%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU293+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 17:43:53 EDT 2023 % Result : Theorem 21.34s 3.60s % Output : Proof 27.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU293+1 : TPTP v8.1.2. Released v3.3.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Aug 24 01:24:36 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.00/1.12 Prover 1: Preprocessing ... % 3.00/1.12 Prover 4: Preprocessing ... % 3.00/1.16 Prover 3: Preprocessing ... % 3.00/1.16 Prover 6: Preprocessing ... % 3.00/1.16 Prover 5: Preprocessing ... % 3.00/1.16 Prover 0: Preprocessing ... % 3.00/1.16 Prover 2: Preprocessing ... % 6.96/1.66 Prover 1: Warning: ignoring some quantifiers % 6.96/1.67 Prover 5: Proving ... % 7.22/1.71 Prover 3: Warning: ignoring some quantifiers % 7.22/1.72 Prover 1: Constructing countermodel ... % 7.22/1.73 Prover 3: Constructing countermodel ... % 7.60/1.76 Prover 6: Proving ... % 8.57/1.89 Prover 2: Proving ... % 9.13/1.96 Prover 4: Warning: ignoring some quantifiers % 9.70/2.06 Prover 4: Constructing countermodel ... % 10.06/2.08 Prover 0: Proving ... % 11.39/2.27 Prover 1: gave up % 11.39/2.27 Prover 3: gave up % 11.39/2.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.39/2.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.39/2.31 Prover 8: Preprocessing ... % 11.95/2.35 Prover 7: Preprocessing ... % 12.42/2.48 Prover 7: Warning: ignoring some quantifiers % 13.46/2.53 Prover 7: Constructing countermodel ... % 13.66/2.56 Prover 8: Warning: ignoring some quantifiers % 13.66/2.58 Prover 8: Constructing countermodel ... % 16.44/2.93 Prover 7: gave up % 16.44/2.93 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 16.44/2.94 Prover 8: gave up % 16.44/2.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.80/3.00 Prover 9: Preprocessing ... % 16.80/3.01 Prover 10: Preprocessing ... % 17.47/3.12 Prover 10: Warning: ignoring some quantifiers % 17.96/3.16 Prover 10: Constructing countermodel ... % 19.01/3.28 Prover 9: Warning: ignoring some quantifiers % 19.01/3.29 Prover 9: Constructing countermodel ... % 19.39/3.33 Prover 10: gave up % 19.39/3.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 19.62/3.40 Prover 11: Preprocessing ... % 21.34/3.58 Prover 11: Warning: ignoring some quantifiers % 21.34/3.59 Prover 2: proved (2968ms) % 21.34/3.59 % 21.34/3.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.34/3.60 % 21.34/3.60 Prover 9: stopped % 21.34/3.60 Prover 0: stopped % 21.34/3.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.34/3.61 Prover 5: stopped % 21.34/3.61 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 21.34/3.61 Prover 11: Constructing countermodel ... % 21.34/3.61 Prover 6: stopped % 21.34/3.61 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 21.34/3.63 Prover 13: Preprocessing ... % 21.34/3.66 Prover 19: Preprocessing ... % 21.34/3.66 Prover 16: Preprocessing ... % 22.29/3.71 Prover 13: Warning: ignoring some quantifiers % 22.29/3.72 Prover 13: Constructing countermodel ... % 22.29/3.72 Prover 16: Warning: ignoring some quantifiers % 22.29/3.72 Prover 16: Constructing countermodel ... % 22.29/3.77 Prover 19: Warning: ignoring some quantifiers % 22.29/3.78 Prover 19: Constructing countermodel ... % 23.94/3.97 Prover 19: gave up % 26.17/4.27 Prover 4: Found proof (size 373) % 26.17/4.27 Prover 4: proved (3639ms) % 26.17/4.27 Prover 16: stopped % 26.17/4.27 Prover 11: stopped % 26.17/4.27 Prover 13: stopped % 26.17/4.27 % 26.17/4.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 26.17/4.27 % 26.53/4.32 % SZS output start Proof for theBenchmark % 26.53/4.33 Assumptions after simplification: % 26.53/4.33 --------------------------------- % 26.53/4.33 % 26.53/4.33 (cc1_funct_1) % 26.53/4.35 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (function(v0) = v1) | ~ $i(v0) | ? % 26.53/4.35 [v2: int] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0: $i] : ( ~ (empty(v0) = % 26.53/4.35 0) | ~ $i(v0) | function(v0) = 0) % 26.53/4.35 % 26.53/4.35 (cc1_relset_1) % 26.53/4.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 26.53/4.35 (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, % 26.53/4.35 v4) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation(v2) = 0) % 26.53/4.35 % 26.53/4.35 (cc2_funct_1) % 26.53/4.36 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2: % 26.53/4.36 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) = % 26.53/4.36 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 26.53/4.36 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 26.53/4.36 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0) % 26.53/4.36 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ % 26.53/4.36 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] % 26.53/4.36 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | % 26.53/4.36 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) % 26.53/4.36 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & % 26.53/4.36 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = % 26.53/4.36 0))) % 26.53/4.36 % 26.53/4.36 (d13_funct_1) % 26.89/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.89/4.38 int] : (v5 = 0 | ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, % 26.89/4.38 v2) = v3) | ~ (in(v4, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 26.89/4.38 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ((apply(v0, v4) = v7 % 26.89/4.38 & in(v7, v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = % 26.89/4.38 0))) | (relation(v0) = v6 & function(v0) = v7 & ( ~ (v7 = 0) | ~ % 26.89/4.38 (v6 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 26.89/4.38 ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(v0) = v1) | ~ % 26.89/4.38 (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ~ $i(v4) % 26.89/4.38 | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: % 26.89/4.38 any] : ((relation(v0) = v6 & function(v0) = v7 & ( ~ (v7 = 0) | ~ (v6 = % 26.89/4.38 0))) | (in(v5, v2) = v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ % 26.89/4.38 (v6 = 0) | (v8 = 0 & v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.89/4.38 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(v0) = v1) % 26.89/4.38 | ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ~ % 26.89/4.38 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 26.89/4.38 ? [v8: any] : ((relation(v0) = v6 & function(v0) = v7 & ( ~ (v7 = 0) | ~ % 26.89/4.38 (v6 = 0))) | (in(v5, v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = v6 & ( % 26.89/4.38 ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 26.89/4.38 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (relation_dom(v0) = % 26.89/4.38 v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = v5) | ~ % 26.89/4.38 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 26.89/4.38 ? [v8: any] : ((apply(v0, v4) = v7 & in(v7, v2) = v8 & in(v4, v3) = v6 & % 26.89/4.38 $i(v7) & ( ~ (v6 = 0) | (v8 = 0 & v5 = 0))) | (relation(v0) = v6 & % 26.89/4.38 function(v0) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v0: $i] : ! % 26.89/4.38 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (relation_dom(v0) = % 26.89/4.38 v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = 0) | ~ % 26.89/4.38 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v5: int] : ? [v6: any] : % 26.89/4.38 ? [v7: int] : ((v7 = 0 & v5 = 0 & apply(v0, v4) = v6 & in(v6, v2) = 0 & % 26.89/4.38 in(v4, v1) = 0 & $i(v6)) | (relation(v0) = v5 & function(v0) = v6 & ( ~ % 26.89/4.38 (v6 = 0) | ~ (v5 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.89/4.38 ! [v3: $i] : ! [v4: $i] : ( ~ (relation_dom(v0) = v1) | ~ % 26.89/4.38 (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = 0) | ~ $i(v4) | ~ % 26.89/4.38 $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] % 26.89/4.38 : ((apply(v0, v4) = v5 & in(v5, v2) = v6 & in(v4, v3) = v7 & $i(v5) & ( ~ % 26.89/4.38 (v6 = 0) | v7 = 0)) | (relation(v0) = v5 & function(v0) = v6 & ( ~ (v6 % 26.89/4.38 = 0) | ~ (v5 = 0))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.89/4.38 ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (relation_dom(v1) = v2) | ~ % 26.89/4.38 (relation_inverse_image(v1, v3) = v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 26.89/4.38 ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? % 26.89/4.38 [v10: $i] : ? [v11: any] : ($i(v7) & ((apply(v1, v7) = v10 & in(v10, v3) = % 26.89/4.38 v11 & in(v7, v2) = v9 & in(v7, v0) = v8 & $i(v10) & ( ~ (v11 = 0) | ~ % 26.89/4.38 (v9 = 0) | ~ (v8 = 0)) & (v8 = 0 | (v11 = 0 & v9 = 0))) | % 26.89/4.38 (relation(v1) = v5 & function(v1) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))))) % 26.89/4.38 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 26.89/4.38 $i] : (relation_dom(v0) = v2 & function(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | % 26.89/4.38 ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ % 26.89/4.38 (relation_inverse_image(v0, v3) = v4) | ~ (in(v5, v4) = v6) | ~ % 26.89/4.38 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: $i] : ? % 26.89/4.38 [v9: any] : (apply(v0, v5) = v8 & in(v8, v3) = v9 & in(v5, v2) = v7 % 26.89/4.38 & $i(v8) & ( ~ (v9 = 0) | ~ (v7 = 0)))) & ! [v3: $i] : ! [v4: % 26.89/4.38 $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (relation_inverse_image(v0, % 26.89/4.38 v3) = v4) | ~ (apply(v0, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 26.89/4.38 $i(v3) | ? [v7: any] : ? [v8: any] : ? [v9: any] : (in(v6, v3) = % 26.89/4.38 v9 & in(v5, v4) = v7 & in(v5, v2) = v8 & ( ~ (v7 = 0) | (v9 = 0 & % 26.89/4.38 v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 26.89/4.38 $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) % 26.89/4.38 = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: % 26.89/4.38 any] : ? [v9: any] : (in(v6, v3) = v8 & in(v5, v4) = v9 & in(v5, % 26.89/4.38 v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0))) & ! [v3: $i] % 26.89/4.38 : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 26.89/4.38 (relation_inverse_image(v0, v3) = v4) | ~ (in(v5, v2) = v6) | ~ % 26.89/4.38 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: $i] : ? % 26.89/4.38 [v9: any] : (apply(v0, v5) = v8 & in(v8, v3) = v9 & in(v5, v4) = v7 % 26.89/4.38 & $i(v8) & ( ~ (v7 = 0) | (v9 = 0 & v6 = 0)))) & ! [v3: $i] : ! % 26.89/4.38 [v4: $i] : ! [v5: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | % 26.89/4.38 ~ (in(v5, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] % 26.89/4.38 : (apply(v0, v5) = v6 & in(v6, v3) = 0 & in(v5, v2) = 0 & $i(v6))) & % 26.89/4.38 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 26.89/4.38 (relation_inverse_image(v0, v3) = v4) | ~ (in(v5, v2) = 0) | ~ % 26.89/4.38 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? % 26.89/4.38 [v8: any] : (apply(v0, v5) = v6 & in(v6, v3) = v7 & in(v5, v4) = v8 % 26.89/4.38 & $i(v6) & ( ~ (v7 = 0) | v8 = 0))) & ? [v3: $i] : ! [v4: $i] : % 26.89/4.38 ! [v5: $i] : (v5 = v3 | ~ (relation_inverse_image(v0, v4) = v5) | ~ % 26.89/4.38 $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? % 26.89/4.38 [v9: $i] : ? [v10: any] : (apply(v0, v6) = v9 & in(v9, v4) = v10 & % 26.89/4.38 in(v6, v3) = v7 & in(v6, v2) = v8 & $i(v9) & $i(v6) & ( ~ (v10 = % 26.89/4.38 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = % 26.89/4.38 0)))))))) & ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | % 26.89/4.38 ? [v1: any] : ? [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & % 26.89/4.38 $i(v2) & ( ~ (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 26.89/4.38 int] : (v6 = 0 | ~ (relation_inverse_image(v0, v3) = v4) | ~ % 26.89/4.38 (in(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] % 26.89/4.38 : ? [v8: $i] : ? [v9: any] : (apply(v0, v5) = v8 & in(v8, v3) = v9 % 26.89/4.38 & in(v5, v2) = v7 & $i(v8) & ( ~ (v9 = 0) | ~ (v7 = 0)))) & ! % 26.89/4.38 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 26.89/4.38 (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) = v6) | ~ % 26.89/4.38 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: any] : ? % 26.89/4.38 [v9: any] : (in(v6, v3) = v9 & in(v5, v4) = v7 & in(v5, v2) = v8 & ( % 26.89/4.38 ~ (v7 = 0) | (v9 = 0 & v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : % 26.89/4.38 ! [v5: $i] : ! [v6: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | % 26.89/4.38 ~ (apply(v0, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? % 26.89/4.38 [v7: any] : ? [v8: any] : ? [v9: any] : (in(v6, v3) = v8 & in(v5, % 26.98/4.38 v4) = v9 & in(v5, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = % 26.98/4.38 0))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : % 26.98/4.38 ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (in(v5, v2) = v6) | ~ % 26.98/4.38 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: $i] : ? % 26.98/4.38 [v9: any] : (apply(v0, v5) = v8 & in(v8, v3) = v9 & in(v5, v4) = v7 % 26.98/4.38 & $i(v8) & ( ~ (v7 = 0) | (v9 = 0 & v6 = 0)))) & ! [v3: $i] : ! % 26.98/4.38 [v4: $i] : ! [v5: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | % 26.98/4.38 ~ (in(v5, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] % 26.98/4.38 : (apply(v0, v5) = v6 & in(v6, v3) = 0 & in(v5, v2) = 0 & $i(v6))) & % 26.98/4.38 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 26.98/4.38 (relation_inverse_image(v0, v3) = v4) | ~ (in(v5, v2) = 0) | ~ % 26.98/4.38 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? % 26.98/4.38 [v8: any] : (apply(v0, v5) = v6 & in(v6, v3) = v7 & in(v5, v4) = v8 % 26.98/4.38 & $i(v6) & ( ~ (v7 = 0) | v8 = 0))) & ? [v3: $i] : ! [v4: $i] : % 26.98/4.38 ! [v5: $i] : (v5 = v3 | ~ (relation_inverse_image(v0, v4) = v5) | ~ % 26.98/4.38 $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? % 26.98/4.38 [v9: $i] : ? [v10: any] : (apply(v0, v6) = v9 & in(v9, v4) = v10 & % 26.98/4.38 in(v6, v3) = v7 & in(v6, v2) = v8 & $i(v9) & $i(v6) & ( ~ (v10 = % 26.98/4.38 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = % 26.98/4.38 0)))))))) % 26.98/4.38 % 26.98/4.38 (d1_funct_2) % 26.98/4.38 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 26.98/4.38 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.98/4.38 $i(v0) | ? [v4: any] : ? [v5: any] : (relation_of2_as_subset(v2, v0, v1) = % 26.98/4.38 v4 & quasi_total(v2, v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v1 = empty_set) | % 26.98/4.38 v0 = empty_set | (( ~ (v5 = 0) | v2 = empty_set) & ( ~ (v2 = % 26.98/4.38 empty_set) | v5 = 0))) & ((v1 = empty_set & ~ (v0 = % 26.98/4.38 empty_set)) | (( ~ (v5 = 0) | v3 = v0) & ( ~ (v3 = v0) | v5 = % 26.98/4.38 0))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 26.98/4.38 any] : ( ~ (quasi_total(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.98/4.38 $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_dom_as_subset(v0, v1, v2) = % 26.98/4.38 v5 & relation_of2_as_subset(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | (( % 26.98/4.38 ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 = % 26.98/4.38 empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set % 26.98/4.38 & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v3 = 0) & ( ~ (v3 = 0) | % 26.98/4.38 v5 = v0))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 26.98/4.38 (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 26.98/4.38 | ? [v3: any] : ? [v4: $i] : (relation_dom_as_subset(v0, v1, v2) = v4 & % 26.98/4.38 quasi_total(v2, v0, v1) = v3 & $i(v4) & ( ~ (v1 = empty_set) | v0 = % 26.98/4.38 empty_set | (( ~ (v3 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v3 % 26.98/4.38 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v4 = v0) | % 26.98/4.38 v3 = 0) & ( ~ (v3 = 0) | v4 = v0))))) % 26.98/4.38 % 26.98/4.38 (dt_k4_relset_1) % 26.98/4.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 26.98/4.39 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.98/4.39 $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (relation_of2(v2, v0, % 26.98/4.39 v1) = v4 & powerset(v0) = v5 & element(v3, v5) = v6 & $i(v5) & ( ~ (v4 = % 26.98/4.39 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 26.98/4.39 (relation_of2(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 26.98/4.39 $i] : ? [v4: $i] : (relation_dom_as_subset(v0, v1, v2) = v3 & % 26.98/4.39 powerset(v0) = v4 & element(v3, v4) = 0 & $i(v4) & $i(v3))) % 26.98/4.39 % 26.98/4.39 (dt_m2_relset_1) % 26.98/4.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.98/4.39 int] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = % 26.98/4.39 v4) | ~ (element(v2, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.98/4.39 [v6: int] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & ! % 26.98/4.39 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0, v1) % 26.98/4.39 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 26.98/4.39 (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0 & % 26.98/4.39 $i(v4) & $i(v3))) % 26.98/4.39 % 26.98/4.39 (fc4_relat_1) % 26.98/4.39 relation(empty_set) = 0 & empty(empty_set) = 0 & $i(empty_set) % 26.98/4.39 % 26.98/4.39 (fc5_relat_1) % 26.98/4.39 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 26.98/4.39 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 & % 26.98/4.39 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = % 26.98/4.39 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ % 26.98/4.39 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & % 26.98/4.39 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & % 26.98/4.39 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 26.98/4.39 : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & % 26.98/4.39 $i(v2) & ( ~ (v3 = 0) | v1 = 0))) % 26.98/4.39 % 26.98/4.39 (fc7_relat_1) % 26.98/4.39 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 26.98/4.39 any] : ? [v3: any] : ? [v4: any] : (relation(v1) = v4 & empty(v1) = v3 & % 26.98/4.39 empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ( ~ % 26.98/4.39 (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (relation_dom(v0) = v1 & % 26.98/4.39 relation(v1) = 0 & empty(v1) = 0 & $i(v1))) % 26.98/4.39 % 26.98/4.39 (rc1_partfun1) % 26.98/4.39 ? [v0: $i] : (one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0 & % 26.98/4.39 empty(v0) = 0 & $i(v0)) % 26.98/4.39 % 26.98/4.39 (rc1_relat_1) % 26.98/4.39 ? [v0: $i] : (relation(v0) = 0 & empty(v0) = 0 & $i(v0)) % 26.98/4.39 % 26.98/4.39 (rc1_subset_1) % 26.98/4.39 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 26.98/4.39 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v0) = v2 & % 26.98/4.39 element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) & $i(v2))) & ! [v0: $i] : % 26.98/4.39 ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] % 26.98/4.39 : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & % 26.98/4.39 element(v3, v1) = 0 & empty(v3) = v5) | (v2 = 0 & empty(v0) = 0)))) % 26.98/4.39 % 26.98/4.39 (rc1_xboole_0) % 26.98/4.39 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 26.98/4.39 % 26.98/4.39 (rc2_funct_1) % 26.98/4.39 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & empty(v0) = 0 & $i(v0)) % 26.98/4.39 % 26.98/4.39 (rc2_xboole_0) % 26.98/4.39 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 26.98/4.39 % 26.98/4.39 (rc3_funct_1) % 26.98/4.39 ? [v0: $i] : (one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0 & % 26.98/4.39 $i(v0)) % 26.98/4.39 % 26.98/4.39 (redefinition_k4_relset_1) % 26.98/4.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 26.98/4.39 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.98/4.39 $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_of2(v2, v0, v1) = v4 & % 26.98/4.39 relation_dom(v2) = v5 & $i(v5) & ( ~ (v4 = 0) | v5 = v3))) & ! [v0: $i] : % 26.98/4.39 ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1) = 0) | ~ $i(v2) | % 26.98/4.40 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (relation_dom_as_subset(v0, v1, v2) = % 26.98/4.40 v3 & relation_dom(v2) = v3 & $i(v3))) % 26.98/4.40 % 26.98/4.40 (redefinition_m2_relset_1) % 26.98/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.98/4.40 (relation_of2(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.98/4.40 [v4: int] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) & ! % 26.98/4.40 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.98/4.40 (relation_of2_as_subset(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.98/4.40 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & ! % 26.98/4.40 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1) = 0) | ~ % 26.98/4.40 $i(v2) | ~ $i(v1) | ~ $i(v0) | relation_of2_as_subset(v2, v0, v1) = 0) & % 26.98/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0, % 26.98/4.40 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation_of2(v2, v0, v1) % 26.98/4.40 = 0) % 26.98/4.40 % 26.98/4.40 (t46_funct_2) % 26.98/4.40 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 26.98/4.40 [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: % 26.98/4.40 any] : ( ~ (v1 = empty_set) & relation_of2_as_subset(v3, v0, v1) = 0 & % 26.98/4.40 quasi_total(v3, v0, v1) = 0 & relation_inverse_image(v3, v2) = v4 & % 26.98/4.40 apply(v3, v5) = v8 & function(v3) = 0 & in(v8, v2) = v9 & in(v5, v4) = v6 & % 26.98/4.40 in(v5, v0) = v7 & $i(v8) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 26.98/4.40 $i(v0) & ((v9 = 0 & v7 = 0 & ~ (v6 = 0)) | (v6 = 0 & ( ~ (v9 = 0) | ~ (v7 % 26.98/4.40 = 0))))) % 26.98/4.40 % 26.98/4.40 (t6_boole) % 26.98/4.40 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 26.98/4.40 $i(v0)) % 26.98/4.40 % 26.98/4.40 (t8_boole) % 26.98/4.40 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 26.98/4.40 | ~ $i(v1) | ~ $i(v0)) % 26.98/4.40 % 26.98/4.40 (function-axioms) % 26.98/4.40 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 26.98/4.40 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ % 26.98/4.40 (relation_of2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.98/4.40 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) % 26.98/4.40 = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0)) & ! [v0: % 26.98/4.