%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU269+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n025.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:43:46 EDT 2023 % Result : Theorem 15.46s 2.91s % Output : Proof 34.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU269+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n025.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Wed Aug 23 16:31:35 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.79/1.09 Prover 1: Preprocessing ... % 2.79/1.09 Prover 4: Preprocessing ... % 3.26/1.12 Prover 5: Preprocessing ... % 3.26/1.12 Prover 2: Preprocessing ... % 3.26/1.12 Prover 3: Preprocessing ... % 3.26/1.12 Prover 6: Preprocessing ... % 3.26/1.12 Prover 0: Preprocessing ... % 6.87/1.64 Prover 1: Warning: ignoring some quantifiers % 6.87/1.68 Prover 3: Warning: ignoring some quantifiers % 6.87/1.69 Prover 1: Constructing countermodel ... % 6.87/1.70 Prover 5: Proving ... % 6.87/1.70 Prover 3: Constructing countermodel ... % 6.87/1.72 Prover 6: Proving ... % 7.42/1.75 Prover 2: Proving ... % 9.06/1.99 Prover 4: Warning: ignoring some quantifiers % 9.63/2.04 Prover 0: Proving ... % 9.63/2.07 Prover 4: Constructing countermodel ... % 10.65/2.18 Prover 3: gave up % 10.65/2.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.65/2.24 Prover 7: Preprocessing ... % 10.65/2.29 Prover 1: gave up % 10.65/2.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.65/2.33 Prover 8: Preprocessing ... % 12.21/2.39 Prover 7: Warning: ignoring some quantifiers % 12.38/2.41 Prover 7: Constructing countermodel ... % 12.49/2.49 Prover 8: Warning: ignoring some quantifiers % 12.49/2.50 Prover 8: Constructing countermodel ... % 15.46/2.91 Prover 0: proved (2270ms) % 15.46/2.91 % 15.46/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.46/2.91 % 15.46/2.91 Prover 2: stopped % 15.46/2.91 Prover 6: stopped % 15.46/2.92 Prover 5: stopped % 15.46/2.94 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.46/2.94 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.46/2.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.46/2.94 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.46/2.95 Prover 8: gave up % 15.46/2.97 Prover 11: Preprocessing ... % 15.46/2.98 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.46/2.99 Prover 13: Preprocessing ... % 15.46/3.00 Prover 10: Preprocessing ... % 15.46/3.01 Prover 19: Preprocessing ... % 15.46/3.01 Prover 16: Preprocessing ... % 16.21/3.08 Prover 10: Warning: ignoring some quantifiers % 16.21/3.09 Prover 10: Constructing countermodel ... % 16.21/3.10 Prover 13: Warning: ignoring some quantifiers % 17.58/3.11 Prover 16: Warning: ignoring some quantifiers % 17.58/3.12 Prover 13: Constructing countermodel ... % 17.58/3.12 Prover 16: Constructing countermodel ... % 17.58/3.17 Prover 10: gave up % 17.58/3.18 Prover 19: Warning: ignoring some quantifiers % 17.58/3.19 Prover 19: Constructing countermodel ... % 18.27/3.25 Prover 11: Warning: ignoring some quantifiers % 18.27/3.25 Prover 11: Constructing countermodel ... % 22.17/3.75 Prover 19: gave up % 33.80/5.30 Prover 11: Found proof (size 190) % 33.80/5.30 Prover 11: proved (2395ms) % 33.80/5.31 Prover 4: stopped % 33.80/5.31 Prover 13: stopped % 33.80/5.31 Prover 16: stopped % 33.80/5.31 Prover 7: stopped % 33.80/5.31 % 33.80/5.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 33.80/5.31 % 33.80/5.32 % SZS output start Proof for theBenchmark % 33.80/5.33 Assumptions after simplification: % 33.80/5.33 --------------------------------- % 33.80/5.33 % 33.80/5.33 (commutativity_k2_xboole_0) % 33.80/5.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 33.80/5.35 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 33.80/5.35 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 33.80/5.35 | (set_union2(v1, v0) = v2 & $i(v2))) % 33.80/5.35 % 33.80/5.35 (d16_relat_2) % 34.45/5.36 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? % 34.45/5.36 [v2: int] : ? [v3: int] : ? [v4: int] : (( ~ (v2 = 0) & relation(v0) = v2) % 34.45/5.36 | (((v4 = 0 & is_transitive_in(v0, v1) = 0) | ( ~ (v3 = 0) & % 34.45/5.36 transitive(v0) = v3)) & ((v3 = 0 & transitive(v0) = 0) | ( ~ (v4 = % 34.45/5.36 0) & is_transitive_in(v0, v1) = v4))))) & ! [v0: $i] : ! [v1: % 34.45/5.36 any] : ( ~ (transitive(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : % 34.45/5.36 ? [v4: int] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v4 = 0 & % 34.45/5.36 relation_field(v0) = v3 & is_transitive_in(v0, v3) = 0 & $i(v3))) & % 34.45/5.36 (v1 = 0 | ( ~ (v4 = 0) & relation_field(v0) = v3 & is_transitive_in(v0, % 34.45/5.36 v3) = v4 & $i(v3)))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ % 34.45/5.36 $i(v0) | ? [v1: int] : ? [v2: $i] : ? [v3: int] : (((v3 = 0 & % 34.45/5.36 relation_field(v0) = v2 & is_transitive_in(v0, v2) = 0 & $i(v2)) | ( ~ % 34.45/5.36 (v1 = 0) & transitive(v0) = v1)) & ((v1 = 0 & transitive(v0) = 0) | ( % 34.45/5.36 ~ (v3 = 0) & relation_field(v0) = v2 & is_transitive_in(v0, v2) = v3 & % 34.45/5.36 $i(v2))))) % 34.45/5.36 % 34.45/5.36 (d1_wellord2) % 34.45/5.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 34.45/5.37 any] : ( ~ (inclusion_relation(v0) = v1) | ~ (subset(v3, v4) = v5) | ~ % 34.45/5.37 (relation_field(v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 34.45/5.37 ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : (( ~ (v7 = 0) & % 34.45/5.37 in(v4, v0) = v7) | ( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & % 34.45/5.37 in(v3, v0) = v6) | (( ~ (v5 = 0) | (v9 = 0 & ordered_pair(v3, v4) = v8 & % 34.45/5.37 in(v8, v1) = 0 & $i(v8))) & (v5 = 0 | ( ~ (v9 = 0) & % 34.45/5.37 ordered_pair(v3, v4) = v8 & in(v8, v1) = v9 & $i(v8)))))) & ! [v0: % 34.45/5.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 34.45/5.37 ( ~ (inclusion_relation(v0) = v1) | ~ (ordered_pair(v3, v4) = v5) | ~ % 34.45/5.37 (relation_field(v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 34.45/5.37 ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : (( ~ (v7 = 0) & % 34.45/5.37 in(v4, v0) = v7) | ( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & % 34.45/5.37 in(v3, v0) = v6) | (((v9 = 0 & subset(v3, v4) = 0) | ( ~ (v8 = 0) & % 34.45/5.37 in(v5, v1) = v8)) & ((v8 = 0 & in(v5, v1) = 0) | ( ~ (v9 = 0) & % 34.45/5.37 subset(v3, v4) = v9))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.45/5.37 (v2 = v1 | ~ (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v0) | % 34.45/5.37 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 34.45/5.37 int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ($i(v5) % 34.45/5.37 & $i(v4) & ((v7 = 0 & v6 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 % 34.45/5.37 & subset(v4, v5) = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & % 34.45/5.37 in(v8, v1) = 0 & $i(v8))) & (( ~ (v10 = 0) & subset(v4, v5) = v10) % 34.45/5.37 | ( ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 & % 34.45/5.37 $i(v8)))) | ( ~ (v3 = 0) & relation(v1) = v3)))) & ! [v0: $i] : % 34.45/5.37 ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (inclusion_relation(v0) = v1) | ~ % 34.45/5.37 (relation_field(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = % 34.45/5.37 0) & relation(v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 34.45/5.37 (inclusion_relation(v0) = v2) | ~ (relation(v1) = 0) | ~ $i(v1) | ~ % 34.45/5.37 $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: % 34.45/5.37 int] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ($i(v5) & $i(v4) & ( ~ % 34.45/5.37 (v2 = v1) | (v3 = v0 & relation_field(v1) = v0 & ! [v11: $i] : ! [v12: % 34.45/5.37 $i] : ! [v13: any] : ( ~ (subset(v11, v12) = v13) | ~ $i(v12) | ~ % 34.45/5.37 $i(v11) | ? [v14: int] : ? [v15: int] : ? [v16: $i] : ? [v17: % 34.45/5.37 int] : (( ~ (v15 = 0) & in(v12, v0) = v15) | ( ~ (v14 = 0) & % 34.45/5.37 in(v11, v0) = v14) | (( ~ (v13 = 0) | (v17 = 0 & % 34.45/5.37 ordered_pair(v11, v12) = v16 & in(v16, v1) = 0 & $i(v16))) & % 34.45/5.37 (v13 = 0 | ( ~ (v17 = 0) & ordered_pair(v11, v12) = v16 & % 34.45/5.37 in(v16, v1) = v17 & $i(v16)))))) & ! [v11: $i] : ! [v12: % 34.45/5.37 $i] : ! [v13: $i] : ( ~ (ordered_pair(v11, v12) = v13) | ~ $i(v12) % 34.45/5.37 | ~ $i(v11) | ? [v14: int] : ? [v15: int] : ? [v16: int] : ? % 34.45/5.37 [v17: int] : (( ~ (v15 = 0) & in(v12, v0) = v15) | ( ~ (v14 = 0) & % 34.45/5.37 in(v11, v0) = v14) | (((v17 = 0 & subset(v11, v12) = 0) | ( ~ % 34.45/5.37 (v16 = 0) & in(v13, v1) = v16)) & ((v16 = 0 & in(v13, v1) = % 34.45/5.37 0) | ( ~ (v17 = 0) & subset(v11, v12) = v17))))))) & (v2 = % 34.45/5.37 v1 | (v7 = 0 & v6 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & % 34.45/5.37 subset(v4, v5) = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, % 34.45/5.37 v1) = 0 & $i(v8))) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( % 34.45/5.37 ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 & % 34.45/5.37 $i(v8)))) | ( ~ (v3 = v0) & relation_field(v1) = v3 & $i(v3))))) % 34.45/5.37 % 34.45/5.37 (d6_relat_1) % 34.45/5.38 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 34.45/5.38 int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & % 34.45/5.38 relation_rng(v0) = v4 & relation_field(v0) = v3 & set_union2(v1, v4) = % 34.45/5.38 v3 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0: % 34.45/5.38 $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: int] : % 34.45/5.38 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & relation_dom(v0) = v4 % 34.45/5.38 & relation_field(v0) = v3 & set_union2(v4, v1) = v3 & $i(v4) & $i(v3)) | % 34.45/5.38 ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 34.45/5.38 (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: % 34.45/5.38 $i] : ? [v5: $i] : ((v5 = v1 & relation_dom(v0) = v3 & relation_rng(v0) = % 34.45/5.38 v4 & set_union2(v3, v4) = v1 & $i(v4) & $i(v3) & $i(v1)) | ( ~ (v2 = 0) % 34.45/5.38 & relation(v0) = v2))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ % 34.45/5.38 $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & % 34.45/5.38 relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1 % 34.45/5.38 & $i(v3) & $i(v2) & $i(v1))) % 34.45/5.38 % 34.45/5.38 (d8_relat_2) % 34.45/5.