67 | % 88.79/14.67 | REDUCE: (61), (82) imply: % 88.79/14.67 | (102) relation_dom(empty_set) = all_88_0 % 88.79/14.67 | % 88.79/14.67 | REDUCE: (77), (87) imply: % 88.79/14.67 | (103) relation_dom(empty_set) = all_92_0 % 88.79/14.67 | % 88.79/14.67 | REDUCE: (58), (77) imply: % 88.79/14.67 | (104) function(empty_set) = 0 % 88.79/14.67 | % 88.79/14.67 | BETA: splitting (96) gives: % 88.79/14.67 | % 88.79/14.67 | Case 1: % 88.79/14.67 | | % 88.79/14.67 | | (105) ~ (all_142_1 = 0) & function(all_48_6) = all_142_1 % 88.79/14.67 | | % 88.79/14.67 | | ALPHA: (105) implies: % 88.79/14.67 | | (106) ~ (all_142_1 = 0) % 88.79/14.67 | | (107) function(all_48_6) = all_142_1 % 88.79/14.67 | | % 88.79/14.67 | | GROUND_INST: instantiating (17) with 0, all_142_1, all_48_6, simplifying % 88.79/14.67 | | with (47), (107) gives: % 88.79/14.67 | | (108) all_142_1 = 0 % 88.79/14.67 | | % 88.79/14.67 | | REDUCE: (106), (108) imply: % 88.79/14.67 | | (109) $false % 88.79/14.67 | | % 88.79/14.67 | | CLOSE: (109) is inconsistent. % 88.79/14.67 | | % 88.79/14.67 | Case 2: % 88.79/14.67 | | % 88.79/14.67 | | (110) relation_dom(all_48_6) = all_142_0 & $i(all_142_0) & ! [v0: $i] : % 88.79/14.67 | | ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 88.79/14.67 | | $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : % 88.79/14.67 | | (( ~ (v3 = 0) & in(v0, all_142_0) = v3) | (((v5 = 0 & in(v2, % 88.79/14.67 | | all_48_6) = 0) | ( ~ (v4 = v1) & apply(all_48_6, v0) = % 88.79/14.67 | | v4 & $i(v4))) & ((v4 = v1 & apply(all_48_6, v0) = v1) | ( % 88.79/14.67 | | ~ (v5 = 0) & in(v2, all_48_6) = v5))))) & ? [v0: $i] : % 88.79/14.67 | | ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_142_0) = v2) | % 88.79/14.67 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 % 88.79/14.67 | | = empty_set & apply(all_48_6, v1) = empty_set)) & (v0 = % 88.79/14.67 | | empty_set | ( ~ (v3 = v0) & apply(all_48_6, v1) = v3 & % 88.79/14.67 | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.79/14.67 | | ~ (apply(all_48_6, v0) = v1) | ~ $i(v1) | ~ $i(v0) | in(v0, % 88.79/14.67 | | all_142_0) = 0) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | % 88.79/14.67 | | ~ (apply(all_48_6, v0) = v1) | ~ $i(v0) | in(v0, all_142_0) = % 88.79/14.67 | | 0) % 88.79/14.67 | | % 88.79/14.67 | | ALPHA: (110) implies: % 88.79/14.67 | | (111) relation_dom(all_48_6) = all_142_0 % 88.79/14.67 | | % 88.79/14.67 | | BETA: splitting (97) gives: % 88.79/14.67 | | % 88.79/14.67 | | Case 1: % 88.79/14.67 | | | % 88.79/14.67 | | | (112) ~ (all_144_1 = 0) & relation(all_48_6) = all_144_1 % 88.79/14.67 | | | % 88.79/14.67 | | | ALPHA: (112) implies: % 88.79/14.67 | | | (113) ~ (all_144_1 = 0) % 88.79/14.67 | | | (114) relation(all_48_6) = all_144_1 % 88.79/14.67 | | | % 88.79/14.67 | | | GROUND_INST: instantiating (18) with 0, all_144_1, all_48_6, simplifying % 88.79/14.67 | | | with (49), (114) gives: % 88.79/14.67 | | | (115) all_144_1 = 0 % 88.79/14.67 | | | % 88.79/14.67 | | | REDUCE: (113), (115) imply: % 88.79/14.67 | | | (116) $false % 88.79/14.67 | | | % 88.79/14.67 | | | CLOSE: (116) is inconsistent. % 88.79/14.67 | | | % 88.79/14.67 | | Case 2: % 88.79/14.67 | | | % 88.79/14.67 | | | (117) relation_dom(all_48_6) = all_144_0 & $i(all_144_0) & ! [v0: $i] % 88.79/14.67 | | | : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | % 88.79/14.67 | | | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: % 88.79/14.67 | | | int] : (( ~ (v3 = 0) & in(v0, all_144_0) = v3) | (((v5 = 0 & % 88.79/14.67 | | | in(v2, all_48_6) = 0) | ( ~ (v4 = v1) & apply(all_48_6, % 88.79/14.67 | | | v0) = v4 & $i(v4))) & ((v4 = v1 & apply(all_48_6, v0) % 88.79/14.67 | | | = v1) | ( ~ (v5 = 0) & in(v2, all_48_6) = v5))))) & ? % 88.79/14.67 | | | [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, % 88.79/14.67 | | | all_144_0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (( % 88.79/14.67 | | | ~ (v0 = empty_set) | (v3 = empty_set & apply(all_48_6, v1) % 88.79/14.67 | | | = empty_set)) & (v0 = empty_set | ( ~ (v3 = v0) & % 88.79/14.67 | | | apply(all_48_6, v1) = v3 & $i(v3))))) & ! [v0: $i] : ! % 88.79/14.67 | | | [v1: $i] : (v1 = empty_set | ~ (apply(all_48_6, v0) = v1) | ~ % 88.79/14.67 | | | $i(v1) | ~ $i(v0) | in(v0, all_144_0) = 0) & ! [v0: $i] : ! % 88.79/14.67 | | | [v1: $i] : (v1 = empty_set | ~ (apply(all_48_6, v0) = v1) | ~ % 88.79/14.67 | | | $i(v0) | in(v0, all_144_0) = 0) % 88.79/14.67 | | | % 88.79/14.67 | | | ALPHA: (117) implies: % 88.79/14.67 | | | (118) relation_dom(all_48_6) = all_144_0 % 88.79/14.67 | | | % 88.79/14.67 | | | BETA: splitting (94) gives: % 88.79/14.67 | | | % 88.79/14.67 | | | Case 1: % 88.79/14.67 | | | | % 88.79/14.67 | | | | (119) (all_118_0 = all_118_1 & relation_composition(all_48_6, % 88.79/14.67 | | | | all_48_3) = all_118_4 & apply(all_118_4, all_48_7) = % 88.79/14.67 | | | | all_118_1 & apply(all_48_3, all_48_4) = all_118_1 & % 88.79/14.67 | | | | $i(all_118_1) & $i(all_118_4)) | ( ~ (all_118_2 = 0) & % 88.79/14.67 | | | | relation_composition(all_48_6, all_48_3) = all_118_4 & % 88.79/14.67 | | | | relation_dom(all_118_4) = all_118_3 & in(all_48_7, all_118_3) % 88.79/14.68 | | | | = all_118_2 & $i(all_118_3) & $i(all_118_4)) % 88.79/14.68 | | | | % 88.79/14.68 | | | | BETA: splitting (119) gives: % 88.79/14.68 | | | | % 88.79/14.68 | | | | Case 1: % 88.79/14.68 | | | | | % 88.79/14.68 | | | | | (120) all_118_0 = all_118_1 & relation_composition(all_48_6, % 88.79/14.68 | | | | | all_48_3) = all_118_4 & apply(all_118_4, all_48_7) = % 88.79/14.68 | | | | | all_118_1 & apply(all_48_3, all_48_4) = all_118_1 & % 88.79/14.68 | | | | | $i(all_118_1) & $i(all_118_4) % 88.79/14.68 | | | | | % 88.79/14.68 | | | | | ALPHA: (120) implies: % 88.79/14.68 | | | | | (121) apply(all_48_3, all_48_4) = all_118_1 % 88.79/14.68 | | | | | (122) apply(all_118_4, all_48_7) = all_118_1 % 88.79/14.68 | | | | | (123) relation_composition(all_48_6, all_48_3) = all_118_4 % 88.79/14.68 | | | | | % 88.79/14.68 | | | | | BETA: splitting (91) gives: % 88.79/14.68 | | | | | % 88.79/14.68 | | | | | Case 1: % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | (124) all_99_2 = 0 & empty(all_44_1) = 0 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | ALPHA: (124) implies: % 88.79/14.68 | | | | | | (125) empty(all_44_1) = 0 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | GROUND_INST: instantiating (16) with all_44_0, 0, all_44_1, % 88.79/14.68 | | | | | | simplifying with (37), (125) gives: % 88.79/14.68 | | | | | | (126) all_44_0 = 0 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | REDUCE: (35), (126) imply: % 88.79/14.68 | | | | | | (127) $false % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | CLOSE: (127) is inconsistent. % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | Case 2: % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | GROUND_INST: instantiating (21) with all_48_0, all_118_1, all_48_4, % 88.79/14.68 | | | | | | all_48_3, simplifying with (52), (121) gives: % 88.79/14.68 | | | | | | (128) all_118_1 = all_48_0 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | GROUND_INST: instantiating (22) with all_48_2, all_118_4, all_48_3, % 88.79/14.68 | | | | | | all_48_6, simplifying with (55), (123) gives: % 88.79/14.68 | | | | | | (129) all_118_4 = all_48_2 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | REDUCE: (122), (128), (129) imply: % 88.79/14.68 | | | | | | (130) apply(all_48_2, all_48_7) = all_48_0 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | REF_CLOSE: (21), (40), (53), (130) are inconsistent by sub-proof #2. % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | End of split % 88.79/14.68 | | | | | % 88.79/14.68 | | | | Case 2: % 88.79/14.68 | | | | | % 88.79/14.68 | | | | | (131) ~ (all_118_2 = 0) & relation_composition(all_48_6, all_48_3) % 88.79/14.68 | | | | | = all_118_4 & relation_dom(all_118_4) = all_118_3 & % 88.79/14.68 | | | | | in(all_48_7, all_118_3) = all_118_2 & $i(all_118_3) & % 88.79/14.68 | | | | | $i(all_118_4) % 88.79/14.68 | | | | | % 88.79/14.68 | | | | | ALPHA: (131) implies: % 88.79/14.68 | | | | | (132) in(all_48_7, all_118_3) = all_118_2 % 88.79/14.68 | | | | | (133) relation_dom(all_118_4) = all_118_3 % 88.79/14.68 | | | | | (134) relation_composition(all_48_6, all_48_3) = all_118_4 % 88.79/14.68 | | | | | % 88.79/14.68 | | | | | BETA: splitting (100) gives: % 88.79/14.68 | | | | | % 88.79/14.68 | | | | | Case 1: % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | (135) ~ (all_150_1 = 0) & function(all_35_0) = all_150_1 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | ALPHA: (135) implies: % 88.79/14.68 | | | | | | (136) ~ (all_150_1 = 0) % 88.79/14.68 | | | | | | (137) function(all_35_0) = all_150_1 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | REDUCE: (61), (137) imply: % 88.79/14.68 | | | | | | (138) function(empty_set) = all_150_1 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | GROUND_INST: instantiating (17) with 0, all_150_1, empty_set, % 88.79/14.68 | | | | | | simplifying with (104), (138) gives: % 88.79/14.68 | | | | | | (139) all_150_1 = 0 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | REDUCE: (136), (139) imply: % 88.79/14.68 | | | | | | (140) $false % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | CLOSE: (140) is inconsistent. % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | Case 2: % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | (141) relation_dom(all_35_0) = all_150_0 & $i(all_150_0) & ! % 88.79/14.68 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 88.79/14.68 | | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 88.79/14.68 | | | | | | [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v3 = 0) & % 88.79/14.68 | | | | | | in(v0, all_150_0) = v3) | (((v5 = 0 & in(v2, % 88.79/14.68 | | | | | | all_35_0) = 0) | ( ~ (v4 = v1) & % 88.79/14.68 | | | | | | apply(all_35_0, v0) = v4 & $i(v4))) & ((v4 = v1 & % 88.79/14.68 | | | | | | apply(all_35_0, v0) = v1) | ( ~ (v5 = 0) & in(v2, % 88.79/14.68 | | | | | | all_35_0) = v5))))) & ? [v0: $i] : ! [v1: $i] % 88.79/14.68 | | | | | | : ! [v2: int] : (v2 = 0 | ~ (in(v1, all_150_0) = v2) | ~ % 88.79/14.68 | | | | | | $i(v1) | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) % 88.79/14.68 | | | | | | | (v3 = empty_set & apply(all_35_0, v1) = empty_set)) % 88.79/14.68 | | | | | | & (v0 = empty_set | ( ~ (v3 = v0) & apply(all_35_0, v1) % 88.79/14.68 | | | | | | = v3 & $i(v3))))) & ! [v0: $i] : ! [v1: $i] : (v1 % 88.79/14.68 | | | | | | = empty_set | ~ (apply(all_35_0, v0) = v1) | ~ $i(v1) | % 88.79/14.68 | | | | | | ~ $i(v0) | in(v0, all_150_0) = 0) & ! [v0: $i] : ! % 88.79/14.68 | | | | | | [v1: $i] : (v1 = empty_set | ~ (apply(all_35_0, v0) = v1) % 88.79/14.68 | | | | | | | ~ $i(v0) | in(v0, all_150_0) = 0) % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | ALPHA: (141) implies: % 88.79/14.68 | | | | | | (142) relation_dom(all_35_0) = all_150_0 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | REDUCE: (61), (142) imply: % 88.79/14.68 | | | | | | (143) relation_dom(empty_set) = all_150_0 % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | BETA: splitting (93) gives: % 88.79/14.68 | | | | | | % 88.79/14.68 | | | | | | Case 1: % 88.79/14.68 | | | | | | | % 88.79/14.68 | | | | | | | (144) (all_108_0 = 0 & all_108_1 = 0 & relation(all_48_2) = 0 & % 88.79/14.68 | | | | | | | function(all_48_2) = 0) | ( ~ (all_108_2 = 0) & % 88.79/14.68 | | | | | | | function(all_48_3) = all_108_2) % 88.79/14.68 | | | | | | | % 88.79/14.68 | | | | | | | BETA: splitting (144) gives: % 88.79/14.68 | | | | | | | % 88.79/14.68 | | | | | | | Case 1: % 88.79/14.68 | | | | | | | | % 88.79/14.68 | | | | | | | | (145) all_108_0 = 0 & all_108_1 = 0 & relation(all_48_2) = 0 % 88.79/14.68 | | | | | | | | & function(all_48_2) = 0 % 88.79/14.68 | | | | | | | | % 88.79/14.68 | | | | | | | | ALPHA: (145) implies: % 88.79/14.68 | | | | | | | | (146) function(all_48_2) = 0 % 88.79/14.68 | | | | | | | | (147) relation(all_48_2) = 0 % 88.79/14.68 | | | | | | | | % 88.79/14.68 | | | | | | | | BETA: splitting (101) gives: % 88.79/14.68 | | | | | | | | % 88.79/14.68 | | | | | | | | Case 1: % 88.79/14.68 | | | | | | | | | % 88.79/14.68 | | | | | | | | | (148) ~ (all_151_1 = 0) & function(empty_set) = all_151_1 % 88.79/14.68 | | | | | | | | | % 88.79/14.68 | | | | | | | | | ALPHA: (148) implies: % 88.79/14.68 | | | | | | | | | (149) ~ (all_151_1 = 0) % 88.79/14.68 | | | | | | | | | (150) function(empty_set) = all_151_1 % 88.79/14.68 | | | | | | | | | % 88.79/14.68 | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_151_1, empty_set, % 88.79/14.68 | | | | | | | | | simplifying with (104), (150) gives: % 88.79/14.68 | | | | | | | | | (151) all_151_1 = 0 % 88.79/14.68 | | | | | | | | | % 88.79/14.68 | | | | | | | | | REDUCE: (149), (151) imply: % 88.79/14.68 | | | | | | | | | (152) $false % 88.79/14.68 | | | | | | | | | % 88.79/14.68 | | | | | | | | | CLOSE: (152) is inconsistent. % 88.79/14.68 | | | | | | | | | % 88.79/14.68 | | | | | | | | Case 2: % 88.79/14.68 | | | | | | | | | % 88.79/14.69 | | | | | | | | | (153) relation_dom(empty_set) = all_151_0 & $i(all_151_0) & % 88.79/14.69 | | | | | | | | | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 88.79/14.69 | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 88.79/14.69 | | | | | | | | | | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ % 88.79/14.69 | | | | | | | | | (v3 = 0) & in(v0, all_151_0) = v3) | (((v5 = 0 % 88.79/14.69 | | | | | | | | | & in(v2, empty_set) = 0) | ( ~ (v4 = v1) & % 88.79/14.69 | | | | | | | | | apply(empty_set, v0) = v4 & $i(v4))) & ((v4 % 88.79/14.69 | | | | | | | | | = v1 & apply(empty_set, v0) = v1) | ( ~ (v5 % 88.79/14.69 | | | | | | | | | = 0) & in(v2, empty_set) = v5))))) & ? % 88.79/14.69 | | | | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 88.79/14.69 | | | | | | | | | (in(v1, all_151_0) = v2) | ~ $i(v1) | ~ $i(v0) | % 88.79/14.69 | | | | | | | | | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 88.79/14.69 | | | | | | | | | empty_set & apply(empty_set, v1) = % 88.79/14.69 | | | | | | | | | empty_set)) & (v0 = empty_set | ( ~ (v3 = v0) % 88.79/14.69 | | | | | | | | | & apply(empty_set, v1) = v3 & $i(v3))))) & ! % 88.79/14.69 | | | | | | | | | [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 88.79/14.69 | | | | | | | | | (apply(empty_set, v0) = v1) | ~ $i(v1) | ~ $i(v0) % 88.79/14.69 | | | | | | | | | | in(v0, all_151_0) = 0) & ! [v0: $i] : ! [v1: % 88.79/14.69 | | | | | | | | | $i] : (v1 = empty_set | ~ (apply(empty_set, v0) = % 88.79/14.69 | | | | | | | | | v1) | ~ $i(v0) | in(v0, all_151_0) = 0) % 88.79/14.69 | | | | | | | | | % 88.79/14.69 | | | | | | | | | ALPHA: (153) implies: % 88.79/14.69 | | | | | | | | | (154) relation_dom(empty_set) = all_151_0 % 88.79/14.69 | | | | | | | | | % 88.79/14.69 | | | | | | | | | BETA: splitting (92) gives: % 88.79/14.69 | | | | | | | | | % 88.79/14.69 | | | | | | | | | Case 1: % 88.79/14.69 | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | (155) all_105_0 = 0 & all_105_1 = 0 & relation(all_48_5) % 88.79/14.69 | | | | | | | | | | = 0 & empty(all_48_5) = 0 % 88.79/14.69 | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | ALPHA: (155) implies: % 88.79/14.69 | | | | | | | | | | (156) empty(all_48_5) = 0 % 88.79/14.69 | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_80_0, all_48_5, % 88.79/14.69 | | | | | | | | | | simplifying with (80), (156) gives: % 88.79/14.69 | | | | | | | | | | (157) all_80_0 = 0 % 88.79/14.69 | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | REDUCE: (79), (157) imply: % 88.79/14.69 | | | | | | | | | | (158) $false % 88.79/14.69 | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | CLOSE: (158) is inconsistent. % 88.79/14.69 | | | | | | | | | | % 88.79/14.69 | | | | | | | | | Case 2: % 88.79/14.69 | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | (159) ~ (all_105_2 = 0) & empty(all_48_6) = all_105_2 % 88.79/14.69 | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | ALPHA: (159) implies: % 88.79/14.69 | | | | | | | | | | (160) ~ (all_105_2 = 0) % 88.79/14.69 | | | | | | | | | | (161) empty(all_48_6) = all_105_2 % 88.79/14.69 | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | BETA: splitting (90) gives: % 88.79/14.69 | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | Case 1: % 88.79/14.69 | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | (162) all_96_2 = 0 & empty(all_48_6) = 0 % 88.79/14.69 | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | ALPHA: (162) implies: % 88.79/14.69 | | | | | | | | | | | (163) empty(all_48_6) = 0 % 88.79/14.69 | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_105_2, all_48_6, % 88.79/14.69 | | | | | | | | | | | simplifying with (161), (163) gives: % 88.79/14.69 | | | | | | | | | | | (164) all_105_2 = 0 % 88.79/14.69 | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | REDUCE: (160), (164) imply: % 88.79/14.69 | | | | | | | | | | | (165) $false % 88.79/14.69 | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | CLOSE: (165) is inconsistent. % 88.79/14.69 | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | Case 2: % 88.79/14.69 | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | (166) ~ (all_96_0 = 0) & relation_dom(all_48_6) = % 88.79/14.69 | | | | | | | | | | | all_96_1 & empty(all_96_1) = all_96_0 & % 88.79/14.69 | | | | | | | | | | | $i(all_96_1) % 88.79/14.69 | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | ALPHA: (166) implies: % 88.79/14.69 | | | | | | | | | | | (167) relation_dom(all_48_6) = all_96_1 % 88.79/14.69 | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | BETA: splitting (98) gives: % 88.79/14.69 | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | Case 1: % 88.79/14.69 | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | (168) ~ (all_146_1 = 0) & relation(all_48_3) = % 88.79/14.69 | | | | | | | | | | | | all_146_1 % 88.79/14.69 | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | ALPHA: (168) implies: % 88.79/14.69 | | | | | | | | | | | | (169) ~ (all_146_1 = 0) % 88.79/14.69 | | | | | | | | | | | | (170) relation(all_48_3) = all_146_1 % 88.79/14.69 | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_146_1, all_48_3, % 88.79/14.69 | | | | | | | | | | | | simplifying with (50), (170) gives: % 88.79/14.69 | | | | | | | | | | | | (171) all_146_1 = 0 % 88.79/14.69 | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | REDUCE: (169), (171) imply: % 88.79/14.69 | | | | | | | | | | | | (172) $false % 88.79/14.69 | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | CLOSE: (172) is inconsistent. % 88.79/14.69 | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | Case 2: % 88.79/14.69 | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | (173) relation_dom(all_48_3) = all_146_0 & $i(all_146_0) % 88.79/14.69 | | | | | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 88.79/14.69 | | | | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 88.79/14.69 | | | | | | | | | | | | $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: % 88.79/14.69 | | | | | | | | | | | | int] : (( ~ (v3 = 0) & in(v0, all_146_0) = v3) % 88.79/14.69 | | | | | | | | | | | | | (((v5 = 0 & in(v2, all_48_3) = 0) | ( ~ (v4 % 88.79/14.69 | | | | | | | | | | | | = v1) & apply(all_48_3, v0) = v4 & % 88.79/14.69 | | | | | | | | | | | | $i(v4))) & ((v4 = v1 & apply(all_48_3, % 88.79/14.69 | | | | | | | | | | | | v0) = v1) | ( ~ (v5 = 0) & in(v2, % 88.79/14.69 | | | | | | | | | | | | all_48_3) = v5))))) & ? [v0: $i] : ! % 88.79/14.69 | | | | | | | | | | | | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, % 88.79/14.69 | | | | | | | | | | | | all_146_0) = v2) | ~ $i(v1) | ~ $i(v0) | % 88.79/14.69 | | | | | | | | | | | | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 88.79/14.69 | | | | | | | | | | | | empty_set & apply(all_48_3, v1) = % 88.79/14.69 | | | | | | | | | | | | empty_set)) & (v0 = empty_set | ( ~ (v3 = % 88.79/14.69 | | | | | | | | | | | | v0) & apply(all_48_3, v1) = v3 & % 88.79/14.69 | | | | | | | | | | | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : % 88.79/14.69 | | | | | | | | | | | | (v1 = empty_set | ~ (apply(all_48_3, v0) = v1) | % 88.79/14.69 | | | | | | | | | | | | ~ $i(v1) | ~ $i(v0) | in(v0, all_146_0) = 0) & % 88.79/14.69 | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 88.79/14.69 | | | | | | | | | | | | (apply(all_48_3, v0) = v1) | ~ $i(v0) | in(v0, % 88.79/14.69 | | | | | | | | | | | | all_146_0) = 0) % 88.79/14.69 | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | ALPHA: (173) implies: % 88.79/14.69 | | | | | | | | | | | | (174) relation_dom(all_48_3) = all_146_0 % 88.79/14.69 | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | BETA: splitting (99) gives: % 88.79/14.69 | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | Case 1: % 88.79/14.69 | | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | | (175) ~ (all_147_1 = 0) & function(all_48_3) = % 88.79/14.69 | | | | | | | | | | | | | all_147_1 % 88.79/14.69 | | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | | ALPHA: (175) implies: % 88.79/14.69 | | | | | | | | | | | | | (176) ~ (all_147_1 = 0) % 88.79/14.69 | | | | | | | | | | | | | (177) function(all_48_3) = all_147_1 % 88.79/14.69 | | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_147_1, all_48_3, % 88.79/14.69 | | | | | | | | | | | | | simplifying with (48), (177) gives: % 88.79/14.69 | | | | | | | | | | | | | (178) all_147_1 = 0 % 88.79/14.69 | | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | | REDUCE: (176), (178) imply: % 88.79/14.69 | | | | | | | | | | | | | (179) $false % 88.79/14.69 | | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 88.79/14.69 | | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | Case 2: % 88.79/14.69 | | | | | | | | | | | | | % 88.79/14.69 | | | | | | | | | | | | | (180) relation_dom(all_48_3) = all_147_0 & $i(all_147_0) % 88.79/14.69 | | | | | | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 88.79/14.69 | | | | | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 88.79/14.69 | | | | | | | | | | | | | $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: % 88.79/14.69 | | | | | | | | | | | | | int] : (( ~ (v3 = 0) & in(v0, all_147_0) = v3) % 88.79/14.69 | | | | | | | | | | | | | | (((v5 = 0 & in(v2, all_48_3) = 0) | ( ~ (v4 % 88.79/14.69 | | | | | | | | | | | | | = v1) & apply(all_48_3, v0) = v4 & % 88.79/14.69 | | | | | | | | | | | | | $i(v4))) & ((v4 = v1 & apply(all_48_3, % 88.79/14.69 | | | | | | | | | | | | | v0) = v1) | ( ~ (v5 = 0) & in(v2, % 88.79/14.69 | | | | | | | | | | | | | all_48_3) = v5))))) & ? [v0: $i] : ! % 88.79/14.69 | | | | | | | | | | | | | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, % 88.79/14.69 | | | | | | | | | | | | | all_147_0) = v2) | ~ $i(v1) | ~ $i(v0) | % 88.79/14.69 | | | | | | | | | | | | | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 88.79/14.69 | | | | | | | | | | | | | empty_set & apply(all_48_3, v1) = % 88.79/14.69 | | | | | | | | | | | | | empty_set)) & (v0 = empty_set | ( ~ (v3 = % 88.79/14.69 | | | | | | | | | | | | | v0) & apply(all_48_3, v1) = v3 & % 88.79/14.69 | | | | | | | | | | | | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : % 88.79/14.69 | | | | | | | | | | | | | (v1 = empty_set | ~ (apply(all_48_3, v0) = v1) | % 88.79/14.69 | | | | | | | | | | | | | ~ $i(v1) | ~ $i(v0) | in(v0, all_147_0) = 0) & % 88.79/14.69 | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 88.79/14.69 | | | | | | | | | | | | | (apply(all_48_3, v0) = v1) | ~ $i(v0) | in(v0, % 88.79/14.69 | | | | | | | | | | | | | all_147_0) = 0) % 88.79/14.70 | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | ALPHA: (180) implies: % 88.79/14.70 | | | | | | | | | | | | | (181) relation_dom(all_48_3) = all_147_0 % 88.79/14.70 | | | | | | | | | | | | | (182) ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 88.79/14.70 | | | | | | | | | | | | | (apply(all_48_3, v0) = v1) | ~ $i(v0) | in(v0, % 88.79/14.70 | | | | | | | | | | | | | all_147_0) = 0) % 88.79/14.70 | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | GROUND_INST: instantiating (182) with all_48_4, all_48_0, % 88.79/14.70 | | | | | | | | | | | | | simplifying with (44), (52) gives: % 88.79/14.70 | | | | | | | | | | | | | (183) all_48_0 = empty_set | in(all_48_4, all_147_0) = 0 % 88.79/14.70 | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | BETA: splitting (63) gives: % 88.79/14.70 | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | Case 1: % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | (184) all_38_0 = 0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | REDUCE: (31), (184) imply: % 88.79/14.70 | | | | | | | | | | | | | | (185) $false % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | CLOSE: (185) is inconsistent. % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | Case 2: % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_92_0, all_94_0, % 88.79/14.70 | | | | | | | | | | | | | | empty_set, simplifying with (89), (103) gives: % 88.79/14.70 | | | | | | | | | | | | | | (186) all_94_0 = all_92_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_150_0, all_151_0, % 88.79/14.70 | | | | | | | | | | | | | | empty_set, simplifying with (143), (154) gives: % 88.79/14.70 | | | | | | | | | | | | | | (187) all_151_0 = all_150_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_94_0, all_151_0, % 88.79/14.70 | | | | | | | | | | | | | | empty_set, simplifying with (89), (154) gives: % 88.79/14.70 | | | | | | | | | | | | | | (188) all_151_0 = all_94_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_88_0, all_151_0, % 88.79/14.70 | | | | | | | | | | | | | | empty_set, simplifying with (102), (154) gives: % 88.79/14.70 | | | | | | | | | | | | | | (189) all_151_0 = all_88_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_96_1, all_142_0, % 88.79/14.70 | | | | | | | | | | | | | | all_48_6, simplifying with (111), (167) gives: % 88.79/14.70 | | | | | | | | | | | | | | (190) all_142_0 = all_96_1 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_48_5, all_144_0, % 88.79/14.70 | | | | | | | | | | | | | | all_48_6, simplifying with (54), (118) gives: % 88.79/14.70 | | | | | | | | | | | | | | (191) all_144_0 = all_48_5 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_142_0, all_144_0, % 88.79/14.70 | | | | | | | | | | | | | | all_48_6, simplifying with (111), (118) gives: % 88.79/14.70 | | | | | | | | | | | | | | (192) all_144_0 = all_142_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_146_0, all_147_0, % 88.79/14.70 | | | | | | | | | | | | | | all_48_3, simplifying with (174), (181) gives: % 88.79/14.70 | | | | | | | | | | | | | | (193) all_147_0 = all_146_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_48_2, all_118_4, % 88.79/14.70 | | | | | | | | | | | | | | all_48_3, all_48_6, simplifying with (55), (134) % 88.79/14.70 | | | | | | | | | | | | | | gives: % 88.79/14.70 | | | | | | | | | | | | | | (194) all_118_4 = all_48_2 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | COMBINE_EQS: (187), (189) imply: % 88.79/14.70 | | | | | | | | | | | | | | (195) all_150_0 = all_88_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | COMBINE_EQS: (187), (188) imply: % 88.79/14.70 | | | | | | | | | | | | | | (196) all_150_0 = all_94_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | COMBINE_EQS: (195), (196) imply: % 88.79/14.70 | | | | | | | | | | | | | | (197) all_94_0 = all_88_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | SIMP: (197) implies: % 88.79/14.70 | | | | | | | | | | | | | | (198) all_94_0 = all_88_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | COMBINE_EQS: (191), (192) imply: % 88.79/14.70 | | | | | | | | | | | | | | (199) all_142_0 = all_48_5 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | SIMP: (199) implies: % 88.79/14.70 | | | | | | | | | | | | | | (200) all_142_0 = all_48_5 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | COMBINE_EQS: (190), (200) imply: % 88.79/14.70 | | | | | | | | | | | | | | (201) all_96_1 = all_48_5 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | COMBINE_EQS: (186), (198) imply: % 88.79/14.70 | | | | | | | | | | | | | | (202) all_92_0 = all_88_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | SIMP: (202) implies: % 88.79/14.70 | | | | | | | | | | | | | | (203) all_92_0 = all_88_0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | REDUCE: (133), (194) imply: % 88.79/14.70 | | | | | | | | | | | | | | (204) relation_dom(all_48_2) = all_118_3 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | REDUCE: (86), (203) imply: % 88.79/14.70 | | | | | | | | | | | | | | (205) relation(all_88_0) = 0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | REDUCE: (85), (203) imply: % 88.79/14.70 | | | | | | | | | | | | | | (206) empty(all_88_0) = 0 % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | REDUCE: (84), (203) imply: % 88.79/14.70 | | | | | | | | | | | | | | (207) $i(all_88_0) % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | BETA: splitting (95) gives: % 88.79/14.70 | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | Case 1: % 88.79/14.70 | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | (208) (all_131_0 = all_131_1 & % 88.79/14.70 | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 88.79/14.70 | | | | | | | | | | | | | | | all_131_4 & apply(all_131_4, all_48_7) = % 88.79/14.70 | | | | | | | | | | | | | | | all_131_1 & apply(all_48_3, all_48_4) = % 88.79/14.70 | | | | | | | | | | | | | | | all_131_1 & $i(all_131_1) & $i(all_131_4)) | ( ~ % 88.79/14.70 | | | | | | | | | | | | | | | (all_131_2 = 0) & relation_composition(all_48_6, % 88.79/14.70 | | | | | | | | | | | | | | | all_48_3) = all_131_4 & % 88.79/14.70 | | | | | | | | | | | | | | | relation_dom(all_131_4) = all_131_3 & % 88.79/14.70 | | | | | | | | | | | | | | | in(all_48_7, all_131_3) = all_131_2 & % 88.79/14.70 | | | | | | | | | | | | | | | $i(all_131_3) & $i(all_131_4)) % 88.79/14.70 | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 88.79/14.70 | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | Case 1: % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | (209) all_131_0 = all_131_1 & % 88.79/14.70 | | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 88.79/14.70 | | | | | | | | | | | | | | | | all_131_4 & apply(all_131_4, all_48_7) = all_131_1 % 88.79/14.70 | | | | | | | | | | | | | | | | & apply(all_48_3, all_48_4) = all_131_1 & % 88.79/14.70 | | | | | | | | | | | | | | | | $i(all_131_1) & $i(all_131_4) % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | ALPHA: (209) implies: % 88.79/14.70 | | | | | | | | | | | | | | | | (210) apply(all_48_3, all_48_4) = all_131_1 % 88.79/14.70 | | | | | | | | | | | | | | | | (211) apply(all_131_4, all_48_7) = all_131_1 % 88.79/14.70 | | | | | | | | | | | | | | | | (212) relation_composition(all_48_6, all_48_3) = % 88.79/14.70 | | | | | | | | | | | | | | | | all_131_4 % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_48_0, all_131_1, % 88.79/14.70 | | | | | | | | | | | | | | | | all_48_4, all_48_3, simplifying with (52), (210) % 88.79/14.70 | | | | | | | | | | | | | | | | gives: % 88.79/14.70 | | | | | | | | | | | | | | | | (213) all_131_1 = all_48_0 % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_48_2, all_131_4, % 88.79/14.70 | | | | | | | | | | | | | | | | all_48_3, all_48_6, simplifying with (55), (212) % 88.79/14.70 | | | | | | | | | | | | | | | | gives: % 88.79/14.70 | | | | | | | | | | | | | | | | (214) all_131_4 = all_48_2 % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | REDUCE: (211), (213), (214) imply: % 88.79/14.70 | | | | | | | | | | | | | | | | (215) apply(all_48_2, all_48_7) = all_48_0 % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | REF_CLOSE: (21), (40), (53), (215) are inconsistent by % 88.79/14.70 | | | | | | | | | | | | | | | | sub-proof #2. % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | Case 2: % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | (216) ~ (all_131_2 = 0) & % 88.79/14.70 | | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 88.79/14.70 | | | | | | | | | | | | | | | | all_131_4 & relation_dom(all_131_4) = all_131_3 & % 88.79/14.70 | | | | | | | | | | | | | | | | in(all_48_7, all_131_3) = all_131_2 & % 88.79/14.70 | | | | | | | | | | | | | | | | $i(all_131_3) & $i(all_131_4) % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | ALPHA: (216) implies: % 88.79/14.70 | | | | | | | | | | | | | | | | (217) ~ (all_131_2 = 0) % 88.79/14.70 | | | | | | | | | | | | | | | | (218) $i(all_131_4) % 88.79/14.70 | | | | | | | | | | | | | | | | (219) in(all_48_7, all_131_3) = all_131_2 % 88.79/14.70 | | | | | | | | | | | | | | | | (220) relation_dom(all_131_4) = all_131_3 % 88.79/14.70 | | | | | | | | | | | | | | | | (221) relation_composition(all_48_6, all_48_3) = % 88.79/14.70 | | | | | | | | | | | | | | | | all_131_4 % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_48_2, all_131_4, % 88.79/14.70 | | | | | | | | | | | | | | | | all_48_3, all_48_6, simplifying with (55), (221) % 88.79/14.70 | | | | | | | | | | | | | | | | gives: % 88.79/14.70 | | | | | | | | | | | | | | | | (222) all_131_4 = all_48_2 % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | REDUCE: (220), (222) imply: % 88.79/14.70 | | | | | | | | | | | | | | | | (223) relation_dom(all_48_2) = all_131_3 % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | REDUCE: (218), (222) imply: % 88.79/14.70 | | | | | | | | | | | | | | | | (224) $i(all_48_2) % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_118_3, all_131_3, % 88.79/14.70 | | | | | | | | | | | | | | | | all_48_2, simplifying with (204), (223) gives: % 88.79/14.70 | | | | | | | | | | | | | | | | (225) all_131_3 = all_118_3 % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | REDUCE: (219), (225) imply: % 88.79/14.70 | | | | | | | | | | | | | | | | (226) in(all_48_7, all_118_3) = all_131_2 % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_118_2, all_131_2, % 88.79/14.70 | | | | | | | | | | | | | | | | all_118_3, all_48_7, simplifying with (132), (226) % 88.79/14.70 | | | | | | | | | | | | | | | | gives: % 88.79/14.70 | | | | | | | | | | | | | | | | (227) all_131_2 = all_118_2 % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | REDUCE: (217), (227) imply: % 88.79/14.70 | | | | | | | | | | | | | | | | (228) ~ (all_118_2 = 0) % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_88_0, simplifying with % 88.79/14.70 | | | | | | | | | | | | | | | | (206), (207) gives: % 88.79/14.70 | | | | | | | | | | | | | | | | (229) all_88_0 = empty_set % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.70 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_88_0, simplifying with % 88.79/14.70 | | | | | | | | | | | | | | | | (206), (207) gives: % 88.79/14.70 | | | | | | | | | | | | | | | | (230) function(all_88_0) = 0 % 88.79/14.70 | | | | | | | | | | | | | | | | % 88.79/14.71 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_88_0, simplifying with % 88.79/14.71 | | | | | | | | | | | | | | | | (206), (207) gives: % 88.79/14.71 | | | | | | | | | | | | | | | | (231) ? [v0: $i] : (relation_dom(all_88_0) = v0 & % 88.79/14.71 | | | | | | | | | | | | | | | | relation(v0) = 0 & empty(v0) = 0 & $i(v0)) % 88.79/14.71 | | | | | | | | | | | | | | | | % 88.79/14.71 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with empty_set, simplifying with % 88.79/14.71 | | | | | | | | | | | | | | | | (14), (104) gives: % 88.79/14.71 | | | | | | | | | | | | | | | | (232) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & % 88.79/14.71 | | | | | | | | | | | | | | | | relation(empty_set) = v0) | % 88.79/14.71 | | | | | | | | | | | | | | | | (relation_dom(empty_set) = v1 & $i(v1) & ! [v2: % 88.79/14.71 | | | | | | | | | | | | | | | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 88.79/14.71 | | | | | | | | | | | | | | | | $i(v2) | ? [v5: int] : ? [v6: $i] : ? % 88.79/14.71 | | | | | | | | | | | | | | | | [v7: int] : (( ~ (v5 = 0) & in(v2, v1) = v5) % 88.79/14.71 | | | | | | | | | | | | | | | | | (((v7 = 0 & in(v4, empty_set) = 0) | ( ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (v6 = v3) & apply(empty_set, v2) = % 88.79/14.71 | | | | | | | | | | | | | | | | v6 & $i(v6))) & ((v6 = v3 & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(empty_set, v2) = v3) | ( ~ (v7 % 88.79/14.71 | | | | | | | | | | | | | | | | = 0) & in(v4, empty_set) = v7))))) % 88.79/14.71 | | | | | | | | | | | | | | | | & ? [v2: $i] : ! [v3: $i] : ! [v4: int] : % 88.79/14.71 | | | | | | | | | | | | | | | | (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | % 88.79/14.71 | | | | | | | | | | | | | | | | ~ $i(v2) | ? [v5: $i] : (( ~ (v2 = % 88.79/14.71 | | | | | | | | | | | | | | | | empty_set) | (v5 = empty_set & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(empty_set, v3) = empty_set)) & % 88.79/14.71 | | | | | | | | | | | | | | | | (v2 = empty_set | ( ~ (v5 = v2) & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(empty_set, v3) = v5 & $i(v5))))) % 88.79/14.71 | | | | | | | | | | | | | | | | & ! [v2: $i] : ! [v3: $i] : (v3 = empty_set % 88.79/14.71 | | | | | | | | | | | | | | | | | ~ (apply(empty_set, v2) = v3) | ~ $i(v3) % 88.79/14.71 | | | | | | | | | | | | | | | | | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 88.79/14.71 | | | | | | | | | | | | | | | | : ! [v3: $i] : (v3 = empty_set | ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (apply(empty_set, v2) = v3) | ~ $i(v2) | % 88.79/14.71 | | | | | | | | | | | | | | | | in(v2, v1) = 0))) % 88.79/14.71 | | | | | | | | | | | | | | | | % 88.79/14.71 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_48_2, simplifying with % 88.79/14.71 | | | | | | | | | | | | | | | | (146), (224) gives: % 88.79/14.71 | | | | | | | | | | | | | | | | (233) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & % 88.79/14.71 | | | | | | | | | | | | | | | | relation(all_48_2) = v0) | % 88.79/14.71 | | | | | | | | | | | | | | | | (relation_dom(all_48_2) = v1 & $i(v1) & ! [v2: % 88.79/14.71 | | | | | | | | | | | | | | | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 88.79/14.71 | | | | | | | | | | | | | | | | $i(v2) | ? [v5: int] : ? [v6: $i] : ? % 88.79/14.71 | | | | | | | | | | | | | | | | [v7: int] : (( ~ (v5 = 0) & in(v2, v1) = v5) % 88.79/14.71 | | | | | | | | | | | | | | | | | (((v7 = 0 & in(v4, all_48_2) = 0) | ( ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (v6 = v3) & apply(all_48_2, v2) = v6 % 88.79/14.71 | | | | | | | | | | | | | | | | & $i(v6))) & ((v6 = v3 & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(all_48_2, v2) = v3) | ( ~ (v7 % 88.79/14.71 | | | | | | | | | | | | | | | | = 0) & in(v4, all_48_2) = v7))))) % 88.79/14.71 | | | | | | | | | | | | | | | | & ? [v2: $i] : ! [v3: $i] : ! [v4: int] : % 88.79/14.71 | | | | | | | | | | | | | | | | (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | % 88.79/14.71 | | | | | | | | | | | | | | | | ~ $i(v2) | ? [v5: $i] : (( ~ (v2 = % 88.79/14.71 | | | | | | | | | | | | | | | | empty_set) | (v5 = empty_set & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(all_48_2, v3) = empty_set)) & % 88.79/14.71 | | | | | | | | | | | | | | | | (v2 = empty_set | ( ~ (v5 = v2) & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(all_48_2, v3) = v5 & $i(v5))))) % 88.79/14.71 | | | | | | | | | | | | | | | | & ! [v2: $i] : ! [v3: $i] : (v3 = empty_set % 88.79/14.71 | | | | | | | | | | | | | | | | | ~ (apply(all_48_2, v2) = v3) | ~ $i(v3) % 88.79/14.71 | | | | | | | | | | | | | | | | | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 88.79/14.71 | | | | | | | | | | | | | | | | : ! [v3: $i] : (v3 = empty_set | ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (apply(all_48_2, v2) = v3) | ~ $i(v2) | % 88.79/14.71 | | | | | | | | | | | | | | | | in(v2, v1) = 0))) % 88.79/14.71 | | | | | | | | | | | | | | | | % 88.79/14.71 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_48_2, simplifying with % 88.79/14.71 | | | | | | | | | | | | | | | | (147), (224) gives: % 88.79/14.71 | | | | | | | | | | | | | | | | (234) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & % 88.79/14.71 | | | | | | | | | | | | | | | | function(all_48_2) = v0) | % 88.79/14.71 | | | | | | | | | | | | | | | | (relation_dom(all_48_2) = v1 & $i(v1) & ! [v2: % 88.79/14.71 | | | | | | | | | | | | | | | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 88.79/14.71 | | | | | | | | | | | | | | | | $i(v2) | ? [v5: int] : ? [v6: $i] : ? % 88.79/14.71 | | | | | | | | | | | | | | | | [v7: int] : (( ~ (v5 = 0) & in(v2, v1) = v5) % 88.79/14.71 | | | | | | | | | | | | | | | | | (((v7 = 0 & in(v4, all_48_2) = 0) | ( ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (v6 = v3) & apply(all_48_2, v2) = v6 % 88.79/14.71 | | | | | | | | | | | | | | | | & $i(v6))) & ((v6 = v3 & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(all_48_2, v2) = v3) | ( ~ (v7 % 88.79/14.71 | | | | | | | | | | | | | | | | = 0) & in(v4, all_48_2) = v7))))) % 88.79/14.71 | | | | | | | | | | | | | | | | & ? [v2: $i] : ! [v3: $i] : ! [v4: int] : % 88.79/14.71 | | | | | | | | | | | | | | | | (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | % 88.79/14.71 | | | | | | | | | | | | | | | | ~ $i(v2) | ? [v5: $i] : (( ~ (v2 = % 88.79/14.71 | | | | | | | | | | | | | | | | empty_set) | (v5 = empty_set & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(all_48_2, v3) = empty_set)) & % 88.79/14.71 | | | | | | | | | | | | | | | | (v2 = empty_set | ( ~ (v5 = v2) & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(all_48_2, v3) = v5 & $i(v5))))) % 88.79/14.71 | | | | | | | | | | | | | | | | & ! [v2: $i] : ! [v3: $i] : (v3 = empty_set % 88.79/14.71 | | | | | | | | | | | | | | | | | ~ (apply(all_48_2, v2) = v3) | ~ $i(v3) % 88.79/14.71 | | | | | | | | | | | | | | | | | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 88.79/14.71 | | | | | | | | | | | | | | | | : ! [v3: $i] : (v3 = empty_set | ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (apply(all_48_2, v2) = v3) | ~ $i(v2) | % 88.79/14.71 | | | | | | | | | | | | | | | | in(v2, v1) = 0))) % 88.79/14.71 | | | | | | | | | | | | | | | | % 88.79/14.71 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_88_0, simplifying with % 88.79/14.71 | | | | | | | | | | | | | | | | (205), (207) gives: % 88.79/14.71 | | | | | | | | | | | | | | | | (235) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & % 88.79/14.71 | | | | | | | | | | | | | | | | function(all_88_0) = v0) | % 88.79/14.71 | | | | | | | | | | | | | | | | (relation_dom(all_88_0) = v1 & $i(v1) & ! [v2: % 88.79/14.71 | | | | | | | | | | | | | | | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 88.79/14.71 | | | | | | | | | | | | | | | | $i(v2) | ? [v5: int] : ? [v6: $i] : ? % 88.79/14.71 | | | | | | | | | | | | | | | | [v7: int] : (( ~ (v5 = 0) & in(v2, v1) = v5) % 88.79/14.71 | | | | | | | | | | | | | | | | | (((v7 = 0 & in(v4, all_88_0) = 0) | ( ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (v6 = v3) & apply(all_88_0, v2) = v6 % 88.79/14.71 | | | | | | | | | | | | | | | | & $i(v6))) & ((v6 = v3 & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(all_88_0, v2) = v3) | ( ~ (v7 % 88.79/14.71 | | | | | | | | | | | | | | | | = 0) & in(v4, all_88_0) = v7))))) % 88.79/14.71 | | | | | | | | | | | | | | | | & ? [v2: $i] : ! [v3: $i] : ! [v4: int] : % 88.79/14.71 | | | | | | | | | | | | | | | | (v4 = 0 | ~ (in(v3, v1) = v4) | ~ $i(v3) | % 88.79/14.71 | | | | | | | | | | | | | | | | ~ $i(v2) | ? [v5: $i] : (( ~ (v2 = % 88.79/14.71 | | | | | | | | | | | | | | | | empty_set) | (v5 = empty_set & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(all_88_0, v3) = empty_set)) & % 88.79/14.71 | | | | | | | | | | | | | | | | (v2 = empty_set | ( ~ (v5 = v2) & % 88.79/14.71 | | | | | | | | | | | | | | | | apply(all_88_0, v3) = v5 & $i(v5))))) % 88.79/14.71 | | | | | | | | | | | | | | | | & ! [v2: $i] : ! [v3: $i] : (v3 = empty_set % 88.79/14.71 | | | | | | | | | | | | | | | | | ~ (apply(all_88_0, v2) = v3) | ~ $i(v3) % 88.79/14.71 | | | | | | | | | | | | | | | | | ~ $i(v2) | in(v2, v1) = 0) & ! [v2: $i] % 88.79/14.71 | | | | | | | | | | | | | | | | : ! [v3: $i] : (v3 = empty_set | ~ % 88.79/14.71 | | | | | | | | | | | | | | | | (apply(all_88_0, v2) = v3) | ~ $i(v2) | % 88.79/14.71 | | | | | | | | | | | | | | | | in(v2, v1) = 0))) % 88.79/14.71 | | | | | | | | | | | | | | | | % 88.79/14.71 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_48_7, empty_set, % 88.79/14.71 | | | | | | | | | | | | | | | | all_88_0, all_48_2, all_48_1, simplifying with % 88.79/14.71 | | | | | | | | | | | | | | | | (14), (41), (53), (102), (224) gives: % 89.02/14.72 | | | | | | | | | | | | | | | | (236) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? % 89.02/14.72 | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: % 89.02/14.72 | | | | | | | | | | | | | | | | int] : ? [v7: int] : (( ~ (v1 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | function(all_48_2) = v1) | ( ~ (v1 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | function(empty_set) = v1) | ( ~ (v0 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation(all_48_2) = v0) | ( ~ (v0 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation(empty_set) = v0) | (((v7 = 0 & v6 = 0 % 89.02/14.72 | | | | | | | | | | | | | | | | & relation_dom(all_48_2) = v5 & % 89.02/14.72 | | | | | | | | | | | | | | | | in(all_48_1, all_88_0) = 0 & in(all_48_7, % 89.02/14.72 | | | | | | | | | | | | | | | | v5) = 0 & $i(v5)) | ( ~ (v4 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation_composition(all_48_2, empty_set) % 89.02/14.72 | | | | | | | | | | | | | | | | = v2 & relation_dom(v2) = v3 & % 89.02/14.72 | | | | | | | | | | | | | | | | in(all_48_7, v3) = v4 & $i(v3) & $i(v2))) % 89.02/14.72 | | | | | | | | | | | | | | | | & ((v4 = 0 & relation_composition(all_48_2, % 89.02/14.72 | | | | | | | | | | | | | | | | empty_set) = v2 & relation_dom(v2) = v3 % 89.02/14.72 | | | | | | | | | | | | | | | | & in(all_48_7, v3) = 0 & $i(v3) & $i(v2)) % 89.02/14.72 | | | | | | | | | | | | | | | | | ( ~ (v7 = 0) & in(all_48_1, all_88_0) = % 89.02/14.72 | | | | | | | | | | | | | | | | v7) | ( ~ (v6 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation_dom(all_48_2) = v5 & in(all_48_7, % 89.02/14.72 | | | | | | | | | | | | | | | | v5) = v6 & $i(v5))))) % 89.02/14.72 | | | | | | | | | | | | | | | | % 89.02/14.72 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_48_7, all_48_3, % 89.02/14.72 | | | | | | | | | | | | | | | | all_146_0, all_48_6, all_48_4, simplifying with % 89.02/14.72 | | | | | | | | | | | | | | | | (41), (42), (45), (51), (174) gives: % 89.02/14.72 | | | | | | | | | | | | | | | | (237) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? % 89.02/14.72 | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: % 89.02/14.72 | | | | | | | | | | | | | | | | int] : ? [v7: int] : (( ~ (v1 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | function(all_48_3) = v1) | ( ~ (v1 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | function(all_48_6) = v1) | ( ~ (v0 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation(all_48_3) = v0) | ( ~ (v0 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation(all_48_6) = v0) | (((v7 = 0 & v6 = 0 % 89.02/14.72 | | | | | | | | | | | | | | | | & relation_dom(all_48_6) = v5 & % 89.02/14.72 | | | | | | | | | | | | | | | | in(all_48_4, all_146_0) = 0 & in(all_48_7, % 89.02/14.72 | | | | | | | | | | | | | | | | v5) = 0 & $i(v5)) | ( ~ (v4 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 89.02/14.72 | | | | | | | | | | | | | | | | v2 & relation_dom(v2) = v3 & in(all_48_7, % 89.02/14.72 | | | | | | | | | | | | | | | | v3) = v4 & $i(v3) & $i(v2))) & ((v4 = 0 % 89.02/14.72 | | | | | | | | | | | | | | | | & relation_composition(all_48_6, all_48_3) % 89.02/14.72 | | | | | | | | | | | | | | | | = v2 & relation_dom(v2) = v3 & % 89.02/14.72 | | | | | | | | | | | | | | | | in(all_48_7, v3) = 0 & $i(v3) & $i(v2)) | % 89.02/14.72 | | | | | | | | | | | | | | | | ( ~ (v7 = 0) & in(all_48_4, all_146_0) = v7) % 89.02/14.72 | | | | | | | | | | | | | | | | | ( ~ (v6 = 0) & relation_dom(all_48_6) = v5 % 89.02/14.72 | | | | | | | | | | | | | | | | & in(all_48_7, v5) = v6 & $i(v5))))) % 89.02/14.72 | | | | | | | | | | | | | | | | % 89.02/14.72 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_48_2, all_118_3, % 89.02/14.72 | | | | | | | | | | | | | | | | all_48_7, all_48_1, simplifying with (41), (53), % 89.02/14.72 | | | | | | | | | | | | | | | | (204), (224) gives: % 89.02/14.72 | | | | | | | | | | | | | | | | (238) all_48_1 = empty_set | ? [v0: int] : ? [v1: int] % 89.02/14.72 | | | | | | | | | | | | | | | | : ((v0 = 0 & in(all_48_7, all_118_3) = 0) | ( ~ % 89.02/14.72 | | | | | | | | | | | | | | | | (v1 = 0) & function(all_48_2) = v1) | ( ~ (v0 % 89.02/14.72 | | | | | | | | | | | | | | | | = 0) & relation(all_48_2) = v0)) % 89.02/14.72 | | | | | | | | | | | | | | | | % 89.02/14.72 | | | | | | | | | | | | | | | | DELTA: instantiating (231) with fresh symbol all_314_0 % 89.02/14.72 | | | | | | | | | | | | | | | | gives: % 89.02/14.72 | | | | | | | | | | | | | | | | (239) relation_dom(all_88_0) = all_314_0 & % 89.02/14.72 | | | | | | | | | | | | | | | | relation(all_314_0) = 0 & empty(all_314_0) = 0 & % 89.02/14.72 | | | | | | | | | | | | | | | | $i(all_314_0) % 89.02/14.72 | | | | | | | | | | | | | | | | % 89.02/14.72 | | | | | | | | | | | | | | | | ALPHA: (239) implies: % 89.02/14.72 | | | | | | | | | | | | | | | | (240) relation(all_314_0) = 0 % 89.02/14.72 | | | | | | | | | | | | | | | | (241) relation_dom(all_88_0) = all_314_0 % 89.02/14.72 | | | | | | | | | | | | | | | | % 89.02/14.72 | | | | | | | | | | | | | | | | DELTA: instantiating (236) with fresh symbols all_360_0, % 89.02/14.72 | | | | | | | | | | | | | | | | all_360_1, all_360_2, all_360_3, all_360_4, % 89.02/14.72 | | | | | | | | | | | | | | | | all_360_5, all_360_6, all_360_7 gives: % 89.02/14.72 | | | | | | | | | | | | | | | | (242) ( ~ (all_360_6 = 0) & function(all_48_2) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_360_6) | ( ~ (all_360_6 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | function(empty_set) = all_360_6) | ( ~ % 89.02/14.72 | | | | | | | | | | | | | | | | (all_360_7 = 0) & relation(all_48_2) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_360_7) | ( ~ (all_360_7 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation(empty_set) = all_360_7) | (((all_360_0 % 89.02/14.72 | | | | | | | | | | | | | | | | = 0 & all_360_1 = 0 & relation_dom(all_48_2) % 89.02/14.72 | | | | | | | | | | | | | | | | = all_360_2 & in(all_48_1, all_88_0) = 0 & % 89.02/14.72 | | | | | | | | | | | | | | | | in(all_48_7, all_360_2) = 0 & $i(all_360_2)) % 89.02/14.72 | | | | | | | | | | | | | | | | | ( ~ (all_360_3 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation_composition(all_48_2, empty_set) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_360_5 & relation_dom(all_360_5) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_360_4 & in(all_48_7, all_360_4) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_360_3 & $i(all_360_4) & $i(all_360_5))) % 89.02/14.72 | | | | | | | | | | | | | | | | & ((all_360_3 = 0 & % 89.02/14.72 | | | | | | | | | | | | | | | | relation_composition(all_48_2, empty_set) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_360_5 & relation_dom(all_360_5) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_360_4 & in(all_48_7, all_360_4) = 0 & % 89.02/14.72 | | | | | | | | | | | | | | | | $i(all_360_4) & $i(all_360_5)) | ( ~ % 89.02/14.72 | | | | | | | | | | | | | | | | (all_360_0 = 0) & in(all_48_1, all_88_0) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_360_0) | ( ~ (all_360_1 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation_dom(all_48_2) = all_360_2 & % 89.02/14.72 | | | | | | | | | | | | | | | | in(all_48_7, all_360_2) = all_360_1 & % 89.02/14.72 | | | | | | | | | | | | | | | | $i(all_360_2)))) % 89.02/14.72 | | | | | | | | | | | | | | | | % 89.02/14.72 | | | | | | | | | | | | | | | | DELTA: instantiating (237) with fresh symbols all_361_0, % 89.02/14.72 | | | | | | | | | | | | | | | | all_361_1, all_361_2, all_361_3, all_361_4, % 89.02/14.72 | | | | | | | | | | | | | | | | all_361_5, all_361_6, all_361_7 gives: % 89.02/14.72 | | | | | | | | | | | | | | | | (243) ( ~ (all_361_6 = 0) & function(all_48_3) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_361_6) | ( ~ (all_361_6 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | function(all_48_6) = all_361_6) | ( ~ (all_361_7 % 89.02/14.72 | | | | | | | | | | | | | | | | = 0) & relation(all_48_3) = all_361_7) | ( ~ % 89.02/14.72 | | | | | | | | | | | | | | | | (all_361_7 = 0) & relation(all_48_6) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_361_7) | (((all_361_0 = 0 & all_361_1 = 0 & % 89.02/14.72 | | | | | | | | | | | | | | | | relation_dom(all_48_6) = all_361_2 & % 89.02/14.72 | | | | | | | | | | | | | | | | in(all_48_4, all_146_0) = 0 & in(all_48_7, % 89.02/14.72 | | | | | | | | | | | | | | | | all_361_2) = 0 & $i(all_361_2)) | ( ~ % 89.02/14.72 | | | | | | | | | | | | | | | | (all_361_3 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_361_5 & relation_dom(all_361_5) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_361_4 & in(all_48_7, all_361_4) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_361_3 & $i(all_361_4) & $i(all_361_5))) % 89.02/14.72 | | | | | | | | | | | | | | | | & ((all_361_3 = 0 & % 89.02/14.72 | | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_361_5 & relation_dom(all_361_5) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_361_4 & in(all_48_7, all_361_4) = 0 & % 89.02/14.72 | | | | | | | | | | | | | | | | $i(all_361_4) & $i(all_361_5)) | ( ~ % 89.02/14.72 | | | | | | | | | | | | | | | | (all_361_0 = 0) & in(all_48_4, all_146_0) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_361_0) | ( ~ (all_361_1 = 0) & % 89.02/14.72 | | | | | | | | | | | | | | | | relation_dom(all_48_6) = all_361_2 & % 89.02/14.72 | | | | | | | | | | | | | | | | in(all_48_7, all_361_2) = all_361_1 & % 89.02/14.72 | | | | | | | | | | | | | | | | $i(all_361_2)))) % 89.02/14.72 | | | | | | | | | | | | | | | | % 89.02/14.72 | | | | | | | | | | | | | | | | DELTA: instantiating (233) with fresh symbols all_366_0, % 89.02/14.72 | | | | | | | | | | | | | | | | all_366_1 gives: % 89.02/14.72 | | | | | | | | | | | | | | | | (244) ( ~ (all_366_1 = 0) & relation(all_48_2) = % 89.02/14.72 | | | | | | | | | | | | | | | | all_366_1) | (relation_dom(all_48_2) = all_366_0 % 89.02/14.72 | | | | | | | | | | | | | | | | & $i(all_366_0) & ! [v0: $i] : ! [v1: $i] : ! % 89.02/14.72 | | | | | | | | | | | | | | | | [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 89.02/14.72 | | | | | | | | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 89.02/14.72 | | | | | | | | | | | | | | | | $i] : ? [v5: int] : (( ~ (v3 = 0) & in(v0, % 89.02/14.72 | | | | | | | | | | | | | | | | all_366_0) = v3) | (((v5 = 0 & in(v2, % 89.02/14.72 | | | | | | | | | | | | | | | | all_48_2) = 0) | ( ~ (v4 = v1) & % 89.02/14.72 | | | | | | | | | | | | | | | | apply(all_48_2, v0) = v4 & $i(v4))) & % 89.02/14.72 | | | | | | | | | | | | | | | | ((v4 = v1 & apply(all_48_2, v0) = v1) | ( % 89.02/14.72 | | | | | | | | | | | | | | | | ~ (v5 = 0) & in(v2, all_48_2) = % 89.02/14.72 | | | | | | | | | | | | | | | | v5))))) & ? [v0: $i] : ! [v1: $i] : % 89.02/14.72 | | | | | | | | | | | | | | | | ! [v2: int] : (v2 = 0 | ~ (in(v1, all_366_0) = % 89.02/14.72 | | | | | | | | | | | | | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 89.02/14.72 | | | | | | | | | | | | | | | | (( ~ (v0 = empty_set) | (v3 = empty_set & % 89.02/14.72 | | | | | | | | | | | | | | | | apply(all_48_2, v1) = empty_set)) & (v0 % 89.02/14.72 | | | | | | | | | | | | | | | | = empty_set | ( ~ (v3 = v0) & % 89.02/14.72 | | | | | | | | | | | | | | | | apply(all_48_2, v1) = v3 & $i(v3))))) & % 89.02/14.72 | | | | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 89.02/14.72 | | | | | | | | | | | | | | | | (apply(all_48_2, v0) = v1) | ~ $i(v1) | ~ % 89.02/14.72 | | | | | | | | | | | | | | | | $i(v0) | in(v0, all_366_0) = 0) & ! [v0: $i] % 89.02/14.72 | | | | | | | | | | | | | | | | : ! [v1: $i] : (v1 = empty_set | ~ % 89.02/14.72 | | | | | | | | | | | | | | | | (apply(all_48_2, v0) = v1) | ~ $i(v0) | % 89.02/14.72 | | | | | | | | | | | | | | | | in(v0, all_366_0) = 0)) % 89.02/14.72 | | | | | | | | | | | | | | | | % 89.02/14.72 | | | | | | | | | | | | | | | | DELTA: instantiating (235) with fresh symbols all_367_0, % 89.02/14.72 | | | | | | | | | | | | | | | | all_367_1 gives: % 89.02/14.73 | | | | | | | | | | | | | | | | (245) ( ~ (all_367_1 = 0) & function(all_88_0) = % 89.02/14.73 | | | | | | | | | | | | | | | | all_367_1) | (relation_dom(all_88_0) = all_367_0 % 89.02/14.73 | | | | | | | | | | | | | | | | & $i(all_367_0) & ! [v0: $i] : ! [v1: $i] : ! % 89.02/14.73 | | | | | | | | | | | | | | | | [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 89.02/14.73 | | | | | | | | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 89.02/14.73 | | | | | | | | | | | | | | | | $i] : ? [v5: int] : (( ~ (v3 = 0) & in(v0, % 89.02/14.73 | | | | | | | | | | | | | | | | all_367_0) = v3) | (((v5 = 0 & in(v2, % 89.02/14.73 | | | | | | | | | | | | | | | | all_88_0) = 0) | ( ~ (v4 = v1) & % 89.02/14.73 | | | | | | | | | | | | | | | | apply(all_88_0, v0) = v4 & $i(v4))) & % 89.02/14.73 | | | | | | | | | | | | | | | | ((v4 = v1 & apply(all_88_0, v0) = v1) | ( % 89.02/14.73 | | | | | | | | | | | | | | | | ~ (v5 = 0) & in(v2, all_88_0) = % 89.02/14.73 | | | | | | | | | | | | | | | | v5))))) & ? [v0: $i] : ! [v1: $i] : % 89.02/14.73 | | | | | | | | | | | | | | | | ! [v2: int] : (v2 = 0 | ~ (in(v1, all_367_0) = % 89.02/14.73 | | | | | | | | | | | | | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 89.02/14.73 | | | | | | | | | | | | | | | | (( ~ (v0 = empty_set) | (v3 = empty_set & % 89.02/14.73 | | | | | | | | | | | | | | | | apply(all_88_0, v1) = empty_set)) & (v0 % 89.02/14.73 | | | | | | | | | | | | | | | | = empty_set | ( ~ (v3 = v0) & % 89.02/14.73 | | | | | | | | | | | | | | | | apply(all_88_0, v1) = v3 & $i(v3))))) & % 89.02/14.73 | | | | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 89.02/14.73 | | | | | | | | | | | | | | | | (apply(all_88_0, v0) = v1) | ~ $i(v1) | ~ % 89.02/14.73 | | | | | | | | | | | | | | | | $i(v0) | in(v0, all_367_0) = 0) & ! [v0: $i] % 89.02/14.73 | | | | | | | | | | | | | | | | : ! [v1: $i] : (v1 = empty_set | ~ % 89.02/14.73 | | | | | | | | | | | | | | | | (apply(all_88_0, v0) = v1) | ~ $i(v0) | % 89.02/14.73 | | | | | | | | | | | | | | | | in(v0, all_367_0) = 0)) % 89.02/14.73 | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | DELTA: instantiating (234) with fresh symbols all_368_0, % 89.02/14.73 | | | | | | | | | | | | | | | | all_368_1 gives: % 89.02/14.73 | | | | | | | | | | | | | | | | (246) ( ~ (all_368_1 = 0) & function(all_48_2) = % 89.02/14.73 | | | | | | | | | | | | | | | | all_368_1) | (relation_dom(all_48_2) = all_368_0 % 89.02/14.73 | | | | | | | | | | | | | | | | & $i(all_368_0) & ! [v0: $i] : ! [v1: $i] : ! % 89.02/14.73 | | | | | | | | | | | | | | | | [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 89.02/14.73 | | | | | | | | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 89.02/14.73 | | | | | | | | | | | | | | | | $i] : ? [v5: int] : (( ~ (v3 = 0) & in(v0, % 89.02/14.73 | | | | | | | | | | | | | | | | all_368_0) = v3) | (((v5 = 0 & in(v2, % 89.02/14.73 | | | | | | | | | | | | | | | | all_48_2) = 0) | ( ~ (v4 = v1) & % 89.02/14.73 | | | | | | | | | | | | | | | | apply(all_48_2, v0) = v4 & $i(v4))) & % 89.02/14.73 | | | | | | | | | | | | | | | | ((v4 = v1 & apply(all_48_2, v0) = v1) | ( % 89.02/14.73 | | | | | | | | | | | | | | | | ~ (v5 = 0) & in(v2, all_48_2) = % 89.02/14.73 | | | | | | | | | | | | | | | | v5))))) & ? [v0: $i] : ! [v1: $i] : % 89.02/14.73 | | | | | | | | | | | | | | | | ! [v2: int] : (v2 = 0 | ~ (in(v1, all_368_0) = % 89.02/14.73 | | | | | | | | | | | | | | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 89.02/14.73 | | | | | | | | | | | | | | | | (( ~ (v0 = empty_set) | (v3 = empty_set & % 89.02/14.73 | | | | | | | | | | | | | | | | apply(all_48_2, v1) = empty_set)) & (v0 % 89.02/14.73 | | | | | | | | | | | | | | | | = empty_set | ( ~ (v3 = v0) & % 89.02/14.73 | | | | | | | | | | | | | | | | apply(all_48_2, v1) = v3 & $i(v3))))) & % 89.02/14.73 | | | | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 89.02/14.73 | | | | | | | | | | | | | | | | (apply(all_48_2, v0) = v1) | ~ $i(v1) | ~ % 89.02/14.73 | | | | | | | | | | | | | | | | $i(v0) | in(v0, all_368_0) = 0) & ! [v0: $i] % 89.02/14.73 | | | | | | | | | | | | | | | | : ! [v1: $i] : (v1 = empty_set | ~ % 89.02/14.73 | | | | | | | | | | | | | | | | (apply(all_48_2, v0) = v1) | ~ $i(v0) | % 89.02/14.73 | | | | | | | | | | | | | | | | in(v0, all_368_0) = 0)) % 89.02/14.73 | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | DELTA: instantiating (232) with fresh symbols all_369_0, % 89.02/14.73 | | | | | | | | | | | | | | | | all_369_1 gives: % 89.02/14.73 | | | | | | | | | | | | | | | | (247) ( ~ (all_369_1 = 0) & relation(empty_set) = % 89.02/14.73 | | | | | | | | | | | | | | | | all_369_1) | (relation_dom(empty_set) = % 89.02/14.73 | | | | | | | | | | | | | | | | all_369_0 & $i(all_369_0) & ! [v0: $i] : ! % 89.02/14.73 | | | | | | | | | | | | | | | | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, % 89.02/14.73 | | | | | | | | | | | | | | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 89.02/14.73 | | | | | | | | | | | | | | | | [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ % 89.02/14.73 | | | | | | | | | | | | | | | | (v3 = 0) & in(v0, all_369_0) = v3) | (((v5 % 89.02/14.73 | | | | | | | | | | | | | | | | = 0 & in(v2, empty_set) = 0) | ( ~ (v4 % 89.02/14.73 | | | | | | | | | | | | | | | | = v1) & apply(empty_set, v0) = v4 & % 89.02/14.73 | | | | | | | | | | | | | | | | $i(v4))) & ((v4 = v1 & % 89.02/14.73 | | | | | | | | | | | | | | | | apply(empty_set, v0) = v1) | ( ~ (v5 = % 89.02/14.73 | | | | | | | | | | | | | | | | 0) & in(v2, empty_set) = v5))))) & % 89.02/14.73 | | | | | | | | | | | | | | | | ? [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 89.02/14.73 | | | | | | | | | | | | | | | | 0 | ~ (in(v1, all_369_0) = v2) | ~ $i(v1) | % 89.02/14.73 | | | | | | | | | | | | | | | | ~ $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) % 89.02/14.73 | | | | | | | | | | | | | | | | | (v3 = empty_set & apply(empty_set, v1) = % 89.02/14.73 | | | | | | | | | | | | | | | | empty_set)) & (v0 = empty_set | ( ~ (v3 % 89.02/14.73 | | | | | | | | | | | | | | | | = v0) & apply(empty_set, v1) = v3 & % 89.02/14.73 | | | | | | | | | | | | | | | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : % 89.02/14.73 | | | | | | | | | | | | | | | | (v1 = empty_set | ~ (apply(empty_set, v0) = v1) % 89.02/14.73 | | | | | | | | | | | | | | | | | ~ $i(v1) | ~ $i(v0) | in(v0, all_369_0) = % 89.02/14.73 | | | | | | | | | | | | | | | | 0) & ! [v0: $i] : ! [v1: $i] : (v1 = % 89.02/14.73 | | | | | | | | | | | | | | | | empty_set | ~ (apply(empty_set, v0) = v1) | % 89.02/14.73 | | | | | | | | | | | | | | | | ~ $i(v0) | in(v0, all_369_0) = 0)) % 89.02/14.73 | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | REDUCE: (229), (241) imply: % 89.02/14.73 | | | | | | | | | | | | | | | | (248) relation_dom(empty_set) = all_314_0 % 89.02/14.73 | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | REDUCE: (102), (229) imply: % 89.02/14.73 | | | | | | | | | | | | | | | | (249) relation_dom(empty_set) = empty_set % 89.02/14.73 | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 89.02/14.73 | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | Case 1: % 89.02/14.73 | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | (250) ~ (all_368_1 = 0) & function(all_48_2) = % 89.02/14.73 | | | | | | | | | | | | | | | | | all_368_1 % 89.02/14.73 | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | ALPHA: (250) implies: % 89.02/14.73 | | | | | | | | | | | | | | | | | (251) ~ (all_368_1 = 0) % 89.02/14.73 | | | | | | | | | | | | | | | | | (252) function(all_48_2) = all_368_1 % 89.02/14.73 | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_368_1, all_48_2, % 89.02/14.73 | | | | | | | | | | | | | | | | | simplifying with (146), (252) gives: % 89.02/14.73 | | | | | | | | | | | | | | | | | (253) all_368_1 = 0 % 89.02/14.73 | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | REDUCE: (251), (253) imply: % 89.02/14.73 | | | | | | | | | | | | | | | | | (254) $false % 89.02/14.73 | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | CLOSE: (254) is inconsistent. % 89.02/14.73 | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | Case 2: % 89.02/14.73 | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | (255) relation_dom(all_48_2) = all_368_0 & $i(all_368_0) % 89.02/14.73 | | | | | | | | | | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 89.02/14.73 | | | | | | | | | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 89.02/14.73 | | | | | | | | | | | | | | | | | $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: % 89.02/14.73 | | | | | | | | | | | | | | | | | int] : (( ~ (v3 = 0) & in(v0, all_368_0) = v3) % 89.02/14.73 | | | | | | | | | | | | | | | | | | (((v5 = 0 & in(v2, all_48_2) = 0) | ( ~ (v4 % 89.02/14.73 | | | | | | | | | | | | | | | | | = v1) & apply(all_48_2, v0) = v4 & % 89.02/14.73 | | | | | | | | | | | | | | | | | $i(v4))) & ((v4 = v1 & apply(all_48_2, % 89.02/14.73 | | | | | | | | | | | | | | | | | v0) = v1) | ( ~ (v5 = 0) & in(v2, % 89.02/14.73 | | | | | | | | | | | | | | | | | all_48_2) = v5))))) & ? [v0: $i] : ! % 89.02/14.73 | | | | | | | | | | | | | | | | | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, % 89.02/14.73 | | | | | | | | | | | | | | | | | all_368_0) = v2) | ~ $i(v1) | ~ $i(v0) | % 89.02/14.73 | | | | | | | | | | | | | | | | | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 89.02/14.73 | | | | | | | | | | | | | | | | | empty_set & apply(all_48_2, v1) = % 89.02/14.73 | | | | | | | | | | | | | | | | | empty_set)) & (v0 = empty_set | ( ~ (v3 = % 89.02/14.73 | | | | | | | | | | | | | | | | | v0) & apply(all_48_2, v1) = v3 & % 89.02/14.73 | | | | | | | | | | | | | | | | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : % 89.02/14.73 | | | | | | | | | | | | | | | | | (v1 = empty_set | ~ (apply(all_48_2, v0) = v1) | % 89.02/14.73 | | | | | | | | | | | | | | | | | ~ $i(v1) | ~ $i(v0) | in(v0, all_368_0) = 0) & % 89.02/14.73 | | | | | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 89.02/14.73 | | | | | | | | | | | | | | | | | (apply(all_48_2, v0) = v1) | ~ $i(v0) | in(v0, % 89.02/14.73 | | | | | | | | | | | | | | | | | all_368_0) = 0) % 89.02/14.73 | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | ALPHA: (255) implies: % 89.02/14.73 | | | | | | | | | | | | | | | | | (256) relation_dom(all_48_2) = all_368_0 % 89.02/14.73 | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 89.02/14.73 | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | Case 1: % 89.02/14.73 | | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | | (257) all_48_1 = empty_set % 89.02/14.73 | | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | | REDUCE: (40), (257) imply: % 89.02/14.73 | | | | | | | | | | | | | | | | | | (258) ~ (all_48_0 = empty_set) % 89.02/14.73 | | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 89.02/14.73 | | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | | Case 1: % 89.02/14.73 | | | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | | | (259) in(all_48_4, all_147_0) = 0 % 89.02/14.73 | | | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | | | REDUCE: (193), (259) imply: % 89.02/14.73 | | | | | | | | | | | | | | | | | | | (260) in(all_48_4, all_146_0) = 0 % 89.02/14.73 | | | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 89.02/14.73 | | | | | | | | | | | | | | | | | | | % 89.02/14.73 | | | | | | | | | | | | | | | | | | | Case 1: % 89.02/14.73 | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | (261) ( ~ (all_361_6 = 0) & function(all_48_3) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | all_361_6) | ( ~ (all_361_6 = 0) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | function(all_48_6) = all_361_6) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | Case 1: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (262) ~ (all_361_6 = 0) & function(all_48_3) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | all_361_6 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (263) ~ (all_361_6 = 0) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (264) function(all_48_3) = all_361_6 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_361_6, all_48_3, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | simplifying with (48), (264) gives: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (265) all_361_6 = 0 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | REDUCE: (263), (265) imply: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (266) $false % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | CLOSE: (266) is inconsistent. % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | Case 2: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (267) ~ (all_361_6 = 0) & function(all_48_6) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | all_361_6 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (268) ~ (all_361_6 = 0) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (269) function(all_48_6) = all_361_6 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_361_6, all_48_6, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | simplifying with (47), (269) gives: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (270) all_361_6 = 0 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (270) imply: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (271) $false % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | CLOSE: (271) is inconsistent. % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | End of split % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | Case 2: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | (272) ( ~ (all_361_7 = 0) & relation(all_48_3) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | all_361_7) | ( ~ (all_361_7 = 0) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | relation(all_48_6) = all_361_7) | (((all_361_0 = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | 0 & all_361_1 = 0 & relation_dom(all_48_6) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | all_361_2 & in(all_48_4, all_146_0) = 0 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | in(all_48_7, all_361_2) = 0 & $i(all_361_2)) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_361_3 = 0) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | all_361_5 & relation_dom(all_361_5) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | all_361_4 & in(all_48_7, all_361_4) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | all_361_3 & $i(all_361_4) & $i(all_361_5))) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | & ((all_361_3 = 0 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | all_361_5 & relation_dom(all_361_5) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | all_361_4 & in(all_48_7, all_361_4) = 0 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | $i(all_361_4) & $i(all_361_5)) | ( ~ % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | (all_361_0 = 0) & in(all_48_4, all_146_0) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | all_361_0) | ( ~ (all_361_1 = 0) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | relation_dom(all_48_6) = all_361_2 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | in(all_48_7, all_361_2) = all_361_1 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | $i(all_361_2)))) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | Case 1: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (273) ~ (all_361_7 = 0) & relation(all_48_3) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | all_361_7 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (274) ~ (all_361_7 = 0) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (275) relation(all_48_3) = all_361_7 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_361_7, all_48_3, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | simplifying with (50), (275) gives: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (276) all_361_7 = 0 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (276) imply: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (277) $false % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | CLOSE: (277) is inconsistent. % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | Case 2: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (278) ( ~ (all_361_7 = 0) & relation(all_48_6) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | all_361_7) | (((all_361_0 = 0 & all_361_1 = 0 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | relation_dom(all_48_6) = all_361_2 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | in(all_48_4, all_146_0) = 0 & in(all_48_7, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | all_361_2) = 0 & $i(all_361_2)) | ( ~ % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (all_361_3 = 0) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | all_361_5 & relation_dom(all_361_5) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | all_361_4 & in(all_48_7, all_361_4) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | all_361_3 & $i(all_361_4) & $i(all_361_5))) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | & ((all_361_3 = 0 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | all_361_5 & relation_dom(all_361_5) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | all_361_4 & in(all_48_7, all_361_4) = 0 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | $i(all_361_4) & $i(all_361_5)) | ( ~ % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | (all_361_0 = 0) & in(all_48_4, all_146_0) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | all_361_0) | ( ~ (all_361_1 = 0) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | relation_dom(all_48_6) = all_361_2 