%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ITP023_1 : TPTP v8.1.2. Bugfixed v7.5.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.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 04:09:03 EDT 2023 % Result : Theorem 20.37s 3.71s % Output : Proof 28.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP023_1 : TPTP v8.1.2. Bugfixed v7.5.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n026.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 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Aug 27 16:48:04 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.69/1.64 Prover 4: Preprocessing ... % 5.69/1.68 Prover 6: Preprocessing ... % 5.69/1.68 Prover 3: Preprocessing ... % 5.69/1.68 Prover 0: Preprocessing ... % 5.69/1.68 Prover 2: Preprocessing ... % 5.69/1.68 Prover 5: Preprocessing ... % 5.69/1.68 Prover 1: Preprocessing ... % 13.80/2.78 Prover 1: Warning: ignoring some quantifiers % 13.80/2.82 Prover 3: Warning: ignoring some quantifiers % 13.80/2.84 Prover 1: Constructing countermodel ... % 13.80/2.85 Prover 3: Constructing countermodel ... % 13.80/2.92 Prover 6: Proving ... % 15.44/3.04 Prover 4: Warning: ignoring some quantifiers % 15.44/3.05 Prover 5: Proving ... % 15.44/3.06 Prover 0: Proving ... % 15.99/3.08 Prover 2: Proving ... % 15.99/3.09 Prover 4: Constructing countermodel ... % 19.32/3.65 Prover 3: gave up % 19.32/3.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.37/3.71 Prover 0: proved (3065ms) % 20.37/3.71 % 20.37/3.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.37/3.71 % 20.37/3.71 Prover 5: stopped % 20.37/3.71 Prover 2: stopped % 20.37/3.72 Prover 6: stopped % 20.37/3.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.37/3.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.37/3.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.37/3.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.51/3.84 Prover 7: Preprocessing ... % 21.51/3.85 Prover 13: Preprocessing ... % 21.51/3.86 Prover 8: Preprocessing ... % 21.51/3.88 Prover 10: Preprocessing ... % 21.51/3.89 Prover 11: Preprocessing ... % 23.84/4.19 Prover 7: Warning: ignoring some quantifiers % 23.84/4.19 Prover 8: Warning: ignoring some quantifiers % 23.84/4.20 Prover 13: Warning: ignoring some quantifiers % 23.84/4.20 Prover 10: Warning: ignoring some quantifiers % 24.44/4.22 Prover 8: Constructing countermodel ... % 24.44/4.22 Prover 7: Constructing countermodel ... % 24.44/4.23 Prover 13: Constructing countermodel ... % 24.44/4.24 Prover 10: Constructing countermodel ... % 24.44/4.35 Prover 11: Warning: ignoring some quantifiers % 24.44/4.37 Prover 11: Constructing countermodel ... % 27.80/4.70 Prover 4: Found proof (size 256) % 27.80/4.70 Prover 4: proved (4051ms) % 27.80/4.70 Prover 7: stopped % 27.80/4.70 Prover 11: stopped % 27.80/4.70 Prover 10: stopped % 27.80/4.70 Prover 1: stopped % 27.80/4.70 Prover 13: stopped % 27.80/4.71 Prover 8: stopped % 27.80/4.71 % 27.80/4.