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 34.45/5.39 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (ordered_pair(v3, v4) = v5) % 34.45/5.39 | ~ (ordered_pair(v2, v4) = v6) | ~ (is_transitive_in(v0, v1) = 0) | ~ % 34.45/5.39 (relation(v0) = 0) | ~ (in(v6, v0) = v7) | ~ (in(v5, v0) = 0) | ~ $i(v4) % 34.45/5.39 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: int] : ? [v9: % 34.45/5.39 int] : ? [v10: int] : ? [v11: $i] : ? [v12: int] : (( ~ (v12 = 0) & % 34.45/5.39 ordered_pair(v2, v3) = v11 & in(v11, v0) = v12 & $i(v11)) | ( ~ (v10 = % 34.45/5.39 0) & in(v4, v1) = v10) | ( ~ (v9 = 0) & in(v3, v1) = v9) | ( ~ (v8 = % 34.45/5.39 0) & in(v2, v1) = v8))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 34.45/5.39 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | % 34.45/5.39 ~ (ordered_pair(v2, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~ % 34.45/5.39 (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = % 34.45/5.39 v7) | ~ (in(v5, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 34.45/5.39 | ~ $i(v0) | ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: $i] : % 34.45/5.39 ? [v12: int] : (( ~ (v12 = 0) & ordered_pair(v3, v4) = v11 & in(v11, v0) = % 34.45/5.39 v12 & $i(v11)) | ( ~ (v10 = 0) & in(v4, v1) = v10) | ( ~ (v9 = 0) & % 34.45/5.39 in(v3, v1) = v9) | ( ~ (v8 = 0) & in(v2, v1) = v8))) & ! [v0: $i] : ! % 34.45/5.39 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 34.45/5.39 int] : (v6 = 0 | ~ (ordered_pair(v2, v4) = v5) | ~ (is_transitive_in(v0, % 34.45/5.39 v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = v6) | ~ (in(v3, v1) % 34.45/5.39 = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: % 34.45/5.39 int] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? % 34.45/5.39 [v12: int] : (( ~ (v12 = 0) & ordered_pair(v3, v4) = v11 & in(v11, v0) = v12 % 34.45/5.39 & $i(v11)) | ( ~ (v10 = 0) & ordered_pair(v2, v3) = v9 & in(v9, v0) = % 34.45/5.39 v10 & $i(v9)) | ( ~ (v8 = 0) & in(v4, v1) = v8) | ( ~ (v7 = 0) & in(v2, % 34.45/5.39 v1) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 34.45/5.39 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v4) = v6) | ~ % 34.45/5.39 (ordered_pair(v2, v3) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ % 34.45/5.39 (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v5, v0) = 0) | ~ $i(v4) | % 34.45/5.39 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] % 34.45/5.39 : ? [v9: int] : ? [v10: $i] : ? [v11: int] : ((v11 = 0 & ordered_pair(v2, % 34.45/5.39 v4) = v10 & in(v10, v0) = 0 & $i(v10)) | ( ~ (v9 = 0) & in(v4, v1) = % 34.45/5.39 v9) | ( ~ (v8 = 0) & in(v3, v1) = v8) | ( ~ (v7 = 0) & in(v2, v1) = % 34.45/5.39 v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 34.45/5.39 $i] : ! [v5: $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ % 34.45/5.39 (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = 0) % 34.45/5.39 | ~ (in(v2, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 34.45/5.39 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: % 34.45/5.39 $i] : ? [v11: int] : ((v11 = 0 & ordered_pair(v2, v4) = v10 & in(v10, v0) % 34.45/5.39 = 0 & $i(v10)) | ( ~ (v9 = 0) & ordered_pair(v2, v3) = v8 & in(v8, v0) = % 34.45/5.39 v9 & $i(v8)) | ( ~ (v7 = 0) & in(v4, v1) = v7) | ( ~ (v6 = 0) & in(v3, % 34.45/5.39 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 34.45/5.39 ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v2, v3) = v5) | ~ % 34.45/5.39 (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = 0) % 34.45/5.39 | ~ (in(v4, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 34.45/5.39 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: % 34.45/5.39 $i] : ? [v11: int] : ((v11 = 0 & ordered_pair(v2, v4) = v10 & in(v10, v0) % 34.45/5.39 = 0 & $i(v10)) | ( ~ (v9 = 0) & ordered_pair(v3, v4) = v8 & in(v8, v0) = % 34.45/5.39 v9 & $i(v8)) | ( ~ (v7 = 0) & in(v3, v1) = v7) | ( ~ (v6 = 0) & in(v2, % 34.45/5.39 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 34.45/5.39 ! [v4: $i] : ( ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ % 34.45/5.39 (in(v4, v1) = 0) | ~ (in(v3, v1) = 0) | ~ (in(v2, v1) = 0) | ~ $i(v4) | % 34.45/5.39 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : % 34.45/5.39 ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: int] : ((v10 = 0 & % 34.45/5.39 ordered_pair(v2, v4) = v9 & in(v9, v0) = 0 & $i(v9)) | ( ~ (v8 = 0) & % 34.45/5.39 ordered_pair(v3, v4) = v7 & in(v7, v0) = v8 & $i(v7)) | ( ~ (v6 = 0) & % 34.45/5.39 ordered_pair(v2, v3) = v5 & in(v5, v0) = v6 & $i(v5)))) & ! [v0: $i] : % 34.45/5.39 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (is_transitive_in(v0, v1) = v2) | ~ % 34.45/5.39 (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 34.45/5.39 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ( ~ (v9 % 34.45/5.39 = 0) & ordered_pair(v4, v5) = v7 & ordered_pair(v3, v5) = v8 & % 34.45/5.39 ordered_pair(v3, v4) = v6 & in(v8, v0) = v9 & in(v7, v0) = 0 & in(v6, v0) % 34.45/5.39 = 0 & in(v5, v1) = 0 & in(v4, v1) = 0 & in(v3, v1) = 0 & $i(v8) & $i(v7) & % 34.45/5.39 $i(v6) & $i(v5) & $i(v4) & $i(v3))) % 34.45/5.39 % 34.45/5.39 (dt_k1_wellord2) % 34.45/5.39 ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ $i(v0) | % 34.45/5.39 relation(v1) = 0) % 34.45/5.39 % 34.45/5.39 (t1_xboole_1) % 34.45/5.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 34.45/5.39 (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 34.45/5.39 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : % 34.45/5.39 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v0, v2) = v3) % 34.45/5.39 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] % 34.45/5.39 : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 34.45/5.39 $i] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ % 34.45/5.39 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0) % 34.45/5.39 % 34.45/5.39 (t3_wellord2) % 34.45/5.39 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 34.45/5.39 inclusion_relation(v0) = v1 & transitive(v1) = v2 & $i(v1) & $i(v0)) % 34.45/5.39 % 34.45/5.39 (function-axioms) % 34.45/5.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 34.45/5.39 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 34.45/5.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 34.45/5.39 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 34.45/5.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.45/5.39 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 34.45/5.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 34.45/5.39 : (v1 = v0 | ~ (is_transitive_in(v3, v2) = v1) | ~ (is_transitive_in(v3, v2) % 34.45/5.39 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 34.45/5.39 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] % 34.45/5.39 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, % 34.45/5.39 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 34.45/5.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 34.45/5.39 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 34.45/5.39 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 34.45/5.39 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 34.45/5.39 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ % 34.45/5.39 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 34.45/5.39 $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & % 34.45/5.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) % 34.45/5.39 | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.45/5.39 (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : % 34.45/5.39 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inclusion_relation(v2) = v1) | ~ % 34.45/5.39 (inclusion_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.45/5.39 (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! % 34.45/5.39 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 34.45/5.39 | ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0)) & ! [v0: % 34.45/5.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 34.45/5.39 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: % 34.45/5.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 34.45/5.39 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 34.45/5.39 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 34.45/5.39 (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: % 34.45/5.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 34.45/5.39 ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : % 34.45/5.39 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 34.45/5.39 (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: % 34.45/5.