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.98/4.40 : ! [v4: $i] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ % 26.98/4.40 (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 26.98/4.40 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 26.98/4.40 ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0)) & ! % 26.98/4.40 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 26.98/4.40 $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! % 26.98/4.40 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.98/4.40 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = % 26.98/4.40 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 26.98/4.40 ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 26.98/4.40 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) % 26.98/4.40 = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 26.98/4.40 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.98/4.40 (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: % 26.98/4.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.98/4.40 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 26.98/4.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 26.98/4.40 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = % 26.98/4.40 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 26.98/4.40 (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: % 26.98/4.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 26.98/4.40 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: $i] : ! [v1: % 26.98/4.40 $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = % 26.98/4.40 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.98/4.40 $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: % 26.98/4.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 26.98/4.40 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] % 26.98/4.40 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | % 26.98/4.40 ~ (empty(v2) = v0)) % 26.98/4.40 % 26.98/4.40 Further assumptions not needed in the proof: % 26.98/4.40 -------------------------------------------- % 26.98/4.40 antisymmetry_r2_hidden, cc1_relat_1, dt_k10_relat_1, dt_k1_funct_1, % 26.98/4.40 dt_k1_relat_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_m1_relset_1, % 26.98/4.40 dt_m1_subset_1, existence_m1_relset_1, existence_m1_subset_1, % 26.98/4.40 existence_m2_relset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_subset_1, % 26.98/4.40 rc1_funct_1, rc1_funct_2, rc2_partfun1, rc2_relat_1, rc2_subset_1, rc3_relat_1, % 26.98/4.40 rc4_funct_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, % 26.98/4.40 t5_subset, t7_boole % 26.98/4.40 % 26.98/4.40 Those formulas are unsatisfiable: % 26.98/4.40 --------------------------------- % 26.98/4.40 % 26.98/4.40 Begin of proof % 26.98/4.41 | % 26.98/4.41 | ALPHA: (cc1_funct_1) implies: % 26.98/4.41 | (1) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | function(v0) = 0) % 26.98/4.41 | % 26.98/4.41 | ALPHA: (cc2_funct_1) implies: % 26.98/4.41 | (2) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 26.98/4.41 | any] : ? [v3: any] : (one_to_one(v0) = v3 & relation(v0) = v1 & % 26.98/4.41 | function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 26.98/4.41 | (3) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 26.98/4.41 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & relation(v0) = v1 & % 26.98/4.41 | empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 26.98/4.41 | (4) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 26.98/4.41 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & % 26.98/4.41 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 26.98/4.41 | (5) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? % 26.98/4.41 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & % 26.98/4.41 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | % 26.98/4.41 | ~ (v2 = 0) | v1 = 0))) % 26.98/4.41 | % 26.98/4.41 | ALPHA: (d13_funct_1) implies: % 26.98/4.41 | (6) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 26.98/4.41 | [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ % 27.15/4.41 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 27.15/4.41 | int] : (v6 = 0 | ~ (relation_inverse_image(v0, v3) = v4) | % 27.15/4.41 | ~ (in(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? % 27.15/4.41 | [v7: any] : ? [v8: $i] : ? [v9: any] : (apply(v0, v5) = v8 % 27.15/4.41 | & in(v8, v3) = v9 & in(v5, v2) = v7 & $i(v8) & ( ~ (v9 = 0) % 27.15/4.41 | | ~ (v7 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 27.15/4.41 | $i] : ! [v6: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) % 27.15/4.41 | | ~ (apply(v0, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 27.15/4.41 | | ? [v7: any] : ? [v8: any] : ? [v9: any] : (in(v6, v3) = % 27.15/4.41 | v9 & in(v5, v4) = v7 & in(v5, v2) = v8 & ( ~ (v7 = 0) | (v9 % 27.15/4.41 | = 0 & v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 27.15/4.41 | $i] : ! [v6: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) % 27.15/4.41 | | ~ (apply(v0, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 27.15/4.42 | | ? [v7: any] : ? [v8: any] : ? [v9: any] : (in(v6, v3) = % 27.15/4.42 | v8 & in(v5, v4) = v9 & in(v5, v2) = v7 & ( ~ (v8 = 0) | ~ % 27.15/4.42 | (v7 = 0) | v9 = 0))) & ! [v3: $i] : ! [v4: $i] : ! % 27.15/4.42 | [v5: $i] : ! [v6: any] : ( ~ (relation_inverse_image(v0, v3) = % 27.15/4.42 | v4) | ~ (in(v5, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 27.15/4.42 | $i(v3) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 27.15/4.42 | (apply(v0, v5) = v8 & in(v8, v3) = v9 & in(v5, v4) = v7 & % 27.15/4.42 | $i(v8) & ( ~ (v7 = 0) | (v9 = 0 & v6 = 0)))) & ! [v3: $i] % 27.15/4.42 | : ! [v4: $i] : ! [v5: $i] : ( ~ (relation_inverse_image(v0, % 27.15/4.42 | v3) = v4) | ~ (in(v5, v4) = 0) | ~ $i(v5) | ~ $i(v4) | % 27.15/4.42 | ~ $i(v3) | ? [v6: $i] : (apply(v0, v5) = v6 & in(v6, v3) = % 27.15/4.42 | 0 & in(v5, v2) = 0 & $i(v6))) & ! [v3: $i] : ! [v4: $i] : % 27.15/4.42 | ! [v5: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ % 27.15/4.42 | (in(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? % 27.15/4.42 | [v6: $i] : ? [v7: any] : ? [v8: any] : (apply(v0, v5) = v6 % 27.15/4.42 | & in(v6, v3) = v7 & in(v5, v4) = v8 & $i(v6) & ( ~ (v7 = 0) % 27.15/4.42 | | v8 = 0))) & ? [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 27.15/4.42 | (v5 = v3 | ~ (relation_inverse_image(v0, v4) = v5) | ~ $i(v4) % 27.15/4.42 | | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? % 27.15/4.42 | [v9: $i] : ? [v10: any] : (apply(v0, v6) = v9 & in(v9, v4) = % 27.15/4.42 | v10 & in(v6, v3) = v7 & in(v6, v2) = v8 & $i(v9) & $i(v6) & % 27.15/4.42 | ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v10 % 27.15/4.42 | = 0 & v8 = 0)))))))) % 27.15/4.42 | (7) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 27.15/4.42 | [v2: $i] : (relation_dom(v0) = v2 & function(v0) = v1 & $i(v2) & ( ~ % 27.15/4.42 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 27.15/4.42 | int] : (v6 = 0 | ~ (relation_inverse_image(v0, v3) = v4) | % 27.15/4.42 | ~ (in(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? % 27.15/4.42 | [v7: any] : ? [v8: $i] : ? [v9: any] : (apply(v0, v5) = v8 % 27.15/4.42 | & in(v8, v3) = v9 & in(v5, v2) = v7 & $i(v8) & ( ~ (v9 = 0) % 27.15/4.42 | | ~ (v7 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 27.15/4.42 | $i] : ! [v6: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) % 27.15/4.42 | | ~ (apply(v0, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 27.15/4.42 | | ? [v7: any] : ? [v8: any] : ? [v9: any] : (in(v6, v3) = % 27.15/4.42 | v9 & in(v5, v4) = v7 & in(v5, v2) = v8 & ( ~ (v7 = 0) | (v9 % 27.15/4.42 | = 0 & v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 27.15/4.42 | $i] : ! [v6: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) % 27.15/4.42 | | ~ (apply(v0, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 27.15/4.42 | | ? [v7: any] : ? [v8: any] : ? [v9: any] : (in(v6, v3) = % 27.15/4.42 | v8 & in(v5, v4) = v9 & in(v5, v2) = v7 & ( ~ (v8 = 0) | ~ % 27.15/4.42 | (v7 = 0) | v9 = 0))) & ! [v3: $i] : ! [v4: $i] : ! % 27.15/4.42 | [v5: $i] : ! [v6: any] : ( ~ (relation_inverse_image(v0, v3) = % 27.15/4.42 | v4) | ~ (in(v5, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 27.15/4.42 | $i(v3) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 27.15/4.42 | (apply(v0, v5) = v8 & in(v8, v3) = v9 & in(v5, v4) = v7 & % 27.15/4.42 | $i(v8) & ( ~ (v7 = 0) | (v9 = 0 & v6 = 0)))) & ! [v3: $i] % 27.15/4.42 | : ! [v4: $i] : ! [v5: $i] : ( ~ (relation_inverse_image(v0, % 27.15/4.42 | v3) = v4) | ~ (in(v5, v4) = 0) | ~ $i(v5) | ~ $i(v4) | % 27.15/4.42 | ~ $i(v3) | ? [v6: $i] : (apply(v0, v5) = v6 & in(v6, v3) = % 27.15/4.42 | 0 & in(v5, v2) = 0 & $i(v6))) & ! [v3: $i] : ! [v4: $i] : % 27.15/4.42 | ! [v5: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ % 27.15/4.42 | (in(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? % 27.15/4.42 | [v6: $i] : ? [v7: any] : ? [v8: any] : (apply(v0, v5) = v6 % 27.15/4.42 | & in(v6, v3) = v7 & in(v5, v4) = v8 & $i(v6) & ( ~ (v7 = 0) % 27.15/4.42 | | v8 = 0))) & ? [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 27.15/4.42 | (v5 = v3 | ~ (relation_inverse_image(v0, v4) = v5) | ~ $i(v4) % 27.15/4.42 | | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? % 27.15/4.42 | [v9: $i] : ? [v10: any] : (apply(v0, v6) = v9 & in(v9, v4) = % 27.15/4.42 | v10 & in(v6, v3) = v7 & in(v6, v2) = v8 & $i(v9) & $i(v6) & % 27.15/4.42 | ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v10 % 27.15/4.42 | = 0 & v8 = 0)))))))) % 27.15/4.42 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 27.15/4.42 | ! [v5: $i] : ( ~ (relation_dom(v0) = v1) | ~ % 27.15/4.42 | (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ~ % 27.15/4.42 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v6: any] : ? [v7: % 27.15/4.42 | any] : ? [v8: any] : ((relation(v0) = v6 & function(v0) = v7 & ( ~ % 27.15/4.42 | (v7 = 0) | ~ (v6 = 0))) | (in(v5, v2) = v7 & in(v4, v3) = v8 & % 27.15/4.42 | in(v4, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0)))) % 27.15/4.42 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 27.15/4.42 | ! [v5: $i] : ( ~ (relation_dom(v0) = v1) | ~ % 27.15/4.42 | (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ~ % 27.15/4.42 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v6: any] : ? [v7: % 27.15/4.42 | any] : ? [v8: any] : ((relation(v0) = v6 & function(v0) = v7 & ( ~ % 27.15/4.42 | (v7 = 0) | ~ (v6 = 0))) | (in(v5, v2) = v8 & in(v4, v3) = v6 & % 27.15/4.42 | in(v4, v1) = v7 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0))))) % 27.15/4.42 | % 27.15/4.42 | ALPHA: (d1_funct_2) implies: % 27.15/4.42 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 27.15/4.42 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | % 27.15/4.42 | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (relation_dom_as_subset(v0, % 27.15/4.42 | v1, v2) = v4 & quasi_total(v2, v0, v1) = v3 & $i(v4) & ( ~ (v1 = % 27.15/4.42 | empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 = empty_set) % 27.15/4.42 | & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set & ~ (v0 % 27.15/4.42 | = empty_set)) | (( ~ (v4 = v0) | v3 = 0) & ( ~ (v3 = 0) | v4 % 27.15/4.42 | = v0))))) % 27.15/4.42 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 27.15/4.42 | (quasi_total(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 27.15/4.42 | ? [v4: any] : ? [v5: $i] : (relation_dom_as_subset(v0, v1, v2) = % 27.15/4.42 | v5 & relation_of2_as_subset(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = % 27.15/4.42 | 0) | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | % 27.15/4.42 | v2 = empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & % 27.15/4.42 | ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v3 % 27.15/4.42 | = 0) & ( ~ (v3 = 0) | v5 = v0))))))) % 27.15/4.42 | % 27.15/4.42 | ALPHA: (dt_k4_relset_1) implies: % 27.15/4.43 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, % 27.15/4.43 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 27.15/4.43 | [v4: $i] : (relation_dom_as_subset(v0, v1, v2) = v3 & powerset(v0) = % 27.15/4.43 | v4 & element(v3, v4) = 0 & $i(v4) & $i(v3))) % 27.15/4.43 | % 27.15/4.43 | ALPHA: (dt_m2_relset_1) implies: % 27.15/4.43 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 27.15/4.43 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | % 27.15/4.43 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (cartesian_product2(v0, v1) = % 27.15/4.43 | v3 & powerset(v3) = v4 & element(v2, v4) = 0 & $i(v4) & $i(v3))) % 27.15/4.43 | % 27.15/4.43 | ALPHA: (fc4_relat_1) implies: % 27.15/4.43 | (14) empty(empty_set) = 0 % 27.15/4.43 | (15) relation(empty_set) = 0 % 27.15/4.43 | % 27.15/4.43 | ALPHA: (fc5_relat_1) implies: % 27.15/4.43 | (16) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 27.15/4.43 | [v2: $i] : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 & % 27.15/4.43 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0))) % 27.15/4.43 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 27.15/4.43 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & % 27.15/4.43 | empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 % 27.15/4.43 | = 0))) % 27.15/4.43 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) % 27.15/4.43 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 % 27.15/4.43 | & relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ % 27.15/4.43 | (v2 = 0)))) % 27.15/4.43 | % 27.15/4.43 | ALPHA: (fc7_relat_1) implies: % 27.15/4.43 | (19) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 27.15/4.43 | (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0 & $i(v1))) % 27.15/4.43 | % 27.15/4.43 | ALPHA: (rc1_subset_1) implies: % 27.15/4.43 | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) % 27.15/4.43 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 27.15/4.43 | powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) % 27.15/4.43 | & $i(v2))) % 27.15/4.43 | % 27.15/4.43 | ALPHA: (redefinition_k4_relset_1) implies: % 27.15/4.43 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, % 27.15/4.43 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 27.15/4.43 | (relation_dom_as_subset(v0, v1, v2) = v3 & relation_dom(v2) = v3 & % 27.15/4.43 | $i(v3))) % 27.15/4.43 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 27.15/4.43 | (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 27.15/4.43 | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_of2(v2, v0, v1) = % 27.15/4.43 | v4 & relation_dom(v2) = v5 & $i(v5) & ( ~ (v4 = 0) | v5 = v3))) % 27.23/4.43 | % 27.23/4.43 | ALPHA: (redefinition_m2_relset_1) implies: % 27.23/4.43 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 27.23/4.43 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | % 27.23/4.43 | ~ $i(v0) | relation_of2(v2, v0, v1) = 0) % 27.23/4.43 | % 27.23/4.43 | ALPHA: (t6_boole) implies: % 27.23/4.43 | (24) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 27.23/4.43 | % 27.23/4.43 | ALPHA: (t46_funct_2) implies: % 27.23/4.43 | (25) $i(empty_set) % 27.23/4.43 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 27.23/4.43 | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] % 27.23/4.43 | : ( ~ (v1 = empty_set) & relation_of2_as_subset(v3, v0, v1) = 0 & % 27.23/4.43 | quasi_total(v3, v0, v1) = 0 & relation_inverse_image(v3, v2) = v4 & % 27.23/4.43 | apply(v3, v5) = v8 & function(v3) = 0 & in(v8, v2) = v9 & in(v5, v4) % 27.23/4.43 | = v6 & in(v5, v0) = v7 & $i(v8) & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 27.23/4.43 | & $i(v1) & $i(v0) & ((v9 = 0 & v7 = 0 & ~ (v6 = 0)) | (v6 = 0 & ( ~ % 27.23/4.43 | (v9 = 0) | ~ (v7 = 0))))) % 27.23/4.43 | % 27.23/4.43 | ALPHA: (function-axioms) implies: % 27.23/4.43 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 27.23/4.43 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 27.23/4.43 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 27.23/4.43 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 27.23/4.43 | (29) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 27.23/4.43 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 27.23/4.43 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 27.23/4.43 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 27.23/4.43 | (31) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 27.23/4.43 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 27.23/4.43 | v0)) % 27.23/4.43 | (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 27.23/4.43 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 27.23/4.43 | (relation_of2_as_subset(v4, v3, v2) = v1) | ~ % 27.23/4.43 | (relation_of2_as_subset(v4, v3, v2) = v0)) % 27.23/4.43 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 27.23/4.43 | (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ % 27.23/4.43 | (relation_dom_as_subset(v4, v3, v2) = v0)) % 27.23/4.43 | % 27.23/4.43 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_30_0 gives: % 27.23/4.43 | (34) empty(all_30_0) = 0 & $i(all_30_0) % 27.23/4.43 | % 27.23/4.44 | ALPHA: (34) implies: % 27.23/4.44 | (35) $i(all_30_0) % 27.23/4.44 | (36) empty(all_30_0) = 0 % 27.23/4.44 | % 27.23/4.44 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_32_0 gives: % 27.23/4.44 | (37) relation(all_32_0) = 0 & empty(all_32_0) = 0 & $i(all_32_0) % 27.23/4.44 | % 27.23/4.44 | ALPHA: (37) implies: % 27.23/4.44 | (38) $i(all_32_0) % 27.23/4.44 | (39) empty(all_32_0) = 0 % 27.23/4.44 | (40) relation(all_32_0) = 0 % 27.23/4.44 | % 27.23/4.44 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_34_0, all_34_1 % 27.23/4.44 | gives: % 27.23/4.44 | (41) ~ (all_34_0 = 0) & empty(all_34_1) = all_34_0 & $i(all_34_1) % 27.23/4.44 | % 27.23/4.44 | ALPHA: (41) implies: % 27.23/4.44 | (42) ~ (all_34_0 = 0) % 27.23/4.44 | (43) $i(all_34_1) % 27.23/4.44 | (44) empty(all_34_1) = all_34_0 % 27.23/4.44 | % 27.23/4.44 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_41_0 gives: % 27.23/4.44 | (45) relation(all_41_0) = 0 & function(all_41_0) = 0 & empty(all_41_0) = 0 % 27.23/4.44 | & $i(all_41_0) % 27.23/4.44 | % 27.23/4.44 | ALPHA: (45) implies: % 27.23/4.44 | (46) $i(all_41_0) % 27.23/4.44 | (47) empty(all_41_0) = 0 % 27.23/4.44 | (48) function(all_41_0) = 0 % 27.23/4.44 | (49) relation(all_41_0) = 0 % 27.23/4.44 | % 27.23/4.44 | DELTA: instantiating (rc3_funct_1) with fresh symbol all_49_0 gives: % 27.23/4.44 | (50) one_to_one(all_49_0) = 0 & relation(all_49_0) = 0 & function(all_49_0) % 27.23/4.44 | = 0 & $i(all_49_0) % 27.23/4.44 | % 27.23/4.44 | ALPHA: (50) implies: % 27.23/4.44 | (51) $i(all_49_0) % 27.23/4.44 | (52) function(all_49_0) = 0 % 27.23/4.44 | (53) relation(all_49_0) = 0 % 27.23/4.44 | % 27.23/4.44 | DELTA: instantiating (rc1_partfun1) with fresh symbol all_51_0 gives: % 27.23/4.44 | (54) one_to_one(all_51_0) = 0 & relation(all_51_0) = 0 & function(all_51_0) % 27.23/4.44 | = 0 & empty(all_51_0) = 0 & $i(all_51_0) % 27.23/4.44 | % 27.23/4.44 | ALPHA: (54) implies: % 27.23/4.44 | (55) $i(all_51_0) % 27.23/4.44 | (56) empty(all_51_0) = 0 % 27.23/4.44 | (57) function(all_51_0) = 0 % 27.23/4.44 | (58) relation(all_51_0) = 0 % 27.23/4.44 | % 27.23/4.44 | DELTA: instantiating (26) with fresh symbols all_57_0, all_57_1, all_57_2, % 27.23/4.44 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, all_57_9 % 27.23/4.44 | gives: % 27.23/4.44 | (59) ~ (all_57_8 = empty_set) & relation_of2_as_subset(all_57_6, all_57_9, % 27.23/4.44 | all_57_8) = 0 & quasi_total(all_57_6, all_57_9, all_57_8) = 0 & % 27.23/4.44 | relation_inverse_image(all_57_6, all_57_7) = all_57_5 & % 27.23/4.44 | apply(all_57_6, all_57_4) = all_57_1 & function(all_57_6) = 0 & % 27.23/4.44 | in(all_57_1, all_57_7) = all_57_0 & in(all_57_4, all_57_5) = all_57_3 % 27.23/4.44 | & in(all_57_4, all_57_9) = all_57_2 & $i(all_57_1) & $i(all_57_4) & % 27.23/4.44 | $i(all_57_5) & $i(all_57_6) & $i(all_57_7) & $i(all_57_8) & % 27.23/4.44 | $i(all_57_9) & ((all_57_0 = 0 & all_57_2 = 0 & ~ (all_57_3 = 0)) | % 27.23/4.44 | (all_57_3 = 0 & ( ~ (all_57_0 = 0) | ~ (all_57_2 = 0)))) % 27.23/4.44 | % 27.23/4.44 | ALPHA: (59) implies: % 27.23/4.44 | (60) ~ (all_57_8 = empty_set) % 27.23/4.44 | (61) $i(all_57_9) % 27.23/4.44 | (62) $i(all_57_8) % 27.23/4.44 | (63) $i(all_57_7) % 27.23/4.44 | (64) $i(all_57_6) % 27.23/4.44 | (65) $i(all_57_5) % 27.23/4.44 | (66) $i(all_57_4) % 27.23/4.44 | (67) in(all_57_4, all_57_9) = all_57_2 % 27.23/4.44 | (68) in(all_57_4, all_57_5) = all_57_3 % 27.23/4.44 | (69) in(all_57_1, all_57_7) = all_57_0 % 27.23/4.44 | (70) function(all_57_6) = 0 % 27.23/4.44 | (71) apply(all_57_6, all_57_4) = all_57_1 % 27.23/4.44 | (72) relation_inverse_image(all_57_6, all_57_7) = all_57_5 % 27.23/4.44 | (73) quasi_total(all_57_6, all_57_9, all_57_8) = 0 % 27.23/4.44 | (74) relation_of2_as_subset(all_57_6, all_57_9, all_57_8) = 0 % 27.23/4.44 | (75) (all_57_0 = 0 & all_57_2 = 0 & ~ (all_57_3 = 0)) | (all_57_3 = 0 & ( % 27.23/4.44 | ~ (all_57_0 = 0) | ~ (all_57_2 = 0))) % 27.23/4.44 | % 27.23/4.44 | GROUND_INST: instantiating (19) with empty_set, simplifying with (14), (25) % 27.23/4.44 | gives: % 27.23/4.44 | (76) ? [v0: $i] : (relation_dom(empty_set) = v0 & relation(v0) = 0 & % 27.23/4.44 | empty(v0) = 0 & $i(v0)) % 27.23/4.44 | % 27.23/4.44 | GROUND_INST: instantiating (19) with all_30_0, simplifying with (35), (36) % 27.23/4.44 | gives: % 27.23/4.44 | (77) ? [v0: $i] : (relation_dom(all_30_0) = v0 & relation(v0) = 0 & % 27.23/4.44 | empty(v0) = 0 & $i(v0)) % 27.23/4.44 | % 27.23/4.44 | GROUND_INST: instantiating (19) with all_32_0, simplifying with (38), (39) % 27.23/4.44 | gives: % 27.23/4.44 | (78) ? [v0: $i] : (relation_dom(all_32_0) = v0 & relation(v0) = 0 & % 27.23/4.44 | empty(v0) = 0 & $i(v0)) % 27.23/4.44 | % 27.23/4.44 | GROUND_INST: instantiating (20) with all_34_1, all_34_0, simplifying with % 27.23/4.44 | (43), (44) gives: % 27.23/4.44 | (79) all_34_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 27.23/4.44 | & powerset(all_34_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2 & % 27.23/4.44 | $i(v1) & $i(v0)) % 27.23/4.44 | % 27.23/4.44 | GROUND_INST: instantiating (t8_boole) with all_32_0, all_41_0, simplifying % 27.23/4.44 | with (38), (39), (46), (47) gives: % 27.23/4.44 | (80) all_41_0 = all_32_0 % 27.23/4.44 | % 27.23/4.44 | GROUND_INST: instantiating (t8_boole) with all_30_0, all_41_0, simplifying % 27.23/4.44 | with (35), (36), (46), (47) gives: % 27.23/4.44 | (81) all_41_0 = all_30_0 % 27.23/4.44 | % 27.23/4.44 | GROUND_INST: instantiating (19) with all_41_0, simplifying with (46), (47) % 27.23/4.44 | gives: % 27.23/4.44 | (82) ? [v0: $i] : (relation_dom(all_41_0) = v0 & relation(v0) = 0 & % 27.23/4.44 | empty(v0) = 0 & $i(v0)) % 27.23/4.44 | % 27.23/4.44 | GROUND_INST: instantiating (t8_boole) with all_41_0, all_51_0, simplifying % 27.23/4.44 | with (46), (47), (55), (56) gives: % 27.23/4.44 | (83) all_51_0 = all_41_0 % 27.23/4.44 | % 27.23/4.44 | GROUND_INST: instantiating (24) with all_51_0, simplifying with (55), (56) % 27.23/4.44 | gives: % 27.23/4.44 | (84) all_51_0 = empty_set % 27.23/4.44 | % 27.23/4.44 | GROUND_INST: instantiating (19) with all_51_0, simplifying with (55), (56) % 27.23/4.44 | gives: % 27.23/4.45 | (85) ? [v0: $i] : (relation_dom(all_51_0) = v0 & relation(v0) = 0 & % 27.23/4.45 | empty(v0) = 0 & $i(v0)) % 27.23/4.45 | % 27.23/4.45 | GROUND_INST: instantiating (6) with all_41_0, simplifying with (46), (48) % 27.23/4.45 | gives: % 27.23/4.45 | (86) ? [v0: any] : ? [v1: $i] : (relation_dom(all_41_0) = v1 & % 27.23/4.45 | relation(all_41_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 27.23/4.45 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 27.23/4.45 | (relation_inverse_image(all_41_0, v2) = v3) | ~ (in(v4, v3) = % 27.23/4.45 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.45 | [v7: $i] : ? [v8: any] : (apply(all_41_0, v4) = v7 & in(v7, % 27.23/4.45 | v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 27.23/4.45 | (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 27.23/4.45 | [v5: $i] : ( ~ (relation_inverse_image(all_41_0, v2) = v3) | ~ % 27.23/4.45 | (apply(all_41_0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 27.23/4.45 | | ? [v6: any] : ? [v7: any] : ? [v8: any] : (in(v5, v2) = % 27.23/4.45 | v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | (v8 % 27.23/4.45 | = 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 27.23/4.45 | $i] : ! [v5: $i] : ( ~ (relation_inverse_image(all_41_0, v2) % 27.23/4.45 | = v3) | ~ (apply(all_41_0, v4) = v5) | ~ $i(v4) | ~ % 27.23/4.45 | $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 27.23/4.45 | any] : (in(v5, v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = v6 % 27.23/4.45 | & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v2: $i] : ! % 27.23/4.45 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 27.23/4.45 | (relation_inverse_image(all_41_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.45 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.45 | [v7: $i] : ? [v8: any] : (apply(all_41_0, v4) = v7 & in(v7, % 27.23/4.45 | v2) = v8 & in(v4, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | (v8 = % 27.23/4.45 | 0 & v5 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 27.23/4.45 | : ( ~ (relation_inverse_image(all_41_0, v2) = v3) | ~ (in(v4, % 27.23/4.45 | v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] % 27.23/4.45 | : (apply(all_41_0, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0 % 27.23/4.45 | & $i(v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 27.23/4.45 | (relation_inverse_image(all_41_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.45 | 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? % 27.23/4.45 | [v6: any] : ? [v7: any] : (apply(all_41_0, v4) = v5 & in(v5, % 27.23/4.45 | v2) = v6 & in(v4, v3) = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = % 27.23/4.45 | 0))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 27.23/4.45 | | ~ (relation_inverse_image(all_41_0, v3) = v4) | ~ $i(v3) | % 27.23/4.45 | ~ $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? % 27.23/4.45 | [v8: $i] : ? [v9: any] : (apply(all_41_0, v5) = v8 & in(v8, % 27.23/4.45 | v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & % 27.23/4.45 | $i(v5) & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 % 27.23/4.45 | | (v9 = 0 & v7 = 0))))))) % 27.23/4.45 | % 27.23/4.45 | GROUND_INST: instantiating (6) with all_51_0, simplifying with (55), (57) % 27.23/4.45 | gives: % 27.23/4.45 | (87) ? [v0: any] : ? [v1: $i] : (relation_dom(all_51_0) = v1 & % 27.23/4.45 | relation(all_51_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 27.23/4.45 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 27.23/4.45 | (relation_inverse_image(all_51_0, v2) = v3) | ~ (in(v4, v3) = % 27.23/4.45 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.45 | [v7: $i] : ? [v8: any] : (apply(all_51_0, v4) = v7 & in(v7, % 27.23/4.45 | v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 27.23/4.45 | (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 27.23/4.45 | [v5: $i] : ( ~ (relation_inverse_image(all_51_0, v2) = v3) | ~ % 27.23/4.45 | (apply(all_51_0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 27.23/4.45 | | ? [v6: any] : ? [v7: any] : ? [v8: any] : (in(v5, v2) = % 27.23/4.45 | v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | (v8 % 27.23/4.45 | = 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 27.23/4.45 | $i] : ! [v5: $i] : ( ~ (relation_inverse_image(all_51_0, v2) % 27.23/4.45 | = v3) | ~ (apply(all_51_0, v4) = v5) | ~ $i(v4) | ~ % 27.23/4.45 | $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 27.23/4.45 | any] : (in(v5, v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = v6 % 27.23/4.45 | & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v2: $i] : ! % 27.23/4.45 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 27.23/4.45 | (relation_inverse_image(all_51_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.45 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.45 | [v7: $i] : ? [v8: any] : (apply(all_51_0, v4) = v7 & in(v7, % 27.23/4.45 | v2) = v8 & in(v4, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | (v8 = % 27.23/4.45 | 0 & v5 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 27.23/4.45 | : ( ~ (relation_inverse_image(all_51_0, v2) = v3) | ~ (in(v4, % 27.23/4.45 | v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] % 27.23/4.45 | : (apply(all_51_0, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0 % 27.23/4.45 | & $i(v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 27.23/4.45 | (relation_inverse_image(all_51_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.45 | 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? % 27.23/4.45 | [v6: any] : ? [v7: any] : (apply(all_51_0, v4) = v5 & in(v5, % 27.23/4.45 | v2) = v6 & in(v4, v3) = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = % 27.23/4.45 | 0))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 27.23/4.45 | | ~ (relation_inverse_image(all_51_0, v3) = v4) | ~ $i(v3) | % 27.23/4.45 | ~ $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? % 27.23/4.45 | [v8: $i] : ? [v9: any] : (apply(all_51_0, v5) = v8 & in(v8, % 27.23/4.45 | v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & % 27.23/4.45 | $i(v5) & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 % 27.23/4.45 | | (v9 = 0 & v7 = 0))))))) % 27.23/4.45 | % 27.23/4.45 | GROUND_INST: instantiating (3) with all_57_6, simplifying with (64), (70) % 27.23/4.45 | gives: % 27.23/4.45 | (88) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_57_6) = % 27.23/4.45 | v2 & relation(all_57_6) = v0 & empty(all_57_6) = v1 & ( ~ (v1 = 0) | % 27.23/4.45 | ~ (v0 = 0) | v2 = 0)) % 27.23/4.45 | % 27.23/4.45 | GROUND_INST: instantiating (6) with all_57_6, simplifying with (64), (70) % 27.23/4.45 | gives: % 27.23/4.45 | (89) ? [v0: any] : ? [v1: $i] : (relation_dom(all_57_6) = v1 & % 27.23/4.45 | relation(all_57_6) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 27.23/4.45 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 27.23/4.45 | (relation_inverse_image(all_57_6, v2) = v3) | ~ (in(v4, v3) = % 27.23/4.45 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.45 | [v7: $i] : ? [v8: any] : (apply(all_57_6, v4) = v7 & in(v7, % 27.23/4.45 | v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 27.23/4.45 | (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 27.23/4.45 | [v5: $i] : ( ~ (relation_inverse_image(all_57_6, v2) = v3) | ~ % 27.23/4.45 | (apply(all_57_6, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 27.23/4.45 | | ? [v6: any] : ? [v7: any] : ? [v8: any] : (in(v5, v2) = % 27.23/4.45 | v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | (v8 % 27.23/4.45 | = 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 27.23/4.45 | $i] : ! [v5: $i] : ( ~ (relation_inverse_image(all_57_6, v2) % 27.23/4.45 | = v3) | ~ (apply(all_57_6, v4) = v5) | ~ $i(v4) | ~ % 27.23/4.45 | $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 27.23/4.45 | any] : (in(v5, v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = v6 % 27.23/4.45 | & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v2: $i] : ! % 27.23/4.45 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 27.23/4.45 | (relation_inverse_image(all_57_6, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.45 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.45 | [v7: $i] : ? [v8: any] : (apply(all_57_6, v4) = v7 & in(v7, % 27.23/4.45 | v2) = v8 & in(v4, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | (v8 = % 27.23/4.45 | 0 & v5 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 27.23/4.45 | : ( ~ (relation_inverse_image(all_57_6, v2) = v3) | ~ (in(v4, % 27.23/4.45 | v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] % 27.23/4.45 | : (apply(all_57_6, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0 % 27.23/4.45 | & $i(v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 27.23/4.45 | (relation_inverse_image(all_57_6, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.45 | 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? % 27.23/4.45 | [v6: any] : ? [v7: any] : (apply(all_57_6, v4) = v5 & in(v5, % 27.23/4.45 | v2) = v6 & in(v4, v3) = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = % 27.23/4.45 | 0))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 27.23/4.45 | | ~ (relation_inverse_image(all_57_6, v3) = v4) | ~ $i(v3) | % 27.23/4.45 | ~ $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? % 27.23/4.45 | [v8: $i] : ? [v9: any] : (apply(all_57_6, v5) = v8 & in(v8, % 27.23/4.45 | v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & % 27.23/4.45 | $i(v5) & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 % 27.23/4.45 | | (v9 = 0 & v7 = 0))))))) % 27.23/4.45 | % 27.23/4.45 | GROUND_INST: instantiating (16) with empty_set, simplifying with (15), (25) % 27.23/4.45 | gives: % 27.23/4.45 | (90) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(empty_set) = % 27.23/4.45 | v1 & empty(v1) = v2 & empty(empty_set) = v0 & $i(v1) & ( ~ (v2 = 0) % 27.23/4.45 | | v0 = 0)) % 27.23/4.45 | % 27.23/4.45 | GROUND_INST: instantiating (7) with empty_set, simplifying with (15), (25) % 27.23/4.45 | gives: % 27.23/4.46 | (91) ? [v0: any] : ? [v1: $i] : (relation_dom(empty_set) = v1 & % 27.23/4.46 | function(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 27.23/4.46 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 27.23/4.46 | (relation_inverse_image(empty_set, v2) = v3) | ~ (in(v4, v3) % 27.23/4.46 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : % 27.23/4.46 | ? [v7: $i] : ? [v8: any] : (apply(empty_set, v4) = v7 & % 27.23/4.46 | in(v7, v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | % 27.23/4.46 | ~ (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 27.23/4.46 | ! [v5: $i] : ( ~ (relation_inverse_image(empty_set, v2) = v3) | % 27.23/4.46 | ~ (apply(empty_set, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 27.23/4.46 | $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (in(v5, % 27.23/4.46 | v2) = v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ (v6 = % 27.23/4.46 | 0) | (v8 = 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : % 27.23/4.46 | ! [v4: $i] : ! [v5: $i] : ( ~ % 27.23/4.46 | (relation_inverse_image(empty_set, v2) = v3) | ~ % 27.23/4.46 | (apply(empty_set, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 27.23/4.46 | $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (in(v5, % 27.23/4.46 | v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = v6 & ( ~ (v7 = % 27.23/4.46 | 0) | ~ (v6 = 0) | v8 = 0))) & ! [v2: $i] : ! [v3: $i] % 27.23/4.46 | : ! [v4: $i] : ! [v5: any] : ( ~ % 27.23/4.46 | (relation_inverse_image(empty_set, v2) = v3) | ~ (in(v4, v1) % 27.23/4.46 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : % 27.23/4.46 | ? [v7: $i] : ? [v8: any] : (apply(empty_set, v4) = v7 & % 27.23/4.46 | in(v7, v2) = v8 & in(v4, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | % 27.23/4.46 | (v8 = 0 & v5 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 27.23/4.46 | $i] : ( ~ (relation_inverse_image(empty_set, v2) = v3) | ~ % 27.23/4.46 | (in(v4, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: % 27.23/4.46 | $i] : (apply(empty_set, v4) = v5 & in(v5, v2) = 0 & in(v4, % 27.23/4.46 | v1) = 0 & $i(v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 27.23/4.46 | $i] : ( ~ (relation_inverse_image(empty_set, v2) = v3) | ~ % 27.23/4.46 | (in(v4, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: % 27.23/4.46 | $i] : ? [v6: any] : ? [v7: any] : (apply(empty_set, v4) = % 27.23/4.46 | v5 & in(v5, v2) = v6 & in(v4, v3) = v7 & $i(v5) & ( ~ (v6 = % 27.23/4.46 | 0) | v7 = 0))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] % 27.23/4.46 | : (v4 = v2 | ~ (relation_inverse_image(empty_set, v3) = v4) | % 27.23/4.46 | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: % 27.23/4.46 | any] : ? [v8: $i] : ? [v9: any] : (apply(empty_set, v5) = % 27.23/4.46 | v8 & in(v8, v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & % 27.23/4.46 | $i(v8) & $i(v5) & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) % 27.23/4.46 | & (v6 = 0 | (v9 = 0 & v7 = 0))))))) % 27.23/4.46 | % 27.23/4.46 | GROUND_INST: instantiating (16) with all_32_0, simplifying with (38), (40) % 27.23/4.46 | gives: % 27.23/4.46 | (92) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_32_0) = % 27.23/4.46 | v1 & empty(v1) = v2 & empty(all_32_0) = v0 & $i(v1) & ( ~ (v2 = 0) | % 27.23/4.46 | v0 = 0)) % 27.23/4.46 | % 27.23/4.46 | GROUND_INST: instantiating (7) with all_32_0, simplifying with (38), (40) % 27.23/4.46 | gives: % 27.23/4.46 | (93) ? [v0: any] : ? [v1: $i] : (relation_dom(all_32_0) = v1 & % 27.23/4.46 | function(all_32_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 27.23/4.46 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 27.23/4.46 | (relation_inverse_image(all_32_0, v2) = v3) | ~ (in(v4, v3) = % 27.23/4.46 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.46 | [v7: $i] : ? [v8: any] : (apply(all_32_0, v4) = v7 & in(v7, % 27.23/4.46 | v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 27.23/4.46 | (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 27.23/4.46 | [v5: $i] : ( ~ (relation_inverse_image(all_32_0, v2) = v3) | ~ % 27.23/4.46 | (apply(all_32_0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 27.23/4.46 | | ? [v6: any] : ? [v7: any] : ? [v8: any] : (in(v5, v2) = % 27.23/4.46 | v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | (v8 % 27.23/4.46 | = 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 27.23/4.46 | $i] : ! [v5: $i] : ( ~ (relation_inverse_image(all_32_0, v2) % 27.23/4.46 | = v3) | ~ (apply(all_32_0, v4) = v5) | ~ $i(v4) | ~ % 27.23/4.46 | $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 27.23/4.46 | any] : (in(v5, v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = v6 % 27.23/4.46 | & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v2: $i] : ! % 27.23/4.46 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 27.23/4.46 | (relation_inverse_image(all_32_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.46 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.46 | [v7: $i] : ? [v8: any] : (apply(all_32_0, v4) = v7 & in(v7, % 27.23/4.46 | v2) = v8 & in(v4, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | (v8 = % 27.23/4.46 | 0 & v5 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 27.23/4.46 | : ( ~ (relation_inverse_image(all_32_0, v2) = v3) | ~ (in(v4, % 27.23/4.46 | v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] % 27.23/4.46 | : (apply(all_32_0, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0 % 27.23/4.46 | & $i(v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 27.23/4.46 | (relation_inverse_image(all_32_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.46 | 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? % 27.23/4.46 | [v6: any] : ? [v7: any] : (apply(all_32_0, v4) = v5 & in(v5, % 27.23/4.46 | v2) = v6 & in(v4, v3) = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = % 27.23/4.46 | 0))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 27.23/4.46 | | ~ (relation_inverse_image(all_32_0, v3) = v4) | ~ $i(v3) | % 27.23/4.46 | ~ $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? % 27.23/4.46 | [v8: $i] : ? [v9: any] : (apply(all_32_0, v5) = v8 & in(v8, % 27.23/4.46 | v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & % 27.23/4.46 | $i(v5) & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 % 27.23/4.46 | | (v9 = 0 & v7 = 0))))))) % 27.23/4.46 | % 27.23/4.46 | GROUND_INST: instantiating (16) with all_41_0, simplifying with (46), (49) % 27.23/4.46 | gives: % 27.23/4.46 | (94) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_41_0) = % 27.23/4.46 | v1 & empty(v1) = v2 & empty(all_41_0) = v0 & $i(v1) & ( ~ (v2 = 0) | % 27.23/4.46 | v0 = 0)) % 27.23/4.46 | % 27.23/4.46 | GROUND_INST: instantiating (7) with all_41_0, simplifying with (46), (49) % 27.23/4.46 | gives: % 27.23/4.46 | (95) ? [v0: any] : ? [v1: $i] : (relation_dom(all_41_0) = v1 & % 27.23/4.46 | function(all_41_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 27.23/4.46 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 27.23/4.46 | (relation_inverse_image(all_41_0, v2) = v3) | ~ (in(v4, v3) = % 27.23/4.46 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.46 | [v7: $i] : ? [v8: any] : (apply(all_41_0, v4) = v7 & in(v7, % 27.23/4.46 | v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 27.23/4.46 | (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 27.23/4.46 | [v5: $i] : ( ~ (relation_inverse_image(all_41_0, v2) = v3) | ~ % 27.23/4.46 | (apply(all_41_0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 27.23/4.46 | | ? [v6: any] : ? [v7: any] : ? [v8: any] : (in(v5, v2) = % 27.23/4.46 | v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | (v8 % 27.23/4.46 | = 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 27.23/4.46 | $i] : ! [v5: $i] : ( ~ (relation_inverse_image(all_41_0, v2) % 27.23/4.46 | = v3) | ~ (apply(all_41_0, v4) = v5) | ~ $i(v4) | ~ % 27.23/4.46 | $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 27.23/4.46 | any] : (in(v5, v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = v6 % 27.23/4.46 | & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v2: $i] : ! % 27.23/4.46 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 27.23/4.46 | (relation_inverse_image(all_41_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.46 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.46 | [v7: $i] : ? [v8: any] : (apply(all_41_0, v4) = v7 & in(v7, % 27.23/4.46 | v2) = v8 & in(v4, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | (v8 = % 27.23/4.46 | 0 & v5 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 27.23/4.46 | : ( ~ (relation_inverse_image(all_41_0, v2) = v3) | ~ (in(v4, % 27.23/4.46 | v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] % 27.23/4.46 | : (apply(all_41_0, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0 % 27.23/4.46 | & $i(v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 27.23/4.46 | (relation_inverse_image(all_41_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.46 | 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? % 27.23/4.46 | [v6: any] : ? [v7: any] : (apply(all_41_0, v4) = v5 & in(v5, % 27.23/4.46 | v2) = v6 & in(v4, v3) = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = % 27.23/4.46 | 0))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 27.23/4.46 | | ~ (relation_inverse_image(all_41_0, v3) = v4) | ~ $i(v3) | % 27.23/4.46 | ~ $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? % 27.23/4.46 | [v8: $i] : ? [v9: any] : (apply(all_41_0, v5) = v8 & in(v8, % 27.23/4.46 | v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & % 27.23/4.46 | $i(v5) & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 % 27.23/4.46 | | (v9 = 0 & v7 = 0))))))) % 27.23/4.46 | % 27.23/4.46 | GROUND_INST: instantiating (7) with all_49_0, simplifying with (51), (53) % 27.23/4.46 | gives: % 27.23/4.47 | (96) ? [v0: any] : ? [v1: $i] : (relation_dom(all_49_0) = v1 & % 27.23/4.47 | function(all_49_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 27.23/4.47 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 27.23/4.47 | (relation_inverse_image(all_49_0, v2) = v3) | ~ (in(v4, v3) = % 27.23/4.47 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.47 | [v7: $i] : ? [v8: any] : (apply(all_49_0, v4) = v7 & in(v7, % 27.23/4.47 | v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 27.23/4.47 | (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 27.23/4.47 | [v5: $i] : ( ~ (relation_inverse_image(all_49_0, v2) = v3) | ~ % 27.23/4.47 | (apply(all_49_0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 27.23/4.47 | | ? [v6: any] : ? [v7: any] : ? [v8: any] : (in(v5, v2) = % 27.23/4.47 | v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | (v8 % 27.23/4.47 | = 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 27.23/4.47 | $i] : ! [v5: $i] : ( ~ (relation_inverse_image(all_49_0, v2) % 27.23/4.47 | = v3) | ~ (apply(all_49_0, v4) = v5) | ~ $i(v4) | ~ % 27.23/4.47 | $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 27.23/4.47 | any] : (in(v5, v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = v6 % 27.23/4.47 | & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v2: $i] : ! % 27.23/4.47 