%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU068+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : 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 17:42:26 EDT 2023 % Result : Theorem 20.16s 4.76s % Output : Proof 95.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SEU068+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.30 % Computer : n009.cluster.edu % 0.09/0.30 % Model : x86_64 x86_64 % 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.30 % Memory : 8042.1875MB % 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.30 % CPULimit : 300 % 0.09/0.30 % WCLimit : 300 % 0.09/0.30 % DateTime : Wed Aug 23 12:12:51 EDT 2023 % 0.09/0.31 % CPUTime : % 0.15/0.54 ________ _____ % 0.15/0.54 ___ __ \_________(_)________________________________ % 0.15/0.54 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.54 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.54 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.54 % 0.15/0.54 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.54 (2023-06-19) % 0.15/0.54 % 0.15/0.54 (c) Philipp Rümmer, 2009-2023 % 0.15/0.54 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.54 Amanda Stjerna. % 0.15/0.54 Free software under BSD-3-Clause. % 0.15/0.54 % 0.15/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.54 % 0.15/0.54 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.15/0.55 Running up to 7 provers in parallel. % 0.15/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.15/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.15/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.15/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.15/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.15/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.15/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.33/1.17 Prover 4: Preprocessing ... % 2.33/1.17 Prover 1: Preprocessing ... % 2.75/1.28 Prover 2: Preprocessing ... % 2.75/1.28 Prover 6: Preprocessing ... % 2.75/1.28 Prover 5: Preprocessing ... % 2.75/1.28 Prover 3: Preprocessing ... % 2.75/1.28 Prover 0: Preprocessing ... % 6.28/2.08 Prover 1: Warning: ignoring some quantifiers % 6.68/2.14 Prover 1: Constructing countermodel ... % 7.14/2.19 Prover 5: Proving ... % 7.14/2.27 Prover 6: Proving ... % 7.14/2.28 Prover 3: Warning: ignoring some quantifiers % 7.14/2.30 Prover 3: Constructing countermodel ... % 8.72/2.54 Prover 2: Proving ... % 8.72/2.58 Prover 4: Warning: ignoring some quantifiers % 9.53/2.70 Prover 4: Constructing countermodel ... % 10.19/2.82 Prover 0: Proving ... % 15.87/3.94 Prover 3: gave up % 15.87/3.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.23/4.06 Prover 7: Preprocessing ... % 16.57/4.14 Prover 7: Warning: ignoring some quantifiers % 17.25/4.20 Prover 7: Constructing countermodel ... % 18.86/4.51 Prover 7: gave up % 18.86/4.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.86/4.58 Prover 8: Preprocessing ... % 20.16/4.76 Prover 0: proved (4170ms) % 20.16/4.76 % 20.16/4.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.16/4.76 % 20.16/4.77 Prover 2: stopped % 20.16/4.79 Prover 5: stopped % 20.16/4.80 Prover 6: stopped % 20.74/4.81 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.74/4.81 Prover 8: Warning: ignoring some quantifiers % 20.74/4.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.74/4.81 Prover 10: Preprocessing ... % 20.74/4.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.74/4.81 Prover 8: Constructing countermodel ... % 20.74/4.81 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 20.74/4.86 Prover 13: Preprocessing ... % 20.74/4.86 Prover 11: Preprocessing ... % 20.74/4.87 Prover 16: Preprocessing ... % 20.74/4.89 Prover 10: Warning: ignoring some quantifiers % 21.28/4.92 Prover 10: Constructing countermodel ... % 21.28/4.98 Prover 16: Warning: ignoring some quantifiers % 21.69/5.01 Prover 16: Constructing countermodel ... % 21.69/5.06 Prover 13: Warning: ignoring some quantifiers % 21.69/5.06 Prover 10: gave up % 21.69/5.08 Prover 13: Constructing countermodel ... % 21.69/5.08 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 22.39/5.13 Prover 19: Preprocessing ... % 23.37/5.33 Prover 11: Warning: ignoring some quantifiers % 23.37/5.34 Prover 19: Warning: ignoring some quantifiers % 23.37/5.34 Prover 19: Constructing countermodel ... % 23.37/5.36 Prover 11: Constructing countermodel ... % 24.45/5.70 Prover 1: gave up % 39.50/8.12 Prover 8: gave up % 48.25/9.81 Prover 19: stopped % 51.24/10.27 Prover 13: stopped % 56.75/11.45 Prover 16: stopped % 93.88/25.33 Prover 4: Found proof (size 283) % 93.88/25.33 Prover 4: proved (24761ms) % 93.88/25.35 Prover 11: stopped % 93.88/25.35 % 93.88/25.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 93.88/25.35 % 94.14/25.38 % SZS output start Proof for theBenchmark % 94.14/25.39 Assumptions after simplification: % 94.14/25.39 --------------------------------- % 94.14/25.39 % 94.14/25.39 (commutativity_k3_xboole_0) % 94.28/25.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2) % 94.28/25.44 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & ! % 94.28/25.44 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 94.28/25.44 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 94.28/25.44 % 94.28/25.44 (d12_funct_1) % 94.28/25.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 94.28/25.50 int] : ! [v6: $i] : (v5 = 0 | ~ (relation_dom(v0) = v1) | ~ % 94.28/25.50 (relation_image(v0, v2) = v3) | ~ (apply(v0, v6) = v4) | ~ (in(v4, v3) = % 94.28/25.50 v5) | ~ $i(v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v7: % 94.28/25.50 any] : ? [v8: any] : ((relation(v0) = v7 & function(v0) = v8 & ( ~ (v8 = % 94.28/25.50 0) | ~ (v7 = 0))) | (in(v6, v2) = v8 & in(v6, v1) = v7 & ( ~ (v8 = % 94.28/25.50 0) | ~ (v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 94.28/25.50 [v3: $i] : ! [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ % 94.28/25.50 (relation_dom(v0) = v1) | ~ (relation_image(v0, v2) = v3) | ~ (in(v6, v2) % 94.28/25.50 = 0) | ~ (in(v4, v3) = v5) | ~ $i(v6) | ~ $i(v4) | ~ $i(v3) | ~ % 94.28/25.50 $i(v2) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : ((apply(v0, v6) = v8 & % 94.28/25.50 in(v6, v1) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7 = 0))) | (relation(v0) % 94.28/25.50 = v7 & function(v0) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v0: $i] % 94.28/25.50 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : ! % 94.28/25.50 [v6: $i] : (v5 = 0 | ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v2) = % 94.28/25.50 v3) | ~ (in(v6, v1) = 0) | ~ (in(v4, v3) = v5) | ~ $i(v6) | ~ $i(v4) | % 94.28/25.50 ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : % 94.28/25.50 ((apply(v0, v6) = v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7 = % 94.28/25.50 0))) | (relation(v0) = v7 & function(v0) = v8 & ( ~ (v8 = 0) | ~ % 94.28/25.50 (v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 94.28/25.50 ! [v4: $i] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v2) = v3) | % 94.28/25.50 ~ (in(v4, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? % 94.28/25.50 [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : ? % 94.28/25.50 [v10: $i] : ($i(v7) & ((v10 = v4 & v9 = 0 & v8 = 0 & apply(v0, v7) = v4 & % 94.28/25.50 in(v7, v2) = 0 & in(v7, v1) = 0) | (relation(v0) = v5 & function(v0) = % 94.28/25.50 v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))))) & ? [v0: $i] : ! [v1: $i] : ! % 94.28/25.50 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (relation_dom(v1) = v2) | % 94.28/25.50 ~ (relation_image(v1, v3) = v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? % 94.28/25.50 [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? % 94.28/25.50 [v10: int] : ? [v11: int] : ? [v12: $i] : ($i(v9) & $i(v7) & % 94.28/25.50 ((relation(v1) = v5 & function(v1) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0))) | % 94.28/25.50 (in(v7, v0) = v8 & ( ~ (v8 = 0) | ( ! [v13: $i] : ( ~ (apply(v1, v13) = % 94.28/25.50 v7) | ~ $i(v13) | ? [v14: any] : ? [v15: any] : (in(v13, % 94.28/25.50 v3) = v15 & in(v13, v2) = v14 & ( ~ (v15 = 0) | ~ (v14 = % 94.28/25.50 0)))) & ! [v13: $i] : ( ~ (in(v13, v3) = 0) | ~ $i(v13) % 94.28/25.50 | ? [v14: any] : ? [v15: $i] : (apply(v1, v13) = v15 & in(v13, % 94.28/25.50 v2) = v14 & $i(v15) & ( ~ (v15 = v7) | ~ (v14 = 0)))) & ! % 94.28/25.50 [v13: $i] : ( ~ (in(v13, v2) = 0) | ~ $i(v13) | ? [v14: any] : % 94.28/25.50 ? [v15: $i] : (apply(v1, v13) = v15 & in(v13, v3) = v14 & % 94.28/25.50 $i(v15) & ( ~ (v15 = v7) | ~ (v14 = 0)))))) & (v8 = 0 | (v12 % 94.28/25.50 = v7 & v11 = 0 & v10 = 0 & apply(v1, v9) = v7 & in(v9, v3) = 0 & % 94.28/25.50 in(v9, v2) = 0)))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ % 94.28/25.50 $i(v0) | ? [v1: any] : ? [v2: $i] : (relation_dom(v0) = v2 & function(v0) % 94.28/25.50 = v1 & $i(v2) & ( ~ (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 94.28/25.50 ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ (relation_image(v0, v3) = v4) % 94.28/25.50 | ~ (apply(v0, v7) = v5) | ~ (in(v5, v4) = v6) | ~ $i(v7) | ~ % 94.28/25.50 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: any] : ? [v9: any] : % 94.28/25.50 (in(v7, v3) = v9 & in(v7, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & % 94.28/25.50 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : ! [v7: $i] : % 94.28/25.50 (v6 = 0 | ~ (relation_image(v0, v3) = v4) | ~ (in(v7, v3) = 0) | ~ % 94.28/25.50 (in(v5, v4) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 94.28/25.50 ? [v8: any] : ? [v9: $i] : (apply(v0, v7) = v9 & in(v7, v2) = v8 & % 94.28/25.50 $i(v9) & ( ~ (v9 = v5) | ~ (v8 = 0)))) & ! [v3: $i] : ! [v4: % 94.28/25.50 $i] : ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ % 94.28/25.50 (relation_image(v0, v3) = v4) | ~ (in(v7, v2) = 0) | ~ (in(v5, v4) % 94.28/25.50 = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: % 94.28/25.50 any] : ? [v9: $i] : (apply(v0, v7) = v9 & in(v7, v3) = v8 & % 94.28/25.50 $i(v9) & ( ~ (v9 = v5) | ~ (v8 = 0)))) & ! [v3: $i] : ! [v4: % 94.28/25.50 $i] : ! [v5: $i] : ( ~ (relation_image(v0, v3) = v4) | ~ (in(v5, % 94.28/25.50 v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : % 94.28/25.50 (apply(v0, v6) = v5 & in(v6, v3) = 0 & in(v6, v2) = 0 & $i(v6))) & % 94.28/25.50 ? [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ % 94.28/25.50 (relation_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] % 94.28/25.50 : ? [v7: any] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ? % 94.28/25.50 [v11: $i] : (in(v6, v3) = v7 & $i(v8) & $i(v6) & ( ~ (v7 = 0) | ( ! % 94.28/25.50 [v12: $i] : ( ~ (apply(v0, v12) = v6) | ~ $i(v12) | ? [v13: % 94.28/25.50 any] : ? [v14: any] : (in(v12, v4) = v14 & in(v12, v2) = % 94.28/25.50 v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v12: $i] : ( ~ % 94.28/25.50 (in(v12, v4) = 0) | ~ $i(v12) | ? [v13: any] : ? [v14: % 94.28/25.50 $i] : (apply(v0, v12) = v14 & in(v12, v2) = v13 & $i(v14) % 94.28/25.50 & ( ~ (v14 = v6) | ~ (v13 = 0)))) & ! [v12: $i] : ( ~ % 94.28/25.50 (in(v12, v2) = 0) | ~ $i(v12) | ? [v13: any] : ? [v14: % 94.28/25.50 $i] : (apply(v0, v12) = v14 & in(v12, v4) = v13 & $i(v14) % 94.28/25.50 & ( ~ (v14 = v6) | ~ (v13 = 0)))))) & (v7 = 0 | (v11 = v6 % 94.28/25.50 & v10 = 0 & v9 = 0 & apply(v0, v8) = v6 & in(v8, v4) = 0 & % 94.28/25.50 in(v8, v2) = 0)))))))) & ! [v0: $i] : ( ~ (function(v0) = 0) % 94.28/25.50 | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : (relation_dom(v0) = v2 & % 94.28/25.50 relation(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : % 94.28/25.50 ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ % 94.28/25.50 (relation_image(v0, v3) = v4) | ~ (apply(v0, v7) = v5) | ~ (in(v5, % 94.28/25.50 v4) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? % 94.28/25.50 [v8: any] : ? [v9: any] : (in(v7, v3) = v9 & in(v7, v2) = v8 & ( ~ % 94.28/25.50 (v9 = 0) | ~ (v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 94.28/25.50 $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ (relation_image(v0, % 94.28/25.50 v3) = v4) | ~ (in(v7, v3) = 0) | ~ (in(v5, v4) = v6) | ~ % 94.28/25.50 $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: any] : ? [v9: % 94.28/25.50 $i] : (apply(v0, v7) = v9 & in(v7, v2) = v8 & $i(v9) & ( ~ (v9 = % 94.28/25.50 v5) | ~ (v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 94.28/25.50 : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ (relation_image(v0, v3) = % 94.28/25.50 v4) | ~ (in(v7, v2) = 0) | ~ (in(v5, v4) = v6) | ~ $i(v7) | ~ % 94.28/25.50 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: any] : ? [v9: $i] : % 94.28/25.50 (apply(v0, v7) = v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ % 94.28/25.50 (v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 94.28/25.50 (relation_image(v0, v3) = v4) | ~ (in(v5, v4) = 0) | ~ $i(v5) | ~ % 94.28/25.50 $i(v4) | ~ $i(v3) | ? [v6: $i] : (apply(v0, v6) = v5 & in(v6, v3) % 94.28/25.50 = 0 & in(v6, v2) = 0 & $i(v6))) & ? [v3: $i] : ! [v4: $i] : ! % 94.28/25.50 [v5: $i] : (v5 = v3 | ~ (relation_image(v0, v4) = v5) | ~ $i(v4) | % 94.28/25.50 ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: int] : % 94.28/25.50 ? [v10: int] : ? [v11: $i] : (in(v6, v3) = v7 & $i(v8) & $i(v6) & % 94.28/25.50 ( ~ (v7 = 0) | ( ! [v12: $i] : ( ~ (apply(v0, v12) = v6) | ~ % 94.28/25.50 $i(v12) | ? [v13: any] : ? [v14: any] : (in(v12, v4) = v14 % 94.28/25.50 & in(v12, v2) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! % 94.28/25.50 [v12: $i] : ( ~ (in(v12, v4) = 0) | ~ $i(v12) | ? [v13: any] % 94.28/25.50 : ? [v14: $i] : (apply(v0, v12) = v14 & in(v12, v2) = v13 & % 94.28/25.50 $i(v14) & ( ~ (v14 = v6) | ~ (v13 = 0)))) & ! [v12: $i] % 94.28/25.50 : ( ~ (in(v12, v2) = 0) | ~ $i(v12) | ? [v13: any] : ? % 94.28/25.50 [v14: $i] : (apply(v0, v12) = v14 & in(v12, v4) = v13 & % 94.28/25.50 $i(v14) & ( ~ (v14 = v6) | ~ (v13 = 0)))))) & (v7 = 0 | % 94.28/25.50 (v11 = v6 & v10 = 0 & v9 = 0 & apply(v0, v8) = v6 & in(v8, v4) = % 94.28/25.50 0 & in(v8, v2) = 0)))))))) % 94.28/25.50 % 94.28/25.50 (d13_funct_1) % 94.28/25.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 94.28/25.53 int] : (v5 = 0 | ~ (relation_inverse_image(v0, v2) = v3) | ~ % 94.28/25.53 (relation_dom(v0) = v1) | ~ (in(v4, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 94.28/25.53 $i(v2) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 94.28/25.53 ((apply(v0, v4) = v7 & in(v7, v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 % 94.28/25.53 = 0) | ~ (v6 = 0))) | (relation(v0) = v6 & function(v0) = v7 & ( ~ % 94.28/25.53 (v7 = 0) | ~ (v6 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 94.28/25.53 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (relation_inverse_image(v0, v2) % 94.28/25.53 = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ $i(v4) | % 94.28/25.53 ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: % 94.28/25.53 any] : ((relation(v0) = v6 & function(v0) = v7 & ( ~ (v7 = 0) | ~ (v6 = % 94.28/25.53 0))) | (in(v5, v2) = v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ % 94.28/25.53 (v6 = 0) | (v8 = 0 & v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 94.28/25.53 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 94.28/25.53 (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ % 94.28/25.53 (apply(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? % 94.28/25.53 [v6: any] : ? [v7: any] : ? [v8: any] : ((relation(v0) = v6 & function(v0) % 94.28/25.53 = v7 & ( ~ (v7 = 0) | ~ (v6 = 0))) | (in(v5, v2) = v7 & in(v4, v3) = v8 % 94.28/25.53 & in(v4, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0)))) & ! [v0: % 94.28/25.53 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : % 94.28/25.53 ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ % 94.28/25.53 (in(v4, v1) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v6: % 94.28/25.53 any] : ? [v7: any] : ? [v8: any] : ((apply(v0, v4) = v7 & in(v7, v2) = % 94.28/25.53 v8 & in(v4, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | (v8 = 0 & v5 = 0))) | % 94.28/25.53 (relation(v0) = v6 & function(v0) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & % 94.28/25.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 94.28/25.53 (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ % 94.28/25.53 (in(v4, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v5: % 94.28/25.53 int] : ? [v6: any] : ? [v7: int] : ((v7 = 0 & v5 = 0 & apply(v0, v4) = % 94.28/25.53 v6 & in(v6, v2) = 0 & in(v4, v1) = 0 & $i(v6)) | (relation(v0) = v5 & % 94.28/25.53 function(v0) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ! [v0: $i] : ! % 94.28/25.53 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 94.28/25.53 (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ % 94.28/25.53 (in(v4, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v5: % 94.28/25.53 any] : ? [v6: any] : ? [v7: any] : ((apply(v0, v4) = v5 & in(v5, v2) = % 94.28/25.53 v6 & in(v4, v3) = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0)) | (relation(v0) % 94.28/25.53 = v5 & function(v0) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ? [v0: $i] % 94.28/25.53 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ % 94.28/25.53 (relation_inverse_image(v1, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ % 94.28/25.53 $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : % 94.28/25.53 ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: any] : ($i(v7) & % 94.28/25.53 ((apply(v1, v7) = v10 & in(v10, v3) = v11 & in(v7, v2) = v9 & in(v7, v0) = % 94.28/25.53 v8 & $i(v10) & ( ~ (v11 = 0) | ~ (v9 = 0) | ~ (v8 = 0)) & (v8 = 0 | % 94.28/25.53 (v11 = 0 & v9 = 0))) | (relation(v1) = v5 & function(v1) = v6 & ( ~ % 94.28/25.53 (v6 = 0) | ~ (v5 = 0)))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | % 94.28/25.53 ~ $i(v0) | ? [v1: any] : ? [v2: $i] : (relation_dom(v0) = v2 & % 94.28/25.53 function(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : % 94.28/25.53 ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (relation_inverse_image(v0, % 94.28/25.53 v3) = v4) | ~ (in(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 94.28/25.53 $i(v3) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : (apply(v0, v5) % 94.28/25.53 = v8 & in(v8, v3) = v9 & in(v5, v2) = v7 & $i(v8) & ( ~ (v9 = 0) | % 94.28/25.53 ~ (v7 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 94.28/25.53 [v6: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, % 94.28/25.53 v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : % 94.28/25.53 ? [v8: any] : ? [v9: any] : (in(v6, v3) = v9 & in(v5, v4) = v7 & % 94.28/25.53 in(v5, v2) = v8 & ( ~ (v7 = 0) | (v9 = 0 & v8 = 0)))) & ! [v3: % 94.28/25.53 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 94.28/25.53 (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) = v6) | ~ % 94.28/25.53 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: any] : ? % 94.28/25.53 [v9: any] : (in(v6, v3) = v8 & in(v5, v4) = v9 & in(v5, v2) = v7 & ( % 94.28/25.53 ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0))) & ! [v3: $i] : ! [v4: $i] % 94.28/25.53 : ! [v5: $i] : ! [v6: any] : ( ~ (relation_inverse_image(v0, v3) = % 94.28/25.53 v4) | ~ (in(v5, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 94.28/25.53 ? [v7: any] : ? [v8: $i] : ? [v9: any] : (apply(v0, v5) = v8 & % 94.28/25.53 in(v8, v3) = v9 & in(v5, v4) = v7 & $i(v8) & ( ~ (v7 = 0) | (v9 = % 94.28/25.53 0 & v6 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 94.28/25.53 (relation_inverse_image(v0, v3) = v4) | ~ (in(v5, v4) = 0) | ~ % 94.28/25.53 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : (apply(v0, v5) = v6 & % 94.28/25.53 in(v6, v3) = 0 & in(v5, v2) = 0 & $i(v6))) & ! [v3: $i] : ! [v4: % 94.28/25.53 $i] : ! [v5: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ % 94.28/25.53 (in(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : % 94.28/25.53 ? [v7: any] : ? [v8: any] : (apply(v0, v5) = v6 & in(v6, v3) = v7 % 94.28/25.53 & in(v5, v4) = v8 & $i(v6) & ( ~ (v7 = 0) | v8 = 0))) & ? [v3: % 94.28/25.53 $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ % 94.28/25.53 (relation_inverse_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? % 94.28/25.53 [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] % 94.28/25.53 : (apply(v0, v6) = v9 & in(v9, v4) = v10 & in(v6, v3) = v7 & in(v6, % 94.28/25.53 v2) = v8 & $i(v9) & $i(v6) & ( ~ (v10 = 0) | ~ (v8 = 0) | ~ % 94.28/25.53 (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = 0)))))))) & ! [v0: $i] : % 94.28/25.53 ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : % 94.28/25.53 (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ! % 94.28/25.53 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ % 94.28/25.53 (relation_inverse_image(v0, v3) = v4) | ~ (in(v5, v4) = v6) | ~ % 94.28/25.53 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: $i] : ? % 94.28/25.53 [v9: any] : (apply(v0, v5) = v8 & in(v8, v3) = v9 & in(v5, v2) = v7 % 94.28/25.53 & $i(v8) & ( ~ (v9 = 0) | ~ (v7 = 0)))) & ! [v3: $i] : ! [v4: % 94.28/25.53 $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (relation_inverse_image(v0, % 94.28/25.53 v3) = v4) | ~ (apply(v0, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 94.28/25.53 $i(v3) | ? [v7: any] : ? [v8: any] : ? [v9: any] : (in(v6, v3) = % 94.28/25.53 v9 & in(v5, v4) = v7 & in(v5, v2) = v8 & ( ~ (v7 = 0) | (v9 = 0 & % 94.28/25.53 v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 94.28/25.53 $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) % 94.28/25.53 = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: % 94.28/25.53 any] : ? [v9: any] : (in(v6, v3) = v8 & in(v5, v4) = v9 & in(v5, % 94.28/25.53 v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0))) & ! [v3: $i] % 94.28/25.53 : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 94.28/25.53 (relation_inverse_image(v0, v3) = v4) | ~ (in(v5, v2) = v6) | ~ % 94.28/25.53 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: $i] : ? % 94.28/25.53 [v9: any] : (apply(v0, v5) = v8 & in(v8, v3) = v9 & in(v5, v4) = v7 % 94.28/25.53 & $i(v8) & ( ~ (v7 = 0) | (v9 = 0 & v6 = 0)))) & ! [v3: $i] : ! % 94.28/25.53 [v4: $i] : ! [v5: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | % 94.28/25.53 ~ (in(v5, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] % 94.28/25.53 : (apply(v0, v5) = v6 & in(v6, v3) = 0 & in(v5, v2) = 0 & $i(v6))) & % 94.28/25.53 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 94.28/25.53 (relation_inverse_image(v0, v3) = v4) | ~ (in(v5, v2) = 0) | ~ % 94.28/25.53 $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? % 94.28/25.53 [v8: any] : (apply(v0, v5) = v6 & in(v6, v3) = v7 & in(v5, v4) = v8 % 94.28/25.53 & $i(v6) & ( ~ (v7 = 0) | v8 = 0))) & ? [v3: $i] : ! [v4: $i] : % 94.28/25.53 ! [v5: $i] : (v5 = v3 | ~ (relation_inverse_image(v0, v4) = v5) | ~ % 94.28/25.53 $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? % 94.28/25.53 [v9: $i] : ? [v10: any] : (apply(v0, v6) = v9 & in(v9, v4) = v10 & % 94.28/25.53 in(v6, v3) = v7 & in(v6, v2) = v8 & $i(v9) & $i(v6) & ( ~ (v10 = % 94.28/25.53 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = % 94.28/25.53 0)))))))) % 94.28/25.53 % 94.28/25.53 (d3_tarski) % 94.28/25.