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 34.45/5.39 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] % 34.45/5.39 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | % 34.45/5.40 ~ (empty(v2) = v0)) % 34.45/5.40 % 34.45/5.40 Further assumptions not needed in the proof: % 34.45/5.40 -------------------------------------------- % 34.45/5.40 antisymmetry_r2_hidden, cc1_funct_1, cc1_ordinal1, cc2_funct_1, cc2_ordinal1, % 34.45/5.40 cc3_ordinal1, commutativity_k2_tarski, d5_tarski, dt_k1_relat_1, dt_k1_tarski, % 34.45/5.40 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_tarski, dt_k2_xboole_0, % 34.45/5.40 dt_k3_relat_1, dt_k4_tarski, dt_m1_subset_1, existence_m1_subset_1, % 34.45/5.40 fc1_xboole_0, fc1_zfmisc_1, fc2_ordinal1, fc2_xboole_0, fc3_xboole_0, % 34.45/5.40 idempotence_k2_xboole_0, rc1_funct_1, rc1_ordinal1, rc1_xboole_0, rc2_funct_1, % 34.45/5.40 rc2_ordinal1, rc2_xboole_0, rc3_funct_1, rc3_ordinal1, rc4_funct_1, % 34.45/5.40 reflexivity_r1_tarski, t1_boole, t1_subset, t2_subset, t3_subset, t4_subset, % 34.45/5.40 t5_subset, t6_boole, t7_boole, t8_boole % 34.45/5.40 % 34.45/5.40 Those formulas are unsatisfiable: % 34.45/5.40 --------------------------------- % 34.45/5.40 % 34.45/5.40 Begin of proof % 34.45/5.40 | % 34.45/5.40 | ALPHA: (commutativity_k2_xboole_0) implies: % 34.68/5.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 34.68/5.40 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 34.68/5.40 | % 34.68/5.40 | ALPHA: (d16_relat_2) implies: % 34.68/5.40 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (transitive(v0) = v1) | ~ $i(v0) | ? % 34.68/5.40 | [v2: int] : ? [v3: $i] : ? [v4: int] : (( ~ (v2 = 0) & relation(v0) % 34.68/5.40 | = v2) | (( ~ (v1 = 0) | (v4 = 0 & relation_field(v0) = v3 & % 34.68/5.40 | is_transitive_in(v0, v3) = 0 & $i(v3))) & (v1 = 0 | ( ~ (v4 = % 34.68/5.40 | 0) & relation_field(v0) = v3 & is_transitive_in(v0, v3) = % 34.68/5.40 | v4 & $i(v3)))))) % 34.68/5.40 | % 34.68/5.40 | ALPHA: (d1_wellord2) implies: % 34.68/5.40 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (inclusion_relation(v0) = % 34.68/5.40 | v2) | ~ (relation(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 34.68/5.40 | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: $i] % 34.68/5.40 | : ? [v9: int] : ? [v10: int] : ($i(v5) & $i(v4) & ( ~ (v2 = v1) | % 34.68/5.40 | (v3 = v0 & relation_field(v1) = v0 & ! [v11: $i] : ! [v12: $i] % 34.68/5.40 | : ! [v13: any] : ( ~ (subset(v11, v12) = v13) | ~ $i(v12) | % 34.68/5.40 | ~ $i(v11) | ? [v14: int] : ? [v15: int] : ? [v16: $i] : ? % 34.68/5.40 | [v17: int] : (( ~ (v15 = 0) & in(v12, v0) = v15) | ( ~ (v14 = % 34.68/5.40 | 0) & in(v11, v0) = v14) | (( ~ (v13 = 0) | (v17 = 0 & % 34.68/5.40 | ordered_pair(v11, v12) = v16 & in(v16, v1) = 0 & % 34.68/5.40 | $i(v16))) & (v13 = 0 | ( ~ (v17 = 0) & % 34.68/5.40 | ordered_pair(v11, v12) = v16 & in(v16, v1) = v17 & % 34.68/5.40 | $i(v16)))))) & ! [v11: $i] : ! [v12: $i] : ! [v13: % 34.68/5.40 | $i] : ( ~ (ordered_pair(v11, v12) = v13) | ~ $i(v12) | ~ % 34.68/5.40 | $i(v11) | ? [v14: int] : ? [v15: int] : ? [v16: int] : ? % 34.68/5.40 | [v17: int] : (( ~ (v15 = 0) & in(v12, v0) = v15) | ( ~ (v14 = % 34.68/5.40 | 0) & in(v11, v0) = v14) | (((v17 = 0 & subset(v11, v12) % 34.68/5.40 | = 0) | ( ~ (v16 = 0) & in(v13, v1) = v16)) & ((v16 = % 34.68/5.40 | 0 & in(v13, v1) = 0) | ( ~ (v17 = 0) & subset(v11, % 34.68/5.40 | v12) = v17))))))) & (v2 = v1 | (v7 = 0 & v6 = 0 & % 34.68/5.40 | in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & subset(v4, v5) = % 34.68/5.40 | 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, v1) = 0 & % 34.68/5.40 | $i(v8))) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( ~ (v9 % 34.68/5.40 | = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 & % 34.68/5.40 | $i(v8)))) | ( ~ (v3 = v0) & relation_field(v1) = v3 & % 34.68/5.40 | $i(v3))))) % 34.68/5.40 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 34.68/5.40 | (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ % 34.68/5.40 | $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & relation(v1) = % 34.68/5.40 | v3)) % 34.68/5.41 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 34.68/5.41 | ! [v5: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ (ordered_pair(v3, % 34.68/5.41 | v4) = v5) | ~ (relation_field(v1) = v2) | ~ $i(v4) | ~ $i(v3) % 34.68/5.41 | | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] % 34.68/5.41 | : ? [v9: int] : (( ~ (v7 = 0) & in(v4, v0) = v7) | ( ~ (v6 = 0) & % 34.68/5.41 | relation(v1) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (((v9 = 0 % 34.68/5.41 | & subset(v3, v4) = 0) | ( ~ (v8 = 0) & in(v5, v1) = v8)) & % 34.68/5.41 | ((v8 = 0 & in(v5, v1) = 0) | ( ~ (v9 = 0) & subset(v3, v4) = % 34.68/5.41 | v9))))) % 34.68/5.41 | % 34.68/5.41 | ALPHA: (d6_relat_1) implies: % 34.68/5.41 | (6) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 34.68/5.41 | [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & relation_rng(v0) = % 34.68/5.41 | v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1 & $i(v3) & % 34.68/5.41 | $i(v2) & $i(v1))) % 34.68/5.41 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | % 34.68/5.41 | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v1 & % 34.68/5.41 | relation_dom(v0) = v3 & relation_rng(v0) = v4 & set_union2(v3, % 34.68/5.41 | v4) = v1 & $i(v4) & $i(v3) & $i(v1)) | ( ~ (v2 = 0) & % 34.68/5.41 | relation(v0) = v2))) % 34.68/5.41 | % 34.68/5.41 | ALPHA: (d8_relat_2) implies: % 34.68/5.41 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 34.68/5.41 | (is_transitive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | % 34.68/5.41 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 34.68/5.41 | ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) & % 34.68/5.41 | ordered_pair(v4, v5) = v7 & ordered_pair(v3, v5) = v8 & % 34.68/5.41 | ordered_pair(v3, v4) = v6 & in(v8, v0) = v9 & in(v7, v0) = 0 & % 34.68/5.41 | in(v6, v0) = 0 & in(v5, v1) = 0 & in(v4, v1) = 0 & in(v3, v1) = 0 & % 34.68/5.41 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3))) % 34.68/5.41 | % 34.68/5.41 | ALPHA: (t1_xboole_1) implies: % 34.68/5.41 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v1, v2) = 0) | ~ % 34.68/5.41 | (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | subset(v0, % 34.68/5.41 | v2) = 0) % 34.68/5.41 | % 34.68/5.41 | ALPHA: (function-axioms) implies: % 34.68/5.41 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 34.68/5.41 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 34.68/5.41 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 34.68/5.41 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 34.68/5.41 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 34.68/5.41 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 34.68/5.41 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 34.68/5.41 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 34.68/5.41 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 34.68/5.41 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 34.68/5.41 | v0)) % 34.68/5.41 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 34.68/5.41 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, % 34.68/5.41 | v2) = v0)) % 34.68/5.41 | % 34.68/5.41 | DELTA: instantiating (t3_wellord2) with fresh symbols all_48_0, all_48_1, % 34.68/5.41 | all_48_2 gives: % 34.68/5.41 | (16) ~ (all_48_0 = 0) & inclusion_relation(all_48_2) = all_48_1 & % 34.68/5.41 | transitive(all_48_1) = all_48_0 & $i(all_48_1) & $i(all_48_2) % 34.68/5.41 | % 34.68/5.41 | ALPHA: (16) implies: % 34.68/5.41 | (17) ~ (all_48_0 = 0) % 34.68/5.41 | (18) $i(all_48_2) % 34.68/5.41 | (19) $i(all_48_1) % 34.68/5.41 | (20) transitive(all_48_1) = all_48_0 % 34.68/5.41 | (21) inclusion_relation(all_48_2) = all_48_1 % 34.68/5.41 | % 34.68/5.41 | GROUND_INST: instantiating (2) with all_48_1, all_48_0, simplifying with (19), % 34.68/5.41 | (20) gives: % 34.68/5.42 | (22) ? [v0: int] : ? [v1: $i] : ? [v2: int] : (( ~ (v0 = 0) & % 34.68/5.42 | relation(all_48_1) = v0) | (( ~ (all_48_0 = 0) | (v2 = 0 & % 34.68/5.42 | relation_field(all_48_1) = v1 & is_transitive_in(all_48_1, v1) % 34.68/5.42 | = 0 & $i(v1))) & (all_48_0 = 0 | ( ~ (v2 = 0) & % 34.68/5.42 | relation_field(all_48_1) = v1 & is_transitive_in(all_48_1, v1) % 34.68/5.42 | = v2 & $i(v1))))) % 34.68/5.42 | % 34.68/5.42 | GROUND_INST: instantiating (dt_k1_wellord2) with all_48_2, all_48_1, % 34.68/5.42 | simplifying with (18), (21) gives: % 34.68/5.42 | (23) relation(all_48_1) = 0 % 34.68/5.42 | % 34.68/5.42 | DELTA: instantiating (22) with fresh symbols all_95_0, all_95_1, all_95_2 % 34.68/5.42 | gives: % 34.68/5.42 | (24) ( ~ (all_95_2 = 0) & relation(all_48_1) = all_95_2) | (( ~ (all_48_0 = % 34.68/5.42 | 0) | (all_95_0 = 0 & relation_field(all_48_1) = all_95_1 & % 34.68/5.42 | is_transitive_in(all_48_1, all_95_1) = 0 & $i(all_95_1))) & % 34.68/5.42 | (all_48_0 = 0 | ( ~ (all_95_0 = 0) & relation_field(all_48_1) = % 34.68/5.42 | all_95_1 & is_transitive_in(all_48_1, all_95_1) = all_95_0 & % 34.68/5.42 | $i(all_95_1)))) % 34.68/5.42 | % 34.68/5.42 | BETA: splitting (24) gives: % 34.68/5.42 | % 34.68/5.42 | Case 1: % 34.68/5.42 | | % 34.68/5.42 | | (25) ~ (all_95_2 = 0) & relation(all_48_1) = all_95_2 % 34.68/5.42 | | % 34.68/5.42 | | ALPHA: (25) implies: % 34.68/5.42 | | (26) ~ (all_95_2 = 0) % 34.68/5.42 | | (27) relation(all_48_1) = all_95_2 % 34.68/5.42 | | % 34.68/5.42 | | GROUND_INST: instantiating (10) with 0, all_95_2, all_48_1, simplifying with % 34.68/5.42 | | (23), (27) gives: % 34.68/5.42 | | (28) all_95_2 = 0 % 34.68/5.42 | | % 34.68/5.42 | | REDUCE: (26), (28) imply: % 34.68/5.42 | | (29) $false % 34.68/5.42 | | % 34.68/5.42 | | CLOSE: (29) is inconsistent. % 34.68/5.42 | | % 34.68/5.42 | Case 2: % 34.68/5.42 | | % 34.68/5.42 | | (30) ( ~ (all_48_0 = 0) | (all_95_0 = 0 & relation_field(all_48_1) = % 34.68/5.42 | | all_95_1 & is_transitive_in(all_48_1, all_95_1) = 0 & % 34.68/5.42 | | $i(all_95_1))) & (all_48_0 = 0 | ( ~ (all_95_0 = 0) & % 34.68/5.42 | | relation_field(all_48_1) = all_95_1 & is_transitive_in(all_48_1, % 34.68/5.42 | | all_95_1) = all_95_0 & $i(all_95_1))) % 34.68/5.42 | | % 34.68/5.42 | | ALPHA: (30) implies: % 34.68/5.42 | | (31) all_48_0 = 0 | ( ~ (all_95_0 = 0) & relation_field(all_48_1) = % 34.68/5.42 | | all_95_1 & is_transitive_in(all_48_1, all_95_1) = all_95_0 & % 34.68/5.42 | | $i(all_95_1)) % 34.68/5.42 | | % 34.68/5.42 | | BETA: splitting (31) gives: % 34.68/5.42 | | % 34.68/5.42 | | Case 1: % 34.68/5.42 | | | % 34.68/5.42 | | | (32) all_48_0 = 0 % 34.68/5.42 | | | % 34.68/5.42 | | | REDUCE: (17), (32) imply: % 34.68/5.42 | | | (33) $false % 34.68/5.42 | | | % 34.68/5.42 | | | CLOSE: (33) is inconsistent. % 34.68/5.42 | | | % 34.68/5.42 | | Case 2: % 34.68/5.42 | | | % 34.68/5.42 | | | (34) ~ (all_95_0 = 0) & relation_field(all_48_1) = all_95_1 & % 34.68/5.42 | | | is_transitive_in(all_48_1, all_95_1) = all_95_0 & $i(all_95_1) % 34.68/5.42 | | | % 34.68/5.42 | | | ALPHA: (34) implies: % 34.68/5.42 | | | (35) ~ (all_95_0 = 0) % 34.68/5.42 | | | (36) $i(all_95_1) % 34.68/5.42 | | | (37) is_transitive_in(all_48_1, all_95_1) = all_95_0 % 34.68/5.42 | | | (38) relation_field(all_48_1) = all_95_1 % 34.68/5.42 | | | % 34.68/5.42 | | | GROUND_INST: instantiating (3) with all_48_2, all_48_1, all_48_1, % 34.68/5.42 | | | simplifying with (18), (19), (21), (23) gives: % 34.68/5.42 | | | (39) ? [v0: $i] : ? [v1: $i] : (relation_field(all_48_1) = all_48_2 & % 34.68/5.42 | | | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 34.68/5.42 | | | (subset(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: int] : % 34.68/5.42 | | | ? [v6: int] : ? [v7: $i] : ? [v8: int] : (( ~ (v6 = 0) & % 34.68/5.42 | | | in(v3, all_48_2) = v6) | ( ~ (v5 = 0) & in(v2, all_48_2) = % 34.68/5.42 | | | v5) | (( ~ (v4 = 0) | (v8 = 0 & ordered_pair(v2, v3) = v7 % 34.68/5.42 | | | & in(v7, all_48_1) = 0 & $i(v7))) & (v4 = 0 | ( ~ (v8 % 34.68/5.43 | | | = 0) & ordered_pair(v2, v3) = v7 & in(v7, all_48_1) % 34.68/5.43 | | | = v8 & $i(v7)))))) & ! [v2: $i] : ! [v3: $i] : ! % 34.68/5.43 | | | [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 34.68/5.43 | | | $i(v2) | ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: % 34.68/5.43 | | | int] : (( ~ (v6 = 0) & in(v3, all_48_2) = v6) | ( ~ (v5 = 0) % 34.68/5.43 | | | & in(v2, all_48_2) = v5) | (((v8 = 0 & subset(v2, v3) = 0) % 34.68/5.43 | | | | ( ~ (v7 = 0) & in(v4, all_48_1) = v7)) & ((v7 = 0 & % 34.68/5.43 | | | in(v4, all_48_1) = 0) | ( ~ (v8 = 0) & subset(v2, v3) % 34.68/5.43 | | | = v8)))))) % 34.68/5.43 | | | % 34.68/5.43 | | | GROUND_INST: instantiating (6) with all_48_1, simplifying with (19), (23) % 34.68/5.43 | | | gives: % 34.68/5.43 | | | (40) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_48_1) % 34.68/5.43 | | | = v1 & relation_rng(all_48_1) = v2 & relation_field(all_48_1) = % 34.68/5.43 | | | v0 & set_union2(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 34.68/5.43 | | | % 34.68/5.43 | | | GROUND_INST: instantiating (8) with all_48_1, all_95_1, all_95_0, % 34.68/5.43 | | | simplifying with (19), (23), (36), (37) gives: % 34.68/5.43 | | | (41) all_95_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 34.68/5.43 | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 34.68/5.43 | | | ordered_pair(v1, v2) = v4 & ordered_pair(v0, v2) = v5 & % 34.68/5.43 | | | ordered_pair(v0, v1) = v3 & in(v5, all_48_1) = v6 & in(v4, % 34.68/5.43 | | | all_48_1) = 0 & in(v3, all_48_1) = 0 & in(v2, all_95_1) = 0 & % 34.68/5.43 | | | in(v1, all_95_1) = 0 & in(v0, all_95_1) = 0 & $i(v5) & $i(v4) & % 34.68/5.43 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 34.68/5.43 | | | % 34.68/5.43 | | | GROUND_INST: instantiating (4) with all_48_2, all_48_1, all_95_1, % 34.68/5.43 | | | simplifying with (18), (19), (21), (38) gives: % 34.68/5.43 | | | (42) all_95_1 = all_48_2 | ? [v0: int] : ( ~ (v0 = 0) & % 34.68/5.43 | | | relation(all_48_1) = v0) % 34.68/5.43 | | | % 34.68/5.43 | | | GROUND_INST: instantiating (7) with all_48_1, all_95_1, simplifying with % 34.68/5.43 | | | (19), (38) gives: % 34.68/5.43 | | | (43) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ((v3 = % 34.68/5.43 | | | all_95_1 & relation_dom(all_48_1) = v1 & % 34.68/5.43 | | | relation_rng(all_48_1) = v2 & set_union2(v1, v2) = all_95_1 & % 34.68/5.43 | | | $i(v2) & $i(v1) & $i(all_95_1)) | ( ~ (v0 = 0) & % 34.68/5.43 | | | relation(all_48_1) = v0)) % 34.68/5.43 | | | % 34.68/5.43 | | | DELTA: instantiating (40) with fresh symbols all_148_0, all_148_1, % 34.68/5.43 | | | all_148_2 gives: % 34.68/5.43 | | | (44) relation_dom(all_48_1) = all_148_1 & relation_rng(all_48_1) = % 34.68/5.43 | | | all_148_0 & relation_field(all_48_1) = all_148_2 & % 34.68/5.43 | | | set_union2(all_148_1, all_148_0) = all_148_2 & $i(all_148_0) & % 34.68/5.43 | | | $i(all_148_1) & $i(all_148_2) % 34.68/5.43 | | | % 34.68/5.43 | | | ALPHA: (44) implies: % 34.68/5.43 | | | (45) set_union2(all_148_1, all_148_0) = all_148_2 % 34.68/5.43 | | | (46) relation_field(all_48_1) = all_148_2 % 34.68/5.43 | | | (47) relation_rng(all_48_1) = all_148_0 % 34.68/5.43 | | | (48) relation_dom(all_48_1) = all_148_1 % 34.68/5.43 | | | % 34.68/5.43 | | | DELTA: instantiating (43) with fresh symbols all_151_0, all_151_1, % 34.68/5.43 | | | all_151_2, all_151_3 gives: % 34.68/5.43 | | | (49) (all_151_0 = all_95_1 & relation_dom(all_48_1) = all_151_2 & % 34.68/5.43 | | | relation_rng(all_48_1) = all_151_1 & set_union2(all_151_2, % 34.68/5.43 | | | all_151_1) = all_95_1 & $i(all_151_1) & $i(all_151_2) & % 34.68/5.43 | | | $i(all_95_1)) | ( ~ (all_151_3 = 0) & relation(all_48_1) = % 34.68/5.43 | | | all_151_3) % 34.68/5.43 | | | % 34.68/5.43 | | | DELTA: instantiating (39) with fresh symbols all_156_0, all_156_1 gives: % 34.68/5.43 | | | (50) relation_field(all_48_1) = all_48_2 & $i(all_156_0) & % 34.68/5.43 | | | $i(all_156_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 34.68/5.43 | | | (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 34.68/5.43 | | | ? [v4: int] : ? [v5: $i] : ? [v6: int] : (( ~ (v4 = 0) & % 34.68/5.43 | | | in(v1, all_48_2) = v4) | ( ~ (v3 = 0) & in(v0, all_48_2) = % 34.68/5.43 | | | v3) | (( ~ (v2 = 0) | (v6 = 0 & ordered_pair(v0, v1) = v5 & % 34.68/5.43 | | | in(v5, all_48_1) = 0 & $i(v5))) & (v2 = 0 | ( ~ (v6 = 0) % 34.68/5.43 | | | & ordered_pair(v0, v1) = v5 & in(v5, all_48_1) = v6 & % 34.68/5.43 | | | $i(v5)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.68/5.43 | | | ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 34.68/5.43 | | | int] : ? [v4: int] : ? [v5: int] : ? [v6: int] : (( ~ (v4 = % 34.68/5.43 | | | 0) & in(v1, all_48_2) = v4) | ( ~ (v3 = 0) & in(v0, % 34.68/5.43 | | | all_48_2) = v3) | (((v6 = 0 & subset(v0, v1) = 0) | ( ~ % 34.68/5.43 | | | (v5 = 0) & in(v2, all_48_1) = v5)) & ((v5 = 0 & in(v2, % 34.68/5.43 | | | all_48_1) = 0) | ( ~ (v6 = 0) & subset(v0, v1) = % 34.68/5.43 | | | v6))))) % 34.68/5.43 | | | % 34.68/5.43 | | | ALPHA: (50) implies: % 34.68/5.43 | | | (51) relation_field(all_48_1) = all_48_2 % 34.68/5.43 | | | (52) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, % 34.68/5.43 | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 34.68/5.43 | | | int] : ? [v5: int] : ? [v6: int] : (( ~ (v4 = 0) & in(v1, % 34.68/5.43 | | | all_48_2) = v4) | ( ~ (v3 = 0) & in(v0, all_48_2) = v3) | % 34.68/5.43 | | | (((v6 = 0 & subset(v0, v1) = 0) | ( ~ (v5 = 0) & in(v2, % 34.68/5.43 | | | all_48_1) = v5)) & ((v5 = 0 & in(v2, all_48_1) = 0) | % 34.68/5.43 | | | ( ~ (v6 = 0) & subset(v0, v1) = v6))))) % 34.68/5.43 | | | % 34.68/5.43 | | | BETA: splitting (49) gives: % 34.68/5.43 | | | % 34.68/5.43 | | | Case 1: % 34.68/5.43 | | | | % 34.68/5.43 | | | | (53) all_151_0 = all_95_1 & relation_dom(all_48_1) = all_151_2 & % 34.68/5.43 | | | | relation_rng(all_48_1) = all_151_1 & set_union2(all_151_2, % 34.68/5.43 | | | | all_151_1) = all_95_1 & $i(all_151_1) & $i(all_151_2) & % 34.68/5.43 | | | | $i(all_95_1) % 34.68/5.43 | | | | % 34.68/5.43 | | | | ALPHA: (53) implies: % 34.68/5.43 | | | | (54) $i(all_151_2) % 34.68/5.43 | | | | (55) $i(all_151_1) % 34.68/5.43 | | | | (56) relation_rng(all_48_1) = all_151_1 % 34.68/5.43 | | | | (57) relation_dom(all_48_1) = all_151_2 % 34.68/5.43 | | | | % 34.68/5.43 | | | | BETA: splitting (41) gives: % 34.68/5.43 | | | | % 34.68/5.43 | | | | Case 1: % 34.68/5.43 | | | | | % 34.68/5.43 | | | | | (58) all_95_0 = 0 % 34.68/5.43 | | | | | % 34.68/5.44 | | | | | REDUCE: (35), (58) imply: % 34.68/5.44 | | | | | (59) $false % 34.68/5.44 | | | | | % 34.68/5.44 | | | | | CLOSE: (59) is inconsistent. % 34.68/5.44 | | | | | % 34.68/5.44 | | | | Case 2: % 34.68/5.44 | | | | | % 34.68/5.44 | | | | | (60) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 34.68/5.44 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 34.68/5.44 | | | | | ordered_pair(v1, v2) = v4 & ordered_pair(v0, v2) = v5 & % 34.68/5.44 | | | | | ordered_pair(v0, v1) = v3 & in(v5, all_48_1) = v6 & in(v4, % 34.68/5.44 | | | | | all_48_1) = 0 & in(v3, all_48_1) = 0 & in(v2, all_95_1) = % 34.68/5.44 | | | | | 0 & in(v1, all_95_1) = 0 & in(v0, all_95_1) = 0 & $i(v5) & % 34.68/5.44 | | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 34.68/5.44 | | | | | % 34.68/5.44 | | | | | DELTA: instantiating (60) with fresh symbols all_166_0, all_166_1, % 34.68/5.44 | | | | | all_166_2, all_166_3, all_166_4, all_166_5, all_166_6 gives: % 34.68/5.44 | | | | | (61) ~ (all_166_0 = 0) & ordered_pair(all_166_5, all_166_4) = % 34.68/5.44 | | | | | all_166_2 & ordered_pair(all_166_6, all_166_4) = all_166_1 & % 34.68/5.44 | | | | | ordered_pair(all_166_6, all_166_5) = all_166_3 & in(all_166_1, % 34.68/5.44 | | | | | all_48_1) = all_166_0 & in(all_166_2, all_48_1) = 0 & % 34.68/5.44 | | | | | in(all_166_3, all_48_1) = 0 & in(all_166_4, all_95_1) = 0 & % 34.68/5.44 | | | | | in(all_166_5, all_95_1) = 0 & in(all_166_6, all_95_1) = 0 & % 34.68/5.44 | | | | | $i(all_166_1) & $i(all_166_2) & $i(all_166_3) & $i(all_166_4) % 34.68/5.44 | | | | | & $i(all_166_5) & $i(all_166_6) % 34.68/5.44 | | | | | % 34.68/5.44 | | | | | ALPHA: (61) implies: % 34.68/5.44 | | | | | (62) ~ (all_166_0 = 0) % 34.68/5.44 | | | | | (63) $i(all_166_6) % 34.68/5.44 | | | | | (64) $i(all_166_5) % 34.68/5.44 | | | | | (65) $i(all_166_4) % 34.68/5.44 | | | | | (66) in(all_166_6, all_95_1) = 0 % 34.68/5.44 | | | | | (67) in(all_166_5, all_95_1) = 0 % 34.68/5.44 | | | | | (68) in(all_166_4, all_95_1) = 0 % 34.68/5.44 | | | | | (69) in(all_166_3, all_48_1) = 0 % 34.68/5.44 | | | | | (70) in(all_166_2, all_48_1) = 0 % 34.68/5.44 | | | | | (71) in(all_166_1, all_48_1) = all_166_0 % 34.68/5.44 | | | | | (72) ordered_pair(all_166_6, all_166_5) = all_166_3 % 34.68/5.44 | | | | | (73) ordered_pair(all_166_6, all_166_4) = all_166_1 % 34.68/5.44 | | | | | (74) ordered_pair(all_166_5, all_166_4) = all_166_2 % 34.68/5.44 | | | | | % 34.68/5.44 | | | | | BETA: splitting (42) gives: % 34.68/5.44 | | | | | % 34.68/5.44 | | | | | Case 1: % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | (75) all_95_1 = all_48_2 % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | REDUCE: (68), (75) imply: % 34.68/5.44 | | | | | | (76) in(all_166_4, all_48_2) = 0 % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | REDUCE: (67), (75) imply: % 34.68/5.44 | | | | | | (77) in(all_166_5, all_48_2) = 0 % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | REDUCE: (66), (75) imply: % 34.68/5.44 | | | | | | (78) in(all_166_6, all_48_2) = 0 % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | GROUND_INST: instantiating (11) with all_48_2, all_148_2, all_48_1, % 34.68/5.44 | | | | | | simplifying with (46), (51) gives: % 34.68/5.44 | | | | | | (79) all_148_2 = all_48_2 % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | GROUND_INST: instantiating (12) with all_148_0, all_151_1, all_48_1, % 34.68/5.44 | | | | | | simplifying with (47), (56) gives: % 34.68/5.44 | | | | | | (80) all_151_1 = all_148_0 % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | GROUND_INST: instantiating (13) with all_148_1, all_151_2, all_48_1, % 34.68/5.44 | | | | | | simplifying with (48), (57) gives: % 34.68/5.44 | | | | | | (81) all_151_2 = all_148_1 % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | REDUCE: (45), (79) imply: % 34.68/5.44 | | | | | | (82) set_union2(all_148_1, all_148_0) = all_48_2 % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | REDUCE: (55), (80) imply: % 34.68/5.44 | | | | | | (83) $i(all_148_0) % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | REDUCE: (54), (81) imply: % 34.68/5.44 | | | | | | (84) $i(all_148_1) % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | GROUND_INST: instantiating (1) with all_148_0, all_148_1, all_48_2, % 34.68/5.44 | | | | | | simplifying with (82), (83), (84) gives: % 34.68/5.44 | | | | | | (85) set_union2(all_148_0, all_148_1) = all_48_2 & $i(all_48_2) % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | GROUND_INST: instantiating (5) with all_48_2, all_48_1, all_48_2, % 34.68/5.44 | | | | | | all_166_6, all_166_5, all_166_3, simplifying with (18), % 34.68/5.44 | | | | | | (19), (21), (51), (63), (64), (72) gives: % 34.68/5.44 | | | | | | (86) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 34.68/5.44 | | | | | | (( ~ (v1 = 0) & in(all_166_5, all_48_2) = v1) | ( ~ (v0 = 0) % 34.68/5.44 | | | | | | & relation(all_48_1) = v0) | ( ~ (v0 = 0) & % 34.68/5.44 | | | | | | in(all_166_6, all_48_2) = v0) | (((v3 = 0 & % 34.68/5.44 | | | | | | subset(all_166_6, all_166_5) = 0) | ( ~ (v2 = 0) & % 34.68/5.44 | | | | | | in(all_166_3, all_48_1) = v2)) & ((v2 = 0 & % 34.68/5.44 | | | | | | in(all_166_3, all_48_1) = 0) | ( ~ (v3 = 0) & % 34.68/5.44 | | | | | | subset(all_166_6, all_166_5) = v3)))) % 34.68/5.44 | | | | | | % 34.68/5.44 | | | | | | GROUND_INST: instantiating (5) with all_48_2, all_48_1, all_48_2, % 34.68/5.44 | | | | | | all_166_6, all_166_4, all_166_1, simplifying with (18), % 34.68/5.44 | | | | | | (19), (21), (51), (63), (65), (73) gives: % 34.90/5.44 | | | | | | (87) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 34.90/5.44 | | | | | | (( ~ (v1 = 0) & in(all_166_4, all_48_2) = v1) | ( ~ (v0 = 0) % 34.90/5.44 | | | | | | & relation(all_48_1) = v0) | ( ~ (v0 = 0) & % 34.90/5.44 | | | | | | in(all_166_6, all_48_2) = v0) | (((v3 = 0 & % 34.90/5.44 | | | | | | subset(all_166_6, all_166_4) = 0) | ( ~ (v2 = 0) & % 34.90/5.44 | | | | | | in(all_166_1, all_48_1) = v2)) & ((v2 = 0 & % 34.90/5.44 | | | | | | in(all_166_1, all_48_1) = 0) | ( ~ (v3 = 0) & % 34.90/5.44 | | | | | | subset(all_166_6, all_166_4) = v3)))) % 34.90/5.44 | | | | | | % 34.90/5.44 | | | | | | GROUND_INST: instantiating (52) with all_166_6, all_166_4, % 34.90/5.44 | | | | | | all_166_1, simplifying with (63), (65), (73) gives: % 34.90/5.44 | | | | | | (88) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 34.90/5.44 | | | | | | (( ~ (v1 = 0) & in(all_166_4, all_48_2) = v1) | ( ~ (v0 = 0) % 34.90/5.44 | | | | | | & in(all_166_6, all_48_2) = v0) | (((v3 = 0 & % 34.90/5.44 | | | | | | subset(all_166_6, all_166_4) = 0) | ( ~ (v2 = 0) & % 34.90/5.44 | | | | | | in(all_166_1, all_48_1) = v2)) & ((v2 = 0 & % 34.90/5.44 | | | | | | in(all_166_1, all_48_1) = 0) | ( ~ (v3 = 0) & % 34.90/5.44 | | | | | | subset(all_166_6, all_166_4) = v3)))) % 34.90/5.44 | | | | | | % 34.90/5.44 | | | | | | GROUND_INST: instantiating (52) with all_166_5, all_166_4, % 34.90/5.44 | | | | | | all_166_2, simplifying with (64), (65), (74) gives: % 34.90/5.44 | | | | | | (89) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 34.90/5.44 | | | | | | (( ~ (v1 = 0) & in(all_166_4, all_48_2) = v1) | ( ~ (v0 = 0) % 34.90/5.44 | | | | | | & in(all_166_5, all_48_2) = v0) | (((v3 = 0 & % 34.90/5.44 | | | | | | subset(all_166_5, all_166_4) = 0) | ( ~ (v2 = 0) & % 34.90/5.44 | | | | | | in(all_166_2, all_48_1) = v2)) & ((v2 = 0 & % 34.90/5.44 | | | | | | in(all_166_2, all_48_1) = 0) | ( ~ (v3 = 0) & % 34.90/5.44 | | | | | | subset(all_166_5, all_166_4) = v3)))) % 34.90/5.44 | | | | | | % 34.90/5.44 | | | | | | DELTA: instantiating (89) with fresh symbols all_228_0, all_228_1, % 34.90/5.44 | | | | | | all_228_2, all_228_3 gives: % 34.90/5.44 | | | | | | (90) ( ~ (all_228_2 = 0) & in(all_166_4, all_48_2) = all_228_2) | % 34.90/5.44 | | | | | | ( ~ (all_228_3 = 0) & in(all_166_5, all_48_2) = all_228_3) | % 34.90/5.44 | | | | | | (((all_228_0 = 0 & subset(all_166_5, all_166_4) = 0) | ( ~ % 34.90/5.44 | | | | | | (all_228_1 = 0) & in(all_166_2, all_48_1) = % 34.90/5.44 | | | | | | all_228_1)) & ((all_228_1 = 0 & in(all_166_2, % 34.90/5.44 | | | | | | all_48_1) = 0) | ( ~ (all_228_0 = 0) & % 34.90/5.44 | | | | | | subset(all_166_5, all_166_4) = all_228_0))) % 34.90/5.44 | | | | | | % 34.90/5.44 | | | | | | DELTA: instantiating (88) with fresh symbols all_230_0, all_230_1, % 34.90/5.44 | | | | | | all_230_2, all_230_3 gives: % 34.90/5.45 | | | | | | (91) ( ~ (all_230_2 = 0) & in(all_166_4, all_48_2) = all_230_2) | % 34.90/5.45 | | | | | | ( ~ (all_230_3 = 0) & in(all_166_6, all_48_2) = all_230_3) | % 34.90/5.45 | | | | | | (((all_230_0 = 0 & subset(all_166_6, all_166_4) = 0) | ( ~ % 34.90/5.45 | | | | | | (all_230_1 = 0) & in(all_166_1, all_48_1) = % 34.90/5.45 | | | | | | all_230_1)) & ((all_230_1 = 0 & in(all_166_1, % 34.90/5.45 | | | | | | all_48_1) = 0) | ( ~ (all_230_0 = 0) & % 34.90/5.45 | | | | | | subset(all_166_6, all_166_4) = all_230_0))) % 34.90/5.45 | | | | | | % 34.90/5.45 | | | | | | DELTA: instantiating (86) with fresh symbols all_231_0, all_231_1, % 34.90/5.45 | | | | | | all_231_2, all_231_3 gives: % 34.90/5.45 | | | | | | (92) ( ~ (all_231_2 = 0) & in(all_166_5, all_48_2) = all_231_2) | % 34.90/5.45 | | | | | | ( ~ (all_231_3 = 0) & relation(all_48_1) = all_231_3) | ( ~ % 34.90/5.45 | | | | | | (all_231_3 = 0) & in(all_166_6, all_48_2) = all_231_3) | % 34.90/5.45 | | | | | | (((all_231_0 = 0 & subset(all_166_6, all_166_5) = 0) | ( ~ % 34.90/5.45 | | | | | | (all_231_1 = 0) & in(all_166_3, all_48_1) = % 34.90/5.45 | | | | | | all_231_1)) & ((all_231_1 = 0 & in(all_166_3, % 34.90/5.45 | | | | | | all_48_1) = 0) | ( ~ (all_231_0 = 0) & % 34.90/5.45 | | | | | | subset(all_166_6, all_166_5) = all_231_0))) % 34.90/5.45 | | | | | | % 34.90/5.45 | | | | | | DELTA: instantiating (87) with fresh symbols all_232_0, all_232_1, % 34.90/5.45 | | | | | | all_232_2, all_232_3 gives: % 34.90/5.45 | | | | | | (93) ( ~ (all_232_2 = 0) & in(all_166_4, all_48_2) = all_232_2) | % 34.90/5.45 | | | | | | ( ~ (all_232_3 = 0) & relation(all_48_1) = all_232_3) | ( ~ % 34.90/5.45 | | | | | | (all_232_3 = 0) & in(all_166_6, all_48_2) = all_232_3) | % 34.90/5.45 | | | | | | (((all_232_0 = 0 & subset(all_166_6, all_166_4) = 0) | ( ~ % 34.90/5.45 | | | | | | (all_232_1 = 0) & in(all_166_1, all_48_1) = % 34.90/5.45 | | | | | | all_232_1)) & ((all_232_1 = 0 & in(all_166_1, % 34.90/5.45 | | | | | | all_48_1) = 0) | ( ~ (all_232_0 = 0) & % 34.90/5.45 | | | | | | subset(all_166_6, all_166_4) = all_232_0))) % 34.90/5.45 | | | | | | % 34.90/5.45 | | | | | | BETA: splitting (90) gives: % 34.90/5.45 | | | | | | % 