%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU270+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 : n029.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 16.88s 3.06s % Output : Proof 123.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU270+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n029.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 21:53:38 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.05/1.10 Prover 1: Preprocessing ... % 3.05/1.10 Prover 4: Preprocessing ... % 3.05/1.14 Prover 6: Preprocessing ... % 3.05/1.14 Prover 3: Preprocessing ... % 3.05/1.14 Prover 2: Preprocessing ... % 3.05/1.14 Prover 5: Preprocessing ... % 3.05/1.14 Prover 0: Preprocessing ... % 6.87/1.69 Prover 1: Warning: ignoring some quantifiers % 7.52/1.73 Prover 1: Constructing countermodel ... % 7.52/1.73 Prover 5: Proving ... % 7.52/1.77 Prover 3: Warning: ignoring some quantifiers % 7.52/1.78 Prover 6: Proving ... % 7.96/1.79 Prover 3: Constructing countermodel ... % 7.96/1.80 Prover 2: Proving ... % 7.96/1.85 Prover 4: Warning: ignoring some quantifiers % 8.64/1.89 Prover 4: Constructing countermodel ... % 9.65/2.06 Prover 0: Proving ... % 10.10/2.17 Prover 3: gave up % 10.10/2.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.10/2.20 Prover 7: Preprocessing ... % 11.34/2.31 Prover 1: gave up % 11.73/2.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.00/2.36 Prover 7: Warning: ignoring some quantifiers % 12.00/2.36 Prover 8: Preprocessing ... % 12.00/2.38 Prover 7: Constructing countermodel ... % 12.60/2.47 Prover 8: Warning: ignoring some quantifiers % 12.94/2.49 Prover 8: Constructing countermodel ... % 15.17/2.83 Prover 7: gave up % 15.17/2.85 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 15.17/2.90 Prover 9: Preprocessing ... % 16.25/3.00 Prover 8: gave up % 16.25/3.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.88/3.05 Prover 0: proved (2419ms) % 16.88/3.06 % 16.88/3.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.88/3.06 % 16.88/3.07 Prover 6: stopped % 16.88/3.07 Prover 5: stopped % 17.32/3.10 Prover 2: stopped % 17.32/3.11 Prover 10: Preprocessing ... % 17.32/3.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.32/3.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.32/3.11 Prover 10: Warning: ignoring some quantifiers % 17.32/3.11 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 17.32/3.11 Prover 13: Preprocessing ... % 17.32/3.12 Prover 11: Preprocessing ... % 17.32/3.12 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 17.32/3.13 Prover 9: Warning: ignoring some quantifiers % 17.32/3.13 Prover 10: Constructing countermodel ... % 17.32/3.14 Prover 9: Constructing countermodel ... % 17.32/3.14 Prover 9: stopped % 17.32/3.15 Prover 16: Preprocessing ... % 17.96/3.16 Prover 19: Preprocessing ... % 18.16/3.20 Prover 16: Warning: ignoring some quantifiers % 18.16/3.22 Prover 13: Warning: ignoring some quantifiers % 18.48/3.22 Prover 16: Constructing countermodel ... % 18.48/3.23 Prover 13: Constructing countermodel ... % 19.14/3.32 Prover 11: Warning: ignoring some quantifiers % 19.14/3.33 Prover 11: Constructing countermodel ... % 19.60/3.37 Prover 10: gave up % 19.60/3.42 Prover 19: Warning: ignoring some quantifiers % 19.60/3.42 Prover 19: Constructing countermodel ... % 23.03/3.83 Prover 19: gave up % 44.54/7.03 Prover 13: gave up % 67.95/10.74 Prover 16: stopped % 112.06/27.97 Prover 4: stopped % 122.52/35.31 Prover 11: Found proof (size 231) % 122.52/35.31 Prover 11: proved (32237ms) % 122.52/35.31 % 122.52/35.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 122.52/35.31 % 122.52/35.32 % SZS output start Proof for theBenchmark % 122.52/35.33 Assumptions after simplification: % 122.52/35.33 --------------------------------- % 122.52/35.33 % 122.52/35.33 (commutativity_k2_xboole_0) % 122.52/35.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 122.52/35.38 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 122.52/35.38 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 122.52/35.38 | (set_union2(v1, v0) = v2 & $i(v2))) % 122.52/35.38 % 122.52/35.38 (connectedness_r1_ordinal1) % 122.52/35.39 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (ordinal_subset(v1, % 122.52/35.39 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ? % 122.52/35.39 [v5: int] : ((v5 = 0 & ordinal_subset(v0, v1) = 0) | ( ~ (v4 = 0) & % 122.52/35.39 ordinal(v1) = v4) | ( ~ (v3 = 0) & ordinal(v0) = v3))) & ! [v0: $i] : % 122.52/35.39 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (ordinal_subset(v0, v1) = v2) | ~ % 122.52/35.39 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & % 122.52/35.39 ordinal_subset(v1, v0) = 0) | ( ~ (v4 = 0) & ordinal(v1) = v4) | ( ~ (v3 % 122.52/35.39 = 0) & ordinal(v0) = v3))) % 122.52/35.39 % 122.52/35.39 (d14_relat_2) % 122.52/35.40 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? % 122.52/35.40 [v2: int] : ? [v3: int] : ? [v4: int] : (( ~ (v2 = 0) & relation(v0) = v2) % 122.52/35.40 | (((v4 = 0 & is_connected_in(v0, v1) = 0) | ( ~ (v3 = 0) & connected(v0) % 122.52/35.40 = v3)) & ((v3 = 0 & connected(v0) = 0) | ( ~ (v4 = 0) & % 122.52/35.40 is_connected_in(v0, v1) = v4))))) & ! [v0: $i] : ! [v1: any] : ( ~ % 122.52/35.40 (connected(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] % 122.52/35.40 : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v4 = 0 & % 122.52/35.40 relation_field(v0) = v3 & is_connected_in(v0, v3) = 0 & $i(v3))) & % 122.52/35.40 (v1 = 0 | ( ~ (v4 = 0) & relation_field(v0) = v3 & is_connected_in(v0, % 122.52/35.40 v3) = v4 & $i(v3)))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ % 122.52/35.40 $i(v0) | ? [v1: int] : ? [v2: $i] : ? [v3: int] : (((v3 = 0 & % 122.52/35.40 relation_field(v0) = v2 & is_connected_in(v0, v2) = 0 & $i(v2)) | ( ~ % 122.52/35.40 (v1 = 0) & connected(v0) = v1)) & ((v1 = 0 & connected(v0) = 0) | ( ~ % 122.52/35.40 (v3 = 0) & relation_field(v0) = v2 & is_connected_in(v0, v2) = v3 & % 122.52/35.40 $i(v2))))) % 122.52/35.40 % 122.52/35.40 (d1_wellord2) % 122.52/35.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 122.52/35.43 any] : ( ~ (inclusion_relation(v0) = v1) | ~ (subset(v3, v4) = v5) | ~ % 122.52/35.43 (relation_field(v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 122.52/35.43 ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : (( ~ (v7 = 0) & % 122.52/35.43 in(v4, v0) = v7) | ( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & % 122.52/35.43 in(v3, v0) = v6) | (( ~ (v5 = 0) | (v9 = 0 & ordered_pair(v3, v4) = v8 & % 122.52/35.43 in(v8, v1) = 0 & $i(v8))) & (v5 = 0 | ( ~ (v9 = 0) & % 122.52/35.43 ordered_pair(v3, v4) = v8 & in(v8, v1) = v9 & $i(v8)))))) & ! [v0: % 122.52/35.43 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 122.52/35.43 ( ~ (inclusion_relation(v0) = v1) | ~ (ordered_pair(v3, v4) = v5) | ~ % 122.52/35.43 (relation_field(v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 122.52/35.43 ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : (( ~ (v7 = 0) & % 122.52/35.43 in(v4, v0) = v7) | ( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & % 122.52/35.43 in(v3, v0) = v6) | (((v9 = 0 & subset(v3, v4) = 0) | ( ~ (v8 = 0) & % 122.52/35.43 in(v5, v1) = v8)) & ((v8 = 0 & in(v5, v1) = 0) | ( ~ (v9 = 0) & % 122.52/35.43 subset(v3, v4) = v9))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 122.52/35.43 (v2 = v1 | ~ (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v0) | % 122.52/35.43 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 122.52/35.43 int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ($i(v5) % 122.52/35.43 & $i(v4) & ((v7 = 0 & v6 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 % 122.52/35.43 & subset(v4, v5) = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & % 122.52/35.43 in(v8, v1) = 0 & $i(v8))) & (( ~ (v10 = 0) & subset(v4, v5) = v10) % 122.52/35.43 | ( ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 & % 122.52/35.43 $i(v8)))) | ( ~ (v3 = 0) & relation(v1) = v3)))) & ! [v0: $i] : % 122.52/35.43 ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (inclusion_relation(v0) = v1) | ~ % 122.52/35.43 (relation_field(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = % 122.52/35.43 0) & relation(v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 122.52/35.43 (inclusion_relation(v0) = v2) | ~ (relation(v1) = 0) | ~ $i(v1) | ~ % 122.52/35.43 $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: % 122.52/35.43 int] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ($i(v5) & $i(v4) & ( ~ % 122.52/35.43 (v2 = v1) | (v3 = v0 & relation_field(v1) = v0 & ! [v11: $i] : ! [v12: % 122.52/35.43 $i] : ! [v13: any] : ( ~ (subset(v11, v12) = v13) | ~ $i(v12) | ~ % 122.52/35.43 $i(v11) | ? [v14: int] : ? [v15: int] : ? [v16: $i] : ? [v17: % 122.52/35.43 int] : (( ~ (v15 = 0) & in(v12, v0) = v15) | ( ~ (v14 = 0) & % 122.52/35.43 in(v11, v0) = v14) | (( ~ (v13 = 0) | (v17 = 0 & % 122.52/35.43 ordered_pair(v11, v12) = v16 & in(v16, v1) = 0 & $i(v16))) & % 122.52/35.43 (v13 = 0 | ( ~ (v17 = 0) & ordered_pair(v11, v12) = v16 & % 122.52/35.43 in(v16, v1) = v17 & $i(v16)))))) & ! [v11: $i] : ! [v12: % 122.52/35.43 $i] : ! [v13: $i] : ( ~ (ordered_pair(v11, v12) = v13) | ~ $i(v12) % 122.52/35.43 | ~ $i(v11) | ? [v14: int] : ? [v15: int] : ? [v16: int] : ? % 122.52/35.43 [v17: int] : (( ~ (v15 = 0) & in(v12, v0) = v15) | ( ~ (v14 = 0) & % 122.52/35.43 in(v11, v0) = v14) | (((v17 = 0 & subset(v11, v12) = 0) | ( ~ % 122.52/35.43 (v16 = 0) & in(v13, v1) = v16)) & ((v16 = 0 & in(v13, v1) = % 122.52/35.43 0) | ( ~ (v17 = 0) & subset(v11, v12) = v17))))))) & (v2 = % 122.52/35.43 v1 | (v7 = 0 & v6 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & % 122.52/35.43 subset(v4, v5) = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, % 122.52/35.43 v1) = 0 & $i(v8))) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( % 122.52/35.43 ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 & % 122.52/35.43 $i(v8)))) | ( ~ (v3 = v0) & relation_field(v1) = v3 & $i(v3))))) % 122.52/35.43 % 122.52/35.43 (d6_relat_1) % 122.52/35.44 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 122.52/35.44 int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & % 122.52/35.44 relation_rng(v0) = v4 & relation_field(v0) = v3 & set_union2(v1, v4) = % 122.52/35.44 v3 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0: % 122.52/35.44 $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: int] : % 122.52/35.44 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & relation_dom(v0) = v4 % 122.52/35.44 & relation_field(v0) = v3 & set_union2(v4, v1) = v3 & $i(v4) & $i(v3)) | % 122.52/35.44 ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 122.52/35.44 (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: % 122.52/35.44 $i] : ? [v5: $i] : ((v5 = v1 & relation_dom(v0) = v3 & relation_rng(v0) = % 122.52/35.44 v4 & set_union2(v3, v4) = v1 & $i(v4) & $i(v3) & $i(v1)) | ( ~ (v2 = 0) % 122.52/35.44 & relation(v0) = v2))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ % 122.52/35.44 $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & % 122.52/35.44 relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1 % 122.52/35.44 & $i(v3) & $i(v2) & $i(v1))) % 122.52/35.44 % 122.52/35.44 (d6_relat_2) % 122.52/35.