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | in(all_48_7, all_361_2) = all_361_1 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | $i(all_361_2)))) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (279) ~ (all_361_7 = 0) & relation(all_48_6) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_361_7 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (280) ~ (all_361_7 = 0) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (281) relation(all_48_6) = all_361_7 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_361_7, all_48_6, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | simplifying with (49), (281) gives: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (282) all_361_7 = 0 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (280), (282) imply: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (283) $false % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent. % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (284) ((all_361_0 = 0 & all_361_1 = 0 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_48_6) = all_361_2 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | in(all_48_4, all_146_0) = 0 & in(all_48_7, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_361_2) = 0 & $i(all_361_2)) | ( ~ % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (all_361_3 = 0) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_361_5 & relation_dom(all_361_5) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_361_4 & in(all_48_7, all_361_4) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_361_3 & $i(all_361_4) & $i(all_361_5))) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | ((all_361_3 = 0 & relation_composition(all_48_6, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_48_3) = all_361_5 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_361_5) = all_361_4 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | in(all_48_7, all_361_4) = 0 & $i(all_361_4) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | $i(all_361_5)) | ( ~ (all_361_0 = 0) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | in(all_48_4, all_146_0) = all_361_0) | ( ~ % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (all_361_1 = 0) & relation_dom(all_48_6) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_361_2 & in(all_48_7, all_361_2) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_361_1 & $i(all_361_2))) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (285) (all_361_3 = 0 & relation_composition(all_48_6, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_48_3) = all_361_5 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_361_5) = all_361_4 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | in(all_48_7, all_361_4) = 0 & $i(all_361_4) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | $i(all_361_5)) | ( ~ (all_361_0 = 0) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | in(all_48_4, all_146_0) = all_361_0) | ( ~ % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (all_361_1 = 0) & relation_dom(all_48_6) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_361_2 & in(all_48_7, all_361_2) = all_361_1 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | & $i(all_361_2)) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (286) (all_361_0 = 0 & all_361_1 = 0 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_48_6) = all_361_2 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | in(all_48_4, all_146_0) = 0 & in(all_48_7, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_361_2) = 0 & $i(all_361_2)) | ( ~ % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | (all_361_3 = 0) & relation_composition(all_48_6, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | all_48_3) = all_361_5 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_361_5) = all_361_4 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | in(all_48_7, all_361_4) = all_361_3 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | $i(all_361_4) & $i(all_361_5)) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | (287) ~ (all_367_1 = 0) & function(all_88_0) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | all_367_1 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (287) implies: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | (288) ~ (all_367_1 = 0) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | (289) function(all_88_0) = all_367_1 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (229), (289) imply: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | (290) function(empty_set) = all_367_1 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_367_1, empty_set, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (104), (290) gives: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | (291) all_367_1 = 0 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (288), (291) imply: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | (292) $false % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent. % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | (293) relation_dom(all_88_0) = all_367_0 & $i(all_367_0) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | int] : (( ~ (v3 = 0) & in(v0, all_367_0) = v3) % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | | (((v5 = 0 & in(v2, all_88_0) = 0) | ( ~ (v4 % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | = v1) & apply(all_88_0, v0) = v4 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | $i(v4))) & ((v4 = v1 & apply(all_88_0, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | v0) = v1) | ( ~ (v5 = 0) & in(v2, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | all_88_0) = v5))))) & ? [v0: $i] : ! % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | all_367_0) = v2) | ~ $i(v1) | ~ $i(v0) | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | empty_set & apply(all_88_0, v1) = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | empty_set)) & (v0 = empty_set | ( ~ (v3 = % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | v0) & apply(all_88_0, v1) = v3 & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | (v1 = empty_set | ~ (apply(all_88_0, v0) = v1) | % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | ~ $i(v1) | ~ $i(v0) | in(v0, all_367_0) = 0) & % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | (apply(all_88_0, v0) = v1) | ~ $i(v0) | in(v0, % 89.02/14.74 | | | | | | | | | | | | | | | | | | | | | | | all_367_0) = 0) % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | (294) relation_dom(all_88_0) = all_367_0 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (229), (294) imply: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | (295) relation_dom(empty_set) = all_367_0 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | (296) all_361_3 = 0 & relation_composition(all_48_6, % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | all_48_3) = all_361_5 & relation_dom(all_361_5) % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | = all_361_4 & in(all_48_7, all_361_4) = 0 & % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_361_4) & $i(all_361_5) % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | (297) all_361_3 = 0 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | (298) in(all_48_7, all_361_4) = 0 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | (299) relation_dom(all_361_5) = all_361_4 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | (300) relation_composition(all_48_6, all_48_3) = % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | all_361_5 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | (301) ~ (all_369_1 = 0) & relation(empty_set) = % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | all_369_1 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | (302) ~ (all_369_1 = 0) % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | (303) relation(empty_set) = all_369_1 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_369_1, empty_set, % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (6), (303) gives: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_369_1 = 0 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (302), (304) imply: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | (305) $false % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent. % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | (306) relation_dom(empty_set) = all_369_0 & % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_369_0) & ! [v0: $i] : ! [v1: $i] : ! % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | : ? [v5: int] : (( ~ (v3 = 0) & in(v0, % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | all_369_0) = v3) | (((v5 = 0 & in(v2, % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | empty_set) = 0) | ( ~ (v4 = v1) & % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | apply(empty_set, v0) = v4 & $i(v4))) & % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | ((v4 = v1 & apply(empty_set, v0) = v1) | ( ~ % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | (v5 = 0) & in(v2, empty_set) = v5))))) & % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | ? [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (in(v1, all_369_0) = v2) | ~ $i(v1) | ~ % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v3: $i] : (( ~ (v0 = empty_set) | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | (v3 = empty_set & apply(empty_set, v1) = % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | empty_set)) & (v0 = empty_set | ( ~ (v3 = % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | v0) & apply(empty_set, v1) = v3 & % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = empty_set | ~ (apply(empty_set, v0) = v1) | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | ~ $i(v1) | ~ $i(v0) | in(v0, all_369_0) = 0) & % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | (apply(empty_set, v0) = v1) | ~ $i(v0) | in(v0, % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | all_369_0) = 0) % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (306) implies: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | (307) relation_dom(empty_set) = all_369_0 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (308) ~ (all_366_1 = 0) & relation(all_48_2) = % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | all_366_1 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies: % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (309) ~ (all_366_1 = 0) % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (310) relation(all_48_2) = all_366_1 % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_366_1, all_48_2, % 89.02/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (147), (310) gives: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_366_1 = 0 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (311) imply: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (312) $false % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (312) is inconsistent. % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (313) relation_dom(all_48_2) = all_366_0 & $i(all_366_0) % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | int] : (( ~ (v3 = 0) & in(v0, all_366_0) = v3) % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (((v5 = 0 & in(v2, all_48_2) = 0) | ( ~ (v4 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | = v1) & apply(all_48_2, v0) = v4 & % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v4))) & ((v4 = v1 & apply(all_48_2, % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | v0) = v1) | ( ~ (v5 = 0) & in(v2, % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | all_48_2) = v5))))) & ? [v0: $i] : ! % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v1, % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | all_366_0) = v2) | ~ $i(v1) | ~ $i(v0) | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ? [v3: $i] : (( ~ (v0 = empty_set) | (v3 = % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | empty_set & apply(all_48_2, v1) = % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | empty_set)) & (v0 = empty_set | ( ~ (v3 = % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | v0) & apply(all_48_2, v1) = v3 & % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v3))))) & ! [v0: $i] : ! [v1: $i] : % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = empty_set | ~ (apply(all_48_2, v0) = v1) | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ $i(v1) | ~ $i(v0) | in(v0, all_366_0) = 0) & % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (apply(all_48_2, v0) = v1) | ~ $i(v0) | in(v0, % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | all_366_0) = 0) % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (314) relation_dom(all_48_2) = all_366_0 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_314_0, all_367_0, % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | empty_set, simplifying with (248), (295) gives: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_367_0 = all_314_0 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_367_0, all_369_0, % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | empty_set, simplifying with (295), (307) gives: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_369_0 = all_367_0 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with empty_set, all_369_0, % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | empty_set, simplifying with (249), (307) gives: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_369_0 = empty_set % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_118_3, all_368_0, % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_48_2, simplifying with (204), (256) gives: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_368_0 = all_118_3 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_366_0, all_368_0, % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_48_2, simplifying with (256), (314) gives: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_368_0 = all_366_0 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_48_2, all_361_5, % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_48_3, all_48_6, simplifying with (55), (300) % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_361_5 = all_48_2 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (317) imply: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_367_0 = empty_set % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (321) implies: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_367_0 = empty_set % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (319) imply: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_366_0 = all_118_3 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (323) implies: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_366_0 = all_118_3 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (322) imply: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_314_0 = empty_set % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (325) implies: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_314_0 = empty_set % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (299), (320) imply: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) relation_dom(all_48_2) = all_361_4 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) ( ~ (all_360_6 = 0) & function(all_48_2) = % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_6) | ( ~ (all_360_6 = 0) & % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | function(empty_set) = all_360_6) % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) ~ (all_360_6 = 0) & function(all_48_2) = % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_6 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) ~ (all_360_6 = 0) % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) function(all_48_2) = all_360_6 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_360_6, all_48_2, % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (146), (331) gives: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_360_6 = 0 % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (332) imply: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) $false % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (333) is inconsistent. % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) ~ (all_360_6 = 0) & function(empty_set) = % 89.16/14.