34.90/5.45 | | | | | | Case 1: % 34.90/5.45 | | | | | | | % 34.90/5.45 | | | | | | | (94) ~ (all_228_2 = 0) & in(all_166_4, all_48_2) = all_228_2 % 34.90/5.45 | | | | | | | % 34.90/5.45 | | | | | | | ALPHA: (94) implies: % 34.90/5.45 | | | | | | | (95) ~ (all_228_2 = 0) % 34.90/5.45 | | | | | | | (96) in(all_166_4, all_48_2) = all_228_2 % 34.90/5.45 | | | | | | | % 34.90/5.45 | | | | | | | GROUND_INST: instantiating (14) with 0, all_228_2, all_48_2, % 34.90/5.45 | | | | | | | all_166_4, simplifying with (76), (96) gives: % 34.90/5.45 | | | | | | | (97) all_228_2 = 0 % 34.90/5.45 | | | | | | | % 34.90/5.45 | | | | | | | REDUCE: (95), (97) imply: % 34.90/5.45 | | | | | | | (98) $false % 34.90/5.45 | | | | | | | % 34.90/5.45 | | | | | | | CLOSE: (98) is inconsistent. % 34.90/5.45 | | | | | | | % 34.90/5.45 | | | | | | Case 2: % 34.90/5.45 | | | | | | | % 34.90/5.45 | | | | | | | (99) ( ~ (all_228_3 = 0) & in(all_166_5, all_48_2) = all_228_3) % 34.90/5.45 | | | | | | | | (((all_228_0 = 0 & subset(all_166_5, all_166_4) = 0) | ( % 34.90/5.45 | | | | | | | ~ (all_228_1 = 0) & in(all_166_2, all_48_1) = % 34.90/5.45 | | | | | | | all_228_1)) & ((all_228_1 = 0 & in(all_166_2, % 34.90/5.45 | | | | | | | all_48_1) = 0) | ( ~ (all_228_0 = 0) & % 34.90/5.45 | | | | | | | subset(all_166_5, all_166_4) = all_228_0))) % 34.90/5.45 | | | | | | | % 34.90/5.45 | | | | | | | BETA: splitting (99) gives: % 34.90/5.45 | | | | | | | % 34.90/5.45 | | | | | | | Case 1: % 34.90/5.45 | | | | | | | | % 34.90/5.45 | | | | | | | | (100) ~ (all_228_3 = 0) & in(all_166_5, all_48_2) = % 34.90/5.45 | | | | | | | | all_228_3 % 34.90/5.45 | | | | | | | | % 34.90/5.45 | | | | | | | | ALPHA: (100) implies: % 34.90/5.45 | | | | | | | | (101) ~ (all_228_3 = 0) % 34.90/5.45 | | | | | | | | (102) in(all_166_5, all_48_2) = all_228_3 % 34.90/5.45 | | | | | | | | % 34.90/5.45 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_228_3, all_48_2, % 34.90/5.45 | | | | | | | | all_166_5, simplifying with (77), (102) gives: % 34.90/5.45 | | | | | | | | (103) all_228_3 = 0 % 34.90/5.45 | | | | | | | | % 34.90/5.45 | | | | | | | | REDUCE: (101), (103) imply: % 34.90/5.45 | | | | | | | | (104) $false % 34.90/5.45 | | | | | | | | % 34.90/5.45 | | | | | | | | CLOSE: (104) is inconsistent. % 34.90/5.45 | | | | | | | | % 34.90/5.45 | | | | | | | Case 2: % 34.90/5.45 | | | | | | | | % 34.90/5.45 | | | | | | | | (105) ((all_228_0 = 0 & subset(all_166_5, all_166_4) = 0) | ( % 34.90/5.45 | | | | | | | | ~ (all_228_1 = 0) & in(all_166_2, all_48_1) = % 34.90/5.45 | | | | | | | | all_228_1)) & ((all_228_1 = 0 & in(all_166_2, % 34.90/5.45 | | | | | | | | all_48_1) = 0) | ( ~ (all_228_0 = 0) & % 34.90/5.45 | | | | | | | | subset(all_166_5, all_166_4) = all_228_0)) % 34.90/5.45 | | | | | | | | % 34.90/5.45 | | | | | | | | ALPHA: (105) implies: % 34.90/5.45 | | | | | | | | (106) (all_228_0 = 0 & subset(all_166_5, all_166_4) = 0) | ( % 34.90/5.45 | | | | | | | | ~ (all_228_1 = 0) & in(all_166_2, all_48_1) = % 34.90/5.45 | | | | | | | | all_228_1) % 34.90/5.45 | | | | | | | | % 34.90/5.45 | | | | | | | | BETA: splitting (93) gives: % 34.90/5.45 | | | | | | | | % 34.90/5.45 | | | | | | | | Case 1: % 34.90/5.45 | | | | | | | | | % 34.90/5.45 | | | | | | | | | (107) ( ~ (all_232_2 = 0) & in(all_166_4, all_48_2) = % 34.90/5.45 | | | | | | | | | all_232_2) | ( ~ (all_232_3 = 0) & % 34.90/5.45 | | | | | | | | | relation(all_48_1) = all_232_3) % 34.90/5.45 | | | | | | | | | % 34.90/5.45 | | | | | | | | | BETA: splitting (107) gives: % 34.90/5.45 | | | | | | | | | % 34.90/5.45 | | | | | | | | | Case 1: % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | (108) ~ (all_232_2 = 0) & in(all_166_4, all_48_2) = % 34.90/5.45 | | | | | | | | | | all_232_2 % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | ALPHA: (108) implies: % 34.90/5.45 | | | | | | | | | | (109) ~ (all_232_2 = 0) % 34.90/5.45 | | | | | | | | | | (110) in(all_166_4, all_48_2) = all_232_2 % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_232_2, all_48_2, % 34.90/5.45 | | | | | | | | | | all_166_4, simplifying with (76), (110) gives: % 34.90/5.45 | | | | | | | | | | (111) all_232_2 = 0 % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | REDUCE: (109), (111) imply: % 34.90/5.45 | | | | | | | | | | (112) $false % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | CLOSE: (112) is inconsistent. % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | Case 2: % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | (113) ~ (all_232_3 = 0) & relation(all_48_1) = all_232_3 % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | ALPHA: (113) implies: % 34.90/5.45 | | | | | | | | | | (114) ~ (all_232_3 = 0) % 34.90/5.45 | | | | | | | | | | (115) relation(all_48_1) = all_232_3 % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_232_3, all_48_1, % 34.90/5.45 | | | | | | | | | | simplifying with (23), (115) gives: % 34.90/5.45 | | | | | | | | | | (116) all_232_3 = 0 % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | REDUCE: (114), (116) imply: % 34.90/5.45 | | | | | | | | | | (117) $false % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | CLOSE: (117) is inconsistent. % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | End of split % 34.90/5.45 | | | | | | | | | % 34.90/5.45 | | | | | | | | Case 2: % 34.90/5.45 | | | | | | | | | % 34.90/5.45 | | | | | | | | | (118) ( ~ (all_232_3 = 0) & in(all_166_6, all_48_2) = % 34.90/5.45 | | | | | | | | | all_232_3) | (((all_232_0 = 0 & subset(all_166_6, % 34.90/5.45 | | | | | | | | | all_166_4) = 0) | ( ~ (all_232_1 = 0) & % 34.90/5.45 | | | | | | | | | in(all_166_1, all_48_1) = all_232_1)) & % 34.90/5.45 | | | | | | | | | ((all_232_1 = 0 & in(all_166_1, all_48_1) = 0) | ( % 34.90/5.45 | | | | | | | | | ~ (all_232_0 = 0) & subset(all_166_6, % 34.90/5.45 | | | | | | | | | all_166_4) = all_232_0))) % 34.90/5.45 | | | | | | | | | % 34.90/5.45 | | | | | | | | | BETA: splitting (118) gives: % 34.90/5.45 | | | | | | | | | % 34.90/5.45 | | | | | | | | | Case 1: % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | (119) ~ (all_232_3 = 0) & in(all_166_6, all_48_2) = % 34.90/5.45 | | | | | | | | | | all_232_3 % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | ALPHA: (119) implies: % 34.90/5.45 | | | | | | | | | | (120) ~ (all_232_3 = 0) % 34.90/5.45 | | | | | | | | | | (121) in(all_166_6, all_48_2) = all_232_3 % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_232_3, all_48_2, % 34.90/5.45 | | | | | | | | | | all_166_6, simplifying with (78), (121) gives: % 34.90/5.45 | | | | | | | | | | (122) all_232_3 = 0 % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | REDUCE: (120), (122) imply: % 34.90/5.45 | | | | | | | | | | (123) $false % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | CLOSE: (123) is inconsistent. % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | Case 2: % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | (124) ((all_232_0 = 0 & subset(all_166_6, all_166_4) = 0) % 34.90/5.45 | | | | | | | | | | | ( ~ (all_232_1 = 0) & in(all_166_1, all_48_1) = % 34.90/5.45 | | | | | | | | | | all_232_1)) & ((all_232_1 = 0 & in(all_166_1, % 34.90/5.45 | | | | | | | | | | all_48_1) = 0) | ( ~ (all_232_0 = 0) & % 34.90/5.45 | | | | | | | | | | subset(all_166_6, all_166_4) = all_232_0)) % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | ALPHA: (124) implies: % 34.90/5.45 | | | | | | | | | | (125) (all_232_1 = 0 & in(all_166_1, all_48_1) = 0) | ( ~ % 34.90/5.45 | | | | | | | | | | (all_232_0 = 0) & subset(all_166_6, all_166_4) = % 34.90/5.45 | | | | | | | | | | all_232_0) % 34.90/5.45 | | | | | | | | | | (126) (all_232_0 = 0 & subset(all_166_6, all_166_4) = 0) % 34.90/5.45 | | | | | | | | | | | ( ~ (all_232_1 = 0) & in(all_166_1, all_48_1) = % 34.90/5.45 | | | | | | | | | | all_232_1) % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | BETA: splitting (125) gives: % 34.90/5.45 | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | Case 1: % 34.90/5.45 | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | | (127) all_232_1 = 0 & in(all_166_1, all_48_1) = 0 % 34.90/5.45 | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | | ALPHA: (127) implies: % 34.90/5.45 | | | | | | | | | | | (128) in(all_166_1, all_48_1) = 0 % 34.90/5.45 | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | | GROUND_INST: instantiating (14) with all_166_0, 0, all_48_1, % 34.90/5.45 | | | | | | | | | | | all_166_1, simplifying with (71), (128) gives: % 34.90/5.45 | | | | | | | | | | | (129) all_166_0 = 0 % 34.90/5.45 | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | | REDUCE: (62), (129) imply: % 34.90/5.45 | | | | | | | | | | | (130) $false % 34.90/5.45 | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | | CLOSE: (130) is inconsistent. % 34.90/5.45 | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | Case 2: % 34.90/5.45 | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | | (131) ~ (all_232_0 = 0) & subset(all_166_6, all_166_4) % 34.90/5.45 | | | | | | | | | | | = all_232_0 % 34.90/5.45 | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | | ALPHA: (131) implies: % 34.90/5.45 | | | | | | | | | | | (132) ~ (all_232_0 = 0) % 34.90/5.45 | | | | | | | | | | | (133) subset(all_166_6, all_166_4) = all_232_0 % 34.90/5.45 | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | | BETA: splitting (126) gives: % 34.90/5.45 | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | | Case 1: % 34.90/5.45 | | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | | | (134) all_232_0 = 0 & subset(all_166_6, all_166_4) = 0 % 34.90/5.45 | | | | | | | | | | | | % 34.90/5.45 | | | | | | | | | | | | ALPHA: (134) implies: % 34.90/5.45 | | | | | | | | | | | | (135) all_232_0 = 0 % 34.90/5.45 | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | REDUCE: (132), (135) imply: % 34.90/5.46 | | | | | | | | | | | | (136) $false % 34.90/5.46 | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | CLOSE: (136) is inconsistent. % 34.90/5.46 | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | Case 2: % 34.90/5.46 | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | (137) ~ (all_232_1 = 0) & in(all_166_1, all_48_1) = % 34.90/5.46 | | | | | | | | | | | | all_232_1 % 34.90/5.46 | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | ALPHA: (137) implies: % 34.90/5.46 | | | | | | | | | | | | (138) in(all_166_1, all_48_1) = all_232_1 % 34.90/5.46 | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | BETA: splitting (91) gives: % 34.90/5.46 | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | Case 1: % 34.90/5.46 | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | (139) ~ (all_230_2 = 0) & in(all_166_4, all_48_2) = % 34.90/5.46 | | | | | | | | | | | | | all_230_2 % 34.90/5.46 | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | ALPHA: (139) implies: % 34.90/5.46 | | | | | | | | | | | | | (140) ~ (all_230_2 = 0) % 34.90/5.46 | | | | | | | | | | | | | (141) in(all_166_4, all_48_2) = all_230_2 % 34.90/5.46 | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_230_2, all_48_2, % 34.90/5.46 | | | | | | | | | | | | | all_166_4, simplifying with (76), (141) gives: % 34.90/5.46 | | | | | | | | | | | | | (142) all_230_2 = 0 % 34.90/5.46 | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | REDUCE: (140), (142) imply: % 34.90/5.46 | | | | | | | | | | | | | (143) $false % 34.90/5.46 | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | CLOSE: (143) is inconsistent. % 34.90/5.46 | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | Case 2: % 34.90/5.46 | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | (144) ( ~ (all_230_3 = 0) & in(all_166_6, all_48_2) = % 34.90/5.46 | | | | | | | | | | | | | all_230_3) | (((all_230_0 = 0 & % 34.90/5.46 | | | | | | | | | | | | | subset(all_166_6, all_166_4) = 0) | ( ~ % 34.90/5.46 | | | | | | | | | | | | | (all_230_1 = 0) & in(all_166_1, all_48_1) = % 34.90/5.46 | | | | | | | | | | | | | all_230_1)) & ((all_230_1 = 0 & % 34.90/5.46 | | | | | | | | | | | | | in(all_166_1, all_48_1) = 0) | ( ~ % 34.90/5.46 | | | | | | | | | | | | | (all_230_0 = 0) & subset(all_166_6, % 34.90/5.46 | | | | | | | | | | | | | all_166_4) = all_230_0))) % 34.90/5.46 | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | BETA: splitting (144) gives: % 34.90/5.46 | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | Case 1: % 34.90/5.46 | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | (145) ~ (all_230_3 = 0) & in(all_166_6, all_48_2) = % 34.90/5.46 | | | | | | | | | | | | | | all_230_3 % 34.90/5.46 | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | ALPHA: (145) implies: % 34.90/5.46 | | | | | | | | | | | | | | (146) ~ (all_230_3 = 0) % 34.90/5.46 | | | | | | | | | | | | | | (147) in(all_166_6, all_48_2) = all_230_3 % 34.90/5.46 | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_230_3, all_48_2, % 34.90/5.46 | | | | | | | | | | | | | | all_166_6, simplifying with (78), (147) gives: % 34.90/5.46 | | | | | | | | | | | | | | (148) all_230_3 = 0 % 34.90/5.46 | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | REDUCE: (146), (148) imply: % 34.90/5.46 | | | | | | | | | | | | | | (149) $false % 34.90/5.46 | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | CLOSE: (149) is inconsistent. % 34.90/5.46 | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | Case 2: % 34.90/5.46 | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | (150) ((all_230_0 = 0 & subset(all_166_6, all_166_4) = % 34.90/5.46 | | | | | | | | | | | | | | 0) | ( ~ (all_230_1 = 0) & in(all_166_1, % 34.90/5.46 | | | | | | | | | | | | | | all_48_1) = all_230_1)) & ((all_230_1 = 0 & % 34.90/5.46 | | | | | | | | | | | | | | in(all_166_1, all_48_1) = 0) | ( ~ (all_230_0 % 34.90/5.46 | | | | | | | | | | | | | | = 0) & subset(all_166_6, all_166_4) = % 34.90/5.46 | | | | | | | | | | | | | | all_230_0)) % 34.90/5.46 | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | ALPHA: (150) implies: % 34.90/5.46 | | | | | | | | | | | | | | (151) (all_230_1 = 0 & in(all_166_1, all_48_1) = 0) | ( % 34.90/5.46 | | | | | | | | | | | | | | ~ (all_230_0 = 0) & subset(all_166_6, all_166_4) % 34.90/5.46 | | | | | | | | | | | | | | = all_230_0) % 34.90/5.46 | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | BETA: splitting (151) gives: % 34.90/5.46 | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | Case 1: % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | (152) all_230_1 = 0 & in(all_166_1, all_48_1) = 0 % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | ALPHA: (152) implies: % 34.90/5.46 | | | | | | | | | | | | | | | (153) in(all_166_1, all_48_1) = 0 % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_166_0, all_232_1, % 34.90/5.46 | | | | | | | | | | | | | | | all_48_1, all_166_1, simplifying with (71), (138) % 34.90/5.46 | | | | | | | | | | | | | | | gives: % 34.90/5.46 | | | | | | | | | | | | | | | (154) all_232_1 = all_166_0 % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_232_1, all_48_1, % 34.90/5.46 | | | | | | | | | | | | | | | all_166_1, simplifying with (138), (153) gives: % 34.90/5.46 | | | | | | | | | | | | | | | (155) all_232_1 = 0 % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | COMBINE_EQS: (154), (155) imply: % 34.90/5.46 | | | | | | | | | | | | | | | (156) all_166_0 = 0 % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | SIMP: (156) implies: % 34.90/5.46 | | | | | | | | | | | | | | | (157) all_166_0 = 0 % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | REDUCE: (62), (157) imply: % 34.90/5.46 | | | | | | | | | | | | | | | (158) $false % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | CLOSE: (158) is inconsistent. % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | Case 2: % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | (159) ~ (all_230_0 = 0) & subset(all_166_6, all_166_4) % 34.90/5.46 | | | | | | | | | | | | | | | = all_230_0 % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | ALPHA: (159) implies: % 34.90/5.46 | | | | | | | | | | | | | | | (160) subset(all_166_6, all_166_4) = all_230_0 % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 34.90/5.46 | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | Case 1: % 34.90/5.46 | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | (161) ( ~ (all_231_2 = 0) & in(all_166_5, all_48_2) = % 34.90/5.46 | | | | | | | | | | | | | | | | all_231_2) | ( ~ (all_231_3 = 0) & % 34.90/5.46 | | | | | | | | | | | | | | | | relation(all_48_1) = all_231_3) % 34.90/5.46 | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 34.90/5.46 | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | Case 1: % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | (162) ~ (all_231_2 = 0) & in(all_166_5, all_48_2) = % 34.90/5.46 | | | | | | | | | | | | | | | | | all_231_2 % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | ALPHA: (162) implies: % 34.90/5.46 | | | | | | | | | | | | | | | | | (163) ~ (all_231_2 = 0) % 34.90/5.46 | | | | | | | | | | | | | | | | | (164) in(all_166_5, all_48_2) = all_231_2 % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_231_2, all_48_2, % 34.90/5.46 | | | | | | | | | | | | | | | | | all_166_5, simplifying with (77), (164) gives: % 34.90/5.46 | | | | | | | | | | | | | | | | | (165) all_231_2 = 0 % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | REDUCE: (163), (165) imply: % 34.90/5.46 | | | | | | | | | | | | | | | | | (166) $false % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent. % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | Case 2: % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | (167) ~ (all_231_3 = 0) & relation(all_48_1) = % 34.90/5.46 | | | | | | | | | | | | | | | | | all_231_3 % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | ALPHA: (167) implies: % 34.90/5.46 | | | | | | | | | | | | | | | | | (168) ~ (all_231_3 = 0) % 34.90/5.46 | | | | | | | | | | | | | | | | | (169) relation(all_48_1) = all_231_3 % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_231_3, all_48_1, % 34.90/5.46 | | | | | | | | | | | | | | | | | simplifying with (23), (169) gives: % 34.90/5.46 | | | | | | | | | | | | | | | | | (170) all_231_3 = 0 % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | REDUCE: (168), (170) imply: % 34.90/5.46 | | | | | | | | | | | | | | | | | (171) $false % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | CLOSE: (171) is inconsistent. % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | End of split % 34.90/5.46 | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | Case 2: % 34.90/5.46 | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | (172) ( ~ (all_231_3 = 0) & in(all_166_6, all_48_2) = % 34.90/5.46 | | | | | | | | | | | | | | | | all_231_3) | (((all_231_0 = 0 & % 34.90/5.46 | | | | | | | | | | | | | | | | subset(all_166_6, all_166_5) = 0) | ( ~ % 34.90/5.46 | | | | | | | | | | | | | | | | (all_231_1 = 0) & in(all_166_3, all_48_1) = % 34.90/5.46 | | | | | | | | | | | | | | | | all_231_1)) & ((all_231_1 = 0 & % 34.90/5.46 | | | | | | | | | | | | | | | | in(all_166_3, all_48_1) = 0) | ( ~ % 34.90/5.46 | | | | | | | | | | | | | | | | (all_231_0 = 0) & subset(all_166_6, % 34.90/5.46 | | | | | | | | | | | | | | | | all_166_5) = all_231_0))) % 