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 94.28/25.53 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 94.28/25.53 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 94.28/25.53 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 94.28/25.53 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 94.28/25.53 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 94.28/25.53 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 94.28/25.53 $i(v0) | in(v2, v1) = 0) % 94.28/25.53 % 94.28/25.53 (d3_xboole_0) % 94.28/25.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 94.28/25.54 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | % 94.28/25.54 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) % 94.28/25.54 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 94.28/25.54 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 94.28/25.54 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 94.28/25.54 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 94.28/25.54 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 94.28/25.54 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 94.28/25.54 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ % 94.28/25.54 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 94.28/25.54 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 94.28/25.54 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 94.28/25.54 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 94.28/25.54 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 94.28/25.54 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | % 94.28/25.54 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 94.28/25.54 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] % 94.28/25.54 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = % 94.28/25.54 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 94.28/25.54 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 % 94.28/25.54 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 94.28/25.54 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 94.28/25.54 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 94.28/25.54 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) % 94.28/25.54 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) % 94.28/25.54 % 94.28/25.54 (fc1_subset_1) % 94.28/25.54 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] % 94.28/25.54 : ( ~ (v2 = 0) & empty(v1) = v2)) % 94.28/25.54 % 94.28/25.54 (fc5_relat_1) % 94.28/25.54 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 94.28/25.54 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 & % 94.28/25.54 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = % 94.28/25.54 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ % 94.28/25.54 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & % 94.28/25.54 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & % 94.28/25.54 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 94.28/25.54 : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & % 94.28/25.54 $i(v2) & ( ~ (v3 = 0) | v1 = 0))) % 94.28/25.54 % 94.28/25.55 (rc1_subset_1) % 94.28/25.55 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 94.28/25.55 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v0) = v2 & % 94.28/25.55 element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) & $i(v2))) & ! [v0: $i] : % 94.28/25.55 ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] % 94.28/25.55 : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & % 94.28/25.55 element(v3, v1) = 0 & empty(v3) = v5) | (v2 = 0 & empty(v0) = 0)))) % 94.28/25.55 % 94.28/25.55 (rc2_xboole_0) % 94.28/25.55 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 94.28/25.55 % 94.28/25.55 (rc3_funct_1) % 94.28/25.55 ? [v0: $i] : (one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0 & % 94.28/25.55 $i(v0)) % 94.28/25.55 % 94.28/25.55 (t149_funct_1) % 94.28/25.55 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 94.28/25.55 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & subset(v5, % 94.28/25.55 v7) = v8 & relation_inverse_image(v2, v1) = v3 & relation_image(v2, v4) = % 94.28/25.55 v5 & relation_image(v2, v0) = v6 & set_intersection2(v6, v1) = v7 & % 94.28/25.55 set_intersection2(v0, v3) = v4 & relation(v2) = 0 & function(v2) = 0 & % 94.28/25.55 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 94.28/25.55 % 94.28/25.55 (t3_subset) % 94.28/25.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 94.28/25.55 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 94.28/25.55 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] % 94.28/25.55 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 94.28/25.55 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, % 94.28/25.55 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 94.28/25.55 (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | % 94.28/25.55 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | % 94.28/25.55 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = % 94.28/25.55 0 & $i(v2))) % 94.28/25.55 % 94.28/25.55 (function-axioms) % 94.28/25.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 94.28/25.56 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 94.28/25.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 94.28/25.56 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 94.28/25.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 94.28/25.56 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = % 94.28/25.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 94.28/25.56 ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! % 94.28/25.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, % 94.28/25.56 v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 94.28/25.56 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ % 94.28/25.56 (set_intersection2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 94.28/25.56 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = % 94.28/25.56 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 94.28/25.56 (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: % 94.28/25.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 94.28/25.56 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = % 94.28/25.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 94.28/25.56 (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: % 94.28/25.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 94.28/25.56 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: % 94.28/25.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 94.28/25.56 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 94.28/25.56 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) % 94.28/25.56 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 94.28/25.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 94.28/25.56 (empty(v2) = v0)) % 94.28/25.56 % 94.28/25.56 Further assumptions not needed in the proof: % 94.28/25.56 -------------------------------------------- % 94.28/25.56 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, % 94.28/25.56 existence_m1_subset_1, fc12_relat_1, fc1_relat_1, fc1_xboole_0, fc4_relat_1, % 94.28/25.56 fc7_relat_1, idempotence_k3_xboole_0, rc1_funct_1, rc1_relat_1, rc1_xboole_0, % 94.28/25.56 rc2_funct_1, rc2_relat_1, rc2_subset_1, rc3_relat_1, reflexivity_r1_tarski, % 94.28/25.56 t1_subset, t2_boole, t2_subset, t4_subset, t5_subset, t6_boole, t7_boole, % 94.28/25.56 t8_boole % 94.28/25.56 % 94.28/25.56 Those formulas are unsatisfiable: % 94.28/25.56 --------------------------------- % 94.28/25.56 % 94.28/25.56 Begin of proof % 94.28/25.56 | % 94.28/25.56 | ALPHA: (commutativity_k3_xboole_0) implies: % 94.28/25.56 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, % 94.28/25.56 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = % 94.28/25.56 | v2 & $i(v2))) % 94.28/25.56 | % 94.28/25.56 | ALPHA: (d12_funct_1) implies: % 94.68/25.57 | (2) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 94.68/25.57 | [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ % 94.68/25.57 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 94.68/25.57 | int] : ! [v7: $i] : (v6 = 0 | ~ (relation_image(v0, v3) = % 94.68/25.57 | v4) | ~ (apply(v0, v7) = v5) | ~ (in(v5, v4) = v6) | ~ % 94.68/25.57 | $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: any] : % 94.68/25.57 | ? [v9: any] : (in(v7, v3) = v9 & in(v7, v2) = v8 & ( ~ (v9 = % 94.68/25.57 | 0) | ~ (v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! % 94.68/25.57 | [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ % 94.68/25.57 | (relation_image(v0, v3) = v4) | ~ (in(v7, v3) = 0) | ~ % 94.68/25.57 | (in(v5, v4) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ % 94.68/25.57 | $i(v3) | ? [v8: any] : ? [v9: $i] : (apply(v0, v7) = v9 & % 94.68/25.57 | in(v7, v2) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8 = 0)))) & % 94.68/25.57 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : ! % 94.68/25.57 | [v7: $i] : (v6 = 0 | ~ (relation_image(v0, v3) = v4) | ~ % 94.68/25.57 | (in(v7, v2) = 0) | ~ (in(v5, v4) = v6) | ~ $i(v7) | ~ % 94.68/25.57 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: any] : ? [v9: $i] : % 94.68/25.57 | (apply(v0, v7) = v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = % 94.68/25.57 | v5) | ~ (v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! % 94.68/25.57 | [v5: $i] : ( ~ (relation_image(v0, v3) = v4) | ~ (in(v5, v4) = % 94.68/25.57 | 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : % 94.68/25.57 | (apply(v0, v6) = v5 & in(v6, v3) = 0 & in(v6, v2) = 0 & % 94.68/25.57 | $i(v6))) & ? [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = % 94.68/25.57 | v3 | ~ (relation_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) % 94.68/25.57 | | ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: int] : % 94.68/25.57 | ? [v10: int] : ? [v11: $i] : (in(v6, v3) = v7 & $i(v8) & % 94.68/25.57 | $i(v6) & ( ~ (v7 = 0) | ( ! [v12: $i] : ( ~ (apply(v0, v12) % 94.68/25.57 | = v6) | ~ $i(v12) | ? [v13: any] : ? [v14: any] % 94.68/25.57 | : (in(v12, v4) = v14 & in(v12, v2) = v13 & ( ~ (v14 = % 94.68/25.57 | 0) | ~ (v13 = 0)))) & ! [v12: $i] : ( ~ % 94.68/25.57 | (in(v12, v4) = 0) | ~ $i(v12) | ? [v13: any] : ? % 94.68/25.57 | [v14: $i] : (apply(v0, v12) = v14 & in(v12, v2) = v13 % 94.68/25.57 | & $i(v14) & ( ~ (v14 = v6) | ~ (v13 = 0)))) & ! % 94.68/25.57 | [v12: $i] : ( ~ (in(v12, v2) = 0) | ~ $i(v12) | ? % 94.68/25.57 | [v13: any] : ? [v14: $i] : (apply(v0, v12) = v14 & % 94.68/25.57 | in(v12, v4) = v13 & $i(v14) & ( ~ (v14 = v6) | ~ % 94.68/25.57 | (v13 = 0)))))) & (v7 = 0 | (v11 = v6 & v10 = 0 & % 94.68/25.57 | v9 = 0 & apply(v0, v8) = v6 & in(v8, v4) = 0 & in(v8, % 94.68/25.57 | v2) = 0)))))))) % 94.68/25.58 | (3) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 94.68/25.58 | [v2: $i] : (relation_dom(v0) = v2 & function(v0) = v1 & $i(v2) & ( ~ % 94.68/25.58 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 94.68/25.58 | int] : ! [v7: $i] : (v6 = 0 | ~ (relation_image(v0, v3) = % 94.68/25.58 | v4) | ~ (apply(v0, v7) = v5) | ~ (in(v5, v4) = v6) | ~ % 94.68/25.58 | $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: any] : % 94.68/25.58 | ? [v9: any] : (in(v7, v3) = v9 & in(v7, v2) = v8 & ( ~ (v9 = % 94.68/25.58 | 0) | ~ (v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! % 94.68/25.58 | [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ % 94.68/25.58 | (relation_image(v0, v3) = v4) | ~ (in(v7, v3) = 0) | ~ % 94.68/25.58 | (in(v5, v4) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ % 94.68/25.58 | $i(v3) | ? [v8: any] : ? [v9: $i] : (apply(v0, v7) = v9 & % 94.68/25.58 | in(v7, v2) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8 = 0)))) & % 94.68/25.58 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : ! % 94.68/25.58 | [v7: $i] : (v6 = 0 | ~ (relation_image(v0, v3) = v4) | ~ % 94.68/25.58 | (in(v7, v2) = 0) | ~ (in(v5, v4) = v6) | ~ $i(v7) | ~ % 94.68/25.58 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v8: any] : ? [v9: $i] : % 94.68/25.58 | (apply(v0, v7) = v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = % 94.68/25.58 | v5) | ~ (v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! % 94.68/25.58 | [v5: $i] : ( ~ (relation_image(v0, v3) = v4) | ~ (in(v5, v4) = % 94.68/25.58 | 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : % 94.68/25.58 | (apply(v0, v6) = v5 & in(v6, v3) = 0 & in(v6, v2) = 0 & % 94.68/25.58 | $i(v6))) & ? [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = % 94.68/25.58 | v3 | ~ (relation_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) % 94.68/25.58 | | ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: int] : % 94.68/25.58 | ? [v10: int] : ? [v11: $i] : (in(v6, v3) = v7 & $i(v8) & % 94.68/25.58 | $i(v6) & ( ~ (v7 = 0) | ( ! [v12: $i] : ( ~ (apply(v0, v12) % 94.68/25.58 | = v6) | ~ $i(v12) | ? [v13: any] : ? [v14: any] % 94.68/25.58 | : (in(v12, v4) = v14 & in(v12, v2) = v13 & ( ~ (v14 = % 94.68/25.58 | 0) | ~ (v13 = 0)))) & ! [v12: $i] : ( ~ % 94.68/25.58 | (in(v12, v4) = 0) | ~ $i(v12) | ? [v13: any] : ? % 94.68/25.58 | [v14: $i] : (apply(v0, v12) = v14 & in(v12, v2) = v13 % 94.68/25.58 | & $i(v14) & ( ~ (v14 = v6) | ~ (v13 = 0)))) & ! % 94.68/25.58 | [v12: $i] : ( ~ (in(v12, v2) = 0) | ~ $i(v12) | ? % 94.68/25.58 | [v13: any] : ? [v14: $i] : (apply(v0, v12) = v14 & % 94.68/25.58 | in(v12, v4) = v13 & $i(v14) & ( ~ (v14 = v6) | ~ % 94.68/25.58 | (v13 = 0)))))) & (v7 = 0 | (v11 = v6 & v10 = 0 & % 94.68/25.58 | v9 = 0 & apply(v0, v8) = v6 & in(v8, v4) = 0 & in(v8, % 94.68/25.58 | v2) = 0)))))))) % 94.68/25.59 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 94.68/25.59 | ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ (relation_dom(v0) = v1) | ~ % 94.68/25.59 | (relation_image(v0, v2) = v3) | ~ (in(v6, v1) = 0) | ~ (in(v4, v3) % 94.68/25.59 | = v5) | ~ $i(v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | % 94.68/25.59 | ? [v7: any] : ? [v8: any] : ((apply(v0, v6) = v8 & in(v6, v2) = v7 % 94.68/25.59 | & $i(v8) & ( ~ (v8 = v4) | ~ (v7 = 0))) | (relation(v0) = v7 & % 94.68/25.59 | function(v0) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))) % 94.68/25.59 | % 94.68/25.59 | ALPHA: (d13_funct_1) implies: % 94.68/25.59 | (5) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 94.68/25.59 | [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ % 94.68/25.59 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 94.68/25.59 | int] : (v6 = 0 | ~ (relation_inverse_image(v0, v3) = v4) | % 94.68/25.59 | ~ (in(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? % 94.68/25.59 | [v7: any] : ? [v8: $i] : ? [v9: any] : (apply(v0, v5) = v8 % 94.68/25.59 | & in(v8, v3) = v9 & in(v5, v2) = v7 & $i(v8) & ( ~ (v9 = 0) % 94.68/25.59 | | ~ (v7 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 94.68/25.59 | $i] : ! [v6: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) % 94.68/25.59 | | ~ (apply(v0, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 94.68/25.59 | | ? [v7: any] : ? [v8: any] : ? [v9: any] : (in(v6, v3) = % 94.68/25.59 | v9 & in(v5, v4) = v7 & in(v5, v2) = v8 & ( ~ (v7 = 0) | (v9 % 94.68/25.59 | = 0 & v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 94.68/25.59 | $i] : ! [v6: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) % 94.68/25.59 | | ~ (apply(v0, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 94.68/25.59 | | ? [v7: any] : ? [v8: any] : ? [v9: any] : (in(v6, v3) = % 94.68/25.59 | v8 & in(v5, v4) = v9 & in(v5, v2) = v7 & ( ~ (v8 = 0) | ~ % 94.68/25.59 | (v7 = 0) | v9 = 0))) & ! [v3: $i] : ! [v4: $i] : ! % 94.68/25.59 | [v5: $i] : ! [v6: any] : ( ~ (relation_inverse_image(v0, v3) = % 94.68/25.59 | v4) | ~ (in(v5, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 94.68/25.59 | $i(v3) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 94.68/25.59 | (apply(v0, v5) = v8 & in(v8, v3) = v9 & in(v5, v4) = v7 & % 94.68/25.59 | $i(v8) & ( ~ (v7 = 0) | (v9 = 0 & v6 = 0)))) & ! [v3: $i] % 94.68/25.59 | : ! [v4: $i] : ! [v5: $i] : ( ~ (relation_inverse_image(v0, % 94.68/25.59 | v3) = v4) | ~ (in(v5, v4) = 0) | ~ $i(v5) | ~ $i(v4) | % 94.68/25.59 | ~ $i(v3) | ? [v6: $i] : (apply(v0, v5) = v6 & in(v6, v3) = % 94.68/25.59 | 0 & in(v5, v2) = 0 & $i(v6))) & ! [v3: $i] : ! [v4: $i] : % 94.68/25.59 | ! [v5: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ % 94.68/25.59 | (in(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? % 94.68/25.59 | [v6: $i] : ? [v7: any] : ? [v8: any] : (apply(v0, v5) = v6 % 94.68/25.59 | & in(v6, v3) = v7 & in(v5, v4) = v8 & $i(v6) & ( ~ (v7 = 0) % 94.68/25.59 | | v8 = 0))) & ? [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 94.68/25.59 | (v5 = v3 | ~ (relation_inverse_image(v0, v4) = v5) | ~ $i(v4) % 94.68/25.60 | | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? % 94.68/25.60 | [v9: $i] : ? [v10: any] : (apply(v0, v6) = v9 & in(v9, v4) = % 94.68/25.60 | v10 & in(v6, v3) = v7 & in(v6, v2) = v8 & $i(v9) & $i(v6) & % 94.68/25.60 | ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v10 % 94.68/25.60 | = 0 & v8 = 0)))))))) % 94.68/25.60 | (6) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 94.68/25.60 | [v2: $i] : (relation_dom(v0) = v2 & function(v0) = v1 & $i(v2) & ( ~ % 94.68/25.60 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 94.68/25.60 | int] : (v6 = 0 | ~ (relation_inverse_image(v0, v3) = v4) | % 94.68/25.60 | ~ (in(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? % 94.68/25.60 | [v7: any] : ? [v8: $i] : ? [v9: any] : (apply(v0, v5) = v8 % 94.68/25.60 | & in(v8, v3) = v9 & in(v5, v2) = v7 & $i(v8) & ( ~ (v9 = 0) % 94.68/25.60 | | ~ (v7 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 94.68/25.60 | $i] : ! [v6: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) % 94.68/25.60 | | ~ (apply(v0, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 94.68/25.60 | | ? [v7: any] : ? [v8: any] : ? [v9: any] : (in(v6, v3) = % 94.68/25.60 | v9 & in(v5, v4) = v7 & in(v5, v2) = v8 & ( ~ (v7 = 0) | (v9 % 94.68/25.60 | = 0 & v8 = 0)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 94.68/25.60 | $i] : ! [v6: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) % 94.68/25.60 | | ~ (apply(v0, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 94.68/25.60 | | ? [v7: any] : ? [v8: any] : ? [v9: any] : (in(v6, v3) = % 94.68/25.60 | v8 & in(v5, v4) = v9 & in(v5, v2) = v7 & ( ~ (v8 = 0) | ~ % 94.68/25.60 | (v7 = 0) | v9 = 0))) & ! [v3: $i] : ! [v4: $i] : ! % 94.68/25.60 | [v5: $i] : ! [v6: any] : ( ~ (relation_inverse_image(v0, v3) = % 94.68/25.60 | v4) | ~ (in(v5, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 94.68/25.60 | $i(v3) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 94.68/25.60 | (apply(v0, v5) = v8 & in(v8, v3) = v9 & in(v5, v4) = v7 & % 94.68/25.60 | $i(v8) & ( ~ (v7 = 0) | (v9 = 0 & v6 = 0)))) & ! [v3: $i] % 94.68/25.60 | : ! [v4: $i] : ! [v5: $i] : ( ~ (relation_inverse_image(v0, % 94.68/25.60 | v3) = v4) | ~ (in(v5, v4) = 0) | ~ $i(v5) | ~ $i(v4) | % 94.68/25.60 | ~ $i(v3) | ? [v6: $i] : (apply(v0, v5) = v6 & in(v6, v3) = % 94.68/25.60 | 0 & in(v5, v2) = 0 & $i(v6))) & ! [v3: $i] : ! [v4: $i] : % 94.68/25.60 | ! [v5: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ % 94.68/25.60 | (in(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? % 94.68/25.60 | [v6: $i] : ? [v7: any] : ? [v8: any] : (apply(v0, v5) = v6 % 94.68/25.60 | & in(v6, v3) = v7 & in(v5, v4) = v8 & $i(v6) & ( ~ (v7 = 0) % 94.68/25.60 | | v8 = 0))) & ? [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 94.68/25.60 | (v5 = v3 | ~ (relation_inverse_image(v0, v4) = v5) | ~ $i(v4) % 94.68/25.60 | | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? % 94.68/25.60 | [v9: $i] : ? [v10: any] : (apply(v0, v6) = v9 & in(v9, v4) = % 94.68/25.60 | v10 & in(v6, v3) = v7 & in(v6, v2) = v8 & $i(v9) & $i(v6) & % 94.68/25.60 | ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v10 % 94.68/25.60 | = 0 & v8 = 0)))))))) % 94.68/25.60 | % 94.68/25.60 | ALPHA: (d3_tarski) implies: % 94.68/25.60 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 94.68/25.60 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 94.68/25.60 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 94.68/25.60 | % 94.68/25.60 | ALPHA: (d3_xboole_0) implies: % 94.68/25.60 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 94.68/25.60 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | % 94.68/25.60 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) % 94.68/25.60 