%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU236+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 : n024.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 17:43:33 EDT 2023 % Result : Theorem 70.92s 10.10s % Output : Proof 71.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU236+1 : TPTP v8.1.2. Released v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n024.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Aug 23 12:33:39 EDT 2023 % 0.12/0.35 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 2.94/1.14 Prover 4: Preprocessing ... % 2.94/1.15 Prover 1: Preprocessing ... % 2.94/1.19 Prover 2: Preprocessing ... % 2.94/1.19 Prover 3: Preprocessing ... % 2.94/1.19 Prover 5: Preprocessing ... % 2.94/1.19 Prover 6: Preprocessing ... % 2.94/1.19 Prover 0: Preprocessing ... % 7.13/1.75 Prover 1: Warning: ignoring some quantifiers % 7.13/1.76 Prover 5: Proving ... % 7.54/1.81 Prover 2: Proving ... % 7.54/1.82 Prover 1: Constructing countermodel ... % 7.54/1.85 Prover 4: Warning: ignoring some quantifiers % 7.92/1.86 Prover 6: Proving ... % 7.92/1.88 Prover 3: Warning: ignoring some quantifiers % 7.92/1.91 Prover 4: Constructing countermodel ... % 7.92/1.92 Prover 3: Constructing countermodel ... % 7.92/1.95 Prover 0: Proving ... % 11.53/2.38 Prover 3: gave up % 11.78/2.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.24/2.47 Prover 7: Preprocessing ... % 12.24/2.50 Prover 1: gave up % 12.77/2.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.77/2.54 Prover 7: Warning: ignoring some quantifiers % 12.77/2.56 Prover 7: Constructing countermodel ... % 12.77/2.56 Prover 8: Preprocessing ... % 14.50/2.75 Prover 8: Warning: ignoring some quantifiers % 14.50/2.77 Prover 8: Constructing countermodel ... % 17.82/3.30 Prover 8: gave up % 17.82/3.31 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 19.21/3.38 Prover 9: Preprocessing ... % 20.76/3.57 Prover 9: Warning: ignoring some quantifiers % 20.76/3.58 Prover 9: Constructing countermodel ... % 22.71/3.84 Prover 7: gave up % 22.71/3.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.71/3.93 Prover 10: Preprocessing ... % 23.62/4.02 Prover 10: Warning: ignoring some quantifiers % 23.62/4.03 Prover 10: Constructing countermodel ... % 27.53/4.49 Prover 10: gave up % 27.53/4.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 27.53/4.57 Prover 11: Preprocessing ... % 29.09/4.72 Prover 11: Warning: ignoring some quantifiers % 29.62/4.74 Prover 11: Constructing countermodel ... % 58.08/8.46 Prover 2: stopped % 58.08/8.48 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 58.08/8.52 Prover 12: Preprocessing ... % 59.81/8.66 Prover 12: Proving ... % 70.53/10.09 Prover 4: Found proof (size 316) % 70.53/10.09 Prover 4: proved (9465ms) % 70.53/10.09 Prover 0: stopped % 70.53/10.09 Prover 12: stopped % 70.53/10.09 Prover 6: stopped % 70.53/10.09 Prover 9: stopped % 70.53/10.09 Prover 5: stopped % 70.92/10.10 Prover 11: stopped % 70.92/10.10 % 70.92/10.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 70.92/10.10 % 71.20/10.16 % SZS output start Proof for theBenchmark % 71.20/10.16 Assumptions after simplification: % 71.20/10.16 --------------------------------- % 71.20/10.16 % 71.20/10.16 (antisymmetry_r2_hidden) % 71.20/10.19 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 71.20/10.19 [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : ( % 71.20/10.19 ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 71.20/10.19 in(v1, v0) = v2)) % 71.20/10.19 % 71.20/10.19 (cc1_ordinal1) % 71.20/10.19 ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_transitive(v0) = v1) | ~ $i(v0) | % 71.20/10.19 ? [v2: any] : ? [v3: any] : (ordinal(v0) = v2 & epsilon_connected(v0) = v3 % 71.20/10.19 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: $i] : ! [v1: any] : ( ~ % 71.20/10.19 (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 71.20/10.19 (epsilon_transitive(v0) = v3 & ordinal(v0) = v2 & ( ~ (v2 = 0) | (v3 = 0 & % 71.20/10.19 v1 = 0)))) & ! [v0: $i] : ( ~ (ordinal(v0) = 0) | ~ $i(v0) | % 71.20/10.19 (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) % 71.20/10.19 % 71.20/10.19 (cc2_funct_1) % 71.20/10.20 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2: % 71.20/10.20 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) = % 71.20/10.20 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 71.20/10.20 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 71.20/10.20 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0) % 71.20/10.20 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ % 71.20/10.20 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] % 71.20/10.20 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | % 71.20/10.20 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) % 71.20/10.20 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & % 71.20/10.20 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = % 71.20/10.20 0))) % 71.20/10.20 % 71.20/10.20 (cc3_ordinal1) % 71.43/10.20 ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_transitive(v0) = v1) | ~ $i(v0) | % 71.43/10.20 ? [v2: any] : ? [v3: any] : ? [v4: any] : (ordinal(v0) = v4 & % 71.43/10.20 epsilon_connected(v0) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 % 71.43/10.20 = 0 & v1 = 0)))) & ! [v0: $i] : ! [v1: any] : ( ~ (ordinal(v0) = v1) % 71.43/10.20 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 71.43/10.20 (epsilon_transitive(v0) = v3 & epsilon_connected(v0) = v4 & empty(v0) = v2 & % 71.43/10.20 ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) & ! [v0: $i] : ! [v1: any] % 71.43/10.20 : ( ~ (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 71.43/10.20 ? [v4: any] : (epsilon_transitive(v0) = v3 & ordinal(v0) = v4 & empty(v0) = % 71.43/10.20 v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) & ! [v0: $i] : ( ~ % 71.43/10.20 (empty(v0) = 0) | ~ $i(v0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 % 71.43/10.20 & epsilon_connected(v0) = 0)) % 71.43/10.20 % 71.43/10.20 (commutativity_k2_xboole_0) % 71.43/10.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 71.43/10.20 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 71.43/10.20 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 71.43/10.20 | (set_union2(v1, v0) = v2 & $i(v2))) % 71.43/10.20 % 71.43/10.20 (connectedness_r1_ordinal1) % 71.43/10.21 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (ordinal_subset(v1, % 71.43/10.21 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 71.43/10.21 [v5: any] : (ordinal_subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = % 71.43/10.21 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : % 71.43/10.21 ! [v2: int] : (v2 = 0 | ~ (ordinal_subset(v0, v1) = v2) | ~ $i(v1) | ~ % 71.43/10.21 $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : (ordinal_subset(v1, % 71.43/10.21 v0) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 71.43/10.21 0) | v5 = 0))) % 71.43/10.21 % 71.43/10.21 (d1_ordinal1) % 71.43/10.21 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 71.43/10.21 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0: % 71.43/10.21 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 71.43/10.21 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2))) % 71.43/10.21 % 71.43/10.21 (d1_tarski) % 71.43/10.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 71.43/10.21 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 71.43/10.21 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = % 71.43/10.21 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 71.43/10.21 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 71.43/10.21 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = % 71.43/10.21 0 | v3 = v1))) % 71.43/10.21 % 71.43/10.21 (d2_ordinal1) % 71.43/10.21 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v1, v0) = v2) % 71.43/10.21 | ~ (epsilon_transitive(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( % 71.43/10.21 ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 71.43/10.21 (epsilon_transitive(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ % 71.43/10.21 (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0 & $i(v2))) & ! [v0: $i] : % 71.43/10.21 ! [v1: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | ~ % 71.43/10.21 $i(v1) | ~ $i(v0) | subset(v1, v0) = 0) % 71.43/10.21 % 71.43/10.21 (d3_tarski) % 71.43/10.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 71.43/10.21 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 71.43/10.21 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 71.43/10.21 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 71.43/10.21 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 71.43/10.21 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 71.43/10.21 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 71.43/10.21 $i(v0) | in(v2, v1) = 0) % 71.43/10.21 % 71.43/10.21 (fc2_ordinal1) % 71.43/10.21 relation_empty_yielding(empty_set) = 0 & one_to_one(empty_set) = 0 & % 71.43/10.21 relation(empty_set) = 0 & epsilon_transitive(empty_set) = 0 & % 71.43/10.21 ordinal(empty_set) = 0 & epsilon_connected(empty_set) = 0 & % 71.43/10.21 function(empty_set) = 0 & empty(empty_set) = 0 & $i(empty_set) % 71.43/10.21 % 71.43/10.21 (fc3_ordinal1) % 71.43/10.22 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: any] : % 71.43/10.22 ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : % 71.43/10.22 (epsilon_transitive(v1) = v4 & ordinal(v1) = v6 & ordinal(v0) = v2 & % 71.43/10.22 epsilon_connected(v1) = v5 & empty(v1) = v3 & ( ~ (v2 = 0) | (v6 = 0 & v5 % 71.43/10.22 = 0 & v4 = 0 & ~ (v3 = 0))))) & ! [v0: $i] : ( ~ (ordinal(v0) = 0) | % 71.43/10.22 ~ $i(v0) | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & succ(v0) = v1 & % 71.43/10.22 epsilon_transitive(v1) = 0 & ordinal(v1) = 0 & epsilon_connected(v1) = 0 & % 71.43/10.22 empty(v1) = v2 & $i(v1))) % 71.43/10.22 % 71.43/10.22 (fc3_xboole_0) % 71.43/10.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 71.43/10.22 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v2) = v4 & % 71.43/10.22 empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 71.43/10.22 % 71.43/10.22 (rc3_ordinal1) % 71.43/10.22 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & epsilon_transitive(v0) = 0 & % 71.43/10.22 ordinal(v0) = 0 & epsilon_connected(v0) = 0 & empty(v0) = v1 & $i(v0)) % 71.43/10.22 % 71.43/10.22 (rc4_funct_1) % 71.43/10.22 ? [v0: $i] : (relation_empty_yielding(v0) = 0 & relation(v0) = 0 & % 71.43/10.22 function(v0) = 0 & $i(v0)) % 71.43/10.22 % 71.43/10.22 (redefinition_r1_ordinal1) % 71.43/10.22 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | ~ % 71.43/10.22 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 71.43/10.22 (ordinal_subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 % 71.43/10.22 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = % 71.43/10.22 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 71.43/10.22 (ordinal_subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? % 71.43/10.22 [v4: any] : ? [v5: any] : (subset(v0, v1) = v5 & ordinal(v1) = v4 & % 71.43/10.22 ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & % 71.43/10.22 ( ~ (v2 = 0) | v5 = 0))))) % 71.43/10.22 % 71.43/10.22 (reflexivity_r1_ordinal1) % 71.43/10.22 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (ordinal_subset(v0, % 71.43/10.22 v0) = v2) | ~ (ordinal(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 71.43/10.22 : ( ~ (v3 = 0) & ordinal(v0) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 71.43/10.22 (ordinal(v1) = 0) | ~ (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 71.43/10.22 ordinal_subset(v0, v0) = 0) % 71.43/10.22 % 71.43/10.22 (t10_ordinal1) % 71.43/10.22 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | in(v0, v1) = 0) % 71.43/10.22 % 71.43/10.22 (t2_subset) % 71.43/10.22 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ % 71.43/10.22 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 & % 71.43/10.22 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( % 71.43/10.22 ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 71.43/10.22 any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 71.43/10.22 % 71.43/10.22 (t33_ordinal1) % 71.43/10.22 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 71.43/10.22 (succ(v0) = v1 & ordinal_subset(v1, v2) = v4 & ordinal(v2) = 0 & ordinal(v0) = % 71.43/10.22 0 & in(v0, v2) = v3 & $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | % 71.43/10.22 (v3 = 0 & ~ (v4 = 0)))) % 71.43/10.22 % 71.43/10.22 (t4_subset) % 71.43/10.