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_6 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) ~ (all_360_6 = 0) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) function(empty_set) = all_360_6 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_360_6, empty_set, % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (104), (336) gives: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_360_6 = 0 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (335), (337) imply: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) $false % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (338) is inconsistent. % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) ( ~ (all_360_7 = 0) & relation(all_48_2) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_7) | ( ~ (all_360_7 = 0) & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation(empty_set) = all_360_7) | (((all_360_0 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0 & all_360_1 = 0 & relation_dom(all_48_2) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_360_2 & in(all_48_1, all_88_0) = 0 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_48_7, all_360_2) = 0 & $i(all_360_2)) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_360_3 = 0) & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_48_2, empty_set) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_5 & relation_dom(all_360_5) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_4 & in(all_48_7, all_360_4) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_3 & $i(all_360_4) & $i(all_360_5))) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ((all_360_3 = 0 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_48_2, empty_set) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_5 & relation_dom(all_360_5) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_4 & in(all_48_7, all_360_4) = 0 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_360_4) & $i(all_360_5)) | ( ~ % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_360_0 = 0) & in(all_48_1, all_88_0) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_0) | ( ~ (all_360_1 = 0) & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_48_2) = all_360_2 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_48_7, all_360_2) = all_360_1 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_360_2)))) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) ~ (all_360_7 = 0) & relation(all_48_2) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_7 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (340) implies: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) ~ (all_360_7 = 0) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) relation(all_48_2) = all_360_7 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_360_7, all_48_2, % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (147), (342) gives: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_360_7 = 0 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (341), (343) imply: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) $false % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (344) is inconsistent. % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) ( ~ (all_360_7 = 0) & relation(empty_set) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_7) | (((all_360_0 = 0 & all_360_1 = 0 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_48_2) = all_360_2 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_48_1, all_88_0) = 0 & in(all_48_7, % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_2) = 0 & $i(all_360_2)) | ( ~ % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_360_3 = 0) & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_48_2, empty_set) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_5 & relation_dom(all_360_5) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_4 & in(all_48_7, all_360_4) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_3 & $i(all_360_4) & $i(all_360_5))) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ((all_360_3 = 0 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_48_2, empty_set) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_5 & relation_dom(all_360_5) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_4 & in(all_48_7, all_360_4) = 0 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_360_4) & $i(all_360_5)) | ( ~ % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_360_0 = 0) & in(all_48_1, all_88_0) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_0) | ( ~ (all_360_1 = 0) & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_48_2) = all_360_2 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_48_7, all_360_2) = all_360_1 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_360_2)))) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) ~ (all_360_7 = 0) & relation(empty_set) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_7 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (346) implies: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) ~ (all_360_7 = 0) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) relation(empty_set) = all_360_7 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_360_7, empty_set, % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (6), (348) gives: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_360_7 = 0 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (349) imply: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) $false % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (350) is inconsistent. % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_118_3, all_361_4, % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_48_2, simplifying with (204), (327) gives: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_361_4 = all_118_3 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (298), (351) imply: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) in(all_48_7, all_118_3) = 0 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (132), (228), (352) are inconsistent by % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) ~ (all_361_3 = 0) & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | relation_composition(all_48_6, all_48_3) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_361_5 & relation_dom(all_361_5) = all_361_4 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | in(all_48_7, all_361_4) = all_361_3 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_361_4) & $i(all_361_5) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_361_3 = 0) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (297), (354) imply: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) $false % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (355) is inconsistent. % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | (356) ( ~ (all_361_0 = 0) & in(all_48_4, all_146_0) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | all_361_0) | ( ~ (all_361_1 = 0) & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_48_6) = all_361_2 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | in(all_48_7, all_361_2) = all_361_1 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_361_2)) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (356) gives: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | (357) ~ (all_361_0 = 0) & in(all_48_4, all_146_0) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | all_361_0 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (357) implies: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | (358) ~ (all_361_0 = 0) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | (359) in(all_48_4, all_146_0) = all_361_0 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_361_0, all_146_0, % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | all_48_4, simplifying with (260), (359) gives: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_361_0 = 0 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (360) imply: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | (361) $false % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (361) is inconsistent. % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | (362) ~ (all_361_1 = 0) & relation_dom(all_48_6) = % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | all_361_2 & in(all_48_7, all_361_2) = all_361_1 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_361_2) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (362) implies: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | (363) ~ (all_361_1 = 0) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | (364) in(all_48_7, all_361_2) = all_361_1 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | (365) relation_dom(all_48_6) = all_361_2 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_361_0 = 0 & all_361_1 = 0 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | relation_dom(all_48_6) = all_361_2 & in(all_48_4, % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | all_146_0) = 0 & in(all_48_7, all_361_2) = 0 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_361_2) % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (366) implies: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_361_1 = 0 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (367) imply: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (368) $false % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (368) is inconsistent. % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_48_5, all_361_2, % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | all_48_6, simplifying with (54), (365) gives: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_361_2 = all_48_5 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (369) imply: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (370) in(all_48_7, all_48_5) = all_361_1 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_361_1, all_48_5, % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | all_48_7, simplifying with (46), (370) gives: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_361_1 = 0 % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (371) imply: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (372) $false % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (372) is inconsistent. % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | (373) all_48_0 = empty_set % 89.16/14.76 | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | REDUCE: (258), (373) imply: % 89.16/14.76 | | | | | | | | | | | | | | | | | | | (374) $false % 89.16/14.76 | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | | CLOSE: (374) is inconsistent. % 89.16/14.76 | | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | End of split % 89.16/14.76 | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.76 | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | (375) ? [v0: int] : ? [v1: int] : ((v0 = 0 & % 89.16/14.76 | | | | | | | | | | | | | | | | | | in(all_48_7, all_118_3) = 0) | ( ~ (v1 = 0) & % 89.16/14.76 | | | | | | | | | | | | | | | | | | function(all_48_2) = v1) | ( ~ (v0 = 0) & % 89.16/14.76 | | | | | | | | | | | | | | | | | | relation(all_48_2) = v0)) % 89.16/14.76 | | | | | | | | | | | | | | | | | | % 89.16/14.76 | | | | | | | | | | | | | | | | | | DELTA: instantiating (375) with fresh symbols all_455_0, % 89.16/14.76 | | | | | | | | | | | | | | | | | | all_455_1 gives: % 89.16/14.77 | | | | | | | | | | | | | | | | | | (376) (all_455_1 = 0 & in(all_48_7, all_118_3) = 0) | ( % 89.16/14.77 | | | | | | | | | | | | | | | | | | ~ (all_455_0 = 0) & function(all_48_2) = % 89.16/14.77 | | | | | | | | | | | | | | | | | | all_455_0) | ( ~ (all_455_1 = 0) & % 89.16/14.77 | | | | | | | | | | | | | | | | | | relation(all_48_2) = all_455_1) % 89.16/14.77 | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | BETA: splitting (376) gives: % 89.16/14.77 | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | Case 1: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | (377) all_455_1 = 0 & in(all_48_7, all_118_3) = 0 % 89.16/14.77 | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | ALPHA: (377) implies: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | (378) in(all_48_7, all_118_3) = 0 % 89.16/14.77 | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (132), (228), (378) are inconsistent by % 89.16/14.77 | | | | | | | | | | | | | | | | | | | sub-proof #1. % 89.16/14.77 | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | (379) ( ~ (all_455_0 = 0) & function(all_48_2) = % 89.16/14.77 | | | | | | | | | | | | | | | | | | | all_455_0) | ( ~ (all_455_1 = 0) & % 89.16/14.77 | | | | | | | | | | | | | | | | | | | relation(all_48_2) = all_455_1) % 89.16/14.77 | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | Case 1: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | (380) ~ (all_455_0 = 0) & function(all_48_2) = % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | all_455_0 % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | (381) ~ (all_455_0 = 0) % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | (382) function(all_48_2) = all_455_0 % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_455_0, all_48_2, % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | simplifying with (146), (382) gives: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | (383) all_455_0 = 0 % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (383) imply: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | (384) $false % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | CLOSE: (384) is inconsistent. % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | Case 2: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | (385) ~ (all_455_1 = 0) & relation(all_48_2) = % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | all_455_1 % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | ALPHA: (385) implies: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | (386) ~ (all_455_1 = 0) % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | (387) relation(all_48_2) = all_455_1 % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_455_1, all_48_2, % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | simplifying with (147), (387) gives: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | (388) all_455_1 = 0 % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | REDUCE: (386), (388) imply: % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | (389) $false % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | CLOSE: (389) is inconsistent. % 89.16/14.77 | | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | Case 2: % 89.16/14.77 | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | (390) ( ~ (all_131_5 = 0) & function(all_48_6) = % 89.16/14.77 | | | | | | | | | | | | | | | all_131_5) | ( ~ (all_131_6 = 0) & % 89.16/14.77 | | | | | | | | | | | | | | | relation(all_48_3) = all_131_6) | ( ~ (all_131_6 % 89.16/14.77 | | | | | | | | | | | | | | | = 0) & relation(all_48_6) = all_131_6) % 89.16/14.77 | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | BETA: splitting (390) gives: % 89.16/14.77 | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | Case 1: % 89.16/14.77 | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | (391) ~ (all_131_5 = 0) & function(all_48_6) = % 89.16/14.77 | | | | | | | | | | | | | | | | all_131_5 % 89.16/14.77 | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | ALPHA: (391) implies: % 89.16/14.77 | | | | | | | | | | | | | | | | (392) ~ (all_131_5 = 0) % 89.16/14.77 | | | | | | | | | | | | | | | | (393) function(all_48_6) = all_131_5 % 89.16/14.77 | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_131_5, all_48_6, % 89.16/14.77 | | | | | | | | | | | | | | | | simplifying with (47), (393) gives: % 89.16/14.77 | | | | | | | | | | | | | | | | (394) all_131_5 = 0 % 89.16/14.77 | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | REDUCE: (392), (394) imply: % 89.16/14.77 | | | | | | | | | | | | | | | | (395) $false % 89.16/14.77 | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | CLOSE: (395) is inconsistent. % 89.16/14.77 | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | Case 2: % 89.16/14.77 | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | (396) ( ~ (all_131_6 = 0) & relation(all_48_3) = % 89.16/14.77 | | | | | | | | | | | | | | | | all_131_6) | ( ~ (all_131_6 = 0) & % 89.16/14.77 | | | | | | | | | | | | | | | | relation(all_48_6) = all_131_6) % 89.16/14.77 | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | BETA: splitting (396) gives: % 89.16/14.77 | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | Case 1: % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | (397) ~ (all_131_6 = 0) & relation(all_48_3) = % 89.16/14.77 | | | | | | | | | | | | | | | | | all_131_6 % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | ALPHA: (397) implies: % 89.16/14.77 | | | | | | | | | | | | | | | | | (398) ~ (all_131_6 = 0) % 89.16/14.77 | | | | | | | | | | | | | | | | | (399) relation(all_48_3) = all_131_6 % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_131_6, all_48_3, % 89.16/14.77 | | | | | | | | | | | | | | | | | simplifying with (50), (399) gives: % 89.16/14.77 | | | | | | | | | | | | | | | | | (400) all_131_6 = 0 % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | REDUCE: (398), (400) imply: % 89.16/14.77 | | | | | | | | | | | | | | | | | (401) $false % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | CLOSE: (401) is inconsistent. % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | Case 2: % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | (402) ~ (all_131_6 = 0) & relation(all_48_6) = % 89.16/14.77 | | | | | | | | | | | | | | | | | all_131_6 % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | ALPHA: (402) implies: % 89.16/14.77 | | | | | | | | | | | | | | | | | (403) ~ (all_131_6 = 0) % 89.16/14.77 | | | | | | | | | | | | | | | | | (404) relation(all_48_6) = all_131_6 % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_131_6, all_48_6, % 89.16/14.77 | | | | | | | | | | | | | | | | | simplifying with (49), (404) gives: % 89.16/14.77 | | | | | | | | | | | | | | | | | (405) all_131_6 = 0 % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | REDUCE: (403), (405) imply: % 89.16/14.77 | | | | | | | | | | | | | | | | | (406) $false % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | | CLOSE: (406) is inconsistent. % 89.16/14.77 | | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | | % 89.16/14.77 | | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | | % 89.16/14.77 | | | | | | | | | End of split % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | End of split % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | Case 2: % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | (407) ~ (all_108_2 = 0) & function(all_48_3) = all_108_2 % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | ALPHA: (407) implies: % 89.16/14.77 | | | | | | | | (408) ~ (all_108_2 = 0) % 89.16/14.77 | | | | | | | | (409) function(all_48_3) = all_108_2 % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | GROUND_INST: instantiating (17) with 0, all_108_2, all_48_3, % 89.16/14.77 | | | | | | | | simplifying with (48), (409) gives: % 89.16/14.77 | | | | | | | | (410) all_108_2 = 0 % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | REDUCE: (408), (410) imply: % 89.16/14.77 | | | | | | | | (411) $false % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | CLOSE: (411) is inconsistent. % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | End of split % 89.16/14.77 | | | | | | | % 89.16/14.77 | | | | | | Case 2: % 89.16/14.77 | | | | | | | % 89.16/14.77 | | | | | | | (412) ( ~ (all_108_3 = 0) & relation(all_48_3) = all_108_3) | ( % 89.16/14.77 | | | | | | | ~ (all_108_4 = 0) & function(all_48_6) = all_108_4) | ( % 89.16/14.77 | | | | | | | ~ (all_108_5 = 0) & relation(all_48_6) = all_108_5) % 89.16/14.77 | | | | | | | % 89.16/14.77 | | | | | | | BETA: splitting (412) gives: % 89.16/14.77 | | | | | | | % 89.16/14.77 | | | | | | | Case 1: % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | (413) ~ (all_108_3 = 0) & relation(all_48_3) = all_108_3 % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | ALPHA: (413) implies: % 89.16/14.77 | | | | | | | | (414) ~ (all_108_3 = 0) % 89.16/14.77 | | | | | | | | (415) relation(all_48_3) = all_108_3 % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | GROUND_INST: instantiating (18) with 0, all_108_3, all_48_3, % 89.16/14.77 | | | | | | | | simplifying with (50), (415) gives: % 89.16/14.77 | | | | | | | | (416) all_108_3 = 0 % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | REDUCE: (414), (416) imply: % 89.16/14.77 | | | | | | | | (417) $false % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | CLOSE: (417) is inconsistent. % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | Case 2: % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | (418) ( ~ (all_108_4 = 0) & function(all_48_6) = all_108_4) | % 89.16/14.77 | | | | | | | | ( ~ (all_108_5 = 0) & relation(all_48_6) = all_108_5) % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | BETA: splitting (418) gives: % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | | Case 1: % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | | (419) ~ (all_108_4 = 0) & function(all_48_6) = all_108_4 % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | | ALPHA: (419) implies: % 89.16/14.77 | | | | | | | | | (420) ~ (all_108_4 = 0) % 89.16/14.77 | | | | | | | | | (421) function(all_48_6) = all_108_4 % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_108_4, all_48_6, % 89.16/14.77 | | | | | | | | | simplifying with (47), (421) gives: % 89.16/14.77 | | | | | | | | | (422) all_108_4 = 0 % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | | REDUCE: (420), (422) imply: % 89.16/14.77 | | | | | | | | | (423) $false % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | | CLOSE: (423) is inconsistent. % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | Case 2: % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | | (424) ~ (all_108_5 = 0) & relation(all_48_6) = all_108_5 % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | | ALPHA: (424) implies: % 89.16/14.77 | | | | | | | | | (425) ~ (all_108_5 = 0) % 89.16/14.77 | | | | | | | | | (426) relation(all_48_6) = all_108_5 % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_108_5, all_48_6, % 89.16/14.77 | | | | | | | | | simplifying with (49), (426) gives: % 89.16/14.77 | | | | | | | | | (427) all_108_5 = 0 % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | | REDUCE: (425), (427) imply: % 89.16/14.77 | | | | | | | | | (428) $false % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | | CLOSE: (428) is inconsistent. % 89.16/14.77 | | | | | | | | | % 89.16/14.77 | | | | | | | | End of split % 89.16/14.77 | | | | | | | | % 89.16/14.77 | | | | | | | End of split % 89.16/14.77 | | | | | | | % 89.16/14.77 | | | | | | End of split % 89.16/14.77 | | | | | | % 89.16/14.77 | | | | | End of split % 89.16/14.77 | | | | | % 89.16/14.77 | | | | End of split % 89.16/14.77 | | | | % 89.16/14.77 | | | Case 2: % 89.16/14.77 | | | | % 89.16/14.77 | | | | (429) ( ~ (all_118_5 = 0) & function(all_48_6) = all_118_5) | ( ~ % 89.16/14.77 | | | | (all_118_6 = 0) & relation(all_48_6) = all_118_6) | ( ~ % 89.16/14.77 | | | | (all_118_6 = 0) & function(all_48_3) = all_118_6) % 89.16/14.77 | | | | % 89.16/14.77 | | | | BETA: splitting (429) gives: % 89.16/14.77 | | | | % 89.16/14.77 | | | | Case 1: % 89.16/14.77 | | | | | % 89.16/14.77 | | | | | (430) ~ (all_118_5 = 0) & function(all_48_6) = all_118_5 % 89.16/14.77 | | | | | % 89.16/14.77 | | | | | ALPHA: (430) implies: % 89.16/14.78 | | | | | (431) ~ (all_118_5 = 0) % 89.16/14.78 | | | | | (432) function(all_48_6) = all_118_5 % 89.16/14.78 | | | | | % 89.16/14.78 | | | | | GROUND_INST: instantiating (17) with 0, all_118_5, all_48_6, % 89.16/14.78 | | | | | simplifying with (47), (432) gives: % 89.16/14.78 | | | | | (433) all_118_5 = 0 % 89.16/14.78 | | | | | % 89.16/14.78 | | | | | REDUCE: (431), (433) imply: % 89.16/14.78 | | | | | (434) $false % 89.16/14.78 | | | | | % 89.16/14.78 | | | | | CLOSE: (434) is inconsistent. % 89.16/14.78 | | | | | % 89.16/14.78 | | | | Case 2: % 89.16/14.78 | | | | | % 89.16/14.78 | | | | | (435) ( ~ (all_118_6 = 0) & relation(all_48_6) = all_118_6) | ( ~ % 89.16/14.78 | | | | | (all_118_6 = 0) & function(all_48_3) = all_118_6) % 89.16/14.78 | | | | | % 89.16/14.78 | | | | | BETA: splitting (435) gives: % 89.16/14.78 | | | | | % 89.16/14.78 | | | | | Case 1: % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | | (436) ~ (all_118_6 = 0) & relation(all_48_6) = all_118_6 % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | | ALPHA: (436) implies: % 89.16/14.78 | | | | | | (437) ~ (all_118_6 = 0) % 89.16/14.78 | | | | | | (438) relation(all_48_6) = all_118_6 % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | | GROUND_INST: instantiating (18) with 0, all_118_6, all_48_6, % 89.16/14.78 | | | | | | simplifying with (49), (438) gives: % 89.16/14.78 | | | | | | (439) all_118_6 = 0 % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | | REDUCE: (437), (439) imply: % 89.16/14.78 | | | | | | (440) $false % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | | CLOSE: (440) is inconsistent. % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | Case 2: % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | | (441) ~ (all_118_6 = 0) & function(all_48_3) = all_118_6 % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | | ALPHA: (441) implies: % 89.16/14.78 | | | | | | (442) ~ (all_118_6 = 0) % 89.16/14.78 | | | | | | (443) function(all_48_3) = all_118_6 % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | | GROUND_INST: instantiating (17) with 0, all_118_6, all_48_3, % 89.16/14.78 | | | | | | simplifying with (48), (443) gives: % 89.16/14.78 | | | | | | (444) all_118_6 = 0 % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | | REDUCE: (442), (444) imply: % 89.16/14.78 | | | | | | (445) $false % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | | CLOSE: (445) is inconsistent. % 89.16/14.78 | | | | | | % 89.16/14.78 | | | | | End of split % 89.16/14.78 | | | | | % 89.16/14.78 | | | | End of split % 89.16/14.78 | | | | % 89.16/14.78 | | | End of split % 89.16/14.78 | | | % 89.16/14.78 | | End of split % 89.16/14.78 | | % 89.16/14.78 | End of split % 89.16/14.78 | % 89.16/14.78 End of proof % 89.16/14.78 % 89.16/14.78 Sub-proof #1 shows that the following formulas are inconsistent: % 89.16/14.78 ---------------------------------------------------------------- % 89.16/14.78 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 89.16/14.78 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 89.16/14.78 (2) in(all_48_7, all_118_3) = all_118_2 % 89.16/14.78 (3) in(all_48_7, all_118_3) = 0 % 89.16/14.78 (4) ~ (all_118_2 = 0) % 89.16/14.78 % 89.16/14.78 Begin of proof % 89.16/14.78 | % 89.16/14.78 | GROUND_INST: instantiating (1) with all_118_2, 0, all_118_3, all_48_7, % 89.16/14.78 | simplifying with (2), (3) gives: % 89.16/14.78 | (5) all_118_2 = 0 % 89.16/14.78 | % 89.16/14.78 | REDUCE: (4), (5) imply: % 89.16/14.78 | (6) $false % 89.16/14.78 | % 89.16/14.78 | CLOSE: (6) is inconsistent. % 89.16/14.78 | % 89.16/14.78 End of proof % 89.16/14.78 % 89.16/14.78 Sub-proof #2 shows that the following formulas are inconsistent: % 89.16/14.78 ---------------------------------------------------------------- % 89.16/14.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 89.16/14.78 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 89.16/14.78 (2) apply(all_48_2, all_48_7) = all_48_0 % 89.16/14.78 (3) apply(all_48_2, all_48_7) = all_48_1 % 89.16/14.78 (4) ~ (all_48_0 = all_48_1) % 89.16/14.78 % 89.16/14.78 Begin of proof % 89.16/14.78 | % 89.16/14.78 | GROUND_INST: instantiating (1) with all_48_1, all_48_0, all_48_7, all_48_2, % 89.16/14.78 | simplifying with (2), (3) gives: % 89.16/14.78 | (5) all_48_0 = all_48_1 % 89.16/14.78 | % 89.16/14.78 | REDUCE: (4), (5) imply: % 89.16/14.78 | (6) $false % 89.16/14.78 | % 89.16/14.78 | CLOSE: (6) is inconsistent. % 89.16/14.78 | % 89.16/14.78 End of proof % 89.16/14.78 % SZS output end Proof for theBenchmark % 89.16/14.78 % 89.16/14.78 14159ms %------------------------------------------------------------------------------