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 94.68/25.60 | (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | % 94.68/25.60 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 94.68/25.60 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 94.68/25.61 | 0)))) % 94.68/25.61 | % 94.68/25.61 | ALPHA: (fc5_relat_1) implies: % 94.68/25.61 | (10) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 94.68/25.61 | [v2: $i] : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 & % 94.68/25.61 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0))) % 94.68/25.61 | (11) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) % 94.68/25.61 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 % 94.68/25.61 | & relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ % 94.68/25.61 | (v2 = 0)))) % 94.68/25.61 | % 94.68/25.61 | ALPHA: (rc1_subset_1) implies: % 94.68/25.61 | (12) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) % 94.68/25.61 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 94.68/25.61 | powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3) % 94.68/25.61 | & $i(v2))) % 94.68/25.61 | % 94.68/25.61 | ALPHA: (t3_subset) implies: % 94.68/25.61 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, % 94.68/25.61 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 94.68/25.61 | ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4 & $i(v3))) % 94.68/25.61 | % 94.68/25.61 | ALPHA: (function-axioms) implies: % 94.68/25.61 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 94.68/25.61 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 94.68/25.61 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 94.68/25.61 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 94.68/25.61 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 94.68/25.61 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 94.68/25.61 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 94.68/25.61 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 94.68/25.61 | v0)) % 94.68/25.61 | % 94.68/25.61 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_32_0, all_32_1 % 94.68/25.61 | gives: % 94.68/25.61 | (18) ~ (all_32_0 = 0) & empty(all_32_1) = all_32_0 & $i(all_32_1) % 94.68/25.61 | % 94.68/25.61 | ALPHA: (18) implies: % 94.68/25.61 | (19) ~ (all_32_0 = 0) % 94.68/25.61 | (20) $i(all_32_1) % 94.68/25.61 | (21) empty(all_32_1) = all_32_0 % 94.68/25.61 | % 94.68/25.61 | DELTA: instantiating (rc3_funct_1) with fresh symbol all_41_0 gives: % 94.68/25.61 | (22) one_to_one(all_41_0) = 0 & relation(all_41_0) = 0 & function(all_41_0) % 94.68/25.61 | = 0 & $i(all_41_0) % 94.68/25.61 | % 94.68/25.61 | ALPHA: (22) implies: % 94.68/25.61 | (23) $i(all_41_0) % 94.68/25.61 | (24) function(all_41_0) = 0 % 94.68/25.61 | (25) relation(all_41_0) = 0 % 94.68/25.61 | % 94.68/25.61 | DELTA: instantiating (t149_funct_1) with fresh symbols all_49_0, all_49_1, % 94.68/25.61 | all_49_2, all_49_3, all_49_4, all_49_5, all_49_6, all_49_7, all_49_8 % 94.68/25.61 | gives: % 94.68/25.61 | (26) ~ (all_49_0 = 0) & subset(all_49_3, all_49_1) = all_49_0 & % 94.68/25.61 | relation_inverse_image(all_49_6, all_49_7) = all_49_5 & % 94.68/25.61 | relation_image(all_49_6, all_49_4) = all_49_3 & % 94.68/25.61 | relation_image(all_49_6, all_49_8) = all_49_2 & % 94.68/25.61 | set_intersection2(all_49_2, all_49_7) = all_49_1 & % 94.68/25.61 | set_intersection2(all_49_8, all_49_5) = all_49_4 & relation(all_49_6) % 94.68/25.61 | = 0 & function(all_49_6) = 0 & $i(all_49_1) & $i(all_49_2) & % 94.68/25.61 | $i(all_49_3) & $i(all_49_4) & $i(all_49_5) & $i(all_49_6) & % 94.68/25.61 | $i(all_49_7) & $i(all_49_8) % 94.68/25.61 | % 94.68/25.61 | ALPHA: (26) implies: % 94.68/25.61 | (27) ~ (all_49_0 = 0) % 94.68/25.61 | (28) $i(all_49_8) % 94.68/25.61 | (29) $i(all_49_7) % 94.68/25.61 | (30) $i(all_49_6) % 94.68/25.61 | (31) $i(all_49_5) % 94.68/25.61 | (32) $i(all_49_3) % 94.68/25.61 | (33) $i(all_49_2) % 94.68/25.61 | (34) function(all_49_6) = 0 % 94.68/25.62 | (35) relation(all_49_6) = 0 % 94.68/25.62 | (36) set_intersection2(all_49_8, all_49_5) = all_49_4 % 94.68/25.62 | (37) set_intersection2(all_49_2, all_49_7) = all_49_1 % 94.68/25.62 | (38) relation_image(all_49_6, all_49_8) = all_49_2 % 94.68/25.62 | (39) relation_image(all_49_6, all_49_4) = all_49_3 % 94.68/25.62 | (40) relation_inverse_image(all_49_6, all_49_7) = all_49_5 % 94.68/25.62 | (41) subset(all_49_3, all_49_1) = all_49_0 % 94.68/25.62 | % 94.68/25.62 | GROUND_INST: instantiating (12) with all_32_1, all_32_0, simplifying with % 94.68/25.62 | (20), (21) gives: % 94.68/25.62 | (42) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 94.68/25.62 | & powerset(all_32_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2 & % 94.68/25.62 | $i(v1) & $i(v0)) % 94.68/25.62 | % 94.68/25.62 | GROUND_INST: instantiating (2) with all_41_0, simplifying with (23), (24) % 94.68/25.62 | gives: % 94.68/25.62 | (43) ? [v0: any] : ? [v1: $i] : (relation_dom(all_41_0) = v1 & % 94.68/25.62 | relation(all_41_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 94.68/25.62 | [v3: $i] : ! [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | % 94.68/25.62 | ~ (relation_image(all_41_0, v2) = v3) | ~ (apply(all_41_0, % 94.68/25.62 | v6) = v4) | ~ (in(v4, v3) = v5) | ~ $i(v6) | ~ $i(v4) | % 94.68/25.62 | ~ $i(v3) | ~ $i(v2) | ? [v7: any] : ? [v8: any] : (in(v6, % 94.68/25.62 | v2) = v8 & in(v6, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) % 94.68/25.62 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : ! % 94.68/25.62 | [v6: $i] : (v5 = 0 | ~ (relation_image(all_41_0, v2) = v3) | ~ % 94.68/25.62 | (in(v6, v2) = 0) | ~ (in(v4, v3) = v5) | ~ $i(v6) | ~ % 94.68/25.62 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v7: any] : ? [v8: $i] : % 94.68/25.62 | (apply(all_41_0, v6) = v8 & in(v6, v1) = v7 & $i(v8) & ( ~ (v8 % 94.68/25.62 | = v4) | ~ (v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! % 94.68/25.62 | [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ % 94.68/25.62 | (relation_image(all_41_0, v2) = v3) | ~ (in(v6, v1) = 0) | ~ % 94.68/25.62 | (in(v4, v3) = v5) | ~ $i(v6) | ~ $i(v4) | ~ $i(v3) | ~ % 94.68/25.62 | $i(v2) | ? [v7: any] : ? [v8: $i] : (apply(all_41_0, v6) = % 94.68/25.62 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7 = % 94.68/25.62 | 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 94.68/25.62 | (relation_image(all_41_0, v2) = v3) | ~ (in(v4, v3) = 0) | ~ % 94.68/25.62 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : % 94.68/25.62 | (apply(all_41_0, v5) = v4 & in(v5, v2) = 0 & in(v5, v1) = 0 & % 94.68/25.62 | $i(v5))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = % 94.68/25.62 | v2 | ~ (relation_image(all_41_0, v3) = v4) | ~ $i(v3) | ~ % 94.68/25.62 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: % 94.68/25.62 | int] : ? [v9: int] : ? [v10: $i] : (in(v5, v2) = v6 & % 94.68/25.62 | $i(v7) & $i(v5) & ( ~ (v6 = 0) | ( ! [v11: $i] : ( ~ % 94.68/25.62 | (apply(all_41_0, v11) = v5) | ~ $i(v11) | ? [v12: % 94.68/25.62 | any] : ? [v13: any] : (in(v11, v3) = v13 & in(v11, % 94.68/25.62 | v1) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! % 94.68/25.62 | [v11: $i] : ( ~ (in(v11, v3) = 0) | ~ $i(v11) | ? % 94.68/25.62 | [v12: any] : ? [v13: $i] : (apply(all_41_0, v11) = % 94.68/25.62 | v13 & in(v11, v1) = v12 & $i(v13) & ( ~ (v13 = v5) | % 94.68/25.62 | ~ (v12 = 0)))) & ! [v11: $i] : ( ~ (in(v11, v1) % 94.68/25.62 | = 0) | ~ $i(v11) | ? [v12: any] : ? [v13: $i] : % 94.68/25.62 | (apply(all_41_0, v11) = v13 & in(v11, v3) = v12 & % 94.68/25.62 | $i(v13) & ( ~ (v13 = v5) | ~ (v12 = 0)))))) & (v6 = % 94.68/25.62 | 0 | (v10 = v5 & v9 = 0 & v8 = 0 & apply(all_41_0, v7) = v5 % 94.68/25.62 | & in(v7, v3) = 0 & in(v7, v1) = 0))))))) % 94.68/25.62 | % 94.68/25.62 | GROUND_INST: instantiating (2) with all_49_6, simplifying with (30), (34) % 94.68/25.62 | gives: % 94.68/25.63 | (44) ? [v0: any] : ? [v1: $i] : (relation_dom(all_49_6) = v1 & % 94.68/25.63 | relation(all_49_6) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 94.68/25.63 | [v3: $i] : ! [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | % 94.68/25.63 | ~ (relation_image(all_49_6, v2) = v3) | ~ (apply(all_49_6, % 94.68/25.63 | v6) = v4) | ~ (in(v4, v3) = v5) | ~ $i(v6) | ~ $i(v4) | % 94.68/25.63 | ~ $i(v3) | ~ $i(v2) | ? [v7: any] : ? [v8: any] : (in(v6, % 94.68/25.63 | v2) = v8 & in(v6, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) % 94.68/25.63 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : ! % 94.68/25.63 | [v6: $i] : (v5 = 0 | ~ (relation_image(all_49_6, v2) = v3) | ~ % 94.68/25.63 | (in(v6, v2) = 0) | ~ (in(v4, v3) = v5) | ~ $i(v6) | ~ % 94.68/25.63 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v7: any] : ? [v8: $i] : % 94.68/25.63 | (apply(all_49_6, v6) = v8 & in(v6, v1) = v7 & $i(v8) & ( ~ (v8 % 94.68/25.63 | = v4) | ~ (v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! % 94.68/25.63 | [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ % 94.68/25.63 | (relation_image(all_49_6, v2) = v3) | ~ (in(v6, v1) = 0) | ~ % 94.68/25.63 | (in(v4, v3) = v5) | ~ $i(v6) | ~ $i(v4) | ~ $i(v3) | ~ % 94.68/25.63 | $i(v2) | ? [v7: any] : ? [v8: $i] : (apply(all_49_6, v6) = % 94.68/25.63 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7 = % 94.68/25.63 | 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 94.68/25.63 | (relation_image(all_49_6, v2) = v3) | ~ (in(v4, v3) = 0) | ~ % 94.68/25.63 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : % 94.68/25.63 | (apply(all_49_6, v5) = v4 & in(v5, v2) = 0 & in(v5, v1) = 0 & % 94.68/25.63 | $i(v5))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = % 94.68/25.63 | v2 | ~ (relation_image(all_49_6, v3) = v4) | ~ $i(v3) | ~ % 94.68/25.63 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: % 94.68/25.63 | int] : ? [v9: int] : ? [v10: $i] : (in(v5, v2) = v6 & % 94.68/25.63 | $i(v7) & $i(v5) & ( ~ (v6 = 0) | ( ! [v11: $i] : ( ~ % 94.68/25.63 | (apply(all_49_6, v11) = v5) | ~ $i(v11) | ? [v12: % 94.68/25.63 | any] : ? [v13: any] : (in(v11, v3) = v13 & in(v11, % 94.68/25.63 | v1) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! % 94.68/25.63 | [v11: $i] : ( ~ (in(v11, v3) = 0) | ~ $i(v11) | ? % 94.68/25.63 | [v12: any] : ? [v13: $i] : (apply(all_49_6, v11) = % 94.68/25.63 | v13 & in(v11, v1) = v12 & $i(v13) & ( ~ (v13 = v5) | % 94.68/25.63 | ~ (v12 = 0)))) & ! [v11: $i] : ( ~ (in(v11, v1) % 94.68/25.63 | = 0) | ~ $i(v11) | ? [v12: any] : ? [v13: $i] : % 94.68/25.63 | (apply(all_49_6, v11) = v13 & in(v11, v3) = v12 & % 94.68/25.63 | $i(v13) & ( ~ (v13 = v5) | ~ (v12 = 0)))))) & (v6 = % 94.68/25.63 | 0 | (v10 = v5 & v9 = 0 & v8 = 0 & apply(all_49_6, v7) = v5 % 94.68/25.63 | & in(v7, v3) = 0 & in(v7, v1) = 0))))))) % 94.68/25.63 | % 94.68/25.63 | GROUND_INST: instantiating (5) with all_49_6, simplifying with (30), (34) % 94.68/25.63 | gives: % 94.68/25.63 | (45) ? [v0: any] : ? [v1: $i] : (relation_dom(all_49_6) = v1 & % 94.68/25.63 | relation(all_49_6) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 94.68/25.63 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 94.68/25.63 | (relation_inverse_image(all_49_6, v2) = v3) | ~ (in(v4, v3) = % 94.68/25.63 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 94.68/25.63 | [v7: $i] : ? [v8: any] : (apply(all_49_6, v4) = v7 & in(v7, % 94.68/25.63 | v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 94.68/25.63 | (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 94.68/25.63 | [v5: $i] : ( ~ (relation_inverse_image(all_49_6, v2) = v3) | ~ % 94.68/25.63 | (apply(all_49_6, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 94.68/25.63 | | ? [v6: any] : ? [v7: any] : ? [v8: any] : (in(v5, v2) = % 94.68/25.63 | v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | (v8 % 94.68/25.63 | = 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 94.68/25.63 | $i] : ! [v5: $i] : ( ~ (relation_inverse_image(all_49_6, v2) % 94.68/25.63 | = v3) | ~ (apply(all_49_6, v4) = v5) | ~ $i(v4) | ~ % 94.68/25.63 | $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 94.68/25.63 | any] : (in(v5, v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = v6 % 94.68/25.63 | & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v2: $i] : ! % 94.68/25.63 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 94.68/25.63 | (relation_inverse_image(all_49_6, v2) = v3) | ~ (in(v4, v1) = % 94.68/25.63 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 94.68/25.63 | [v7: $i] : ? [v8: any] : (apply(all_49_6, v4) = v7 & in(v7, % 94.68/25.63 | v2) = v8 & in(v4, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | (v8 = % 94.68/25.63 | 0 & v5 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 94.68/25.63 | : ( ~ (relation_inverse_image(all_49_6, v2) = v3) | ~ (in(v4, % 94.68/25.63 | v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] % 94.68/25.63 | : (apply(all_49_6, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0 % 94.68/25.63 | & $i(v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 94.68/25.63 | (relation_inverse_image(all_49_6, v2) = v3) | ~ (in(v4, v1) = % 94.68/25.63 | 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? % 94.68/25.63 | [v6: any] : ? [v7: any] : (apply(all_49_6, v4) = v5 & in(v5, % 94.68/25.63 | v2) = v6 & in(v4, v3) = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = % 94.68/25.63 | 0))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 94.68/25.63 | | ~ (relation_inverse_image(all_49_6, v3) = v4) | ~ $i(v3) | % 94.68/25.63 | ~ $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? % 94.68/25.63 | [v8: $i] : ? [v9: any] : (apply(all_49_6, v5) = v8 & in(v8, % 94.68/25.63 | v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & % 94.68/25.63 | $i(v5) & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 % 94.68/25.63 | | (v9 = 0 & v7 = 0))))))) % 94.68/25.63 | % 94.68/25.63 | GROUND_INST: instantiating (10) with all_49_6, simplifying with (30), (35) % 94.68/25.63 | gives: % 94.68/25.64 | (46) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_49_6) = % 94.68/25.64 | v1 & empty(v1) = v2 & empty(all_49_6) = v0 & $i(v1) & ( ~ (v2 = 0) | % 94.68/25.64 | v0 = 0)) % 94.68/25.64 | % 94.68/25.64 | GROUND_INST: instantiating (3) with all_49_6, simplifying with (30), (35) % 94.68/25.64 | gives: % 94.68/25.64 | (47) ? [v0: any] : ? [v1: $i] : (relation_dom(all_49_6) = v1 & % 94.68/25.64 | function(all_49_6) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 94.68/25.64 | [v3: $i] : ! [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | % 94.68/25.64 | ~ (relation_image(all_49_6, v2) = v3) | ~ (apply(all_49_6, % 94.68/25.64 | v6) = v4) | ~ (in(v4, v3) = v5) | ~ $i(v6) | ~ $i(v4) | % 94.68/25.64 | ~ $i(v3) | ~ $i(v2) | ? [v7: any] : ? [v8: any] : (in(v6, % 94.68/25.64 | v2) = v8 & in(v6, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) % 94.68/25.64 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : ! % 94.68/25.64 | [v6: $i] : (v5 = 0 | ~ (relation_image(all_49_6, v2) = v3) | ~ % 94.68/25.64 | (in(v6, v2) = 0) | ~ (in(v4, v3) = v5) | ~ $i(v6) | ~ % 94.68/25.64 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v7: any] : ? [v8: $i] : % 94.68/25.64 | (apply(all_49_6, v6) = v8 & in(v6, v1) = v7 & $i(v8) & ( ~ (v8 % 94.68/25.64 | = v4) | ~ (v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! % 94.68/25.64 | [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ % 94.68/25.64 | (relation_image(all_49_6, v2) = v3) | ~ (in(v6, v1) = 0) | ~ % 94.68/25.64 | (in(v4, v3) = v5) | ~ $i(v6) | ~ $i(v4) | ~ $i(v3) | ~ % 94.68/25.64 | $i(v2) | ? [v7: any] : ? [v8: $i] : (apply(all_49_6, v6) = % 94.68/25.64 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7 = % 94.68/25.64 | 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 94.68/25.64 | (relation_image(all_49_6, v2) = v3) | ~ (in(v4, v3) = 0) | ~ % 94.68/25.64 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : % 94.68/25.64 | (apply(all_49_6, v5) = v4 & in(v5, v2) = 0 & in(v5, v1) = 0 & % 94.68/25.64 | $i(v5))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = % 94.68/25.64 | v2 | ~ (relation_image(all_49_6, v3) = v4) | ~ $i(v3) | ~ % 94.68/25.64 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: % 94.68/25.64 | int] : ? [v9: int] : ? [v10: $i] : (in(v5, v2) = v6 & % 94.68/25.64 | $i(v7) & $i(v5) & ( ~ (v6 = 0) | ( ! [v11: $i] : ( ~ % 94.68/25.64 | (apply(all_49_6, v11) = v5) | ~ $i(v11) | ? [v12: % 94.68/25.64 | any] : ? [v13: any] : (in(v11, v3) = v13 & in(v11, % 94.68/25.64 | v1) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! % 94.68/25.64 | [v11: $i] : ( ~ (in(v11, v3) = 0) | ~ $i(v11) | ? % 94.68/25.64 | [v12: any] : ? [v13: $i] : (apply(all_49_6, v11) = % 94.68/25.64 | v13 & in(v11, v1) = v12 & $i(v13) & ( ~ (v13 = v5) | % 94.68/25.64 | ~ (v12 = 0)))) & ! [v11: $i] : ( ~ (in(v11, v1) % 94.68/25.64 | = 0) | ~ $i(v11) | ? [v12: any] : ? [v13: $i] : % 94.68/25.64 | (apply(all_49_6, v11) = v13 & in(v11, v3) = v12 & % 94.68/25.64 | $i(v13) & ( ~ (v13 = v5) | ~ (v12 = 0)))))) & (v6 = % 94.68/25.64 | 0 | (v10 = v5 & v9 = 0 & v8 = 0 & apply(all_49_6, v7) = v5 % 94.68/25.64 | & in(v7, v3) = 0 & in(v7, v1) = 0))))))) % 94.68/25.64 | % 94.68/25.64 | GROUND_INST: instantiating (6) with all_49_6, simplifying with (30), (35) % 94.68/25.64 | gives: % 94.68/25.64 | (48) ? [v0: any] : ? [v1: $i] : (relation_dom(all_49_6) = v1 & % 94.68/25.64 | function(all_49_6) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 94.68/25.64 | [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 94.68/25.64 | (relation_inverse_image(all_49_6, v2) = v3) | ~ (in(v4, v3) = % 94.68/25.64 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 94.68/25.64 | [v7: $i] : ? [v8: any] : (apply(all_49_6, v4) = v7 & in(v7, % 94.68/25.64 | v2) = v8 & in(v4, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 94.68/25.64 | (v6 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 94.68/25.64 | [v5: $i] : ( ~ (relation_inverse_image(all_49_6, v2) = v3) | ~ % 94.68/25.64 | (apply(all_49_6, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 94.68/25.64 | | ? [v6: any] : ? [v7: any] : ? [v8: any] : (in(v5, v2) = % 94.68/25.64 | v8 & in(v4, v3) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | (v8 % 94.68/25.64 | = 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 94.68/25.64 | $i] : ! [v5: $i] : ( ~ (relation_inverse_image(all_49_6, v2) % 94.68/25.64 | = v3) | ~ (apply(all_49_6, v4) = v5) | ~ $i(v4) | ~ % 94.68/25.65 | $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 94.68/25.65 | any] : (in(v5, v2) = v7 & in(v4, v3) = v8 & in(v4, v1) = v6 % 94.68/25.65 | & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v2: $i] : ! % 94.68/25.65 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 94.68/25.65 | (relation_inverse_image(all_49_6, v2) = v3) | ~ (in(v4, v1) = % 94.68/25.65 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 94.68/25.65 | [v7: $i] : ? [v8: any] : (apply(all_49_6, v4) = v7 & in(v7, % 94.68/25.65 | v2) = v8 & in(v4, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | (v8 = % 94.68/25.65 | 0 & v5 = 0)))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 94.68/25.65 | : ( ~ (relation_inverse_image(all_49_6, v2) = v3) | ~ (in(v4, % 94.68/25.65 | v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] % 94.68/25.65 | : (apply(all_49_6, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0 % 94.68/25.65 | & $i(v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 94.68/25.65 | (relation_inverse_image(all_49_6, v2) = v3) | ~ (in(v4, v1) = % 94.68/25.65 | 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : ? % 94.68/25.65 | [v6: any] : ? [v7: any] : (apply(all_49_6, v4) = v5 & in(v5, % 94.68/25.65 | v2) = v6 & in(v4, v3) = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = % 94.68/25.65 | 0))) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 94.68/25.65 | | ~ (relation_inverse_image(all_49_6, v3) = v4) | ~ $i(v3) | % 94.68/25.65 | ~ $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? % 94.68/25.65 | [v8: $i] : ? [v9: any] : (apply(all_49_6, v5) = v8 & in(v8, % 94.68/25.65 | v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & % 94.68/25.65 | $i(v5) & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 % 94.68/25.65 | | (v9 = 0 & v7 = 0))))))) % 94.68/25.65 | % 94.68/25.65 | GROUND_INST: instantiating (1) with all_49_5, all_49_8, all_49_4, simplifying % 94.68/25.65 | with (28), (31), (36) gives: % 94.68/25.65 | (49) set_intersection2(all_49_5, all_49_8) = all_49_4 & $i(all_49_4) % 94.68/25.65 | % 94.68/25.65 | ALPHA: (49) implies: % 94.68/25.65 | (50) $i(all_49_4) % 94.68/25.65 | % 94.68/25.65 | GROUND_INST: instantiating (1) with all_49_7, all_49_2, all_49_1, simplifying % 94.68/25.65 | with (29), (33), (37) gives: % 94.68/25.65 | (51) set_intersection2(all_49_7, all_49_2) = all_49_1 & $i(all_49_1) % 94.68/25.65 | % 94.68/25.65 | ALPHA: (51) implies: % 94.68/25.65 | (52) $i(all_49_1) % 94.68/25.65 | (53) set_intersection2(all_49_7, all_49_2) = all_49_1 % 94.68/25.65 | % 94.68/25.65 | GROUND_INST: instantiating (13) with all_49_3, all_49_1, all_49_0, simplifying % 94.68/25.65 | with (32), (41), (52) gives: % 94.68/25.65 | (54) all_49_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 94.68/25.65 | powerset(all_49_1) = v0 & element(all_49_3, v0) = v1 & $i(v0)) % 94.68/25.65 | % 94.68/25.65 | GROUND_INST: instantiating (7) with all_49_3, all_49_1, all_49_0, simplifying % 94.68/25.65 | with (32), (41), (52) gives: % 94.68/25.65 | (55) all_49_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 94.68/25.65 | all_49_1) = v1 & in(v0, all_49_3) = 0 & $i(v0)) % 94.68/25.65 | % 94.68/25.65 | DELTA: instantiating (46) with fresh symbols all_83_0, all_83_1, all_83_2 % 94.68/25.65 | gives: % 94.68/25.65 | (56) relation_dom(all_49_6) = all_83_1 & empty(all_83_1) = all_83_0 & % 94.68/25.65 | empty(all_49_6) = all_83_2 & $i(all_83_1) & ( ~ (all_83_0 = 0) | % 94.68/25.65 | all_83_2 = 0) % 94.68/25.65 | % 94.68/25.65 | ALPHA: (56) implies: % 94.68/25.65 | (57) relation_dom(all_49_6) = all_83_1 % 94.68/25.65 | % 94.68/25.65 | DELTA: instantiating (44) with fresh symbols all_127_0, all_127_1 gives: % 94.68/25.65 | (58) relation_dom(all_49_6) = all_127_0 & relation(all_49_6) = all_127_1 & % 94.68/25.65 | $i(all_127_0) & ( ~ (all_127_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 94.68/25.65 | [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ % 94.68/25.65 | (relation_image(all_49_6, v0) = v1) | ~ (apply(all_49_6, v4) = % 94.68/25.65 | v2) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) % 94.68/25.65 | | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v4, v0) = v6 & % 94.68/25.65 | in(v4, all_127_0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! % 94.68/25.65 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] % 94.68/25.65 | : (v3 = 0 | ~ (relation_image(all_49_6, v0) = v1) | ~ (in(v4, % 94.68/25.65 | v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 94.68/25.65 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : % 94.68/25.65 | (apply(all_49_6, v4) = v6 & in(v4, all_127_0) = v5 & $i(v6) & ( % 94.68/25.65 | ~ (v6 = v2) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 94.68/25.65 | ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ % 94.68/25.65 | (relation_image(all_49_6, v0) = v1) | ~ (in(v4, all_127_0) = 0) % 94.68/25.65 | | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ % 94.68/25.65 | $i(v0) | ? [v5: any] : ? [v6: $i] : (apply(all_49_6, v4) = v6 % 94.68/25.65 | & in(v4, v0) = v5 & $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0)))) & % 94.68/25.65 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 94.68/25.65 | (relation_image(all_49_6, v0) = v1) | ~ (in(v2, v1) = 0) | ~ % 94.68/25.65 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (apply(all_49_6, % 94.68/25.65 | v3) = v2 & in(v3, v0) = 0 & in(v3, all_127_0) = 0 & $i(v3))) % 94.68/25.65 | & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 94.68/25.65 | (relation_image(all_49_6, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 94.68/25.65 | [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: % 94.68/25.65 | int] : ? [v8: $i] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ % 94.68/25.65 | (v4 = 0) | ( ! [v9: $i] : ( ~ (apply(all_49_6, v9) = v3) | % 94.68/25.65 | ~ $i(v9) | ? [v10: any] : ? [v11: any] : (in(v9, v1) = % 94.68/25.65 | v11 & in(v9, all_127_0) = v10 & ( ~ (v11 = 0) | ~ % 94.68/25.65 | (v10 = 0)))) & ! [v9: $i] : ( ~ (in(v9, v1) = 0) | % 94.68/25.65 | ~ $i(v9) | ? [v10: any] : ? [v11: $i] : % 94.68/25.65 | (apply(all_49_6, v9) = v11 & in(v9, all_127_0) = v10 & % 94.68/25.65 | $i(v11) & ( ~ (v11 = v3) | ~ (v10 = 0)))) & ! [v9: % 94.68/25.65 | $i] : ( ~ (in(v9, all_127_0) = 0) | ~ $i(v9) | ? [v10: % 94.68/25.65 | any] : ? [v11: $i] : (apply(all_49_6, v9) = v11 & % 94.68/25.65 | in(v9, v1) = v10 & $i(v11) & ( ~ (v11 = v3) | ~ (v10 % 94.68/25.65 | = 0)))))) & (v4 = 0 | (v8 = v3 & v7 = 0 & v6 = 0 & % 94.68/25.65 | apply(all_49_6, v5) = v3 & in(v5, v1) = 0 & in(v5, % 94.68/25.65 | all_127_0) = 0)))))) % 94.68/25.65 | % 94.68/25.65 | ALPHA: (58) implies: % 94.68/25.65 | (59) relation(all_49_6) = all_127_1 % 94.68/25.65 | (60) relation_dom(all_49_6) = all_127_0 % 94.68/25.66 | (61) ~ (all_127_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 94.68/25.66 | [v3: int] : ! [v4: $i] : (v3 = 0 | ~ (relation_image(all_49_6, v0) % 94.68/25.66 | = v1) | ~ (apply(all_49_6, v4) = v2) | ~ (in(v2, v1) = v3) | % 94.68/25.66 | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 94.68/25.66 | [v6: any] : (in(v4, v0) = v6 & in(v4, all_127_0) = v5 & ( ~ (v6 = % 94.68/25.66 | 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 94.68/25.66 | $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ % 94.68/25.66 | (relation_image(all_49_6, v0) = v1) | ~ (in(v4, v0) = 0) | ~ % 94.68/25.66 | (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 94.68/25.66 | | ? [v5: any] : ? [v6: $i] : (apply(all_49_6, v4) = v6 & in(v4, % 94.68/25.66 | all_127_0) = v5 & $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0)))) & ! % 94.68/25.66 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : % 94.68/25.66 | (v3 = 0 | ~ (relation_image(all_49_6, v0) = v1) | ~ (in(v4, % 94.68/25.66 | all_127_0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 94.68/25.66 | | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : % 94.68/25.66 | (apply(all_49_6, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( ~ (v6 = % 94.68/25.66 | v2) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 94.68/25.66 | $i] : ( ~ (relation_image(all_49_6, v0) = v1) | ~ (in(v2, v1) = % 94.68/25.66 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 94.68/25.66 | (apply(all_49_6, v3) = v2 & in(v3, v0) = 0 & in(v3, all_127_0) = 0 % 94.68/25.66 | & $i(v3))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 % 94.68/25.66 | | ~ (relation_image(all_49_6, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 94.68/25.66 | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: % 94.68/25.66 | int] : ? [v8: $i] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ % 94.68/25.66 | (v4 = 0) | ( ! [v9: $i] : ( ~ (apply(all_49_6, v9) = v3) | ~ % 94.68/25.66 | $i(v9) | ? [v10: any] : ? [v11: any] : (in(v9, v1) = v11 % 94.68/25.66 | & in(v9, all_127_0) = v10 & ( ~ (v11 = 0) | ~ (v10 = % 94.68/25.66 | 0)))) & ! [v9: $i] : ( ~ (in(v9, v1) = 0) | ~ % 94.68/25.66 | $i(v9) | ? [v10: any] : ? [v11: $i] : (apply(all_49_6, % 94.68/25.66 | v9) = v11 & in(v9, all_127_0) = v10 & $i(v11) & ( ~ % 94.68/25.66 | (v11 = v3) | ~ (v10 = 0)))) & ! [v9: $i] : ( ~ % 94.68/25.66 | (in(v9, all_127_0) = 0) | ~ $i(v9) | ? [v10: any] : ? % 94.68/25.66 | [v11: $i] : (apply(all_49_6, v9) = v11 & in(v9, v1) = v10 % 94.68/25.66 | & $i(v11) & ( ~ (v11 = v3) | ~ (v10 = 0)))))) & (v4 = 0 % 94.68/25.66 | | (v8 = v3 & v7 = 0 & v6 = 0 & apply(all_49_6, v5) = v3 & % 94.68/25.66 | in(v5, v1) = 0 & in(v5, all_127_0) = 0))))) % 94.68/25.66 | % 94.68/25.66 | DELTA: instantiating (47) with fresh symbols all_131_0, all_131_1 gives: % 94.68/25.66 | (62) relation_dom(all_49_6) = all_131_0 & function(all_49_6) = all_131_1 & % 94.68/25.66 | $i(all_131_0) & ( ~ (all_131_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 94.68/25.66 | [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ % 94.68/25.66 | (relation_image(all_49_6, v0) = v1) | ~ (apply(all_49_6, v4) = % 94.68/25.66 | v2) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) % 94.68/25.66 | | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v4, v0) = v6 & % 94.68/25.66 | in(v4, all_131_0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! % 94.68/25.66 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] % 94.68/25.66 | : (v3 = 0 | ~ (relation_image(all_49_6, v0) = v1) | ~ (in(v4, % 94.68/25.66 | v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 94.68/25.66 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : % 94.68/25.66 | (apply(all_49_6, v4) = v6 & in(v4, all_131_0) = v5 & $i(v6) & ( % 94.68/25.66 | ~ (v6 = v2) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 94.68/25.66 | ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ % 94.68/25.66 | (relation_image(all_49_6, v0) = v1) | ~ (in(v4, all_131_0) = 0) % 94.68/25.66 | | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ % 94.68/25.66 | $i(v0) | ? [v5: any] : ? [v6: $i] : (apply(all_49_6, v4) = v6 % 94.68/25.66 | & in(v4, v0) = v5 & $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0)))) & % 94.68/25.66 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 94.68/25.66 | (relation_image(all_49_6, v0) = v1) | ~ (in(v2, v1) = 0) | ~ % 94.68/25.66 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (apply(all_49_6, % 94.68/25.66 | v3) = v2 & in(v3, v0) = 0 & in(v3, all_131_0) = 0 & $i(v3))) % 94.68/25.66 | & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 94.68/25.66 | (relation_image(all_49_6, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 94.68/25.66 | [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: % 94.68/25.66 | int] : ? [v8: $i] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ % 94.68/25.66 | (v4 = 0) | ( ! [v9: $i] : ( ~ (apply(all_49_6, v9) = v3) | % 94.68/25.66 | ~ $i(v9) | ? [v10: any] : ? [v11: any] : (in(v9, v1) = % 94.68/25.66 | v11 & in(v9, all_131_0) = v10 & ( ~ (v11 = 0) | ~ % 94.68/25.66 | (v10 = 0)))) & ! [v9: $i] : ( ~ (in(v9, v1) = 0) | % 94.68/25.66 | ~ $i(v9) | ? [v10: any] : ? [v11: $i] : % 94.68/25.66 | (apply(all_49_6, v9) = v11 & in(v9, all_131_0) = v10 & % 94.68/25.66 | $i(v11) & ( ~ (v11 = v3) | ~ (v10 = 0)))) & ! [v9: % 94.68/25.66 | $i] : ( ~ (in(v9, all_131_0) = 0) | ~ $i(v9) | ? [v10: % 94.68/25.66 | any] : ? [v11: $i] : (apply(all_49_6, v9) = v11 & % 94.68/25.66 | in(v9, v1) = v10 & $i(v11) & ( ~ (v11 = v3) | ~ (v10 % 94.68/25.66 | = 0)))))) & (v4 = 0 | (v8 = v3 & v7 = 0 & v6 = 0 & % 94.68/25.66 | apply(all_49_6, v5) = v3 & in(v5, v1) = 0 & in(v5, % 94.68/25.66 | all_131_0) = 0)))))) % 94.68/25.66 | % 94.68/25.66 | ALPHA: (62) implies: % 94.68/25.66 | (63) function(all_49_6) = all_131_1 % 94.68/25.66 | (64) relation_dom(all_49_6) = all_131_0 % 95.43/25.67 | (65) ~ (all_131_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 95.43/25.67 | [v3: int] : ! [v4: $i] : (v3 = 0 | ~ (relation_image(all_49_6, v0) % 95.43/25.67 | = v1) | ~ (apply(all_49_6, v4) = v2) | ~ (in(v2, v1) = v3) | % 95.43/25.67 | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 95.43/25.67 | [v6: any] : (in(v4, v0) = v6 & in(v4, all_131_0) = v5 & ( ~ (v6 = % 95.43/25.67 | 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 95.43/25.67 | $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ % 95.43/25.67 | (relation_image(all_49_6, v0) = v1) | ~ (in(v4, v0) = 0) | ~ % 95.43/25.67 | (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 95.43/25.67 | | ? [v5: any] : ? [v6: $i] : (apply(all_49_6, v4) = v6 & in(v4, % 95.43/25.67 | all_131_0) = v5 & $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0)))) & ! % 95.43/25.67 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : % 95.43/25.67 | (v3 = 0 | ~ (relation_image(all_49_6, v0) = v1) | ~ (in(v4, % 95.43/25.67 | all_131_0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 95.43/25.67 | | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : % 95.43/25.67 | (apply(all_49_6, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( ~ (v6 = % 95.43/25.67 | v2) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 95.43/25.67 | $i] : ( ~ (relation_image(all_49_6, v0) = v1) | ~ (in(v2, v1) = % 95.43/25.67 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 95.43/25.67 | (apply(all_49_6, v3) = v2 & in(v3, v0) = 0 & in(v3, all_131_0) = 0 % 95.43/25.67 | & $i(v3))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 % 95.43/25.67 | | ~ (relation_image(all_49_6, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 95.43/25.67 | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: % 95.43/25.67 | int] : ? [v8: $i] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ % 95.43/25.67 | (v4 = 0) | ( ! [v9: $i] : ( ~ (apply(all_49_6, v9) = v3) | ~ % 95.43/25.67 | $i(v9) | ? [v10: any] : ? [v11: any] : (in(v9, v1) = v11 % 95.43/25.67 | & in(v9, all_131_0) = v10 & ( ~ (v11 = 0) | ~ (v10 = % 95.43/25.67 | 0)))) & ! [v9: $i] : ( ~ (in(v9, v1) = 0) | ~ % 95.43/25.67 | $i(v9) | ? [v10: any] : ? [v11: $i] : (apply(all_49_6, % 95.43/25.67 | v9) = v11 & in(v9, all_131_0) = v10 & $i(v11) & ( ~ % 95.43/25.67 | (v11 = v3) | ~ (v10 = 0)))) & ! [v9: $i] : ( ~ % 95.43/25.67 | (in(v9, all_131_0) = 0) | ~ $i(v9) | ? [v10: any] : ? % 95.43/25.67 | [v11: $i] : (apply(all_49_6, v9) = v11 & in(v9, v1) = v10 % 95.43/25.67 | & $i(v11) & ( ~ (v11 = v3) | ~ (v10 = 0)))))) & (v4 = 0 % 95.43/25.67 | | (v8 = v3 & v7 = 0 & v6 = 0 & apply(all_49_6, v5) = v3 & % 95.43/25.67 | in(v5, v1) = 0 & in(v5, all_131_0) = 0))))) % 95.43/25.67 | % 95.43/25.67 | DELTA: instantiating (48) with fresh symbols all_147_0, all_147_1 gives: % 95.43/25.67 | (66) relation_dom(all_49_6) = all_147_0 & function(all_49_6) = all_147_1 & % 95.43/25.67 | $i(all_147_0) & ( ~ (all_147_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 95.43/25.67 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 95.43/25.67 | (relation_inverse_image(all_49_6, v0) = v1) | ~ (in(v2, v1) = % 95.43/25.67 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 95.43/25.67 | [v5: $i] : ? [v6: any] : (apply(all_49_6, v2) = v5 & in(v5, v0) % 95.43/25.67 | = v6 & in(v2, all_147_0) = v4 & $i(v5) & ( ~ (v6 = 0) | ~ (v4 % 95.43/25.67 | = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 95.43/25.67 | [v3: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.43/25.67 | (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 95.43/25.67 | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v6 & % 95.43/25.67 | in(v2, v1) = v4 & in(v2, all_147_0) = v5 & ( ~ (v4 = 0) | (v6 % 95.43/25.67 | = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 95.43/25.67 | : ! [v3: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | % 95.43/25.67 | ~ (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 95.43/25.67 | | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v5 % 95.43/25.67 | & in(v2, v1) = v6 & in(v2, all_147_0) = v4 & ( ~ (v5 = 0) | ~ % 95.43/25.67 | (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 95.43/25.67 | $i] : ! [v3: any] : ( ~ (relation_inverse_image(all_49_6, v0) = % 95.43/25.67 | v1) | ~ (in(v2, all_147_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 95.43/25.67 | $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 95.43/25.67 | (apply(all_49_6, v2) = v5 & in(v5, v0) = v6 & in(v2, v1) = v4 & % 95.43/25.67 | $i(v5) & ( ~ (v4 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : % 95.43/25.67 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_inverse_image(all_49_6, % 95.43/25.67 | v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 95.43/25.67 | $i(v0) | ? [v3: $i] : (apply(all_49_6, v2) = v3 & in(v3, v0) = % 95.43/25.67 | 0 & in(v2, all_147_0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: % 95.43/25.67 | $i] : ! [v2: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = % 95.43/25.67 | v1) | ~ (in(v2, all_147_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 95.43/25.67 | $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 95.43/25.67 | (apply(all_49_6, v2) = v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & % 95.43/25.67 | $i(v3) & ( ~ (v4 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] % 95.43/25.67 | : ! [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_49_6, % 95.43/25.67 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 95.43/25.67 | any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 95.43/25.67 | (apply(all_49_6, v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & % 95.43/25.67 | in(v3, all_147_0) = v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ % 95.43/25.67 | (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))))) % 95.43/25.67 | % 95.43/25.67 | ALPHA: (66) implies: % 95.43/25.67 | (67) function(all_49_6) = all_147_1 % 95.43/25.67 | (68) relation_dom(all_49_6) = all_147_0 % 95.43/25.68 | (69) ~ (all_147_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 95.43/25.68 | [v3: int] : (v3 = 0 | ~ (relation_inverse_image(all_49_6, v0) = v1) % 95.43/25.68 | | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 95.43/25.68 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_49_6, v2) = v5 % 95.43/25.68 | & in(v5, v0) = v6 & in(v2, all_147_0) = v4 & $i(v5) & ( ~ (v6 = % 95.43/25.68 | 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 95.43/25.68 | $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = % 95.43/25.68 | v1) | ~ (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 95.43/25.68 | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) % 95.43/25.68 | = v6 & in(v2, v1) = v4 & in(v2, all_147_0) = v5 & ( ~ (v4 = 0) | % 95.43/25.68 | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 95.43/25.68 | : ! [v3: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.43/25.68 | (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 95.43/25.68 | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v5 & % 95.43/25.68 | in(v2, v1) = v6 & in(v2, all_147_0) = v4 & ( ~ (v5 = 0) | ~ (v4 % 95.43/25.68 | = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 95.43/25.68 | ! [v3: any] : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.43/25.68 | (in(v2, all_147_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 95.43/25.68 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_49_6, v2) = v5 % 95.43/25.68 | & in(v5, v0) = v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | % 95.43/25.68 | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 95.43/25.68 | : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ (in(v2, v1) = % 95.43/25.68 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 95.43/25.68 | (apply(all_49_6, v2) = v3 & in(v3, v0) = 0 & in(v2, all_147_0) = 0 % 95.43/25.68 | & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 95.43/25.68 | (relation_inverse_image(all_49_6, v0) = v1) | ~ (in(v2, % 95.43/25.68 | all_147_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 95.43/25.68 | $i] : ? [v4: any] : ? [v5: any] : (apply(all_49_6, v2) = v3 & % 95.43/25.68 | in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = % 95.43/25.68 | 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 95.43/25.68 | (relation_inverse_image(all_49_6, v1) = v2) | ~ $i(v1) | ~ % 95.43/25.68 | $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : % 95.43/25.68 | ? [v7: any] : (apply(all_49_6, v3) = v6 & in(v6, v1) = v7 & % 95.43/25.68 | in(v3, v0) = v4 & in(v3, all_147_0) = v5 & $i(v6) & $i(v3) & ( ~ % 95.43/25.68 | (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 % 95.43/25.68 | = 0))))) % 95.43/25.68 | % 95.43/25.68 | DELTA: instantiating (45) with fresh symbols all_155_0, all_155_1 gives: % 95.43/25.68 | (70) relation_dom(all_49_6) = all_155_0 & relation(all_49_6) = all_155_1 & % 95.43/25.68 | $i(all_155_0) & ( ~ (all_155_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 95.43/25.68 | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 95.43/25.68 | (relation_inverse_image(all_49_6, v0) = v1) | ~ (in(v2, v1) = % 95.43/25.68 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 95.43/25.68 | [v5: $i] : ? [v6: any] : (apply(all_49_6, v2) = v5 & in(v5, v0) % 95.43/25.68 | = v6 & in(v2, all_155_0) = v4 & $i(v5) & ( ~ (v6 = 0) | ~ (v4 % 95.43/25.68 | = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 95.43/25.68 | [v3: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.43/25.68 | (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 95.43/25.68 | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v6 & % 95.43/25.68 | in(v2, v1) = v4 & in(v2, all_155_0) = v5 & ( ~ (v4 = 0) | (v6 % 95.43/25.68 | = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 95.43/25.68 | : ! [v3: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | % 95.43/25.68 | ~ (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 95.43/25.68 | | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v5 % 95.43/25.68 | & in(v2, v1) = v6 & in(v2, all_155_0) = v4 & ( ~ (v5 = 0) | ~ % 95.43/25.68 | (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 95.43/25.68 | $i] : ! [v3: any] : ( ~ (relation_inverse_image(all_49_6, v0) = % 95.43/25.68 | v1) | ~ (in(v2, all_155_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 95.43/25.68 | $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 95.43/25.68 | (apply(all_49_6, v2) = v5 & in(v5, v0) = v6 & in(v2, v1) = v4 & % 95.43/25.68 | $i(v5) & ( ~ (v4 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : % 95.43/25.68 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_inverse_image(all_49_6, % 95.43/25.68 | v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 95.43/25.68 | $i(v0) | ? [v3: $i] : (apply(all_49_6, v2) = v3 & in(v3, v0) = % 95.43/25.68 | 0 & in(v2, all_155_0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: % 95.43/25.68 | $i] : ! [v2: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = % 95.43/25.68 | v1) | ~ (in(v2, all_155_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 95.43/25.68 | $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 95.43/25.68 | (apply(all_49_6, v2) = v3 & in(v3, v0) = v4 & in(v2, v1) = v5 & % 95.43/25.68 | $i(v3) & ( ~ (v4 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] % 95.43/25.68 | : ! [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_49_6, % 95.43/25.68 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 95.43/25.68 | any] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 95.43/25.68 | (apply(all_49_6, v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & % 95.43/25.68 | in(v3, all_155_0) = v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ % 95.43/25.68 | (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))))) % 95.43/25.68 | % 95.43/25.68 | ALPHA: (70) implies: % 95.43/25.68 | (71) relation(all_49_6) = all_155_1 % 95.43/25.68 | (72) relation_dom(all_49_6) = all_155_0 % 95.43/25.69 | (73) ~ (all_155_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 95.43/25.69 | [v3: int] : (v3 = 0 | ~ (relation_inverse_image(all_49_6, v0) = v1) % 95.43/25.69 | | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 95.43/25.69 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_49_6, v2) = v5 % 95.43/25.69 | & in(v5, v0) = v6 & in(v2, all_155_0) = v4 & $i(v5) & ( ~ (v6 = % 95.43/25.69 | 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 95.43/25.69 | $i] : ! [v3: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = % 95.43/25.69 | v1) | ~ (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 95.43/25.69 | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) % 