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 27.80/4.71 % 27.80/4.75 % SZS output start Proof for theBenchmark % 27.80/4.75 Assumptions after simplification: % 27.80/4.75 --------------------------------- % 27.80/4.76 % 27.80/4.76 (arityeq1_2Ec_2Ebool_2E_7E_2E1) % 28.30/4.78 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0) % 28.30/4.78 & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) % 28.30/4.78 | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: mono_2Etyop_2Emin_2Ebool] : % 28.30/4.78 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.30/4.78 v0) = v2 & p(v2) = 0 & mono_2Etyop_2Emin_2Ebool(v2))) & ! [v0: % 28.30/4.78 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ( ~ % 28.30/4.78 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.30/4.78 v0) = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: any] : ? [v3: % 28.30/4.78 any] : (p(v1) = v3 & p(v0) = v2 & (v3 = 0 | v2 = 0))) & ! [v0: % 28.30/4.78 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ( ~ % 28.30/4.78 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.30/4.78 v0) = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: any] : ? [v3: % 28.30/4.78 any] : (p(v1) = v2 & p(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: % 28.30/4.78 mono_2Etyop_2Emin_2Ebool] : ( ~ (p(v0) = 0) | ~ % 28.30/4.78 mono_2Etyop_2Emin_2Ebool(v0) | ? [v1: mono_2Etyop_2Emin_2Ebool] : ? [v2: % 28.30/4.78 int] : ( ~ (v2 = 0) & % 28.30/4.78 mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.30/4.78 v0) = v1 & p(v1) = v2 & mono_2Etyop_2Emin_2Ebool(v1))) % 28.30/4.78 % 28.30/4.78 (reserved_2Eho_2Enotfalse) % 28.30/4.79 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: int] : ( ~ (v0 = % 28.30/4.79 0) & p(mono_2Ec_2Ebool_2EF_2E0) = v0) % 28.30/4.79 % 28.30/4.79 (reserved_2Elogic_2E_7E) % 28.30/4.79 ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | % 28.30/4.79 ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: mono_2Etyop_2Emin_2Ebool] : % 28.30/4.79 (mono_2Ec_2Ebool_2E_7E_2E1(v0) = v2 & p(v2) = 0 & % 28.30/4.79 mono_2Etyop_2Emin_2Ebool(v2))) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! % 28.30/4.79 [v1: mono_2Etyop_2Emin_2Ebool] : ( ~ (mono_2Ec_2Ebool_2E_7E_2E1(v0) = v1) | ~ % 28.30/4.79 mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: any] : ? [v3: any] : (p(v1) = v3 & % 28.30/4.79 p(v0) = v2 & (v3 = 0 | v2 = 0))) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! % 28.30/4.79 [v1: mono_2Etyop_2Emin_2Ebool] : ( ~ (mono_2Ec_2Ebool_2E_7E_2E1(v0) = v1) | ~ % 28.30/4.79 mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: any] : ? [v3: any] : (p(v1) = v2 & % 28.30/4.79 p(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: % 28.30/4.79 mono_2Etyop_2Emin_2Ebool] : ( ~ (p(v0) = 0) | ~ % 28.30/4.79 mono_2Etyop_2Emin_2Ebool(v0) | ? [v1: mono_2Etyop_2Emin_2Ebool] : ? [v2: % 28.30/4.79 int] : ( ~ (v2 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(v0) = v1 & p(v1) = v2 & % 28.30/4.79 mono_2Etyop_2Emin_2Ebool(v1))) % 28.30/4.79 % 28.30/4.79 (thm_2Ebool_2EEQ__CLAUSES) % 28.30/4.79 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0) & % 28.30/4.79 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ~ % 28.30/4.79 (p(mono_2Ec_2Ebool_2EF_2E0) = 0) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: % 28.30/4.79 int] : (v1 = 0 | v0 = mono_2Ec_2Ebool_2EF_2E0 | ~ (p(v0) = v1) | ~ % 28.30/4.79 mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : (v0 = % 28.30/4.79 mono_2Ec_2Ebool_2ET_2E0 | ~ (p(v0) = 0) | ~ mono_2Etyop_2Emin_2Ebool(v0)) % 28.30/4.79 & ! [v0: int] : (v0 = 0 | ~ (p(mono_2Ec_2Ebool_2ET_2E0) = v0)) % 28.30/4.79 % 28.30/4.79 (thm_2Ebool_2EF__IMP) % 28.30/4.79 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: MultipleValueBool] % 28.30/4.79 : (p(mono_2Ec_2Ebool_2EF_2E0) = v0) % 28.30/4.79 % 28.30/4.79 (thm_2Ebool_2EIMP__CLAUSES) % 28.37/4.79 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0) & % 28.37/4.79 