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 71.43/10.23 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = % 71.43/10.23 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 71.43/10.23 in(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] % 71.43/10.23 : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ % 71.43/10.23 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 71.43/10.23 powerset(v2) = v4 & element(v1, v4) = v5 & $i(v4))) & ! [v0: $i] : ! % 71.43/10.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = v3) | ~ % 71.43/10.23 (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 71.43/10.23 $i(v0) | element(v0, v2) = 0) % 71.43/10.23 % 71.43/10.23 (t6_boole) % 71.43/10.23 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 71.43/10.23 $i(v0)) % 71.43/10.23 % 71.43/10.23 (t8_xboole_1) % 71.43/10.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 71.43/10.23 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ~ $i(v2) | ~ % 71.43/10.23 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (subset(v2, v1) = v6 & % 71.43/10.23 subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 71.43/10.23 % 71.43/10.23 (function-axioms) % 71.43/10.23 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 71.43/10.23 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 71.43/10.23 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 71.43/10.23 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 71.43/10.23 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 71.43/10.23 $i] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~ (ordinal_subset(v3, % 71.43/10.23 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 71.43/10.23 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! % 71.43/10.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 71.43/10.23 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] % 71.43/10.23 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 71.43/10.23 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 71.43/10.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 71.43/10.23 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 71.43/10.23 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ % 71.43/10.23 (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 71.43/10.23 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: MultipleValueBool] % 71.43/10.23 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = % 71.43/10.23 v1) | ~ (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 71.43/10.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 71.43/10.23 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 71.43/10.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) = % 71.43/10.23 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 71.43/10.23 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ % 71.43/10.23 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 71.43/10.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) = % 71.43/10.23 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 71.43/10.23 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 71.43/10.23 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 71.43/10.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 71.43/10.23 (empty(v2) = v0)) % 71.43/10.23 % 71.43/10.23 Further assumptions not needed in the proof: % 71.43/10.23 -------------------------------------------- % 71.43/10.23 cc1_funct_1, cc1_relat_1, cc2_ordinal1, dt_k1_ordinal1, dt_k1_tarski, % 71.43/10.23 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_xboole_0, dt_m1_subset_1, % 71.43/10.23 existence_m1_subset_1, fc12_relat_1, fc1_ordinal1, fc1_xboole_0, fc2_relat_1, % 71.43/10.23 fc2_xboole_0, fc4_relat_1, idempotence_k2_xboole_0, rc1_funct_1, rc1_ordinal1, % 71.43/10.23 rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_ordinal1, rc2_relat_1, rc2_xboole_0, % 71.43/10.23 rc3_funct_1, rc3_relat_1, reflexivity_r1_tarski, t1_boole, t1_subset, t3_subset, % 71.43/10.23 t5_subset, t7_boole, t8_boole % 71.43/10.23 % 71.43/10.23 Those formulas are unsatisfiable: % 71.43/10.23 --------------------------------- % 71.43/10.23 % 71.43/10.23 Begin of proof % 71.43/10.24 | % 71.43/10.24 | ALPHA: (antisymmetry_r2_hidden) implies: % 71.43/10.24 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ % 71.43/10.24 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 71.43/10.24 | % 71.43/10.24 | ALPHA: (cc1_ordinal1) implies: % 71.43/10.24 | (2) ! [v0: $i] : ( ~ (ordinal(v0) = 0) | ~ $i(v0) | % 71.43/10.24 | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) % 71.43/10.24 | % 71.43/10.24 | ALPHA: (cc2_funct_1) implies: % 71.43/10.24 | (3) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 71.43/10.24 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & relation(v0) = v1 & % 71.43/10.24 | empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 71.43/10.24 | (4) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 71.43/10.24 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & % 71.43/10.24 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 71.43/10.24 | (5) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? % 71.43/10.24 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & % 71.43/10.24 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | % 71.43/10.24 | ~ (v2 = 0) | v1 = 0))) % 71.43/10.24 | % 71.43/10.24 | ALPHA: (cc3_ordinal1) implies: % 71.43/10.24 | (6) ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_connected(v0) = v1) | ~ % 71.43/10.24 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 71.43/10.24 | (epsilon_transitive(v0) = v3 & ordinal(v0) = v4 & empty(v0) = v2 & ( % 71.43/10.24 | ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) % 71.43/10.24 | (7) ! [v0: $i] : ! [v1: any] : ( ~ (ordinal(v0) = v1) | ~ $i(v0) | ? % 71.43/10.24 | [v2: any] : ? [v3: any] : ? [v4: any] : (epsilon_transitive(v0) = % 71.43/10.24 | v3 & epsilon_connected(v0) = v4 & empty(v0) = v2 & ( ~ (v2 = 0) | % 71.43/10.24 | (v4 = 0 & v3 = 0 & v1 = 0)))) % 71.66/10.24 | (8) ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_transitive(v0) = v1) | ~ % 71.66/10.24 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (ordinal(v0) = % 71.66/10.24 | v4 & epsilon_connected(v0) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | % 71.66/10.24 | (v4 = 0 & v3 = 0 & v1 = 0)))) % 71.66/10.24 | % 71.66/10.24 | ALPHA: (commutativity_k2_xboole_0) implies: % 71.66/10.24 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 71.66/10.24 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 71.66/10.25 | % 71.66/10.25 | ALPHA: (connectedness_r1_ordinal1) implies: % 71.66/10.25 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 71.66/10.25 | (ordinal_subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] % 71.66/10.25 | : ? [v4: any] : ? [v5: any] : (ordinal_subset(v1, v0) = v5 & % 71.66/10.25 | ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | % 71.66/10.25 | v5 = 0))) % 71.66/10.25 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 71.66/10.25 | (ordinal_subset(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] % 71.66/10.25 | : ? [v4: any] : ? [v5: any] : (ordinal_subset(v0, v1) = v5 & % 71.66/10.25 | ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | % 71.66/10.25 | v5 = 0))) % 71.66/10.25 | % 71.66/10.25 | ALPHA: (d1_ordinal1) implies: % 71.66/10.25 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: % 71.66/10.25 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & % 71.66/10.25 | $i(v1))) % 71.66/10.25 | % 71.66/10.25 | ALPHA: (d1_tarski) implies: % 71.66/10.25 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 71.66/10.25 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 71.66/10.25 | % 71.66/10.25 | ALPHA: (d2_ordinal1) implies: % 71.66/10.25 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~ % 71.66/10.25 | (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v1, v0) = 0) % 71.66/10.25 | % 71.66/10.25 | ALPHA: (d3_tarski) implies: % 71.66/10.25 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | % 71.66/10.25 | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) % 71.66/10.25 | = 0) % 71.66/10.25 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, % 71.66/10.25 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 71.66/10.25 | ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 71.66/10.25 | % 71.66/10.25 | ALPHA: (fc2_ordinal1) implies: % 71.66/10.25 | (17) ordinal(empty_set) = 0 % 71.66/10.25 | % 71.66/10.25 | ALPHA: (fc3_ordinal1) implies: % 71.66/10.25 | (18) ! [v0: $i] : ( ~ (ordinal(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 71.66/10.25 | [v2: int] : ( ~ (v2 = 0) & succ(v0) = v1 & epsilon_transitive(v1) = % 71.66/10.25 | 0 & ordinal(v1) = 0 & epsilon_connected(v1) = 0 & empty(v1) = v2 & % 71.66/10.25 | $i(v1))) % 71.66/10.25 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: % 71.66/10.25 | any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : % 71.66/10.25 | (epsilon_transitive(v1) = v4 & ordinal(v1) = v6 & ordinal(v0) = v2 & % 71.66/10.25 | epsilon_connected(v1) = v5 & empty(v1) = v3 & ( ~ (v2 = 0) | (v6 = % 71.66/10.25 | 0 & v5 = 0 & v4 = 0 & ~ (v3 = 0))))) % 71.66/10.25 | % 71.66/10.25 | ALPHA: (redefinition_r1_ordinal1) implies: % 71.66/10.26 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (ordinal_subset(v0, v1) % 71.66/10.26 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 71.66/10.26 | [v5: any] : (subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = % 71.66/10.26 | v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ % 71.66/10.26 | (v2 = 0) | v5 = 0))))) % 71.66/10.26 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | % 71.66/10.26 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 71.66/10.26 | (ordinal_subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & % 71.66/10.26 | ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = % 71.66/10.26 | 0) | v5 = 0))))) % 71.66/10.26 | % 71.66/10.26 | ALPHA: (reflexivity_r1_ordinal1) implies: % 71.66/10.26 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (ordinal(v1) = 0) | ~ (ordinal(v0) = % 71.66/10.26 | 0) | ~ $i(v1) | ~ $i(v0) | ordinal_subset(v0, v0) = 0) % 71.66/10.26 | % 71.66/10.26 | ALPHA: (t2_subset) implies: % 71.66/10.26 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = % 71.66/10.26 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 