95.43/25.69 | = v6 & in(v2, v1) = v4 & in(v2, all_155_0) = v5 & ( ~ (v4 = 0) | % 95.43/25.69 | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 95.43/25.69 | : ! [v3: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.43/25.69 | (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 95.43/25.69 | ? [v4: any] : ? [v5: any] : ? [v6: any] : (in(v3, v0) = v5 & % 95.43/25.69 | in(v2, v1) = v6 & in(v2, all_155_0) = v4 & ( ~ (v5 = 0) | ~ (v4 % 95.43/25.69 | = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 95.43/25.69 | ! [v3: any] : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.43/25.69 | (in(v2, all_155_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 95.43/25.69 | [v4: any] : ? [v5: $i] : ? [v6: any] : (apply(all_49_6, v2) = v5 % 95.43/25.69 | & in(v5, v0) = v6 & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | % 95.43/25.69 | (v6 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 95.43/25.69 | : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ (in(v2, v1) = % 95.43/25.69 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 95.43/25.69 | (apply(all_49_6, v2) = v3 & in(v3, v0) = 0 & in(v2, all_155_0) = 0 % 95.43/25.69 | & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 95.43/25.69 | (relation_inverse_image(all_49_6, v0) = v1) | ~ (in(v2, % 95.43/25.69 | all_155_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 95.43/25.69 | $i] : ? [v4: any] : ? [v5: any] : (apply(all_49_6, v2) = v3 & % 95.43/25.69 | in(v3, v0) = v4 & in(v2, v1) = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = % 95.43/25.69 | 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 95.43/25.69 | (relation_inverse_image(all_49_6, v1) = v2) | ~ $i(v1) | ~ % 95.43/25.69 | $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: $i] : % 95.43/25.69 | ? [v7: any] : (apply(all_49_6, v3) = v6 & in(v6, v1) = v7 & % 95.43/25.69 | in(v3, v0) = v4 & in(v3, all_155_0) = v5 & $i(v6) & $i(v3) & ( ~ % 95.43/25.69 | (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 % 95.43/25.69 | = 0))))) % 95.43/25.69 | % 95.43/25.69 | DELTA: instantiating (43) with fresh symbols all_163_0, all_163_1 gives: % 95.43/25.69 | (74) relation_dom(all_41_0) = all_163_0 & relation(all_41_0) = all_163_1 & % 95.43/25.69 | $i(all_163_0) & ( ~ (all_163_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 95.43/25.69 | [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ % 95.43/25.69 | (relation_image(all_41_0, v0) = v1) | ~ (apply(all_41_0, v4) = % 95.43/25.69 | v2) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) % 95.43/25.69 | | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v4, v0) = v6 & % 95.43/25.69 | in(v4, all_163_0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! % 95.43/25.69 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] % 95.43/25.69 | : (v3 = 0 | ~ (relation_image(all_41_0, v0) = v1) | ~ (in(v4, % 95.43/25.69 | v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 95.43/25.69 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : % 95.43/25.69 | (apply(all_41_0, v4) = v6 & in(v4, all_163_0) = v5 & $i(v6) & ( % 95.43/25.69 | ~ (v6 = v2) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 95.43/25.69 | ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ % 95.43/25.69 | (relation_image(all_41_0, v0) = v1) | ~ (in(v4, all_163_0) = 0) % 95.43/25.69 | | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ % 95.43/25.69 | $i(v0) | ? [v5: any] : ? [v6: $i] : (apply(all_41_0, v4) = v6 % 95.43/25.69 | & in(v4, v0) = v5 & $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0)))) & % 95.43/25.69 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 95.43/25.69 | (relation_image(all_41_0, v0) = v1) | ~ (in(v2, v1) = 0) | ~ % 95.43/25.69 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (apply(all_41_0, % 95.43/25.69 | v3) = v2 & in(v3, v0) = 0 & in(v3, all_163_0) = 0 & $i(v3))) % 95.43/25.69 | & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 95.43/25.69 | (relation_image(all_41_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 95.43/25.69 | [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: % 95.43/25.69 | int] : ? [v8: $i] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ % 95.43/25.69 | (v4 = 0) | ( ! [v9: $i] : ( ~ (apply(all_41_0, v9) = v3) | % 95.43/25.69 | ~ $i(v9) | ? [v10: any] : ? [v11: any] : (in(v9, v1) = % 95.43/25.69 | v11 & in(v9, all_163_0) = v10 & ( ~ (v11 = 0) | ~ % 95.43/25.69 | (v10 = 0)))) & ! [v9: $i] : ( ~ (in(v9, v1) = 0) | % 95.43/25.69 | ~ $i(v9) | ? [v10: any] : ? [v11: $i] : % 95.43/25.69 | (apply(all_41_0, v9) = v11 & in(v9, all_163_0) = v10 & % 95.43/25.69 | $i(v11) & ( ~ (v11 = v3) | ~ (v10 = 0)))) & ! [v9: % 95.43/25.69 | $i] : ( ~ (in(v9, all_163_0) = 0) | ~ $i(v9) | ? [v10: % 95.43/25.69 | any] : ? [v11: $i] : (apply(all_41_0, v9) = v11 & % 95.43/25.69 | in(v9, v1) = v10 & $i(v11) & ( ~ (v11 = v3) | ~ (v10 % 95.43/25.69 | = 0)))))) & (v4 = 0 | (v8 = v3 & v7 = 0 & v6 = 0 & % 95.43/25.69 | apply(all_41_0, v5) = v3 & in(v5, v1) = 0 & in(v5, % 95.43/25.69 | all_163_0) = 0)))))) % 95.43/25.69 | % 95.43/25.69 | ALPHA: (74) implies: % 95.43/25.69 | (75) relation(all_41_0) = all_163_1 % 95.43/25.70 | (76) ~ (all_163_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 95.43/25.70 | [v3: int] : ! [v4: $i] : (v3 = 0 | ~ (relation_image(all_41_0, v0) % 95.43/25.70 | = v1) | ~ (apply(all_41_0, v4) = v2) | ~ (in(v2, v1) = v3) | % 95.43/25.70 | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 95.43/25.70 | [v6: any] : (in(v4, v0) = v6 & in(v4, all_163_0) = v5 & ( ~ (v6 = % 95.43/25.70 | 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 95.43/25.70 | $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ % 95.43/25.70 | (relation_image(all_41_0, v0) = v1) | ~ (in(v4, v0) = 0) | ~ % 95.43/25.70 | (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 95.43/25.70 | | ? [v5: any] : ? [v6: $i] : (apply(all_41_0, v4) = v6 & in(v4, % 95.43/25.70 | all_163_0) = v5 & $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0)))) & ! % 95.43/25.70 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : % 95.43/25.70 | (v3 = 0 | ~ (relation_image(all_41_0, v0) = v1) | ~ (in(v4, % 95.43/25.70 | all_163_0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 95.43/25.70 | | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : % 95.43/25.70 | (apply(all_41_0, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( ~ (v6 = % 95.43/25.70 | v2) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 95.43/25.70 | $i] : ( ~ (relation_image(all_41_0, v0) = v1) | ~ (in(v2, v1) = % 95.43/25.70 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 95.43/25.70 | (apply(all_41_0, v3) = v2 & in(v3, v0) = 0 & in(v3, all_163_0) = 0 % 95.43/25.70 | & $i(v3))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 % 95.43/25.70 | | ~ (relation_image(all_41_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 95.43/25.70 | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: % 95.43/25.70 | int] : ? [v8: $i] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ % 95.43/25.70 | (v4 = 0) | ( ! [v9: $i] : ( ~ (apply(all_41_0, v9) = v3) | ~ % 95.43/25.70 | $i(v9) | ? [v10: any] : ? [v11: any] : (in(v9, v1) = v11 % 95.43/25.70 | & in(v9, all_163_0) = v10 & ( ~ (v11 = 0) | ~ (v10 = % 95.43/25.70 | 0)))) & ! [v9: $i] : ( ~ (in(v9, v1) = 0) | ~ % 95.43/25.70 | $i(v9) | ? [v10: any] : ? [v11: $i] : (apply(all_41_0, % 95.43/25.70 | v9) = v11 & in(v9, all_163_0) = v10 & $i(v11) & ( ~ % 95.43/25.70 | (v11 = v3) | ~ (v10 = 0)))) & ! [v9: $i] : ( ~ % 95.43/25.70 | (in(v9, all_163_0) = 0) | ~ $i(v9) | ? [v10: any] : ? % 95.43/25.70 | [v11: $i] : (apply(all_41_0, v9) = v11 & in(v9, v1) = v10 % 95.43/25.70 | & $i(v11) & ( ~ (v11 = v3) | ~ (v10 = 0)))))) & (v4 = 0 % 95.43/25.70 | | (v8 = v3 & v7 = 0 & v6 = 0 & apply(all_41_0, v5) = v3 & % 95.43/25.70 | in(v5, v1) = 0 & in(v5, all_163_0) = 0))))) % 95.43/25.70 | % 95.43/25.70 | BETA: splitting (55) gives: % 95.43/25.70 | % 95.43/25.70 | Case 1: % 95.43/25.70 | | % 95.43/25.70 | | (77) all_49_0 = 0 % 95.43/25.70 | | % 95.43/25.70 | | REDUCE: (27), (77) imply: % 95.43/25.70 | | (78) $false % 95.43/25.70 | | % 95.43/25.70 | | CLOSE: (78) is inconsistent. % 95.43/25.70 | | % 95.43/25.70 | Case 2: % 95.43/25.70 | | % 95.43/25.70 | | (79) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_49_1) = v1 & % 95.43/25.70 | | in(v0, all_49_3) = 0 & $i(v0)) % 95.43/25.70 | | % 95.43/25.70 | | DELTA: instantiating (79) with fresh symbols all_180_0, all_180_1 gives: % 95.43/25.70 | | (80) ~ (all_180_0 = 0) & in(all_180_1, all_49_1) = all_180_0 & % 95.43/25.70 | | in(all_180_1, all_49_3) = 0 & $i(all_180_1) % 95.43/25.70 | | % 95.43/25.70 | | ALPHA: (80) implies: % 95.43/25.70 | | (81) ~ (all_180_0 = 0) % 95.43/25.70 | | (82) $i(all_180_1) % 95.43/25.70 | | (83) in(all_180_1, all_49_3) = 0 % 95.43/25.70 | | (84) in(all_180_1, all_49_1) = all_180_0 % 95.43/25.70 | | % 95.43/25.70 | | BETA: splitting (54) gives: % 95.43/25.70 | | % 95.43/25.70 | | Case 1: % 95.43/25.70 | | | % 95.43/25.70 | | | (85) all_49_0 = 0 % 95.43/25.70 | | | % 95.43/25.70 | | | REDUCE: (27), (85) imply: % 95.43/25.70 | | | (86) $false % 95.43/25.70 | | | % 95.43/25.70 | | | CLOSE: (86) is inconsistent. % 95.43/25.70 | | | % 95.43/25.70 | | Case 2: % 95.43/25.70 | | | % 95.43/25.70 | | | (87) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & powerset(all_49_1) = % 95.43/25.70 | | | v0 & element(all_49_3, v0) = v1 & $i(v0)) % 95.43/25.70 | | | % 95.43/25.70 | | | DELTA: instantiating (87) with fresh symbols all_185_0, all_185_1 gives: % 95.43/25.70 | | | (88) ~ (all_185_0 = 0) & powerset(all_49_1) = all_185_1 & % 95.43/25.70 | | | element(all_49_3, all_185_1) = all_185_0 & $i(all_185_1) % 95.43/25.70 | | | % 95.43/25.70 | | | ALPHA: (88) implies: % 95.43/25.70 | | | (89) $i(all_185_1) % 95.43/25.70 | | | (90) powerset(all_49_1) = all_185_1 % 95.43/25.70 | | | % 95.43/25.70 | | | BETA: splitting (42) gives: % 95.43/25.70 | | | % 95.43/25.70 | | | Case 1: % 95.43/25.70 | | | | % 95.43/25.70 | | | | (91) all_32_0 = 0 % 95.43/25.70 | | | | % 95.43/25.70 | | | | REDUCE: (19), (91) imply: % 95.43/25.70 | | | | (92) $false % 95.43/25.70 | | | | % 95.43/25.70 | | | | CLOSE: (92) is inconsistent. % 95.43/25.70 | | | | % 95.43/25.70 | | | Case 2: % 95.43/25.70 | | | | % 95.43/25.70 | | | | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 95.43/25.70 | | | | powerset(all_32_1) = v0 & element(v1, v0) = 0 & empty(v1) = v2 % 95.43/25.70 | | | | & $i(v1) & $i(v0)) % 95.43/25.70 | | | | % 95.43/25.70 | | | | DELTA: instantiating (93) with fresh symbols all_200_0, all_200_1, % 95.43/25.70 | | | | all_200_2 gives: % 95.43/25.70 | | | | (94) ~ (all_200_0 = 0) & powerset(all_32_1) = all_200_2 & % 95.43/25.70 | | | | element(all_200_1, all_200_2) = 0 & empty(all_200_1) = all_200_0 % 95.43/25.70 | | | | & $i(all_200_1) & $i(all_200_2) % 95.43/25.70 | | | | % 95.43/25.70 | | | | ALPHA: (94) implies: % 95.43/25.71 | | | | (95) ~ (all_200_0 = 0) % 95.43/25.71 | | | | (96) $i(all_200_2) % 95.43/25.71 | | | | (97) $i(all_200_1) % 95.43/25.71 | | | | (98) empty(all_200_1) = all_200_0 % 95.43/25.71 | | | | (99) powerset(all_32_1) = all_200_2 % 95.43/25.71 | | | | % 95.43/25.71 | | | | GROUND_INST: instantiating (14) with 0, all_147_1, all_49_6, simplifying % 95.43/25.71 | | | | with (34), (67) gives: % 95.43/25.71 | | | | (100) all_147_1 = 0 % 95.43/25.71 | | | | % 95.43/25.71 | | | | GROUND_INST: instantiating (14) with all_131_1, all_147_1, all_49_6, % 95.43/25.71 | | | | simplifying with (63), (67) gives: % 95.43/25.71 | | | | (101) all_147_1 = all_131_1 % 95.43/25.71 | | | | % 95.43/25.71 | | | | GROUND_INST: instantiating (15) with 0, all_163_1, all_41_0, simplifying % 95.43/25.71 | | | | with (25), (75) gives: % 95.43/25.71 | | | | (102) all_163_1 = 0 % 95.43/25.71 | | | | % 95.43/25.71 | | | | GROUND_INST: instantiating (15) with 0, all_155_1, all_49_6, simplifying % 95.43/25.71 | | | | with (35), (71) gives: % 95.43/25.71 | | | | (103) all_155_1 = 0 % 95.43/25.71 | | | | % 95.43/25.71 | | | | GROUND_INST: instantiating (15) with all_127_1, all_155_1, all_49_6, % 95.43/25.71 | | | | simplifying with (59), (71) gives: % 95.43/25.71 | | | | (104) all_155_1 = all_127_1 % 95.43/25.71 | | | | % 95.43/25.71 | | | | GROUND_INST: instantiating (16) with all_127_0, all_131_0, all_49_6, % 95.43/25.71 | | | | simplifying with (60), (64) gives: % 95.43/25.71 | | | | (105) all_131_0 = all_127_0 % 95.43/25.71 | | | | % 95.43/25.71 | | | | GROUND_INST: instantiating (16) with all_131_0, all_147_0, all_49_6, % 95.43/25.71 | | | | simplifying with (64), (68) gives: % 95.43/25.71 | | | | (106) all_147_0 = all_131_0 % 95.43/25.71 | | | | % 95.43/25.71 | | | | GROUND_INST: instantiating (16) with all_147_0, all_155_0, all_49_6, % 95.43/25.71 | | | | simplifying with (68), (72) gives: % 95.43/25.71 | | | | (107) all_155_0 = all_147_0 % 95.43/25.71 | | | | % 95.43/25.71 | | | | GROUND_INST: instantiating (16) with all_83_1, all_155_0, all_49_6, % 95.43/25.71 | | | | simplifying with (57), (72) gives: % 95.43/25.71 | | | | (108) all_155_0 = all_83_1 % 95.43/25.71 | | | | % 95.43/25.71 | | | | COMBINE_EQS: (107), (108) imply: % 95.43/25.71 | | | | (109) all_147_0 = all_83_1 % 95.43/25.71 | | | | % 95.43/25.71 | | | | SIMP: (109) implies: % 95.43/25.71 | | | | (110) all_147_0 = all_83_1 % 95.43/25.71 | | | | % 95.43/25.71 | | | | COMBINE_EQS: (103), (104) imply: % 95.43/25.71 | | | | (111) all_127_1 = 0 % 95.43/25.71 | | | | % 95.43/25.71 | | | | SIMP: (111) implies: % 95.43/25.71 | | | | (112) all_127_1 = 0 % 95.43/25.71 | | | | % 95.43/25.71 | | | | COMBINE_EQS: (106), (110) imply: % 95.43/25.71 | | | | (113) all_131_0 = all_83_1 % 95.43/25.71 | | | | % 95.43/25.71 | | | | SIMP: (113) implies: % 95.43/25.71 | | | | (114) all_131_0 = all_83_1 % 95.43/25.71 | | | | % 95.43/25.71 | | | | COMBINE_EQS: (100), (101) imply: % 95.43/25.71 | | | | (115) all_131_1 = 0 % 95.43/25.71 | | | | % 95.43/25.71 | | | | COMBINE_EQS: (105), (114) imply: % 95.43/25.71 | | | | (116) all_127_0 = all_83_1 % 95.43/25.71 | | | | % 95.43/25.71 | | | | SIMP: (116) implies: % 95.43/25.71 | | | | (117) all_127_0 = all_83_1 % 95.43/25.71 | | | | % 95.43/25.71 | | | | BETA: splitting (65) gives: % 95.43/25.71 | | | | % 95.43/25.71 | | | | Case 1: % 95.43/25.71 | | | | | % 95.43/25.71 | | | | | (118) ~ (all_131_1 = 0) % 95.43/25.71 | | | | | % 95.43/25.71 | | | | | REDUCE: (115), (118) imply: % 95.43/25.71 | | | | | (119) $false % 95.43/25.71 | | | | | % 95.43/25.71 | | | | | CLOSE: (119) is inconsistent. % 95.43/25.71 | | | | | % 95.43/25.71 | | | | Case 2: % 95.43/25.71 | | | | | % 95.43/25.71 | | | | | (120) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! % 95.43/25.71 | | | | | [v4: $i] : (v3 = 0 | ~ (relation_image(all_49_6, v0) = v1) | % 95.43/25.71 | | | | | ~ (apply(all_49_6, v4) = v2) | ~ (in(v2, v1) = v3) | ~ % 95.43/25.71 | | | | | $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : % 95.43/25.71 | | | | | ? [v6: any] : (in(v4, v0) = v6 & in(v4, all_131_0) = v5 & % 95.43/25.71 | | | | | ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] % 95.43/25.71 | | | | | : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ % 95.43/25.71 | | | | | (relation_image(all_49_6, v0) = v1) | ~ (in(v4, v0) = 0) | % 95.43/25.71 | | | | | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | % 95.43/25.71 | | | | | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : (apply(all_49_6, % 95.43/25.71 | | | | | v4) = v6 & in(v4, all_131_0) = v5 & $i(v6) & ( ~ (v6 = % 95.43/25.71 | | | | | v2) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 95.43/25.71 | | | | | [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ % 95.43/25.71 | | | | | (relation_image(all_49_6, v0) = v1) | ~ (in(v4, all_131_0) % 95.43/25.71 | | | | | = 0) | ~ (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 95.43/25.71 | | | | | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : % 95.43/25.71 | | | | | (apply(all_49_6, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( ~ % 95.43/25.71 | | | | | (v6 = v2) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] % 95.43/25.71 | | | | | : ! [v2: $i] : ( ~ (relation_image(all_49_6, v0) = v1) | ~ % 95.43/25.71 | | | | | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 95.43/25.71 | | | | | [v3: $i] : (apply(all_49_6, v3) = v2 & in(v3, v0) = 0 & % 95.43/25.71 | | | | | in(v3, all_131_0) = 0 & $i(v3))) & ? [v0: $i] : ! [v1: % 95.43/25.71 | | | | | $i] : ! [v2: $i] : (v2 = v0 | ~ (relation_image(all_49_6, % 95.43/25.71 | | | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 95.43/25.71 | | | | | [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? % 95.43/25.71 | | | | | [v8: $i] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ (v4 = % 95.43/25.71 | | | | | 0) | ( ! [v9: $i] : ( ~ (apply(all_49_6, v9) = v3) | % 95.43/25.71 | | | | | ~ $i(v9) | ? [v10: any] : ? [v11: any] : (in(v9, % 95.43/25.71 | | | | | v1) = v11 & in(v9, all_131_0) = v10 & ( ~ (v11 % 95.43/25.71 | | | | | = 0) | ~ (v10 = 0)))) & ! [v9: $i] : ( ~ % 95.43/25.71 | | | | | (in(v9, v1) = 0) | ~ $i(v9) | ? [v10: any] : ? % 95.43/25.71 | | | | | [v11: $i] : (apply(all_49_6, v9) = v11 & in(v9, % 95.43/25.71 | | | | | all_131_0) = v10 & $i(v11) & ( ~ (v11 = v3) | % 95.43/25.71 | | | | | ~ (v10 = 0)))) & ! [v9: $i] : ( ~ (in(v9, % 95.43/25.71 | | | | | all_131_0) = 0) | ~ $i(v9) | ? [v10: any] : % 95.43/25.71 | | | | | ? [v11: $i] : (apply(all_49_6, v9) = v11 & in(v9, % 95.43/25.71 | | | | | v1) = v10 & $i(v11) & ( ~ (v11 = v3) | ~ (v10 % 95.43/25.71 | | | | | = 0)))))) & (v4 = 0 | (v8 = v3 & v7 = 0 & v6 % 95.43/25.71 | | | | | = 0 & apply(all_49_6, v5) = v3 & in(v5, v1) = 0 & % 95.43/25.71 | | | | | in(v5, all_131_0) = 0)))) % 95.43/25.71 | | | | | % 95.43/25.71 | | | | | ALPHA: (120) implies: % 95.43/25.72 | | | | | (121) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 95.43/25.72 | | | | | (relation_image(all_49_6, v0) = v1) | ~ (in(v2, v1) = 0) | % 95.43/25.72 | | | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 95.43/25.72 | | | | | (apply(all_49_6, v3) = v2 & in(v3, v0) = 0 & in(v3, % 95.43/25.72 | | | | | all_131_0) = 0 & $i(v3))) % 95.43/25.72 | | | | | (122) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 95.43/25.72 | | | | | (relation_image(all_49_6, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 95.43/25.72 | | | | | | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : % 95.43/25.72 | | | | | ? [v7: int] : ? [v8: $i] : (in(v3, v0) = v4 & $i(v5) & % 95.43/25.72 | | | | | $i(v3) & ( ~ (v4 = 0) | ( ! [v9: $i] : ( ~ % 95.43/25.72 | | | | | (apply(all_49_6, v9) = v3) | ~ $i(v9) | ? [v10: % 95.43/25.72 | | | | | any] : ? [v11: any] : (in(v9, v1) = v11 & in(v9, % 95.43/25.72 | | | | | all_131_0) = v10 & ( ~ (v11 = 0) | ~ (v10 = % 95.43/25.72 | | | | | 0)))) & ! [v9: $i] : ( ~ (in(v9, v1) = 0) | % 95.43/25.72 | | | | | ~ $i(v9) | ? [v10: any] : ? [v11: $i] : % 95.43/25.72 | | | | | (apply(all_49_6, v9) = v11 & in(v9, all_131_0) = % 95.43/25.72 | | | | | v10 & $i(v11) & ( ~ (v11 = v3) | ~ (v10 = 0)))) % 95.43/25.72 | | | | | & ! [v9: $i] : ( ~ (in(v9, all_131_0) = 0) | ~ % 95.43/25.72 | | | | | $i(v9) | ? [v10: any] : ? [v11: $i] : % 95.43/25.72 | | | | | (apply(all_49_6, v9) = v11 & in(v9, v1) = v10 & % 95.43/25.72 | | | | | $i(v11) & ( ~ (v11 = v3) | ~ (v10 = 0)))))) & % 95.43/25.72 | | | | | (v4 = 0 | (v8 = v3 & v7 = 0 & v6 = 0 & apply(all_49_6, % 95.43/25.72 | | | | | v5) = v3 & in(v5, v1) = 0 & in(v5, all_131_0) = % 95.43/25.72 | | | | | 0)))) % 95.43/25.72 | | | | | % 95.43/25.72 | | | | | DELTA: instantiating (122) with fresh symbol all_256_0 gives: % 95.43/25.72 | | | | | (123) ! [v0: $i] : ! [v1: int] : (v1 = all_256_0 | ~ % 95.43/25.72 | | | | | (relation_image(all_49_6, v0) = v1) | ~ $i(v0) | ~ % 95.43/25.72 | | | | | $i(all_256_0) | ? [v2: $i] : ? [v3: any] : ? [v4: $i] : % 95.43/25.72 | | | | | ? [v5: int] : ? [v6: int] : ? [v7: $i] : (in(v2, % 95.43/25.72 | | | | | all_256_0) = v3 & $i(v4) & $i(v2) & ( ~ (v3 = 0) | ( ! % 95.43/25.72 | | | | | [v8: $i] : ( ~ (apply(all_49_6, v8) = v2) | ~ $i(v8) % 95.43/25.72 | | | | | | ? [v9: any] : ? [v10: any] : (in(v8, v0) = v10 % 95.43/25.72 | | | | | & in(v8, all_131_0) = v9 & ( ~ (v10 = 0) | ~ (v9 % 95.43/25.72 | | | | | = 0)))) & ! [v8: $i] : ( ~ (in(v8, v0) = 0) % 95.43/25.72 | | | | | | ~ $i(v8) | ? [v9: any] : ? [v10: $i] : % 95.43/25.72 | | | | | (apply(all_49_6, v8) = v10 & in(v8, all_131_0) = v9 % 95.43/25.72 | | | | | & $i(v10) & ( ~ (v10 = v2) | ~ (v9 = 0)))) & ! % 95.43/25.72 | | | | | [v8: $i] : ( ~ (in(v8, all_131_0) = 0) | ~ $i(v8) | % 95.43/25.72 | | | | | ? [v9: any] : ? [v10: $i] : (apply(all_49_6, v8) = % 95.43/25.72 | | | | | v10 & in(v8, v0) = v9 & $i(v10) & ( ~ (v10 = v2) % 95.43/25.72 | | | | | | ~ (v9 = 0)))))) & (v3 = 0 | (v7 = v2 & v6 = % 95.43/25.72 | | | | | 0 & v5 = 0 & apply(all_49_6, v4) = v2 & in(v4, v0) = % 95.43/25.72 | | | | | 0 & in(v4, all_131_0) = 0)))) % 95.43/25.72 | | | | | % 95.43/25.72 | | | | | GROUND_INST: instantiating (123) with all_49_8, all_49_2, simplifying % 95.43/25.72 | | | | | with (28), (38) gives: % 95.43/25.72 | | | | | (124) all_256_0 = all_49_2 | ~ $i(all_256_0) | ? [v0: $i] : ? % 95.43/25.72 | | | | | [v1: any] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ? % 95.43/25.72 | | | | | [v5: $i] : (in(v0, all_256_0) = v1 & $i(v2) & $i(v0) & ( ~ % 95.43/25.72 | | | | | (v1 = 0) | ( ! [v6: $i] : ( ~ (apply(all_49_6, v6) = v0) % 95.43/25.72 | | | | | | ~ $i(v6) | ? [v7: any] : ? [v8: any] : (in(v6, % 95.43/25.72 | | | | | all_131_0) = v7 & in(v6, all_49_8) = v8 & ( ~ (v8 % 95.43/25.72 | | | | | = 0) | ~ (v7 = 0)))) & ! [v6: $i] : ( ~ % 95.43/25.72 | | | | | (in(v6, all_131_0) = 0) | ~ $i(v6) | ? [v7: any] : % 95.43/25.72 | | | | | ? [v8: $i] : (apply(all_49_6, v6) = v8 & in(v6, % 95.43/25.72 | | | | | all_49_8) = v7 & $i(v8) & ( ~ (v8 = v0) | ~ (v7 % 95.43/25.72 | | | | | = 0)))) & ! [v6: $i] : ( ~ (in(v6, all_49_8) = % 95.43/25.72 | | | | | 0) | ~ $i(v6) | ? [v7: any] : ? [v8: $i] : % 95.43/25.72 | | | | | (apply(all_49_6, v6) = v8 & in(v6, all_131_0) = v7 & % 95.43/25.72 | | | | | $i(v8) & ( ~ (v8 = v0) | ~ (v7 = 0)))))) & (v1 = 0 % 95.43/25.72 | | | | | | (v5 = v0 & v4 = 0 & v3 = 0 & apply(all_49_6, v2) = v0 & % 95.43/25.72 | | | | | in(v2, all_131_0) = 0 & in(v2, all_49_8) = 0))) % 95.43/25.72 | | | | | % 95.43/25.72 | | | | | GROUND_INST: instantiating (123) with all_49_4, all_49_3, simplifying % 95.43/25.72 | | | | | with (39), (50) gives: % 95.43/25.72 | | | | | (125) all_256_0 = all_49_3 | ~ $i(all_256_0) | ? [v0: $i] : ? % 95.43/25.72 | | | | | [v1: any] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ? % 95.43/25.72 | | | | | [v5: $i] : (in(v0, all_256_0) = v1 & $i(v2) & $i(v0) & ( ~ % 95.43/25.72 | | | | | (v1 = 0) | ( ! [v6: $i] : ( ~ (apply(all_49_6, v6) = v0) % 95.43/25.72 | | | | | | ~ $i(v6) | ? [v7: any] : ? [v8: any] : (in(v6, % 95.43/25.72 | | | | | all_131_0) = v7 & in(v6, all_49_4) = v8 & ( ~ (v8 % 95.43/25.72 | | | | | = 0) | ~ (v7 = 0)))) & ! [v6: $i] : ( ~ % 95.43/25.72 | | | | | (in(v6, all_131_0) = 0) | ~ $i(v6) | ? [v7: any] : % 95.43/25.72 | | | | | ? [v8: $i] : (apply(all_49_6, v6) = v8 & in(v6, % 95.43/25.72 | | | | | all_49_4) = v7 & $i(v8) & ( ~ (v8 = v0) | ~ (v7 % 95.43/25.72 | | | | | = 0)))) & ! [v6: $i] : ( ~ (in(v6, all_49_4) = % 95.43/25.72 | | | | | 0) | ~ $i(v6) | ? [v7: any] : ? [v8: $i] : % 95.43/25.72 | | | | | (apply(all_49_6, v6) = v8 & in(v6, all_131_0) = v7 & % 95.43/25.72 | | | | | $i(v8) & ( ~ (v8 = v0) | ~ (v7 = 0)))))) & (v1 = 0 % 95.43/25.72 | | | | | | (v5 = v0 & v4 = 0 & v3 = 0 & apply(all_49_6, v2) = v0 & % 95.43/25.72 | | | | | in(v2, all_131_0) = 0 & in(v2, all_49_4) = 0))) % 95.43/25.72 | | | | | % 95.43/25.72 | | | | | BETA: splitting (61) gives: % 95.43/25.72 | | | | | % 95.43/25.72 | | | | | Case 1: % 95.43/25.72 | | | | | | % 95.43/25.72 | | | | | | (126) ~ (all_127_1 = 0) % 95.43/25.72 | | | | | | % 95.43/25.72 | | | | | | REDUCE: (112), (126) imply: % 95.43/25.72 | | | | | | (127) $false % 95.43/25.72 | | | | | | % 95.43/25.72 | | | | | | CLOSE: (127) is inconsistent. % 95.43/25.72 | | | | | | % 95.43/25.72 | | | | | Case 2: % 95.43/25.72 | | | | | | % 95.68/25.73 | | | | | | (128) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! % 95.68/25.73 | | | | | | [v4: $i] : (v3 = 0 | ~ (relation_image(all_49_6, v0) = v1) % 95.68/25.73 | | | | | | | ~ (apply(all_49_6, v4) = v2) | ~ (in(v2, v1) = v3) | % 95.68/25.73 | | | | | | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 95.68/25.73 | | | | | | any] : ? [v6: any] : (in(v4, v0) = v6 & in(v4, % 95.68/25.73 | | | | | | all_127_0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! % 95.68/25.73 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! % 95.68/25.73 | | | | | | [v4: $i] : (v3 = 0 | ~ (relation_image(all_49_6, v0) = v1) % 95.68/25.73 | | | | | | | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v4) % 95.68/25.73 | | | | | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 95.68/25.73 | | | | | | [v6: $i] : (apply(all_49_6, v4) = v6 & in(v4, all_127_0) % 95.68/25.73 | | | | | | = v5 & $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0)))) & ! % 95.68/25.73 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! % 95.68/25.73 | | | | | | [v4: $i] : (v3 = 0 | ~ (relation_image(all_49_6, v0) = v1) % 95.68/25.73 | | | | | | | ~ (in(v4, all_127_0) = 0) | ~ (in(v2, v1) = v3) | ~ % 95.68/25.73 | | | | | | $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] % 95.68/25.73 | | | | | | : ? [v6: $i] : (apply(all_49_6, v4) = v6 & in(v4, v0) = % 95.68/25.73 | | | | | | v5 & $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0)))) & ! [v0: % 95.68/25.73 | | | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 95.68/25.73 | | | | | | (relation_image(all_49_6, v0) = v1) | ~ (in(v2, v1) = 0) % 95.68/25.73 | | | | | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 95.68/25.73 | | | | | | (apply(all_49_6, v3) = v2 & in(v3, v0) = 0 & in(v3, % 95.68/25.73 | | | | | | all_127_0) = 0 & $i(v3))) & ? [v0: $i] : ! [v1: $i] % 95.68/25.73 | | | | | | : ! [v2: $i] : (v2 = v0 | ~ (relation_image(all_49_6, v1) % 95.68/25.73 | | | | | | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 95.68/25.73 | | | | | | any] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? % 95.68/25.73 | | | | | | [v8: $i] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ (v4 = % 95.68/25.73 | | | | | | 0) | ( ! [v9: $i] : ( ~ (apply(all_49_6, v9) = v3) % 95.68/25.73 | | | | | | | ~ $i(v9) | ? [v10: any] : ? [v11: any] : % 95.68/25.73 | | | | | | (in(v9, v1) = v11 & in(v9, all_127_0) = v10 & ( ~ % 95.68/25.73 | | | | | | (v11 = 0) | ~ (v10 = 0)))) & ! [v9: $i] : ( % 95.68/25.73 | | | | | | ~ (in(v9, v1) = 0) | ~ $i(v9) | ? [v10: any] : % 95.68/25.73 | | | | | | ? [v11: $i] : (apply(all_49_6, v9) = v11 & in(v9, % 95.68/25.73 | | | | | | all_127_0) = v10 & $i(v11) & ( ~ (v11 = v3) | % 95.68/25.73 | | | | | | ~ (v10 = 0)))) & ! [v9: $i] : ( ~ (in(v9, % 95.68/25.73 | | | | | | all_127_0) = 0) | ~ $i(v9) | ? [v10: any] : % 95.68/25.73 | | | | | | ? [v11: $i] : (apply(all_49_6, v9) = v11 & % 95.68/25.73 | | | | | | in(v9, v1) = v10 & $i(v11) & ( ~ (v11 = v3) | % 95.68/25.73 | | | | | | ~ (v10 = 0)))))) & (v4 = 0 | (v8 = v3 & v7 = % 95.68/25.73 | | | | | | 0 & v6 = 0 & apply(all_49_6, v5) = v3 & in(v5, v1) % 95.68/25.73 | | | | | | = 0 & in(v5, all_127_0) = 0)))) % 95.68/25.73 | | | | | | % 95.68/25.73 | | | | | | ALPHA: (128) implies: % 95.68/25.73 | | | | | | (129) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 95.68/25.73 | | | | | | (relation_image(all_49_6, v0) = v1) | ~ (in(v2, v1) = 0) % 95.68/25.73 | | | | | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 95.68/25.73 | | | | | | (apply(all_49_6, v3) = v2 & in(v3, v0) = 0 & in(v3, % 95.68/25.73 | | | | | | all_127_0) = 0 & $i(v3))) % 95.68/25.73 | | | | | | (130) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! % 95.68/25.73 | | | | | | [v4: $i] : (v3 = 0 | ~ (relation_image(all_49_6, v0) = v1) % 95.68/25.73 | | | | | | | ~ (apply(all_49_6, v4) = v2) | ~ (in(v2, v1) = v3) | % 95.68/25.73 | | | | | | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 95.68/25.73 | | | | | | any] : ? [v6: any] : (in(v4, v0) = v6 & in(v4, % 95.68/25.73 | | | | | | all_127_0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 95.68/25.73 | | | | | | % 95.68/25.73 | | | | | | BETA: splitting (69) gives: % 95.68/25.73 | | | | | | % 95.68/25.73 | | | | | | Case 1: % 95.68/25.73 | | | | | | | % 95.68/25.73 | | | | | | | (131) ~ (all_147_1 = 0) % 95.68/25.73 | | | | | | | % 95.68/25.73 | | | | | | | REDUCE: (100), (131) imply: % 95.68/25.73 | | | | | | | (132) $false % 95.68/25.73 | | | | | | | % 95.68/25.73 | | | | | | | CLOSE: (132) is inconsistent. % 95.68/25.73 | | | | | | | % 95.68/25.73 | | | | | | Case 2: % 95.68/25.73 | | | | | | | % 95.68/25.74 | | | | | | | (133) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : % 95.68/25.74 | | | | | | | (v3 = 0 | ~ (relation_inverse_image(all_49_6, v0) = v1) % 95.68/25.74 | | | | | | | | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 95.68/25.74 | | | | | | | $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 95.68/25.74 | | | | | | | (apply(all_49_6, v2) = v5 & in(v5, v0) = v6 & in(v2, % 95.68/25.74 | | | | | | | all_147_0) = v4 & $i(v5) & ( ~ (v6 = 0) | ~ (v4 = % 95.68/25.74 | | | | | | | 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 95.68/25.74 | | | | | | | ! [v3: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = % 95.68/25.74 | | | | | | | v1) | ~ (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ % 95.68/25.74 | | | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 95.68/25.74 | | | | | | | [v6: any] : (in(v3, v0) = v6 & in(v2, v1) = v4 & in(v2, % 95.68/25.74 | | | | | | | all_147_0) = v5 & ( ~ (v4 = 0) | (v6 = 0 & v5 = % 95.68/25.74 | | | | | | | 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 95.68/25.74 | | | | | | | ! [v3: $i] : ( ~ (relation_inverse_image(all_49_6, v0) = % 95.68/25.74 | | | | | | | v1) | ~ (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ % 95.68/25.74 | | | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 95.68/25.74 | | | | | | | [v6: any] : (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, % 95.68/25.74 | | | | | | | all_147_0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = % 95.68/25.74 | | | | | | | 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 95.68/25.74 | | | | | | | [v3: any] : ( ~ (relation_inverse_image(all_49_6, v0) = % 95.68/25.74 | | | | | | | v1) | ~ (in(v2, all_147_0) = v3) | ~ $i(v2) | ~ % 95.68/25.74 | | | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? % 95.68/25.74 | | | | | | | [v6: any] : (apply(all_49_6, v2) = v5 & in(v5, v0) = v6 % 95.68/25.74 | | | | | | | & in(v2, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | (v6 = 0 & % 95.68/25.74 | | | | | | | v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 95.68/25.74 | | | | | | | $i] : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | % 95.68/25.74 | | | | | | | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 95.68/25.74 | | | | | | | | ? [v3: $i] : (apply(all_49_6, v2) = v3 & in(v3, v0) % 95.68/25.74 | | | | | | | = 0 & in(v2, all_147_0) = 0 & $i(v3))) & ! [v0: $i] % 95.68/25.74 | | | | | | | : ! [v1: $i] : ! [v2: $i] : ( ~ % 95.68/25.74 | | | | | | | (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.68/25.74 | | | | | | | (in(v2, all_147_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 95.68/25.74 | | | | | | | $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 95.68/25.74 | | | | | | | (apply(all_49_6, v2) = v3 & in(v3, v0) = v4 & in(v2, % 95.68/25.74 | | | | | | | v1) = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))) & ? % 95.68/25.74 | | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 95.68/25.74 | | | | | | | (relation_inverse_image(all_49_6, v1) = v2) | ~ $i(v1) % 95.68/25.74 | | | | | | | | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] % 95.68/25.74 | | | | | | | : ? [v6: $i] : ? [v7: any] : (apply(all_49_6, v3) = % 95.68/25.74 | | | | | | | v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, % 95.68/25.74 | | | | | | | all_147_0) = v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | % 95.68/25.74 | | | | | | | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 % 95.68/25.74 | | | | | | | = 0)))) % 95.68/25.74 | | | | | | | % 95.68/25.74 | | | | | | | ALPHA: (133) implies: % 95.68/25.74 | | | | | | | (134) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 95.68/25.74 | | | | | | | ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.68/25.74 | | | | | | | (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 95.68/25.74 | | | | | | | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 95.68/25.74 | | | | | | | (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, all_147_0) % 95.68/25.74 | | | | | | | = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) % 95.68/25.74 | | | | | | | (135) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 95.68/25.74 | | | | | | | ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.68/25.74 | | | | | | | (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 95.68/25.74 | | | | | | | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 95.68/25.74 | | | | | | | (in(v3, v0) = v6 & in(v2, v1) = v4 & in(v2, all_147_0) % 95.68/25.74 | | | | | | | = v5 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) % 95.68/25.74 | | | | | | | % 95.68/25.74 | | | | | | | BETA: splitting (73) gives: % 95.68/25.74 | | | | | | | % 95.68/25.74 | | | | | | | Case 1: % 95.68/25.74 | | | | | | | | % 95.68/25.74 | | | | | | | | (136) ~ (all_155_1 = 0) % 95.68/25.74 | | | | | | | | % 95.68/25.74 | | | | | | | | REDUCE: (103), (136) imply: % 95.68/25.74 | | | | | | | | (137) $false % 95.68/25.74 | | | | | | | | % 95.68/25.74 | | | | | | | | CLOSE: (137) is inconsistent. % 95.68/25.74 | | | | | | | | % 95.68/25.74 | | | | | | | Case 2: % 95.68/25.74 | | | | | | | | % 95.68/25.74 | | | | | | | | (138) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] % 95.68/25.74 | | | | | | | | : (v3 = 0 | ~ (relation_inverse_image(all_49_6, v0) = % 95.68/25.74 | | | | | | | | v1) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 95.68/25.74 | | | | | | | | | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: % 95.68/25.74 | | | | | | | | any] : (apply(all_49_6, v2) = v5 & in(v5, v0) = v6 % 95.68/25.74 | | | | | | | | & in(v2, all_155_0) = v4 & $i(v5) & ( ~ (v6 = 0) | % 95.68/25.74 | | | | | | | | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 95.68/25.74 | | | | | | | | [v2: $i] : ! [v3: $i] : ( ~ % 95.68/25.74 | | | | | | | | (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.68/25.74 | | | | | | | | (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 95.68/25.74 | | | | | | | | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 95.68/25.74 | | | | | | | | : (in(v3, v0) = v6 & in(v2, v1) = v4 & in(v2, % 95.68/25.74 | | | | | | | | all_155_0) = v5 & ( ~ (v4 = 0) | (v6 = 0 & v5 = % 95.68/25.74 | | | | | | | | 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 95.68/25.74 | | | | | | | | : ! [v3: $i] : ( ~ (relation_inverse_image(all_49_6, % 95.68/25.74 | | | | | | | | v0) = v1) | ~ (apply(all_49_6, v2) = v3) | ~ % 95.68/25.74 | | | | | | | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 95.68/25.74 | | | | | | | | [v5: any] : ? [v6: any] : (in(v3, v0) = v5 & in(v2, % 95.68/25.74 | | | | | | | | v1) = v6 & in(v2, all_155_0) = v4 & ( ~ (v5 = 0) % 95.68/25.74 | | | | | | | | | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: % 95.68/25.74 | | | | | | | | $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 95.68/25.74 | | | | | | | | (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.68/25.74 | | | | | | | | (in(v2, all_155_0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 95.68/25.74 | | | | | | | | $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 95.68/25.74 | | | | | | | | (apply(all_49_6, v2) = v5 & in(v5, v0) = v6 & in(v2, % 95.68/25.74 | | | | | | | | v1) = v4 & $i(v5) & ( ~ (v4 = 0) | (v6 = 0 & v3 = % 95.68/25.74 | | | | | | | | 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 95.68/25.74 | | | | | | | | : ( ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.68/25.74 | | | | | | | | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 95.68/25.74 | | | | | | | | | ? [v3: $i] : (apply(all_49_6, v2) = v3 & in(v3, % 95.68/25.74 | | | | | | | | v0) = 0 & in(v2, all_155_0) = 0 & $i(v3))) & ! % 95.68/25.74 | | | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 95.68/25.74 | | | | | | | | (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.68/25.74 | | | | | | | | (in(v2, all_155_0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 95.68/25.74 | | | | | | | | $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 95.68/25.74 | | | | | | | | (apply(all_49_6, v2) = v3 & in(v3, v0) = v4 & in(v2, % 95.68/25.74 | | | | | | | | v1) = v5 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))) & ? % 95.68/25.74 | | | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 95.68/25.74 | | | | | | | | (relation_inverse_image(all_49_6, v1) = v2) | ~ % 95.68/25.74 | | | | | | | | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? % 95.68/25.74 | | | | | | | | [v5: any] : ? [v6: $i] : ? [v7: any] : % 95.68/25.74 | | | | | | | | (apply(all_49_6, v3) = v6 & in(v6, v1) = v7 & in(v3, % 95.68/25.74 | | | | | | | | v0) = v4 & in(v3, all_155_0) = v5 & $i(v6) & % 95.68/25.74 | | | | | | | | $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) % 95.68/25.74 | | | | | | | | & (v4 = 0 | (v7 = 0 & v5 = 0)))) % 95.68/25.74 | | | | | | | | % 95.68/25.74 | | | | | | | | ALPHA: (138) implies: % 95.68/25.74 | | | | | | | | (139) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 95.68/25.74 | | | | | | | | ( ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.68/25.74 | | | | | | | | (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 95.68/25.74 | | | | | | | | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 95.68/25.74 | | | | | | | | : (in(v3, v0) = v5 & in(v2, v1) = v6 & in(v2, % 95.68/25.74 | | | | | | | | all_155_0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 % 95.68/25.74 | | | | | | | | = 0))) % 95.68/25.75 | | | | | | | | (140) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 95.68/25.75 | | | | | | | | ( ~ (relation_inverse_image(all_49_6, v0) = v1) | ~ % 95.68/25.75 | | | | | | | | (apply(all_49_6, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 95.68/25.75 | | | | | | | | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 95.68/25.75 | | | | | | | | : (in(v3, v0) = v6 & in(v2, v1) = v4 & in(v2, % 95.68/25.75 | | | | | | | | all_155_0) = v5 & ( ~ (v4 = 0) | (v6 = 0 & v5 = % 95.68/25.75 | | | | | | | | 0)))) % 95.68/25.75 | | | | | | | | % 95.68/25.75 | | | | | | | | BETA: splitting (76) gives: % 95.68/25.75 | | | | | | | | % 95.68/25.75 | | | | | | | | Case 1: % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | (141) ~ (all_163_1 = 0) % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | REDUCE: (102), (141) imply: % 95.68/25.75 | | | | | | | | | (142) $false % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | CLOSE: (142) is inconsistent. % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | Case 2: % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | GROUND_INST: instantiating (121) with all_49_4, all_49_3, % 95.68/25.75 | | | | | | | | | all_180_1, simplifying with (32), (39), (50), % 95.68/25.75 | | | | | | | | | (82), (83) gives: % 95.68/25.75 | | | | | | | | | (143) ? [v0: $i] : (apply(all_49_6, v0) = all_180_1 & % 95.68/25.75 | | | | | | | | | in(v0, all_131_0) = 0 & in(v0, all_49_4) = 0 & % 95.68/25.75 | | | | | | | | | $i(v0)) % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | GROUND_INST: instantiating (129) with all_49_4, all_49_3, % 95.68/25.75 | | | | | | | | | all_180_1, simplifying with (32), (39), (50), % 95.68/25.75 | | | | | | | | | (82), (83) gives: % 95.68/25.75 | | | | | | | | | (144) ? [v0: $i] : (apply(all_49_6, v0) = all_180_1 & % 95.68/25.75 | | | | | | | | | in(v0, all_127_0) = 0 & in(v0, all_49_4) = 0 & % 95.68/25.75 | | | | | | | | | $i(v0)) % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | GROUND_INST: instantiating (12) with all_200_1, all_200_0, % 95.68/25.75 | | | | | | | | | simplifying with (97), (98) gives: % 95.68/25.75 | | | | | | | | | (145) all_200_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: % 95.68/25.75 | | | | | | | | | int] : ( ~ (v2 = 0) & powerset(all_200_1) = v0 & % 95.68/25.75 | | | | | | | | | element(v1, v0) = 0 & empty(v1) = v2 & $i(v1) & % 95.68/25.75 | | | | | | | | | $i(v0)) % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | GROUND_INST: instantiating (9) with all_49_7, all_49_2, % 95.68/25.75 | | | | | | | | | all_49_1, all_180_1, all_180_0, simplifying with % 95.68/25.75 | | | | | | | | | (29), (33), (52), (53), (82), (84) gives: % 95.68/25.75 | | | | | | | | | (146) all_180_0 = 0 | ? [v0: any] : ? [v1: any] : % 95.68/25.75 | | | | | | | | | (in(all_180_1, all_49_2) = v1 & in(all_180_1, % 95.68/25.75 | | | | | | | | | all_49_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | GROUND_INST: instantiating (fc1_subset_1) with all_32_1, % 95.68/25.75 | | | | | | | | | all_200_2, simplifying with (20), (99) gives: % 95.68/25.75 | | | | | | | | | (147) ? [v0: int] : ( ~ (v0 = 0) & empty(all_200_2) = v0) % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | GROUND_INST: instantiating (fc1_subset_1) with all_49_1, % 95.68/25.75 | | | | | | | | | all_185_1, simplifying with (52), (90) gives: % 95.68/25.75 | | | | | | | | | (148) ? [v0: int] : ( ~ (v0 = 0) & empty(all_185_1) = v0) % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | DELTA: instantiating (148) with fresh symbol all_365_0 gives: % 95.68/25.75 | | | | | | | | | (149) ~ (all_365_0 = 0) & empty(all_185_1) = all_365_0 % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | ALPHA: (149) implies: % 95.68/25.75 | | | | | | | | | (150) ~ (all_365_0 = 0) % 95.68/25.75 | | | | | | | | | (151) empty(all_185_1) = all_365_0 % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | DELTA: instantiating (147) with fresh symbol all_369_0 gives: % 95.68/25.75 | | | | | | | | | (152) ~ (all_369_0 = 0) & empty(all_200_2) = all_369_0 % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | ALPHA: (152) implies: % 95.68/25.75 | | | | | | | | | (153) ~ (all_369_0 = 0) % 95.68/25.75 | | | | | | | | | (154) empty(all_200_2) = all_369_0 % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | DELTA: instantiating (144) with fresh symbol all_385_0 gives: % 95.68/25.75 | | | | | | | | | (155) apply(all_49_6, all_385_0) = all_180_1 & % 95.68/25.75 | | | | | | | | | in(all_385_0, all_127_0) = 0 & in(all_385_0, % 95.68/25.75 | | | | | | | | | all_49_4) = 0 & $i(all_385_0) % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | ALPHA: (155) implies: % 95.68/25.75 | | | | | | | | | (156) $i(all_385_0) % 95.68/25.75 | | | | | | | | | (157) in(all_385_0, all_49_4) = 0 % 95.68/25.75 | | | | | | | | | (158) in(all_385_0, all_127_0) = 0 % 95.68/25.75 | | | | | | | | | (159) apply(all_49_6, all_385_0) = all_180_1 % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | DELTA: instantiating (143) with fresh symbol all_387_0 gives: % 95.68/25.75 | | | | | | | | | (160) apply(all_49_6, all_387_0) = all_180_1 & % 95.68/25.75 | | | | | | | | | in(all_387_0, all_131_0) = 0 & in(all_387_0, % 95.68/25.75 | | | | | | | | | all_49_4) = 0 & $i(all_387_0) % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | ALPHA: (160) implies: % 95.68/25.75 | | | | | | | | | (161) $i(all_387_0) % 95.68/25.75 | | | | | | | | | (162) in(all_387_0, all_49_4) = 0 % 95.68/25.75 | | | | | | | | | (163) in(all_387_0, all_131_0) = 0 % 95.68/25.75 | | | | | | | | | (164) apply(all_49_6, all_387_0) = all_180_1 % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | REDUCE: (114), (163) imply: % 95.68/25.75 | | | | | | | | | (165) in(all_387_0, all_83_1) = 0 % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | REDUCE: (117), (158) imply: % 95.68/25.75 | | | | | | | | | (166) in(all_385_0, all_83_1) = 0 % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | BETA: splitting (145) gives: % 95.68/25.75 | | | | | | | | | % 95.68/25.75 | | | | | | | | | Case 1: % 95.68/25.75 | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | (167) all_200_0 = 0 % 95.68/25.75 | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | REDUCE: (95), (167) imply: % 95.68/25.75 | | | | | | | | | | (168) $false % 95.68/25.75 | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | CLOSE: (168) is inconsistent. % 95.68/25.75 | | | | | | | | | | % 95.68/25.75 | | | | | | | | | Case 2: % 95.68/25.75 | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | (169) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 % 95.68/25.75 | | | | | | | | | | = 0) & powerset(all_200_1) = v0 & element(v1, % 95.68/25.75 | | | | | | | | | | v0) = 0 & empty(v1) = v2 & $i(v1) & $i(v0)) % 95.68/25.75 | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | DELTA: instantiating (169) with fresh symbols all_462_0, % 95.68/25.75 | | | | | | | | | | all_462_1, all_462_2 gives: % 95.68/25.75 | | | | | | | | | | (170) ~ (all_462_0 = 0) & powerset(all_200_1) = % 95.68/25.75 | | | | | | | | | | all_462_2 & element(all_462_1, all_462_2) = 0 & % 95.68/25.75 | | | | | | | | | | empty(all_462_1) = all_462_0 & $i(all_462_1) & % 95.68/25.75 | | | | | | | | | | $i(all_462_2) % 95.68/25.75 | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | ALPHA: (170) implies: % 95.68/25.75 | | | | | | | | | | (171) ~ (all_462_0 = 0) % 95.68/25.75 | | | | | | | | | | (172) $i(all_462_1) % 95.68/25.75 | | | | | | | | | | (173) empty(all_462_1) = all_462_0 % 95.68/25.75 | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | BETA: splitting (146) gives: % 95.68/25.75 | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | Case 1: % 95.68/25.75 | | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | | (174) all_180_0 = 0 % 95.68/25.75 | | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | | REDUCE: (81), (174) imply: % 95.68/25.75 | | | | | | | | | | | (175) $false % 95.68/25.75 | | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | | CLOSE: (175) is inconsistent. % 95.68/25.75 | | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | Case 2: % 95.68/25.75 | | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | | (176) ? [v0: any] : ? [v1: any] : (in(all_180_1, % 95.68/25.75 | | | | | | | | | | | all_49_2) = v1 & in(all_180_1, all_49_7) = v0 % 95.68/25.75 | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 95.68/25.75 | | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | | DELTA: instantiating (176) with fresh symbols all_482_0, % 95.68/25.75 | | | | | | | | | | | all_482_1 gives: % 95.68/25.75 | | | | | | | | | | | (177) in(all_180_1, all_49_2) = all_482_0 & % 95.68/25.75 | | | | | | | | | | | in(all_180_1, all_49_7) = all_482_1 & ( ~ % 95.68/25.75 | | | | | | | | | | | (all_482_0 = 0) | ~ (all_482_1 = 0)) % 95.68/25.75 | | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | | ALPHA: (177) implies: % 95.68/25.75 | | | | | | | | | | | (178) in(all_180_1, all_49_7) = all_482_1 % 95.68/25.75 | | | | | | | | | | | (179) in(all_180_1, all_49_2) = all_482_0 % 95.68/25.75 | | | | | | | | | | | (180) ~ (all_482_0 = 0) | ~ (all_482_1 = 0) % 95.68/25.75 | | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | | BETA: splitting (124) gives: % 95.68/25.75 | | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | | Case 1: % 95.68/25.75 | | | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | | | % 95.68/25.75 | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_49_8, all_49_5, % 95.68/25.75 | | | | | | | | | | | | all_49_4, all_385_0, simplifying with (28), (31), % 95.68/25.75 | | | | | | | | | | | | (36), (50), (156), (157) gives: % 95.68/25.75 | | | | | | | | | | | | (181) in(all_385_0, all_49_5) = 0 & in(all_385_0, % 95.68/25.75 | | | | | | | | | | | | all_49_8) = 0 % 95.68/25.76 | | | | | | | | | | | | % 95.68/25.76 | | | | | | | | | | | | ALPHA: (181) implies: % 95.68/25.76 | | | | | | | | | | | | (182) in(all_385_0, all_49_5) = 0 % 95.68/25.76 | | | | | | | | | | | | % 95.68/25.76 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_49_6, all_83_1, % 95.68/25.76 | | | | | | | | | | | | all_49_8, all_49_2, all_180_1, all_482_0, % 95.68/25.76 | | | | | | | | | | | | all_385_0, simplifying with (28), (30), (33), % 95.68/25.76 | | | | | | | | | | | | (38), (57), (82), (156), (166), (179) gives: % 95.68/25.76 | | | | | | | | | | | | (183) all_482_0 = 0 | ? [v0: any] : ? [v1: any] : % 95.68/25.76 | | | | | | | | | | | | ((apply(all_49_6, all_385_0) = v1 & in(all_385_0, % 95.68/25.76 | | | | | | | | | | | | all_49_8) = v0 & $i(v1) & ( ~ (v1 = % 95.68/25.76 | | | | | | | | | | | | all_180_1) | ~ (v0 = 0))) | % 95.68/25.76 | | | | | | | | | | | | (relation(all_49_6) = v0 & function(all_49_6) = % 95.68/25.76 | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 95.68/25.76 | | | | | | | | | | | | % 95.68/25.76 | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_49_8, all_49_5, % 95.68/25.76 | | | | | | | | | | | | all_49_4, all_387_0, simplifying with (28), (31), % 95.68/25.76 | | | | | | | | | | | | (36), (50), (161), (162) gives: % 95.68/25.76 | | | | | | | | | | | | (184) in(all_387_0, all_49_5) = 0 & in(all_387_0, % 95.68/25.76 | | | | | | | | | | | | all_49_8) = 0 % 95.68/25.76 | | | | | | | | | | | | % 95.68/25.76 | | | | | | | | | | | | ALPHA: (184) implies: % 95.68/25.76 | | | | | | | | | | | | (185) in(all_387_0, all_49_8) = 0 % 95.68/25.76 | | | | | | | | | | | | % 95.68/25.76 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_185_1, all_365_0, % 95.68/25.76 | | | | | | | | | | | | simplifying with (89), (151) gives: % 95.68/25.76 | | | | | | | | | | | | (186) all_365_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 95.68/25.76 | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & powerset(all_185_1) = % 95.68/25.76 | | | | | | | | | | | | v0 & element(v1, v0) = 0 & empty(v1) = v2 & % 95.68/25.76 | | | | | | | | | | | | $i(v1) & $i(v0)) % 95.68/25.76 | | | | | | | | | | | | % 95.68/25.76 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_200_2, all_369_0, % 95.68/25.76 | | | | | | | | | | | | simplifying with (96), (154) gives: % 95.68/25.76 | | | | | | | | | | | | (187) all_369_0 = 0 | ? [v0: any] : ? [v1: $i] : ? % 95.68/25.76 | | | | | | | | | | | | [v2: any] : (relation_dom(all_200_2) = v1 & % 95.68/25.76 | | | | | | | | | | | | relation(all_200_2) = v0 & empty(v1) = v2 & % 95.68/25.76 | | | | | | | | | | | | $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) % 95.68/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | GROUND_INST: instantiating (140) with all_49_7, all_49_5, % 95.82/25.76 | | | | | | | | | | | | all_385_0, all_180_1, simplifying with (29), (31), % 95.82/25.76 | | | | | | | | | | | | (40), (156), (159) gives: % 95.82/25.76 | | | | | | | | | | | | (188) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 95.82/25.76 | | | | | | | | | | | | (in(all_385_0, all_155_0) = v1 & in(all_385_0, % 95.82/25.76 | | | | | | | | | | | | all_49_5) = v0 & in(all_180_1, all_49_7) = v2 % 95.82/25.76 | | | | | | | | | | | | & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | GROUND_INST: instantiating (130) with all_49_8, all_49_2, % 95.82/25.76 | | | | | | | | | | | | all_180_1, all_482_0, all_387_0, simplifying with % 95.82/25.76 | | | | | | | | | | | | (28), (33), (38), (82), (161), (164), (179) gives: % 95.82/25.76 | | | | | | | | | | | | (189) all_482_0 = 0 | ? [v0: any] : ? [v1: any] : % 95.82/25.76 | | | | | | | | | | | | (in(all_387_0, all_127_0) = v0 & in(all_387_0, % 95.82/25.76 | | | | | | | | | | | | all_49_8) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | GROUND_INST: instantiating (140) with all_49_7, all_49_5, % 95.82/25.76 | | | | | | | | | | | | all_387_0, all_180_1, simplifying with (29), (31), % 95.82/25.76 | | | | | | | | | | | | (40), (161), (164) gives: % 95.82/25.76 | | | | | | | | | | | | (190) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 95.82/25.76 | | | | | | | | | | | | (in(all_387_0, all_155_0) = v1 & in(all_387_0, % 95.82/25.76 | | | | | | | | | | | | all_49_5) = v0 & in(all_180_1, all_49_7) = v2 % 95.82/25.76 | | | | | | | | | | | | & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | GROUND_INST: instantiating (135) with all_49_7, all_49_5, % 95.82/25.76 | | | | | | | | | | | | all_387_0, all_180_1, simplifying with (29), (31), % 95.82/25.76 | | | | | | | | | | | | (40), (161), (164) gives: % 95.82/25.76 | | | | | | | | | | | | (191) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 95.82/25.76 | | | | | | | | | | | | (in(all_387_0, all_147_0) = v1 & in(all_387_0, % 95.82/25.76 | | | | | | | | | | | | all_49_5) = v0 & in(all_180_1, all_49_7) = v2 % 95.82/25.76 | | | | | | | | | | | | & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | GROUND_INST: instantiating (139) with all_49_7, all_49_5, % 95.82/25.76 | | | | | | | | | | | | all_387_0, all_180_1, simplifying with (29), (31), % 95.82/25.76 | | | | | | | | | | | | (40), (161), (164) gives: % 95.82/25.76 | | | | | | | | | | | | (192) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 95.82/25.76 | | | | | | | | | | | | (in(all_387_0, all_155_0) = v0 & in(all_387_0, % 95.82/25.76 | | | | | | | | | | | | all_49_5) = v2 & in(all_180_1, all_49_7) = v1 % 95.82/25.76 | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | GROUND_INST: instantiating (134) with all_49_7, all_49_5, % 95.82/25.76 | | | | | | | | | | | | all_387_0, all_180_1, simplifying with (29), (31), % 95.82/25.76 | | | | | | | | | | | | (40), (161), (164) gives: % 95.82/25.76 | | | | | | | | | | | | (193) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 95.82/25.76 | | | | | | | | | | | | (in(all_387_0, all_147_0) = v0 & in(all_387_0, % 95.82/25.76 | | | | | | | | | | | | all_49_5) = v2 & in(all_180_1, all_49_7) = v1 % 95.82/25.76 | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | DELTA: instantiating (193) with fresh symbols all_911_0, % 95.82/25.76 | | | | | | | | | | | | all_911_1, all_911_2 gives: % 95.82/25.76 | | | | | | | | | | | | (194) in(all_387_0, all_147_0) = all_911_2 & % 95.82/25.76 | | | | | | | | | | | | in(all_387_0, all_49_5) = all_911_0 & % 95.82/25.76 | | | | | | | | | | | | in(all_180_1, all_49_7) = all_911_1 & ( ~ % 95.82/25.76 | | | | | | | | | | | | (all_911_1 = 0) | ~ (all_911_2 = 0) | all_911_0 % 95.82/25.76 | | | | | | | | | | | | = 0) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | ALPHA: (194) implies: % 95.82/25.76 | | | | | | | | | | | | (195) in(all_387_0, all_147_0) = all_911_2 % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | DELTA: instantiating (191) with fresh symbols all_913_0, % 95.82/25.76 | | | | | | | | | | | | all_913_1, all_913_2 gives: % 95.82/25.76 | | | | | | | | | | | | (196) in(all_387_0, all_147_0) = all_913_1 & % 95.82/25.76 | | | | | | | | | | | | in(all_387_0, all_49_5) = all_913_2 & % 95.82/25.76 | | | | | | | | | | | | in(all_180_1, all_49_7) = all_913_0 & ( ~ % 95.82/25.76 | | | | | | | | | | | | (all_913_2 = 0) | (all_913_0 = 0 & all_913_1 = % 95.82/25.76 | | | | | | | | | | | | 0)) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | ALPHA: (196) implies: % 95.82/25.76 | | | | | | | | | | | | (197) in(all_387_0, all_147_0) = all_913_1 % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | DELTA: instantiating (190) with fresh symbols all_915_0, % 95.82/25.76 | | | | | | | | | | | | all_915_1, all_915_2 gives: % 95.82/25.76 | | | | | | | | | | | | (198) in(all_387_0, all_155_0) = all_915_1 & % 95.82/25.76 | | | | | | | | | | | | in(all_387_0, all_49_5) = all_915_2 & % 95.82/25.76 | | | | | | | | | | | | in(all_180_1, all_49_7) = all_915_0 & ( ~ % 95.82/25.76 | | | | | | | | | | | | (all_915_2 = 0) | (all_915_0 = 0 & all_915_1 = % 95.82/25.76 | | | | | | | | | | | | 0)) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | ALPHA: (198) implies: % 95.82/25.76 | | | | | | | | | | | | (199) in(all_387_0, all_155_0) = all_915_1 % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | DELTA: instantiating (192) with fresh symbols all_919_0, % 95.82/25.76 | | | | | | | | | | | | all_919_1, all_919_2 gives: % 95.82/25.76 | | | | | | | | | | | | (200) in(all_387_0, all_155_0) = all_919_2 & % 95.82/25.76 | | | | | | | | | | | | in(all_387_0, all_49_5) = all_919_0 & % 95.82/25.76 | | | | | | | | | | | | in(all_180_1, all_49_7) = all_919_1 & ( ~ % 95.82/25.76 | | | | | | | | | | | | (all_919_1 = 0) | ~ (all_919_2 = 0) | all_919_0 % 95.82/25.76 | | | | | | | | | | | | = 0) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | ALPHA: (200) implies: % 95.82/25.76 | | | | | | | | | | | | (201) in(all_387_0, all_155_0) = all_919_2 % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | DELTA: instantiating (188) with fresh symbols all_923_0, % 95.82/25.76 | | | | | | | | | | | | all_923_1, all_923_2 gives: % 95.82/25.76 | | | | | | | | | | | | (202) in(all_385_0, all_155_0) = all_923_1 & % 95.82/25.76 | | | | | | | | | | | | in(all_385_0, all_49_5) = all_923_2 & % 95.82/25.76 | | | | | | | | | | | | in(all_180_1, all_49_7) = all_923_0 & ( ~ % 95.82/25.76 | | | | | | | | | | | | (all_923_2 = 0) | (all_923_0 = 0 & all_923_1 = % 95.82/25.76 | | | | | | | | | | | | 0)) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | ALPHA: (202) implies: % 95.82/25.76 | | | | | | | | | | | | (203) in(all_180_1, all_49_7) = all_923_0 % 95.82/25.76 | | | | | | | | | | | | (204) in(all_385_0, all_49_5) = all_923_2 % 95.82/25.76 | | | | | | | | | | | | (205) ~ (all_923_2 = 0) | (all_923_0 = 0 & all_923_1 = % 95.82/25.76 | | | | | | | | | | | | 0) % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | REDUCE: (108), (201) imply: % 95.82/25.76 | | | | | | | | | | | | (206) in(all_387_0, all_83_1) = all_919_2 % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | REDUCE: (108), (199) imply: % 95.82/25.76 | | | | | | | | | | | | (207) in(all_387_0, all_83_1) = all_915_1 % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | REDUCE: (110), (197) imply: % 95.82/25.76 | | | | | | | | | | | | (208) in(all_387_0, all_83_1) = all_913_1 % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | REDUCE: (110), (195) imply: % 95.82/25.76 | | | | | | | | | | | | (209) in(all_387_0, all_83_1) = all_911_2 % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | BETA: splitting (183) gives: % 95.82/25.76 | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | Case 1: % 95.82/25.76 | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | (210) all_482_0 = 0 % 95.82/25.76 | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | BETA: splitting (187) gives: % 95.82/25.76 | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | Case 1: % 95.82/25.76 | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | (211) all_369_0 = 0 % 95.82/25.76 | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | REDUCE: (153), (211) imply: % 95.82/25.76 | | | | | | | | | | | | | | (212) $false % 95.82/25.76 | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | CLOSE: (212) is inconsistent. % 95.82/25.76 | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | Case 2: % 95.82/25.76 | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_482_1, all_923_0, % 95.82/25.76 | | | | | | | | | | | | | | all_49_7, all_180_1, simplifying with (178), (203) % 95.82/25.76 | | | | | | | | | | | | | | gives: % 95.82/25.76 | | | | | | | | | | | | | | (213) all_923_0 = all_482_1 % 95.82/25.76 | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_923_2, all_49_5, % 95.82/25.76 | | | | | | | | | | | | | | all_385_0, simplifying with (182), (204) gives: % 95.82/25.76 | | | | | | | | | | | | | | (214) all_923_2 = 0 % 95.82/25.76 | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | BETA: splitting (180) gives: % 95.82/25.76 | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | Case 1: % 95.82/25.76 | | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | | (215) ~ (all_482_0 = 0) % 95.82/25.76 | | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | | REDUCE: (210), (215) imply: % 95.82/25.76 | | | | | | | | | | | | | | | (216) $false % 95.82/25.76 | | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | | CLOSE: (216) is inconsistent. % 95.82/25.76 | | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | Case 2: % 95.82/25.76 | | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | | (217) ~ (all_482_1 = 0) % 95.82/25.76 | | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | | BETA: splitting (205) gives: % 95.82/25.76 | | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | | Case 1: % 95.82/25.76 | | | | | | | | | | | | | | | | % 95.82/25.76 | | | | | | | | | | | | | | | | (218) ~ (all_923_2 = 0) % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | REDUCE: (214), (218) imply: % 95.82/25.77 | | | | | | | | | | | | | | | | (219) $false % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent. % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | Case 2: % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | (220) all_923_0 = 0 & all_923_1 = 0 % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | ALPHA: (220) implies: % 95.82/25.77 | | | | | | | | | | | | | | | | (221) all_923_0 = 0 % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (221) imply: % 95.82/25.77 | | | | | | | | | | | | | | | | (222) all_482_1 = 0 % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | REDUCE: (217), (222) imply: % 95.82/25.77 | | | | | | | | | | | | | | | | (223) $false % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent. % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | End of split % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | End of split % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | End of split % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | Case 2: % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | (224) ~ (all_482_0 = 0) % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | BETA: splitting (189) gives: % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | Case 1: % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | (225) all_482_0 = 0 % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | REDUCE: (224), (225) imply: % 95.82/25.77 | | | | | | | | | | | | | | (226) $false % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | CLOSE: (226) is inconsistent. % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | Case 2: % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | (227) ? [v0: any] : ? [v1: any] : (in(all_387_0, % 95.82/25.77 | | | | | | | | | | | | | | all_127_0) = v0 & in(all_387_0, all_49_8) = v1 % 95.82/25.77 | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | DELTA: instantiating (227) with fresh symbols all_1120_0, % 95.82/25.77 | | | | | | | | | | | | | | all_1120_1 gives: % 95.82/25.77 | | | | | | | | | | | | | | (228) in(all_387_0, all_127_0) = all_1120_1 & % 95.82/25.77 | | | | | | | | | | | | | | in(all_387_0, all_49_8) = all_1120_0 & ( ~ % 95.82/25.77 | | | | | | | | | | | | | | (all_1120_0 = 0) | ~ (all_1120_1 = 0)) % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | ALPHA: (228) implies: % 95.82/25.77 | | | | | | | | | | | | | | (229) in(all_387_0, all_49_8) = all_1120_0 % 95.82/25.77 | | | | | | | | | | | | | | (230) in(all_387_0, all_127_0) = all_1120_1 % 95.82/25.77 | | | | | | | | | | | | | | (231) ~ (all_1120_0 = 0) | ~ (all_1120_1 = 0) % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | REDUCE: (117), (230) imply: % 95.82/25.77 | | | | | | | | | | | | | | (232) in(all_387_0, all_83_1) = all_1120_1 % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | BETA: splitting (186) gives: % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | Case 1: % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | (233) all_365_0 = 0 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | REDUCE: (150), (233) imply: % 95.82/25.77 | | | | | | | | | | | | | | | (234) $false % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent. % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | Case 2: % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_1120_0, all_49_8, % 95.82/25.77 | | | | | | | | | | | | | | | all_387_0, simplifying with (185), (229) gives: % 95.82/25.77 | | | | | | | | | | | | | | | (235) all_1120_0 = 0 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_913_1, all_83_1, % 95.82/25.77 | | | | | | | | | | | | | | | all_387_0, simplifying with (165), (208) gives: % 95.82/25.77 | | | | | | | | | | | | | | | (236) all_913_1 = 0 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_915_1, all_919_2, % 95.82/25.77 | | | | | | | | | | | | | | | all_83_1, all_387_0, simplifying with (206), (207) % 95.82/25.77 | | | | | | | | | | | | | | | gives: % 95.82/25.77 | | | | | | | | | | | | | | | (237) all_919_2 = all_915_1 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_913_1, all_919_2, % 95.82/25.77 | | | | | | | | | | | | | | | all_83_1, all_387_0, simplifying with (206), (208) % 95.82/25.77 | | | | | | | | | | | | | | | gives: % 95.82/25.77 | | | | | | | | | | | | | | | (238) all_919_2 = all_913_1 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_919_2, all_1120_1, % 95.82/25.77 | | | | | | | | | | | | | | | all_83_1, all_387_0, simplifying