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2 % 122.52/35.45 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_connected_in(v0, v1) = 0) | ~ % 122.52/35.45 (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 122.52/35.45 int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : ((v9 = 0 % 122.52/35.45 & in(v4, v0) = 0) | (v8 = 0 & ordered_pair(v2, v3) = v7 & in(v7, v0) = 0 % 122.52/35.45 & $i(v7)) | ( ~ (v6 = 0) & in(v3, v1) = v6) | ( ~ (v5 = 0) & in(v2, v1) % 122.52/35.45 = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 122.52/35.45 [v4: $i] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ (is_connected_in(v0, % 122.52/35.45 v1) = 0) | ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 122.52/35.45 ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? % 122.52/35.45 [v9: int] : ((v9 = 0 & ordered_pair(v3, v2) = v8 & in(v8, v0) = 0 & $i(v8)) % 122.52/35.45 | (v7 = 0 & in(v4, v0) = 0) | ( ~ (v6 = 0) & in(v3, v1) = v6) | ( ~ (v5 = % 122.52/35.45 0) & in(v2, v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 122.52/35.45 (v2 = 0 | ~ (is_connected_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ % 122.52/35.45 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] % 122.52/35.45 : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = v3) & % 122.52/35.45 ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & % 122.52/35.45 in(v5, v0) = v6 & in(v4, v1) = 0 & in(v3, v1) = 0 & $i(v7) & $i(v5) & % 122.52/35.45 $i(v4) & $i(v3))) % 122.52/35.45 % 122.52/35.45 (dt_k1_wellord2) % 122.52/35.45 ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ $i(v0) | % 122.52/35.45 relation(v1) = 0) % 122.52/35.45 % 122.52/35.45 (redefinition_r1_ordinal1) % 122.52/35.45 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | ~ % 122.52/35.45 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] : (( ~ (v4 = % 122.52/35.45 0) & ordinal(v1) = v4) | ( ~ (v3 = 0) & ordinal(v0) = v3) | (( ~ (v2 = % 122.52/35.45 0) | (v5 = 0 & ordinal_subset(v0, v1) = 0)) & (v2 = 0 | ( ~ (v5 = 0) % 122.52/35.45 & ordinal_subset(v0, v1) = v5))))) & ! [v0: $i] : ! [v1: $i] : ! % 122.52/35.45 [v2: any] : ( ~ (ordinal_subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 122.52/35.45 [v3: int] : ? [v4: int] : ? [v5: int] : (( ~ (v4 = 0) & ordinal(v1) = v4) % 122.52/35.45 | ( ~ (v3 = 0) & ordinal(v0) = v3) | (( ~ (v2 = 0) | (v5 = 0 & subset(v0, % 122.52/35.45 v1) = 0)) & (v2 = 0 | ( ~ (v5 = 0) & subset(v0, v1) = v5))))) % 122.52/35.45 % 122.52/35.45 (t23_ordinal1) % 122.52/35.46 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 122.52/35.46 [v2: int] : ? [v3: int] : ((v3 = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & % 122.52/35.46 ordinal(v1) = v2))) % 122.52/35.46 % 122.52/35.46 (t4_wellord2) % 122.52/35.46 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 122.52/35.46 inclusion_relation(v0) = v1 & connected(v1) = v2 & ordinal(v0) = 0 & $i(v1) % 122.52/35.46 & $i(v0)) % 122.52/35.46 % 122.52/35.46 (function-axioms) % 122.52/35.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 122.52/35.46 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 122.52/35.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 122.52/35.46 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 122.52/35.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 122.52/35.46 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 122.52/35.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 122.52/35.46 : (v1 = v0 | ~ (is_connected_in(v3, v2) = v1) | ~ (is_connected_in(v3, v2) = % 122.52/35.46 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 122.52/35.46 $i] : ! [v3: $i] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~ % 122.52/35.46 (ordinal_subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 122.52/35.46 ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) % 122.52/35.46 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 122.52/35.46 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! % 122.52/35.46 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 122.52/35.46 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] % 122.52/35.47 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 122.52/35.47 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 122.52/35.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 122.52/35.47 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 122.52/35.47 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = % 122.52/35.47 v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 122.52/35.47 $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & % 122.52/35.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | % 122.52/35.47 ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 122.52/35.47 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) & ! % 122.52/35.47 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) % 122.52/35.47 | ~ (relation_field(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 122.52/35.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (connected(v2) = v1) | ~ % 122.52/35.47 (connected(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 122.52/35.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 122.52/35.47 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 122.52/35.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 122.52/35.47 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 122.52/35.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) = % 122.52/35.47 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 122.52/35.47 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ % 122.52/35.47 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 122.52/35.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) = % 122.52/35.47 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 122.52/35.47 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 122.52/35.47 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 122.52/35.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 122.52/35.47 (empty(v2) = v0)) % 122.52/35.47 % 122.52/35.47 Further assumptions not needed in the proof: % 122.52/35.47 -------------------------------------------- % 122.52/35.47 antisymmetry_r2_hidden, cc1_funct_1, cc1_ordinal1, cc2_funct_1, cc2_ordinal1, % 122.52/35.47 cc3_ordinal1, commutativity_k2_tarski, d5_tarski, dt_k1_relat_1, dt_k1_tarski, % 122.52/35.47 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_tarski, dt_k2_xboole_0, % 122.52/35.47 dt_k3_relat_1, dt_k4_tarski, dt_m1_subset_1, existence_m1_subset_1, % 122.52/35.47 fc1_xboole_0, fc1_zfmisc_1, fc2_ordinal1, fc2_xboole_0, fc3_xboole_0, % 122.52/35.47 idempotence_k2_xboole_0, rc1_funct_1, rc1_ordinal1, rc1_xboole_0, rc2_funct_1, % 122.52/35.47 rc2_ordinal1, rc2_xboole_0, rc3_funct_1, rc3_ordinal1, rc4_funct_1, % 122.52/35.47 reflexivity_r1_ordinal1, reflexivity_r1_tarski, t1_boole, t1_subset, t2_subset, % 122.52/35.47 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 122.52/35.47 % 122.52/35.47 Those formulas are unsatisfiable: % 122.52/35.47 --------------------------------- % 122.52/35.47 % 122.52/35.47 Begin of proof % 122.52/35.47 | % 122.52/35.47 | ALPHA: (commutativity_k2_xboole_0) implies: % 122.52/35.47 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 122.52/35.47 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 122.52/35.47 | % 122.52/35.47 | ALPHA: (connectedness_r1_ordinal1) implies: % 122.52/35.47 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 122.52/35.47 | (ordinal_subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 122.52/35.47 | : ? [v4: int] : ? [v5: int] : ((v5 = 0 & ordinal_subset(v1, v0) = % 122.52/35.47 | 0) | ( ~ (v4 = 0) & ordinal(v1) = v4) | ( ~ (v3 = 0) & % 122.52/35.47 | ordinal(v0) = v3))) % 122.52/35.47 | % 122.52/35.47 | ALPHA: (d14_relat_2) implies: % 122.52/35.47 | (3) ! [v0: $i] : ! [v1: any] : ( ~ (connected(v0) = v1) | ~ $i(v0) | ? % 122.52/35.47 | [v2: int] : ? [v3: $i] : ? [v4: int] : (( ~ (v2 = 0) & relation(v0) % 122.52/35.47 | = v2) | (( ~ (v1 = 0) | (v4 = 0 & relation_field(v0) = v3 & % 122.52/35.47 | is_connected_in(v0, v3) = 0 & $i(v3))) & (v1 = 0 | ( ~ (v4 = % 122.52/35.47 | 0) & relation_field(v0) = v3 & is_connected_in(v0, v3) = v4 % 122.52/35.47 | & $i(v3)))))) % 122.52/35.47 | % 122.52/35.47 | ALPHA: (d1_wellord2) implies: % 122.52/35.48 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (inclusion_relation(v0) = % 122.52/35.48 | v2) | ~ (relation(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 122.52/35.48 | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: $i] % 122.52/35.48 | : ? [v9: int] : ? [v10: int] : ($i(v5) & $i(v4) & ( ~ (v2 = v1) | % 122.52/35.48 | (v3 = v0 & relation_field(v1) = v0 & ! [v11: $i] : ! [v12: $i] % 122.52/35.48 | : ! [v13: any] : ( ~ (subset(v11, v12) = v13) | ~ $i(v12) | % 122.52/35.48 | ~ $i(v11) | ? [v14: int] : ? [v15: int] : ? [v16: $i] : ? % 122.52/35.48 | [v17: int] : (( ~ (v15 = 0) & in(v12, v0) = v15) | ( ~ (v14 = % 122.52/35.48 | 0) & in(v11, v0) = v14) | (( ~ (v13 = 0) | (v17 = 0 & % 122.52/35.48 | ordered_pair(v11, v12) = v16 & in(v16, v1) = 0 & % 122.52/35.48 | $i(v16))) & (v13 = 0 | ( ~ (v17 = 0) & % 122.52/35.48 | ordered_pair(v11, v12) = v16 & in(v16, v1) = v17 & % 122.52/35.48 | $i(v16)))))) & ! [v11: $i] : ! [v12: $i] : ! [v13: % 122.52/35.48 | $i] : ( ~ (ordered_pair(v11, v12) = v13) | ~ $i(v12) | ~ % 122.52/35.48 | $i(v11) | ? [v14: int] : ? [v15: int] : ? [v16: int] : ? % 122.52/35.48 | [v17: int] : (( ~ (v15 = 0) & in(v12, v0) = v15) | ( ~ (v14 = % 122.52/35.48 | 0) & in(v11, v0) = v14) | (((v17 = 0 & subset(v11, v12) % 122.52/35.48 | = 0) | ( ~ (v16 = 0) & in(v13, v1) = v16)) & ((v16 = % 122.52/35.48 | 0 & in(v13, v1) = 0) | ( ~ (v17 = 0) & subset(v11, % 122.52/35.48 | v12) = v17))))))) & (v2 = v1 | (v7 = 0 & v6 = 0 & % 122.52/35.48 | in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & subset(v4, v5) = % 122.52/35.48 | 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, v1) = 0 & % 122.52/35.48 | $i(v8))) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( ~ (v9 % 122.52/35.48 | = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 & % 122.52/35.48 | $i(v8)))) | ( ~ (v3 = v0) & relation_field(v1) = v3 & % 122.52/35.48 | $i(v3))))) % 122.52/35.48 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 122.52/35.48 | (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ % 122.52/35.48 | $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & relation(v1) = % 