71.66/10.26 | (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) % 71.66/10.26 | % 71.66/10.26 | ALPHA: (t4_subset) implies: % 71.66/10.26 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 71.66/10.26 | (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) % 71.66/10.26 | | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 71.66/10.26 | powerset(v2) = v4 & element(v1, v4) = v5 & $i(v4))) % 71.66/10.26 | % 71.66/10.26 | ALPHA: (t6_boole) implies: % 71.66/10.26 | (25) $i(empty_set) % 71.66/10.26 | (26) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 71.66/10.26 | % 71.66/10.26 | ALPHA: (function-axioms) implies: % 71.66/10.26 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 71.66/10.26 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 71.66/10.26 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 71.66/10.26 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 71.66/10.26 | (29) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 71.66/10.26 | : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ % 71.66/10.26 | (epsilon_connected(v2) = v0)) % 71.66/10.26 | (30) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 71.66/10.26 | : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) % 71.66/10.26 | (31) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 71.66/10.26 | : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ % 71.66/10.26 | (epsilon_transitive(v2) = v0)) % 71.66/10.26 | (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 71.66/10.26 | : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 71.66/10.26 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 71.66/10.26 | v1) | ~ (succ(v2) = v0)) % 71.66/10.26 | (34) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 71.66/10.26 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 71.66/10.26 | v0)) % 71.66/10.26 | (35) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 71.66/10.26 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, % 71.66/10.26 | v2) = v0)) % 71.66/10.26 | % 71.66/10.26 | DELTA: instantiating (rc4_funct_1) with fresh symbol all_56_0 gives: % 71.66/10.27 | (36) relation_empty_yielding(all_56_0) = 0 & relation(all_56_0) = 0 & % 71.66/10.27 | function(all_56_0) = 0 & $i(all_56_0) % 71.66/10.27 | % 71.66/10.27 | ALPHA: (36) implies: % 71.66/10.27 | (37) $i(all_56_0) % 71.66/10.27 | (38) function(all_56_0) = 0 % 71.66/10.27 | (39) relation(all_56_0) = 0 % 71.66/10.27 | % 71.66/10.27 | DELTA: instantiating (rc3_ordinal1) with fresh symbols all_58_0, all_58_1 % 71.66/10.27 | gives: % 71.66/10.27 | (40) ~ (all_58_0 = 0) & epsilon_transitive(all_58_1) = 0 & % 71.66/10.27 | ordinal(all_58_1) = 0 & epsilon_connected(all_58_1) = 0 & % 71.66/10.27 | empty(all_58_1) = all_58_0 & $i(all_58_1) % 71.66/10.27 | % 71.66/10.27 | ALPHA: (40) implies: % 71.66/10.27 | (41) $i(all_58_1) % 71.66/10.27 | (42) ordinal(all_58_1) = 0 % 71.66/10.27 | % 71.66/10.27 | DELTA: instantiating (t33_ordinal1) with fresh symbols all_64_0, all_64_1, % 71.66/10.27 | all_64_2, all_64_3, all_64_4 gives: % 71.66/10.27 | (43) succ(all_64_4) = all_64_3 & ordinal_subset(all_64_3, all_64_2) = % 71.66/10.27 | all_64_0 & ordinal(all_64_2) = 0 & ordinal(all_64_4) = 0 & % 71.66/10.27 | in(all_64_4, all_64_2) = all_64_1 & $i(all_64_2) & $i(all_64_3) & % 71.66/10.27 | $i(all_64_4) & ((all_64_0 = 0 & ~ (all_64_1 = 0)) | (all_64_1 = 0 & % 71.66/10.27 | ~ (all_64_0 = 0))) % 71.66/10.27 | % 71.66/10.27 | ALPHA: (43) implies: % 71.66/10.27 | (44) $i(all_64_4) % 71.66/10.27 | (45) $i(all_64_3) % 71.66/10.27 | (46) $i(all_64_2) % 71.66/10.27 | (47) in(all_64_4, all_64_2) = all_64_1 % 71.66/10.27 | (48) ordinal(all_64_4) = 0 % 71.66/10.27 | (49) ordinal(all_64_2) = 0 % 71.66/10.27 | (50) ordinal_subset(all_64_3, all_64_2) = all_64_0 % 71.66/10.27 | (51) succ(all_64_4) = all_64_3 % 71.66/10.27 | (52) (all_64_0 = 0 & ~ (all_64_1 = 0)) | (all_64_1 = 0 & ~ (all_64_0 = % 71.66/10.27 | 0)) % 71.66/10.27 | % 71.66/10.27 | GROUND_INST: instantiating (3) with all_56_0, simplifying with (37), (38) % 71.66/10.27 | gives: % 71.66/10.27 | (53) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_56_0) = % 71.66/10.27 | v2 & relation(all_56_0) = v0 & empty(all_56_0) = v1 & ( ~ (v1 = 0) | % 71.66/10.27 | ~ (v0 = 0) | v2 = 0)) % 71.66/10.27 | % 71.66/10.27 | GROUND_INST: instantiating (18) with all_58_1, simplifying with (41), (42) % 71.66/10.27 | gives: % 71.66/10.27 | (54) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & succ(all_58_1) = v0 & % 71.66/10.27 | epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) % 71.66/10.27 | = 0 & empty(v0) = v1 & $i(v0)) % 71.66/10.27 | % 71.66/10.27 | GROUND_INST: instantiating (18) with all_64_4, simplifying with (44), (48) % 71.66/10.27 | gives: % 71.66/10.27 | (55) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & succ(all_64_4) = v0 & % 71.66/10.27 | epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) % 71.66/10.27 | = 0 & empty(v0) = v1 & $i(v0)) % 71.66/10.27 | % 71.66/10.27 | GROUND_INST: instantiating (2) with all_64_4, simplifying with (44), (48) % 71.66/10.27 | gives: % 71.66/10.27 | (56) epsilon_transitive(all_64_4) = 0 & epsilon_connected(all_64_4) = 0 % 71.66/10.27 | % 71.66/10.27 | ALPHA: (56) implies: % 71.66/10.27 | (57) epsilon_connected(all_64_4) = 0 % 71.66/10.27 | (58) epsilon_transitive(all_64_4) = 0 % 71.66/10.27 | % 71.66/10.27 | GROUND_INST: instantiating (7) with all_64_4, 0, simplifying with (44), (48) % 71.66/10.27 | gives: % 71.66/10.27 | (59) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 71.66/10.27 | (epsilon_transitive(all_64_4) = v1 & epsilon_connected(all_64_4) = v2 % 71.66/10.27 | & empty(all_64_4) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 71.66/10.27 | % 71.66/10.27 | GROUND_INST: instantiating (22) with all_64_4, all_64_2, simplifying with % 71.66/10.27 | (44), (46), (48), (49) gives: % 71.66/10.27 | (60) ordinal_subset(all_64_4, all_64_4) = 0 % 71.66/10.27 | % 71.66/10.27 | GROUND_INST: instantiating (22) with all_64_2, empty_set, simplifying with % 71.66/10.27 | (17), (25), (46), (49) gives: % 71.66/10.27 | (61) ordinal_subset(all_64_2, all_64_2) = 0 % 71.66/10.27 | % 71.66/10.27 | GROUND_INST: instantiating (2) with all_64_2, simplifying with (46), (49) % 71.66/10.27 | gives: % 71.66/10.27 | (62) epsilon_transitive(all_64_2) = 0 & epsilon_connected(all_64_2) = 0 % 71.66/10.27 | % 71.66/10.27 | ALPHA: (62) implies: % 71.66/10.27 | (63) epsilon_connected(all_64_2) = 0 % 71.66/10.27 | (64) epsilon_transitive(all_64_2) = 0 % 71.66/10.27 | % 71.66/10.27 | GROUND_INST: instantiating (7) with all_64_2, 0, simplifying with (46), (49) % 71.66/10.27 | gives: % 71.66/10.28 | (65) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 71.66/10.28 | (epsilon_transitive(all_64_2) = v1 & epsilon_connected(all_64_2) = v2 % 71.66/10.28 | & empty(all_64_2) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 71.66/10.28 | % 71.66/10.28 | GROUND_INST: instantiating (4) with all_56_0, simplifying with (37), (39) % 71.66/10.28 | gives: % 71.66/10.28 | (66) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_56_0) = % 71.66/10.28 | v2 & function(all_56_0) = v1 & empty(all_56_0) = v0 & ( ~ (v1 = 0) | % 71.66/10.28 | ~ (v0 = 0) | v2 = 0)) % 71.66/10.28 | % 71.66/10.28 | GROUND_INST: instantiating (11) with all_64_2, all_64_3, all_64_0, simplifying % 71.66/10.28 | with (45), (46), (50) gives: % 71.66/10.28 | (67) all_64_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 71.66/10.28 | (ordinal_subset(all_64_2, all_64_3) = v2 & ordinal(all_64_2) = v0 & % 71.66/10.28 | ordinal(all_64_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 71.66/10.28 | % 71.66/10.28 | GROUND_INST: instantiating (10) with all_64_3, all_64_2, all_64_0, simplifying % 71.66/10.28 | with (45), (46), (50) gives: % 71.66/10.28 | (68) all_64_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 71.66/10.28 | (ordinal_subset(all_64_2, all_64_3) = v2 & ordinal(all_64_2) = v1 & % 71.66/10.28 | ordinal(all_64_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 71.66/10.28 | % 71.66/10.28 | GROUND_INST: instantiating (20) with all_64_3, all_64_2, all_64_0, simplifying % 71.66/10.28 | with (45), (46), (50) gives: % 71.66/10.28 | (69) ? [v0: any] : ? [v1: any] : ? [v2: any] : (subset(all_64_3, % 71.66/10.28 | all_64_2) = v2 & ordinal(all_64_2) = v1 & ordinal(all_64_3) = v0 & % 71.66/10.28 | ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v2 = 0) | all_64_0 = 0) & ( ~ % 71.66/10.28 | (all_64_0 = 0) | v2 = 0)))) % 71.66/10.28 | % 71.66/10.28 | GROUND_INST: instantiating (t10_ordinal1) with all_64_4, all_64_3, simplifying % 71.66/10.28 | with (44), (51) gives: % 71.66/10.28 | (70) in(all_64_4, all_64_3) = 0 % 71.66/10.28 | % 71.66/10.28 | GROUND_INST: instantiating (19) with all_64_4, all_64_3, simplifying with % 71.66/10.28 | (44), (51) gives: % 71.66/10.28 | (71) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 71.66/10.28 | any] : (epsilon_transitive(all_64_3) = v2 & ordinal(all_64_3) = v4 & % 71.66/10.28 | ordinal(all_64_4) = v0 & epsilon_connected(all_64_3) = v3 & % 71.66/10.28 | empty(all_64_3) = v1 & ( ~ (v0 = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ % 71.66/10.28 | (v1 = 0)))) % 71.66/10.28 | % 71.66/10.28 | GROUND_INST: instantiating (12) with all_64_4, all_64_3, simplifying with % 71.66/10.28 | (44), (51) gives: % 71.66/10.28 | (72) ? [v0: $i] : (singleton(all_64_4) = v0 & set_union2(all_64_4, v0) = % 71.66/10.28 | all_64_3 & $i(v0) & $i(all_64_3)) % 71.66/10.28 | % 71.66/10.28 | DELTA: instantiating (72) with fresh symbol all_76_0 gives: % 71.66/10.28 | (73) singleton(all_64_4) = all_76_0 & set_union2(all_64_4, all_76_0) = % 71.66/10.28 | all_64_3 & $i(all_76_0) & $i(all_64_3) % 71.66/10.28 | % 71.66/10.28 | ALPHA: (73) implies: % 71.66/10.28 | (74) $i(all_76_0) % 71.66/10.28 | (75) set_union2(all_64_4, all_76_0) = all_64_3 % 71.66/10.28 | (76) singleton(all_64_4) = all_76_0 % 71.66/10.28 | % 71.66/10.28 | DELTA: instantiating (66) with fresh symbols all_86_0, all_86_1, all_86_2 % 71.66/10.28 | gives: % 71.66/10.28 | (77) one_to_one(all_56_0) = all_86_0 & function(all_56_0) = all_86_1 & % 71.66/10.28 | empty(all_56_0) = all_86_2 & ( ~ (all_86_1 = 0) | ~ (all_86_2 = 0) | % 71.66/10.28 | all_86_0 = 0) % 71.66/10.28 | % 71.66/10.28 | ALPHA: (77) implies: % 71.66/10.28 | (78) empty(all_56_0) = all_86_2 % 71.66/10.28 | (79) function(all_56_0) = all_86_1 % 71.66/10.28 | (80) one_to_one(all_56_0) = all_86_0 % 71.66/10.28 | % 71.66/10.28 | DELTA: instantiating (65) with fresh symbols all_106_0, all_106_1, all_106_2 % 71.66/10.28 | gives: % 71.66/10.28 | (81) epsilon_transitive(all_64_2) = all_106_1 & epsilon_connected(all_64_2) % 71.66/10.28 | = all_106_0 & empty(all_64_2) = all_106_2 & ( ~ (all_106_2 = 0) | % 71.66/10.28 | (all_106_0 = 0 & all_106_1 = 0)) % 71.66/10.28 | % 71.66/10.28 | ALPHA: (81) implies: % 71.66/10.28 | (82) epsilon_connected(all_64_2) = all_106_0 % 71.66/10.28 | (83) epsilon_transitive(all_64_2) = all_106_1 % 71.66/10.28 | % 71.66/10.28 | DELTA: instantiating (59) with fresh symbols all_110_0, all_110_1, all_110_2 % 71.66/10.28 | gives: % 71.66/10.28 | (84) epsilon_transitive(all_64_4) = all_110_1 & epsilon_connected(all_64_4) % 71.66/10.28 | = all_110_0 & empty(all_64_4) = all_110_2 & ( ~ (all_110_2 = 0) | % 71.66/10.28 | (all_110_0 = 0 & all_110_1 = 0)) % 71.66/10.28 | % 71.66/10.28 | ALPHA: (84) implies: % 71.66/10.28 | (85) epsilon_connected(all_64_4) = all_110_0 % 71.66/10.28 | (86) epsilon_transitive(all_64_4) = all_110_1 % 71.66/10.28 | % 71.66/10.28 | DELTA: instantiating (53) with fresh symbols all_112_0, all_112_1, all_112_2 % 71.66/10.28 | gives: % 71.66/10.28 | (87) one_to_one(all_56_0) = all_112_0 & relation(all_56_0) = all_112_2 & % 71.66/10.28 | empty(all_56_0) = all_112_1 & ( ~ (all_112_1 = 0) | ~ (all_112_2 = 0) % 71.66/10.28 | | all_112_0 = 0) % 71.66/10.28 | % 71.66/10.28 | ALPHA: (87) implies: % 71.66/10.28 | (88) empty(all_56_0) = all_112_1 % 71.66/10.28 | (89) one_to_one(all_56_0) = all_112_0 % 71.66/10.28 | (90) ~ (all_112_1 = 0) | ~ (all_112_2 = 0) | all_112_0 = 0 % 71.66/10.28 | % 71.66/10.28 | DELTA: instantiating (55) with fresh symbols all_122_0, all_122_1 gives: % 71.66/10.28 | (91) ~ (all_122_0 = 0) & succ(all_64_4) = all_122_1 & % 71.66/10.28 | epsilon_transitive(all_122_1) = 0 & ordinal(all_122_1) = 0 & % 71.66/10.28 | epsilon_connected(all_122_1) = 0 & empty(all_122_1) = all_122_0 & % 71.66/10.28 | $i(all_122_1) % 71.66/10.28 | % 71.66/10.28 | ALPHA: (91) implies: % 71.66/10.28 | (92) $i(all_122_1) % 71.66/10.28 | (93) succ(all_64_4) = all_122_1 % 71.66/10.28 | % 71.66/10.28 | DELTA: instantiating (54) with fresh symbols all_126_0, all_126_1 gives: % 71.66/10.29 | (94) ~ (all_126_0 = 0) & succ(all_58_1) = all_126_1 & % 71.66/10.29 | epsilon_transitive(all_126_1) = 0 & ordinal(all_126_1) = 0 & % 71.66/10.29 | epsilon_connected(all_126_1) = 0 & empty(all_126_1) = all_126_0 & % 71.66/10.29 | $i(all_126_1) % 71.66/10.29 | % 71.66/10.29 | ALPHA: (94) implies: % 71.66/10.29 | (95) $i(all_126_1) % 71.66/10.29 | (96) ordinal(all_126_1) = 0 % 71.66/10.29 | % 71.66/10.29 | DELTA: instantiating (69) with fresh symbols all_128_0, all_128_1, all_128_2 % 71.66/10.29 | gives: % 71.66/10.29 | (97) subset(all_64_3, all_64_2) = all_128_0 & ordinal(all_64_2) = all_128_1 % 71.66/10.29 | & ordinal(all_64_3) = all_128_2 & ( ~ (all_128_1 = 0) | ~ (all_128_2 % 71.66/10.29 | = 0) | (( ~ (all_128_0 = 0) | all_64_0 = 0) & ( ~ (all_64_0 = 0) | % 71.66/10.29 | all_128_0 = 0))) % 71.66/10.29 | % 71.66/10.29 | ALPHA: (97) implies: % 71.66/10.29 | (98) ordinal(all_64_3) = all_128_2 % 71.66/10.29 | (99) ordinal(all_64_2) = all_128_1 % 71.66/10.29 | (100) subset(all_64_3, all_64_2) = all_128_0 % 71.66/10.29 | (101) ~ (all_128_1 = 0) | ~ (all_128_2 = 0) | (( ~ (all_128_0 = 0) | % 71.66/10.29 | all_64_0 = 0) & ( ~ (all_64_0 = 0) | all_128_0 = 0)) % 71.66/10.29 | % 71.66/10.29 | DELTA: instantiating (71) with fresh symbols all_130_0, all_130_1, all_130_2, % 71.66/10.29 | all_130_3, all_130_4 gives: % 71.66/10.29 | (102) epsilon_transitive(all_64_3) = all_130_2 & ordinal(all_64_3) = % 71.66/10.29 | all_130_0 & ordinal(all_64_4) = all_130_4 & % 71.66/10.29 | epsilon_connected(all_64_3) = all_130_1 & empty(all_64_3) = all_130_3 % 71.66/10.29 | & ( ~ (all_130_4 = 0) | (all_130_0 = 0 & all_130_1 = 0 & all_130_2 = % 71.66/10.29 | 0 & ~ (all_130_3 = 0))) % 71.66/10.29 | % 71.66/10.29 | ALPHA: (102) implies: % 71.66/10.29 | (103) ordinal(all_64_4) = all_130_4 % 71.66/10.29 | (104) ordinal(all_64_3) = all_130_0 % 71.66/10.29 | (105) epsilon_transitive(all_64_3) = all_130_2 % 71.66/10.29 | (106) ~ (all_130_4 = 0) | (all_130_0 = 0 & all_130_1 = 0 & all_130_2 = 0 & % 71.66/10.29 | ~ (all_130_3 = 0)) % 71.66/10.29 | % 71.66/10.29 | GROUND_INST: instantiating (27) with all_86_2, all_112_1, all_56_0, % 71.66/10.29 | simplifying with (78), (88) gives: % 71.66/10.29 | (107) all_112_1 = all_86_2 % 71.66/10.29 | % 71.66/10.29 | GROUND_INST: instantiating (28) with 0, all_86_1, all_56_0, simplifying with % 71.66/10.29 | (38), (79) gives: % 71.66/10.29 | (108) all_86_1 = 0 % 71.66/10.29 | % 71.66/10.29 | GROUND_INST: instantiating (29) with 0, all_110_0, all_64_4, simplifying with % 71.66/10.29 | (57), (85) gives: % 71.66/10.29 | (109) all_110_0 = 0 % 71.66/10.29 | % 71.66/10.29 | GROUND_INST: instantiating (29) with 0, all_106_0, all_64_2, simplifying with % 71.66/10.29 | (63), (82) gives: % 71.66/10.29 | (110) all_106_0 = 0 % 71.66/10.29 | % 71.66/10.29 | GROUND_INST: instantiating (30) with 0, all_130_4, all_64_4, simplifying with % 71.66/10.29 | (48), (103) gives: % 71.66/10.29 | (111) all_130_4 = 0 % 71.66/10.29 | % 71.66/10.29 | GROUND_INST: instantiating (30) with all_128_2, all_130_0, all_64_3, % 71.66/10.29 | simplifying with (98), (104) gives: % 71.66/10.29 | (112) all_130_0 = all_128_2 % 71.66/10.29 | % 71.66/10.29 | GROUND_INST: instantiating (30) with 0, all_128_1, all_64_2, simplifying with % 71.66/10.29 | (49), (99) gives: % 71.66/10.29 | (113) all_128_1 = 0 % 71.66/10.29 | % 71.66/10.29 | GROUND_INST: instantiating (31) with 0, all_110_1, all_64_4, simplifying with % 71.66/10.29 | (58), (86) gives: % 71.66/10.29 | (114) all_110_1 = 0 % 71.66/10.29 | % 71.66/10.29 | GROUND_INST: instantiating (31) with 0, all_106_1, all_64_2, simplifying with % 71.66/10.29 | (64), (83) gives: % 71.66/10.29 | (115) all_106_1 = 0 % 71.66/10.29 | % 71.66/10.29 | GROUND_INST: instantiating (32) with all_86_0, all_112_0, all_56_0, % 71.66/10.29 | simplifying with (80), (89) gives: % 71.66/10.29 | (116) all_112_0 = all_86_0 % 71.66/10.29 | % 71.66/10.29 | GROUND_INST: instantiating (33) with all_64_3, all_122_1, all_64_4, % 71.66/10.29 | simplifying with (51), (93) gives: % 71.66/10.29 | (117) all_122_1 = all_64_3 % 71.66/10.29 | % 71.66/10.29 | BETA: splitting (106) gives: % 71.66/10.29 | % 71.66/10.29 | Case 1: % 71.66/10.29 | | % 71.66/10.29 | | (118) ~ (all_130_4 = 0) % 71.66/10.29 | | % 71.66/10.29 | | REDUCE: (111), (118) imply: % 71.66/10.29 | | (119) $false % 71.66/10.29 | | % 71.66/10.29 | | CLOSE: (119) is inconsistent. % 71.66/10.29 | | % 71.66/10.29 | Case 2: % 71.66/10.29 | | % 71.66/10.29 | | (120) all_130_0 = 0 & all_130_1 = 0 & all_130_2 = 0 & ~ (all_130_3 = 0) % 71.66/10.29 | | % 71.66/10.29 | | ALPHA: (120) implies: % 71.66/10.29 | | (121) all_130_2 = 0 % 71.66/10.29 | | (122) all_130_0 = 0 % 71.66/10.29 | | % 71.66/10.29 | | COMBINE_EQS: (112), (122) imply: % 71.66/10.29 | | (123) all_128_2 = 0 % 71.66/10.29 | | % 71.66/10.29 | | REDUCE: (105), (121) imply: % 71.66/10.29 | | (124) epsilon_transitive(all_64_3) = 0 % 71.66/10.29 | | % 71.66/10.29 | | REDUCE: (98), (123) imply: % 71.66/10.29 | | (125) ordinal(all_64_3) = 0 % 71.66/10.29 | | % 71.66/10.29 | | GROUND_INST: instantiating (1) with all_64_3, all_64_4, simplifying with % 71.66/10.29 | | (44), (45), (70) gives: % 71.66/10.29 | | (126) ? [v0: int] : ( ~ (v0 = 0) & in(all_64_3, all_64_4) = v0) % 71.66/10.29 | | % 71.66/10.29 | | GROUND_INST: instantiating (6) with all_64_4, 0, simplifying with (44), (57) % 71.66/10.29 | | gives: % 71.66/10.29 | | (127) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 71.66/10.29 | | (epsilon_transitive(all_64_4) = v1 & ordinal(all_64_4) = v2 & % 71.66/10.29 | | empty(all_64_4) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 71.66/10.29 | | % 71.66/10.29 | | GROUND_INST: instantiating (6) with all_64_2, 0, simplifying with (46), (63) % 71.66/10.29 | | gives: % 71.66/10.29 | | (128) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 71.66/10.29 | | (epsilon_transitive(all_64_2) = v1 & ordinal(all_64_2) = v2 & % 71.66/10.29 | | empty(all_64_2) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 71.66/10.29 | | % 71.66/10.29 | | GROUND_INST: instantiating (18) with all_64_3, simplifying with (45), (125) % 71.66/10.29 | | gives: % 71.66/10.30 | | (129) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & succ(all_64_3) = v0 & % 71.66/10.30 | | epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & % 71.66/10.30 | | epsilon_connected(v0) = 0 & empty(v0) = v1 & $i(v0)) % 71.66/10.30 | | % 71.66/10.30 | | GROUND_INST: instantiating (22) with all_64_3, all_126_1, simplifying with % 71.66/10.30 | | (45), (95), (96), (125) gives: % 71.66/10.30 | | (130) ordinal_subset(all_64_3, all_64_3) = 0 % 71.66/10.30 | | % 71.66/10.30 | | GROUND_INST: instantiating (8) with all_64_4, 0, simplifying with (44), (58) % 71.66/10.30 | | gives: % 71.66/10.30 | | (131) ? [v0: any] : ? [v1: any] : ? [v2: any] : (ordinal(all_64_4) = % 71.66/10.30 | | v2 & epsilon_connected(all_64_4) = v1 & empty(all_64_4) = v0 & ( % 71.66/10.30 | | ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 71.66/10.30 | | % 71.66/10.30 | | GROUND_INST: instantiating (14) with all_64_3, all_64_4, simplifying with % 71.66/10.30 | | (44), (45), (70), (124) gives: % 71.66/10.30 | | (132) subset(all_64_4, all_64_3) = 0 % 71.66/10.30 | | % 71.66/10.30 | | GROUND_INST: instantiating (8) with all_64_2, 0, simplifying with (46), (64) % 71.66/10.30 | | gives: % 71.66/10.30 | | (133) ? [v0: any] : ? [v1: any] : ? [v2: any] : (ordinal(all_64_2) = % 71.66/10.30 | | v2 & epsilon_connected(all_64_2) = v1 & empty(all_64_2) = v0 & ( % 71.66/10.30 | | ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 71.66/10.30 | | % 71.66/10.30 | | GROUND_INST: instantiating (5) with all_56_0, all_86_0, simplifying with % 71.66/10.30 | | (37), (80) gives: % 71.66/10.30 | | (134) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_56_0) = % 71.66/10.30 | | v0 & function(all_56_0) = v2 & empty(all_56_0) = v1 & ( ~ (v2 = % 71.66/10.30 | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | all_86_0 = 0)) % 71.66/10.30 | | % 71.66/10.30 | | GROUND_INST: instantiating (9) with all_76_0, all_64_4, all_64_3, % 71.66/10.30 | | simplifying with (44), (74), (75) gives: % 71.66/10.30 | | (135) set_union2(all_76_0, all_64_4) = all_64_3 & $i(all_64_3) % 71.66/10.30 | | % 71.66/10.30 | | ALPHA: (135) implies: % 71.66/10.30 | | (136) set_union2(all_76_0, all_64_4) = all_64_3 % 71.66/10.30 | | % 71.66/10.30 | | GROUND_INST: instantiating (20) with all_64_4, all_64_4, 0, simplifying with % 71.66/10.30 | | (44), (60) gives: % 71.66/10.30 | | (137) ? [v0: any] : ? [v1: any] : ? [v2: any] : (subset(all_64_4, % 71.66/10.30 | | all_64_4) = v2 & ordinal(all_64_4) = v1 & ordinal(all_64_4) = % 71.66/10.30 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 71.66/10.30 | | % 71.66/10.30 | | GROUND_INST: instantiating (20) with all_64_2, all_64_2, 0, simplifying with % 71.66/10.30 | | (46), (61) gives: % 71.66/10.30 | | (138) ? [v0: any] : ? [v1: any] : ? [v2: any] : (subset(all_64_2, % 71.66/10.30 | | all_64_2) = v2 & ordinal(all_64_2) = v1 & ordinal(all_64_2) = % 71.66/10.30 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 71.66/10.30 | | % 71.66/10.30 | | GROUND_INST: instantiating (t8_xboole_1) with all_64_4, all_64_2, all_76_0, % 71.66/10.30 | | all_64_3, all_128_0, simplifying with (44), (46), (74), (75), % 71.66/10.30 | | (100) gives: % 71.66/10.30 | | (139) all_128_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_76_0, % 71.66/10.30 | | all_64_2) = v1 & subset(all_64_4, all_64_2) = v0 & ( ~ (v1 = 0) % 71.66/10.30 | | | ~ (v0 = 0))) % 71.66/10.30 | | % 71.66/10.30 | | GROUND_INST: instantiating (21) with all_64_3, all_64_2, all_128_0, % 71.66/10.30 | | simplifying with (45), (46), (100) gives: % 71.66/10.30 | | (140) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 71.66/10.30 | | (ordinal_subset(all_64_3, all_64_2) = v2 & ordinal(all_64_2) = v1 & % 71.66/10.30 | | ordinal(all_64_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v2 = % 71.66/10.30 | | 0) | all_128_0 = 0) & ( ~ (all_128_0 = 0) | v2 = 0)))) % 71.66/10.30 | | % 71.66/10.30 | | DELTA: instantiating (126) with fresh symbol all_150_0 gives: % 71.66/10.30 | | (141) ~ (all_150_0 = 0) & in(all_64_3, all_64_4) = all_150_0 % 71.66/10.30 | | % 71.66/10.30 | | ALPHA: (141) implies: % 71.66/10.30 | | (142) ~ (all_150_0 = 0) % 71.66/10.30 | | (143) in(all_64_3, all_64_4) = all_150_0 % 71.66/10.30 | | % 71.66/10.30 | | DELTA: instantiating (128) with fresh symbols all_166_0, all_166_1, % 71.66/10.30 | | all_166_2 gives: % 71.66/10.30 | | (144) epsilon_transitive(all_64_2) = all_166_1 & ordinal(all_64_2) = % 71.66/10.30 | | all_166_0 & empty(all_64_2) = all_166_2 & ( ~ (all_166_2 = 0) | % 71.66/10.30 | | (all_166_0 = 0 & all_166_1 = 0)) % 71.66/10.30 | | % 71.66/10.30 | | ALPHA: (144) implies: % 71.66/10.30 | | (145) ordinal(all_64_2) = all_166_0 % 71.66/10.30 | | (146) epsilon_transitive(all_64_2) = all_166_1 % 71.66/10.30 | | % 71.66/10.30 | | DELTA: instantiating (127) with fresh symbols all_168_0, all_168_1, % 71.66/10.30 | | all_168_2 gives: % 71.66/10.30 | | (147) epsilon_transitive(all_64_4) = all_168_1 & ordinal(all_64_4) = % 71.66/10.30 | | all_168_0 & empty(all_64_4) = all_168_2 & ( ~ (all_168_2 = 0) | % 71.66/10.30 | | (all_168_0 = 0 & all_168_1 = 0)) % 71.66/10.30 | | % 71.66/10.30 | | ALPHA: (147) implies: % 71.66/10.30 | | (148) ordinal(all_64_4) = all_168_0 % 71.66/10.30 | | % 71.66/10.30 | | DELTA: instantiating (133) with fresh symbols all_172_0, all_172_1, % 71.66/10.30 | | all_172_2 gives: % 71.66/10.30 | | (149) ordinal(all_64_2) = all_172_0 & epsilon_connected(all_64_2) = % 71.66/10.30 | | all_172_1 & empty(all_64_2) = all_172_2 & ( ~ (all_172_2 = 0) | % 71.66/10.30 | | (all_172_0 = 0 & all_172_1 = 0)) % 71.66/10.30 | | % 71.66/10.30 | | ALPHA: (149) implies: % 71.66/10.30 | | (150) ordinal(all_64_2) = all_172_0 % 71.66/10.30 | | % 71.66/10.30 | | DELTA: instantiating (138) with fresh symbols all_174_0, all_174_1, % 71.66/10.30 | | all_174_2 gives: % 71.66/10.30 | | (151) subset(all_64_2, all_64_2) = all_174_0 & ordinal(all_64_2) = % 71.66/10.30 | | all_174_1 & ordinal(all_64_2) = all_174_2 & ( ~ (all_174_1 = 0) | % 71.66/10.30 | | ~ (all_174_2 = 0) | all_174_0 = 0) % 71.66/10.30 | | % 71.66/10.30 | | ALPHA: (151) implies: % 71.66/10.30 | | (152) ordinal(all_64_2) = all_174_2 % 71.66/10.30 | | (153) ordinal(all_64_2) = all_174_1 % 71.66/10.30 | | % 71.66/10.30 | | DELTA: instantiating (137) with fresh symbols all_176_0, all_176_1, % 71.66/10.30 | | all_176_2 gives: % 71.66/10.30 | | (154) subset(all_64_4, all_64_4) = all_176_0 & ordinal(all_64_4) = % 71.66/10.30 | | all_176_1 & ordinal(all_64_4) = all_176_2 & ( ~ (all_176_1 = 0) | % 71.66/10.30 | | ~ (all_176_2 = 0) | all_176_0 = 0) % 71.66/10.30 | | % 71.66/10.30 | | ALPHA: (154) implies: % 71.66/10.30 | | (155) ordinal(all_64_4) = all_176_2 % 71.66/10.30 | | (156) ordinal(all_64_4) = all_176_1 % 71.66/10.30 | | (157) ~ (all_176_1 = 0) | ~ (all_176_2 = 0) | all_176_0 = 0 % 71.66/10.30 | | % 71.66/10.30 | | DELTA: instantiating (131) with fresh symbols all_182_0, all_182_1, % 71.66/10.30 | | all_182_2 gives: % 71.66/10.30 | | (158) ordinal(all_64_4) = all_182_0 & epsilon_connected(all_64_4) = % 71.66/10.30 | | all_182_1 & empty(all_64_4) = all_182_2 & ( ~ (all_182_2 = 0) | % 71.66/10.30 | | (all_182_0 = 0 & all_182_1 = 0)) % 71.66/10.30 | | % 71.66/10.30 | | ALPHA: (158) implies: % 71.66/10.30 | | (159) ordinal(all_64_4) = all_182_0 % 71.66/10.30 | | % 71.66/10.30 | | DELTA: instantiating (134) with fresh symbols all_186_0, all_186_1, % 71.66/10.30 | | all_186_2 gives: % 71.66/10.30 | | (160) relation(all_56_0) = all_186_2 & function(all_56_0) = all_186_0 & % 71.66/10.30 | | empty(all_56_0) = all_186_1 & ( ~ (all_186_0 = 0) | ~ (all_186_1 = % 71.66/10.30 | | 0) | ~ (all_186_2 = 0) | all_86_0 = 0) % 71.66/10.30 | | % 71.66/10.30 | | ALPHA: (160) implies: % 71.66/10.30 | | (161) empty(all_56_0) = all_186_1 % 71.66/10.30 | | (162) function(all_56_0) = all_186_0 % 71.66/10.30 | | (163) ~ (all_186_0 = 0) | ~ (all_186_1 = 0) | ~ (all_186_2 = 0) | % 71.66/10.30 | | all_86_0 = 0 % 71.66/10.30 | | % 71.66/10.30 | | DELTA: instantiating (129) with fresh symbols all_196_0, all_196_1 gives: % 71.66/10.31 | | (164) ~ (all_196_0 = 0) & succ(all_64_3) = all_196_1 & % 71.66/10.31 | | epsilon_transitive(all_196_1) = 0 & ordinal(all_196_1) = 0 & % 71.66/10.31 | | epsilon_connected(all_196_1) = 0 & empty(all_196_1) = all_196_0 & % 71.66/10.31 | | $i(all_196_1) % 71.66/10.31 | | % 71.66/10.31 | | ALPHA: (164) implies: % 71.66/10.31 | | (165) succ(all_64_3) = all_196_1 % 71.66/10.31 | | % 71.66/10.31 | | DELTA: instantiating (140) with fresh symbols all_202_0, all_202_1, % 71.66/10.31 | | all_202_2 gives: % 71.66/10.31 | | (166) ordinal_subset(all_64_3, all_64_2) = all_202_0 & ordinal(all_64_2) % 71.66/10.31 | | = all_202_1 & ordinal(all_64_3) = all_202_2 & ( ~ (all_202_1 = 0) | % 71.66/10.31 | | ~ (all_202_2 = 0) | (( ~ (all_202_0 = 0) | all_128_0 = 0) & ( ~ % 71.66/10.31 | | (all_128_0 = 0) | all_202_0 = 0))) % 71.66/10.31 | | % 71.66/10.31 | | ALPHA: (166) implies: % 71.66/10.31 | | (167) ordinal(all_64_3) = all_202_2 % 71.66/10.31 | | (168) ordinal(all_64_2) = all_202_1 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (27) with all_86_2, all_186_1, all_56_0, % 71.66/10.31 | | simplifying with (78), (161) gives: % 71.66/10.31 | | (169) all_186_1 = all_86_2 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (28) with 0, all_186_0, all_56_0, simplifying % 71.66/10.31 | | with (38), (162) gives: % 71.66/10.31 | | (170) all_186_0 = 0 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (30) with 0, all_176_2, all_64_4, simplifying % 71.66/10.31 | | with (48), (155) gives: % 71.66/10.31 | | (171) all_176_2 = 0 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (30) with all_176_1, all_182_0, all_64_4, % 71.66/10.31 | | simplifying with (156), (159) gives: % 71.66/10.31 | | (172) all_182_0 = all_176_1 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (30) with all_176_2, all_182_0, all_64_4, % 71.66/10.31 | | simplifying with (155), (159) gives: % 71.66/10.31 | | (173) all_182_0 = all_176_2 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (30) with all_168_0, all_182_0, all_64_4, % 71.66/10.31 | | simplifying with (148), (159) gives: % 71.66/10.31 | | (174) all_182_0 = all_168_0 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (30) with 0, all_202_2, all_64_3, simplifying % 71.66/10.31 | | with (125), (167) gives: % 71.66/10.31 | | (175) all_202_2 = 0 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (30) with all_172_0, all_174_2, all_64_2, % 71.66/10.31 | | simplifying with (150), (152) gives: % 71.66/10.31 | | (176) all_174_2 = all_172_0 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (30) with all_166_0, all_174_2, all_64_2, % 71.66/10.31 | | simplifying with (145), (152) gives: % 71.66/10.31 | | (177) all_174_2 = all_166_0 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (30) with all_172_0, all_174_1, all_64_2, % 71.66/10.31 | | simplifying with (150), (153) gives: % 71.66/10.31 | | (178) all_174_1 = all_172_0 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (30) with 0, all_202_1, all_64_2, simplifying % 71.66/10.31 | | with (49), (168) gives: % 71.66/10.31 | | (179) all_202_1 = 0 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (30) with all_174_1, all_202_1, all_64_2, % 71.66/10.31 | | simplifying with (153), (168) gives: % 71.66/10.31 | | (180) all_202_1 = all_174_1 % 71.66/10.31 | | % 71.66/10.31 | | GROUND_INST: instantiating (31) with 0, all_166_1, all_64_2, simplifying % 71.66/10.31 | | with (64), (146) gives: % 71.66/10.31 | | (181) all_166_1 = 0 % 71.66/10.31 | | % 71.66/10.31 | | COMBINE_EQS: (179), (180) imply: % 71.66/10.31 | | (182) all_174_1 = 0 % 71.66/10.31 | | % 71.66/10.31 | | SIMP: (182) implies: % 71.66/10.31 | | (183) all_174_1 = 0 % 71.66/10.31 | | % 71.66/10.31 | | COMBINE_EQS: (172), (174) imply: % 71.66/10.31 | | (184) all_176_1 = all_168_0 % 71.66/10.31 | | % 71.66/10.31 | | COMBINE_EQS: (172), (173) imply: % 71.66/10.31 | | (185) all_176_1 = all_176_2 % 71.66/10.31 | | % 71.66/10.31 | | COMBINE_EQS: (184), (185) imply: % 71.66/10.31 | | (186) all_176_2 = all_168_0 % 71.66/10.31 | | % 71.66/10.31 | | SIMP: (186) implies: % 71.66/10.31 | | (187) all_176_2 = all_168_0 % 71.66/10.31 | | % 71.66/10.31 | | COMBINE_EQS: (171), (187) imply: % 71.66/10.31 | | (188) all_168_0 = 0 % 71.66/10.31 | | % 71.66/10.31 | | SIMP: (188) implies: % 71.66/10.31 | | (189) all_168_0 = 0 % 71.66/10.31 | | % 71.66/10.31 | | COMBINE_EQS: (178), (183) imply: % 71.66/10.31 | | (190) all_172_0 = 0 % 71.66/10.31 | | % 71.66/10.31 | | SIMP: (190) implies: % 71.66/10.31 | | (191) all_172_0 = 0 % 71.66/10.31 | | % 71.66/10.31 | | COMBINE_EQS: (176), (177) imply: % 71.66/10.31 | | (192) all_172_0 = all_166_0 % 71.66/10.31 | | % 71.66/10.31 | | SIMP: (192) implies: % 71.66/10.31 | | (193) all_172_0 = all_166_0 % 71.66/10.31 | | % 71.66/10.31 | | COMBINE_EQS: (191), (193) imply: % 71.66/10.31 | | (194) all_166_0 = 0 % 71.66/10.31 | | % 71.66/10.31 | | SIMP: (194) implies: % 71.66/10.31 | | (195) all_166_0 = 0 % 71.66/10.31 | | % 71.66/10.31 | | COMBINE_EQS: (184), (189) imply: % 71.66/10.31 | | (196) all_176_1 = 0 % 71.66/10.31 | | % 71.66/10.31 | | BETA: splitting (157) gives: % 71.66/10.31 | | % 71.66/10.31 | | Case 1: % 71.66/10.31 | | | % 71.66/10.31 | | | (197) ~ (all_176_1 = 0) % 71.66/10.31 | | | % 71.66/10.31 | | | REDUCE: (196), (197) imply: % 71.66/10.31 | | | (198) $false % 71.66/10.31 | | | % 71.66/10.31 | | | CLOSE: (198) is inconsistent. % 71.66/10.31 | | | % 71.66/10.31 | | Case 2: % 71.66/10.31 | | | % 71.66/10.31 | | | (199) ~ (all_176_2 = 0) | all_176_0 = 0 % 71.66/10.31 | | | % 71.66/10.31 | | | BETA: splitting (199) gives: % 71.66/10.31 | | | % 71.66/10.31 | | | Case 1: % 71.66/10.31 | | | | % 71.66/10.31 | | | | (200) ~ (all_176_2 = 0) % 71.66/10.31 | | | | % 71.66/10.31 | | | | REDUCE: (171), (200) imply: % 71.66/10.31 | | | | (201) $false % 71.66/10.31 | | | | % 71.66/10.31 | | | | CLOSE: (201) is inconsistent. % 71.66/10.31 | | | | % 71.66/10.31 | | | Case 2: % 71.66/10.31 | | | | % 71.66/10.31 | | | | % 71.66/10.31 | | | | GROUND_INST: instantiating (23) with all_64_3, all_64_4, all_150_0, % 71.66/10.31 | | | | simplifying with (44), (45), (143) gives: % 71.66/10.31 | | | | (202) all_150_0 = 0 | ? [v0: any] : ? [v1: any] : % 71.66/10.31 | | | | (element(all_64_3, all_64_4) = v0 & empty(all_64_4) = v1 & ( ~ % 71.66/10.31 | | | | (v0 = 0) | v1 = 0)) % 71.66/10.31 | | | | % 71.66/10.31 | | | | GROUND_INST: instantiating (t8_xboole_1) with all_76_0, all_64_2, % 71.66/10.31 | | | | all_64_4, all_64_3, all_128_0, simplifying with (44), (46), % 71.66/10.31 | | | | (74), (100), (136) gives: % 71.66/10.31 | | | | (203) all_128_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_76_0, % 71.66/10.31 | | | | all_64_2) = v0 & subset(all_64_4, all_64_2) = v1 & ( ~ (v1 % 71.66/10.31 | | | | = 0) | ~ (v0 = 0))) % 71.66/10.31 | | | | % 71.66/10.31 | | | | GROUND_INST: instantiating (fc3_xboole_0) with all_64_4, all_76_0, % 71.66/10.31 | | | | all_64_3, simplifying with (44), (74), (136) gives: % 71.66/10.31 | | | | (204) ? [v0: any] : ? [v1: any] : (empty(all_64_3) = v1 & % 71.66/10.31 | | | | empty(all_64_4) = v0 & ( ~ (v1 = 0) | v0 = 0)) % 71.66/10.31 | | | | % 71.66/10.31 | | | | GROUND_INST: instantiating (20) with all_64_3, all_64_3, 0, simplifying % 71.66/10.31 | | | | with (45), (130) gives: % 71.66/10.31 | | | | (205) ? [v0: any] : ? [v1: any] : ? [v2: any] : (subset(all_64_3, % 71.66/10.31 | | | | all_64_3) = v2 & ordinal(all_64_3) = v1 & ordinal(all_64_3) % 71.66/10.31 | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 71.66/10.31 | | | | % 71.66/10.31 | | | | GROUND_INST: instantiating (t10_ordinal1) with all_64_3, all_196_1, % 71.66/10.31 | | | | simplifying with (45), (165) gives: % 71.66/10.31 | | | | (206) in(all_64_3, all_196_1) = 0 % 71.66/10.31 | | | | % 71.66/10.31 | | | | GROUND_INST: instantiating (12) with all_64_3, all_196_1, simplifying % 71.66/10.31 | | | | with (45), (165) gives: % 71.66/10.31 | | | | (207) ? [v0: $i] : (singleton(all_64_3) = v0 & set_union2(all_64_3, % 71.66/10.31 | | | | v0) = all_196_1 & $i(v0) & $i(all_196_1)) % 71.66/10.31 | | | | % 71.66/10.31 | | | | GROUND_INST: instantiating (21) with all_64_4, all_64_3, 0, simplifying % 71.66/10.31 | | | | with (44), (45), (132) gives: % 71.66/10.31 | | | | (208) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 71.66/10.31 | | | | (ordinal_subset(all_64_4, all_64_3) = v2 & ordinal(all_64_3) = % 71.66/10.31 | | | | v1 & ordinal(all_64_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 % 71.66/10.31 | | | | = 0)) % 71.66/10.31 | | | | % 71.66/10.31 | | | | DELTA: instantiating (204) with fresh symbols all_290_0, all_290_1 % 71.66/10.31 | | | | gives: % 71.66/10.31 | | | | (209) empty(all_64_3) = all_290_0 & empty(all_64_4) = all_290_1 & ( ~ % 71.66/10.31 | | | | (all_290_0 = 0) | all_290_1 = 0) % 71.66/10.31 | | | | % 71.66/10.31 | | | | ALPHA: (209) implies: % 71.66/10.32 | | | | (210) empty(all_64_4) = all_290_1 % 71.66/10.32 | | | | % 71.66/10.32 | | | | DELTA: instantiating (207) with fresh symbol all_302_0 gives: % 71.66/10.32 | | | | (211) singleton(all_64_3) = all_302_0 & set_union2(all_64_3, % 71.66/10.32 | | | | all_302_0) = all_196_1 & $i(all_302_0) & $i(all_196_1) % 71.66/10.32 | | | | % 71.66/10.32 | | | | ALPHA: (211) implies: % 71.66/10.32 | | | | (212) $i(all_302_0) % 71.66/10.32 | | | | (213) set_union2(all_64_3, all_302_0) = all_196_1 % 71.66/10.32 | | | | % 71.66/10.32 | | | | DELTA: instantiating (205) with fresh symbols all_322_0, all_322_1, % 71.66/10.32 | | | | all_322_2 gives: % 71.66/10.32 | | | | (214) subset(all_64_3, all_64_3) = all_322_0 & ordinal(all_64_3) = % 71.66/10.32 | | | | all_322_1 & ordinal(all_64_3) = all_322_2 & ( ~ (all_322_1 = 0) % 71.66/10.32 | | | | | ~ (all_322_2 = 0) | all_322_0 = 0) % 71.66/10.32 | | | | % 71.66/10.32 | | | | ALPHA: (214) implies: % 71.66/10.32 | | | | (215) ordinal(all_64_3) = all_322_2 % 71.66/10.32 | | | | (216) ordinal(all_64_3) = all_322_1 % 71.66/10.32 | | | | % 71.66/10.32 | | | | DELTA: instantiating (208) with fresh symbols all_324_0, all_324_1, % 71.66/10.32 | | | | all_324_2 gives: % 71.66/10.32 | | | | (217) ordinal_subset(all_64_4, all_64_3) = all_324_0 & % 71.66/10.32 | | | | ordinal(all_64_3) = all_324_1 & ordinal(all_64_4) = all_324_2 & % 71.66/10.32 | | | | ( ~ (all_324_1 = 0) | ~ (all_324_2 = 0) | all_324_0 = 0) % 71.66/10.32 | | | | % 71.66/10.32 | | | | ALPHA: (217) implies: % 71.66/10.32 | | | | (218) ordinal(all_64_3) = all_324_1 % 71.66/10.32 | | | | % 71.66/10.32 | | | | BETA: splitting (202) gives: % 71.66/10.32 | | | | % 71.66/10.32 | | | | Case 1: % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | (219) all_150_0 = 0 % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | REDUCE: (142), (219) imply: % 71.66/10.32 | | | | | (220) $false % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | CLOSE: (220) is inconsistent. % 71.66/10.32 | | | | | % 71.66/10.32 | | | | Case 2: % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | (221) ? [v0: any] : ? [v1: any] : (element(all_64_3, all_64_4) = % 71.66/10.32 | | | | | v0 & empty(all_64_4) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | DELTA: instantiating (221) with fresh symbols all_364_0, all_364_1 % 71.66/10.32 | | | | | gives: % 71.66/10.32 | | | | | (222) element(all_64_3, all_64_4) = all_364_1 & empty(all_64_4) = % 71.66/10.32 | | | | | all_364_0 & ( ~ (all_364_1 = 0) | all_364_0 = 0) % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | ALPHA: (222) implies: % 71.66/10.32 | | | | | (223) empty(all_64_4) = all_364_0 % 71.66/10.32 | | | | | (224) element(all_64_3, all_64_4) = all_364_1 % 71.66/10.32 | | | | | (225) ~ (all_364_1 = 0) | all_364_0 = 0 % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | GROUND_INST: instantiating (27) with all_290_1, all_364_0, all_64_4, % 71.66/10.32 | | | | | simplifying with (210), (223) gives: % 71.66/10.32 | | | | | (226) all_364_0 = all_290_1 % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | GROUND_INST: instantiating (30) with all_322_2, all_322_1, all_64_3, % 71.66/10.32 | | | | | simplifying with (215), (216) gives: % 71.66/10.32 | | | | | (227) all_322_1 = all_322_2 % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | GROUND_INST: instantiating (30) with 0, all_324_1, all_64_3, % 71.66/10.32 | | | | | simplifying with (125), (218) gives: % 71.66/10.32 | | | | | (228) all_324_1 = 0 % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | GROUND_INST: instantiating (30) with all_322_1, all_324_1, all_64_3, % 71.66/10.32 | | | | | simplifying with (216), (218) gives: % 71.66/10.32 | | | | | (229) all_324_1 = all_322_1 % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | COMBINE_EQS: (228), (229) imply: % 71.66/10.32 | | | | | (230) all_322_1 = 0 % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | SIMP: (230) implies: % 71.66/10.32 | | | | | (231) all_322_1 = 0 % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | COMBINE_EQS: (227), (231) imply: % 71.66/10.32 | | | | | (232) all_322_2 = 0 % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | BETA: splitting (52) gives: % 71.66/10.32 | | | | | % 71.66/10.32 | | | | | Case 1: % 71.66/10.32 | | | | | | % 71.66/10.32 | | | | | | (233) all_64_0 = 0 & ~ (all_64_1 = 0) % 71.66/10.32 | | | | | | % 71.66/10.32 | | | | | | ALPHA: (233) implies: % 71.66/10.32 | | | | | | (234) all_64_0 = 0 % 71.66/10.32 | | | | | | (235) ~ (all_64_1 = 0) % 71.66/10.32 | | | | | | % 71.66/10.32 | | | | | | BETA: splitting (101) gives: % 71.66/10.32 | | | | | | % 71.66/10.32 | | | | | | Case 1: % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | (236) ~ (all_128_1 = 0) % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | REDUCE: (113), (236) imply: % 71.66/10.32 | | | | | | | (237) $false % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | CLOSE: (237) is inconsistent. % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | Case 2: % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | (238) ~ (all_128_2 = 0) | (( ~ (all_128_0 = 0) | all_64_0 = 0) % 71.66/10.32 | | | | | | | & ( ~ (all_64_0 = 0) | all_128_0 = 0)) % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | BETA: splitting (238) gives: % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | Case 1: % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | (239) ~ (all_128_2 = 0) % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | REDUCE: (123), (239) imply: % 71.66/10.32 | | | | | | | | (240) $false % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | CLOSE: (240) is inconsistent. % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | Case 2: % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | (241) ( ~ (all_128_0 = 0) | all_64_0 = 0) & ( ~ (all_64_0 = % 71.66/10.32 | | | | | | | | 0) | all_128_0 = 0) % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | ALPHA: (241) implies: % 71.66/10.32 | | | | | | | | (242) ~ (all_64_0 = 0) | all_128_0 = 0 % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | BETA: splitting (242) gives: % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | Case 1: % 71.66/10.32 | | | | | | | | | % 71.66/10.32 | | | | | | | | | (243) ~ (all_64_0 = 0) % 71.66/10.32 | | | | | | | | | % 71.66/10.32 | | | | | | | | | REDUCE: (234), (243) imply: % 71.66/10.32 | | | | | | | | | (244) $false % 71.66/10.32 | | | | | | | | | % 71.66/10.32 | | | | | | | | | CLOSE: (244) is inconsistent. % 71.66/10.32 | | | | | | | | | % 71.66/10.32 | | | | | | | | Case 2: % 71.66/10.32 | | | | | | | | | % 71.66/10.32 | | | | | | | | | (245) all_128_0 = 0 % 71.66/10.32 | | | | | | | | | % 71.66/10.32 | | | | | | | | | REDUCE: (100), (245) imply: % 71.66/10.32 | | | | | | | | | (246) subset(all_64_3, all_64_2) = 0 % 71.66/10.32 | | | | | | | | | % 71.66/10.32 | | | | | | | | | BETA: splitting (90) gives: % 71.66/10.32 | | | | | | | | | % 71.66/10.32 | | | | | | | | | Case 1: % 71.66/10.32 | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | REF_CLOSE: (15), (34), (44), (45), (46), (47), (70), (235), % 71.66/10.32 | | | | | | | | | | (246) are inconsistent by sub-proof #1. % 71.66/10.32 | | | | | | | | | | % 71.66/10.32 | | | | | | | | | Case 2: % 71.66/10.32 | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | (247) all_112_1 = 0 % 71.66/10.32 | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | COMBINE_EQS: (107), (247) imply: % 71.66/10.32 | | | | | | | | | | (248) all_86_2 = 0 % 71.66/10.32 | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | SIMP: (248) implies: % 71.66/10.32 | | | | | | | | | | (249) all_86_2 = 0 % 71.66/10.32 | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | COMBINE_EQS: (169), (249) imply: % 71.66/10.32 | | | | | | | | | | (250) all_186_1 = 0 % 71.66/10.32 | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | BETA: splitting (163) gives: % 71.66/10.32 | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | Case 1: % 71.66/10.32 | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | (251) ~ (all_186_0 = 0) % 71.66/10.32 | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | REDUCE: (170), (251) imply: % 71.66/10.32 | | | | | | | | | | | (252) $false % 71.66/10.32 | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | CLOSE: (252) is inconsistent. % 71.66/10.32 | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | Case 2: % 71.66/10.32 | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | (253) ~ (all_186_1 = 0) | ~ (all_186_2 = 0) | all_86_0 % 71.66/10.32 | | | | | | | | | | | = 0 % 71.66/10.32 | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | BETA: splitting (253) gives: % 71.66/10.32 | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | Case 1: % 71.66/10.32 | | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | | (254) ~ (all_186_1 = 0) % 71.66/10.32 | | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | | REDUCE: (250), (254) imply: % 71.66/10.32 | | | | | | | | | | | | (255) $false % 71.66/10.32 | | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | | CLOSE: (255) is inconsistent. % 71.66/10.32 | | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | Case 2: % 71.66/10.32 | | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | | REF_CLOSE: (15), (34), (44), (45), (46), (47), (70), (235), % 71.66/10.32 | | | | | | | | | | | | (246) are inconsistent by sub-proof #1. % 71.66/10.32 | | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | | End of split % 71.66/10.32 | | | | | | | | | | | % 71.66/10.32 | | | | | | | | | | End of split % 71.66/10.32 | | | | | | | | | | % 71.66/10.32 | | | | | | | | | End of split % 71.66/10.32 | | | | | | | | | % 71.66/10.32 | | | | | | | | End of split % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | End of split % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | End of split % 71.66/10.32 | | | | | | % 71.66/10.32 | | | | | Case 2: % 71.66/10.32 | | | | | | % 71.66/10.32 | | | | | | (256) all_64_1 = 0 & ~ (all_64_0 = 0) % 71.66/10.32 | | | | | | % 71.66/10.32 | | | | | | ALPHA: (256) implies: % 71.66/10.32 | | | | | | (257) all_64_1 = 0 % 71.66/10.32 | | | | | | (258) ~ (all_64_0 = 0) % 71.66/10.32 | | | | | | % 71.66/10.32 | | | | | | REDUCE: (47), (257) imply: % 71.66/10.32 | | | | | | (259) in(all_64_4, all_64_2) = 0 % 71.66/10.32 | | | | | | % 71.66/10.32 | | | | | | BETA: splitting (67) gives: % 71.66/10.32 | | | | | | % 71.66/10.32 | | | | | | Case 1: % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | (260) all_64_0 = 0 % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | REDUCE: (258), (260) imply: % 71.66/10.32 | | | | | | | (261) $false % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | CLOSE: (261) is inconsistent. % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | Case 2: % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | (262) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 71.66/10.32 | | | | | | | (ordinal_subset(all_64_2, all_64_3) = v2 & % 71.66/10.32 | | | | | | | ordinal(all_64_2) = v0 & ordinal(all_64_3) = v1 & ( ~ % 71.66/10.32 | | | | | | | (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | DELTA: instantiating (262) with fresh symbols all_428_0, % 71.66/10.32 | | | | | | | all_428_1, all_428_2 gives: % 71.66/10.32 | | | | | | | (263) ordinal_subset(all_64_2, all_64_3) = all_428_0 & % 71.66/10.32 | | | | | | | ordinal(all_64_2) = all_428_2 & ordinal(all_64_3) = % 71.66/10.32 | | | | | | | all_428_1 & ( ~ (all_428_1 = 0) | ~ (all_428_2 = 0) | % 71.66/10.32 | | | | | | | all_428_0 = 0) % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | ALPHA: (263) implies: % 71.66/10.32 | | | | | | | (264) ordinal(all_64_3) = all_428_1 % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | BETA: splitting (68) gives: % 71.66/10.32 | | | | | | | % 71.66/10.32 | | | | | | | Case 1: % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | (265) all_64_0 = 0 % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | REDUCE: (258), (265) imply: % 71.66/10.32 | | | | | | | | (266) $false % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | CLOSE: (266) is inconsistent. % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | Case 2: % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | (267) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 71.66/10.32 | | | | | | | | (ordinal_subset(all_64_2, all_64_3) = v2 & % 71.66/10.32 | | | | | | | | ordinal(all_64_2) = v1 & ordinal(all_64_3) = v0 & ( ~ % 71.66/10.32 | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 71.66/10.32 | | | | | | | | % 71.66/10.32 | | | | | | | | DELTA: instantiating (267) with fresh symbols all_434_0, % 71.66/10.32 | | | | | | | | all_434_1, all_434_2 gives: % 71.66/10.33 | | | | | | | | (268) ordinal_subset(all_64_2, all_64_3) = all_434_0 & % 71.66/10.33 | | | | | | | | ordinal(all_64_2) = all_434_1 & ordinal(all_64_3) = % 71.66/10.33 | | | | | | | | all_434_2 & ( ~ (all_434_1 = 0) | ~ (all_434_2 = 0) | % 71.66/10.33 | | | | | | | | all_434_0 = 0) % 71.66/10.33 | | | | | | | | % 71.66/10.33 | | | | | | | | ALPHA: (268) implies: % 71.66/10.33 | | | | | | | | (269) ordinal(all_64_3) = all_434_2 % 71.66/10.33 | | | | | | | | (270) ordinal(all_64_2) = all_434_1 % 71.66/10.33 | | | | | | | | (271) ~ (all_434_1 = 0) | ~ (all_434_2 = 0) | all_434_0 = 0 % 71.66/10.33 | | | | | | | | % 71.66/10.33 | | | | | | | | BETA: splitting (101) gives: % 71.66/10.33 | | | | | | | | % 71.66/10.33 | | | | | | | | Case 1: % 71.66/10.33 | | | | | | | | | % 71.66/10.33 | | | | | | | | | (272) ~ (all_128_1 = 0) % 71.66/10.33 | | | | | | | | | % 71.66/10.33 | | | | | | | | | REDUCE: (113), (272) imply: % 71.66/10.33 | | | | | | | | | (273) $false % 71.66/10.33 | | | | | | | | | % 71.66/10.33 | | | | | | | | | CLOSE: (273) is inconsistent. % 71.66/10.33 | | | | | | | | | % 71.66/10.33 | | | | | | | | Case 2: % 71.66/10.33 | | | | | | | | | % 71.66/10.33 | | | | | | | | | (274) ~ (all_128_2 = 0) | (( ~ (all_128_0 = 0) | all_64_0 % 71.66/10.33 | | | | | | | | | = 0) & ( ~ (all_64_0 = 0) | all_128_0 = 0)) % 71.66/10.33 | | | | | | | | | % 71.66/10.33 | | | | | | | | | BETA: splitting (274) gives: % 71.66/10.33 | | | | | | | | | % 71.66/10.33 | | | | | | | | | Case 1: % 71.66/10.33 | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | (275) ~ (all_128_2 = 0) % 71.66/10.33 | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | REDUCE: (123), (275) imply: % 71.66/10.33 | | | | | | | | | | (276) $false % 71.66/10.33 | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | CLOSE: (276) is inconsistent. % 71.66/10.33 | | | | | | | | | | % 71.66/10.33 | | | | | | | | | Case 2: % 71.66/10.33 | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | (277) ( ~ (all_128_0 = 0) | all_64_0 = 0) & ( ~ (all_64_0 % 71.66/10.33 | | | | | | | | | | = 0) | all_128_0 = 0) % 71.66/10.33 | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | ALPHA: (277) implies: % 71.66/10.33 | | | | | | | | | | (278) ~ (all_128_0 = 0) | all_64_0 = 0 % 71.66/10.33 | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | BETA: splitting (278) gives: % 71.66/10.33 | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | Case 1: % 71.66/10.33 | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | (279) ~ (all_128_0 = 0) % 71.66/10.33 | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | BETA: splitting (139) gives: % 71.66/10.33 | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | Case 1: % 71.66/10.33 | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | (280) all_128_0 = 0 % 71.66/10.33 | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | REDUCE: (279), (280) imply: % 71.66/10.33 | | | | | | | | | | | | (281) $false % 71.66/10.33 | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | CLOSE: (281) is inconsistent. % 71.66/10.33 | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | Case 2: % 71.66/10.33 | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | (282) ? [v0: any] : ? [v1: any] : (subset(all_76_0, % 71.66/10.33 | | | | | | | | | | | | all_64_2) = v1 & subset(all_64_4, all_64_2) = % 71.66/10.33 | | | | | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 71.66/10.33 | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | DELTA: instantiating (282) with fresh symbols all_467_0, % 71.66/10.33 | | | | | | | | | | | | all_467_1 gives: % 71.66/10.33 | | | | | | | | | | | | (283) subset(all_76_0, all_64_2) = all_467_0 & % 71.66/10.33 | | | | | | | | | | | | subset(all_64_4, all_64_2) = all_467_1 & ( ~ % 71.66/10.33 | | | | | | | | | | | | (all_467_0 = 0) | ~ (all_467_1 = 0)) % 71.66/10.33 | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | ALPHA: (283) implies: % 71.66/10.33 | | | | | | | | | | | | (284) subset(all_64_4, all_64_2) = all_467_1 % 71.66/10.33 | | | | | | | | | | | | (285) subset(all_76_0, all_64_2) = all_467_0 % 71.66/10.33 | | | | | | | | | | | | (286) ~ (all_467_0 = 0) | ~ (all_467_1 = 0) % 71.66/10.33 | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | BETA: splitting (203) gives: % 71.66/10.33 | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | Case 1: % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | (287) all_128_0 = 0 % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | REDUCE: (279), (287) imply: % 71.66/10.33 | | | | | | | | | | | | | (288) $false % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | CLOSE: (288) is inconsistent. % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | Case 2: % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | (289) ? [v0: any] : ? [v1: any] : (subset(all_76_0, % 71.66/10.33 | | | | | | | | | | | | | all_64_2) = v0 & subset(all_64_4, all_64_2) = % 71.66/10.33 | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | DELTA: instantiating (289) with fresh symbols all_472_0, % 71.66/10.33 | | | | | | | | | | | | | all_472_1 gives: % 71.66/10.33 | | | | | | | | | | | | | (290) subset(all_76_0, all_64_2) = all_472_1 & % 71.66/10.33 | | | | | | | | | | | | | subset(all_64_4, all_64_2) = all_472_0 & ( ~ % 71.66/10.33 | | | | | | | | | | | | | (all_472_0 = 0) | ~ (all_472_1 = 0)) % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | ALPHA: (290) implies: % 71.66/10.33 | | | | | | | | | | | | | (291) subset(all_64_4, all_64_2) = all_472_0 % 71.66/10.33 | | | | | | | | | | | | | (292) subset(all_76_0, all_64_2) = all_472_1 % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | GROUND_INST: instantiating (30) with 0, all_434_2, all_64_3, % 71.66/10.33 | | | | | | | | | | | | | simplifying with (125), (269) gives: % 71.66/10.33 | | | | | | | | | | | | | (293) all_434_2 = 0 % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_428_1, all_434_2, % 71.66/10.33 | | | | | | | | | | | | | all_64_3, simplifying with (264), (269) gives: % 71.66/10.33 | | | | | | | | | | | | | (294) all_434_2 = all_428_1 % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | GROUND_INST: instantiating (30) with 0, all_434_1, all_64_2, % 71.66/10.33 | | | | | | | | | | | | | simplifying with (49), (270) gives: % 71.66/10.33 | | | | | | | | | | | | | (295) all_434_1 = 0 % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_467_1, all_472_0, % 71.66/10.33 | | | | | | | | | | | | | all_64_2, all_64_4, simplifying with (284), (291) % 71.66/10.33 | | | | | | | | | | | | | gives: % 71.66/10.33 | | | | | | | | | | | | | (296) all_472_0 = all_467_1 % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_467_0, all_472_1, % 71.66/10.33 | | | | | | | | | | | | | all_64_2, all_76_0, simplifying with (285), (292) % 71.66/10.33 | | | | | | | | | | | | | gives: % 71.66/10.33 | | | | | | | | | | | | | (297) all_472_1 = all_467_0 % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | COMBINE_EQS: (293), (294) imply: % 71.66/10.33 | | | | | | | | | | | | | (298) all_428_1 = 0 % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | BETA: splitting (271) gives: % 71.66/10.33 | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | Case 1: % 71.66/10.33 | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | (299) ~ (all_434_1 = 0) % 71.66/10.33 | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | REDUCE: (295), (299) imply: % 71.66/10.33 | | | | | | | | | | | | | | (300) $false % 71.66/10.33 | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | CLOSE: (300) is inconsistent. % 71.66/10.33 | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | Case 2: % 71.66/10.33 | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | (301) ~ (all_434_2 = 0) | all_434_0 = 0 % 71.66/10.33 | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | BETA: splitting (301) gives: % 71.66/10.33 | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | Case 1: % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | (302) ~ (all_434_2 = 0) % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | REDUCE: (293), (302) imply: % 71.66/10.33 | | | | | | | | | | | | | | | (303) $false % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent. % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | Case 2: % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_64_2, all_64_4, % 71.66/10.33 | | | | | | | | | | | | | | | simplifying with (44), (46), (64), (259) gives: % 71.66/10.33 | | | | | | | | | | | | | | | (304) subset(all_64_4, all_64_2) = 0 % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_302_0, all_64_3, % 71.66/10.33 | | | | | | | | | | | | | | | all_196_1, simplifying with (45), (212), (213) % 71.66/10.33 | | | | | | | | | | | | | | | gives: % 71.66/10.33 | | | | | | | | | | | | | | | (305) set_union2(all_302_0, all_64_3) = all_196_1 & % 71.66/10.33 | | | | | | | | | | | | | | | $i(all_196_1) % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | ALPHA: (305) implies: % 71.66/10.33 | | | | | | | | | | | | | | | (306) $i(all_196_1) % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_76_0, all_64_2, % 71.66/10.33 | | | | | | | | | | | | | | | all_467_0, simplifying with (46), (74), (285) % 71.66/10.33 | | | | | | | | | | | | | | | gives: % 71.66/10.33 | | | | | | | | | | | | | | | (307) all_467_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ % 71.66/10.33 | | | | | | | | | | | | | | | (v1 = 0) & in(v0, all_76_0) = 0 & in(v0, % 71.66/10.33 | | | | | | | | | | | | | | | all_64_2) = v1 & $i(v0)) % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_64_3, all_196_1, % 71.66/10.33 | | | | | | | | | | | | | | | all_64_4, all_364_1, simplifying with (44), (45), % 71.66/10.33 | | | | | | | | | | | | | | | (206), (224), (306) gives: % 71.66/10.33 | | | | | | | | | | | | | | | (308) all_364_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ % 71.66/10.33 | | | | | | | | | | | | | | | (v1 = 0) & powerset(all_64_4) = v0 & % 71.66/10.33 | | | | | | | | | | | | | | | element(all_196_1, v0) = v1 & $i(v0)) % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 71.66/10.33 | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | Case 1: % 71.66/10.33 | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | (309) ~ (all_467_0 = 0) % 71.66/10.33 | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | BETA: splitting (307) gives: % 71.66/10.33 | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | Case 1: % 71.66/10.33 | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | (310) all_467_0 = 0 % 71.66/10.33 | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | REDUCE: (309), (310) imply: % 71.66/10.33 | | | | | | | | | | | | | | | | | (311) $false % 71.66/10.33 | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | CLOSE: (311) is inconsistent. % 71.66/10.33 | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | Case 2: % 71.66/10.33 | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | (312) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 71.66/10.33 | | | | | | | | | | | | | | | | | all_76_0) = 0 & in(v0, all_64_2) = v1 & % 71.66/10.33 | | | | | | | | | | | | | | | | | $i(v0)) % 71.66/10.33 | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | DELTA: instantiating (312) with fresh symbols all_835_0, % 71.66/10.33 | | | | | | | | | | | | | | | | | all_835_1 gives: % 71.66/10.33 | | | | | | | | | | | | | | | | | (313) ~ (all_835_0 = 0) & in(all_835_1, all_76_0) = 0 & % 71.66/10.33 | | | | | | | | | | | | | | | | | in(all_835_1, all_64_2) = all_835_0 & % 71.66/10.33 | | | | | | | | | | | | | | | | | $i(all_835_1) % 71.66/10.33 | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | ALPHA: (313) implies: % 71.66/10.33 | | | | | | | | | | | | | | | | | (314) ~ (all_835_0 = 0) % 71.66/10.33 | | | | | | | | | | | | | | | | | (315) $i(all_835_1) % 71.66/10.33 | | | | | | | | | | | | | | | | | (316) in(all_835_1, all_64_2) = all_835_0 % 71.66/10.33 | | | | | | | | | | | | | | | | | (317) in(all_835_1, all_76_0) = 0 % 71.66/10.33 | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 71.66/10.33 | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | Case 1: % 71.66/10.33 | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | (318) ~ (all_364_1 = 0) % 71.66/10.33 | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives: % 71.66/10.33 | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | Case 1: % 71.66/10.33 | | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | | (319) all_364_1 = 0 % 71.66/10.33 | | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | | REDUCE: (318), (319) imply: % 71.66/10.33 | | | | | | | | | | | | | | | | | | | (320) $false % 71.66/10.33 | | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | | CLOSE: (320) is inconsistent. % 71.66/10.33 | | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | Case 2: % 71.66/10.33 | | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_64_4, all_76_0, % 71.66/10.33 | | | | | | | | | | | | | | | | | | | all_835_1, simplifying with (44), (74), (76), % 71.66/10.33 | | | | | | | | | | | | | | | | | | | (315), (317) gives: % 71.66/10.33 | | | | | | | | | | | | | | | | | | | (321) all_835_1 = all_64_4 % 71.66/10.33 | | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | | REDUCE: (316), (321) imply: % 71.66/10.33 | | | | | | | | | | | | | | | | | | | (322) in(all_64_4, all_64_2) = all_835_0 % 71.66/10.33 | | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with 0, all_835_0, all_64_2, % 71.66/10.33 | | | | | | | | | | | | | | | | | | | all_64_4, simplifying with (259), (322) gives: % 71.66/10.33 | | | | | | | | | | | | | | | | | | | (323) all_835_0 = 0 % 71.66/10.33 | | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | | REDUCE: (314), (323) imply: % 71.66/10.33 | | | | | | | | | | | | | | | | | | | (324) $false % 71.66/10.33 | | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | | CLOSE: (324) is inconsistent. % 71.66/10.33 | | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | End of split % 71.66/10.33 | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | Case 2: % 71.66/10.33 | | | | | | | | | | | | | | | | | | % 71.66/10.33 | | | | | | | | | | | | | | | | | | (325) all_364_0 = 0 % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (325) imply: % 71.66/10.34 | | | | | | | | | | | | | | | | | | (326) all_290_1 = 0 % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | | SIMP: (326) implies: % 71.66/10.34 | | | | | | | | | | | | | | | | | | (327) all_290_1 = 0 % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | | REDUCE: (210), (327) imply: % 71.66/10.34 | | | | | | | | | | | | | | | | | | (328) empty(all_64_4) = 0 % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_64_4, all_76_0, % 71.66/10.34 | | | | | | | | | | | | | | | | | | all_835_1, simplifying with (44), (74), (76), % 71.66/10.34 | | | | | | | | | | | | | | | | | | (315), (317) gives: % 71.66/10.34 | | | | | | | | | | | | | | | | | | (329) all_835_1 = all_64_4 % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_64_4, simplifying with % 71.66/10.34 | | | | | | | | | | | | | | | | | | (44), (328) gives: % 71.66/10.34 | | | | | | | | | | | | | | | | | | (330) all_64_4 = empty_set % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (330) imply: % 71.66/10.34 | | | | | | | | | | | | | | | | | | (331) all_835_1 = empty_set % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | | REDUCE: (316), (331) imply: % 71.66/10.34 | | | | | | | | | | | | | | | | | | (332) in(empty_set, all_64_2) = all_835_0 % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | | REDUCE: (259), (330) imply: % 71.66/10.34 | | | | | | | | | | | | | | | | | | (333) in(empty_set, all_64_2) = 0 % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with 0, all_835_0, all_64_2, % 71.66/10.34 | | | | | | | | | | | | | | | | | | empty_set, simplifying with (332), (333) gives: % 71.66/10.34 | | | | | | | | | | | | | | | | | | (334) all_835_0 = 0 % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | | REDUCE: (314), (334) imply: % 71.66/10.34 | | | | | | | | | | | | | | | | | | (335) $false % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | | CLOSE: (335) is inconsistent. % 71.66/10.34 | | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | | End of split % 71.66/10.34 | | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | End of split % 71.66/10.34 | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | Case 2: % 71.66/10.34 | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | (336) ~ (all_467_1 = 0) % 71.66/10.34 | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_467_1, 0, all_64_2, % 71.66/10.34 | | | | | | | | | | | | | | | | all_64_4, simplifying with (284), (304) gives: % 71.66/10.34 | | | | | | | | | | | | | | | | (337) all_467_1 = 0 % 71.66/10.34 | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | REDUCE: (336), (337) imply: % 71.66/10.34 | | | | | | | | | | | | | | | | (338) $false % 71.66/10.34 | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | | CLOSE: (338) is inconsistent. % 71.66/10.34 | | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | | End of split % 71.66/10.34 | | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | | End of split % 71.66/10.34 | | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | | End of split % 71.66/10.34 | | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | | End of split % 71.66/10.34 | | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | End of split % 71.66/10.34 | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | Case 2: % 71.66/10.34 | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | (339) all_64_0 = 0 % 71.66/10.34 | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | REDUCE: (258), (339) imply: % 71.66/10.34 | | | | | | | | | | | (340) $false % 71.66/10.34 | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | | CLOSE: (340) is inconsistent. % 71.66/10.34 | | | | | | | | | | | % 71.66/10.34 | | | | | | | | | | End of split % 71.66/10.34 | | | | | | | | | | % 71.66/10.34 | | | | | | | | | End of split % 71.66/10.34 | | | | | | | | | % 71.66/10.34 | | | | | | | | End of split % 71.66/10.34 | | | | | | | | % 71.66/10.34 | | | | | | | End of split % 71.66/10.34 | | | | | | | % 71.66/10.34 | | | | | | End of split % 71.66/10.34 | | | | | | % 71.66/10.34 | | | | | End of split % 71.66/10.34 | | | | | % 71.66/10.34 | | | | End of split % 71.66/10.34 | | | | % 71.66/10.34 | | | End of split % 71.66/10.34 | | | % 71.66/10.34 | | End of split % 71.66/10.34 | | % 71.66/10.34 | End of split % 71.66/10.34 | % 71.66/10.34 End of proof % 71.66/10.34 % 71.66/10.34 Sub-proof #1 shows that the following formulas are inconsistent: % 71.66/10.34 ---------------------------------------------------------------- % 71.66/10.34 (1) $i(all_64_2) % 71.66/10.34 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 71.66/10.34 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 71.66/10.34 (3) subset(all_64_3, all_64_2) = 0 % 71.66/10.34 (4) $i(all_64_3) % 71.66/10.34 (5) $i(all_64_4) % 71.66/10.34 (6) in(all_64_4, all_64_3) = 0 % 71.66/10.34 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 71.66/10.34 (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) = 0) % 71.66/10.34 (8) ~ (all_64_1 = 0) % 71.66/10.34 (9) in(all_64_4, all_64_2) = all_64_1 % 71.66/10.34 % 71.66/10.34 Begin of proof % 71.66/10.34 | % 71.66/10.34 | GROUND_INST: instantiating (7) with all_64_3, all_64_2, all_64_4, simplifying % 71.66/10.34 | with (1), (3), (4), (5), (6) gives: % 71.66/10.34 | (10) in(all_64_4, all_64_2) = 0 % 71.66/10.34 | % 71.66/10.34 | GROUND_INST: instantiating (2) with all_64_1, 0, all_64_2, all_64_4, % 71.66/10.34 | simplifying with (9), (10) gives: % 71.66/10.34 | (11) all_64_1 = 0 % 71.66/10.34 | % 71.66/10.34 | REDUCE: (8), (11) imply: % 71.66/10.34 | (12) $false % 71.66/10.34 | % 71.66/10.34 | CLOSE: (12) is inconsistent. % 71.66/10.34 | % 71.66/10.34 End of proof % 71.66/10.34 % SZS output end Proof for theBenchmark % 71.66/10.34 % 71.66/10.34 9739ms %------------------------------------------------------------------------------