with (206), (232) % 95.82/25.77 | | | | | | | | | | | | | | | gives: % 95.82/25.77 | | | | | | | | | | | | | | | (239) all_1120_1 = all_919_2 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_911_2, all_1120_1, % 95.82/25.77 | | | | | | | | | | | | | | | all_83_1, all_387_0, simplifying with (209), (232) % 95.82/25.77 | | | | | | | | | | | | | | | gives: % 95.82/25.77 | | | | | | | | | | | | | | | (240) all_1120_1 = all_911_2 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | COMBINE_EQS: (239), (240) imply: % 95.82/25.77 | | | | | | | | | | | | | | | (241) all_919_2 = all_911_2 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | SIMP: (241) implies: % 95.82/25.77 | | | | | | | | | | | | | | | (242) all_919_2 = all_911_2 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | COMBINE_EQS: (237), (238) imply: % 95.82/25.77 | | | | | | | | | | | | | | | (243) all_915_1 = all_913_1 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | COMBINE_EQS: (237), (242) imply: % 95.82/25.77 | | | | | | | | | | | | | | | (244) all_915_1 = all_911_2 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | COMBINE_EQS: (243), (244) imply: % 95.82/25.77 | | | | | | | | | | | | | | | (245) all_913_1 = all_911_2 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | SIMP: (245) implies: % 95.82/25.77 | | | | | | | | | | | | | | | (246) all_913_1 = all_911_2 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | COMBINE_EQS: (236), (246) imply: % 95.82/25.77 | | | | | | | | | | | | | | | (247) all_911_2 = 0 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | COMBINE_EQS: (240), (247) imply: % 95.82/25.77 | | | | | | | | | | | | | | | (248) all_1120_1 = 0 % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | Case 1: % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | (249) ~ (all_1120_0 = 0) % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | REDUCE: (235), (249) imply: % 95.82/25.77 | | | | | | | | | | | | | | | | (250) $false % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | CLOSE: (250) is inconsistent. % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | Case 2: % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | (251) ~ (all_1120_1 = 0) % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | REDUCE: (248), (251) imply: % 95.82/25.77 | | | | | | | | | | | | | | | | (252) $false % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | | CLOSE: (252) is inconsistent. % 95.82/25.77 | | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | | End of split % 95.82/25.77 | | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | | End of split % 95.82/25.77 | | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | End of split % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | End of split % 95.82/25.77 | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | Case 2: % 95.82/25.77 | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | (253) $i(all_256_0) % 95.82/25.77 | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | BETA: splitting (125) gives: % 95.82/25.77 | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | Case 1: % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | (254) ~ $i(all_256_0) % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | PRED_UNIFY: (253), (254) imply: % 95.82/25.77 | | | | | | | | | | | | | (255) $false % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | CLOSE: (255) is inconsistent. % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | Case 2: % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_49_8, all_49_5, % 95.82/25.77 | | | | | | | | | | | | | all_49_4, all_387_0, simplifying with (28), (31), % 95.82/25.77 | | | | | | | | | | | | | (36), (50), (161), (162) gives: % 95.82/25.77 | | | | | | | | | | | | | (256) in(all_387_0, all_49_5) = 0 & in(all_387_0, % 95.82/25.77 | | | | | | | | | | | | | all_49_8) = 0 % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | ALPHA: (256) implies: % 95.82/25.77 | | | | | | | | | | | | | (257) in(all_387_0, all_49_8) = 0 % 95.82/25.77 | | | | | | | | | | | | | (258) in(all_387_0, all_49_5) = 0 % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_185_1, all_365_0, % 95.82/25.77 | | | | | | | | | | | | | simplifying with (89), (151) gives: % 95.82/25.77 | | | | | | | | | | | | | (259) all_365_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 95.82/25.77 | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & powerset(all_185_1) = % 95.82/25.77 | | | | | | | | | | | | | v0 & element(v1, v0) = 0 & empty(v1) = v2 & % 95.82/25.77 | | | | | | | | | | | | | $i(v1) & $i(v0)) % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_462_1, all_462_0, % 95.82/25.77 | | | | | | | | | | | | | simplifying with (172), (173) gives: % 95.82/25.77 | | | | | | | | | | | | | (260) all_462_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 95.82/25.77 | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & powerset(all_462_1) = % 95.82/25.77 | | | | | | | | | | | | | v0 & element(v1, v0) = 0 & empty(v1) = v2 & % 95.82/25.77 | | | | | | | | | | | | | $i(v1) & $i(v0)) % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | GROUND_INST: instantiating (130) with all_49_8, all_49_2, % 95.82/25.77 | | | | | | | | | | | | | all_180_1, all_482_0, all_387_0, simplifying with % 95.82/25.77 | | | | | | | | | | | | | (28), (33), (38), (82), (161), (164), (179) gives: % 95.82/25.77 | | | | | | | | | | | | | (261) all_482_0 = 0 | ? [v0: any] : ? [v1: any] : % 95.82/25.77 | | | | | | | | | | | | | (in(all_387_0, all_127_0) = v0 & in(all_387_0, % 95.82/25.77 | | | | | | | | | | | | | all_49_8) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | GROUND_INST: instantiating (140) with all_49_7, all_49_5, % 95.82/25.77 | | | | | | | | | | | | | all_387_0, all_180_1, simplifying with (29), (31), % 95.82/25.77 | | | | | | | | | | | | | (40), (161), (164) gives: % 95.82/25.77 | | | | | | | | | | | | | (262) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 95.82/25.77 | | | | | | | | | | | | | (in(all_387_0, all_155_0) = v1 & in(all_387_0, % 95.82/25.77 | | | | | | | | | | | | | all_49_5) = v0 & in(all_180_1, all_49_7) = v2 % 95.82/25.77 | | | | | | | | | | | | | & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | GROUND_INST: instantiating (135) with all_49_7, all_49_5, % 95.82/25.77 | | | | | | | | | | | | | all_387_0, all_180_1, simplifying with (29), (31), % 95.82/25.77 | | | | | | | | | | | | | (40), (161), (164) gives: % 95.82/25.77 | | | | | | | | | | | | | (263) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 95.82/25.77 | | | | | | | | | | | | | (in(all_387_0, all_147_0) = v1 & in(all_387_0, % 95.82/25.77 | | | | | | | | | | | | | all_49_5) = v0 & in(all_180_1, all_49_7) = v2 % 95.82/25.77 | | | | | | | | | | | | | & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | GROUND_INST: instantiating (139) with all_49_7, all_49_5, % 95.82/25.77 | | | | | | | | | | | | | all_387_0, all_180_1, simplifying with (29), (31), % 95.82/25.77 | | | | | | | | | | | | | (40), (161), (164) gives: % 95.82/25.77 | | | | | | | | | | | | | (264) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 95.82/25.77 | | | | | | | | | | | | | (in(all_387_0, all_155_0) = v0 & in(all_387_0, % 95.82/25.77 | | | | | | | | | | | | | all_49_5) = v2 & in(all_180_1, all_49_7) = v1 % 95.82/25.77 | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | GROUND_INST: instantiating (134) with all_49_7, all_49_5, % 95.82/25.77 | | | | | | | | | | | | | all_387_0, all_180_1, simplifying with (29), (31), % 95.82/25.77 | | | | | | | | | | | | | (40), (161), (164) gives: % 95.82/25.77 | | | | | | | | | | | | | (265) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 95.82/25.77 | | | | | | | | | | | | | (in(all_387_0, all_147_0) = v0 & in(all_387_0, % 95.82/25.77 | | | | | | | | | | | | | all_49_5) = v2 & in(all_180_1, all_49_7) = v1 % 95.82/25.77 | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.77 | | | | | | | | | | | | | DELTA: instantiating (265) with fresh symbols all_917_0, % 95.82/25.77 | | | | | | | | | | | | | all_917_1, all_917_2 gives: % 95.82/25.77 | | | | | | | | | | | | | (266) in(all_387_0, all_147_0) = all_917_2 & % 95.82/25.77 | | | | | | | | | | | | | in(all_387_0, all_49_5) = all_917_0 & % 95.82/25.77 | | | | | | | | | | | | | in(all_180_1, all_49_7) = all_917_1 & ( ~ % 95.82/25.77 | | | | | | | | | | | | | (all_917_1 = 0) | ~ (all_917_2 = 0) | all_917_0 % 95.82/25.77 | | | | | | | | | | | | | = 0) % 95.82/25.77 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | ALPHA: (266) implies: % 95.82/25.78 | | | | | | | | | | | | | (267) in(all_387_0, all_147_0) = all_917_2 % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | DELTA: instantiating (263) with fresh symbols all_919_0, % 95.82/25.78 | | | | | | | | | | | | | all_919_1, all_919_2 gives: % 95.82/25.78 | | | | | | | | | | | | | (268) in(all_387_0, all_147_0) = all_919_1 & % 95.82/25.78 | | | | | | | | | | | | | in(all_387_0, all_49_5) = all_919_2 & % 95.82/25.78 | | | | | | | | | | | | | in(all_180_1, all_49_7) = all_919_0 & ( ~ % 95.82/25.78 | | | | | | | | | | | | | (all_919_2 = 0) | (all_919_0 = 0 & all_919_1 = % 95.82/25.78 | | | | | | | | | | | | | 0)) % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | ALPHA: (268) implies: % 95.82/25.78 | | | | | | | | | | | | | (269) in(all_180_1, all_49_7) = all_919_0 % 95.82/25.78 | | | | | | | | | | | | | (270) in(all_387_0, all_49_5) = all_919_2 % 95.82/25.78 | | | | | | | | | | | | | (271) in(all_387_0, all_147_0) = all_919_1 % 95.82/25.78 | | | | | | | | | | | | | (272) ~ (all_919_2 = 0) | (all_919_0 = 0 & all_919_1 = % 95.82/25.78 | | | | | | | | | | | | | 0) % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | DELTA: instantiating (262) with fresh symbols all_921_0, % 95.82/25.78 | | | | | | | | | | | | | all_921_1, all_921_2 gives: % 95.82/25.78 | | | | | | | | | | | | | (273) in(all_387_0, all_155_0) = all_921_1 & % 95.82/25.78 | | | | | | | | | | | | | in(all_387_0, all_49_5) = all_921_2 & % 95.82/25.78 | | | | | | | | | | | | | in(all_180_1, all_49_7) = all_921_0 & ( ~ % 95.82/25.78 | | | | | | | | | | | | | (all_921_2 = 0) | (all_921_0 = 0 & all_921_1 = % 95.82/25.78 | | | | | | | | | | | | | 0)) % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | ALPHA: (273) implies: % 95.82/25.78 | | | | | | | | | | | | | (274) in(all_387_0, all_155_0) = all_921_1 % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | DELTA: instantiating (264) with fresh symbols all_925_0, % 95.82/25.78 | | | | | | | | | | | | | all_925_1, all_925_2 gives: % 95.82/25.78 | | | | | | | | | | | | | (275) in(all_387_0, all_155_0) = all_925_2 & % 95.82/25.78 | | | | | | | | | | | | | in(all_387_0, all_49_5) = all_925_0 & % 95.82/25.78 | | | | | | | | | | | | | in(all_180_1, all_49_7) = all_925_1 & ( ~ % 95.82/25.78 | | | | | | | | | | | | | (all_925_1 = 0) | ~ (all_925_2 = 0) | all_925_0 % 95.82/25.78 | | | | | | | | | | | | | = 0) % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | ALPHA: (275) implies: % 95.82/25.78 | | | | | | | | | | | | | (276) in(all_387_0, all_155_0) = all_925_2 % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | REDUCE: (108), (276) imply: % 95.82/25.78 | | | | | | | | | | | | | (277) in(all_387_0, all_83_1) = all_925_2 % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | REDUCE: (108), (274) imply: % 95.82/25.78 | | | | | | | | | | | | | (278) in(all_387_0, all_83_1) = all_921_1 % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | REDUCE: (110), (271) imply: % 95.82/25.78 | | | | | | | | | | | | | (279) in(all_387_0, all_83_1) = all_919_1 % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | REDUCE: (110), (267) imply: % 95.82/25.78 | | | | | | | | | | | | | (280) in(all_387_0, all_83_1) = all_917_2 % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | BETA: splitting (261) gives: % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | Case 1: % 95.82/25.78 | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | (281) all_482_0 = 0 % 95.82/25.78 | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | BETA: splitting (180) gives: % 95.82/25.78 | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | Case 1: % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | (282) ~ (all_482_0 = 0) % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | REDUCE: (281), (282) imply: % 95.82/25.78 | | | | | | | | | | | | | | | (283) $false % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent. % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | Case 2: % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | (284) ~ (all_482_1 = 0) % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | BETA: splitting (259) gives: % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | Case 1: % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | (285) all_365_0 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | REDUCE: (150), (285) imply: % 95.82/25.78 | | | | | | | | | | | | | | | | (286) $false % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | CLOSE: (286) is inconsistent. % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | Case 2: % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_482_1, all_919_0, % 95.82/25.78 | | | | | | | | | | | | | | | | all_49_7, all_180_1, simplifying with (178), (269) % 95.82/25.78 | | | | | | | | | | | | | | | | gives: % 95.82/25.78 | | | | | | | | | | | | | | | | (287) all_919_0 = all_482_1 % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_919_2, all_49_5, % 95.82/25.78 | | | | | | | | | | | | | | | | all_387_0, simplifying with (258), (270) gives: % 95.82/25.78 | | | | | | | | | | | | | | | | (288) all_919_2 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | Case 1: % 95.82/25.78 | | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | | (289) ~ (all_919_2 = 0) % 95.82/25.78 | | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | | REDUCE: (288), (289) imply: % 95.82/25.78 | | | | | | | | | | | | | | | | | (290) $false % 95.82/25.78 | | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | | CLOSE: (290) is inconsistent. % 95.82/25.78 | | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | Case 2: % 95.82/25.78 | | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | | (291) all_919_0 = 0 & all_919_1 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | | ALPHA: (291) implies: % 95.82/25.78 | | | | | | | | | | | | | | | | | (292) all_919_0 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (292) imply: % 95.82/25.78 | | | | | | | | | | | | | | | | | (293) all_482_1 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | | REDUCE: (284), (293) imply: % 95.82/25.78 | | | | | | | | | | | | | | | | | (294) $false % 95.82/25.78 | | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent. % 95.82/25.78 | | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | End of split % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | End of split % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | End of split % 95.82/25.78 | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | Case 2: % 95.82/25.78 | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | (295) ? [v0: any] : ? [v1: any] : (in(all_387_0, % 95.82/25.78 | | | | | | | | | | | | | | all_127_0) = v0 & in(all_387_0, all_49_8) = v1 % 95.82/25.78 | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 95.82/25.78 | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | DELTA: instantiating (295) with fresh symbols all_1146_0, % 95.82/25.78 | | | | | | | | | | | | | | all_1146_1 gives: % 95.82/25.78 | | | | | | | | | | | | | | (296) in(all_387_0, all_127_0) = all_1146_1 & % 95.82/25.78 | | | | | | | | | | | | | | in(all_387_0, all_49_8) = all_1146_0 & ( ~ % 95.82/25.78 | | | | | | | | | | | | | | (all_1146_0 = 0) | ~ (all_1146_1 = 0)) % 95.82/25.78 | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | ALPHA: (296) implies: % 95.82/25.78 | | | | | | | | | | | | | | (297) in(all_387_0, all_49_8) = all_1146_0 % 95.82/25.78 | | | | | | | | | | | | | | (298) in(all_387_0, all_127_0) = all_1146_1 % 95.82/25.78 | | | | | | | | | | | | | | (299) ~ (all_1146_0 = 0) | ~ (all_1146_1 = 0) % 95.82/25.78 | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | REDUCE: (117), (298) imply: % 95.82/25.78 | | | | | | | | | | | | | | (300) in(all_387_0, all_83_1) = all_1146_1 % 95.82/25.78 | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | BETA: splitting (260) gives: % 95.82/25.78 | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | Case 1: % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | (301) all_462_0 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | REDUCE: (171), (301) imply: % 95.82/25.78 | | | | | | | | | | | | | | | (302) $false % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | CLOSE: (302) is inconsistent. % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | Case 2: % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_1146_0, all_49_8, % 95.82/25.78 | | | | | | | | | | | | | | | all_387_0, simplifying with (257), (297) gives: % 95.82/25.78 | | | | | | | | | | | | | | | (303) all_1146_0 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_925_2, all_83_1, % 95.82/25.78 | | | | | | | | | | | | | | | all_387_0, simplifying with (165), (277) gives: % 95.82/25.78 | | | | | | | | | | | | | | | (304) all_925_2 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_921_1, all_925_2, % 95.82/25.78 | | | | | | | | | | | | | | | all_83_1, all_387_0, simplifying with (277), (278) % 95.82/25.78 | | | | | | | | | | | | | | | gives: % 95.82/25.78 | | | | | | | | | | | | | | | (305) all_925_2 = all_921_1 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_919_1, all_925_2, % 95.82/25.78 | | | | | | | | | | | | | | | all_83_1, all_387_0, simplifying with (277), (279) % 95.82/25.78 | | | | | | | | | | | | | | | gives: % 95.82/25.78 | | | | | | | | | | | | | | | (306) all_925_2 = all_919_1 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_919_1, all_1146_1, % 95.82/25.78 | | | | | | | | | | | | | | | all_83_1, all_387_0, simplifying with (279), (300) % 95.82/25.78 | | | | | | | | | | | | | | | gives: % 95.82/25.78 | | | | | | | | | | | | | | | (307) all_1146_1 = all_919_1 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_917_2, all_1146_1, % 95.82/25.78 | | | | | | | | | | | | | | | all_83_1, all_387_0, simplifying with (280), (300) % 95.82/25.78 | | | | | | | | | | | | | | | gives: % 95.82/25.78 | | | | | | | | | | | | | | | (308) all_1146_1 = all_917_2 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | COMBINE_EQS: (307), (308) imply: % 95.82/25.78 | | | | | | | | | | | | | | | (309) all_919_1 = all_917_2 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | SIMP: (309) implies: % 95.82/25.78 | | | | | | | | | | | | | | | (310) all_919_1 = all_917_2 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | COMBINE_EQS: (304), (305) imply: % 95.82/25.78 | | | | | | | | | | | | | | | (311) all_921_1 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | COMBINE_EQS: (305), (306) imply: % 95.82/25.78 | | | | | | | | | | | | | | | (312) all_921_1 = all_919_1 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | COMBINE_EQS: (311), (312) imply: % 95.82/25.78 | | | | | | | | | | | | | | | (313) all_919_1 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | SIMP: (313) implies: % 95.82/25.78 | | | | | | | | | | | | | | | (314) all_919_1 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | COMBINE_EQS: (310), (314) imply: % 95.82/25.78 | | | | | | | | | | | | | | | (315) all_917_2 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | SIMP: (315) implies: % 95.82/25.78 | | | | | | | | | | | | | | | (316) all_917_2 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | COMBINE_EQS: (308), (316) imply: % 95.82/25.78 | | | | | | | | | | | | | | | (317) all_1146_1 = 0 % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | Case 1: % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | (318) ~ (all_1146_0 = 0) % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | REDUCE: (303), (318) imply: % 95.82/25.78 | | | | | | | | | | | | | | | | (319) $false % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | CLOSE: (319) is inconsistent. % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | Case 2: % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | (320) ~ (all_1146_1 = 0) % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | REDUCE: (317), (320) imply: % 95.82/25.78 | | | | | | | | | | | | | | | | (321) $false % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent. % 95.82/25.78 | | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | | End of split % 95.82/25.78 | | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | | End of split % 95.82/25.78 | | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | | End of split % 95.82/25.78 | | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | | End of split % 95.82/25.78 | | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | | End of split % 95.82/25.78 | | | | | | | | | | | % 95.82/25.78 | | | | | | | | | | End of split % 95.82/25.78 | | | | | | | | | | % 95.82/25.78 | | | | | | | | | End of split % 95.82/25.78 | | | | | | | | | % 95.82/25.78 | | | | | | | | End of split % 95.82/25.78 | | | | | | | | % 95.82/25.78 | | | | | | | End of split % 95.82/25.78 | | | | | | | % 95.82/25.78 | | | | | | End of split % 95.82/25.78 | | | | | | % 95.82/25.78 | | | | | End of split % 95.82/25.78 | | | | | % 95.82/25.78 | | | | End of split % 95.82/25.78 | | | | % 95.82/25.78 | | | End of split % 95.82/25.78 | | | % 95.82/25.78 | | End of split % 95.82/25.78 | | % 95.82/25.78 | End of split % 95.82/25.78 | % 95.82/25.78 End of proof % 95.82/25.78 % SZS output end Proof for theBenchmark % 95.82/25.78 % 95.82/25.78 25240ms %------------------------------------------------------------------------------