%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU241+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 : n017.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 17:43:35 EDT 2023 % Result : Theorem 8.79s 2.17s % Output : Proof 17.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU241+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n017.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 18:43:38 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.37/1.03 Prover 1: Preprocessing ... % 2.37/1.03 Prover 4: Preprocessing ... % 2.37/1.07 Prover 0: Preprocessing ... % 2.37/1.07 Prover 2: Preprocessing ... % 2.37/1.07 Prover 3: Preprocessing ... % 2.37/1.07 Prover 5: Preprocessing ... % 2.37/1.07 Prover 6: Preprocessing ... % 5.34/1.52 Prover 1: Warning: ignoring some quantifiers % 5.34/1.52 Prover 5: Proving ... % 5.83/1.52 Prover 2: Proving ... % 5.83/1.52 Prover 3: Warning: ignoring some quantifiers % 5.86/1.54 Prover 1: Constructing countermodel ... % 5.86/1.54 Prover 3: Constructing countermodel ... % 5.86/1.54 Prover 6: Proving ... % 5.86/1.57 Prover 4: Warning: ignoring some quantifiers % 5.86/1.59 Prover 0: Proving ... % 5.86/1.60 Prover 4: Constructing countermodel ... % 7.79/1.88 Prover 3: gave up % 8.30/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.30/1.94 Prover 7: Preprocessing ... % 8.79/1.99 Prover 1: gave up % 8.79/2.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.79/2.05 Prover 7: Warning: ignoring some quantifiers % 8.79/2.07 Prover 8: Preprocessing ... % 8.79/2.09 Prover 7: Constructing countermodel ... % 8.79/2.17 Prover 0: proved (1546ms) % 8.79/2.17 % 8.79/2.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.79/2.17 % 8.79/2.17 Prover 6: stopped % 8.79/2.17 Prover 5: stopped % 8.79/2.18 Prover 2: stopped % 8.79/2.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.79/2.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.79/2.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.79/2.20 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.75/2.22 Prover 10: Preprocessing ... % 9.75/2.22 Prover 11: Preprocessing ... % 10.41/2.24 Prover 13: Preprocessing ... % 10.41/2.25 Prover 16: Preprocessing ... % 10.62/2.27 Prover 8: Warning: ignoring some quantifiers % 10.62/2.29 Prover 10: Warning: ignoring some quantifiers % 10.62/2.30 Prover 8: Constructing countermodel ... % 10.62/2.32 Prover 10: Constructing countermodel ... % 10.62/2.32 Prover 13: Warning: ignoring some quantifiers % 10.62/2.33 Prover 16: Warning: ignoring some quantifiers % 11.08/2.34 Prover 16: Constructing countermodel ... % 11.08/2.34 Prover 13: Constructing countermodel ... % 11.27/2.40 Prover 11: Warning: ignoring some quantifiers % 11.27/2.41 Prover 11: Constructing countermodel ... % 11.71/2.43 Prover 10: gave up % 11.71/2.44 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.94/2.48 Prover 19: Preprocessing ... % 12.67/2.63 Prover 19: Warning: ignoring some quantifiers % 13.11/2.64 Prover 19: Constructing countermodel ... % 13.11/2.64 Prover 8: gave up % 15.45/2.99 Prover 13: gave up % 16.24/3.10 Prover 19: gave up % 16.24/3.11 Prover 4: Found proof (size 212) % 16.24/3.11 Prover 4: proved (2476ms) % 16.24/3.11 Prover 7: stopped % 16.24/3.11 Prover 11: stopped % 16.42/3.12 Prover 16: stopped % 16.42/3.12 % 16.42/3.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.42/3.12 % 16.47/3.15 % SZS output start Proof for theBenchmark % 16.47/3.15 Assumptions after simplification: % 16.47/3.15 --------------------------------- % 16.47/3.15 % 16.47/3.15 (cc2_funct_1) % 16.47/3.18 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2: % 16.47/3.18 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) = % 16.47/3.19 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 16.47/3.19 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 16.47/3.19 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0) % 16.47/3.19 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ % 16.47/3.19 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] % 16.47/3.19 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | % 16.47/3.19 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) % 16.47/3.19 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & % 16.47/3.19 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = % 16.47/3.19 0))) % 16.47/3.19 % 16.47/3.19 (commutativity_k2_xboole_0) % 16.47/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 16.47/3.19 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 16.47/3.19 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 16.47/3.19 | (set_union2(v1, v0) = v2 & $i(v2))) % 16.47/3.19 % 16.47/3.19 (d12_relat_2) % 16.47/3.19 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? % 16.47/3.19 [v2: any] : ? [v3: any] : ? [v4: any] : (antisymmetric(v0) = v3 & % 16.47/3.19 is_antisymmetric_in(v0, v1) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ % 16.47/3.19 (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0))))) & ! [v0: $i] : ! % 16.47/3.19 [v1: any] : ( ~ (antisymmetric(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 16.47/3.19 $i] : ? [v4: any] : (relation_field(v0) = v3 & is_antisymmetric_in(v0, % 16.47/3.19 v3) = v4 & relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v4 = 0) | % 16.47/3.19 v1 = 0) & ( ~ (v1 = 0) | v4 = 0))))) & ! [v0: $i] : ( ~ % 16.47/3.19 (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 16.47/3.19 (relation_field(v0) = v2 & antisymmetric(v0) = v1 & is_antisymmetric_in(v0, % 16.47/3.19 v2) = v3 & $i(v2) & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))) % 16.47/3.19 % 16.47/3.19 (d4_relat_2) % 16.47/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2 % 16.47/3.20 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_antisymmetric_in(v0, v1) = 0) | ~ % 16.47/3.20 (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 16.47/3.20 any] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : % 16.47/3.20 (ordered_pair(v2, v3) = v7 & in(v7, v0) = v8 & in(v4, v0) = v9 & in(v3, v1) % 16.47/3.20 = v6 & in(v2, v1) = v5 & $i(v7) & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v6 = 0) % 16.47/3.20 | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 16.47/3.20 : ! [v4: $i] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ % 16.47/3.20 (is_antisymmetric_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ $i(v3) | ~ % 16.47/3.20 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] % 16.47/3.20 : ? [v8: $i] : ? [v9: any] : (ordered_pair(v3, v2) = v8 & in(v8, v0) = v9 % 16.47/3.20 & in(v4, v0) = v7 & in(v3, v1) = v6 & in(v2, v1) = v5 & $i(v8) & ( ~ (v9 = % 16.47/3.20 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 16.47/3.20 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (is_antisymmetric_in(v0, v1) = v2) | ~ % 16.47/3.20 (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 16.47/3.20 [v5: $i] : ? [v6: $i] : ( ~ (v4 = v3) & ordered_pair(v4, v3) = v6 & % 16.47/3.20 ordered_pair(v3, v4) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0 & in(v4, v1) = % 16.47/3.20 0 & in(v3, v1) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3))) % 16.47/3.20 % 16.47/3.20 (d6_relat_1) % 16.47/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 16.47/3.20 any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v4 & % 16.47/3.20 relation_field(v0) = v3 & set_union2(v1, v4) = v5 & relation(v0) = v2 & % 16.47/3.20 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : ! % 16.47/3.20 [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 16.47/3.20 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 & % 16.47/3.20 relation_field(v0) = v3 & set_union2(v4, v1) = v5 & relation(v0) = v2 & % 16.47/3.20 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : ! % 16.47/3.20 [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 16.47/3.20 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v3 & % 16.47/3.20 relation_rng(v0) = v4 & set_union2(v3, v4) = v5 & relation(v0) = v2 & % 16.47/3.20 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v1))) & ! [v0: $i] : ( ~ % 16.47/3.20 (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 16.47/3.20 (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & % 16.47/3.20 set_union2(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) % 16.47/3.20 % 16.47/3.20 (l3_wellord1) % 16.47/3.20 ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 16.47/3.20 int] : ? [v6: $i] : ? [v7: int] : (antisymmetric(v0) = v1 & relation(v0) = % 16.47/3.20 0 & $i(v3) & $i(v2) & $i(v0) & ((v7 = 0 & v5 = 0 & v1 = 0 & ~ (v3 = v2) & % 16.47/3.20 ordered_pair(v3, v2) = v6 & ordered_pair(v2, v3) = v4 & in(v6, v0) = 0 & % 16.47/3.20 in(v4, v0) = 0 & $i(v6) & $i(v4)) | ( ~ (v1 = 0) & ! [v8: $i] : ! [v9: % 16.47/3.20 $i] : ! [v10: $i] : (v9 = v8 | ~ (ordered_pair(v9, v8) = v10) | ~ % 16.47/3.20 $i(v9) | ~ $i(v8) | ? [v11: $i] : ? [v12: any] : ? [v13: any] : % 16.47/3.20 (ordered_pair(v8, v9) = v11 & in(v11, v0) = v12 & in(v10, v0) = v13 & % 16.47/3.20 $i(v11) & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v8: $i] : ! [v9: % 16.47/3.20 $i] : ! [v10: $i] : (v9 = v8 | ~ (ordered_pair(v8, v9) = v10) | ~ % 16.47/3.20 $i(v9) | ~ $i(v8) | ? [v11: any] : ? [v12: $i] : ? [v13: any] : % 16.47/3.20 (ordered_pair(v9, v8) = v12 & in(v12, v0) = v13 & in(v10, v0) = v11 & % 16.47/3.20 $i(v12) & ( ~ (v13 = 0) | ~ (v11 = 0))))))) % 16.47/3.20 % 16.47/3.20 (t30_relat_1) % 16.86/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, % 16.86/3.21 v1) = v3) | ~ (in(v3, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.86/3.21 [v4: any] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : (relation_field(v2) % 16.86/3.21 = v5 & relation(v2) = v4 & in(v1, v5) = v7 & in(v0, v5) = v6 & $i(v5) & ( % 16.86/3.21 ~ (v4 = 0) | (v7 = 0 & v6 = 0)))) % 16.86/3.21 % 16.86/3.21 (function-axioms) % 16.86/3.21 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.86/3.21 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 16.86/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.86/3.21 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 16.86/3.