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 27.23/4.47 | (relation_inverse_image(all_49_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.47 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.47 | [v7: $i] : ? [v8: any] : (apply(all_49_0, v4) = v7 & in(v7, % 27.23/4.47 | v2) = v8 & in(v4, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | (v8 = % 27.23/4.47 | 0 & v5 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 27.23/4.47 | : ( ~ (relation_inverse_image(all_49_0, v2) = v3) | ~ (in(v4, % 27.23/4.47 | v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] % 27.23/4.47 | : (apply(all_49_0, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0 % 27.23/4.47 | & $i(v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 27.23/4.47 | (relation_inverse_image(all_49_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.47 | 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? % 27.23/4.47 | [v6: any] : ? [v7: any] : (apply(all_49_0, v4) = v5 & in(v5, % 27.23/4.47 | v2) = v6 & in(v4, v3) = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = % 27.23/4.47 | 0))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 27.23/4.47 | | ~ (relation_inverse_image(all_49_0, v3) = v4) | ~ $i(v3) | % 27.23/4.47 | ~ $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? % 27.23/4.47 | [v8: $i] : ? [v9: any] : (apply(all_49_0, v5) = v8 & in(v8, % 27.23/4.47 | v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & % 27.23/4.47 | $i(v5) & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 % 27.23/4.47 | | (v9 = 0 & v7 = 0))))))) % 27.23/4.47 | % 27.23/4.47 | GROUND_INST: instantiating (16) with all_51_0, simplifying with (55), (58) % 27.23/4.47 | gives: % 27.23/4.47 | (97) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_51_0) = % 27.23/4.47 | v1 & empty(v1) = v2 & empty(all_51_0) = v0 & $i(v1) & ( ~ (v2 = 0) | % 27.23/4.47 | v0 = 0)) % 27.23/4.47 | % 27.23/4.47 | GROUND_INST: instantiating (7) with all_51_0, simplifying with (55), (58) % 27.23/4.47 | gives: % 27.23/4.47 | (98) ? [v0: any] : ? [v1: $i] : (relation_dom(all_51_0) = v1 & % 27.23/4.47 | function(all_51_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 27.23/4.47 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 27.23/4.47 | (relation_inverse_image(all_51_0, v2) = v3) | ~ (in(v4, v3) = % 27.23/4.47 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.47 | [v7: $i] : ? [v8: any] : (apply(all_51_0, v4) = v7 & in(v7, % 27.23/4.47 | v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 27.23/4.47 | (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 27.23/4.47 | [v5: $i] : ( ~ (relation_inverse_image(all_51_0, v2) = v3) | ~ % 27.23/4.47 | (apply(all_51_0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 27.23/4.47 | | ? [v6: any] : ? [v7: any] : ? [v8: any] : (in(v5, v2) = % 27.23/4.47 | v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | (v8 % 27.23/4.47 | = 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 27.23/4.47 | $i] : ! [v5: $i] : ( ~ (relation_inverse_image(all_51_0, v2) % 27.23/4.47 | = v3) | ~ (apply(all_51_0, v4) = v5) | ~ $i(v4) | ~ % 27.23/4.47 | $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 27.23/4.47 | any] : (in(v5, v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = v6 % 27.23/4.47 | & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v2: $i] : ! % 27.23/4.47 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 27.23/4.47 | (relation_inverse_image(all_51_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.47 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 27.23/4.47 | [v7: $i] : ? [v8: any] : (apply(all_51_0, v4) = v7 & in(v7, % 27.23/4.47 | v2) = v8 & in(v4, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | (v8 = % 27.23/4.47 | 0 & v5 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 27.23/4.47 | : ( ~ (relation_inverse_image(all_51_0, v2) = v3) | ~ (in(v4, % 27.23/4.47 | v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] % 27.23/4.47 | : (apply(all_51_0, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0 % 27.23/4.47 | & $i(v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 27.23/4.47 | (relation_inverse_image(all_51_0, v2) = v3) | ~ (in(v4, v1) = % 27.23/4.47 | 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? % 27.23/4.47 | [v6: any] : ? [v7: any] : (apply(all_51_0, v4) = v5 & in(v5, % 27.23/4.47 | v2) = v6 & in(v4, v3) = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = % 27.23/4.47 | 0))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 27.23/4.47 | | ~ (relation_inverse_image(all_51_0, v3) = v4) | ~ $i(v3) | % 27.23/4.47 | ~ $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? % 27.23/4.47 | [v8: $i] : ? [v9: any] : (apply(all_51_0, v5) = v8 & in(v8, % 27.23/4.47 | v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & % 27.23/4.47 | $i(v5) & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 % 27.23/4.47 | | (v9 = 0 & v7 = 0))))))) % 27.23/4.47 | % 27.23/4.47 | GROUND_INST: instantiating (11) with all_57_9, all_57_8, all_57_6, 0, % 27.23/4.47 | simplifying with (61), (62), (64), (73) gives: % 27.23/4.47 | (99) ? [v0: any] : ? [v1: $i] : (relation_dom_as_subset(all_57_9, % 27.23/4.47 | all_57_8, all_57_6) = v1 & relation_of2_as_subset(all_57_6, % 27.23/4.47 | all_57_9, all_57_8) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (all_57_8 % 27.23/4.47 | = empty_set) | all_57_6 = empty_set | all_57_9 = empty_set) % 27.23/4.47 | & (v1 = all_57_9 | (all_57_8 = empty_set & ~ (all_57_9 = % 27.23/4.47 | empty_set)))))) % 27.23/4.47 | % 27.23/4.47 | GROUND_INST: instantiating (23) with all_57_9, all_57_8, all_57_6, simplifying % 27.23/4.47 | with (61), (62), (64), (74) gives: % 27.23/4.47 | (100) relation_of2(all_57_6, all_57_9, all_57_8) = 0 % 27.23/4.47 | % 27.23/4.47 | GROUND_INST: instantiating (10) with all_57_9, all_57_8, all_57_6, simplifying % 27.23/4.47 | with (61), (62), (64), (74) gives: % 27.23/4.47 | (101) ? [v0: any] : ? [v1: $i] : (relation_dom_as_subset(all_57_9, % 27.23/4.47 | all_57_8, all_57_6) = v1 & quasi_total(all_57_6, all_57_9, % 27.23/4.47 | all_57_8) = v0 & $i(v1) & ( ~ (all_57_8 = empty_set) | all_57_9 = % 27.23/4.47 | empty_set | (( ~ (v0 = 0) | all_57_6 = empty_set) & ( ~ (all_57_6 % 27.23/4.47 | = empty_set) | v0 = 0))) & ((all_57_8 = empty_set & ~ % 27.23/4.47 | (all_57_9 = empty_set)) | (( ~ (v1 = all_57_9) | v0 = 0) & ( ~ % 27.23/4.47 | (v0 = 0) | v1 = all_57_9)))) % 27.23/4.47 | % 27.23/4.47 | GROUND_INST: instantiating (13) with all_57_9, all_57_8, all_57_6, simplifying % 27.23/4.47 | with (61), (62), (64), (74) gives: % 27.23/4.47 | (102) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(all_57_9, all_57_8) = % 27.23/4.47 | v0 & powerset(v0) = v1 & element(all_57_6, v1) = 0 & $i(v1) & % 27.23/4.47 | $i(v0)) % 27.23/4.47 | % 27.23/4.47 | COMBINE_EQS: (83), (84) imply: % 27.23/4.47 | (103) all_41_0 = empty_set % 27.23/4.47 | % 27.23/4.47 | SIMP: (103) implies: % 27.23/4.47 | (104) all_41_0 = empty_set % 27.23/4.47 | % 27.23/4.47 | COMBINE_EQS: (80), (104) imply: % 27.23/4.47 | (105) all_32_0 = empty_set % 27.23/4.47 | % 27.23/4.47 | COMBINE_EQS: (80), (81) imply: % 27.23/4.47 | (106) all_32_0 = all_30_0 % 27.23/4.47 | % 27.23/4.47 | COMBINE_EQS: (105), (106) imply: % 27.23/4.47 | (107) all_30_0 = empty_set % 27.23/4.47 | % 27.23/4.47 | SIMP: (107) implies: % 27.23/4.47 | (108) all_30_0 = empty_set % 27.23/4.47 | % 27.23/4.47 | DELTA: instantiating (85) with fresh symbol all_67_0 gives: % 27.23/4.47 | (109) relation_dom(all_51_0) = all_67_0 & relation(all_67_0) = 0 & % 27.23/4.47 | empty(all_67_0) = 0 & $i(all_67_0) % 27.23/4.47 | % 27.23/4.47 | ALPHA: (109) implies: % 27.23/4.47 | (110) relation_dom(all_51_0) = all_67_0 % 27.23/4.47 | % 27.23/4.47 | DELTA: instantiating (77) with fresh symbol all_69_0 gives: % 27.23/4.47 | (111) relation_dom(all_30_0) = all_69_0 & relation(all_69_0) = 0 & % 27.23/4.47 | empty(all_69_0) = 0 & $i(all_69_0) % 27.23/4.47 | % 27.23/4.47 | ALPHA: (111) implies: % 27.23/4.47 | (112) $i(all_69_0) % 27.23/4.47 | (113) empty(all_69_0) = 0 % 27.23/4.47 | (114) relation(all_69_0) = 0 % 27.23/4.47 | (115) relation_dom(all_30_0) = all_69_0 % 27.23/4.47 | % 27.23/4.47 | DELTA: instantiating (82) with fresh symbol all_71_0 gives: % 27.23/4.47 | (116) relation_dom(all_41_0) = all_71_0 & relation(all_71_0) = 0 & % 27.23/4.47 | empty(all_71_0) = 0 & $i(all_71_0) % 27.23/4.47 | % 27.23/4.47 | ALPHA: (116) implies: % 27.23/4.47 | (117) relation_dom(all_41_0) = all_71_0 % 27.23/4.47 | % 27.23/4.47 | DELTA: instantiating (78) with fresh symbol all_73_0 gives: % 27.23/4.47 | (118) relation_dom(all_32_0) = all_73_0 & relation(all_73_0) = 0 & % 27.23/4.47 | empty(all_73_0) = 0 & $i(all_73_0) % 27.23/4.47 | % 27.23/4.47 | ALPHA: (118) implies: % 27.23/4.47 | (119) relation_dom(all_32_0) = all_73_0 % 27.23/4.47 | % 27.23/4.47 | DELTA: instantiating (76) with fresh symbol all_75_0 gives: % 27.23/4.47 | (120) relation_dom(empty_set) = all_75_0 & relation(all_75_0) = 0 & % 27.23/4.47 | empty(all_75_0) = 0 & $i(all_75_0) % 27.23/4.48 | % 27.23/4.48 | ALPHA: (120) implies: % 27.23/4.48 | (121) relation_dom(empty_set) = all_75_0 % 27.23/4.48 | % 27.23/4.48 | DELTA: instantiating (102) with fresh symbols all_77_0, all_77_1 gives: % 27.23/4.48 | (122) cartesian_product2(all_57_9, all_57_8) = all_77_1 & % 27.23/4.48 | powerset(all_77_1) = all_77_0 & element(all_57_6, all_77_0) = 0 & % 27.23/4.48 | $i(all_77_0) & $i(all_77_1) % 27.23/4.48 | % 27.23/4.48 | ALPHA: (122) implies: % 27.23/4.48 | (123) element(all_57_6, all_77_0) = 0 % 27.23/4.48 | (124) powerset(all_77_1) = all_77_0 % 27.23/4.48 | (125) cartesian_product2(all_57_9, all_57_8) = all_77_1 % 27.23/4.48 | % 27.23/4.48 | DELTA: instantiating (94) with fresh symbols all_85_0, all_85_1, all_85_2 % 27.23/4.48 | gives: % 27.23/4.48 | (126) relation_dom(all_41_0) = all_85_1 & empty(all_85_1) = all_85_0 & % 27.23/4.48 | empty(all_41_0) = all_85_2 & $i(all_85_1) & ( ~ (all_85_0 = 0) | % 27.23/4.48 | all_85_2 = 0) % 27.23/4.48 | % 27.23/4.48 | ALPHA: (126) implies: % 27.23/4.48 | (127) empty(all_85_1) = all_85_0 % 27.23/4.48 | (128) relation_dom(all_41_0) = all_85_1 % 27.23/4.48 | % 27.23/4.48 | DELTA: instantiating (97) with fresh symbols all_89_0, all_89_1, all_89_2 % 27.23/4.48 | gives: % 27.23/4.48 | (129) relation_dom(all_51_0) = all_89_1 & empty(all_89_1) = all_89_0 & % 27.23/4.48 | empty(all_51_0) = all_89_2 & $i(all_89_1) & ( ~ (all_89_0 = 0) | % 27.23/4.48 | all_89_2 = 0) % 27.23/4.48 | % 27.23/4.48 | ALPHA: (129) implies: % 27.23/4.48 | (130) empty(all_89_1) = all_89_0 % 27.23/4.48 | (131) relation_dom(all_51_0) = all_89_1 % 27.23/4.48 | % 27.23/4.48 | DELTA: instantiating (88) with fresh symbols all_93_0, all_93_1, all_93_2 % 27.23/4.48 | gives: % 27.23/4.48 | (132) one_to_one(all_57_6) = all_93_0 & relation(all_57_6) = all_93_2 & % 27.23/4.48 | empty(all_57_6) = all_93_1 & ( ~ (all_93_1 = 0) | ~ (all_93_2 = 0) | % 27.23/4.48 | all_93_0 = 0) % 27.23/4.48 | % 27.23/4.48 | ALPHA: (132) implies: % 27.23/4.48 | (133) relation(all_57_6) = all_93_2 % 27.23/4.48 | (134) one_to_one(all_57_6) = all_93_0 % 27.23/4.48 | % 27.23/4.48 | DELTA: instantiating (92) with fresh symbols all_107_0, all_107_1, all_107_2 % 27.23/4.48 | gives: % 27.23/4.48 | (135) relation_dom(all_32_0) = all_107_1 & empty(all_107_1) = all_107_0 & % 27.23/4.48 | empty(all_32_0) = all_107_2 & $i(all_107_1) & ( ~ (all_107_0 = 0) | % 27.23/4.48 | all_107_2 = 0) % 27.23/4.48 | % 27.23/4.48 | ALPHA: (135) implies: % 27.23/4.48 | (136) empty(all_107_1) = all_107_0 % 27.23/4.48 | (137) relation_dom(all_32_0) = all_107_1 % 27.23/4.48 | % 27.23/4.48 | DELTA: instantiating (90) with fresh symbols all_111_0, all_111_1, all_111_2 % 27.23/4.48 | gives: % 27.23/4.48 | (138) relation_dom(empty_set) = all_111_1 & empty(all_111_1) = all_111_0 & % 27.23/4.48 | empty(empty_set) = all_111_2 & $i(all_111_1) & ( ~ (all_111_0 = 0) | % 27.23/4.48 | all_111_2 = 0) % 27.23/4.48 | % 27.23/4.48 | ALPHA: (138) implies: % 27.23/4.48 | (139) empty(all_111_1) = all_111_0 % 27.23/4.48 | (140) relation_dom(empty_set) = all_111_1 % 27.23/4.48 | % 27.23/4.48 | DELTA: instantiating (99) with fresh symbols all_131_0, all_131_1 gives: % 27.23/4.48 | (141) relation_dom_as_subset(all_57_9, all_57_8, all_57_6) = all_131_0 & % 27.23/4.48 | relation_of2_as_subset(all_57_6, all_57_9, all_57_8) = all_131_1 & % 27.23/4.48 | $i(all_131_0) & ( ~ (all_131_1 = 0) | (( ~ (all_57_8 = empty_set) | % 27.23/4.48 | all_57_6 = empty_set | all_57_9 = empty_set) & (all_131_0 = % 27.23/4.48 | all_57_9 | (all_57_8 = empty_set & ~ (all_57_9 = % 27.23/4.48 | empty_set))))) % 27.23/4.48 | % 27.23/4.48 | ALPHA: (141) implies: % 27.23/4.48 | (142) relation_of2_as_subset(all_57_6, all_57_9, all_57_8) = all_131_1 % 27.23/4.48 | (143) relation_dom_as_subset(all_57_9, all_57_8, all_57_6) = all_131_0 % 27.23/4.48 | (144) ~ (all_131_1 = 0) | (( ~ (all_57_8 = empty_set) | all_57_6 = % 27.23/4.48 | empty_set | all_57_9 = empty_set) & (all_131_0 = all_57_9 | % 27.23/4.48 | (all_57_8 = empty_set & ~ (all_57_9 = empty_set)))) % 27.23/4.48 | % 27.23/4.48 | DELTA: instantiating (101) with fresh symbols all_133_0, all_133_1 gives: % 27.23/4.48 | (145) relation_dom_as_subset(all_57_9, all_57_8, all_57_6) = all_133_0 & % 27.23/4.48 | quasi_total(all_57_6, all_57_9, all_57_8) = all_133_1 & $i(all_133_0) % 27.23/4.48 | & ( ~ (all_57_8 = empty_set) | all_57_9 = empty_set | (( ~ (all_133_1 % 27.23/4.48 | = 0) | all_57_6 = empty_set) & ( ~ (all_57_6 = empty_set) | % 27.23/4.48 | all_133_1 = 0))) & ((all_57_8 = empty_set & ~ (all_57_9 = % 27.23/4.48 | empty_set)) | (( ~ (all_133_0 = all_57_9) | all_133_1 = 0) & ( % 27.23/4.48 | ~ (all_133_1 = 0) | all_133_0 = all_57_9))) % 27.23/4.48 | % 27.23/4.48 | ALPHA: (145) implies: % 27.23/4.48 | (146) $i(all_133_0) % 27.23/4.48 | (147) relation_dom_as_subset(all_57_9, all_57_8, all_57_6) = all_133_0 % 27.23/4.48 | % 27.23/4.48 | DELTA: instantiating (89) with fresh symbols all_137_0, all_137_1 gives: % 27.23/4.49 | (148) relation_dom(all_57_6) = all_137_0 & relation(all_57_6) = all_137_1 & % 27.23/4.49 | $i(all_137_0) & ( ~ (all_137_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.49 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 27.23/4.49 | (relation_inverse_image(all_57_6, v0) = v1) | ~ (in(v2, v1) = % 27.23/4.49 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 27.23/4.49 | [v5: $i] : ? [v6: any] : (apply(all_57_6, v2) = v5 & in(v5, % 27.23/4.49 | v0) = v6 & in(v2, all_137_0) = v4 & $i(v5) & ( ~ (v6 = 0) | % 27.23/4.49 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.23/4.49 | ! [v3: $i] : ( ~ (relation_inverse_image(all_57_6, v0) = v1) | ~ % 27.23/4.49 | (apply(all_57_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.23/4.49 | | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v6 % 27.23/4.49 | & in(v2, v1) = v4 & in(v2, all_137_0) = v5 & ( ~ (v4 = 0) | % 27.23/4.49 | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 27.23/4.49 | $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_57_6, v0) = % 27.23/4.49 | v1) | ~ (apply(all_57_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 27.23/4.49 | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.23/4.49 | (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, all_137_0) = v4 & ( % 27.23/4.49 | ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! % 27.23/4.49 | [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 27.23/4.49 | (relation_inverse_image(all_57_6, v0) = v1) | ~ (in(v2, % 27.23/4.49 | all_137_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.23/4.49 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_57_6, v2) = % 27.23/4.49 | v5 & in(v5, v0) = v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = % 27.23/4.49 | 0) | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 27.23/4.49 | ! [v2: $i] : ( ~ (relation_inverse_image(all_57_6, v0) = v1) | ~ % 27.23/4.49 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 27.23/4.49 | $i] : (apply(all_57_6, v2) = v3 & in(v3, v0) = 0 & in(v2, % 27.23/4.49 | all_137_0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.49 | [v2: $i] : ( ~ (relation_inverse_image(all_57_6, v0) = v1) | ~ % 27.23/4.49 | (in(v2, all_137_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 27.23/4.49 | ? [v3: $i] : ? [v4: any] : ? [v5: any] : (apply(all_57_6, v2) % 27.23/4.49 | = v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = % 27.23/4.49 | 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] % 27.23/4.49 | : (v2 = v0 | ~ (relation_inverse_image(all_57_6, v1) = v2) | ~ % 27.23/4.49 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] % 27.23/4.49 | : ? [v6: $i] : ? [v7: any] : (apply(all_57_6, v3) = v6 & % 27.23/4.49 | in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_137_0) = v5 & % 27.23/4.49 | $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & % 27.23/4.49 | (v4 = 0 | (v7 = 0 & v5 = 0)))))) % 27.23/4.49 | % 27.23/4.49 | ALPHA: (148) implies: % 27.23/4.49 | (149) relation(all_57_6) = all_137_1 % 27.23/4.49 | (150) relation_dom(all_57_6) = all_137_0 % 27.23/4.50 | (151) ~ (all_137_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 27.23/4.50 | [v3: int] : (v3 = 0 | ~ (relation_inverse_image(all_57_6, v0) = % 27.23/4.50 | v1) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.23/4.50 | | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_57_6, % 27.23/4.50 | v2) = v5 & in(v5, v0) = v6 & in(v2, all_137_0) = v4 & $i(v5) % 27.23/4.50 | & ( ~ (v6 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 27.23/4.50 | ! [v2: $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_57_6, % 27.23/4.50 | v0) = v1) | ~ (apply(all_57_6, v2) = v3) | ~ $i(v2) | ~ % 27.23/4.50 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.23/4.50 | (in(v3, v0) = v6 & in(v2, v1) = v4 & in(v2, all_137_0) = v5 & ( ~ % 27.23/4.50 | (v4 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 27.23/4.50 | ! [v2: $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_57_6, % 27.23/4.50 | v0) = v1) | ~ (apply(all_57_6, v2) = v3) | ~ $i(v2) | ~ % 27.23/4.50 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.23/4.50 | (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, all_137_0) = v4 & ( ~ % 27.23/4.50 | (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: % 27.23/4.50 | $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 27.23/4.50 | (relation_inverse_image(all_57_6, v0) = v1) | ~ (in(v2, % 27.23/4.50 | all_137_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.23/4.50 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_57_6, v2) = % 27.23/4.50 | v5 & in(v5, v0) = v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = 0) % 27.23/4.50 | | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 27.23/4.50 | $i] : ( ~ (relation_inverse_image(all_57_6, v0) = v1) | ~ % 27.23/4.50 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 27.23/4.50 | $i] : (apply(all_57_6, v2) = v3 & in(v3, v0) = 0 & in(v2, % 27.23/4.50 | all_137_0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.50 | [v2: $i] : ( ~ (relation_inverse_image(all_57_6, v0) = v1) | ~ % 27.23/4.50 | (in(v2, all_137_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.23/4.50 | [v3: $i] : ? [v4: any] : ? [v5: any] : (apply(all_57_6, v2) = % 27.23/4.50 | v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = 0) % 27.23/4.50 | | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = % 27.23/4.50 | v0 | ~ (relation_inverse_image(all_57_6, v1) = v2) | ~ $i(v1) | % 27.23/4.50 | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: % 27.23/4.50 | $i] : ? [v7: any] : (apply(all_57_6, v3) = v6 & in(v6, v1) = % 27.23/4.50 | v7 & in(v3, v0) = v4 & in(v3, all_137_0) = v5 & $i(v6) & $i(v3) % 27.23/4.50 | & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 % 27.23/4.50 | & v5 = 0))))) % 27.23/4.50 | % 27.23/4.50 | DELTA: instantiating (87) with fresh symbols all_139_0, all_139_1 gives: % 27.23/4.50 | (152) relation_dom(all_51_0) = all_139_0 & relation(all_51_0) = all_139_1 & % 27.23/4.50 | $i(all_139_0) & ( ~ (all_139_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.50 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 27.23/4.50 | (relation_inverse_image(all_51_0, v0) = v1) | ~ (in(v2, v1) = % 27.23/4.50 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 27.23/4.50 | [v5: $i] : ? [v6: any] : (apply(all_51_0, v2) = v5 & in(v5, % 27.23/4.50 | v0) = v6 & in(v2, all_139_0) = v4 & $i(v5) & ( ~ (v6 = 0) | % 27.23/4.50 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.23/4.50 | ! [v3: $i] : ( ~ (relation_inverse_image(all_51_0, v0) = v1) | ~ % 27.23/4.50 | (apply(all_51_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.23/4.50 | | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v6 % 27.23/4.50 | & in(v2, v1) = v4 & in(v2, all_139_0) = v5 & ( ~ (v4 = 0) | % 27.23/4.50 | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 27.23/4.50 | $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_51_0, v0) = % 27.23/4.50 | v1) | ~ (apply(all_51_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 27.23/4.50 | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.23/4.50 | (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, all_139_0) = v4 & ( % 27.23/4.50 | ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! % 27.23/4.50 | [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 27.23/4.50 | (relation_inverse_image(all_51_0, v0) = v1) | ~ (in(v2, % 27.23/4.50 | all_139_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.23/4.50 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_51_0, v2) = % 27.23/4.50 | v5 & in(v5, v0) = v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = % 27.23/4.50 | 0) | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 27.23/4.50 | ! [v2: $i] : ( ~ (relation_inverse_image(all_51_0, v0) = v1) | ~ % 27.23/4.50 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 27.23/4.50 | $i] : (apply(all_51_0, v2) = v3 & in(v3, v0) = 0 & in(v2, % 27.23/4.50 | all_139_0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.50 | [v2: $i] : ( ~ (relation_inverse_image(all_51_0, v0) = v1) | ~ % 27.23/4.50 | (in(v2, all_139_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 