34.90/5.46 | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | BETA: splitting (172) gives: % 34.90/5.46 | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | Case 1: % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | (173) ~ (all_231_3 = 0) & in(all_166_6, all_48_2) = % 34.90/5.46 | | | | | | | | | | | | | | | | | all_231_3 % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | ALPHA: (173) implies: % 34.90/5.46 | | | | | | | | | | | | | | | | | (174) ~ (all_231_3 = 0) % 34.90/5.46 | | | | | | | | | | | | | | | | | (175) in(all_166_6, all_48_2) = all_231_3 % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_231_3, all_48_2, % 34.90/5.46 | | | | | | | | | | | | | | | | | all_166_6, simplifying with (78), (175) gives: % 34.90/5.46 | | | | | | | | | | | | | | | | | (176) all_231_3 = 0 % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | REDUCE: (174), (176) imply: % 34.90/5.46 | | | | | | | | | | | | | | | | | (177) $false % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | CLOSE: (177) is inconsistent. % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | Case 2: % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | (178) ((all_231_0 = 0 & subset(all_166_6, all_166_5) = % 34.90/5.46 | | | | | | | | | | | | | | | | | 0) | ( ~ (all_231_1 = 0) & in(all_166_3, % 34.90/5.46 | | | | | | | | | | | | | | | | | all_48_1) = all_231_1)) & ((all_231_1 = 0 & % 34.90/5.46 | | | | | | | | | | | | | | | | | in(all_166_3, all_48_1) = 0) | ( ~ (all_231_0 % 34.90/5.46 | | | | | | | | | | | | | | | | | = 0) & subset(all_166_6, all_166_5) = % 34.90/5.46 | | | | | | | | | | | | | | | | | all_231_0)) % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | ALPHA: (178) implies: % 34.90/5.46 | | | | | | | | | | | | | | | | | (179) (all_231_0 = 0 & subset(all_166_6, all_166_5) = 0) % 34.90/5.46 | | | | | | | | | | | | | | | | | | ( ~ (all_231_1 = 0) & in(all_166_3, all_48_1) = % 34.90/5.46 | | | | | | | | | | | | | | | | | all_231_1) % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 34.90/5.46 | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | Case 1: % 34.90/5.46 | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | (180) all_231_0 = 0 & subset(all_166_6, all_166_5) = 0 % 34.90/5.46 | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | ALPHA: (180) implies: % 34.90/5.46 | | | | | | | | | | | | | | | | | | (181) subset(all_166_6, all_166_5) = 0 % 34.90/5.46 | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives: % 34.90/5.46 | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | Case 1: % 34.90/5.46 | | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | | (182) all_228_0 = 0 & subset(all_166_5, all_166_4) = 0 % 34.90/5.46 | | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies: % 34.90/5.46 | | | | | | | | | | | | | | | | | | | (183) subset(all_166_5, all_166_4) = 0 % 34.90/5.46 | | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_230_0, all_232_0, % 34.90/5.46 | | | | | | | | | | | | | | | | | | | all_166_4, all_166_6, simplifying with (133), % 34.90/5.46 | | | | | | | | | | | | | | | | | | | (160) gives: % 34.90/5.46 | | | | | | | | | | | | | | | | | | | (184) all_232_0 = all_230_0 % 34.90/5.46 | | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | | REDUCE: (132), (184) imply: % 34.90/5.46 | | | | | | | | | | | | | | | | | | | (185) ~ (all_230_0 = 0) % 34.90/5.46 | | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_166_6, all_166_5, % 34.90/5.46 | | | | | | | | | | | | | | | | | | | all_166_4, simplifying with (63), (64), (65), % 34.90/5.46 | | | | | | | | | | | | | | | | | | | (181), (183) gives: % 34.90/5.46 | | | | | | | | | | | | | | | | | | | (186) subset(all_166_6, all_166_4) = 0 % 34.90/5.46 | | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_230_0, 0, all_166_4, % 34.90/5.46 | | | | | | | | | | | | | | | | | | | all_166_6, simplifying with (160), (186) gives: % 34.90/5.46 | | | | | | | | | | | | | | | | | | | (187) all_230_0 = 0 % 34.90/5.46 | | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | | REDUCE: (185), (187) imply: % 34.90/5.46 | | | | | | | | | | | | | | | | | | | (188) $false % 34.90/5.46 | | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent. % 34.90/5.46 | | | | | | | | | | | | | | | | | | | % 34.90/5.46 | | | | | | | | | | | | | | | | | | Case 2: % 34.90/5.46 | | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | | | (189) ~ (all_228_1 = 0) & in(all_166_2, all_48_1) = % 34.90/5.47 | | | | | | | | | | | | | | | | | | | all_228_1 % 34.90/5.47 | | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies: % 34.90/5.47 | | | | | | | | | | | | | | | | | | | (190) ~ (all_228_1 = 0) % 34.90/5.47 | | | | | | | | | | | | | | | | | | | (191) in(all_166_2, all_48_1) = all_228_1 % 34.90/5.47 | | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_228_1, all_48_1, % 34.90/5.47 | | | | | | | | | | | | | | | | | | | all_166_2, simplifying with (70), (191) gives: % 34.90/5.47 | | | | | | | | | | | | | | | | | | | (192) all_228_1 = 0 % 34.90/5.47 | | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | | | REDUCE: (190), (192) imply: % 34.90/5.47 | | | | | | | | | | | | | | | | | | | (193) $false % 34.90/5.47 | | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | | | CLOSE: (193) is inconsistent. % 34.90/5.47 | | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | | End of split % 34.90/5.47 | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | Case 2: % 34.90/5.47 | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | | (194) ~ (all_231_1 = 0) & in(all_166_3, all_48_1) = % 34.90/5.47 | | | | | | | | | | | | | | | | | | all_231_1 % 34.90/5.47 | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | | ALPHA: (194) implies: % 34.90/5.47 | | | | | | | | | | | | | | | | | | (195) ~ (all_231_1 = 0) % 34.90/5.47 | | | | | | | | | | | | | | | | | | (196) in(all_166_3, all_48_1) = all_231_1 % 34.90/5.47 | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_231_1, all_48_1, % 34.90/5.47 | | | | | | | | | | | | | | | | | | all_166_3, simplifying with (69), (196) gives: % 34.90/5.47 | | | | | | | | | | | | | | | | | | (197) all_231_1 = 0 % 34.90/5.47 | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | | REDUCE: (195), (197) imply: % 34.90/5.47 | | | | | | | | | | | | | | | | | | (198) $false % 34.90/5.47 | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | | CLOSE: (198) is inconsistent. % 34.90/5.47 | | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | | End of split % 34.90/5.47 | | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | | End of split % 34.90/5.47 | | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | | End of split % 34.90/5.47 | | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | | End of split % 34.90/5.47 | | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | | End of split % 34.90/5.47 | | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | | End of split % 34.90/5.47 | | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | | End of split % 34.90/5.47 | | | | | | | | | | | % 34.90/5.47 | | | | | | | | | | End of split % 34.90/5.47 | | | | | | | | | | % 34.90/5.47 | | | | | | | | | End of split % 34.90/5.47 | | | | | | | | | % 34.90/5.47 | | | | | | | | End of split % 34.90/5.47 | | | | | | | | % 34.90/5.47 | | | | | | | End of split % 34.90/5.47 | | | | | | | % 34.90/5.47 | | | | | | End of split % 34.90/5.47 | | | | | | % 34.90/5.47 | | | | | Case 2: % 34.90/5.47 | | | | | | % 34.90/5.47 | | | | | | (199) ~ (all_95_1 = all_48_2) % 34.90/5.47 | | | | | | % 34.90/5.47 | | | | | | GROUND_INST: instantiating (11) with all_95_1, all_148_2, all_48_1, % 34.90/5.47 | | | | | | simplifying with (38), (46) gives: % 34.90/5.47 | | | | | | (200) all_148_2 = all_95_1 % 34.90/5.47 | | | | | | % 34.90/5.47 | | | | | | GROUND_INST: instantiating (11) with all_48_2, all_148_2, all_48_1, % 34.90/5.47 | | | | | | simplifying with (46), (51) gives: % 34.90/5.47 | | | | | | (201) all_148_2 = all_48_2 % 34.90/5.47 | | | | | | % 34.90/5.47 | | | | | | COMBINE_EQS: (200), (201) imply: % 34.90/5.47 | | | | | | (202) all_95_1 = all_48_2 % 34.90/5.47 | | | | | | % 34.90/5.47 | | | | | | SIMP: (202) implies: % 34.90/5.47 | | | | | | (203) all_95_1 = all_48_2 % 34.90/5.47 | | | | | | % 34.90/5.47 | | | | | | REDUCE: (199), (203) imply: % 34.90/5.47 | | | | | | (204) $false % 34.90/5.47 | | | | | | % 34.90/5.47 | | | | | | CLOSE: (204) is inconsistent. % 34.90/5.47 | | | | | | % 34.90/5.47 | | | | | End of split % 34.90/5.47 | | | | | % 34.90/5.47 | | | | End of split % 34.90/5.47 | | | | % 34.90/5.47 | | | Case 2: % 34.90/5.47 | | | | % 34.90/5.47 | | | | (205) ~ (all_151_3 = 0) & relation(all_48_1) = all_151_3 % 34.90/5.47 | | | | % 34.90/5.47 | | | | ALPHA: (205) implies: % 34.90/5.47 | | | | (206) ~ (all_151_3 = 0) % 34.90/5.47 | | | | (207) relation(all_48_1) = all_151_3 % 34.90/5.47 | | | | % 34.90/5.47 | | | | GROUND_INST: instantiating (10) with 0, all_151_3, all_48_1, simplifying % 34.90/5.47 | | | | with (23), (207) gives: % 34.90/5.47 | | | | (208) all_151_3 = 0 % 34.90/5.47 | | | | % 34.90/5.47 | | | | REDUCE: (206), (208) imply: % 34.90/5.47 | | | | (209) $false % 34.90/5.47 | | | | % 34.90/5.47 | | | | CLOSE: (209) is inconsistent. % 34.90/5.47 | | | | % 34.90/5.47 | | | End of split % 34.90/5.47 | | | % 34.90/5.47 | | End of split % 34.90/5.47 | | % 34.90/5.47 | End of split % 34.90/5.47 | % 34.90/5.47 End of proof % 34.90/5.47 % SZS output end Proof for theBenchmark % 34.90/5.47 % 34.90/5.47 4851ms %------------------------------------------------------------------------------