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.86/3.21 : (v1 = v0 | ~ (is_antisymmetric_in(v3, v2) = v1) | ~ % 16.86/3.21 (is_antisymmetric_in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 16.86/3.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ % 16.86/3.21 (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.86/3.21 [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 16.86/3.21 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.86/3.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = % 16.86/3.21 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.86/3.21 (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: % 16.86/3.21 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ % 16.86/3.21 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 16.86/3.21 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 16.86/3.21 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ % 16.86/3.21 (relation_field(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.86/3.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (antisymmetric(v2) = v1) | % 16.86/3.21 ~ (antisymmetric(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.86/3.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 16.86/3.21 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.86/3.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 16.86/3.21 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.86/3.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 16.86/3.21 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.86/3.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 16.86/3.21 (empty(v2) = v0)) % 16.86/3.21 % 16.86/3.21 Further assumptions not needed in the proof: % 16.86/3.21 -------------------------------------------- % 16.86/3.21 antisymmetry_r2_hidden, cc1_funct_1, commutativity_k2_tarski, d5_tarski, % 16.86/3.21 dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0, dt_k2_relat_1, dt_k2_tarski, % 16.86/3.21 dt_k2_xboole_0, dt_k3_relat_1, dt_k4_tarski, dt_m1_subset_1, % 16.86/3.21 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0, % 16.86/3.21 idempotence_k2_xboole_0, rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0, % 16.86/3.21 rc3_funct_1, t1_boole, t1_subset, t2_subset, t6_boole, t7_boole, t8_boole % 16.86/3.21 % 16.86/3.21 Those formulas are unsatisfiable: % 16.86/3.21 --------------------------------- % 16.86/3.21 % 16.86/3.21 Begin of proof % 16.86/3.21 | % 16.86/3.21 | ALPHA: (cc2_funct_1) implies: % 16.86/3.21 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 16.86/3.21 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & % 16.86/3.21 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 16.86/3.21 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? % 16.86/3.21 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & % 16.86/3.21 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | % 16.86/3.21 | ~ (v2 = 0) | v1 = 0))) % 16.86/3.21 | % 16.86/3.21 | ALPHA: (commutativity_k2_xboole_0) implies: % 16.86/3.21 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 16.86/3.21 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 16.86/3.21 | % 16.86/3.21 | ALPHA: (d12_relat_2) implies: % 16.86/3.22 | (4) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 16.86/3.22 | [v2: $i] : ? [v3: any] : (relation_field(v0) = v2 & % 16.86/3.22 | antisymmetric(v0) = v1 & is_antisymmetric_in(v0, v2) = v3 & $i(v2) % 16.86/3.22 | & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))) % 16.86/3.22 | (5) ! [v0: $i] : ! [v1: any] : ( ~ (antisymmetric(v0) = v1) | ~ $i(v0) | % 16.86/3.22 | ? [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_field(v0) = v3 % 16.86/3.22 | & is_antisymmetric_in(v0, v3) = v4 & relation(v0) = v2 & $i(v3) & ( % 16.86/3.22 | ~ (v2 = 0) | (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) | v4 = 0))))) % 16.86/3.22 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | % 16.86/3.22 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (antisymmetric(v0) = v3 % 16.86/3.22 | & is_antisymmetric_in(v0, v1) = v4 & relation(v0) = v2 & ( ~ (v2 = % 16.86/3.22 | 0) | (( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0))))) % 16.86/3.22 | % 16.86/3.22 | ALPHA: (d4_relat_2) implies: % 16.86/3.22 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 16.86/3.22 | (is_antisymmetric_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ % 16.86/3.22 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 16.86/3.22 | [v6: $i] : ( ~ (v4 = v3) & ordered_pair(v4, v3) = v6 & % 16.86/3.22 | ordered_pair(v3, v4) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0 & % 16.86/3.22 | in(v4, v1) = 0 & in(v3, v1) = 0 & $i(v6) & $i(v5) & $i(v4) & % 16.86/3.22 | $i(v3))) % 16.86/3.22 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 16.86/3.22 | (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ (is_antisymmetric_in(v0, % 16.86/3.22 | v1) = 0) | ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 16.86/3.22 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? % 16.86/3.22 | [v8: $i] : ? [v9: any] : (ordered_pair(v3, v2) = v8 & in(v8, v0) = % 16.86/3.22 | v9 & in(v4, v0) = v7 & in(v3, v1) = v6 & in(v2, v1) = v5 & $i(v8) & % 16.86/3.22 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) % 16.86/3.22 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 16.86/3.22 | (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_antisymmetric_in(v0, % 16.86/3.22 | v1) = 0) | ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 16.86/3.22 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? % 16.86/3.22 | [v8: any] : ? [v9: any] : (ordered_pair(v2, v3) = v7 & in(v7, v0) = % 16.86/3.22 | v8 & in(v4, v0) = v9 & in(v3, v1) = v6 & in(v2, v1) = v5 & $i(v7) & % 16.86/3.22 | ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) % 16.86/3.22 | % 16.86/3.22 | ALPHA: (d6_relat_1) implies: % 16.86/3.22 | (10) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 16.86/3.22 | [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & relation_rng(v0) = % 16.86/3.22 | v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1 & $i(v3) & % 16.86/3.22 | $i(v2) & $i(v1))) % 16.86/3.22 | % 16.86/3.22 | ALPHA: (function-axioms) implies: % 16.86/3.22 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.86/3.22 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 16.86/3.22 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.86/3.22 | : (v1 = v0 | ~ (antisymmetric(v2) = v1) | ~ (antisymmetric(v2) = % 16.86/3.22 | v0)) % 16.86/3.22 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.86/3.22 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 16.86/3.22 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.86/3.22 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 16.86/3.22 | v0)) % 16.86/3.22 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.86/3.22 | : ! [v3: $i] : (v1 = v0 | ~ (is_antisymmetric_in(v3, v2) = v1) | ~ % 16.86/3.22 | (is_antisymmetric_in(v3, v2) = v0)) % 16.86/3.22 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.86/3.22 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 16.86/3.22 | % 16.86/3.23 | DELTA: instantiating (l3_wellord1) with fresh symbols all_35_0, all_35_1, % 16.86/3.23 | all_35_2, all_35_3, all_35_4, all_35_5, all_35_6, all_35_7 gives: % 16.86/3.23 | (17) antisymmetric(all_35_7) = all_35_6 & relation(all_35_7) = 0 & % 16.86/3.23 | $i(all_35_4) & $i(all_35_5) & $i(all_35_7) & ((all_35_0 = 0 & all_35_2 % 16.86/3.23 | = 0 & all_35_6 = 0 & ~ (all_35_4 = all_35_5) & % 16.86/3.23 | ordered_pair(all_35_4, all_35_5) = all_35_1 & % 16.86/3.23 | ordered_pair(all_35_5, all_35_4) = all_35_3 & in(all_35_1, % 16.86/3.23 | all_35_7) = 0 & in(all_35_3, all_35_7) = 0 & $i(all_35_1) & % 16.86/3.23 | $i(all_35_3)) | ( ~ (all_35_6 = 0) & ! [v0: $i] : ! [v1: $i] : % 16.86/3.23 | ! [v2: $i] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ~ $i(v1) % 16.86/3.23 | | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 16.86/3.23 | (ordered_pair(v0, v1) = v3 & in(v3, all_35_7) = v4 & in(v2, % 16.86/3.23 | all_35_7) = v5 & $i(v3) & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! % 16.86/3.23 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.86/3.23 | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 16.86/3.23 | any] : ? [v4: $i] : ? [v5: any] : (ordered_pair(v1, v0) = v4 % 16.86/3.23 | & in(v4, all_35_7) = v5 & in(v2, all_35_7) = v3 & $i(v4) & ( ~ % 16.86/3.23 | (v5 = 0) | ~ (v3 = 0)))))) % 16.86/3.23 | % 16.86/3.23 | ALPHA: (17) implies: % 16.86/3.23 | (18) $i(all_35_7) % 16.86/3.23 | (19) $i(all_35_5) % 16.86/3.23 | (20) $i(all_35_4) % 16.86/3.23 | (21) relation(all_35_7) = 0 % 16.86/3.23 | (22) antisymmetric(all_35_7) = all_35_6 % 16.86/3.23 | (23) (all_35_0 = 0 & all_35_2 = 0 & all_35_6 = 0 & ~ (all_35_4 = all_35_5) % 16.86/3.23 | & ordered_pair(all_35_4, all_35_5) = all_35_1 & % 16.86/3.23 | ordered_pair(all_35_5, all_35_4) = all_35_3 & in(all_35_1, all_35_7) % 16.86/3.23 | = 0 & in(all_35_3, all_35_7) = 0 & $i(all_35_1) & $i(all_35_3)) | ( % 16.86/3.23 | ~ (all_35_6 = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 16.86/3.23 | v0 | ~ (ordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.86/3.23 | [v3: $i] : ? [v4: any] : ? [v5: any] : (ordered_pair(v0, v1) = % 16.86/3.23 | v3 & in(v3, all_35_7) = v4 & in(v2, all_35_7) = v5 & $i(v3) & ( % 16.86/3.23 | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 16.86/3.23 | [v2: $i] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | % 16.86/3.23 | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 16.86/3.23 | (ordered_pair(v1, v0) = v4 & in(v4, all_35_7) = v5 & in(v2, % 16.86/3.23 | all_35_7) = v3 & $i(v4) & ( ~ (v5 = 0) | ~ (v3 = 0))))) % 16.86/3.23 | % 16.86/3.23 | GROUND_INST: instantiating (10) with all_35_7, simplifying with (18), (21) % 16.86/3.23 | gives: % 16.86/3.23 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_35_7) = v1 % 16.86/3.23 | & relation_rng(all_35_7) = v2 & relation_field(all_35_7) = v0 & % 16.86/3.23 | set_union2(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 16.86/3.23 | % 16.86/3.23 | GROUND_INST: instantiating (4) with all_35_7, simplifying with (18), (21) % 16.86/3.23 | gives: % 16.86/3.23 | (25) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_field(all_35_7) % 16.86/3.23 | = v1 & antisymmetric(all_35_7) = v0 & is_antisymmetric_in(all_35_7, % 16.86/3.23 | v1) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = % 16.86/3.23 | 0)) % 16.86/3.23 | % 16.86/3.23 | GROUND_INST: instantiating (1) with all_35_7, simplifying with (18), (21) % 16.86/3.23 | gives: % 16.86/3.23 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_35_7) = % 16.86/3.23 | v2 & function(all_35_7) = v1 & empty(all_35_7) = v0 & ( ~ (v1 = 0) | % 16.86/3.23 | ~ (v0 = 0) | v2 = 0)) % 16.86/3.23 | % 16.86/3.23 | GROUND_INST: instantiating (5) with all_35_7, all_35_6, simplifying with (18), % 16.86/3.23 | (22) gives: % 16.86/3.24 | (27) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_field(all_35_7) % 16.86/3.24 | = v1 & is_antisymmetric_in(all_35_7, v1) = v2 & relation(all_35_7) = % 16.86/3.24 | v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (v2 = 0) | all_35_6 = 0) & ( ~ % 16.86/3.24 | (all_35_6 = 0) | v2 = 0)))) % 16.86/3.24 | % 16.86/3.24 | DELTA: instantiating (26) with fresh symbols all_49_0, all_49_1, all_49_2 % 16.86/3.24 | gives: % 16.86/3.24 | (28) one_to_one(all_35_7) = all_49_0 & function(all_35_7) = all_49_1 & % 16.86/3.24 | empty(all_35_7) = all_49_2 & ( ~ (all_49_1 = 0) | ~ (all_49_2 = 0) | % 16.86/3.24 | all_49_0 = 0) % 16.86/3.24 | % 16.86/3.24 | ALPHA: (28) implies: % 16.86/3.24 | (29) one_to_one(all_35_7) = all_49_0 % 16.86/3.24 | % 16.86/3.24 | DELTA: instantiating (24) with fresh symbols all_65_0, all_65_1, all_65_2 % 16.86/3.24 | gives: % 16.86/3.24 | (30) relation_dom(all_35_7) = all_65_1 & relation_rng(all_35_7) = all_65_0 % 16.86/3.24 | & relation_field(all_35_7) = all_65_2 & set_union2(all_65_1, all_65_0) % 16.86/3.24 | = all_65_2 & $i(all_65_0) & $i(all_65_1) & $i(all_65_2) % 16.86/3.24 | % 16.86/3.24 | ALPHA: (30) implies: % 16.86/3.24 | (31) $i(all_65_1) % 16.86/3.24 | (32) $i(all_65_0) % 16.86/3.24 | (33) set_union2(all_65_1, all_65_0) = all_65_2 % 16.86/3.24 | (34) relation_field(all_35_7) = all_65_2 % 16.86/3.24 | % 16.86/3.24 | DELTA: instantiating (25) with fresh symbols all_73_0, all_73_1, all_73_2 % 16.86/3.24 | gives: % 16.86/3.24 | (35) relation_field(all_35_7) = all_73_1 & antisymmetric(all_35_7) = % 16.86/3.24 | all_73_2 & is_antisymmetric_in(all_35_7, all_73_1) = all_73_0 & % 16.86/3.24 | $i(all_73_1) & ( ~ (all_73_0 = 0) | all_73_2 = 0) & ( ~ (all_73_2 = 0) % 16.86/3.24 | | all_73_0 = 0) % 16.86/3.24 | % 16.86/3.24 | ALPHA: (35) implies: % 16.86/3.24 | (36) is_antisymmetric_in(all_35_7, all_73_1) = all_73_0 % 16.86/3.24 | (37) antisymmetric(all_35_7) = all_73_2 % 16.86/3.24 | (38) relation_field(all_35_7) = all_73_1 % 16.86/3.24 | % 16.86/3.24 | DELTA: instantiating (27) with fresh symbols all_81_0, all_81_1, all_81_2 % 16.86/3.24 | gives: % 16.86/3.24 | (39) relation_field(all_35_7) = all_81_1 & is_antisymmetric_in(all_35_7, % 16.86/3.24 | all_81_1) = all_81_0 & relation(all_35_7) = all_81_2 & $i(all_81_1) % 16.86/3.24 | & ( ~ (all_81_2 = 0) | (( ~ (all_81_0 = 0) | all_35_6 = 0) & ( ~ % 16.86/3.24 | (all_35_6 = 0) | all_81_0 = 0))) % 16.86/3.24 | % 16.86/3.24 | ALPHA: (39) implies: % 16.86/3.24 | (40) relation(all_35_7) = all_81_2 % 16.86/3.24 | (41) is_antisymmetric_in(all_35_7, all_81_1) = all_81_0 % 16.86/3.24 | (42) relation_field(all_35_7) = all_81_1 % 16.86/3.24 | % 16.86/3.24 | GROUND_INST: instantiating (11) with 0, all_81_2, all_35_7, simplifying with % 16.86/3.24 | (21), (40) gives: % 16.86/3.24 | (43) all_81_2 = 0 % 16.86/3.24 | % 16.86/3.24 | GROUND_INST: instantiating (12) with all_35_6, all_73_2, all_35_7, simplifying % 16.86/3.24 | with (22), (37) gives: % 16.86/3.24 | (44) all_73_2 = all_35_6 % 16.86/3.24 | % 16.86/3.24 | GROUND_INST: instantiating (13) with all_73_1, all_81_1, all_35_7, simplifying % 16.86/3.24 | with (38), (42) gives: % 16.86/3.24 | (45) all_81_1 = all_73_1 % 16.86/3.24 | % 16.86/3.24 | GROUND_INST: instantiating (13) with all_65_2, all_81_1, all_35_7, simplifying % 16.86/3.24 | with (34), (42) gives: % 16.86/3.24 | (46) all_81_1 = all_65_2 % 16.86/3.24 | % 16.86/3.24 | COMBINE_EQS: (45), (46) imply: % 16.86/3.24 | (47) all_73_1 = all_65_2 % 16.86/3.24 | % 16.86/3.24 | SIMP: (47) implies: % 16.86/3.24 | (48) all_73_1 = all_65_2 % 16.86/3.24 | % 16.86/3.24 | REDUCE: (41), (46) imply: % 16.86/3.24 | (49) is_antisymmetric_in(all_35_7, all_65_2) = all_81_0 % 16.86/3.24 | % 16.86/3.24 | REDUCE: (36), (48) imply: % 16.86/3.24 | (50) is_antisymmetric_in(all_35_7, all_65_2) = all_73_0 % 16.86/3.24 | % 16.86/3.24 | GROUND_INST: instantiating (15) with all_73_0, all_81_0, all_65_2, all_35_7, % 16.86/3.24 | simplifying with (49), (50) gives: % 16.86/3.24 | (51) all_81_0 = all_73_0 % 16.86/3.24 | % 16.86/3.24 | GROUND_INST: instantiating (2) with all_35_7, all_49_0, simplifying with (18), % 16.86/3.24 | (29) gives: % 16.86/3.24 | (52) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_35_7) = v0 % 16.86/3.24 | & function(all_35_7) = v2 & empty(all_35_7) = v1 & ( ~ (v2 = 0) | ~ % 16.86/3.24 | (v1 = 0) | ~ (v0 = 0) | all_49_0 = 0)) % 16.86/3.24 | % 16.86/3.24 | GROUND_INST: instantiating (3) with all_65_0, all_65_1, all_65_2, simplifying % 16.86/3.24 | with (31), (32), (33) gives: % 16.86/3.24 | (53) set_union2(all_65_0, all_65_1) = all_65_2 & $i(all_65_2) % 16.86/3.24 | % 16.86/3.24 | ALPHA: (53) implies: % 16.86/3.24 | (54) $i(all_65_2) % 16.86/3.24 | % 16.86/3.24 | GROUND_INST: instantiating (7) with all_35_7, all_65_2, all_73_0, simplifying % 16.86/3.24 | with (18), (21), (50), (54) gives: % 16.86/3.24 | (55) all_73_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 16.86/3.24 | ( ~ (v1 = v0) & ordered_pair(v1, v0) = v3 & ordered_pair(v0, v1) = v2 % 16.86/3.25 | & in(v3, all_35_7) = 0 & in(v2, all_35_7) = 0 & in(v1, all_65_2) = 0 % 16.86/3.25 | & in(v0, all_65_2) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.86/3.25 | % 16.86/3.25 | GROUND_INST: instantiating (6) with all_35_7, all_65_2, simplifying with (18), % 16.86/3.25 | (34) gives: % 16.86/3.25 | (56) ? [v0: any] : ? [v1: any] : ? [v2: any] : (antisymmetric(all_35_7) % 16.86/3.25 | = v1 & is_antisymmetric_in(all_35_7, all_65_2) = v2 & % 16.86/3.25 | relation(all_35_7) = v0 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 = 0) & ( % 16.86/3.25 | ~ (v1 = 0) | v2 = 0)))) % 16.86/3.25 | % 16.86/3.25 | DELTA: instantiating (52) with fresh symbols all_133_0, all_133_1, all_133_2 % 16.86/3.25 | gives: % 16.86/3.25 | (57) relation(all_35_7) = all_133_2 & function(all_35_7) = all_133_0 & % 16.86/3.25 | empty(all_35_7) = all_133_1 & ( ~ (all_133_0 = 0) | ~ (all_133_1 = 0) % 16.86/3.25 | | ~ (all_133_2 = 0) | all_49_0 = 0) % 16.86/3.25 | % 16.86/3.25 | ALPHA: (57) implies: % 16.86/3.25 | (58) relation(all_35_7) = all_133_2 % 16.86/3.25 | % 16.86/3.25 | DELTA: instantiating (56) with fresh symbols all_137_0, all_137_1, all_137_2 % 16.86/3.25 | gives: % 16.86/3.25 | (59) antisymmetric(all_35_7) = all_137_1 & is_antisymmetric_in(all_35_7, % 16.86/3.25 | all_65_2) = all_137_0 & relation(all_35_7) = all_137_2 & ( ~ % 16.86/3.25 | (all_137_2 = 0) | (( ~ (all_137_0 = 0) | all_137_1 = 0) & ( ~ % 16.86/3.25 | (all_137_1 = 0) | all_137_0 = 0))) % 16.86/3.25 | % 16.86/3.25 | ALPHA: (59) implies: % 16.86/3.25 | (60) relation(all_35_7) = all_137_2 % 16.86/3.25 | (61) is_antisymmetric_in(all_35_7, all_65_2) = all_137_0 % 16.86/3.25 | (62) antisymmetric(all_35_7) = all_137_1 % 16.86/3.25 | (63) ~ (all_137_2 = 0) | (( ~ (all_137_0 = 0) | all_137_1 = 0) & ( ~ % 16.86/3.25 | (all_137_1 = 0) | all_137_0 = 0)) % 16.86/3.25 | % 16.86/3.25 | GROUND_INST: instantiating (11) with 0, all_137_2, all_35_7, simplifying with % 16.86/3.25 | (21), (60) gives: % 16.86/3.25 | (64) all_137_2 = 0 % 16.86/3.25 | % 16.86/3.25 | GROUND_INST: instantiating (11) with all_133_2, all_137_2, all_35_7, % 16.86/3.25 | simplifying with (58), (60) gives: % 16.86/3.25 | (65) all_137_2 = all_133_2 % 16.86/3.25 | % 16.86/3.25 | GROUND_INST: instantiating (15) with all_73_0, all_137_0, all_65_2, all_35_7, % 16.86/3.25 | simplifying with (50), (61) gives: % 16.86/3.25 | (66) all_137_0 = all_73_0 % 16.86/3.25 | % 16.86/3.25 | GROUND_INST: instantiating (12) with all_35_6, all_137_1, all_35_7, % 16.86/3.25 | simplifying with (22), (62) gives: % 16.86/3.25 | (67) all_137_1 = all_35_6 % 16.86/3.25 | % 16.86/3.25 | COMBINE_EQS: (64), (65) imply: % 16.86/3.25 | (68) all_133_2 = 0 % 16.86/3.25 | % 16.86/3.25 | BETA: splitting (23) gives: % 16.86/3.25 | % 16.86/3.25 | Case 1: % 16.86/3.25 | | % 16.86/3.25 | | (69) all_35_0 = 0 & all_35_2 = 0 & all_35_6 = 0 & ~ (all_35_4 = % 16.86/3.25 | | all_35_5) & ordered_pair(all_35_4, all_35_5) = all_35_1 & % 16.86/3.25 | | ordered_pair(all_35_5, all_35_4) = all_35_3 & in(all_35_1, all_35_7) % 16.86/3.25 | | = 0 & in(all_35_3, all_35_7) = 0 & $i(all_35_1) & $i(all_35_3) % 16.86/3.25 | | % 16.86/3.25 | | ALPHA: (69) implies: % 16.86/3.25 | | (70) all_35_6 = 0 % 16.86/3.25 | | (71) ~ (all_35_4 = all_35_5) % 16.86/3.25 | | (72) in(all_35_3, all_35_7) = 0 % 16.86/3.25 | | (73) in(all_35_1, all_35_7) = 0 % 16.86/3.25 | | (74) ordered_pair(all_35_5, all_35_4) = all_35_3 % 16.86/3.25 | | (75) ordered_pair(all_35_4, all_35_5) = all_35_1 % 16.86/3.25 | | % 16.86/3.25 | | COMBINE_EQS: (67), (70) imply: % 16.86/3.25 | | (76) all_137_1 = 0 % 16.86/3.25 | | % 16.86/3.25 | | BETA: splitting (63) gives: % 16.86/3.25 | | % 16.86/3.25 | | Case 1: % 16.86/3.25 | | | % 16.86/3.25 | | | (77) ~ (all_137_2 = 0) % 16.86/3.25 | | | % 16.86/3.25 | | | REDUCE: (64), (77) imply: % 16.86/3.25 | | | (78) $false % 16.86/3.25 | | | % 16.86/3.25 | | | CLOSE: (78) is inconsistent. % 16.86/3.25 | | | % 16.86/3.25 | | Case 2: % 16.86/3.25 | | | % 16.86/3.25 | | | (79) ( ~ (all_137_0 = 0) | all_137_1 = 0) & ( ~ (all_137_1 = 0) | % 16.86/3.25 | | | all_137_0 = 0) % 16.86/3.25 | | | % 16.86/3.25 | | | ALPHA: (79) implies: % 16.86/3.25 | | | (80) ~ (all_137_1 = 0) | all_137_0 = 0 % 16.86/3.25 | | | % 16.86/3.25 | | | BETA: splitting (80) gives: % 16.86/3.25 | | | % 16.86/3.25 | | | Case 1: % 16.86/3.25 | | | | % 16.86/3.25 | | | | (81) ~ (all_137_1 = 0) % 16.86/3.25 | | | | % 16.86/3.25 | | | | REDUCE: (76), (81) imply: % 16.86/3.26 | | | | (82) $false % 16.86/3.26 | | | | % 16.86/3.26 | | | | CLOSE: (82) is inconsistent. % 16.86/3.26 | | | | % 16.86/3.26 | | | Case 2: % 16.86/3.26 | | | | % 16.86/3.26 | | | | (83) all_137_0 = 0 % 16.86/3.26 | | | | % 16.86/3.26 | | | | COMBINE_EQS: (66), (83) imply: % 16.86/3.26 | | | | (84) all_73_0 = 0 % 16.86/3.26 | | | | % 16.86/3.26 | | | | SIMP: (84) implies: % 16.86/3.26 | | | | (85) all_73_0 = 0 % 16.86/3.26 | | | | % 16.86/3.26 | | | | REDUCE: (50), (85) imply: % 16.86/3.26 | | | | (86) is_antisymmetric_in(all_35_7, all_65_2) = 0 % 16.86/3.26 | | | | % 16.86/3.26 | | | | GROUND_INST: instantiating (9) with all_35_7, all_65_2, all_35_4, % 16.86/3.26 | | | | all_35_5, all_35_3, simplifying with (18), (19), (20), % 16.86/3.26 | | | | (21), (54), (74), (86) gives: % 16.86/3.26 | | | | (87) all_35_4 = all_35_5 | ? [v0: any] : ? [v1: any] : ? [v2: $i] % 16.86/3.26 | | | | : ? [v3: any] : ? [v4: any] : (ordered_pair(all_35_4, % 16.86/3.26 | | | | all_35_5) = v2 & in(v2, all_35_7) = v3 & in(all_35_3, % 16.86/3.26 | | | | all_35_7) = v4 & in(all_35_4, all_65_2) = v0 & in(all_35_5, % 16.86/3.26 | | | | all_65_2) = v1 & $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ % 16.86/3.26 | | | | (v1 = 0) | ~ (v0 = 0))) % 16.86/3.26 | | | | % 16.86/3.26 | | | | GROUND_INST: instantiating (8) with all_35_7, all_65_2, all_35_5, % 16.86/3.26 | | | | all_35_4, all_35_3, simplifying with (18), (19), (20), % 16.86/3.26 | | | | (21), (54), (74), (86) gives: % 16.86/3.26 | | | | (88) all_35_4 = all_35_5 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 16.86/3.26 | | | | : ? [v3: $i] : ? [v4: any] : (ordered_pair(all_35_4, all_35_5) % 16.86/3.26 | | | | = v3 & in(v3, all_35_7) = v4 & in(all_35_3, all_35_7) = v2 & % 16.86/3.26 | | | | in(all_35_4, all_65_2) = v1 & in(all_35_5, all_65_2) = v0 & % 16.86/3.26 | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 16.86/3.26 | | | | 0))) % 16.86/3.26 | | | | % 16.86/3.26 | | | | GROUND_INST: instantiating (t30_relat_1) with all_35_5, all_35_4, % 16.86/3.26 | | | | all_35_7, all_35_3, simplifying with (18), (19), (20), % 16.86/3.26 | | | | (72), (74) gives: % 16.86/3.26 | | | | (89) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 16.86/3.26 | | | | (relation_field(all_35_7) = v1 & relation(all_35_7) = v0 & % 16.86/3.26 | | | | in(all_35_4, v1) = v3 & in(all_35_5, v1) = v2 & $i(v1) & ( ~ % 16.86/3.26 | | | | (v0 = 0) | (v3 = 0 & v2 = 0))) % 16.86/3.26 | | | | % 16.86/3.26 | | | | GROUND_INST: instantiating (9) with all_35_7, all_65_2, all_35_5, % 16.86/3.26 | | | | all_35_4, all_35_1, simplifying with (18), (19), (20), % 16.86/3.26 | | | | (21), (54), (75), (86) gives: % 16.86/3.26 | | | | (90) all_35_4 = all_35_5 | ? [v0: any] : ? [v1: any] : ? [v2: $i] % 16.86/3.26 | | | | : ? [v3: any] : ? [v4: any] : (ordered_pair(all_35_5, % 16.86/3.26 | | | | all_35_4) = v2 & in(v2, all_35_7) = v3 & in(all_35_1, % 16.86/3.26 | | | | all_35_7) = v4 & in(all_35_4, all_65_2) = v1 & in(all_35_5, % 16.86/3.26 | | | | all_65_2) = v0 & $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ % 16.86/3.26 | | | | (v1 = 0) | ~ (v0 = 0))) % 16.86/3.26 | | | | % 16.86/3.26 | | | | GROUND_INST: instantiating (8) with all_35_7, all_65_2, all_35_4, % 16.86/3.26 | | | | all_35_5, all_35_1, simplifying with (18), (19), (20), % 16.86/3.26 | | | | (21), (54), (75), (86) gives: % 16.86/3.26 | | | | (91) all_35_4 = all_35_5 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 16.86/3.26 | | | | : ? [v3: $i] : ? [v4: any] : (ordered_pair(all_35_5, all_35_4) % 16.86/3.26 | | | | = v3 & in(v3, all_35_7) = v4 & in(all_35_1, all_35_7) = v2 & % 16.86/3.26 | | | | in(all_35_4, all_65_2) = v0 & in(all_35_5, all_65_2) = v1 & % 16.86/3.26 | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 16.86/3.26 | | | | 0))) % 16.86/3.26 | | | | % 16.86/3.26 | | | | GROUND_INST: instantiating (t30_relat_1) with all_35_4, all_35_5, % 16.86/3.26 | | | | all_35_7, all_35_1, simplifying with (18), (19), (20), % 16.86/3.26 | | | | (73), (75) gives: % 16.86/3.26 | | | | (92) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 16.86/3.26 | | | | (relation_field(all_35_7) = v1 & relation(all_35_7) = v0 & % 16.86/3.26 | | | | in(all_35_4, v1) = v2 & in(all_35_5, v1) = v3 & $i(v1) & ( ~ % 16.86/3.26 | | | | (v0 = 0) | (v3 = 0 & v2 = 0))) % 16.86/3.26 | | | | % 16.86/3.26 | | | | DELTA: instantiating (89) with fresh symbols all_250_0, all_250_1, % 16.86/3.26 | | | | all_250_2, all_250_3 gives: % 16.86/3.26 | | | | (93) relation_field(all_35_7) = all_250_2 & relation(all_35_7) = % 16.86/3.26 | | | | all_250_3 & in(all_35_4, all_250_2) = all_250_0 & in(all_35_5, % 16.86/3.26 | | | | all_250_2) = all_250_1 & $i(all_250_2) & ( ~ (all_250_3 = 0) | % 16.86/3.26 | | | | (all_250_0 = 0 & all_250_1 = 0)) % 16.86/3.26 | | | | % 16.86/3.27 | | | | ALPHA: (93) implies: % 16.86/3.27 | | | | (94) in(all_35_5, all_250_2) = all_250_1 % 16.86/3.27 | | | | (95) in(all_35_4, all_250_2) = all_250_0 % 16.86/3.27 | | | | (96) relation(all_35_7) = all_250_3 % 16.86/3.27 | | | | (97) relation_field(all_35_7) = all_250_2 % 16.86/3.27 | | | | (98) ~ (all_250_3 = 0) | (all_250_0 = 0 & all_250_1 = 0) % 16.86/3.27 | | | | % 16.86/3.27 | | | | DELTA: instantiating (92) with fresh symbols all_252_0, all_252_1, % 16.86/3.27 | | | | all_252_2, all_252_3 gives: % 16.86/3.27 | | | | (99) relation_field(all_35_7) = all_252_2 & relation(all_35_7) = % 16.86/3.27 | | | | all_252_3 & in(all_35_4, all_252_2) = all_252_1 & in(all_35_5, % 16.86/3.27 | | | | all_252_2) = all_252_0 & $i(all_252_2) & ( ~ (all_252_3 = 0) | % 16.86/3.27 | | | | (all_252_0 = 0 & all_252_1 = 0)) % 16.86/3.27 | | | | % 16.86/3.27 | | | | ALPHA: (99) implies: % 16.86/3.27 | | | | (100) relation(all_35_7) = all_252_3 % 16.86/3.27 | | | | (101) relation_field(all_35_7) = all_252_2 % 16.86/3.27 | | | | % 16.86/3.27 | | | | BETA: splitting (91) gives: % 16.86/3.27 | | | | % 16.86/3.27 | | | | Case 1: % 16.86/3.27 | | | | | % 16.86/3.27 | | | | | (102) all_35_4 = all_35_5 % 16.86/3.27 | | | | | % 16.86/3.27 | | | | | REDUCE: (71), (102) imply: % 16.86/3.27 | | | | | (103) $false % 16.86/3.27 | | | | | % 16.86/3.27 | | | | | CLOSE: (103) is inconsistent. % 16.86/3.27 | | | | | % 16.86/3.27 | | | | Case 2: % 16.86/3.27 | | | | | % 16.86/3.27 | | | | | (104) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? % 16.86/3.27 | | | | | [v4: any] : (ordered_pair(all_35_5, all_35_4) = v3 & in(v3, % 16.86/3.27 | | | | | all_35_7) = v4 & in(all_35_1, all_35_7) = v2 & % 16.86/3.27 | | | | | in(all_35_4, all_65_2) = v0 & in(all_35_5, all_65_2) = v1 & % 16.86/3.27 | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 % 16.86/3.27 | | | | | = 0))) % 16.86/3.27 | | | | | % 16.86/3.27 | | | | | DELTA: instantiating (104) with fresh symbols all_258_0, all_258_1, % 16.86/3.27 | | | | | all_258_2, all_258_3, all_258_4 gives: % 16.86/3.27 | | | | | (105) ordered_pair(all_35_5, all_35_4) = all_258_1 & in(all_258_1, % 16.86/3.27 | | | | | all_35_7) = all_258_0 & in(all_35_1, all_35_7) = all_258_2 % 16.86/3.27 | | | | | & in(all_35_4, all_65_2) = all_258_4 & in(all_35_5, all_65_2) % 16.86/3.27 | | | | | = all_258_3 & $i(all_258_1) & ( ~ (all_258_0 = 0) | ~ % 16.86/3.27 | | | | | (all_258_2 = 0) | ~ (all_258_3 = 0) | ~ (all_258_4 = 0)) % 16.86/3.27 | | | | | % 16.86/3.27 | | | | | ALPHA: (105) implies: % 16.86/3.27 | | | | | (106) in(all_35_5, all_65_2) = all_258_3 % 16.86/3.27 | | | | | (107) in(all_35_4, all_65_2) = all_258_4 % 16.86/3.27 | | | | | (108) in(all_35_1, all_35_7) = all_258_2 % 16.86/3.27 | | | | | % 16.86/3.27 | | | | | BETA: splitting (88) gives: % 16.86/3.27 | | | | | % 16.86/3.27 | | | | | Case 1: % 16.86/3.27 | | | | | | % 16.86/3.27 | | | | | | (109) all_35_4 = all_35_5 % 16.86/3.27 | | | | | | % 16.86/3.27 | | | | | | REDUCE: (71), (109) imply: % 16.86/3.27 | | | | | | (110) $false % 16.86/3.27 | | | | | | % 16.86/3.27 | | | | | | CLOSE: (110) is inconsistent. % 16.86/3.27 | | | | | | % 16.86/3.27 | | | | | Case 2: % 16.86/3.27 | | | | | | % 16.86/3.27 | | | | | | (111) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : % 16.86/3.27 | | | | | | ? [v4: any] : (ordered_pair(all_35_4, all_35_5) = v3 & % 16.86/3.27 | | | | | | in(v3, all_35_7) = v4 & in(all_35_3, all_35_7) = v2 & % 16.86/3.27 | | | | | | in(all_35_4, all_65_2) = v1 & in(all_35_5, all_65_2) = v0 % 16.86/3.27 | | | | | | & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ % 16.86/3.27 | | | | | | (v0 = 0))) % 16.86/3.27 | | | | | | % 16.86/3.27 | | | | | | DELTA: instantiating (111) with fresh symbols all_263_0, all_263_1, % 16.86/3.27 | | | | | | all_263_2, all_263_3, all_263_4 gives: % 16.86/3.27 | | | | | | (112) ordered_pair(all_35_4, all_35_5) = all_263_1 & % 16.86/3.27 | | | | | | in(all_263_1, all_35_7) = all_263_0 & in(all_35_3, % 16.86/3.27 | | | | | | all_35_7) = all_263_2 & in(all_35_4, all_65_2) = % 16.86/3.27 | | | | | | all_263_3 & in(all_35_5, all_65_2) = all_263_4 & % 16.86/3.27 | | | | | | $i(all_263_1) & ( ~ (all_263_0 = 0) | ~ (all_263_2 = 0) | % 16.86/3.27 | | | | | | ~ (all_263_3 = 0) | ~ (all_263_4 = 0)) % 16.86/3.27 | | | | | | % 16.86/3.27 | | | | | | ALPHA: (112) implies: % 16.86/3.27 | | | | | | (113) in(all_35_5, all_65_2) = all_263_4 % 16.86/3.27 | | | | | | (114) in(all_35_4, all_65_2) = all_263_3 % 16.86/3.27 | | | | | | (115) in(all_35_3, all_35_7) = all_263_2 % 16.86/3.27 | | | | | | (116) in(all_263_1, all_35_7) = all_263_0 % 16.86/3.27 | | | | | | (117) ordered_pair(all_35_4, all_35_5) = all_263_1 % 16.86/3.27 | | | | | | % 16.86/3.27 | | | | | | BETA: splitting (90) gives: % 16.86/3.27 | | | | | | % 16.86/3.27 | | | | | | Case 1: % 16.86/3.27 | | | | | | | % 16.86/3.27 | | | | | | | (118) all_35_4 = all_35_5 % 16.86/3.27 | | | | | | | % 16.86/3.27 | | | | | | | REDUCE: (71), (118) imply: % 16.86/3.27 | | | | | | | (119) $false % 16.86/3.27 | | | | | | | % 16.86/3.27 | | | | | | | CLOSE: (119) is inconsistent. % 16.86/3.27 | | | | | | | % 16.86/3.27 | | | | | | Case 2: % 16.86/3.27 | | | | | | | % 16.86/3.27 | | | | | | | (120) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] % 16.86/3.27 | | | | | | | : ? [v4: any] : (ordered_pair(all_35_5, all_35_4) = v2 & % 16.86/3.27 | | | | | | | in(v2, all_35_7) = v3 & in(all_35_1, all_35_7) = v4 & % 16.86/3.27 | | | | | | | in(all_35_4, all_65_2) = v1 & in(all_35_5, all_65_2) = % 16.86/3.27 | | | | | | | v0 & $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v1 = 0) % 16.86/3.27 | | | | | | | | ~ (v0 = 0))) % 16.86/3.27 | | | | | | | % 16.86/3.27 | | | | | | | DELTA: instantiating (120) with fresh symbols all_268_0, % 16.86/3.27 | | | | | | | all_268_1, all_268_2, all_268_3, all_268_4 gives: % 16.86/3.27 | | | | | | | (121) ordered_pair(all_35_5, all_35_4) = all_268_2 & % 16.86/3.27 | | | | | | | in(all_268_2, all_35_7) = all_268_1 & in(all_35_1, % 16.86/3.27 | | | | | | | all_35_7) = all_268_0 & in(all_35_4, all_65_2) = % 16.86/3.27 | | | | | | | all_268_3 & in(all_35_5, all_65_2) = all_268_4 & % 16.86/3.27 | | | | | | | $i(all_268_2) & ( ~ (all_268_0 = 0) | ~ (all_268_1 = 0) % 16.86/3.27 | | | | | | | | ~ (all_268_3 = 0) | ~ (all_268_4 = 0)) % 16.86/3.27 | | | | | | | % 16.86/3.27 | | | | | | | ALPHA: (121) implies: % 16.86/3.27 | | | | | | | (122) in(all_35_5, all_65_2) = all_268_4 % 16.86/3.27 | | | | | | | (123) in(all_35_4, all_65_2) = all_268_3 % 16.86/3.27 | | | | | | | (124) in(all_35_1, all_35_7) = all_268_0 % 16.86/3.27 | | | | | | | % 16.86/3.27 | | | | | | | BETA: splitting (87) gives: % 16.86/3.27 | | | | | | | % 16.86/3.27 | | | | | | | Case 1: % 16.86/3.27 | | | | | | | | % 16.86/3.27 | | | | | | | | (125) all_35_4 = all_35_5 % 16.86/3.27 | | | | | | | | % 16.86/3.27 | | | | | | | | REDUCE: (71), (125) imply: % 16.86/3.27 | | | | | | | | (126) $false % 16.86/3.27 | | | | | | | | % 16.86/3.27 | | | | | | | | CLOSE: (126) is inconsistent. % 16.86/3.27 | | | | | | | | % 16.86/3.27 | | | | | | | Case 2: % 16.86/3.27 | | | | | | | | % 16.86/3.28 | | | | | | | | (127) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: % 16.86/3.28 | | | | | | | | any] : ? [v4: any] : (ordered_pair(all_35_4, % 16.86/3.28 | | | | | | | | all_35_5) = v2 & in(v2, all_35_7) = v3 & % 16.86/3.28 | | | | | | | | in(all_35_3, all_35_7) = v4 & in(all_35_4, all_65_2) % 16.86/3.28 | | | | | | | | = v0 & in(all_35_5, all_65_2) = v1 & $i(v2) & ( ~ (v4 % 16.86/3.28 | | | | | | | | = 0) | ~ (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 16.86/3.28 | | | | | | | | % 16.86/3.28 | | | | | | | | DELTA: instantiating (127) with fresh symbols all_273_0, % 16.86/3.28 | | | | | | | | all_273_1, all_273_2, all_273_3, all_273_4 gives: % 17.21/3.28 | | | | | | | | (128) ordered_pair(all_35_4, all_35_5) = all_273_2 & % 17.21/3.28 | | | | | | | | in(all_273_2, all_35_7) = all_273_1 & in(all_35_3, % 17.21/3.28 | | | | | | | | all_35_7) = all_273_0 & in(all_35_4, all_65_2) = % 17.21/3.28 | | | | | | | | all_273_4 & in(all_35_5, all_65_2) = all_273_3 & % 17.21/3.28 | | | | | | | | $i(all_273_2) & ( ~ (all_273_0 = 0) | ~ (all_273_1 = % 17.21/3.28 | | | | | | | | 0) | ~ (all_273_3 = 0) | ~ (all_273_4 = 0)) % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | ALPHA: (128) implies: % 17.21/3.28 | | | | | | | | (129) in(all_35_5, all_65_2) = all_273_3 % 17.21/3.28 | | | | | | | | (130) in(all_35_4, all_65_2) = all_273_4 % 17.21/3.28 | | | | | | | | (131) in(all_35_3, all_35_7) = all_273_0 % 17.21/3.28 | | | | | | | | (132) in(all_273_2, all_35_7) = all_273_1 % 17.21/3.28 | | | | | | | | (133) ordered_pair(all_35_4, all_35_5) = all_273_2 % 17.21/3.28 | | | | | | | | (134) ~ (all_273_0 = 0) | ~ (all_273_1 = 0) | ~ (all_273_3 % 17.21/3.28 | | | | | | | | = 0) | ~ (all_273_4 = 0) % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (14) with all_263_4, all_268_4, % 17.21/3.28 | | | | | | | | all_65_2, all_35_5, simplifying with (113), (122) % 17.21/3.28 | | | | | | | | gives: % 17.21/3.28 | | | | | | | | (135) all_268_4 = all_263_4 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (14) with all_268_4, all_273_3, % 17.21/3.28 | | | | | | | | all_65_2, all_35_5, simplifying with (122), (129) % 17.21/3.28 | | | | | | | | gives: % 17.21/3.28 | | | | | | | | (136) all_273_3 = all_268_4 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (14) with all_258_3, all_273_3, % 17.21/3.28 | | | | | | | | all_65_2, all_35_5, simplifying with (106), (129) % 17.21/3.28 | | | | | | | | gives: % 17.21/3.28 | | | | | | | | (137) all_273_3 = all_258_3 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (14) with all_263_3, all_268_3, % 17.21/3.28 | | | | | | | | all_65_2, all_35_4, simplifying with (114), (123) % 17.21/3.28 | | | | | | | | gives: % 17.21/3.28 | | | | | | | | (138) all_268_3 = all_263_3 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (14) with all_268_3, all_273_4, % 17.21/3.28 | | | | | | | | all_65_2, all_35_4, simplifying with (123), (130) % 17.21/3.28 | | | | | | | | gives: % 17.21/3.28 | | | | | | | | (139) all_273_4 = all_268_3 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (14) with all_258_4, all_273_4, % 17.21/3.28 | | | | | | | | all_65_2, all_35_4, simplifying with (107), (130) % 17.21/3.28 | | | | | | | | gives: % 17.21/3.28 | | | | | | | | (140) all_273_4 = all_258_4 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_273_0, all_35_7, % 17.21/3.28 | | | | | | | | all_35_3, simplifying with (72), (131) gives: % 17.21/3.28 | | | | | | | | (141) all_273_0 = 0 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (14) with all_263_2, all_273_0, % 17.21/3.28 | | | | | | | | all_35_7, all_35_3, simplifying with (115), (131) % 17.21/3.28 | | | | | | | | gives: % 17.21/3.28 | | | | | | | | (142) all_273_0 = all_263_2 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_268_0, all_35_7, % 17.21/3.28 | | | | | | | | all_35_1, simplifying with (73), (124) gives: % 17.21/3.28 | | | | | | | | (143) all_268_0 = 0 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (14) with all_258_2, all_268_0, % 17.21/3.28 | | | | | | | | all_35_7, all_35_1, simplifying with (108), (124) % 17.21/3.28 | | | | | | | | gives: % 17.21/3.28 | | | | | | | | (144) all_268_0 = all_258_2 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (11) with 0, all_252_3, all_35_7, % 17.21/3.28 | | | | | | | | simplifying with (21), (100) gives: % 17.21/3.28 | | | | | | | | (145) all_252_3 = 0 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (11) with all_250_3, all_252_3, % 17.21/3.28 | | | | | | | | all_35_7, simplifying with (96), (100) gives: % 17.21/3.28 | | | | | | | | (146) all_252_3 = all_250_3 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (13) with all_65_2, all_252_2, % 17.21/3.28 | | | | | | | | all_35_7, simplifying with (34), (101) gives: % 17.21/3.28 | | | | | | | | (147) all_252_2 = all_65_2 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (13) with all_250_2, all_252_2, % 17.21/3.28 | | | | | | | | all_35_7, simplifying with (97), (101) gives: % 17.21/3.28 | | | | | | | | (148) all_252_2 = all_250_2 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (16) with all_35_1, all_273_2, % 17.21/3.28 | | | | | | | | all_35_5, all_35_4, simplifying with (75), (133) % 17.21/3.28 | | | | | | | | gives: % 17.21/3.28 | | | | | | | | (149) all_273_2 = all_35_1 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | GROUND_INST: instantiating (16) with all_263_1, all_273_2, % 17.21/3.28 | | | | | | | | all_35_5, all_35_4, simplifying with (117), (133) % 17.21/3.28 | | | | | | | | gives: % 17.21/3.28 | | | | | | | | (150) all_273_2 = all_263_1 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | COMBINE_EQS: (141), (142) imply: % 17.21/3.28 | | | | | | | | (151) all_263_2 = 0 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | COMBINE_EQS: (149), (150) imply: % 17.21/3.28 | | | | | | | | (152) all_263_1 = all_35_1 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | SIMP: (152) implies: % 17.21/3.28 | | | | | | | | (153) all_263_1 = all_35_1 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | COMBINE_EQS: (136), (137) imply: % 17.21/3.28 | | | | | | | | (154) all_268_4 = all_258_3 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | SIMP: (154) implies: % 17.21/3.28 | | | | | | | | (155) all_268_4 = all_258_3 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | COMBINE_EQS: (139), (140) imply: % 17.21/3.28 | | | | | | | | (156) all_268_3 = all_258_4 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | SIMP: (156) implies: % 17.21/3.28 | | | | | | | | (157) all_268_3 = all_258_4 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | COMBINE_EQS: (143), (144) imply: % 17.21/3.28 | | | | | | | | (158) all_258_2 = 0 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | COMBINE_EQS: (138), (157) imply: % 17.21/3.28 | | | | | | | | (159) all_263_3 = all_258_4 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | COMBINE_EQS: (135), (155) imply: % 17.21/3.28 | | | | | | | | (160) all_263_4 = all_258_3 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | SIMP: (160) implies: % 17.21/3.28 | | | | | | | | (161) all_263_4 = all_258_3 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | COMBINE_EQS: (147), (148) imply: % 17.21/3.28 | | | | | | | | (162) all_250_2 = all_65_2 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | COMBINE_EQS: (145), (146) imply: % 17.21/3.28 | | | | | | | | (163) all_250_3 = 0 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | SIMP: (163) implies: % 17.21/3.28 | | | | | | | | (164) all_250_3 = 0 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | REDUCE: (132), (149) imply: % 17.21/3.28 | | | | | | | | (165) in(all_35_1, all_35_7) = all_273_1 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | REDUCE: (116), (153) imply: % 17.21/3.28 | | | | | | | | (166) in(all_35_1, all_35_7) = all_263_0 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | REDUCE: (95), (162) imply: % 17.21/3.28 | | | | | | | | (167) in(all_35_4, all_65_2) = all_250_0 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | REDUCE: (94), (162) imply: % 17.21/3.28 | | | | | | | | (168) in(all_35_5, all_65_2) = all_250_1 % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | BETA: splitting (98) gives: % 17.21/3.28 | | | | | | | | % 17.21/3.28 | | | | | | | | Case 1: % 17.21/3.28 | | | | | | | | | % 17.21/3.28 | | | | | | | | | (169) ~ (all_250_3 = 0) % 17.21/3.28 | | | | | | | | | % 17.21/3.28 | | | | | | | | | REDUCE: (164), (169) imply: % 17.21/3.28 | | | | | | | | | (170) $false % 17.21/3.28 | | | | | | | | | % 17.21/3.28 | | | | | | | | | CLOSE: (170) is inconsistent. % 17.21/3.28 | | | | | | | | | % 17.21/3.28 | | | | | | | | Case 2: % 17.21/3.28 | | | | | | | | | % 17.21/3.28 | | | | | | | | | (171) all_250_0 = 0 & all_250_1 = 0 % 17.21/3.28 | | | | | | | | | % 17.21/3.28 | | | | | | | | | ALPHA: (171) implies: % 17.21/3.28 | | | | | | | | | (172) all_250_1 = 0 % 17.21/3.28 | | | | | | | | | (173) all_250_0 = 0 % 17.21/3.28 | | | | | | | | | % 17.21/3.28 | | | | | | | | | REDUCE: (167), (173) imply: % 17.21/3.29 | | | | | | | | | (174) in(all_35_4, all_65_2) = 0 % 17.21/3.29 | | | | | | | | | % 17.21/3.29 | | | | | | | | | REDUCE: (168), (172) imply: % 17.21/3.29 | | | | | | | | | (175) in(all_35_5, all_65_2) = 0 % 17.21/3.29 | | | | | | | | | % 17.21/3.29 | | | | | | | | | GROUND_INST: instantiating (14) with all_258_3, 0, all_65_2, % 17.21/3.29 | | | | | | | | | all_35_5, simplifying with (106), (175) gives: % 17.21/3.29 | | | | | | | | | (176) all_258_3 = 0 % 17.21/3.29 | | | | | | | | | % 17.21/3.29 | | | | | | | | | GROUND_INST: instantiating (14) with all_258_4, 0, all_65_2, % 17.21/3.29 | | | | | | | | | all_35_4, simplifying with (107), (174) gives: % 17.21/3.29 | | | | | | | | | (177) all_258_4 = 0 % 17.21/3.29 | | | | | | | | | % 17.21/3.29 | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_273_1, all_35_7, % 17.21/3.29 | | | | | | | | | all_35_1, simplifying with (73), (165) gives: % 17.21/3.29 | | | | | | | | | (178) all_273_1 = 0 % 17.21/3.29 | | | | | | | | | % 17.21/3.29 | | | | | | | | | GROUND_INST: instantiating (14) with all_263_0, all_273_1, % 17.21/3.29 | | | | | | | | | all_35_7, all_35_1, simplifying with (165), (166) % 17.21/3.29 | | | | | | | | | gives: % 17.21/3.29 | | | | | | | | | (179) all_273_1 = all_263_0 % 17.21/3.29 | | | | | | | | | % 17.21/3.29 | | | | | | | | | COMBINE_EQS: (178), (179) imply: % 17.21/3.29 | | | | | | | | | (180) all_263_0 = 0 % 17.21/3.29 | | | | | | | | | % 17.21/3.29 | | | | | | | | | COMBINE_EQS: (140), (177) imply: % 17.21/3.29 | | | | | | | | | (181) all_273_4 = 0 % 17.21/3.29 | | | | | | | | | % 17.21/3.29 | | | | | | | | | COMBINE_EQS: (137), (176) imply: % 17.21/3.29 | | | | | | | | | (182) all_273_3 = 0 % 17.21/3.29 | | | | | | | | | % 17.21/3.29 | | | | | | | | | BETA: splitting (134) gives: % 17.21/3.29 | | | | | | | | | % 17.21/3.29 | | | | | | | | | Case 1: % 17.21/3.29 | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | (183) ~ (all_273_0 = 0) % 17.21/3.29 | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | REDUCE: (141), (183) imply: % 17.21/3.29 | | | | | | | | | | (184) $false % 17.21/3.29 | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | CLOSE: (184) is inconsistent. % 17.21/3.29 | | | | | | | | | | % 17.21/3.29 | | | | | | | | | Case 2: % 17.21/3.29 | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | (185) ~ (all_273_1 = 0) | ~ (all_273_3 = 0) | ~ % 17.21/3.29 | | | | | | | | | | (all_273_4 = 0) % 17.21/3.29 | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | BETA: splitting (185) gives: % 17.21/3.29 | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | Case 1: % 17.21/3.29 | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | (186) ~ (all_273_1 = 0) % 17.21/3.29 | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | REDUCE: (178), (186) imply: % 17.21/3.29 | | | | | | | | | | | (187) $false % 17.21/3.29 | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | CLOSE: (187) is inconsistent. % 17.21/3.29 | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | Case 2: % 17.21/3.29 | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | (188) ~ (all_273_3 = 0) | ~ (all_273_4 = 0) % 17.21/3.29 | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | BETA: splitting (188) gives: % 17.21/3.29 | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | Case 1: % 17.21/3.29 | | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | | (189) ~ (all_273_3 = 0) % 17.21/3.29 | | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | | REDUCE: (182), (189) imply: % 17.21/3.29 | | | | | | | | | | | | (190) $false % 17.21/3.29 | | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | | CLOSE: (190) is inconsistent. % 17.21/3.29 | | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | Case 2: % 17.21/3.29 | | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | | (191) ~ (all_273_4 = 0) % 17.21/3.29 | | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | | REDUCE: (181), (191) imply: % 17.21/3.29 | | | | | | | | | | | | (192) $false % 17.21/3.29 | | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 17.21/3.29 | | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | | End of split % 17.21/3.29 | | | | | | | | | | | % 17.21/3.29 | | | | | | | | | | End of split % 17.21/3.29 | | | | | | | | | | % 17.21/3.29 | | | | | | | | | End of split % 17.21/3.29 | | | | | | | | | % 17.21/3.29 | | | | | | | | End of split % 17.21/3.29 | | | | | | | | % 17.21/3.29 | | | | | | | End of split % 17.21/3.29 | | | | | | | % 17.21/3.29 | | | | | | End of split % 17.21/3.29 | | | | | | % 17.21/3.29 | | | | | End of split % 17.21/3.29 | | | | | % 17.21/3.29 | | | | End of split % 17.21/3.29 | | | | % 17.21/3.29 | | | End of split % 17.21/3.29 | | | % 17.21/3.29 | | End of split % 17.21/3.29 | | % 17.21/3.29 | Case 2: % 17.21/3.29 | | % 17.21/3.29 | | (193) ~ (all_35_6 = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 17.21/3.29 | | v0 | ~ (ordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.21/3.29 | | [v3: $i] : ? [v4: any] : ? [v5: any] : (ordered_pair(v0, v1) = % 17.21/3.29 | | v3 & in(v3, all_35_7) = v4 & in(v2, all_35_7) = v5 & $i(v3) & ( % 17.21/3.29 | | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 17.21/3.29 | | [v2: $i] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | % 17.21/3.29 | | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 17.21/3.29 | | (ordered_pair(v1, v0) = v4 & in(v4, all_35_7) = v5 & in(v2, % 17.21/3.29 | | all_35_7) = v3 & $i(v4) & ( ~ (v5 = 0) | ~ (v3 = 0)))) % 17.21/3.29 | | % 17.21/3.29 | | ALPHA: (193) implies: % 17.21/3.29 | | (194) ~ (all_35_6 = 0) % 17.21/3.29 | | (195) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.21/3.29 | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 17.21/3.29 | | any] : ? [v4: $i] : ? [v5: any] : (ordered_pair(v1, v0) = v4 % 17.21/3.29 | | & in(v4, all_35_7) = v5 & in(v2, all_35_7) = v3 & $i(v4) & ( ~ % 17.21/3.29 | | (v5 = 0) | ~ (v3 = 0)))) % 17.21/3.29 | | (196) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.21/3.29 | | (ordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 17.21/3.29 | | : ? [v4: any] : ? [v5: any] : (ordered_pair(v0, v1) = v3 & % 17.21/3.29 | | in(v3, all_35_7) = v4 & in(v2, all_35_7) = v5 & $i(v3) & ( ~ % 17.21/3.29 | | (v5 = 0) | ~ (v4 = 0)))) % 17.21/3.29 | | % 17.21/3.29 | | BETA: splitting (63) gives: % 17.21/3.29 | | % 17.21/3.29 | | Case 1: % 17.21/3.29 | | | % 17.21/3.29 | | | (197) ~ (all_137_2 = 0) % 17.21/3.29 | | | % 17.21/3.29 | | | REDUCE: (64), (197) imply: % 17.21/3.29 | | | (198) $false % 17.21/3.29 | | | % 17.21/3.29 | | | CLOSE: (198) is inconsistent. % 17.21/3.29 | | | % 17.21/3.29 | | Case 2: % 17.21/3.29 | | | % 17.21/3.29 | | | (199) ( ~ (all_137_0 = 0) | all_137_1 = 0) & ( ~ (all_137_1 = 0) | % 17.21/3.29 | | | all_137_0 = 0) % 17.21/3.29 | | | % 17.21/3.29 | | | ALPHA: (199) implies: % 17.21/3.29 | | | (200) ~ (all_137_0 = 0) | all_137_1 = 0 % 17.21/3.29 | | | % 17.21/3.29 | | | BETA: splitting (200) gives: % 17.21/3.29 | | | % 17.21/3.29 | | | Case 1: % 17.21/3.29 | | | | % 17.21/3.29 | | | | (201) ~ (all_137_0 = 0) % 17.21/3.29 | | | | % 17.21/3.29 | | | | REDUCE: (66), (201) imply: % 17.21/3.29 | | | | (202) ~ (all_73_0 = 0) % 17.21/3.29 | | | | % 17.21/3.29 | | | | BETA: splitting (55) gives: % 17.21/3.29 | | | | % 17.21/3.29 | | | | Case 1: % 17.21/3.29 | | | | | % 17.21/3.29 | | | | | (203) all_73_0 = 0 % 17.21/3.29 | | | | | % 17.21/3.29 | | | | | REDUCE: (202), (203) imply: % 17.21/3.29 | | | | | (204) $false % 17.21/3.29 | | | | | % 17.21/3.29 | | | | | CLOSE: (204) is inconsistent. % 17.21/3.29 | | | | | % 17.21/3.29 | | | | Case 2: % 17.21/3.29 | | | | | % 17.21/3.30 | | | | | (205) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ % 17.21/3.30 | | | | | (v1 = v0) & ordered_pair(v1, v0) = v3 & ordered_pair(v0, % 17.21/3.30 | | | | | v1) = v2 & in(v3, all_35_7) = 0 & in(v2, all_35_7) = 0 & % 17.21/3.30 | | | | | in(v1, all_65_2) = 0 & in(v0, all_65_2) = 0 & $i(v3) & % 17.21/3.30 | | | | | $i(v2) & $i(v1) & $i(v0)) % 17.21/3.30 | | | | | % 17.21/3.30 | | | | | DELTA: instantiating (205) with fresh symbols all_215_0, all_215_1, % 17.21/3.30 | | | | | all_215_2, all_215_3 gives: % 17.21/3.30 | | | | | (206) ~ (all_215_2 = all_215_3) & ordered_pair(all_215_2, % 17.21/3.30 | | | | | all_215_3) = all_215_0 & ordered_pair(all_215_3, all_215_2) % 17.21/3.30 | | | | | = all_215_1 & in(all_215_0, all_35_7) = 0 & in(all_215_1, % 17.21/3.30 | | | | | all_35_7) = 0 & in(all_215_2, all_65_2) = 0 & in(all_215_3, % 17.21/3.30 | | | | | all_65_2) = 0 & $i(all_215_0) & $i(all_215_1) & % 17.21/3.30 | | | | | $i(all_215_2) & $i(all_215_3) % 17.21/3.30 | | | | | % 17.21/3.30 | | | | | ALPHA: (206) implies: % 17.21/3.30 | | | | | (207) ~ (all_215_2 = all_215_3) % 17.21/3.30 | | | | | (208) $i(all_215_3) % 17.21/3.30 | | | | | (209) $i(all_215_2) % 17.21/3.30 | | | | | (210) in(all_215_1, all_35_7) = 0 % 17.21/3.30 | | | | | (211) in(all_215_0, all_35_7) = 0 % 17.21/3.30 | | | | | (212) ordered_pair(all_215_3, all_215_2) = all_215_1 % 17.21/3.30 | | | | | (213) ordered_pair(all_215_2, all_215_3) = all_215_0 % 17.21/3.30 | | | | | % 17.21/3.30 | | | | | GROUND_INST: instantiating (196) with all_215_2, all_215_3, all_215_1, % 17.21/3.30 | | | | | simplifying with (208), (209), (212) gives: % 17.21/3.30 | | | | | (214) all_215_2 = all_215_3 | ? [v0: $i] : ? [v1: any] : ? [v2: % 17.21/3.30 | | | | | any] : (ordered_pair(all_215_2, all_215_3) = v0 & in(v0, % 17.21/3.30 | | | | | all_35_7) = v1 & in(all_215_1, all_35_7) = v2 & $i(v0) & % 17.21/3.30 | | | | | ( ~ (v2 = 0) | ~ (v1 = 0))) % 17.21/3.30 | | | | | % 17.21/3.30 | | | | | GROUND_INST: instantiating (195) with all_215_3, all_215_2, all_215_1, % 17.21/3.30 | | | | | simplifying with (208), (209), (212) gives: % 17.21/3.30 | | | | | (215) all_215_2 = all_215_3 | ? [v0: any] : ? [v1: $i] : ? [v2: % 17.21/3.30 | | | | | any] : (ordered_pair(all_215_2, all_215_3) = v1 & in(v1, % 17.21/3.30 | | | | | all_35_7) = v2 & in(all_215_1, all_35_7) = v0 & $i(v1) & % 17.21/3.30 | | | | | ( ~ (v2 = 0) | ~ (v0 = 0))) % 17.21/3.30 | | | | | % 17.21/3.30 | | | | | GROUND_INST: instantiating (195) with all_215_2, all_215_3, all_215_0, % 17.21/3.30 | | | | | simplifying with (208), (209), (213) gives: % 17.21/3.30 | | | | | (216) all_215_2 = all_215_3 | ? [v0: any] : ? [v1: $i] : ? [v2: % 17.21/3.30 | | | | | any] : (ordered_pair(all_215_3, all_215_2) = v1 & in(v1, % 17.21/3.30 | | | | | all_35_7) = v2 & in(all_215_0, all_35_7) = v0 & $i(v1) & % 17.21/3.30 | | | | | ( ~ (v2 = 0) | ~ (v0 = 0))) % 17.21/3.30 | | | | | % 17.21/3.30 | | | | | BETA: splitting (216) gives: % 17.21/3.30 | | | | | % 17.21/3.30 | | | | | Case 1: % 17.21/3.30 | | | | | | % 17.21/3.30 | | | | | | (217) all_215_2 = all_215_3 % 17.21/3.30 | | | | | | % 17.21/3.30 | | | | | | REDUCE: (207), (217) imply: % 17.21/3.30 | | | | | | (218) $false % 17.21/3.30 | | | | | | % 17.21/3.30 | | | | | | CLOSE: (218) is inconsistent. % 17.21/3.30 | | | | | | % 17.21/3.30 | | | | | Case 2: % 17.21/3.30 | | | | | | % 17.21/3.30 | | | | | | (219) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 17.21/3.30 | | | | | | (ordered_pair(all_215_3, all_215_2) = v1 & in(v1, all_35_7) % 17.21/3.30 | | | | | | = v2 & in(all_215_0, all_35_7) = v0 & $i(v1) & ( ~ (v2 = % 17.21/3.30 | | | | | | 0) | ~ (v0 = 0))) % 17.21/3.30 | | | | | | % 17.21/3.30 | | | | | | DELTA: instantiating (219) with fresh symbols all_261_0, all_261_1, % 17.21/3.30 | | | | | | all_261_2 gives: % 17.21/3.30 | | | | | | (220) ordered_pair(all_215_3, all_215_2) = all_261_1 & % 17.21/3.30 | | | | | | in(all_261_1, all_35_7) = all_261_0 & in(all_215_0, % 17.21/3.30 | | | | | | all_35_7) = all_261_2 & $i(all_261_1) & ( ~ (all_261_0 = % 17.21/3.30 | | | | | | 0) | ~ (all_261_2 = 0)) % 17.21/3.30 | | | | | | % 17.21/3.30 | | | | | | ALPHA: (220) implies: % 17.21/3.30 | | | | | | (221) in(all_215_0, all_35_7) = all_261_2 % 17.21/3.30 | | | | | | (222) in(all_261_1, all_35_7) = all_261_0 % 17.21/3.30 | | | | | | (223) ordered_pair(all_215_3, all_215_2) = all_261_1 % 17.21/3.30 | | | | | | (224) ~ (all_261_0 = 0) | ~ (all_261_2 = 0) % 17.21/3.30 | | | | | | % 17.21/3.30 | | | | | | BETA: splitting (215) gives: % 17.21/3.30 | | | | | | % 17.21/3.30 | | | | | | Case 1: % 17.21/3.30 | | | | | | | % 17.21/3.30 | | | | | | | (225) all_215_2 = all_215_3 % 17.21/3.30 | | | | | | | % 17.21/3.30 | | | | | | | REDUCE: (207), (225) imply: % 17.21/3.30 | | | | | | | (226) $false % 17.21/3.30 | | | | | | | % 17.21/3.30 | | | | | | | CLOSE: (226) is inconsistent. % 17.21/3.30 | | | | | | | % 17.21/3.30 | | | | | | Case 2: % 17.21/3.30 | | | | | | | % 17.21/3.30 | | | | | | | (227) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 17.21/3.30 | | | | | | | (ordered_pair(all_215_2, all_215_3) = v1 & in(v1, % 17.21/3.30 | | | | | | | all_35_7) = v2 & in(all_215_1, all_35_7) = v0 & % 17.21/3.30 | | | | | | | $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) % 17.21/3.30 | | | | | | | % 17.21/3.30 | | | | | | | DELTA: instantiating (227) with fresh symbols all_267_0, % 17.21/3.30 | | | | | | | all_267_1, all_267_2 gives: % 17.21/3.30 | | | | | | | (228) ordered_pair(all_215_2, all_215_3) = all_267_1 & % 17.21/3.30 | | | | | | | in(all_267_1, all_35_7) = all_267_0 & in(all_215_1, % 17.21/3.30 | | | | | | | all_35_7) = all_267_2 & $i(all_267_1) & ( ~ (all_267_0 % 17.21/3.30 | | | | | | | = 0) | ~ (all_267_2 = 0)) % 17.21/3.30 | | | | | | | % 17.21/3.30 | | | | | | | ALPHA: (228) implies: % 17.21/3.30 | | | | | | | (229) in(all_215_1, all_35_7) = all_267_2 % 17.21/3.30 | | | | | | | % 17.21/3.30 | | | | | | | GROUND_INST: instantiating (14) with 0, all_267_2, all_35_7, % 17.21/3.30 | | | | | | | all_215_1, simplifying with (210), (229) gives: % 17.21/3.30 | | | | | | | (230) all_267_2 = 0 % 17.21/3.30 | | | | | | | % 17.21/3.30 | | | | | | | GROUND_INST: instantiating (14) with 0, all_261_2, all_35_7, % 17.21/3.30 | | | | | | | all_215_0, simplifying with (211), (221) gives: % 17.21/3.30 | | | | | | | (231) all_261_2 = 0 % 17.21/3.30 | | | | | | | % 17.21/3.30 | | | | | | | GROUND_INST: instantiating (16) with all_215_1, all_261_1, % 17.21/3.30 | | | | | | | all_215_2, all_215_3, simplifying with (212), (223) % 17.21/3.30 | | | | | | | gives: % 17.21/3.30 | | | | | | | (232) all_261_1 = all_215_1 % 17.21/3.30 | | | | | | | % 17.21/3.30 | | | | | | | REDUCE: (222), (232) imply: % 17.21/3.30 | | | | | | | (233) in(all_215_1, all_35_7) = all_261_0 % 17.21/3.30 | | | | | | | % 17.21/3.31 | | | | | | | BETA: splitting (224) gives: % 17.21/3.31 | | | | | | | % 17.21/3.31 | | | | | | | Case 1: % 17.21/3.31 | | | | | | | | % 17.21/3.31 | | | | | | | | (234) ~ (all_261_0 = 0) % 17.21/3.31 | | | | | | | | % 17.21/3.31 | | | | | | | | BETA: splitting (214) gives: % 17.21/3.31 | | | | | | | | % 17.21/3.31 | | | | | | | | Case 1: % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | | (235) all_215_2 = all_215_3 % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | | REDUCE: (207), (235) imply: % 17.21/3.31 | | | | | | | | | (236) $false % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | | CLOSE: (236) is inconsistent. % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | Case 2: % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | | (237) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 17.21/3.31 | | | | | | | | | (ordered_pair(all_215_2, all_215_3) = v0 & in(v0, % 17.21/3.31 | | | | | | | | | all_35_7) = v1 & in(all_215_1, all_35_7) = v2 & % 17.21/3.31 | | | | | | | | | $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0))) % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | | DELTA: instantiating (237) with fresh symbols all_287_0, % 17.21/3.31 | | | | | | | | | all_287_1, all_287_2 gives: % 17.21/3.31 | | | | | | | | | (238) ordered_pair(all_215_2, all_215_3) = all_287_2 & % 17.21/3.31 | | | | | | | | | in(all_287_2, all_35_7) = all_287_1 & in(all_215_1, % 17.21/3.31 | | | | | | | | | all_35_7) = all_287_0 & $i(all_287_2) & ( ~ % 17.21/3.31 | | | | | | | | | (all_287_0 = 0) | ~ (all_287_1 = 0)) % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | | ALPHA: (238) implies: % 17.21/3.31 | | | | | | | | | (239) in(all_215_1, all_35_7) = all_287_0 % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_287_0, all_35_7, % 17.21/3.31 | | | | | | | | | all_215_1, simplifying with (210), (239) gives: % 17.21/3.31 | | | | | | | | | (240) all_287_0 = 0 % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | | GROUND_INST: instantiating (14) with all_261_0, all_287_0, % 17.21/3.31 | | | | | | | | | all_35_7, all_215_1, simplifying with (233), (239) % 17.21/3.31 | | | | | | | | | gives: % 17.21/3.31 | | | | | | | | | (241) all_287_0 = all_261_0 % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | | COMBINE_EQS: (240), (241) imply: % 17.21/3.31 | | | | | | | | | (242) all_261_0 = 0 % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | | REDUCE: (234), (242) imply: % 17.21/3.31 | | | | | | | | | (243) $false % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | | CLOSE: (243) is inconsistent. % 17.21/3.31 | | | | | | | | | % 17.21/3.31 | | | | | | | | End of split % 17.21/3.31 | | | | | | | | % 17.21/3.31 | | | | | | | Case 2: % 17.21/3.31 | | | | | | | | % 17.21/3.31 | | | | | | | | (244) ~ (all_261_2 = 0) % 17.21/3.31 | | | | | | | | % 17.21/3.31 | | | | | | | | REDUCE: (231), (244) imply: % 17.21/3.31 | | | | | | | | (245) $false % 17.21/3.31 | | | | | | | | % 17.21/3.31 | | | | | | | | CLOSE: (245) is inconsistent. % 17.21/3.31 | | | | | | | | % 17.21/3.31 | | | | | | | End of split % 17.21/3.31 | | | | | | | % 17.21/3.31 | | | | | | End of split % 17.21/3.31 | | | | | | % 17.21/3.31 | | | | | End of split % 17.21/3.31 | | | | | % 17.21/3.31 | | | | End of split % 17.21/3.31 | | | | % 17.21/3.31 | | | Case 2: % 17.21/3.31 | | | | % 17.21/3.31 | | | | (246) all_137_1 = 0 % 17.21/3.31 | | | | % 17.21/3.31 | | | | COMBINE_EQS: (67), (246) imply: % 17.21/3.31 | | | | (247) all_35_6 = 0 % 17.21/3.31 | | | | % 17.21/3.31 | | | | SIMP: (247) implies: % 17.21/3.31 | | | | (248) all_35_6 = 0 % 17.21/3.31 | | | | % 17.21/3.31 | | | | REDUCE: (194), (248) imply: % 17.21/3.31 | | | | (249) $false % 17.21/3.31 | | | | % 17.21/3.31 | | | | CLOSE: (249) is inconsistent. % 17.21/3.31 | | | | % 17.21/3.31 | | | End of split % 17.21/3.31 | | | % 17.21/3.31 | | End of split % 17.21/3.31 | | % 17.21/3.31 | End of split % 17.21/3.31 | % 17.21/3.31 End of proof % 17.21/3.31 % SZS output end Proof for theBenchmark % 17.21/3.31 % 17.21/3.31 2704ms %------------------------------------------------------------------------------