27.23/4.50 | ? [v3: $i] : ? [v4: any] : ? [v5: any] : (apply(all_51_0, v2) % 27.23/4.50 | = v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = % 27.23/4.50 | 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] % 27.23/4.50 | : (v2 = v0 | ~ (relation_inverse_image(all_51_0, v1) = v2) | ~ % 27.23/4.50 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] % 27.23/4.50 | : ? [v6: $i] : ? [v7: any] : (apply(all_51_0, v3) = v6 & % 27.23/4.50 | in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_139_0) = v5 & % 27.23/4.50 | $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & % 27.23/4.50 | (v4 = 0 | (v7 = 0 & v5 = 0)))))) % 27.23/4.50 | % 27.23/4.50 | ALPHA: (152) implies: % 27.23/4.50 | (153) relation_dom(all_51_0) = all_139_0 % 27.23/4.50 | % 27.23/4.50 | DELTA: instantiating (98) with fresh symbols all_143_0, all_143_1 gives: % 27.23/4.50 | (154) relation_dom(all_51_0) = all_143_0 & function(all_51_0) = all_143_1 & % 27.23/4.50 | $i(all_143_0) & ( ~ (all_143_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.50 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 27.23/4.50 | (relation_inverse_image(all_51_0, v0) = v1) | ~ (in(v2, v1) = % 27.23/4.50 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 27.23/4.50 | [v5: $i] : ? [v6: any] : (apply(all_51_0, v2) = v5 & in(v5, % 27.23/4.50 | v0) = v6 & in(v2, all_143_0) = v4 & $i(v5) & ( ~ (v6 = 0) | % 27.23/4.50 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.23/4.50 | ! [v3: $i] : ( ~ (relation_inverse_image(all_51_0, v0) = v1) | ~ % 27.23/4.50 | (apply(all_51_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.23/4.50 | | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v6 % 27.23/4.50 | & in(v2, v1) = v4 & in(v2, all_143_0) = v5 & ( ~ (v4 = 0) | % 27.23/4.50 | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 27.23/4.50 | $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_51_0, v0) = % 27.23/4.50 | v1) | ~ (apply(all_51_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 27.23/4.50 | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.23/4.50 | (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, all_143_0) = v4 & ( % 27.23/4.50 | ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! % 27.23/4.50 | [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 27.23/4.50 | (relation_inverse_image(all_51_0, v0) = v1) | ~ (in(v2, % 27.23/4.50 | all_143_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.23/4.50 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_51_0, v2) = % 27.23/4.50 | v5 & in(v5, v0) = v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = % 27.23/4.50 | 0) | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 27.23/4.50 | ! [v2: $i] : ( ~ (relation_inverse_image(all_51_0, v0) = v1) | ~ % 27.23/4.50 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 27.23/4.50 | $i] : (apply(all_51_0, v2) = v3 & in(v3, v0) = 0 & in(v2, % 27.23/4.50 | all_143_0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.50 | [v2: $i] : ( ~ (relation_inverse_image(all_51_0, v0) = v1) | ~ % 27.23/4.50 | (in(v2, all_143_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 27.23/4.50 | ? [v3: $i] : ? [v4: any] : ? [v5: any] : (apply(all_51_0, v2) % 27.23/4.50 | = v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = % 27.23/4.50 | 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] % 27.23/4.50 | : (v2 = v0 | ~ (relation_inverse_image(all_51_0, v1) = v2) | ~ % 27.23/4.50 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] % 27.23/4.50 | : ? [v6: $i] : ? [v7: any] : (apply(all_51_0, v3) = v6 & % 27.23/4.50 | in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_143_0) = v5 & % 27.23/4.50 | $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & % 27.23/4.50 | (v4 = 0 | (v7 = 0 & v5 = 0)))))) % 27.23/4.50 | % 27.23/4.50 | ALPHA: (154) implies: % 27.23/4.50 | (155) relation_dom(all_51_0) = all_143_0 % 27.23/4.50 | % 27.23/4.50 | DELTA: instantiating (96) with fresh symbols all_147_0, all_147_1 gives: % 27.23/4.51 | (156) relation_dom(all_49_0) = all_147_0 & function(all_49_0) = all_147_1 & % 27.23/4.51 | $i(all_147_0) & ( ~ (all_147_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.51 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 27.23/4.51 | (relation_inverse_image(all_49_0, v0) = v1) | ~ (in(v2, v1) = % 27.23/4.51 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 27.23/4.51 | [v5: $i] : ? [v6: any] : (apply(all_49_0, v2) = v5 & in(v5, % 27.23/4.51 | v0) = v6 & in(v2, all_147_0) = v4 & $i(v5) & ( ~ (v6 = 0) | % 27.23/4.51 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.23/4.51 | ! [v3: $i] : ( ~ (relation_inverse_image(all_49_0, v0) = v1) | ~ % 27.23/4.51 | (apply(all_49_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.23/4.51 | | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v6 % 27.23/4.51 | & in(v2, v1) = v4 & in(v2, all_147_0) = v5 & ( ~ (v4 = 0) | % 27.23/4.51 | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 27.23/4.51 | $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_49_0, v0) = % 27.23/4.51 | v1) | ~ (apply(all_49_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 27.23/4.51 | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.23/4.51 | (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, all_147_0) = v4 & ( % 27.23/4.51 | ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! % 27.23/4.51 | [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 27.23/4.51 | (relation_inverse_image(all_49_0, v0) = v1) | ~ (in(v2, % 27.23/4.51 | all_147_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.23/4.51 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_49_0, v2) = % 27.23/4.51 | v5 & in(v5, v0) = v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = % 27.23/4.51 | 0) | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 27.23/4.51 | ! [v2: $i] : ( ~ (relation_inverse_image(all_49_0, v0) = v1) | ~ % 27.23/4.51 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 27.23/4.51 | $i] : (apply(all_49_0, v2) = v3 & in(v3, v0) = 0 & in(v2, % 27.23/4.51 | all_147_0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.51 | [v2: $i] : ( ~ (relation_inverse_image(all_49_0, v0) = v1) | ~ % 27.23/4.51 | (in(v2, all_147_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 27.23/4.51 | ? [v3: $i] : ? [v4: any] : ? [v5: any] : (apply(all_49_0, v2) % 27.23/4.51 | = v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = % 27.23/4.51 | 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] % 27.23/4.51 | : (v2 = v0 | ~ (relation_inverse_image(all_49_0, v1) = v2) | ~ % 27.23/4.51 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] % 27.23/4.51 | : ? [v6: $i] : ? [v7: any] : (apply(all_49_0, v3) = v6 & % 27.23/4.51 | in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_147_0) = v5 & % 27.23/4.51 | $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & % 27.23/4.51 | (v4 = 0 | (v7 = 0 & v5 = 0)))))) % 27.23/4.51 | % 27.23/4.51 | ALPHA: (156) implies: % 27.23/4.51 | (157) function(all_49_0) = all_147_1 % 27.23/4.51 | (158) ~ (all_147_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 27.23/4.51 | [v3: int] : (v3 = 0 | ~ (relation_inverse_image(all_49_0, v0) = % 27.23/4.51 | v1) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.23/4.51 | | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_49_0, % 27.23/4.51 | v2) = v5 & in(v5, v0) = v6 & in(v2, all_147_0) = v4 & $i(v5) % 27.23/4.51 | & ( ~ (v6 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 27.23/4.51 | ! [v2: $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_49_0, % 27.23/4.51 | v0) = v1) | ~ (apply(all_49_0, v2) = v3) | ~ $i(v2) | ~ % 27.23/4.51 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.23/4.51 | (in(v3, v0) = v6 & in(v2, v1) = v4 & in(v2, all_147_0) = v5 & ( ~ % 27.23/4.51 | (v4 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 27.23/4.51 | ! [v2: $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_49_0, % 27.23/4.51 | v0) = v1) | ~ (apply(all_49_0, v2) = v3) | ~ $i(v2) | ~ % 27.23/4.51 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.23/4.51 | (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, all_147_0) = v4 & ( ~ % 27.23/4.51 | (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: % 27.23/4.51 | $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 27.23/4.51 | (relation_inverse_image(all_49_0, v0) = v1) | ~ (in(v2, % 27.23/4.51 | all_147_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.23/4.51 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_49_0, v2) = % 27.23/4.51 | v5 & in(v5, v0) = v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = 0) % 27.23/4.51 | | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 27.23/4.51 | $i] : ( ~ (relation_inverse_image(all_49_0, v0) = v1) | ~ % 27.23/4.51 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 27.23/4.51 | $i] : (apply(all_49_0, v2) = v3 & in(v3, v0) = 0 & in(v2, % 27.23/4.51 | all_147_0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.51 | [v2: $i] : ( ~ (relation_inverse_image(all_49_0, v0) = v1) | ~ % 27.23/4.51 | (in(v2, all_147_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.23/4.51 | [v3: $i] : ? [v4: any] : ? [v5: any] : (apply(all_49_0, v2) = % 27.23/4.51 | v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = 0) % 27.23/4.51 | | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = % 27.23/4.51 | v0 | ~ (relation_inverse_image(all_49_0, v1) = v2) | ~ $i(v1) | % 27.23/4.51 | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: % 27.23/4.51 | $i] : ? [v7: any] : (apply(all_49_0, v3) = v6 & in(v6, v1) = % 27.23/4.51 | v7 & in(v3, v0) = v4 & in(v3, all_147_0) = v5 & $i(v6) & $i(v3) % 27.23/4.51 | & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 % 27.23/4.51 | & v5 = 0))))) % 27.23/4.51 | % 27.23/4.51 | DELTA: instantiating (93) with fresh symbols all_155_0, all_155_1 gives: % 27.23/4.51 | (159) relation_dom(all_32_0) = all_155_0 & function(all_32_0) = all_155_1 & % 27.23/4.51 | $i(all_155_0) & ( ~ (all_155_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.51 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 27.23/4.51 | (relation_inverse_image(all_32_0, v0) = v1) | ~ (in(v2, v1) = % 27.23/4.51 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 27.23/4.51 | [v5: $i] : ? [v6: any] : (apply(all_32_0, v2) = v5 & in(v5, % 27.23/4.51 | v0) = v6 & in(v2, all_155_0) = v4 & $i(v5) & ( ~ (v6 = 0) | % 27.23/4.51 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.23/4.51 | ! [v3: $i] : ( ~ (relation_inverse_image(all_32_0, v0) = v1) | ~ % 27.23/4.51 | (apply(all_32_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.23/4.51 | | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v6 % 27.23/4.51 | & in(v2, v1) = v4 & in(v2, all_155_0) = v5 & ( ~ (v4 = 0) | % 27.23/4.51 | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 27.23/4.51 | $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_32_0, v0) = % 27.23/4.51 | v1) | ~ (apply(all_32_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 27.23/4.51 | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.23/4.51 | (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, all_155_0) = v4 & ( % 27.23/4.51 | ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! % 27.23/4.51 | [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 27.23/4.51 | (relation_inverse_image(all_32_0, v0) = v1) | ~ (in(v2, % 27.23/4.51 | all_155_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.23/4.51 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_32_0, v2) = % 27.23/4.51 | v5 & in(v5, v0) = v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = % 27.23/4.51 | 0) | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 27.23/4.51 | ! [v2: $i] : ( ~ (relation_inverse_image(all_32_0, v0) = v1) | ~ % 27.23/4.51 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 27.23/4.51 | $i] : (apply(all_32_0, v2) = v3 & in(v3, v0) = 0 & in(v2, % 27.23/4.51 | all_155_0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 27.23/4.51 | [v2: $i] : ( ~ (relation_inverse_image(all_32_0, v0) = v1) | ~ % 27.23/4.51 | (in(v2, all_155_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 27.23/4.51 | ? [v3: $i] : ? [v4: any] : ? [v5: any] : (apply(all_32_0, v2) % 27.23/4.51 | = v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = % 27.23/4.51 | 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] % 27.23/4.51 | : (v2 = v0 | ~ (relation_inverse_image(all_32_0, v1) = v2) | ~ % 27.23/4.51 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] % 27.23/4.51 | : ? [v6: $i] : ? [v7: any] : (apply(all_32_0, v3) = v6 & % 27.23/4.51 | in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_155_0) = v5 & % 27.23/4.51 | $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & % 27.23/4.51 | (v4 = 0 | (v7 = 0 & v5 = 0)))))) % 27.23/4.51 | % 27.23/4.51 | ALPHA: (159) implies: % 27.23/4.51 | (160) relation_dom(all_32_0) = all_155_0 % 27.23/4.51 | % 27.23/4.51 | DELTA: instantiating (91) with fresh symbols all_157_0, all_157_1 gives: % 27.60/4.51 | (161) relation_dom(empty_set) = all_157_0 & function(empty_set) = all_157_1 % 27.60/4.51 | & $i(all_157_0) & ( ~ (all_157_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : % 27.60/4.51 | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 27.60/4.51 | (relation_inverse_image(empty_set, v0) = v1) | ~ (in(v2, v1) = % 27.60/4.51 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 27.60/4.51 | [v5: $i] : ? [v6: any] : (apply(empty_set, v2) = v5 & in(v5, % 27.60/4.51 | v0) = v6 & in(v2, all_157_0) = v4 & $i(v5) & ( ~ (v6 = 0) | % 27.60/4.51 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.60/4.51 | ! [v3: $i] : ( ~ (relation_inverse_image(empty_set, v0) = v1) | % 27.60/4.51 | ~ (apply(empty_set, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 27.60/4.51 | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, % 27.60/4.51 | v0) = v6 & in(v2, v1) = v4 & in(v2, all_157_0) = v5 & ( ~ % 27.60/4.51 | (v4 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] % 27.60/4.51 | : ! [v2: $i] : ! [v3: $i] : ( ~ % 27.60/4.51 | (relation_inverse_image(empty_set, v0) = v1) | ~ % 27.60/4.51 | (apply(empty_set, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.60/4.51 | | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v5 % 27.60/4.51 | & in(v2, v1) = v6 & in(v2, all_157_0) = v4 & ( ~ (v5 = 0) | % 27.60/4.51 | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! % 27.60/4.51 | [v2: $i] : ! [v3: any] : ( ~ (relation_inverse_image(empty_set, % 27.60/4.51 | v0) = v1) | ~ (in(v2, all_157_0) = v3) | ~ $i(v2) | ~ % 27.60/4.51 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] % 27.60/4.51 | : (apply(empty_set, v2) = v5 & in(v5, v0) = v6 & in(v2, v1) = % 27.60/4.51 | v4 & $i(v5) & ( ~ (v4 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0: % 27.60/4.51 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 27.60/4.51 | (relation_inverse_image(empty_set, v0) = v1) | ~ (in(v2, v1) = % 27.60/4.51 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 27.60/4.51 | (apply(empty_set, v2) = v3 & in(v3, v0) = 0 & in(v2, all_157_0) % 27.60/4.51 | = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( % 27.60/4.51 | ~ (relation_inverse_image(empty_set, v0) = v1) | ~ (in(v2, % 27.60/4.51 | all_157_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.60/4.51 | [v3: $i] : ? [v4: any] : ? [v5: any] : (apply(empty_set, v2) % 27.60/4.51 | = v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = % 27.60/4.51 | 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] % 27.60/4.51 | : (v2 = v0 | ~ (relation_inverse_image(empty_set, v1) = v2) | ~ % 27.60/4.51 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] % 27.60/4.51 | : ? [v6: $i] : ? [v7: any] : (apply(empty_set, v3) = v6 & % 27.60/4.51 | in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_157_0) = v5 & % 27.60/4.51 | $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & % 27.60/4.51 | (v4 = 0 | (v7 = 0 & v5 = 0)))))) % 27.60/4.51 | % 27.60/4.51 | ALPHA: (161) implies: % 27.60/4.51 | (162) relation_dom(empty_set) = all_157_0 % 27.60/4.51 | % 27.60/4.51 | DELTA: instantiating (95) with fresh symbols all_161_0, all_161_1 gives: % 27.60/4.52 | (163) relation_dom(all_41_0) = all_161_0 & function(all_41_0) = all_161_1 & % 27.60/4.52 | $i(all_161_0) & ( ~ (all_161_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 27.60/4.52 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 27.60/4.52 | (relation_inverse_image(all_41_0, v0) = v1) | ~ (in(v2, v1) = % 27.60/4.52 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 27.60/4.52 | [v5: $i] : ? [v6: any] : (apply(all_41_0, v2) = v5 & in(v5, % 27.60/4.52 | v0) = v6 & in(v2, all_161_0) = v4 & $i(v5) & ( ~ (v6 = 0) | % 27.60/4.52 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.60/4.52 | ! [v3: $i] : ( ~ (relation_inverse_image(all_41_0, v0) = v1) | ~ % 27.60/4.52 | (apply(all_41_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.60/4.52 | | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v6 % 27.60/4.52 | & in(v2, v1) = v4 & in(v2, all_161_0) = v5 & ( ~ (v4 = 0) | % 27.60/4.52 | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 27.60/4.52 | $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_41_0, v0) = % 27.60/4.52 | v1) | ~ (apply(all_41_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 27.60/4.52 | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.60/4.52 | (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, all_161_0) = v4 & ( % 27.60/4.52 | ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! % 27.60/4.52 | [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 27.60/4.52 | (relation_inverse_image(all_41_0, v0) = v1) | ~ (in(v2, % 27.60/4.52 | all_161_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.60/4.52 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_41_0, v2) = % 27.60/4.52 | v5 & in(v5, v0) = v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = % 27.60/4.52 | 0) | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 27.60/4.52 | ! [v2: $i] : ( ~ (relation_inverse_image(all_41_0, v0) = v1) | ~ % 27.60/4.52 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 27.60/4.52 | $i] : (apply(all_41_0, v2) = v3 & in(v3, v0) = 0 & in(v2, % 27.60/4.52 | all_161_0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 27.60/4.52 | [v2: $i] : ( ~ (relation_inverse_image(all_41_0, v0) = v1) | ~ % 27.60/4.52 | (in(v2, all_161_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 27.60/4.52 | ? [v3: $i] : ? [v4: any] : ? [v5: any] : (apply(all_41_0, v2) % 27.60/4.52 | = v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = % 27.60/4.52 | 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] % 27.60/4.52 | : (v2 = v0 | ~ (relation_inverse_image(all_41_0, v1) = v2) | ~ % 27.60/4.52 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] % 27.60/4.52 | : ? [v6: $i] : ? [v7: any] : (apply(all_41_0, v3) = v6 & % 27.60/4.52 | in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_161_0) = v5 & % 27.60/4.52 | $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & % 27.60/4.52 | (v4 = 0 | (v7 = 0 & v5 = 0)))))) % 27.60/4.52 | % 27.60/4.52 | ALPHA: (163) implies: % 27.60/4.52 | (164) relation_dom(all_41_0) = all_161_0 % 27.60/4.52 | % 27.60/4.52 | DELTA: instantiating (86) with fresh symbols all_163_0, all_163_1 gives: % 27.60/4.52 | (165) relation_dom(all_41_0) = all_163_0 & relation(all_41_0) = all_163_1 & % 27.60/4.52 | $i(all_163_0) & ( ~ (all_163_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 27.60/4.52 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 27.60/4.52 | (relation_inverse_image(all_41_0, v0) = v1) | ~ (in(v2, v1) = % 27.60/4.52 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 27.60/4.52 | [v5: $i] : ? [v6: any] : (apply(all_41_0, v2) = v5 & in(v5, % 27.60/4.52 | v0) = v6 & in(v2, all_163_0) = v4 & $i(v5) & ( ~ (v6 = 0) | % 27.60/4.52 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.60/4.52 | ! [v3: $i] : ( ~ (relation_inverse_image(all_41_0, v0) = v1) | ~ % 27.60/4.52 | (apply(all_41_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.60/4.52 | | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v6 % 27.60/4.52 | & in(v2, v1) = v4 & in(v2, all_163_0) = v5 & ( ~ (v4 = 0) | % 27.60/4.52 | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 27.60/4.52 | $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_41_0, v0) = % 27.60/4.52 | v1) | ~ (apply(all_41_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 27.60/4.52 | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.60/4.52 | (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, all_163_0) = v4 & ( % 27.60/4.52 | ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! % 27.60/4.52 | [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 27.60/4.52 | (relation_inverse_image(all_41_0, v0) = v1) | ~ (in(v2, % 27.60/4.52 | all_163_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.60/4.52 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_41_0, v2) = % 27.60/4.52 | v5 & in(v5, v0) = v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = % 27.60/4.52 | 0) | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 27.60/4.52 | ! [v2: $i] : ( ~ (relation_inverse_image(all_41_0, v0) = v1) | ~ % 27.60/4.52 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 27.60/4.52 | $i] : (apply(all_41_0, v2) = v3 & in(v3, v0) = 0 & in(v2, % 27.60/4.52 | all_163_0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 27.60/4.52 | [v2: $i] : ( ~ (relation_inverse_image(all_41_0, v0) = v1) | ~ % 27.60/4.52 | (in(v2, all_163_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 27.60/4.52 | ? [v3: $i] : ? [v4: any] : ? [v5: any] : (apply(all_41_0, v2) % 27.60/4.52 | = v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = % 27.60/4.52 | 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] % 27.60/4.52 | : (v2 = v0 | ~ (relation_inverse_image(all_41_0, v1) = v2) | ~ % 27.60/4.52 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] % 27.60/4.52 | : ? [v6: $i] : ? [v7: any] : (apply(all_41_0, v3) = v6 & % 27.60/4.52 | in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_163_0) = v5 & % 27.60/4.52 | $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & % 27.60/4.52 | (v4 = 0 | (v7 = 0 & v5 = 0)))))) % 27.60/4.52 | % 27.60/4.52 | ALPHA: (165) implies: % 27.60/4.52 | (166) relation_dom(all_41_0) = all_163_0 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (84), (155) imply: % 27.60/4.52 | (167) relation_dom(empty_set) = all_143_0 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (84), (153) imply: % 27.60/4.52 | (168) relation_dom(empty_set) = all_139_0 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (84), (131) imply: % 27.60/4.52 | (169) relation_dom(empty_set) = all_89_1 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (84), (110) imply: % 27.60/4.52 | (170) relation_dom(empty_set) = all_67_0 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (104), (166) imply: % 27.60/4.52 | (171) relation_dom(empty_set) = all_163_0 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (104), (164) imply: % 27.60/4.52 | (172) relation_dom(empty_set) = all_161_0 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (104), (128) imply: % 27.60/4.52 | (173) relation_dom(empty_set) = all_85_1 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (104), (117) imply: % 27.60/4.52 | (174) relation_dom(empty_set) = all_71_0 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (105), (160) imply: % 27.60/4.52 | (175) relation_dom(empty_set) = all_155_0 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (105), (137) imply: % 27.60/4.52 | (176) relation_dom(empty_set) = all_107_1 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (105), (119) imply: % 27.60/4.52 | (177) relation_dom(empty_set) = all_73_0 % 27.60/4.52 | % 27.60/4.52 | REDUCE: (108), (115) imply: % 27.60/4.52 | (178) relation_dom(empty_set) = all_69_0 % 27.60/4.52 | % 27.60/4.52 | BETA: splitting (79) gives: % 27.60/4.52 | % 27.60/4.52 | Case 1: % 27.60/4.52 | | % 27.60/4.52 | | (179) all_34_0 = 0 % 27.60/4.52 | | % 27.60/4.52 | | REDUCE: (42), (179) imply: % 27.60/4.52 | | (180) $false % 27.60/4.52 | | % 27.60/4.52 | | CLOSE: (180) is inconsistent. % 27.60/4.52 | | % 27.60/4.52 | Case 2: % 27.60/4.52 | | % 27.60/4.52 | | (181) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 27.60/4.52 | | powerset(all_34_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2 & % 27.60/4.52 | | $i(v1) & $i(v0)) % 27.60/4.52 | | % 27.60/4.52 | | DELTA: instantiating (181) with fresh symbols all_179_0, all_179_1, % 27.60/4.52 | | all_179_2 gives: % 27.60/4.52 | | (182) ~ (all_179_0 = 0) & powerset(all_34_1) = all_179_2 & % 27.60/4.52 | | element(all_179_1, all_179_2) = 0 & empty(all_179_1) = all_179_0 & % 27.60/4.52 | | $i(all_179_1) & $i(all_179_2) % 27.60/4.52 | | % 27.60/4.52 | | ALPHA: (182) implies: % 27.60/4.52 | | (183) ~ (all_179_0 = 0) % 27.60/4.52 | | (184) $i(all_179_1) % 27.60/4.52 | | (185) empty(all_179_1) = all_179_0 % 27.60/4.52 | | % 27.60/4.52 | | GROUND_INST: instantiating (28) with 0, all_147_1, all_49_0, simplifying % 27.60/4.52 | | with (52), (157) gives: % 27.60/4.52 | | (186) all_147_1 = 0 % 27.60/4.52 | | % 27.60/4.52 | | GROUND_INST: instantiating (29) with all_93_2, all_137_1, all_57_6, % 27.60/4.52 | | simplifying with (133), (149) gives: % 27.60/4.52 | | (187) all_137_1 = all_93_2 % 27.60/4.52 | | % 27.60/4.52 | | GROUND_INST: instantiating (30) with all_67_0, all_71_0, empty_set, % 27.60/4.52 | | simplifying with (170), (174) gives: % 27.60/4.52 | | (188) all_71_0 = all_67_0 % 27.60/4.52 | | % 27.60/4.52 | | GROUND_INST: instantiating (30) with all_71_0, all_73_0, empty_set, % 27.60/4.53 | | simplifying with (174), (177) gives: % 27.60/4.53 | | (189) all_73_0 = all_71_0 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_73_0, all_75_0, empty_set, % 27.60/4.53 | | simplifying with (121), (177) gives: % 27.60/4.53 | | (190) all_75_0 = all_73_0 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_75_0, all_85_1, empty_set, % 27.60/4.53 | | simplifying with (121), (173) gives: % 27.60/4.53 | | (191) all_85_1 = all_75_0 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_85_1, all_107_1, empty_set, % 27.60/4.53 | | simplifying with (173), (176) gives: % 27.60/4.53 | | (192) all_107_1 = all_85_1 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_107_1, all_111_1, empty_set, % 27.60/4.53 | | simplifying with (140), (176) gives: % 27.60/4.53 | | (193) all_111_1 = all_107_1 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_155_0, all_157_0, empty_set, % 27.60/4.53 | | simplifying with (162), (175) gives: % 27.60/4.53 | | (194) all_157_0 = all_155_0 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_143_0, all_157_0, empty_set, % 27.60/4.53 | | simplifying with (162), (167) gives: % 27.60/4.53 | | (195) all_157_0 = all_143_0 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_139_0, all_157_0, empty_set, % 27.60/4.53 | | simplifying with (162), (168) gives: % 27.60/4.53 | | (196) all_157_0 = all_139_0 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_111_1, all_157_0, empty_set, % 27.60/4.53 | | simplifying with (140), (162) gives: % 27.60/4.53 | | (197) all_157_0 = all_111_1 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_143_0, all_161_0, empty_set, % 27.60/4.53 | | simplifying with (167), (172) gives: % 27.60/4.53 | | (198) all_161_0 = all_143_0 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_89_1, all_161_0, empty_set, % 27.60/4.53 | | simplifying with (169), (172) gives: % 27.60/4.53 | | (199) all_161_0 = all_89_1 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_107_1, all_163_0, empty_set, % 27.60/4.53 | | simplifying with (171), (176) gives: % 27.60/4.53 | | (200) all_163_0 = all_107_1 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (30) with all_69_0, all_163_0, empty_set, % 27.60/4.53 | | simplifying with (171), (178) gives: % 27.60/4.53 | | (201) all_163_0 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (32) with 0, all_131_1, all_57_8, all_57_9, % 27.60/4.53 | | all_57_6, simplifying with (74), (142) gives: % 27.60/4.53 | | (202) all_131_1 = 0 % 27.60/4.53 | | % 27.60/4.53 | | GROUND_INST: instantiating (33) with all_131_0, all_133_0, all_57_6, % 27.60/4.53 | | all_57_8, all_57_9, simplifying with (143), (147) gives: % 27.60/4.53 | | (203) all_133_0 = all_131_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (200), (201) imply: % 27.60/4.53 | | (204) all_107_1 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | SIMP: (204) implies: % 27.60/4.53 | | (205) all_107_1 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (198), (199) imply: % 27.60/4.53 | | (206) all_143_0 = all_89_1 % 27.60/4.53 | | % 27.60/4.53 | | SIMP: (206) implies: % 27.60/4.53 | | (207) all_143_0 = all_89_1 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (194), (196) imply: % 27.60/4.53 | | (208) all_155_0 = all_139_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (194), (195) imply: % 27.60/4.53 | | (209) all_155_0 = all_143_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (194), (197) imply: % 27.60/4.53 | | (210) all_155_0 = all_111_1 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (208), (209) imply: % 27.60/4.53 | | (211) all_143_0 = all_139_0 % 27.60/4.53 | | % 27.60/4.53 | | SIMP: (211) implies: % 27.60/4.53 | | (212) all_143_0 = all_139_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (208), (210) imply: % 27.60/4.53 | | (213) all_139_0 = all_111_1 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (207), (212) imply: % 27.60/4.53 | | (214) all_139_0 = all_89_1 % 27.60/4.53 | | % 27.60/4.53 | | SIMP: (214) implies: % 27.60/4.53 | | (215) all_139_0 = all_89_1 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (213), (215) imply: % 27.60/4.53 | | (216) all_111_1 = all_89_1 % 27.60/4.53 | | % 27.60/4.53 | | SIMP: (216) implies: % 27.60/4.53 | | (217) all_111_1 = all_89_1 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (193), (217) imply: % 27.60/4.53 | | (218) all_107_1 = all_89_1 % 27.60/4.53 | | % 27.60/4.53 | | SIMP: (218) implies: % 27.60/4.53 | | (219) all_107_1 = all_89_1 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (192), (219) imply: % 27.60/4.53 | | (220) all_89_1 = all_85_1 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (205), (219) imply: % 27.60/4.53 | | (221) all_89_1 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (220), (221) imply: % 27.60/4.53 | | (222) all_85_1 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | SIMP: (222) implies: % 27.60/4.53 | | (223) all_85_1 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (191), (223) imply: % 27.60/4.53 | | (224) all_75_0 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | SIMP: (224) implies: % 27.60/4.53 | | (225) all_75_0 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (190), (225) imply: % 27.60/4.53 | | (226) all_73_0 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | SIMP: (226) implies: % 27.60/4.53 | | (227) all_73_0 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (189), (227) imply: % 27.60/4.53 | | (228) all_71_0 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | SIMP: (228) implies: % 27.60/4.53 | | (229) all_71_0 = all_69_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (188), (229) imply: % 27.60/4.53 | | (230) all_69_0 = all_67_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (223), (230) imply: % 27.60/4.53 | | (231) all_85_1 = all_67_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (221), (230) imply: % 27.60/4.53 | | (232) all_89_1 = all_67_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (219), (232) imply: % 27.60/4.53 | | (233) all_107_1 = all_67_0 % 27.60/4.53 | | % 27.60/4.53 | | COMBINE_EQS: (217), (232) imply: % 27.60/4.53 | | (234) all_111_1 = all_67_0 % 27.60/4.53 | | % 27.60/4.53 | | REDUCE: (114), (230) imply: % 27.60/4.53 | | (235) relation(all_67_0) = 0 % 27.60/4.53 | | % 27.60/4.53 | | REDUCE: (139), (234) imply: % 27.60/4.53 | | (236) empty(all_67_0) = all_111_0 % 27.60/4.53 | | % 27.60/4.53 | | REDUCE: (136), (233) imply: % 27.60/4.53 | | (237) empty(all_67_0) = all_107_0 % 27.60/4.53 | | % 27.60/4.53 | | REDUCE: (130), (232) imply: % 27.60/4.53 | | (238) empty(all_67_0) = all_89_0 % 27.60/4.53 | | % 27.60/4.53 | | REDUCE: (127), (231) imply: % 27.60/4.53 | | (239) empty(all_67_0) = all_85_0 % 27.60/4.53 | | % 27.60/4.53 | | REDUCE: (113), (230) imply: % 27.60/4.53 | | (240) empty(all_67_0) = 0 % 27.60/4.53 | | % 27.60/4.53 | | REDUCE: (146), (203) imply: % 27.60/4.53 | | (241) $i(all_131_0) % 27.60/4.53 | | % 27.60/4.53 | | REDUCE: (112), (230) imply: % 27.60/4.53 | | (242) $i(all_67_0) % 27.60/4.53 | | % 27.60/4.53 | | BETA: splitting (144) gives: % 27.60/4.53 | | % 27.60/4.53 | | Case 1: % 27.60/4.53 | | | % 27.60/4.53 | | | (243) ~ (all_131_1 = 0) % 27.60/4.53 | | | % 27.60/4.53 | | | REDUCE: (202), (243) imply: % 27.60/4.53 | | | (244) $false % 27.60/4.53 | | | % 27.60/4.53 | | | CLOSE: (244) is inconsistent. % 27.60/4.53 | | | % 27.60/4.53 | | Case 2: % 27.60/4.53 | | | % 27.60/4.53 | | | (245) ( ~ (all_57_8 = empty_set) | all_57_6 = empty_set | all_57_9 = % 27.60/4.53 | | | empty_set) & (all_131_0 = all_57_9 | (all_57_8 = empty_set & ~ % 27.60/4.53 | | | (all_57_9 = empty_set))) % 27.60/4.53 | | | % 27.60/4.53 | | | ALPHA: (245) implies: % 27.60/4.53 | | | (246) all_131_0 = all_57_9 | (all_57_8 = empty_set & ~ (all_57_9 = % 27.60/4.53 | | | empty_set)) % 27.60/4.53 | | | % 27.60/4.53 | | | BETA: splitting (246) gives: % 27.60/4.53 | | | % 27.60/4.53 | | | Case 1: % 27.60/4.53 | | | | % 27.60/4.53 | | | | (247) all_131_0 = all_57_9 % 27.60/4.53 | | | | % 27.60/4.53 | | | | REDUCE: (143), (247) imply: % 27.60/4.53 | | | | (248) relation_dom_as_subset(all_57_9, all_57_8, all_57_6) = all_57_9 % 27.60/4.53 | | | | % 27.60/4.53 | | | | BETA: splitting (158) gives: % 27.60/4.53 | | | | % 27.60/4.53 | | | | Case 1: % 27.60/4.53 | | | | | % 27.60/4.53 | | | | | (249) ~ (all_147_1 = 0) % 27.60/4.53 | | | | | % 27.60/4.53 | | | | | REDUCE: (186), (249) imply: % 27.60/4.53 | | | | | (250) $false % 27.60/4.53 | | | | | % 27.60/4.53 | | | | | CLOSE: (250) is inconsistent. % 27.60/4.53 | | | | | % 27.60/4.53 | | | | Case 2: % 27.60/4.53 | | | | | % 27.60/4.53 | | | | | % 27.60/4.53 | | | | | GROUND_INST: instantiating (27) with all_85_0, all_89_0, all_67_0, % 27.60/4.53 | | | | | simplifying with (238), (239) gives: % 27.60/4.53 | | | | | (251) all_89_0 = all_85_0 % 27.60/4.53 | | | | | % 27.60/4.53 | | | | | GROUND_INST: instantiating (27) with 0, all_111_0, all_67_0, % 27.60/4.53 | | | | | simplifying with (236), (240) gives: % 27.60/4.53 | | | | | (252) all_111_0 = 0 % 27.60/4.53 | | | | | % 27.60/4.53 | | | | | GROUND_INST: instantiating (27) with all_107_0, all_111_0, all_67_0, % 27.60/4.53 | | | | | simplifying with (236), (237) gives: % 27.60/4.53 | | | | | (253) all_111_0 = all_107_0 % 27.60/4.53 | | | | | % 27.60/4.53 | | | | | GROUND_INST: instantiating (27) with all_89_0, all_111_0, all_67_0, % 27.60/4.53 | | | | | simplifying with (236), (238) gives: % 27.60/4.53 | | | | | (254) all_111_0 = all_89_0 % 27.60/4.53 | | | | | % 27.60/4.54 | | | | | COMBINE_EQS: (252), (253) imply: % 27.60/4.54 | | | | | (255) all_107_0 = 0 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | COMBINE_EQS: (253), (254) imply: % 27.60/4.54 | | | | | (256) all_107_0 = all_89_0 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | COMBINE_EQS: (255), (256) imply: % 27.60/4.54 | | | | | (257) all_89_0 = 0 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | SIMP: (257) implies: % 27.60/4.54 | | | | | (258) all_89_0 = 0 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | COMBINE_EQS: (251), (258) imply: % 27.60/4.54 | | | | | (259) all_85_0 = 0 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | SIMP: (259) implies: % 27.60/4.54 | | | | | (260) all_85_0 = 0 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (24) with all_67_0, simplifying with (240), % 27.60/4.54 | | | | | (242) gives: % 27.60/4.54 | | | | | (261) all_67_0 = empty_set % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (1) with all_67_0, simplifying with (240), % 27.60/4.54 | | | | | (242) gives: % 27.60/4.54 | | | | | (262) function(all_67_0) = 0 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (2) with all_67_0, simplifying with (240), % 27.60/4.54 | | | | | (242) gives: % 27.60/4.54 | | | | | (263) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.60/4.54 | | | | | (one_to_one(all_67_0) = v2 & relation(all_67_0) = v0 & % 27.60/4.54 | | | | | function(all_67_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = % 27.60/4.54 | | | | | 0)) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (18) with all_179_1, all_179_0, simplifying % 27.60/4.54 | | | | | with (184), (185) gives: % 27.60/4.54 | | | | | (264) all_179_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 27.60/4.54 | | | | | (relation_dom(all_179_1) = v1 & relation(all_179_1) = v0 & % 27.60/4.54 | | | | | empty(v1) = v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (4) with all_67_0, simplifying with (235), % 27.60/4.54 | | | | | (242) gives: % 27.60/4.54 | | | | | (265) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.60/4.54 | | | | | (one_to_one(all_67_0) = v2 & function(all_67_0) = v1 & % 27.60/4.54 | | | | | empty(all_67_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = % 27.60/4.54 | | | | | 0)) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (7) with all_67_0, simplifying with (235), % 27.60/4.54 | | | | | (242) gives: % 27.60/4.54 | | | | | (266) ? [v0: any] : ? [v1: $i] : (relation_dom(all_67_0) = v1 & % 27.60/4.54 | | | | | function(all_67_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: % 27.60/4.54 | | | | | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 % 27.60/4.54 | | | | | = 0 | ~ (relation_inverse_image(all_67_0, v2) = v3) % 27.60/4.54 | | | | | | ~ (in(v4, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 27.60/4.54 | | | | | $i(v2) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 27.60/4.54 | | | | | (apply(all_67_0, v4) = v7 & in(v7, v2) = v8 & in(v4, % 27.60/4.54 | | | | | v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0)))) % 27.60/4.54 | | | | | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 27.60/4.54 | | | | | : ( ~ (relation_inverse_image(all_67_0, v2) = v3) | ~ % 27.60/4.54 | | | | | (apply(all_67_0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | % 27.60/4.54 | | | | | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: any] % 27.60/4.54 | | | | | : (in(v5, v2) = v8 & in(v4, v3) = v6 & in(v4, v1) = % 27.60/4.54 | | | | | v7 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0)))) & ! [v2: % 27.60/4.54 | | | | | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 27.60/4.54 | | | | | (relation_inverse_image(all_67_0, v2) = v3) | ~ % 27.60/4.54 | | | | | (apply(all_67_0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | % 27.60/4.54 | | | | | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: any] % 27.60/4.54 | | | | | : (in(v5, v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = % 27.60/4.54 | | | | | v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! % 27.60/4.54 | | | | | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( % 27.60/4.54 | | | | | ~ (relation_inverse_image(all_67_0, v2) = v3) | ~ % 27.60/4.54 | | | | | (in(v4, v1) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 27.60/4.54 | | | | | | ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 27.60/4.54 | | | | | (apply(all_67_0, v4) = v7 & in(v7, v2) = v8 & in(v4, % 27.60/4.54 | | | | | v3) = v6 & $i(v7) & ( ~ (v6 = 0) | (v8 = 0 & v5 = % 27.60/4.54 | | | | | 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 27.60/4.54 | | | | | : ( ~ (relation_inverse_image(all_67_0, v2) = v3) | ~ % 27.60/4.54 | | | | | (in(v4, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 27.60/4.54 | | | | | | ? [v5: $i] : (apply(all_67_0, v4) = v5 & in(v5, % 27.60/4.54 | | | | | v2) = 0 & in(v4, v1) = 0 & $i(v5))) & ! [v2: $i] % 27.60/4.54 | | | | | : ! [v3: $i] : ! [v4: $i] : ( ~ % 27.60/4.54 | | | | | (relation_inverse_image(all_67_0, v2) = v3) | ~ % 27.60/4.54 | | | | | (in(v4, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 27.60/4.54 | | | | | | ? [v5: $i] : ? [v6: any] : ? [v7: any] : % 27.60/4.54 | | | | | (apply(all_67_0, v4) = v5 & in(v5, v2) = v6 & in(v4, % 27.60/4.54 | | | | | v3) = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0))) & ? % 27.60/4.54 | | | | | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 27.60/4.54 | | | | | (relation_inverse_image(all_67_0, v3) = v4) | ~ % 27.60/4.54 | | | | | $i(v3) | ~ $i(v2) | ? [v5: $i] : ? [v6: any] : ? % 27.60/4.54 | | | | | [v7: any] : ? [v8: $i] : ? [v9: any] : % 27.60/4.54 | | | | | (apply(all_67_0, v5) = v8 & in(v8, v3) = v9 & in(v5, % 27.60/4.54 | | | | | v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) & ( % 27.60/4.54 | | | | | ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 % 27.60/4.54 | | | | | | (v9 = 0 & v7 = 0))))))) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (cc1_relset_1) with all_57_9, all_57_8, % 27.60/4.54 | | | | | all_57_6, all_77_1, all_77_0, simplifying with (61), % 27.60/4.54 | | | | | (62), (64), (123), (124), (125) gives: % 27.60/4.54 | | | | | (267) relation(all_57_6) = 0 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (5) with all_57_6, all_93_0, simplifying % 27.60/4.54 | | | | | with (64), (134) gives: % 27.60/4.54 | | | | | (268) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.60/4.54 | | | | | (relation(all_57_6) = v0 & function(all_57_6) = v2 & % 27.60/4.54 | | | | | empty(all_57_6) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 % 27.60/4.54 | | | | | = 0) | all_93_0 = 0)) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (9) with all_57_6, all_137_0, all_57_7, % 27.60/4.54 | | | | | all_57_5, all_57_4, all_57_1, simplifying with (63), % 27.60/4.54 | | | | | (64), (65), (66), (71), (72), (150) gives: % 27.60/4.54 | | | | | (269) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.60/4.54 | | | | | ((relation(all_57_6) = v0 & function(all_57_6) = v1 & ( ~ (v1 % 27.60/4.54 | | | | | = 0) | ~ (v0 = 0))) | (in(all_57_1, all_57_7) = v2 & % 27.60/4.54 | | | | | in(all_57_4, all_137_0) = v1 & in(all_57_4, all_57_5) = % 27.60/4.54 | | | | | v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (8) with all_57_6, all_137_0, all_57_7, % 27.60/4.54 | | | | | all_57_5, all_57_4, all_57_1, simplifying with (63), % 27.60/4.54 | | | | | (64), (65), (66), (71), (72), (150) gives: % 27.60/4.54 | | | | | (270) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.60/4.54 | | | | | ((relation(all_57_6) = v0 & function(all_57_6) = v1 & ( ~ (v1 % 27.60/4.54 | | | | | = 0) | ~ (v0 = 0))) | (in(all_57_1, all_57_7) = v1 & % 27.60/4.54 | | | | | in(all_57_4, all_137_0) = v0 & in(all_57_4, all_57_5) = % 27.60/4.54 | | | | | v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (17) with all_57_6, all_137_0, simplifying % 27.60/4.54 | | | | | with (64), (150) gives: % 27.60/4.54 | | | | | (271) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.60/4.54 | | | | | (relation(all_57_6) = v1 & empty(all_137_0) = v2 & % 27.60/4.54 | | | | | empty(all_57_6) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = % 27.60/4.54 | | | | | 0)) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (22) with all_57_9, all_57_8, all_57_6, % 27.60/4.54 | | | | | all_57_9, simplifying with (61), (62), (64), (248) gives: % 27.60/4.54 | | | | | (272) ? [v0: any] : ? [v1: $i] : (relation_of2(all_57_6, % 27.60/4.54 | | | | | all_57_9, all_57_8) = v0 & relation_dom(all_57_6) = v1 & % 27.60/4.54 | | | | | $i(v1) & ( ~ (v0 = 0) | v1 = all_57_9)) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (12) with all_57_9, all_57_8, all_57_6, % 27.60/4.54 | | | | | simplifying with (61), (62), (64), (100) gives: % 27.60/4.54 | | | | | (273) ? [v0: $i] : ? [v1: $i] : (relation_dom_as_subset(all_57_9, % 27.60/4.54 | | | | | all_57_8, all_57_6) = v0 & powerset(all_57_9) = v1 & % 27.60/4.54 | | | | | element(v0, v1) = 0 & $i(v1) & $i(v0)) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | GROUND_INST: instantiating (21) with all_57_9, all_57_8, all_57_6, % 27.60/4.54 | | | | | simplifying with (61), (62), (64), (100) gives: % 27.60/4.54 | | | | | (274) ? [v0: $i] : (relation_dom_as_subset(all_57_9, all_57_8, % 27.60/4.54 | | | | | all_57_6) = v0 & relation_dom(all_57_6) = v0 & $i(v0)) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | DELTA: instantiating (274) with fresh symbol all_295_0 gives: % 27.60/4.54 | | | | | (275) relation_dom_as_subset(all_57_9, all_57_8, all_57_6) = % 27.60/4.54 | | | | | all_295_0 & relation_dom(all_57_6) = all_295_0 & % 27.60/4.54 | | | | | $i(all_295_0) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | ALPHA: (275) implies: % 27.60/4.54 | | | | | (276) relation_dom(all_57_6) = all_295_0 % 27.60/4.54 | | | | | (277) relation_dom_as_subset(all_57_9, all_57_8, all_57_6) = % 27.60/4.54 | | | | | all_295_0 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | DELTA: instantiating (273) with fresh symbols all_311_0, all_311_1 % 27.60/4.54 | | | | | gives: % 27.60/4.54 | | | | | (278) relation_dom_as_subset(all_57_9, all_57_8, all_57_6) = % 27.60/4.54 | | | | | all_311_1 & powerset(all_57_9) = all_311_0 & % 27.60/4.54 | | | | | element(all_311_1, all_311_0) = 0 & $i(all_311_0) & % 27.60/4.54 | | | | | $i(all_311_1) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | ALPHA: (278) implies: % 27.60/4.54 | | | | | (279) relation_dom_as_subset(all_57_9, all_57_8, all_57_6) = % 27.60/4.54 | | | | | all_311_1 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | DELTA: instantiating (272) with fresh symbols all_313_0, all_313_1 % 27.60/4.54 | | | | | gives: % 27.60/4.54 | | | | | (280) relation_of2(all_57_6, all_57_9, all_57_8) = all_313_1 & % 27.60/4.54 | | | | | relation_dom(all_57_6) = all_313_0 & $i(all_313_0) & ( ~ % 27.60/4.54 | | | | | (all_313_1 = 0) | all_313_0 = all_57_9) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | ALPHA: (280) implies: % 27.60/4.54 | | | | | (281) relation_dom(all_57_6) = all_313_0 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | DELTA: instantiating (263) with fresh symbols all_323_0, all_323_1, % 27.60/4.54 | | | | | all_323_2 gives: % 27.60/4.54 | | | | | (282) one_to_one(all_67_0) = all_323_0 & relation(all_67_0) = % 27.60/4.54 | | | | | all_323_2 & function(all_67_0) = all_323_1 & ( ~ (all_323_1 = % 27.60/4.54 | | | | | 0) | ~ (all_323_2 = 0) | all_323_0 = 0) % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | ALPHA: (282) implies: % 27.60/4.54 | | | | | (283) function(all_67_0) = all_323_1 % 27.60/4.54 | | | | | % 27.60/4.54 | | | | | DELTA: instantiating (265) with fresh symbols all_325_0, all_325_1, % 27.60/4.54 | | | | | all_325_2 gives: % 27.60/4.54 | | | | | (284) one_to_one(all_67_0) = all_325_0 & function(all_67_0) = % 27.60/4.54 | | | | | all_325_1 & empty(all_67_0) = all_325_2 & ( ~ (all_325_1 = 0) % 27.60/4.54 | | | | | | ~ (all_325_2 = 0) | all_325_0 = 0) % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | ALPHA: (284) implies: % 27.60/4.55 | | | | | (285) function(all_67_0) = all_325_1 % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | DELTA: instantiating (271) with fresh symbols all_339_0, all_339_1, % 27.60/4.55 | | | | | all_339_2 gives: % 27.60/4.55 | | | | | (286) relation(all_57_6) = all_339_1 & empty(all_137_0) = all_339_0 % 27.60/4.55 | | | | | & empty(all_57_6) = all_339_2 & ( ~ (all_339_0 = 0) | ~ % 27.60/4.55 | | | | | (all_339_1 = 0) | all_339_2 = 0) % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | ALPHA: (286) implies: % 27.60/4.55 | | | | | (287) relation(all_57_6) = all_339_1 % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | DELTA: instantiating (268) with fresh symbols all_351_0, all_351_1, % 27.60/4.55 | | | | | all_351_2 gives: % 27.60/4.55 | | | | | (288) relation(all_57_6) = all_351_2 & function(all_57_6) = % 27.60/4.55 | | | | | all_351_0 & empty(all_57_6) = all_351_1 & ( ~ (all_351_0 = 0) % 27.60/4.55 | | | | | | ~ (all_351_1 = 0) | ~ (all_351_2 = 0) | all_93_0 = 0) % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | ALPHA: (288) implies: % 27.60/4.55 | | | | | (289) function(all_57_6) = all_351_0 % 27.60/4.55 | | | | | (290) relation(all_57_6) = all_351_2 % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | DELTA: instantiating (270) with fresh symbols all_365_0, all_365_1, % 27.60/4.55 | | | | | all_365_2 gives: % 27.60/4.55 | | | | | (291) (relation(all_57_6) = all_365_2 & function(all_57_6) = % 27.60/4.55 | | | | | all_365_1 & ( ~ (all_365_1 = 0) | ~ (all_365_2 = 0))) | % 27.60/4.55 | | | | | (in(all_57_1, all_57_7) = all_365_1 & in(all_57_4, all_137_0) % 27.60/4.55 | | | | | = all_365_2 & in(all_57_4, all_57_5) = all_365_0 & ( ~ % 27.60/4.55 | | | | | (all_365_1 = 0) | ~ (all_365_2 = 0) | all_365_0 = 0)) % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | DELTA: instantiating (269) with fresh symbols all_366_0, all_366_1, % 27.60/4.55 | | | | | all_366_2 gives: % 27.60/4.55 | | | | | (292) (relation(all_57_6) = all_366_2 & function(all_57_6) = % 27.60/4.55 | | | | | all_366_1 & ( ~ (all_366_1 = 0) | ~ (all_366_2 = 0))) | % 27.60/4.55 | | | | | (in(all_57_1, all_57_7) = all_366_0 & in(all_57_4, all_137_0) % 27.60/4.55 | | | | | = all_366_1 & in(all_57_4, all_57_5) = all_366_2 & ( ~ % 27.60/4.55 | | | | | (all_366_2 = 0) | (all_366_0 = 0 & all_366_1 = 0))) % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | DELTA: instantiating (266) with fresh symbols all_367_0, all_367_1 % 27.60/4.55 | | | | | gives: % 27.60/4.55 | | | | | (293) relation_dom(all_67_0) = all_367_0 & function(all_67_0) = % 27.60/4.55 | | | | | all_367_1 & $i(all_367_0) & ( ~ (all_367_1 = 0) | ( ! [v0: % 27.60/4.55 | | | | | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 27.60/4.55 | | | | | 0 | ~ (relation_inverse_image(all_67_0, v0) = v1) | ~ % 27.60/4.55 | | | | | (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 27.60/4.55 | | | | | ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 27.60/4.55 | | | | | (apply(all_67_0, v2) = v5 & in(v5, v0) = v6 & in(v2, % 27.60/4.55 | | | | | all_367_0) = v4 & $i(v5) & ( ~ (v6 = 0) | ~ (v4 = % 27.60/4.55 | | | | | 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.60/4.55 | | | | | ! [v3: $i] : ( ~ (relation_inverse_image(all_67_0, v0) = % 27.60/4.55 | | | | | v1) | ~ (apply(all_67_0, v2) = v3) | ~ $i(v2) | ~ % 27.60/4.55 | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 27.60/4.55 | | | | | [v6: any] : (in(v3, v0) = v6 & in(v2, v1) = v4 & in(v2, % 27.60/4.55 | | | | | all_367_0) = v5 & ( ~ (v4 = 0) | (v6 = 0 & v5 = % 27.60/4.55 | | | | | 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.60/4.55 | | | | | ! [v3: $i] : ( ~ (relation_inverse_image(all_67_0, v0) = % 27.60/4.55 | | | | | v1) | ~ (apply(all_67_0, v2) = v3) | ~ $i(v2) | ~ % 27.60/4.55 | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 27.60/4.55 | | | | | [v6: any] : (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, % 27.60/4.55 | | | | | all_367_0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = % 27.60/4.55 | | | | | 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 27.60/4.55 | | | | | [v3: any] : ( ~ (relation_inverse_image(all_67_0, v0) = % 27.60/4.55 | | | | | v1) | ~ (in(v2, all_367_0) = v3) | ~ $i(v2) | ~ % 27.60/4.55 | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? % 27.60/4.55 | | | | | [v6: any] : (apply(all_67_0, v2) = v5 & in(v5, v0) = v6 % 27.60/4.55 | | | | | & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | (v6 = 0 & % 27.60/4.55 | | | | | v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 27.60/4.55 | | | | | $i] : ( ~ (relation_inverse_image(all_67_0, v0) = v1) | % 27.60/4.55 | | | | | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.60/4.55 | | | | | | ? [v3: $i] : (apply(all_67_0, v2) = v3 & in(v3, v0) % 27.60/4.55 | | | | | = 0 & in(v2, all_367_0) = 0 & $i(v3))) & ! [v0: $i] % 27.60/4.55 | | | | | : ! [v1: $i] : ! [v2: $i] : ( ~ % 27.60/4.55 | | | | | (relation_inverse_image(all_67_0, v0) = v1) | ~ % 27.60/4.55 | | | | | (in(v2, all_367_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 27.60/4.55 | | | | | $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 27.60/4.55 | | | | | (apply(all_67_0, v2) = v3 & in(v3, v0) = v4 & in(v2, % 27.60/4.55 | | | | | v1) = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))) & ? % 27.60/4.55 | | | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 27.60/4.55 | | | | | (relation_inverse_image(all_67_0, v1) = v2) | ~ $i(v1) % 27.60/4.55 | | | | | | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] % 27.60/4.55 | | | | | : ? [v6: $i] : ? [v7: any] : (apply(all_67_0, v3) = % 27.60/4.55 | | | | | v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, % 27.60/4.55 | | | | | all_367_0) = v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | % 27.60/4.55 | | | | | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 % 27.60/4.55 | | | | | = 0)))))) % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | ALPHA: (293) implies: % 27.60/4.55 | | | | | (294) function(all_67_0) = all_367_1 % 27.60/4.55 | | | | | (295) ~ (all_367_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 27.60/4.55 | | | | | : ! [v3: int] : (v3 = 0 | ~ % 27.60/4.55 | | | | | (relation_inverse_image(all_67_0, v0) = v1) | ~ (in(v2, % 27.60/4.55 | | | | | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.60/4.55 | | | | | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_67_0, % 27.60/4.55 | | | | | v2) = v5 & in(v5, v0) = v6 & in(v2, all_367_0) = v4 & % 27.60/4.55 | | | | | $i(v5) & ( ~ (v6 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : % 27.60/4.55 | | | | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 27.60/4.55 | | | | | (relation_inverse_image(all_67_0, v0) = v1) | ~ % 27.60/4.55 | | | | | (apply(all_67_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 27.60/4.55 | | | | | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.60/4.55 | | | | | (in(v3, v0) = v6 & in(v2, v1) = v4 & in(v2, all_367_0) = % 27.60/4.55 | | | | | v5 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] % 27.60/4.55 | | | | | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 27.60/4.55 | | | | | (relation_inverse_image(all_67_0, v0) = v1) | ~ % 27.60/4.55 | | | | | (apply(all_67_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 27.60/4.55 | | | | | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 27.60/4.55 | | | | | (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, all_367_0) = % 27.60/4.55 | | | | | v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0: % 27.60/4.55 | | | | | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 27.60/4.55 | | | | | (relation_inverse_image(all_67_0, v0) = v1) | ~ (in(v2, % 27.60/4.55 | | | | | all_367_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 27.60/4.55 | | | | | | ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 27.60/4.55 | | | | | (apply(all_67_0, v2) = v5 & in(v5, v0) = v6 & in(v2, v1) % 27.60/4.55 | | | | | = v4 & $i(v5) & ( ~ (v4 = 0) | (v6 = 0 & v3 = 0)))) & % 27.60/4.55 | | | | | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 27.60/4.55 | | | | | (relation_inverse_image(all_67_0, v0) = v1) | ~ (in(v2, % 27.60/4.55 | | | | | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.60/4.55 | | | | | [v3: $i] : (apply(all_67_0, v2) = v3 & in(v3, v0) = 0 & % 27.60/4.55 | | | | | in(v2, all_367_0) = 0 & $i(v3))) & ! [v0: $i] : ! % 27.60/4.55 | | | | | [v1: $i] : ! [v2: $i] : ( ~ % 27.60/4.55 | | | | | (relation_inverse_image(all_67_0, v0) = v1) | ~ (in(v2, % 27.60/4.55 | | | | | all_367_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 27.60/4.55 | | | | | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 27.60/4.55 | | | | | (apply(all_67_0, v2) = v3 & in(v3, v0) = v4 & in(v2, v1) % 27.60/4.55 | | | | | = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))) & ? [v0: $i] % 27.60/4.55 | | | | | : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 27.60/4.55 | | | | | (relation_inverse_image(all_67_0, v1) = v2) | ~ $i(v1) | % 27.60/4.55 | | | | | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 27.60/4.55 | | | | | ? [v6: $i] : ? [v7: any] : (apply(all_67_0, v3) = v6 & % 27.60/4.55 | | | | | in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_367_0) = % 27.60/4.55 | | | | | v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ % 27.60/4.55 | | | | | (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0))))) % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | REDUCE: (261), (294) imply: % 27.60/4.55 | | | | | (296) function(empty_set) = all_367_1 % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | REDUCE: (261), (285) imply: % 27.60/4.55 | | | | | (297) function(empty_set) = all_325_1 % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | REDUCE: (261), (283) imply: % 27.60/4.55 | | | | | (298) function(empty_set) = all_323_1 % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | REDUCE: (261), (262) imply: % 27.60/4.55 | | | | | (299) function(empty_set) = 0 % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | BETA: splitting (264) gives: % 27.60/4.55 | | | | | % 27.60/4.55 | | | | | Case 1: % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | (300) all_179_0 = 0 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | REDUCE: (183), (300) imply: % 27.60/4.55 | | | | | | (301) $false % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | CLOSE: (301) is inconsistent. % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | Case 2: % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | GROUND_INST: instantiating (28) with 0, all_325_1, empty_set, % 27.60/4.55 | | | | | | simplifying with (297), (299) gives: % 27.60/4.55 | | | | | | (302) all_325_1 = 0 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | GROUND_INST: instantiating (28) with all_325_1, all_367_1, % 27.60/4.55 | | | | | | empty_set, simplifying with (296), (297) gives: % 27.60/4.55 | | | | | | (303) all_367_1 = all_325_1 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | GROUND_INST: instantiating (28) with all_323_1, all_367_1, % 27.60/4.55 | | | | | | empty_set, simplifying with (296), (298) gives: % 27.60/4.55 | | | | | | (304) all_367_1 = all_323_1 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | GROUND_INST: instantiating (28) with 0, all_351_0, all_57_6, % 27.60/4.55 | | | | | | simplifying with (70), (289) gives: % 27.60/4.55 | | | | | | (305) all_351_0 = 0 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | GROUND_INST: instantiating (29) with 0, all_339_1, all_57_6, % 27.60/4.55 | | | | | | simplifying with (267), (287) gives: % 27.60/4.55 | | | | | | (306) all_339_1 = 0 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | GROUND_INST: instantiating (29) with all_93_2, all_351_2, all_57_6, % 27.60/4.55 | | | | | | simplifying with (133), (290) gives: % 27.60/4.55 | | | | | | (307) all_351_2 = all_93_2 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | GROUND_INST: instantiating (29) with all_339_1, all_351_2, all_57_6, % 27.60/4.55 | | | | | | simplifying with (287), (290) gives: % 27.60/4.55 | | | | | | (308) all_351_2 = all_339_1 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | GROUND_INST: instantiating (30) with all_137_0, all_313_0, all_57_6, % 27.60/4.55 | | | | | | simplifying with (150), (281) gives: % 27.60/4.55 | | | | | | (309) all_313_0 = all_137_0 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | GROUND_INST: instantiating (30) with all_295_0, all_313_0, all_57_6, % 27.60/4.55 | | | | | | simplifying with (276), (281) gives: % 27.60/4.55 | | | | | | (310) all_313_0 = all_295_0 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | GROUND_INST: instantiating (33) with all_57_9, all_311_1, all_57_6, % 27.60/4.55 | | | | | | all_57_8, all_57_9, simplifying with (248), (279) % 27.60/4.55 | | | | | | gives: % 27.60/4.55 | | | | | | (311) all_311_1 = all_57_9 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | GROUND_INST: instantiating (33) with all_295_0, all_311_1, all_57_6, % 27.60/4.55 | | | | | | all_57_8, all_57_9, simplifying with (277), (279) % 27.60/4.55 | | | | | | gives: % 27.60/4.55 | | | | | | (312) all_311_1 = all_295_0 % 27.60/4.55 | | | | | | % 27.60/4.55 | | | | | | COMBINE_EQS: (303), (304) imply: % 27.60/4.56 | | | | | | (313) all_325_1 = all_323_1 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | SIMP: (313) implies: % 27.60/4.56 | | | | | | (314) all_325_1 = all_323_1 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | COMBINE_EQS: (307), (308) imply: % 27.60/4.56 | | | | | | (315) all_339_1 = all_93_2 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | SIMP: (315) implies: % 27.60/4.56 | | | | | | (316) all_339_1 = all_93_2 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | COMBINE_EQS: (306), (316) imply: % 27.60/4.56 | | | | | | (317) all_93_2 = 0 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | SIMP: (317) implies: % 27.60/4.56 | | | | | | (318) all_93_2 = 0 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | COMBINE_EQS: (302), (314) imply: % 27.60/4.56 | | | | | | (319) all_323_1 = 0 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | COMBINE_EQS: (309), (310) imply: % 27.60/4.56 | | | | | | (320) all_295_0 = all_137_0 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | COMBINE_EQS: (311), (312) imply: % 27.60/4.56 | | | | | | (321) all_295_0 = all_57_9 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | SIMP: (321) implies: % 27.60/4.56 | | | | | | (322) all_295_0 = all_57_9 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | COMBINE_EQS: (320), (322) imply: % 27.60/4.56 | | | | | | (323) all_137_0 = all_57_9 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | COMBINE_EQS: (187), (318) imply: % 27.60/4.56 | | | | | | (324) all_137_1 = 0 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | COMBINE_EQS: (304), (319) imply: % 27.60/4.56 | | | | | | (325) all_367_1 = 0 % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | BETA: splitting (291) gives: % 27.60/4.56 | | | | | | % 27.60/4.56 | | | | | | Case 1: % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | | (326) relation(all_57_6) = all_365_2 & function(all_57_6) = % 27.60/4.56 | | | | | | | all_365_1 & ( ~ (all_365_1 = 0) | ~ (all_365_2 = 0)) % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | | ALPHA: (326) implies: % 27.60/4.56 | | | | | | | (327) function(all_57_6) = all_365_1 % 27.60/4.56 | | | | | | | (328) relation(all_57_6) = all_365_2 % 27.60/4.56 | | | | | | | (329) ~ (all_365_1 = 0) | ~ (all_365_2 = 0) % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | | GROUND_INST: instantiating (28) with 0, all_365_1, all_57_6, % 27.60/4.56 | | | | | | | simplifying with (70), (327) gives: % 27.60/4.56 | | | | | | | (330) all_365_1 = 0 % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | | GROUND_INST: instantiating (29) with 0, all_365_2, all_57_6, % 27.60/4.56 | | | | | | | simplifying with (267), (328) gives: % 27.60/4.56 | | | | | | | (331) all_365_2 = 0 % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | | BETA: splitting (329) gives: % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | | Case 1: % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | (332) ~ (all_365_1 = 0) % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | REDUCE: (330), (332) imply: % 27.60/4.56 | | | | | | | | (333) $false % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | CLOSE: (333) is inconsistent. % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | Case 2: % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | (334) ~ (all_365_2 = 0) % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | REDUCE: (331), (334) imply: % 27.60/4.56 | | | | | | | | (335) $false % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | CLOSE: (335) is inconsistent. % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | End of split % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | Case 2: % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | | (336) in(all_57_1, all_57_7) = all_365_1 & in(all_57_4, % 27.60/4.56 | | | | | | | all_137_0) = all_365_2 & in(all_57_4, all_57_5) = % 27.60/4.56 | | | | | | | all_365_0 & ( ~ (all_365_1 = 0) | ~ (all_365_2 = 0) | % 27.60/4.56 | | | | | | | all_365_0 = 0) % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | | ALPHA: (336) implies: % 27.60/4.56 | | | | | | | (337) in(all_57_4, all_57_5) = all_365_0 % 27.60/4.56 | | | | | | | (338) in(all_57_4, all_137_0) = all_365_2 % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | | REDUCE: (323), (338) imply: % 27.60/4.56 | | | | | | | (339) in(all_57_4, all_57_9) = all_365_2 % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | | BETA: splitting (292) gives: % 27.60/4.56 | | | | | | | % 27.60/4.56 | | | | | | | Case 1: % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | (340) relation(all_57_6) = all_366_2 & function(all_57_6) = % 27.60/4.56 | | | | | | | | all_366_1 & ( ~ (all_366_1 = 0) | ~ (all_366_2 = 0)) % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | ALPHA: (340) implies: % 27.60/4.56 | | | | | | | | (341) function(all_57_6) = all_366_1 % 27.60/4.56 | | | | | | | | (342) relation(all_57_6) = all_366_2 % 27.60/4.56 | | | | | | | | (343) ~ (all_366_1 = 0) | ~ (all_366_2 = 0) % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | GROUND_INST: instantiating (28) with 0, all_366_1, all_57_6, % 27.60/4.56 | | | | | | | | simplifying with (70), (341) gives: % 27.60/4.56 | | | | | | | | (344) all_366_1 = 0 % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | GROUND_INST: instantiating (29) with 0, all_366_2, all_57_6, % 27.60/4.56 | | | | | | | | simplifying with (267), (342) gives: % 27.60/4.56 | | | | | | | | (345) all_366_2 = 0 % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | BETA: splitting (343) gives: % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | Case 1: % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | (346) ~ (all_366_1 = 0) % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | REDUCE: (344), (346) imply: % 27.60/4.56 | | | | | | | | | (347) $false % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | CLOSE: (347) is inconsistent. % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | Case 2: % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | (348) ~ (all_366_2 = 0) % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | REDUCE: (345), (348) imply: % 27.60/4.56 | | | | | | | | | (349) $false % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | CLOSE: (349) is inconsistent. % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | End of split % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | Case 2: % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | (350) in(all_57_1, all_57_7) = all_366_0 & in(all_57_4, % 27.60/4.56 | | | | | | | | all_137_0) = all_366_1 & in(all_57_4, all_57_5) = % 27.60/4.56 | | | | | | | | all_366_2 & ( ~ (all_366_2 = 0) | (all_366_0 = 0 & % 27.60/4.56 | | | | | | | | all_366_1 = 0)) % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | ALPHA: (350) implies: % 27.60/4.56 | | | | | | | | (351) in(all_57_4, all_57_5) = all_366_2 % 27.60/4.56 | | | | | | | | (352) in(all_57_4, all_137_0) = all_366_1 % 27.60/4.56 | | | | | | | | (353) in(all_57_1, all_57_7) = all_366_0 % 27.60/4.56 | | | | | | | | (354) ~ (all_366_2 = 0) | (all_366_0 = 0 & all_366_1 = 0) % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | REDUCE: (323), (352) imply: % 27.60/4.56 | | | | | | | | (355) in(all_57_4, all_57_9) = all_366_1 % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | BETA: splitting (151) gives: % 27.60/4.56 | | | | | | | | % 27.60/4.56 | | | | | | | | Case 1: % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | (356) ~ (all_137_1 = 0) % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | REDUCE: (324), (356) imply: % 27.60/4.56 | | | | | | | | | (357) $false % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | CLOSE: (357) is inconsistent. % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | Case 2: % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | (358) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 27.60/4.56 | | | | | | | | | int] : (v3 = 0 | ~ % 27.60/4.56 | | | | | | | | | (relation_inverse_image(all_57_6, v0) = v1) | ~ % 27.60/4.56 | | | | | | | | | (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 27.60/4.56 | | | | | | | | | $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] % 27.60/4.56 | | | | | | | | | : (apply(all_57_6, v2) = v5 & in(v5, v0) = v6 & % 27.60/4.56 | | | | | | | | | in(v2, all_137_0) = v4 & $i(v5) & ( ~ (v6 = 0) | % 27.60/4.56 | | | | | | | | | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 27.60/4.56 | | | | | | | | | [v2: $i] : ! [v3: $i] : ( ~ % 27.60/4.56 | | | | | | | | | (relation_inverse_image(all_57_6, v0) = v1) | ~ % 27.60/4.56 | | | | | | | | | (apply(all_57_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 27.60/4.56 | | | | | | | | | | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 27.60/4.56 | | | | | | | | | any] : (in(v3, v0) = v6 & in(v2, v1) = v4 & % 27.60/4.56 | | | | | | | | | in(v2, all_137_0) = v5 & ( ~ (v4 = 0) | (v6 = 0 & % 27.60/4.56 | | | | | | | | | v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 27.60/4.56 | | | | | | | | | [v2: $i] : ! [v3: $i] : ( ~ % 27.60/4.56 | | | | | | | | | (relation_inverse_image(all_57_6, v0) = v1) | ~ % 27.60/4.56 | | | | | | | | | (apply(all_57_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 27.60/4.56 | | | | | | | | | | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 27.60/4.56 | | | | | | | | | any] : (in(v3, v0) = v5 & in(v2, v1) = v6 & % 27.60/4.56 | | | | | | | | | in(v2, all_137_0) = v4 & ( ~ (v5 = 0) | ~ (v4 = % 27.60/4.56 | | | | | | | | | 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 27.60/4.56 | | | | | | | | | ! [v2: $i] : ! [v3: any] : ( ~ % 27.60/4.56 | | | | | | | | | (relation_inverse_image(all_57_6, v0) = v1) | ~ % 27.60/4.56 | | | | | | | | | (in(v2, all_137_0) = v3) | ~ $i(v2) | ~ $i(v1) | % 27.60/4.56 | | | | | | | | | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: % 27.60/4.56 | | | | | | | | | any] : (apply(all_57_6, v2) = v5 & in(v5, v0) = % 27.60/4.56 | | | | | | | | | v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | % 27.60/4.56 | | | | | | | | | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: % 27.60/4.56 | | | | | | | | | $i] : ! [v2: $i] : ( ~ % 27.60/4.56 | | | | | | | | | (relation_inverse_image(all_57_6, v0) = v1) | ~ % 27.60/4.56 | | | | | | | | | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 27.60/4.56 | | | | | | | | | $i(v0) | ? [v3: $i] : (apply(all_57_6, v2) = v3 & % 27.60/4.56 | | | | | | | | | in(v3, v0) = 0 & in(v2, all_137_0) = 0 & $i(v3))) % 27.60/4.56 | | | | | | | | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 27.60/4.56 | | | | | | | | | (relation_inverse_image(all_57_6, v0) = v1) | ~ % 27.60/4.56 | | | | | | | | | (in(v2, all_137_0) = 0) | ~ $i(v2) | ~ $i(v1) | % 27.60/4.56 | | | | | | | | | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: % 27.60/4.56 | | | | | | | | | any] : (apply(all_57_6, v2) = v3 & in(v3, v0) = % 27.60/4.56 | | | | | | | | | v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = 0) | v5 % 27.60/4.56 | | | | | | | | | = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: % 27.60/4.56 | | | | | | | | | $i] : (v2 = v0 | ~ % 27.60/4.56 | | | | | | | | | (relation_inverse_image(all_57_6, v1) = v2) | ~ % 27.60/4.56 | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : % 27.60/4.56 | | | | | | | | | ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 27.60/4.56 | | | | | | | | | (apply(all_57_6, v3) = v6 & in(v6, v1) = v7 & % 27.60/4.56 | | | | | | | | | in(v3, v0) = v4 & in(v3, all_137_0) = v5 & $i(v6) % 27.60/4.56 | | | | | | | | | & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = % 27.60/4.56 | | | | | | | | | 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | ALPHA: (358) implies: % 27.60/4.56 | | | | | | | | | (359) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 27.60/4.56 | | | | | | | | | : ( ~ (relation_inverse_image(all_57_6, v0) = v1) | % 27.60/4.56 | | | | | | | | | ~ (apply(all_57_6, v2) = v3) | ~ $i(v2) | ~ % 27.60/4.56 | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 27.60/4.56 | | | | | | | | | ? [v6: any] : (in(v3, v0) = v5 & in(v2, v1) = v6 & % 27.60/4.56 | | | | | | | | | in(v2, all_137_0) = v4 & ( ~ (v5 = 0) | ~ (v4 = % 27.60/4.56 | | | | | | | | | 0) | v6 = 0))) % 27.60/4.56 | | | | | | | | | (360) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 27.60/4.56 | | | | | | | | | : ( ~ (relation_inverse_image(all_57_6, v0) = v1) | % 27.60/4.56 | | | | | | | | | ~ (apply(all_57_6, v2) = v3) | ~ $i(v2) | ~ % 27.60/4.56 | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 27.60/4.56 | | | | | | | | | ? [v6: any] : (in(v3, v0) = v6 & in(v2, v1) = v4 & % 27.60/4.56 | | | | | | | | | in(v2, all_137_0) = v5 & ( ~ (v4 = 0) | (v6 = 0 & % 27.60/4.56 | | | | | | | | | v5 = 0)))) % 27.60/4.56 | | | | | | | | | % 27.60/4.56 | | | | | | | | | GROUND_INST: instantiating (360) with all_57_7, all_57_5, % 27.60/4.56 | | | | | | | | | all_57_4, all_57_1, simplifying with (63), (65), % 27.60/4.56 | | | | | | | | | (66), (71), (72) gives: % 27.60/4.57 | | | | | | | | | (361) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.60/4.57 | | | | | | | | | (in(all_57_1, all_57_7) = v2 & in(all_57_4, % 27.60/4.57 | | | | | | | | | all_137_0) = v1 & in(all_57_4, all_57_5) = v0 & ( % 27.60/4.57 | | | | | | | | | ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 27.60/4.57 | | | | | | | | | % 27.60/4.57 | | | | | | | | | GROUND_INST: instantiating (359) with all_57_7, all_57_5, % 27.60/4.57 | | | | | | | | | all_57_4, all_57_1, simplifying with (63), (65), % 27.60/4.57 | | | | | | | | | (66), (71), (72) gives: % 27.60/4.57 | | | | | | | | | (362) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 27.60/4.57 | | | | | | | | | (in(all_57_1, all_57_7) = v1 & in(all_57_4, % 27.60/4.57 | | | | | | | | | all_137_0) = v0 & in(all_57_4, all_57_5) = v2 & ( % 27.60/4.57 | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 27.60/4.57 | | | | | | | | | % 27.60/4.57 | | | | | | | | | BETA: splitting (295) gives: % 27.60/4.57 | | | | | | | | | % 27.60/4.57 | | | | | | | | | Case 1: % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | (363) ~ (all_367_1 = 0) % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | REDUCE: (325), (363) imply: % 27.60/4.57 | | | | | | | | | | (364) $false % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | CLOSE: (364) is inconsistent. % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | Case 2: % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | DELTA: instantiating (362) with fresh symbols all_443_0, % 27.60/4.57 | | | | | | | | | | all_443_1, all_443_2 gives: % 27.60/4.57 | | | | | | | | | | (365) in(all_57_1, all_57_7) = all_443_1 & in(all_57_4, % 27.60/4.57 | | | | | | | | | | all_137_0) = all_443_2 & in(all_57_4, all_57_5) = % 27.60/4.57 | | | | | | | | | | all_443_0 & ( ~ (all_443_1 = 0) | ~ (all_443_2 = % 27.60/4.57 | | | | | | | | | | 0) | all_443_0 = 0) % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | ALPHA: (365) implies: % 27.60/4.57 | | | | | | | | | | (366) in(all_57_4, all_57_5) = all_443_0 % 27.60/4.57 | | | | | | | | | | (367) in(all_57_4, all_137_0) = all_443_2 % 27.60/4.57 | | | | | | | | | | (368) in(all_57_1, all_57_7) = all_443_1 % 27.60/4.57 | | | | | | | | | | (369) ~ (all_443_1 = 0) | ~ (all_443_2 = 0) | all_443_0 % 27.60/4.57 | | | | | | | | | | = 0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | DELTA: instantiating (361) with fresh symbols all_445_0, % 27.60/4.57 | | | | | | | | | | all_445_1, all_445_2 gives: % 27.60/4.57 | | | | | | | | | | (370) in(all_57_1, all_57_7) = all_445_0 & in(all_57_4, % 27.60/4.57 | | | | | | | | | | all_137_0) = all_445_1 & in(all_57_4, all_57_5) = % 27.60/4.57 | | | | | | | | | | all_445_2 & ( ~ (all_445_2 = 0) | (all_445_0 = 0 & % 27.60/4.57 | | | | | | | | | | all_445_1 = 0)) % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | ALPHA: (370) implies: % 27.60/4.57 | | | | | | | | | | (371) in(all_57_4, all_57_5) = all_445_2 % 27.60/4.57 | | | | | | | | | | (372) in(all_57_4, all_137_0) = all_445_1 % 27.60/4.57 | | | | | | | | | | (373) in(all_57_1, all_57_7) = all_445_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | REDUCE: (323), (372) imply: % 27.60/4.57 | | | | | | | | | | (374) in(all_57_4, all_57_9) = all_445_1 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | REDUCE: (323), (367) imply: % 27.60/4.57 | | | | | | | | | | (375) in(all_57_4, all_57_9) = all_443_2 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | GROUND_INST: instantiating (31) with all_366_1, all_443_2, % 27.60/4.57 | | | | | | | | | | all_57_9, all_57_4, simplifying with (355), (375) % 27.60/4.57 | | | | | | | | | | gives: % 27.60/4.57 | | | | | | | | | | (376) all_443_2 = all_366_1 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | GROUND_INST: instantiating (31) with all_365_2, all_443_2, % 27.60/4.57 | | | | | | | | | | all_57_9, all_57_4, simplifying with (339), (375) % 27.60/4.57 | | | | | | | | | | gives: % 27.60/4.57 | | | | | | | | | | (377) all_443_2 = all_365_2 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | GROUND_INST: instantiating (31) with all_57_2, all_445_1, % 27.60/4.57 | | | | | | | | | | all_57_9, all_57_4, simplifying with (67), (374) % 27.60/4.57 | | | | | | | | | | gives: % 27.60/4.57 | | | | | | | | | | (378) all_445_1 = all_57_2 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | GROUND_INST: instantiating (31) with all_366_1, all_445_1, % 27.60/4.57 | | | | | | | | | | all_57_9, all_57_4, simplifying with (355), (374) % 27.60/4.57 | | | | | | | | | | gives: % 27.60/4.57 | | | | | | | | | | (379) all_445_1 = all_366_1 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | GROUND_INST: instantiating (31) with all_57_3, all_443_0, % 27.60/4.57 | | | | | | | | | | all_57_5, all_57_4, simplifying with (68), (366) % 27.60/4.57 | | | | | | | | | | gives: % 27.60/4.57 | | | | | | | | | | (380) all_443_0 = all_57_3 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | GROUND_INST: instantiating (31) with all_366_2, all_443_0, % 27.60/4.57 | | | | | | | | | | all_57_5, all_57_4, simplifying with (351), (366) % 27.60/4.57 | | | | | | | | | | gives: % 27.60/4.57 | | | | | | | | | | (381) all_443_0 = all_366_2 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | GROUND_INST: instantiating (31) with all_443_0, all_445_2, % 27.60/4.57 | | | | | | | | | | all_57_5, all_57_4, simplifying with (366), (371) % 27.60/4.57 | | | | | | | | | | gives: % 27.60/4.57 | | | | | | | | | | (382) all_445_2 = all_443_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | GROUND_INST: instantiating (31) with all_365_0, all_445_2, % 27.60/4.57 | | | | | | | | | | all_57_5, all_57_4, simplifying with (337), (371) % 27.60/4.57 | | | | | | | | | | gives: % 27.60/4.57 | | | | | | | | | | (383) all_445_2 = all_365_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | GROUND_INST: instantiating (31) with all_57_0, all_445_0, % 27.60/4.57 | | | | | | | | | | all_57_7, all_57_1, simplifying with (69), (373) % 27.60/4.57 | | | | | | | | | | gives: % 27.60/4.57 | | | | | | | | | | (384) all_445_0 = all_57_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | GROUND_INST: instantiating (31) with all_443_1, all_445_0, % 27.60/4.57 | | | | | | | | | | all_57_7, all_57_1, simplifying with (368), (373) % 27.60/4.57 | | | | | | | | | | gives: % 27.60/4.57 | | | | | | | | | | (385) all_445_0 = all_443_1 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | GROUND_INST: instantiating (31) with all_366_0, all_445_0, % 27.60/4.57 | | | | | | | | | | all_57_7, all_57_1, simplifying with (353), (373) % 27.60/4.57 | | | | | | | | | | gives: % 27.60/4.57 | | | | | | | | | | (386) all_445_0 = all_366_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | COMBINE_EQS: (384), (385) imply: % 27.60/4.57 | | | | | | | | | | (387) all_443_1 = all_57_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | COMBINE_EQS: (385), (386) imply: % 27.60/4.57 | | | | | | | | | | (388) all_443_1 = all_366_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | COMBINE_EQS: (378), (379) imply: % 27.60/4.57 | | | | | | | | | | (389) all_366_1 = all_57_2 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | SIMP: (389) implies: % 27.60/4.57 | | | | | | | | | | (390) all_366_1 = all_57_2 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | COMBINE_EQS: (382), (383) imply: % 27.60/4.57 | | | | | | | | | | (391) all_443_0 = all_365_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | SIMP: (391) implies: % 27.60/4.57 | | | | | | | | | | (392) all_443_0 = all_365_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | COMBINE_EQS: (381), (392) imply: % 27.60/4.57 | | | | | | | | | | (393) all_366_2 = all_365_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | COMBINE_EQS: (380), (381) imply: % 27.60/4.57 | | | | | | | | | | (394) all_366_2 = all_57_3 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | COMBINE_EQS: (387), (388) imply: % 27.60/4.57 | | | | | | | | | | (395) all_366_0 = all_57_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | SIMP: (395) implies: % 27.60/4.57 | | | | | | | | | | (396) all_366_0 = all_57_0 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | COMBINE_EQS: (376), (377) imply: % 27.60/4.57 | | | | | | | | | | (397) all_366_1 = all_365_2 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | SIMP: (397) implies: % 27.60/4.57 | | | | | | | | | | (398) all_366_1 = all_365_2 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | COMBINE_EQS: (390), (398) imply: % 27.60/4.57 | | | | | | | | | | (399) all_365_2 = all_57_2 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | COMBINE_EQS: (393), (394) imply: % 27.60/4.57 | | | | | | | | | | (400) all_365_0 = all_57_3 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | COMBINE_EQS: (377), (399) imply: % 27.60/4.57 | | | | | | | | | | (401) all_443_2 = all_57_2 % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | BETA: splitting (75) gives: % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | Case 1: % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | (402) all_57_0 = 0 & all_57_2 = 0 & ~ (all_57_3 = 0) % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | ALPHA: (402) implies: % 27.60/4.57 | | | | | | | | | | | (403) all_57_2 = 0 % 27.60/4.57 | | | | | | | | | | | (404) all_57_0 = 0 % 27.60/4.57 | | | | | | | | | | | (405) ~ (all_57_3 = 0) % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | COMBINE_EQS: (401), (403) imply: % 27.60/4.57 | | | | | | | | | | | (406) all_443_2 = 0 % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | COMBINE_EQS: (387), (404) imply: % 27.60/4.57 | | | | | | | | | | | (407) all_443_1 = 0 % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | BETA: splitting (369) gives: % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | Case 1: % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | (408) ~ (all_443_1 = 0) % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | REDUCE: (407), (408) imply: % 27.60/4.57 | | | | | | | | | | | | (409) $false % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | CLOSE: (409) is inconsistent. % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | Case 2: % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | (410) ~ (all_443_2 = 0) | all_443_0 = 0 % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | BETA: splitting (410) gives: % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | Case 1: % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | (411) ~ (all_443_2 = 0) % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | REDUCE: (406), (411) imply: % 27.60/4.57 | | | | | | | | | | | | | (412) $false % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | CLOSE: (412) is inconsistent. % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | Case 2: % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | (413) all_443_0 = 0 % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | COMBINE_EQS: (380), (413) imply: % 27.60/4.57 | | | | | | | | | | | | | (414) all_57_3 = 0 % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | REDUCE: (405), (414) imply: % 27.60/4.57 | | | | | | | | | | | | | (415) $false % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | CLOSE: (415) is inconsistent. % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | End of split % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | End of split % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | Case 2: % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | (416) all_57_3 = 0 & ( ~ (all_57_0 = 0) | ~ (all_57_2 = % 27.60/4.57 | | | | | | | | | | | 0)) % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | ALPHA: (416) implies: % 27.60/4.57 | | | | | | | | | | | (417) all_57_3 = 0 % 27.60/4.57 | | | | | | | | | | | (418) ~ (all_57_0 = 0) | ~ (all_57_2 = 0) % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | COMBINE_EQS: (394), (417) imply: % 27.60/4.57 | | | | | | | | | | | (419) all_366_2 = 0 % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | BETA: splitting (354) gives: % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | Case 1: % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | (420) ~ (all_366_2 = 0) % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | REDUCE: (419), (420) imply: % 27.60/4.57 | | | | | | | | | | | | (421) $false % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | CLOSE: (421) is inconsistent. % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | Case 2: % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | (422) all_366_0 = 0 & all_366_1 = 0 % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | ALPHA: (422) implies: % 27.60/4.57 | | | | | | | | | | | | (423) all_366_1 = 0 % 27.60/4.57 | | | | | | | | | | | | (424) all_366_0 = 0 % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | COMBINE_EQS: (396), (424) imply: % 27.60/4.57 | | | | | | | | | | | | (425) all_57_0 = 0 % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | COMBINE_EQS: (390), (423) imply: % 27.60/4.57 | | | | | | | | | | | | (426) all_57_2 = 0 % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | BETA: splitting (418) gives: % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | Case 1: % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | (427) ~ (all_57_0 = 0) % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | REDUCE: (425), (427) imply: % 27.60/4.57 | | | | | | | | | | | | | (428) $false % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | CLOSE: (428) is inconsistent. % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | Case 2: % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | (429) ~ (all_57_2 = 0) % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | REDUCE: (426), (429) imply: % 27.60/4.57 | | | | | | | | | | | | | (430) $false % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | | CLOSE: (430) is inconsistent. % 27.60/4.57 | | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | | End of split % 27.60/4.57 | | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | | End of split % 27.60/4.57 | | | | | | | | | | | % 27.60/4.57 | | | | | | | | | | End of split % 27.60/4.57 | | | | | | | | | | % 27.60/4.57 | | | | | | | | | End of split % 27.60/4.57 | | | | | | | | | % 27.60/4.57 | | | | | | | | End of split % 27.60/4.57 | | | | | | | | % 27.60/4.57 | | | | | | | End of split % 27.60/4.57 | | | | | | | % 27.60/4.57 | | | | | | End of split % 27.60/4.57 | | | | | | % 27.60/4.57 | | | | | End of split % 27.60/4.57 | | | | | % 27.60/4.58 | | | | End of split % 27.60/4.58 | | | | % 27.60/4.58 | | | Case 2: % 27.60/4.58 | | | | % 27.60/4.58 | | | | (431) all_57_8 = empty_set & ~ (all_57_9 = empty_set) % 27.60/4.58 | | | | % 27.60/4.58 | | | | ALPHA: (431) implies: % 27.60/4.58 | | | | (432) all_57_8 = empty_set % 27.60/4.58 | | | | % 27.60/4.58 | | | | REDUCE: (60), (432) imply: % 27.60/4.58 | | | | (433) $false % 27.60/4.58 | | | | % 27.60/4.58 | | | | CLOSE: (433) is inconsistent. % 27.60/4.58 | | | | % 27.60/4.58 | | | End of split % 27.60/4.58 | | | % 27.60/4.58 | | End of split % 27.60/4.58 | | % 27.60/4.58 | End of split % 27.60/4.58 | % 27.60/4.58 End of proof % 27.60/4.58 % SZS output end Proof for theBenchmark % 27.60/4.58 % 27.60/4.58 3979ms %------------------------------------------------------------------------------