122.52/35.48 | v3)) % 122.52/35.48 | % 122.52/35.48 | ALPHA: (d6_relat_1) implies: % 122.52/35.48 | (6) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 122.52/35.48 | [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & relation_rng(v0) = % 122.52/35.48 | v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1 & $i(v3) & % 122.52/35.48 | $i(v2) & $i(v1))) % 122.52/35.48 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | % 122.52/35.48 | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v1 & % 122.52/35.48 | relation_dom(v0) = v3 & relation_rng(v0) = v4 & set_union2(v3, % 122.52/35.48 | v4) = v1 & $i(v4) & $i(v3) & $i(v1)) | ( ~ (v2 = 0) & % 122.52/35.48 | relation(v0) = v2))) % 122.52/35.48 | % 122.52/35.48 | ALPHA: (d6_relat_2) implies: % 122.52/35.49 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 122.52/35.49 | (is_connected_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | % 122.52/35.49 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 122.52/35.49 | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = v3) % 122.52/35.49 | & ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, % 122.52/35.49 | v0) = v8 & in(v5, v0) = v6 & in(v4, v1) = 0 & in(v3, v1) = 0 & % 122.52/35.49 | $i(v7) & $i(v5) & $i(v4) & $i(v3))) % 122.52/35.49 | % 122.52/35.49 | ALPHA: (redefinition_r1_ordinal1) implies: % 122.52/35.49 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | % 122.52/35.49 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] : % 122.52/35.49 | (( ~ (v4 = 0) & ordinal(v1) = v4) | ( ~ (v3 = 0) & ordinal(v0) = v3) % 122.52/35.49 | | (( ~ (v2 = 0) | (v5 = 0 & ordinal_subset(v0, v1) = 0)) & (v2 = 0 % 122.52/35.49 | | ( ~ (v5 = 0) & ordinal_subset(v0, v1) = v5))))) % 122.52/35.49 | % 122.52/35.49 | ALPHA: (function-axioms) implies: % 122.52/35.49 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 122.52/35.49 | : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) % 122.52/35.49 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 122.52/35.49 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 122.52/35.49 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 122.52/35.49 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 122.52/35.49 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 122.52/35.49 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 122.52/35.49 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 122.52/35.49 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 122.52/35.49 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 122.52/35.49 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 122.52/35.49 | v0)) % 122.52/35.49 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 122.52/35.49 | : ! [v3: $i] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~ % 122.52/35.49 | (ordinal_subset(v3, v2) = v0)) % 122.52/35.49 | % 122.52/35.49 | DELTA: instantiating (t4_wellord2) with fresh symbols all_51_0, all_51_1, % 122.52/35.49 | all_51_2 gives: % 122.52/35.49 | (17) ~ (all_51_0 = 0) & inclusion_relation(all_51_2) = all_51_1 & % 122.52/35.49 | connected(all_51_1) = all_51_0 & ordinal(all_51_2) = 0 & $i(all_51_1) % 122.52/35.49 | & $i(all_51_2) % 122.52/35.49 | % 122.52/35.49 | ALPHA: (17) implies: % 122.52/35.49 | (18) ~ (all_51_0 = 0) % 122.52/35.49 | (19) $i(all_51_2) % 122.52/35.49 | (20) $i(all_51_1) % 122.52/35.49 | (21) ordinal(all_51_2) = 0 % 122.52/35.49 | (22) connected(all_51_1) = all_51_0 % 122.52/35.49 | (23) inclusion_relation(all_51_2) = all_51_1 % 122.52/35.50 | % 122.52/35.50 | GROUND_INST: instantiating (3) with all_51_1, all_51_0, simplifying with (20), % 122.52/35.50 | (22) gives: % 122.52/35.50 | (24) ? [v0: int] : ? [v1: $i] : ? [v2: int] : (( ~ (v0 = 0) & % 122.52/35.50 | relation(all_51_1) = v0) | (( ~ (all_51_0 = 0) | (v2 = 0 & % 122.52/35.50 | relation_field(all_51_1) = v1 & is_connected_in(all_51_1, v1) % 122.52/35.50 | = 0 & $i(v1))) & (all_51_0 = 0 | ( ~ (v2 = 0) & % 122.52/35.50 | relation_field(all_51_1) = v1 & is_connected_in(all_51_1, v1) % 122.52/35.50 | = v2 & $i(v1))))) % 122.52/35.50 | % 122.52/35.50 | GROUND_INST: instantiating (dt_k1_wellord2) with all_51_2, all_51_1, % 122.52/35.50 | simplifying with (19), (23) gives: % 122.52/35.50 | (25) relation(all_51_1) = 0 % 122.52/35.50 | % 122.52/35.50 | DELTA: instantiating (24) with fresh symbols all_97_0, all_97_1, all_97_2 % 122.52/35.50 | gives: % 122.52/35.50 | (26) ( ~ (all_97_2 = 0) & relation(all_51_1) = all_97_2) | (( ~ (all_51_0 = % 122.52/35.50 | 0) | (all_97_0 = 0 & relation_field(all_51_1) = all_97_1 & % 122.52/35.50 | is_connected_in(all_51_1, all_97_1) = 0 & $i(all_97_1))) & % 122.52/35.50 | (all_51_0 = 0 | ( ~ (all_97_0 = 0) & relation_field(all_51_1) = % 122.52/35.50 | all_97_1 & is_connected_in(all_51_1, all_97_1) = all_97_0 & % 122.52/35.50 | $i(all_97_1)))) % 122.52/35.50 | % 122.52/35.50 | BETA: splitting (26) gives: % 122.52/35.50 | % 122.52/35.50 | Case 1: % 122.52/35.50 | | % 122.52/35.50 | | (27) ~ (all_97_2 = 0) & relation(all_51_1) = all_97_2 % 122.52/35.50 | | % 122.52/35.50 | | ALPHA: (27) implies: % 122.52/35.50 | | (28) ~ (all_97_2 = 0) % 122.52/35.50 | | (29) relation(all_51_1) = all_97_2 % 122.52/35.50 | | % 122.52/35.50 | | GROUND_INST: instantiating (11) with 0, all_97_2, all_51_1, simplifying with % 122.52/35.50 | | (25), (29) gives: % 122.52/35.50 | | (30) all_97_2 = 0 % 122.52/35.50 | | % 122.52/35.50 | | REDUCE: (28), (30) imply: % 122.52/35.50 | | (31) $false % 122.52/35.50 | | % 122.52/35.50 | | CLOSE: (31) is inconsistent. % 122.52/35.50 | | % 122.52/35.50 | Case 2: % 122.52/35.50 | | % 122.52/35.50 | | (32) ( ~ (all_51_0 = 0) | (all_97_0 = 0 & relation_field(all_51_1) = % 122.52/35.50 | | all_97_1 & is_connected_in(all_51_1, all_97_1) = 0 & % 122.52/35.50 | | $i(all_97_1))) & (all_51_0 = 0 | ( ~ (all_97_0 = 0) & % 122.52/35.50 | | relation_field(all_51_1) = all_97_1 & is_connected_in(all_51_1, % 122.52/35.50 | | all_97_1) = all_97_0 & $i(all_97_1))) % 122.52/35.50 | | % 122.52/35.50 | | ALPHA: (32) implies: % 122.52/35.51 | | (33) all_51_0 = 0 | ( ~ (all_97_0 = 0) & relation_field(all_51_1) = % 122.52/35.51 | | all_97_1 & is_connected_in(all_51_1, all_97_1) = all_97_0 & % 122.52/35.51 | | $i(all_97_1)) % 122.52/35.51 | | % 122.52/35.51 | | BETA: splitting (33) gives: % 122.52/35.51 | | % 122.52/35.51 | | Case 1: % 122.52/35.51 | | | % 122.52/35.51 | | | (34) all_51_0 = 0 % 122.52/35.51 | | | % 122.52/35.51 | | | REDUCE: (18), (34) imply: % 122.52/35.51 | | | (35) $false % 122.52/35.51 | | | % 122.52/35.51 | | | CLOSE: (35) is inconsistent. % 122.52/35.51 | | | % 122.52/35.51 | | Case 2: % 122.52/35.51 | | | % 122.52/35.51 | | | (36) ~ (all_97_0 = 0) & relation_field(all_51_1) = all_97_1 & % 122.52/35.51 | | | is_connected_in(all_51_1, all_97_1) = all_97_0 & $i(all_97_1) % 122.52/35.51 | | | % 122.52/35.51 | | | ALPHA: (36) implies: % 122.52/35.51 | | | (37) ~ (all_97_0 = 0) % 122.52/35.51 | | | (38) $i(all_97_1) % 122.52/35.51 | | | (39) is_connected_in(all_51_1, all_97_1) = all_97_0 % 122.52/35.51 | | | (40) relation_field(all_51_1) = all_97_1 % 122.52/35.51 | | | % 122.52/35.51 | | | GROUND_INST: instantiating (4) with all_51_2, all_51_1, all_51_1, % 122.52/35.51 | | | simplifying with (19), (20), (23), (25) gives: % 122.52/35.51 | | | (41) ? [v0: $i] : ? [v1: $i] : (relation_field(all_51_1) = all_51_2 & % 122.52/35.51 | | | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 122.52/35.51 | | | (subset(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: int] : % 122.52/35.51 | | | ? [v6: int] : ? [v7: $i] : ? [v8: int] : (( ~ (v6 = 0) & % 122.52/35.51 | | | in(v3, all_51_2) = v6) | ( ~ (v5 = 0) & in(v2, all_51_2) = % 122.52/35.51 | | | v5) | (( ~ (v4 = 0) | (v8 = 0 & ordered_pair(v2, v3) = v7 % 122.52/35.51 | | | & in(v7, all_51_1) = 0 & $i(v7))) & (v4 = 0 | ( ~ (v8 % 122.52/35.51 | | | = 0) & ordered_pair(v2, v3) = v7 & in(v7, all_51_1) % 122.52/35.51 | | | = v8 & $i(v7)))))) & ! [v2: $i] : ! [v3: $i] : ! % 122.52/35.51 | | | [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 122.52/35.51 | | | $i(v2) | ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: % 122.52/35.51 | | | int] : (( ~ (v6 = 0) & in(v3, all_51_2) = v6) | ( ~ (v5 = 0) % 122.52/35.51 | | | & in(v2, all_51_2) = v5) | (((v8 = 0 & subset(v2, v3) = 0) % 122.52/35.51 | | | | ( ~ (v7 = 0) & in(v4, all_51_1) = v7)) & ((v7 = 0 & % 122.52/35.51 | | | in(v4, all_51_1) = 0) | ( ~ (v8 = 0) & subset(v2, v3) % 122.52/35.51 | | | = v8)))))) % 122.52/35.51 | | | % 122.52/35.51 | | | GROUND_INST: instantiating (6) with all_51_1, simplifying with (20), (25) % 122.52/35.51 | | | gives: % 122.52/35.51 | | | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_51_1) % 122.52/35.51 | | | = v1 & relation_rng(all_51_1) = v2 & relation_field(all_51_1) = % 122.52/35.51 | | | v0 & set_union2(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 122.52/35.51 | | | % 122.52/35.51 | | | GROUND_INST: instantiating (8) with all_51_1, all_97_1, all_97_0, % 122.52/35.51 | | | simplifying with (20), (25), (38), (39) gives: % 122.52/35.51 | | | (43) all_97_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 122.52/35.51 | | | int] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & ~ (v3 = 0) & % 122.52/35.51 | | | ~ (v1 = v0) & ordered_pair(v1, v0) = v4 & ordered_pair(v0, v1) % 122.52/35.51 | | | = v2 & in(v4, all_51_1) = v5 & in(v2, all_51_1) = v3 & in(v1, % 122.52/35.51 | | | all_97_1) = 0 & in(v0, all_97_1) = 0 & $i(v4) & $i(v2) & % 122.52/35.51 | | | $i(v1) & $i(v0)) % 122.52/35.51 | | | % 122.52/35.52 | | | GROUND_INST: instantiating (5) with all_51_2, all_51_1, all_97_1, % 122.52/35.52 | | | simplifying with (19), (20), (23), (40) gives: % 122.52/35.52 | | | (44) all_97_1 = all_51_2 | ? [v0: int] : ( ~ (v0 = 0) & % 122.52/35.52 | | | relation(all_51_1) = v0) % 122.52/35.52 | | | % 122.52/35.52 | | | GROUND_INST: instantiating (7) with all_51_1, all_97_1, simplifying with % 122.52/35.52 | | | (20), (40) gives: % 122.52/35.52 | | | (45) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ((v3 = % 122.52/35.52 | | | all_97_1 & relation_dom(all_51_1) = v1 & % 122.52/35.52 | | | relation_rng(all_51_1) = v2 & set_union2(v1, v2) = all_97_1 & % 122.52/35.52 | | | $i(v2) & $i(v1) & $i(all_97_1)) | ( ~ (v0 = 0) & % 122.52/35.52 | | | relation(all_51_1) = v0)) % 122.52/35.52 | | | % 122.52/35.52 | | | DELTA: instantiating (42) with fresh symbols all_158_0, all_158_1, % 122.52/35.52 | | | all_158_2 gives: % 122.52/35.52 | | | (46) relation_dom(all_51_1) = all_158_1 & relation_rng(all_51_1) = % 122.52/35.52 | | | all_158_0 & relation_field(all_51_1) = all_158_2 & % 122.52/35.52 | | | set_union2(all_158_1, all_158_0) = all_158_2 & $i(all_158_0) & % 122.52/35.52 | | | $i(all_158_1) & $i(all_158_2) % 122.52/35.52 | | | % 122.52/35.52 | | | ALPHA: (46) implies: % 122.52/35.52 | | | (47) $i(all_158_2) % 122.52/35.52 | | | (48) set_union2(all_158_1, all_158_0) = all_158_2 % 122.52/35.52 | | | (49) relation_field(all_51_1) = all_158_2 % 122.52/35.52 | | | (50) relation_rng(all_51_1) = all_158_0 % 122.52/35.52 | | | (51) relation_dom(all_51_1) = all_158_1 % 122.52/35.52 | | | % 122.52/35.52 | | | DELTA: instantiating (45) with fresh symbols all_161_0, all_161_1, % 122.52/35.52 | | | all_161_2, all_161_3 gives: % 122.52/35.52 | | | (52) (all_161_0 = all_97_1 & relation_dom(all_51_1) = all_161_2 & % 122.52/35.52 | | | relation_rng(all_51_1) = all_161_1 & set_union2(all_161_2, % 122.52/35.52 | | | all_161_1) = all_97_1 & $i(all_161_1) & $i(all_161_2) & % 122.52/35.52 | | | $i(all_97_1)) | ( ~ (all_161_3 = 0) & relation(all_51_1) = % 122.52/35.52 | | | all_161_3) % 122.52/35.52 | | | % 122.52/35.52 | | | DELTA: instantiating (41) with fresh symbols all_166_0, all_166_1 gives: % 122.52/35.53 | | | (53) relation_field(all_51_1) = all_51_2 & $i(all_166_0) & % 122.52/35.53 | | | $i(all_166_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 122.52/35.53 | | | (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 122.52/35.53 | | | ? [v4: int] : ? [v5: $i] : ? [v6: int] : (( ~ (v4 = 0) & % 122.52/35.53 | | | in(v1, all_51_2) = v4) | ( ~ (v3 = 0) & in(v0, all_51_2) = % 122.52/35.53 | | | v3) | (( ~ (v2 = 0) | (v6 = 0 & ordered_pair(v0, v1) = v5 & % 122.52/35.53 | | | in(v5, all_51_1) = 0 & $i(v5))) & (v2 = 0 | ( ~ (v6 = 0) % 122.52/35.53 | | | & ordered_pair(v0, v1) = v5 & in(v5, all_51_1) = v6 & % 122.52/35.53 | | | $i(v5)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 122.52/35.53 | | | ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 122.52/35.53 | | | int] : ? [v4: int] : ? [v5: int] : ? [v6: int] : (( ~ (v4 = % 122.52/35.53 | | | 0) & in(v1, all_51_2) = v4) | ( ~ (v3 = 0) & in(v0, % 122.52/35.53 | | | all_51_2) = v3) | (((v6 = 0 & subset(v0, v1) = 0) | ( ~ % 122.52/35.53 | | | (v5 = 0) & in(v2, all_51_1) = v5)) & ((v5 = 0 & in(v2, % 122.52/35.53 | | | all_51_1) = 0) | ( ~ (v6 = 0) & subset(v0, v1) = % 122.52/35.53 | | | v6))))) % 122.52/35.53 | | | % 122.52/35.53 | | | ALPHA: (53) implies: % 122.52/35.53 | | | (54) relation_field(all_51_1) = all_51_2 % 122.52/35.53 | | | (55) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, % 122.52/35.53 | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 122.52/35.53 | | | int] : ? [v5: int] : ? [v6: int] : (( ~ (v4 = 0) & in(v1, % 122.52/35.53 | | | all_51_2) = v4) | ( ~ (v3 = 0) & in(v0, all_51_2) = v3) | % 122.52/35.53 | | | (((v6 = 0 & subset(v0, v1) = 0) | ( ~ (v5 = 0) & in(v2, % 122.52/35.53 | | | all_51_1) = v5)) & ((v5 = 0 & in(v2, all_51_1) = 0) | % 122.52/35.53 | | | ( ~ (v6 = 0) & subset(v0, v1) = v6))))) % 122.52/35.53 | | | % 122.52/35.53 | | | BETA: splitting (43) gives: % 122.52/35.53 | | | % 122.52/35.53 | | | Case 1: % 122.52/35.53 | | | | % 122.52/35.53 | | | | (56) all_97_0 = 0 % 122.52/35.53 | | | | % 122.52/35.53 | | | | REDUCE: (37), (56) imply: % 122.52/35.53 | | | | (57) $false % 122.52/35.53 | | | | % 122.52/35.53 | | | | CLOSE: (57) is inconsistent. % 122.52/35.53 | | | | % 122.52/35.53 | | | Case 2: % 122.52/35.53 | | | | % 122.52/35.53 | | | | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: % 122.52/35.53 | | | | $i] : ? [v5: int] : ( ~ (v5 = 0) & ~ (v3 = 0) & ~ (v1 = v0) % 122.52/35.53 | | | | & ordered_pair(v1, v0) = v4 & ordered_pair(v0, v1) = v2 & % 122.52/35.53 | | | | in(v4, all_51_1) = v5 & in(v2, all_51_1) = v3 & in(v1, % 122.52/35.53 | | | | all_97_1) = 0 & in(v0, all_97_1) = 0 & $i(v4) & $i(v2) & % 122.52/35.53 | | | | $i(v1) & $i(v0)) % 122.52/35.53 | | | | % 122.52/35.53 | | | | DELTA: instantiating (58) with fresh symbols all_176_0, all_176_1, % 122.52/35.53 | | | | all_176_2, all_176_3, all_176_4, all_176_5 gives: % 122.52/35.53 | | | | (59) ~ (all_176_0 = 0) & ~ (all_176_2 = 0) & ~ (all_176_4 = % 122.52/35.53 | | | | all_176_5) & ordered_pair(all_176_4, all_176_5) = all_176_1 & % 122.52/35.53 | | | | ordered_pair(all_176_5, all_176_4) = all_176_3 & in(all_176_1, % 122.52/35.53 | | | | all_51_1) = all_176_0 & in(all_176_3, all_51_1) = all_176_2 & % 122.52/35.53 | | | | in(all_176_4, all_97_1) = 0 & in(all_176_5, all_97_1) = 0 & % 122.52/35.53 | | | | $i(all_176_1) & $i(all_176_3) & $i(all_176_4) & $i(all_176_5) % 122.52/35.53 | | | | % 122.52/35.53 | | | | ALPHA: (59) implies: % 122.52/35.53 | | | | (60) ~ (all_176_2 = 0) % 122.52/35.53 | | | | (61) ~ (all_176_0 = 0) % 122.52/35.53 | | | | (62) $i(all_176_5) % 122.52/35.53 | | | | (63) $i(all_176_4) % 122.52/35.53 | | | | (64) in(all_176_5, all_97_1) = 0 % 122.52/35.53 | | | | (65) in(all_176_4, all_97_1) = 0 % 122.52/35.53 | | | | (66) in(all_176_3, all_51_1) = all_176_2 % 122.52/35.53 | | | | (67) in(all_176_1, all_51_1) = all_176_0 % 123.21/35.53 | | | | (68) ordered_pair(all_176_5, all_176_4) = all_176_3 % 123.21/35.53 | | | | (69) ordered_pair(all_176_4, all_176_5) = all_176_1 % 123.21/35.53 | | | | % 123.21/35.53 | | | | BETA: splitting (44) gives: % 123.21/35.53 | | | | % 123.21/35.53 | | | | Case 1: % 123.21/35.53 | | | | | % 123.21/35.53 | | | | | (70) all_97_1 = all_51_2 % 123.21/35.53 | | | | | % 123.21/35.53 | | | | | REDUCE: (39), (70) imply: % 123.21/35.53 | | | | | (71) is_connected_in(all_51_1, all_51_2) = all_97_0 % 123.21/35.53 | | | | | % 123.21/35.53 | | | | | REDUCE: (65), (70) imply: % 123.21/35.53 | | | | | (72) in(all_176_4, all_51_2) = 0 % 123.21/35.53 | | | | | % 123.21/35.53 | | | | | REDUCE: (64), (70) imply: % 123.21/35.53 | | | | | (73) in(all_176_5, all_51_2) = 0 % 123.21/35.53 | | | | | % 123.21/35.53 | | | | | BETA: splitting (52) gives: % 123.21/35.53 | | | | | % 123.21/35.53 | | | | | Case 1: % 123.21/35.53 | | | | | | % 123.21/35.53 | | | | | | (74) all_161_0 = all_97_1 & relation_dom(all_51_1) = all_161_2 & % 123.21/35.53 | | | | | | relation_rng(all_51_1) = all_161_1 & set_union2(all_161_2, % 123.21/35.53 | | | | | | all_161_1) = all_97_1 & $i(all_161_1) & $i(all_161_2) & % 123.21/35.53 | | | | | | $i(all_97_1) % 123.21/35.53 | | | | | | % 123.21/35.53 | | | | | | ALPHA: (74) implies: % 123.21/35.54 | | | | | | (75) $i(all_161_2) % 123.21/35.54 | | | | | | (76) $i(all_161_1) % 123.21/35.54 | | | | | | (77) relation_rng(all_51_1) = all_161_1 % 123.21/35.54 | | | | | | (78) relation_dom(all_51_1) = all_161_2 % 123.21/35.54 | | | | | | % 123.21/35.54 | | | | | | GROUND_INST: instantiating (12) with all_51_2, all_158_2, all_51_1, % 123.21/35.54 | | | | | | simplifying with (49), (54) gives: % 123.21/35.54 | | | | | | (79) all_158_2 = all_51_2 % 123.21/35.54 | | | | | | % 123.21/35.54 | | | | | | GROUND_INST: instantiating (13) with all_158_0, all_161_1, all_51_1, % 123.63/35.54 | | | | | | simplifying with (50), (77) gives: % 123.63/35.54 | | | | | | (80) all_161_1 = all_158_0 % 123.63/35.54 | | | | | | % 123.63/35.54 | | | | | | GROUND_INST: instantiating (14) with all_158_1, all_161_2, all_51_1, % 123.63/35.54 | | | | | | simplifying with (51), (78) gives: % 123.63/35.54 | | | | | | (81) all_161_2 = all_158_1 % 123.63/35.54 | | | | | | % 123.63/35.54 | | | | | | REDUCE: (48), (79) imply: % 123.63/35.54 | | | | | | (82) set_union2(all_158_1, all_158_0) = all_51_2 % 123.63/35.54 | | | | | | % 123.63/35.54 | | | | | | REDUCE: (76), (80) imply: % 123.63/35.54 | | | | | | (83) $i(all_158_0) % 123.63/35.54 | | | | | | % 123.63/35.54 | | | | | | REDUCE: (75), (81) imply: % 123.63/35.54 | | | | | | (84) $i(all_158_1) % 123.63/35.54 | | | | | | % 123.63/35.54 | | | | | | GROUND_INST: instantiating (t23_ordinal1) with all_176_5, all_51_2, % 123.63/35.54 | | | | | | simplifying with (19), (62), (73) gives: % 123.63/35.54 | | | | | | (85) ? [v0: int] : ? [v1: int] : ((v1 = 0 & ordinal(all_176_5) % 123.63/35.54 | | | | | | = 0) | ( ~ (v0 = 0) & ordinal(all_51_2) = v0)) % 123.63/35.54 | | | | | | % 123.63/35.54 | | | | | | GROUND_INST: instantiating (t23_ordinal1) with all_176_4, all_51_2, % 123.63/35.54 | | | | | | simplifying with (19), (63), (72) gives: % 123.63/35.54 | | | | | | (86) ? [v0: int] : ? [v1: int] : ((v1 = 0 & ordinal(all_176_4) % 123.63/35.54 | | | | | | = 0) | ( ~ (v0 = 0) & ordinal(all_51_2) = v0)) % 123.63/35.54 | | | | | | % 123.63/35.54 | | | | | | GROUND_INST: instantiating (1) with all_158_0, all_158_1, all_51_2, % 123.63/35.54 | | | | | | simplifying with (82), (83), (84) gives: % 123.63/35.54 | | | | | | (87) set_union2(all_158_0, all_158_1) = all_51_2 & $i(all_51_2) % 123.63/35.54 | | | | | | % 123.63/35.54 | | | | | | GROUND_INST: instantiating (8) with all_51_1, all_51_2, all_97_0, % 123.63/35.54 | | | | | | simplifying with (19), (20), (25), (71) gives: % 123.63/35.54 | | | | | | (88) all_97_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 123.63/35.54 | | | | | | [v3: int] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & ~ % 123.63/35.54 | | | | | | (v3 = 0) & ~ (v1 = v0) & ordered_pair(v1, v0) = v4 & % 123.63/35.54 | | | | | | ordered_pair(v0, v1) = v2 & in(v4, all_51_1) = v5 & in(v2, % 123.63/35.54 | | | | | | all_51_1) = v3 & in(v1, all_51_2) = 0 & in(v0, all_51_2) % 123.63/35.54 | | | | | | = 0 & $i(v4) & $i(v2) & $i(v1) & $i(v0)) % 123.63/35.54 | | | | | | % 123.63/35.54 | | | | | | GROUND_INST: instantiating (55) with all_176_5, all_176_4, % 123.63/35.54 | | | | | | all_176_3, simplifying with (62), (63), (68) gives: % 123.63/35.54 | | | | | | (89) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 123.63/35.54 | | | | | | (( ~ (v1 = 0) & in(all_176_4, all_51_2) = v1) | ( ~ (v0 = 0) % 123.63/35.54 | | | | | | & in(all_176_5, all_51_2) = v0) | (((v3 = 0 & % 123.63/35.54 | | | | | | subset(all_176_5, all_176_4) = 0) | ( ~ (v2 = 0) & % 123.63/35.54 | | | | | | in(all_176_3, all_51_1) = v2)) & ((v2 = 0 & % 123.63/35.54 | | | | | | in(all_176_3, all_51_1) = 0) | ( ~ (v3 = 0) & % 123.63/35.54 | | | | | | subset(all_176_5, all_176_4) = v3)))) % 123.63/35.54 | | | | | | % 123.63/35.54 | | | | | | GROUND_INST: instantiating (55) with all_176_4, all_176_5, % 123.63/35.54 | | | | | | all_176_1, simplifying with (62), (63), (69) gives: % 123.63/35.54 | | | | | | (90) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : % 123.63/35.54 | | | | | | (( ~ (v1 = 0) & in(all_176_5, all_51_2) = v1) | ( ~ (v0 = 0) % 123.63/35.54 | | | | | | & in(all_176_4, all_51_2) = v0) | (((v3 = 0 & % 123.63/35.54 | | | | | | subset(all_176_4, all_176_5) = 0) | ( ~ (v2 = 0) & % 123.63/35.54 | | | | | | in(all_176_1, all_51_1) = v2)) & ((v2 = 0 & % 123.63/35.54 | | | | | | in(all_176_1, all_51_1) = 0) | ( ~ (v3 = 0) & % 123.63/35.54 | | | | | | subset(all_176_4, all_176_5) = v3)))) % 123.63/35.54 | | | | | | % 123.63/35.54 | | | | | | DELTA: instantiating (86) with fresh symbols all_244_0, all_244_1 % 123.63/35.54 | | | | | | gives: % 123.63/35.55 | | | | | | (91) (all_244_0 = 0 & ordinal(all_176_4) = 0) | ( ~ (all_244_1 = % 123.63/35.55 | | | | | | 0) & ordinal(all_51_2) = all_244_1) % 123.63/35.55 | | | | | | % 123.63/35.55 | | | | | | DELTA: instantiating (85) with fresh symbols all_245_0, all_245_1 % 123.63/35.55 | | | | | | gives: % 123.63/35.55 | | | | | | (92) (all_245_0 = 0 & ordinal(all_176_5) = 0) | ( ~ (all_245_1 = % 123.63/35.55 | | | | | | 0) & ordinal(all_51_2) = all_245_1) % 123.63/35.55 | | | | | | % 123.63/35.55 | | | | | | DELTA: instantiating (90) with fresh symbols all_258_0, all_258_1, % 123.63/35.55 | | | | | | all_258_2, all_258_3 gives: % 123.63/35.55 | | | | | | (93) ( ~ (all_258_2 = 0) & in(all_176_5, all_51_2) = all_258_2) | % 123.63/35.55 | | | | | | ( ~ (all_258_3 = 0) & in(all_176_4, all_51_2) = all_258_3) | % 123.63/35.55 | | | | | | (((all_258_0 = 0 & subset(all_176_4, all_176_5) = 0) | ( ~ % 123.63/35.55 | | | | | | (all_258_1 = 0) & in(all_176_1, all_51_1) = % 123.63/35.55 | | | | | | all_258_1)) & ((all_258_1 = 0 & in(all_176_1, % 123.63/35.55 | | | | | | all_51_1) = 0) | ( ~ (all_258_0 = 0) & % 123.63/35.55 | | | | | | subset(all_176_4, all_176_5) = all_258_0))) % 123.63/35.55 | | | | | | % 123.63/35.55 | | | | | | DELTA: instantiating (89) with fresh symbols all_259_0, all_259_1, % 123.63/35.55 | | | | | | all_259_2, all_259_3 gives: % 123.63/35.55 | | | | | | (94) ( ~ (all_259_2 = 0) & in(all_176_4, all_51_2) = all_259_2) | % 123.63/35.55 | | | | | | ( ~ (all_259_3 = 0) & in(all_176_5, all_51_2) = all_259_3) | % 123.63/35.55 | | | | | | (((all_259_0 = 0 & subset(all_176_5, all_176_4) = 0) | ( ~ % 123.63/35.55 | | | | | | (all_259_1 = 0) & in(all_176_3, all_51_1) = % 123.63/35.55 | | | | | | all_259_1)) & ((all_259_1 = 0 & in(all_176_3, % 123.63/35.55 | | | | | | all_51_1) = 0) | ( ~ (all_259_0 = 0) & % 123.63/35.55 | | | | | | subset(all_176_5, all_176_4) = all_259_0))) % 123.63/35.55 | | | | | | % 123.63/35.55 | | | | | | BETA: splitting (94) gives: % 123.63/35.55 | | | | | | % 123.63/35.55 | | | | | | Case 1: % 123.63/35.55 | | | | | | | % 123.63/35.55 | | | | | | | (95) ~ (all_259_2 = 0) & in(all_176_4, all_51_2) = all_259_2 % 123.63/35.55 | | | | | | | % 123.63/35.55 | | | | | | | ALPHA: (95) implies: % 123.63/35.55 | | | | | | | (96) ~ (all_259_2 = 0) % 123.63/35.55 | | | | | | | (97) in(all_176_4, all_51_2) = all_259_2 % 123.63/35.55 | | | | | | | % 123.63/35.55 | | | | | | | GROUND_INST: instantiating (15) with 0, all_259_2, all_51_2, % 123.63/35.55 | | | | | | | all_176_4, simplifying with (72), (97) gives: % 123.63/35.55 | | | | | | | (98) all_259_2 = 0 % 123.63/35.55 | | | | | | | % 123.63/35.55 | | | | | | | REDUCE: (96), (98) imply: % 123.63/35.55 | | | | | | | (99) $false % 123.63/35.55 | | | | | | | % 123.63/35.55 | | | | | | | CLOSE: (99) is inconsistent. % 123.63/35.55 | | | | | | | % 123.63/35.55 | | | | | | Case 2: % 123.63/35.55 | | | | | | | % 123.63/35.55 | | | | | | | (100) ( ~ (all_259_3 = 0) & in(all_176_5, all_51_2) = % 123.63/35.55 | | | | | | | all_259_3) | (((all_259_0 = 0 & subset(all_176_5, % 123.63/35.55 | | | | | | | all_176_4) = 0) | ( ~ (all_259_1 = 0) & % 123.63/35.55 | | | | | | | in(all_176_3, all_51_1) = all_259_1)) & ((all_259_1 % 123.63/35.55 | | | | | | | = 0 & in(all_176_3, all_51_1) = 0) | ( ~ (all_259_0 % 123.63/35.55 | | | | | | | = 0) & subset(all_176_5, all_176_4) = % 123.63/35.55 | | | | | | | all_259_0))) % 123.63/35.55 | | | | | | | % 123.63/35.55 | | | | | | | BETA: splitting (100) gives: % 123.63/35.55 | | | | | | | % 123.63/35.55 | | | | | | | Case 1: % 123.63/35.55 | | | | | | | | % 123.63/35.55 | | | | | | | | (101) ~ (all_259_3 = 0) & in(all_176_5, all_51_2) = % 123.63/35.55 | | | | | | | | all_259_3 % 123.63/35.55 | | | | | | | | % 123.63/35.55 | | | | | | | | ALPHA: (101) implies: % 123.63/35.55 | | | | | | | | (102) ~ (all_259_3 = 0) % 123.63/35.55 | | | | | | | | (103) in(all_176_5, all_51_2) = all_259_3 % 123.63/35.55 | | | | | | | | % 123.63/35.55 | | | | | | | | GROUND_INST: instantiating (15) with 0, all_259_3, all_51_2, % 123.63/35.55 | | | | | | | | all_176_5, simplifying with (73), (103) gives: % 123.63/35.55 | | | | | | | | (104) all_259_3 = 0 % 123.63/35.55 | | | | | | | | % 123.63/35.55 | | | | | | | | REDUCE: (102), (104) imply: % 123.63/35.55 | | | | | | | | (105) $false % 123.63/35.55 | | | | | | | | % 123.63/35.55 | | | | | | | | CLOSE: (105) is inconsistent. % 123.63/35.55 | | | | | | | | % 123.63/35.55 | | | | | | | Case 2: % 123.63/35.55 | | | | | | | | % 123.63/35.55 | | | | | | | | (106) ((all_259_0 = 0 & subset(all_176_5, all_176_4) = 0) | ( % 123.63/35.55 | | | | | | | | ~ (all_259_1 = 0) & in(all_176_3, all_51_1) = % 123.63/35.55 | | | | | | | | all_259_1)) & ((all_259_1 = 0 & in(all_176_3, % 123.63/35.55 | | | | | | | | all_51_1) = 0) | ( ~ (all_259_0 = 0) & % 123.63/35.55 | | | | | | | | subset(all_176_5, all_176_4) = all_259_0)) % 123.63/35.55 | | | | | | | | % 123.63/35.55 | | | | | | | | ALPHA: (106) implies: % 123.63/35.55 | | | | | | | | (107) (all_259_1 = 0 & in(all_176_3, all_51_1) = 0) | ( ~ % 123.63/35.55 | | | | | | | | (all_259_0 = 0) & subset(all_176_5, all_176_4) = % 123.63/35.55 | | | | | | | | all_259_0) % 123.63/35.55 | | | | | | | | % 123.63/35.55 | | | | | | | | BETA: splitting (91) gives: % 123.63/35.55 | | | | | | | | % 123.63/35.55 | | | | | | | | Case 1: % 123.63/35.55 | | | | | | | | | % 123.63/35.55 | | | | | | | | | (108) all_244_0 = 0 & ordinal(all_176_4) = 0 % 123.63/35.55 | | | | | | | | | % 123.63/35.55 | | | | | | | | | ALPHA: (108) implies: % 123.63/35.55 | | | | | | | | | (109) ordinal(all_176_4) = 0 % 123.63/35.55 | | | | | | | | | % 123.63/35.55 | | | | | | | | | BETA: splitting (107) gives: % 123.63/35.55 | | | | | | | | | % 123.63/35.55 | | | | | | | | | Case 1: % 123.63/35.55 | | | | | | | | | | % 123.63/35.55 | | | | | | | | | | (110) all_259_1 = 0 & in(all_176_3, all_51_1) = 0 % 123.63/35.55 | | | | | | | | | | % 123.63/35.55 | | | | | | | | | | ALPHA: (110) implies: % 123.63/35.55 | | | | | | | | | | (111) in(all_176_3, all_51_1) = 0 % 123.63/35.55 | | | | | | | | | | % 123.63/35.55 | | | | | | | | | | GROUND_INST: instantiating (15) with all_176_2, 0, all_51_1, % 123.63/35.55 | | | | | | | | | | all_176_3, simplifying with (66), (111) gives: % 123.63/35.56 | | | | | | | | | | (112) all_176_2 = 0 % 123.63/35.56 | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | REDUCE: (60), (112) imply: % 123.63/35.56 | | | | | | | | | | (113) $false % 123.63/35.56 | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | CLOSE: (113) is inconsistent. % 123.63/35.56 | | | | | | | | | | % 123.63/35.56 | | | | | | | | | Case 2: % 123.63/35.56 | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | (114) ~ (all_259_0 = 0) & subset(all_176_5, all_176_4) = % 123.63/35.56 | | | | | | | | | | all_259_0 % 123.63/35.56 | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | ALPHA: (114) implies: % 123.63/35.56 | | | | | | | | | | (115) ~ (all_259_0 = 0) % 123.63/35.56 | | | | | | | | | | (116) subset(all_176_5, all_176_4) = all_259_0 % 123.63/35.56 | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | BETA: splitting (92) gives: % 123.63/35.56 | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | Case 1: % 123.63/35.56 | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | (117) all_245_0 = 0 & ordinal(all_176_5) = 0 % 123.63/35.56 | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | ALPHA: (117) implies: % 123.63/35.56 | | | | | | | | | | | (118) ordinal(all_176_5) = 0 % 123.63/35.56 | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | BETA: splitting (93) gives: % 123.63/35.56 | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | Case 1: % 123.63/35.56 | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | (119) ~ (all_258_2 = 0) & in(all_176_5, all_51_2) = % 123.63/35.56 | | | | | | | | | | | | all_258_2 % 123.63/35.56 | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | ALPHA: (119) implies: % 123.63/35.56 | | | | | | | | | | | | (120) ~ (all_258_2 = 0) % 123.63/35.56 | | | | | | | | | | | | (121) in(all_176_5, all_51_2) = all_258_2 % 123.63/35.56 | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_258_2, all_51_2, % 123.63/35.56 | | | | | | | | | | | | all_176_5, simplifying with (73), (121) gives: % 123.63/35.56 | | | | | | | | | | | | (122) all_258_2 = 0 % 123.63/35.56 | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | REDUCE: (120), (122) imply: % 123.63/35.56 | | | | | | | | | | | | (123) $false % 123.63/35.56 | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | CLOSE: (123) is inconsistent. % 123.63/35.56 | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | Case 2: % 123.63/35.56 | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | (124) ( ~ (all_258_3 = 0) & in(all_176_4, all_51_2) = % 123.63/35.56 | | | | | | | | | | | | all_258_3) | (((all_258_0 = 0 & % 123.63/35.56 | | | | | | | | | | | | subset(all_176_4, all_176_5) = 0) | ( ~ % 123.63/35.56 | | | | | | | | | | | | (all_258_1 = 0) & in(all_176_1, all_51_1) = % 123.63/35.56 | | | | | | | | | | | | all_258_1)) & ((all_258_1 = 0 & % 123.63/35.56 | | | | | | | | | | | | in(all_176_1, all_51_1) = 0) | ( ~ % 123.63/35.56 | | | | | | | | | | | | (all_258_0 = 0) & subset(all_176_4, % 123.63/35.56 | | | | | | | | | | | | all_176_5) = all_258_0))) % 123.63/35.56 | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | BETA: splitting (124) gives: % 123.63/35.56 | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | Case 1: % 123.63/35.56 | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | (125) ~ (all_258_3 = 0) & in(all_176_4, all_51_2) = % 123.63/35.56 | | | | | | | | | | | | | all_258_3 % 123.63/35.56 | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | ALPHA: (125) implies: % 123.63/35.56 | | | | | | | | | | | | | (126) ~ (all_258_3 = 0) % 123.63/35.56 | | | | | | | | | | | | | (127) in(all_176_4, all_51_2) = all_258_3 % 123.63/35.56 | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_258_3, all_51_2, % 123.63/35.56 | | | | | | | | | | | | | all_176_4, simplifying with (72), (127) gives: % 123.63/35.56 | | | | | | | | | | | | | (128) all_258_3 = 0 % 123.63/35.56 | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | REDUCE: (126), (128) imply: % 123.63/35.56 | | | | | | | | | | | | | (129) $false % 123.63/35.56 | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | CLOSE: (129) is inconsistent. % 123.63/35.56 | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | Case 2: % 123.63/35.56 | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | (130) ((all_258_0 = 0 & subset(all_176_4, all_176_5) = % 123.63/35.56 | | | | | | | | | | | | | 0) | ( ~ (all_258_1 = 0) & in(all_176_1, % 123.63/35.56 | | | | | | | | | | | | | all_51_1) = all_258_1)) & ((all_258_1 = 0 & % 123.63/35.56 | | | | | | | | | | | | | in(all_176_1, all_51_1) = 0) | ( ~ (all_258_0 % 123.63/35.56 | | | | | | | | | | | | | = 0) & subset(all_176_4, all_176_5) = % 123.63/35.56 | | | | | | | | | | | | | all_258_0)) % 123.63/35.56 | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | ALPHA: (130) implies: % 123.63/35.56 | | | | | | | | | | | | | (131) (all_258_1 = 0 & in(all_176_1, all_51_1) = 0) | ( % 123.63/35.56 | | | | | | | | | | | | | ~ (all_258_0 = 0) & subset(all_176_4, all_176_5) % 123.63/35.56 | | | | | | | | | | | | | = all_258_0) % 123.63/35.56 | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | BETA: splitting (131) gives: % 123.63/35.56 | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | Case 1: % 123.63/35.56 | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | (132) all_258_1 = 0 & in(all_176_1, all_51_1) = 0 % 123.63/35.56 | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | ALPHA: (132) implies: % 123.63/35.56 | | | | | | | | | | | | | | (133) in(all_176_1, all_51_1) = 0 % 123.63/35.56 | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_176_0, 0, all_51_1, % 123.63/35.56 | | | | | | | | | | | | | | all_176_1, simplifying with (67), (133) gives: % 123.63/35.56 | | | | | | | | | | | | | | (134) all_176_0 = 0 % 123.63/35.56 | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | REDUCE: (61), (134) imply: % 123.63/35.56 | | | | | | | | | | | | | | (135) $false % 123.63/35.56 | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | CLOSE: (135) is inconsistent. % 123.63/35.56 | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | Case 2: % 123.63/35.56 | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | (136) ~ (all_258_0 = 0) & subset(all_176_4, all_176_5) % 123.63/35.56 | | | | | | | | | | | | | | = all_258_0 % 123.63/35.56 | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | ALPHA: (136) implies: % 123.63/35.56 | | | | | | | | | | | | | | (137) ~ (all_258_0 = 0) % 123.63/35.56 | | | | | | | | | | | | | | (138) subset(all_176_4, all_176_5) = all_258_0 % 123.63/35.56 | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | BETA: splitting (88) gives: % 123.63/35.56 | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | Case 1: % 123.63/35.56 | | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | | (139) all_97_0 = 0 % 123.63/35.56 | | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | | REDUCE: (37), (139) imply: % 123.63/35.56 | | | | | | | | | | | | | | | (140) $false % 123.63/35.56 | | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent. % 123.63/35.56 | | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | Case 2: % 123.63/35.56 | | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | | (141) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 123.63/35.56 | | | | | | | | | | | | | | | int] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) % 123.63/35.56 | | | | | | | | | | | | | | | & ~ (v3 = 0) & ~ (v1 = v0) & ordered_pair(v1, % 123.63/35.56 | | | | | | | | | | | | | | | v0) = v4 & ordered_pair(v0, v1) = v2 & in(v4, % 123.63/35.56 | | | | | | | | | | | | | | | all_51_1) = v5 & in(v2, all_51_1) = v3 & % 123.63/35.56 | | | | | | | | | | | | | | | in(v1, all_51_2) = 0 & in(v0, all_51_2) = 0 & % 123.63/35.56 | | | | | | | | | | | | | | | $i(v4) & $i(v2) & $i(v1) & $i(v0)) % 123.63/35.56 | | | | | | | | | | | | | | | % 123.63/35.56 | | | | | | | | | | | | | | | DELTA: instantiating (141) with fresh symbols all_305_0, % 123.63/35.56 | | | | | | | | | | | | | | | all_305_1, all_305_2, all_305_3, all_305_4, % 123.63/35.56 | | | | | | | | | | | | | | | all_305_5 gives: % 123.63/35.56 | | | | | | | | | | | | | | | (142) ~ (all_305_0 = 0) & ~ (all_305_2 = 0) & ~ % 123.63/35.56 | | | | | | | | | | | | | | | (all_305_4 = all_305_5) & ordered_pair(all_305_4, % 123.63/35.56 | | | | | | | | | | | | | | | all_305_5) = all_305_1 & ordered_pair(all_305_5, % 123.63/35.56 | | | | | | | | | | | | | | | all_305_4) = all_305_3 & in(all_305_1, all_51_1) % 123.63/35.56 | | | | | | | | | | | | | | | = all_305_0 & in(all_305_3, all_51_1) = all_305_2 % 123.63/35.56 | | | | | | | | | | | | | | | & in(all_305_4, all_51_2) = 0 & in(all_305_5, % 123.63/35.56 | | | | | | | | | | | | | | | all_51_2) = 0 & $i(all_305_1) & $i(all_305_3) & % 123.63/35.56 | | | | | | | | | | | | | | | $i(all_305_4) & $i(all_305_5) % 123.63/35.56 | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | ALPHA: (142) implies: % 123.63/35.57 | | | | | | | | | | | | | | | (143) ~ (all_305_2 = 0) % 123.63/35.57 | | | | | | | | | | | | | | | (144) $i(all_305_5) % 123.63/35.57 | | | | | | | | | | | | | | | (145) $i(all_305_4) % 123.63/35.57 | | | | | | | | | | | | | | | (146) in(all_305_5, all_51_2) = 0 % 123.63/35.57 | | | | | | | | | | | | | | | (147) in(all_305_4, all_51_2) = 0 % 123.63/35.57 | | | | | | | | | | | | | | | (148) in(all_305_3, all_51_1) = all_305_2 % 123.63/35.57 | | | | | | | | | | | | | | | (149) ordered_pair(all_305_5, all_305_4) = all_305_3 % 123.63/35.57 | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | GROUND_INST: instantiating (55) with all_305_5, all_305_4, % 123.63/35.57 | | | | | | | | | | | | | | | all_305_3, simplifying with (144), (145), (149) % 123.63/35.57 | | | | | | | | | | | | | | | gives: % 123.63/35.57 | | | | | | | | | | | | | | | (150) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 123.63/35.57 | | | | | | | | | | | | | | | [v3: int] : (( ~ (v1 = 0) & in(all_305_4, % 123.63/35.57 | | | | | | | | | | | | | | | all_51_2) = v1) | ( ~ (v0 = 0) & % 123.63/35.57 | | | | | | | | | | | | | | | in(all_305_5, all_51_2) = v0) | (((v3 = 0 & % 123.63/35.57 | | | | | | | | | | | | | | | subset(all_305_5, all_305_4) = 0) | ( ~ % 123.63/35.57 | | | | | | | | | | | | | | | (v2 = 0) & in(all_305_3, all_51_1) = v2)) % 123.63/35.57 | | | | | | | | | | | | | | | & ((v2 = 0 & in(all_305_3, all_51_1) = 0) | ( % 123.63/35.57 | | | | | | | | | | | | | | | ~ (v3 = 0) & subset(all_305_5, all_305_4) % 123.63/35.57 | | | | | | | | | | | | | | | = v3)))) % 123.63/35.57 | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_176_5, all_176_4, % 123.63/35.57 | | | | | | | | | | | | | | | all_259_0, simplifying with (62), (63), (116) % 123.63/35.57 | | | | | | | | | | | | | | | gives: % 123.63/35.57 | | | | | | | | | | | | | | | (151) ? [v0: int] : ? [v1: int] : ? [v2: int] : (( ~ % 123.63/35.57 | | | | | | | | | | | | | | | (v1 = 0) & ordinal(all_176_4) = v1) | ( ~ (v0 % 123.63/35.57 | | | | | | | | | | | | | | | = 0) & ordinal(all_176_5) = v0) | (( ~ % 123.63/35.57 | | | | | | | | | | | | | | | (all_259_0 = 0) | (v2 = 0 & % 123.63/35.57 | | | | | | | | | | | | | | | ordinal_subset(all_176_5, all_176_4) = 0)) % 123.63/35.57 | | | | | | | | | | | | | | | & (all_259_0 = 0 | ( ~ (v2 = 0) & % 123.63/35.57 | | | | | | | | | | | | | | | ordinal_subset(all_176_5, all_176_4) = % 123.63/35.57 | | | | | | | | | | | | | | | v2)))) % 123.63/35.57 | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_176_4, all_176_5, % 123.63/35.57 | | | | | | | | | | | | | | | all_258_0, simplifying with (62), (63), (138) % 123.63/35.57 | | | | | | | | | | | | | | | gives: % 123.63/35.57 | | | | | | | | | | | | | | | (152) ? [v0: int] : ? [v1: int] : ? [v2: int] : (( ~ % 123.63/35.57 | | | | | | | | | | | | | | | (v1 = 0) & ordinal(all_176_5) = v1) | ( ~ (v0 % 123.63/35.57 | | | | | | | | | | | | | | | = 0) & ordinal(all_176_4) = v0) | (( ~ % 123.63/35.57 | | | | | | | | | | | | | | | (all_258_0 = 0) | (v2 = 0 & % 123.63/35.57 | | | | | | | | | | | | | | | ordinal_subset(all_176_4, all_176_5) = 0)) % 123.63/35.57 | | | | | | | | | | | | | | | & (all_258_0 = 0 | ( ~ (v2 = 0) & % 123.63/35.57 | | | | | | | | | | | | | | | ordinal_subset(all_176_4, all_176_5) = % 123.63/35.57 | | | | | | | | | | | | | | | v2)))) % 123.63/35.57 | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | DELTA: instantiating (152) with fresh symbols all_667_0, % 123.63/35.57 | | | | | | | | | | | | | | | all_667_1, all_667_2 gives: % 123.63/35.57 | | | | | | | | | | | | | | | (153) ( ~ (all_667_1 = 0) & ordinal(all_176_5) = % 123.63/35.57 | | | | | | | | | | | | | | | all_667_1) | ( ~ (all_667_2 = 0) & % 123.63/35.57 | | | | | | | | | | | | | | | ordinal(all_176_4) = all_667_2) | (( ~ % 123.63/35.57 | | | | | | | | | | | | | | | (all_258_0 = 0) | (all_667_0 = 0 & % 123.63/35.57 | | | | | | | | | | | | | | | ordinal_subset(all_176_4, all_176_5) = 0)) & % 123.63/35.57 | | | | | | | | | | | | | | | (all_258_0 = 0 | ( ~ (all_667_0 = 0) & % 123.63/35.57 | | | | | | | | | | | | | | | ordinal_subset(all_176_4, all_176_5) = % 123.63/35.57 | | | | | | | | | | | | | | | all_667_0))) % 123.63/35.57 | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | DELTA: instantiating (151) with fresh symbols all_668_0, % 123.63/35.57 | | | | | | | | | | | | | | | all_668_1, all_668_2 gives: % 123.63/35.57 | | | | | | | | | | | | | | | (154) ( ~ (all_668_1 = 0) & ordinal(all_176_4) = % 123.63/35.57 | | | | | | | | | | | | | | | all_668_1) | ( ~ (all_668_2 = 0) & % 123.63/35.57 | | | | | | | | | | | | | | | ordinal(all_176_5) = all_668_2) | (( ~ % 123.63/35.57 | | | | | | | | | | | | | | | (all_259_0 = 0) | (all_668_0 = 0 & % 123.63/35.57 | | | | | | | | | | | | | | | ordinal_subset(all_176_5, all_176_4) = 0)) & % 123.63/35.57 | | | | | | | | | | | | | | | (all_259_0 = 0 | ( ~ (all_668_0 = 0) & % 123.63/35.57 | | | | | | | | | | | | | | | ordinal_subset(all_176_5, all_176_4) = % 123.63/35.57 | | | | | | | | | | | | | | | all_668_0))) % 123.63/35.57 | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | DELTA: instantiating (150) with fresh symbols all_674_0, % 123.63/35.57 | | | | | | | | | | | | | | | all_674_1, all_674_2, all_674_3 gives: % 123.63/35.57 | | | | | | | | | | | | | | | (155) ( ~ (all_674_2 = 0) & in(all_305_4, all_51_2) = % 123.63/35.57 | | | | | | | | | | | | | | | all_674_2) | ( ~ (all_674_3 = 0) & in(all_305_5, % 123.63/35.57 | | | | | | | | | | | | | | | all_51_2) = all_674_3) | (((all_674_0 = 0 & % 123.63/35.57 | | | | | | | | | | | | | | | subset(all_305_5, all_305_4) = 0) | ( ~ % 123.63/35.57 | | | | | | | | | | | | | | | (all_674_1 = 0) & in(all_305_3, all_51_1) = % 123.63/35.57 | | | | | | | | | | | | | | | all_674_1)) & ((all_674_1 = 0 & % 123.63/35.57 | | | | | | | | | | | | | | | in(all_305_3, all_51_1) = 0) | ( ~ % 123.63/35.57 | | | | | | | | | | | | | | | (all_674_0 = 0) & subset(all_305_5, % 123.63/35.57 | | | | | | | | | | | | | | | all_305_4) = all_674_0))) % 123.63/35.57 | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | BETA: splitting (153) gives: % 123.63/35.57 | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | Case 1: % 123.63/35.57 | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | (156) ~ (all_667_1 = 0) & ordinal(all_176_5) = % 123.63/35.57 | | | | | | | | | | | | | | | | all_667_1 % 123.63/35.57 | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | ALPHA: (156) implies: % 123.63/35.57 | | | | | | | | | | | | | | | | (157) ~ (all_667_1 = 0) % 123.63/35.57 | | | | | | | | | | | | | | | | (158) ordinal(all_176_5) = all_667_1 % 123.63/35.57 | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_667_1, all_176_5, % 123.63/35.57 | | | | | | | | | | | | | | | | simplifying with (118), (158) gives: % 123.63/35.57 | | | | | | | | | | | | | | | | (159) all_667_1 = 0 % 123.63/35.57 | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | REDUCE: (157), (159) imply: % 123.63/35.57 | | | | | | | | | | | | | | | | (160) $false % 123.63/35.57 | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | CLOSE: (160) is inconsistent. % 123.63/35.57 | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | Case 2: % 123.63/35.57 | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | (161) ( ~ (all_667_2 = 0) & ordinal(all_176_4) = % 123.63/35.57 | | | | | | | | | | | | | | | | all_667_2) | (( ~ (all_258_0 = 0) | (all_667_0 = % 123.63/35.57 | | | | | | | | | | | | | | | | 0 & ordinal_subset(all_176_4, all_176_5) = % 123.63/35.57 | | | | | | | | | | | | | | | | 0)) & (all_258_0 = 0 | ( ~ (all_667_0 = 0) & % 123.63/35.57 | | | | | | | | | | | | | | | | ordinal_subset(all_176_4, all_176_5) = % 123.63/35.57 | | | | | | | | | | | | | | | | all_667_0))) % 123.63/35.57 | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 123.63/35.57 | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | Case 1: % 123.63/35.57 | | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | | (162) ~ (all_667_2 = 0) & ordinal(all_176_4) = % 123.63/35.57 | | | | | | | | | | | | | | | | | all_667_2 % 123.63/35.57 | | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | | ALPHA: (162) implies: % 123.63/35.57 | | | | | | | | | | | | | | | | | (163) ~ (all_667_2 = 0) % 123.63/35.57 | | | | | | | | | | | | | | | | | (164) ordinal(all_176_4) = all_667_2 % 123.63/35.57 | | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_667_2, all_176_4, % 123.63/35.57 | | | | | | | | | | | | | | | | | simplifying with (109), (164) gives: % 123.63/35.57 | | | | | | | | | | | | | | | | | (165) all_667_2 = 0 % 123.63/35.57 | | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | | REDUCE: (163), (165) imply: % 123.63/35.57 | | | | | | | | | | | | | | | | | (166) $false % 123.63/35.57 | | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent. % 123.63/35.57 | | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | Case 2: % 123.63/35.57 | | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | | (167) ( ~ (all_258_0 = 0) | (all_667_0 = 0 & % 123.63/35.57 | | | | | | | | | | | | | | | | | ordinal_subset(all_176_4, all_176_5) = 0)) & % 123.63/35.57 | | | | | | | | | | | | | | | | | (all_258_0 = 0 | ( ~ (all_667_0 = 0) & % 123.63/35.57 | | | | | | | | | | | | | | | | | ordinal_subset(all_176_4, all_176_5) = % 123.63/35.57 | | | | | | | | | | | | | | | | | all_667_0)) % 123.63/35.57 | | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | | ALPHA: (167) implies: % 123.63/35.57 | | | | | | | | | | | | | | | | | (168) all_258_0 = 0 | ( ~ (all_667_0 = 0) & % 123.63/35.57 | | | | | | | | | | | | | | | | | ordinal_subset(all_176_4, all_176_5) = % 123.63/35.57 | | | | | | | | | | | | | | | | | all_667_0) % 123.63/35.57 | | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 123.63/35.57 | | | | | | | | | | | | | | | | | % 123.63/35.57 | | | | | | | | | | | | | | | | | Case 1: % 123.63/35.57 | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | (169) all_258_0 = 0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | REDUCE: (137), (169) imply: % 123.63/35.58 | | | | | | | | | | | | | | | | | | (170) $false % 123.63/35.58 | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | CLOSE: (170) is inconsistent. % 123.63/35.58 | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | Case 2: % 123.63/35.58 | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | (171) ~ (all_667_0 = 0) & ordinal_subset(all_176_4, % 123.63/35.58 | | | | | | | | | | | | | | | | | | all_176_5) = all_667_0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | ALPHA: (171) implies: % 123.63/35.58 | | | | | | | | | | | | | | | | | | (172) ~ (all_667_0 = 0) % 123.63/35.58 | | | | | | | | | | | | | | | | | | (173) ordinal_subset(all_176_4, all_176_5) = all_667_0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives: % 123.63/35.58 | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | Case 1: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | (174) ~ (all_674_2 = 0) & in(all_305_4, all_51_2) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | all_674_2 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | (175) ~ (all_674_2 = 0) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | (176) in(all_305_4, all_51_2) = all_674_2 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_674_2, all_51_2, % 123.63/35.58 | | | | | | | | | | | | | | | | | | | all_305_4, simplifying with (147), (176) gives: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | (177) all_674_2 = 0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | REDUCE: (175), (177) imply: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | (178) $false % 123.63/35.58 | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | CLOSE: (178) is inconsistent. % 123.63/35.58 | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | Case 2: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | (179) ( ~ (all_674_3 = 0) & in(all_305_5, all_51_2) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | all_674_3) | (((all_674_0 = 0 & % 123.63/35.58 | | | | | | | | | | | | | | | | | | | subset(all_305_5, all_305_4) = 0) | ( ~ % 123.63/35.58 | | | | | | | | | | | | | | | | | | | (all_674_1 = 0) & in(all_305_3, all_51_1) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | all_674_1)) & ((all_674_1 = 0 & % 123.63/35.58 | | | | | | | | | | | | | | | | | | | in(all_305_3, all_51_1) = 0) | ( ~ % 123.63/35.58 | | | | | | | | | | | | | | | | | | | (all_674_0 = 0) & subset(all_305_5, % 123.63/35.58 | | | | | | | | | | | | | | | | | | | all_305_4) = all_674_0))) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | Case 1: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | (180) ~ (all_674_3 = 0) & in(all_305_5, all_51_2) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | all_674_3 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | (181) ~ (all_674_3 = 0) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | (182) in(all_305_5, all_51_2) = all_674_3 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_674_3, all_51_2, % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | all_305_5, simplifying with (146), (182) gives: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | (183) all_674_3 = 0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (183) imply: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | (184) $false % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent. % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | Case 2: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | (185) ((all_674_0 = 0 & subset(all_305_5, all_305_4) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | 0) | ( ~ (all_674_1 = 0) & in(all_305_3, % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | all_51_1) = all_674_1)) & ((all_674_1 = 0 & % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | in(all_305_3, all_51_1) = 0) | ( ~ (all_674_0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | = 0) & subset(all_305_5, all_305_4) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | all_674_0)) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | (186) (all_674_1 = 0 & in(all_305_3, all_51_1) = 0) | ( % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | ~ (all_674_0 = 0) & subset(all_305_5, all_305_4) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | = all_674_0) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | (187) (all_674_0 = 0 & subset(all_305_5, all_305_4) = 0) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_674_1 = 0) & in(all_305_3, all_51_1) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | all_674_1) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | Case 1: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | (188) ~ (all_668_1 = 0) & ordinal(all_176_4) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | all_668_1 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | (189) ~ (all_668_1 = 0) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | (190) ordinal(all_176_4) = all_668_1 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_668_1, all_176_4, % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | simplifying with (109), (190) gives: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | (191) all_668_1 = 0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (191) imply: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | (192) $false % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | Case 2: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | (193) ( ~ (all_668_2 = 0) & ordinal(all_176_5) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | all_668_2) | (( ~ (all_259_0 = 0) | (all_668_0 = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | 0 & ordinal_subset(all_176_5, all_176_4) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | 0)) & (all_259_0 = 0 | ( ~ (all_668_0 = 0) & % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | ordinal_subset(all_176_5, all_176_4) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | all_668_0))) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | Case 1: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | (194) ~ (all_668_2 = 0) & ordinal(all_176_5) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | all_668_2 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | (195) ~ (all_668_2 = 0) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | (196) ordinal(all_176_5) = all_668_2 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_668_2, all_176_5, % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | simplifying with (118), (196) gives: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | (197) all_668_2 = 0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (195), (197) imply: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | (198) $false % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (198) is inconsistent. % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | Case 2: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | (199) ( ~ (all_259_0 = 0) | (all_668_0 = 0 & % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | ordinal_subset(all_176_5, all_176_4) = 0)) & % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | (all_259_0 = 0 | ( ~ (all_668_0 = 0) & % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | ordinal_subset(all_176_5, all_176_4) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | all_668_0)) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | (200) all_259_0 = 0 | ( ~ (all_668_0 = 0) & % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | ordinal_subset(all_176_5, all_176_4) = % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | all_668_0) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | (201) all_259_0 = 0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (201) imply: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | (202) $false % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent. % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | (203) ~ (all_668_0 = 0) & ordinal_subset(all_176_5, % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | all_176_4) = all_668_0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | (204) ~ (all_668_0 = 0) % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | (205) ordinal_subset(all_176_5, all_176_4) = all_668_0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | | (206) all_674_1 = 0 & in(all_305_3, all_51_1) = 0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | | (207) in(all_305_3, all_51_1) = 0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_305_2, 0, all_51_1, % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | | all_305_3, simplifying with (148), (207) gives: % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | | (208) all_305_2 = 0 % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.58 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (208) imply: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | (209) $false % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent. % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | (210) ~ (all_674_0 = 0) & subset(all_305_5, all_305_4) % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | = all_674_0 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | (211) ~ (all_674_0 = 0) % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_674_0 = 0 & subset(all_305_5, all_305_4) = 0 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_674_0 = 0 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (211), (213) imply: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | (214) $false % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent. % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_176_5, all_176_4, % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | all_668_0, simplifying with (62), (63), (205) % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_668_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | [v2: int] : ((v2 = 0 & ordinal_subset(all_176_4, % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | all_176_5) = 0) | ( ~ (v1 = 0) & % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | ordinal(all_176_4) = v1) | ( ~ (v0 = 0) & % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | ordinal(all_176_5) = v0)) % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_668_0 = 0 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (204), (216) imply: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (217) $false % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (217) is inconsistent. % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (218) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | = 0 & ordinal_subset(all_176_4, all_176_5) = % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ( ~ (v1 = 0) & ordinal(all_176_4) = v1) | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v0 = 0) & ordinal(all_176_5) = v0)) % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (218) with fresh symbols all_1369_0, % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1369_1, all_1369_2 gives: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (219) (all_1369_0 = 0 & ordinal_subset(all_176_4, % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | all_176_5) = 0) | ( ~ (all_1369_1 = 0) & % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | ordinal(all_176_4) = all_1369_1) | ( ~ % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_1369_2 = 0) & ordinal(all_176_5) = % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | all_1369_2) % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_1369_0 = 0 & ordinal_subset(all_176_4, % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_176_5) = 0 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) ordinal_subset(all_176_4, all_176_5) = 0 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_667_0, 0, all_176_5, % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_176_4, simplifying with (173), (221) gives: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_667_0 = 0 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (222) imply: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) $false % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent. % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) ( ~ (all_1369_1 = 0) & ordinal(all_176_4) = % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1369_1) | ( ~ (all_1369_2 = 0) & % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | ordinal(all_176_5) = all_1369_2) % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) ~ (all_1369_1 = 0) & ordinal(all_176_4) = % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1369_1 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) ~ (all_1369_1 = 0) % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) ordinal(all_176_4) = all_1369_1 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_1369_1, all_176_4, % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (109), (227) gives: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_1369_1 = 0 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (226), (228) imply: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) $false % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent. % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) ~ (all_1369_2 = 0) & ordinal(all_176_5) = % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_1369_2 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) ~ (all_1369_2 = 0) % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) ordinal(all_176_5) = all_1369_2 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_1369_2, all_176_5, % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (118), (232) gives: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_1369_2 = 0 % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (231), (233) imply: % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) $false % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent. % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | Case 2: % 123.63/35.59 | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | (235) ~ (all_245_1 = 0) & ordinal(all_51_2) = all_245_1 % 123.63/35.59 | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | ALPHA: (235) implies: % 123.63/35.59 | | | | | | | | | | | (236) ~ (all_245_1 = 0) % 123.63/35.59 | | | | | | | | | | | (237) ordinal(all_51_2) = all_245_1 % 123.63/35.59 | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_245_1, all_51_2, % 123.63/35.59 | | | | | | | | | | | simplifying with (21), (237) gives: % 123.63/35.59 | | | | | | | | | | | (238) all_245_1 = 0 % 123.63/35.59 | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | REDUCE: (236), (238) imply: % 123.63/35.59 | | | | | | | | | | | (239) $false % 123.63/35.59 | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | | CLOSE: (239) is inconsistent. % 123.63/35.59 | | | | | | | | | | | % 123.63/35.59 | | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | | % 123.63/35.59 | | | | | | | | | End of split % 123.63/35.59 | | | | | | | | | % 123.63/35.59 | | | | | | | | Case 2: % 123.63/35.59 | | | | | | | | | % 123.63/35.59 | | | | | | | | | (240) ~ (all_244_1 = 0) & ordinal(all_51_2) = all_244_1 % 123.63/35.59 | | | | | | | | | % 123.63/35.59 | | | | | | | | | ALPHA: (240) implies: % 123.63/35.59 | | | | | | | | | (241) ~ (all_244_1 = 0) % 123.63/35.59 | | | | | | | | | (242) ordinal(all_51_2) = all_244_1 % 123.63/35.59 | | | | | | | | | % 123.63/35.59 | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_244_1, all_51_2, % 123.63/35.59 | | | | | | | | | simplifying with (21), (242) gives: % 123.63/35.59 | | | | | | | | | (243) all_244_1 = 0 % 123.63/35.59 | | | | | | | | | % 123.63/35.59 | | | | | | | | | REDUCE: (241), (243) imply: % 123.63/35.59 | | | | | | | | | (244) $false % 123.63/35.59 | | | | | | | | | % 123.63/35.59 | | | | | | | | | CLOSE: (244) is inconsistent. % 123.63/35.59 | | | | | | | | | % 123.63/35.59 | | | | | | | | End of split % 123.63/35.59 | | | | | | | | % 123.63/35.59 | | | | | | | End of split % 123.63/35.59 | | | | | | | % 123.63/35.59 | | | | | | End of split % 123.63/35.59 | | | | | | % 123.63/35.59 | | | | | Case 2: % 123.63/35.59 | | | | | | % 123.63/35.59 | | | | | | (245) ~ (all_161_3 = 0) & relation(all_51_1) = all_161_3 % 123.63/35.59 | | | | | | % 123.63/35.59 | | | | | | ALPHA: (245) implies: % 123.63/35.59 | | | | | | (246) ~ (all_161_3 = 0) % 123.63/35.59 | | | | | | (247) relation(all_51_1) = all_161_3 % 123.63/35.59 | | | | | | % 123.63/35.59 | | | | | | GROUND_INST: instantiating (11) with 0, all_161_3, all_51_1, % 123.63/35.59 | | | | | | simplifying with (25), (247) gives: % 123.63/35.59 | | | | | | (248) all_161_3 = 0 % 123.63/35.59 | | | | | | % 123.63/35.59 | | | | | | REDUCE: (246), (248) imply: % 123.63/35.59 | | | | | | (249) $false % 123.63/35.59 | | | | | | % 123.63/35.59 | | | | | | CLOSE: (249) is inconsistent. % 123.63/35.59 | | | | | | % 123.63/35.59 | | | | | End of split % 123.63/35.59 | | | | | % 123.63/35.59 | | | | Case 2: % 123.63/35.59 | | | | | % 123.63/35.60 | | | | | (250) ~ (all_97_1 = all_51_2) % 123.63/35.60 | | | | | % 123.63/35.60 | | | | | GROUND_INST: instantiating (12) with all_97_1, all_158_2, all_51_1, % 123.63/35.60 | | | | | simplifying with (40), (49) gives: % 123.63/35.60 | | | | | (251) all_158_2 = all_97_1 % 123.63/35.60 | | | | | % 123.63/35.60 | | | | | GROUND_INST: instantiating (12) with all_51_2, all_158_2, all_51_1, % 123.63/35.60 | | | | | simplifying with (49), (54) gives: % 123.63/35.60 | | | | | (252) all_158_2 = all_51_2 % 123.63/35.60 | | | | | % 123.63/35.60 | | | | | COMBINE_EQS: (251), (252) imply: % 123.63/35.60 | | | | | (253) all_97_1 = all_51_2 % 123.63/35.60 | | | | | % 123.63/35.60 | | | | | REDUCE: (250), (253) imply: % 123.63/35.60 | | | | | (254) $false % 123.63/35.60 | | | | | % 123.63/35.60 | | | | | CLOSE: (254) is inconsistent. % 123.63/35.60 | | | | | % 123.63/35.60 | | | | End of split % 123.63/35.60 | | | | % 123.63/35.60 | | | End of split % 123.63/35.60 | | | % 123.63/35.60 | | End of split % 123.63/35.60 | | % 123.63/35.60 | End of split % 123.63/35.60 | % 123.63/35.60 End of proof % 123.63/35.60 % SZS output end Proof for theBenchmark % 123.92/35.60 % 123.92/35.60 34982ms %------------------------------------------------------------------------------