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: any] : ? [v1: % 28.37/4.79 any] : (p(mono_2Ec_2Ebool_2ET_2E0) = v0 & p(mono_2Ec_2Ebool_2EF_2E0) = v1 & % 28.37/4.79 ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: int] : ( ~ (v1 = 0) | ~ (v0 = 0) % 28.37/4.79 | v3 = 0 | ~ (p(v2) = v3) | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: % 28.37/4.79 mono_2Etyop_2Emin_2Ebool] : ! [v3: int] : (v3 = 0 | v0 = 0 | ~ (p(v2) = % 28.37/4.79 v3) | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: % 28.37/4.79 mono_2Etyop_2Emin_2Ebool] : ! [v3: MultipleValueBool] : (v1 = 0 | v0 = 0 % 28.37/4.79 | ~ (p(v2) = v3) | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: % 28.37/4.79 mono_2Etyop_2Emin_2Ebool] : ( ~ (v1 = 0) | ~ (p(v2) = 0) | ~ % 28.37/4.79 mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: mono_2Etyop_2Emin_2Ebool] : (v0 = % 28.37/4.79 0 | ~ (p(v2) = 0) | ~ mono_2Etyop_2Emin_2Ebool(v2))) % 28.37/4.79 % 28.37/4.79 (thm_2Ebool_2EIMP__F) % 28.37/4.80 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: any] : % 28.37/4.80 (p(mono_2Ec_2Ebool_2EF_2E0) = v0 & ! [v1: mono_2Etyop_2Emin_2Ebool] : ( ~ (v0 % 28.37/4.80 = 0) | ~ (p(v1) = 0) | ~ mono_2Etyop_2Emin_2Ebool(v1))) % 28.37/4.80 % 28.37/4.80 (thm_2Ebool_2ENOT__CLAUSES) % 28.37/4.80 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0) & % 28.37/4.80 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: any] : ? [v1: % 28.37/4.80 any] : (p(mono_2Ec_2Ebool_2ET_2E0) = v0 & p(mono_2Ec_2Ebool_2EF_2E0) = v1 & % 28.37/4.80 ((v1 = 0 & ~ (v0 = 0)) | (v0 = 0 & ~ (v1 = 0)))) % 28.37/4.80 % 28.37/4.80 (thm_2Ereal__topology_2EBALL__SUBSET__CBALL) % 28.37/4.80 ! [v0: mono_2Etyop_2Erealax_2Ereal] : ! [v1: mono_2Etyop_2Erealax_2Ereal] : % 28.37/4.80 ! [v2: % 28.37/4.80 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.37/4.80 : ( ~ % 28.37/4.80 (mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(v0, % 28.37/4.80 v1) = v2) | ~ mono_2Etyop_2Erealax_2Ereal(v1) | ~ % 28.37/4.80 mono_2Etyop_2Erealax_2Ereal(v0) | ? [v3: % 28.37/4.80 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : % 28.37/4.80 ? [v4: % 28.37/4.80 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : % 28.37/4.80 ? [v5: mono_2Etyop_2Emin_2Ebool] : % 28.37/4.80 (mono_2Ec_2Ereal__topology_2Ecball_2E1(v2) = v4 & % 28.37/4.80 mono_2Ec_2Ereal__topology_2Eball_2E1(v2) = v3 & % 28.37/4.80 mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(v3, v4) = % 28.37/4.80 v5 & p(v5) = 0 & % 28.37/4.80 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v4) % 28.37/4.80 & % 28.37/4.80 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v3) % 28.37/4.80 & mono_2Etyop_2Emin_2Ebool(v5))) % 28.37/4.80 % 28.37/4.80 (thm_2Ereal__topology_2EBOUNDED__BALL) % 28.37/4.80 ? [v0: mono_2Etyop_2Erealax_2Ereal] : ? [v1: mono_2Etyop_2Erealax_2Ereal] : % 28.37/4.80 ? [v2: % 28.37/4.80 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.37/4.80 : ? [v3: % 28.37/4.80 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ? % 28.37/4.80 [v4: mono_2Etyop_2Emin_2Ebool] : ? [v5: int] : ( ~ (v5 = 0) & % 28.37/4.80 mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(v3) = v4 & % 28.37/4.80 mono_2Ec_2Ereal__topology_2Eball_2E1(v2) = v3 & % 28.37/4.80 mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(v0, % 28.37/4.80 v1) = v2 & p(v4) = v5 & mono_2Etyop_2Erealax_2Ereal(v1) & % 28.37/4.80 mono_2Etyop_2Erealax_2Ereal(v0) & % 28.37/4.80 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2) % 28.37/4.80 & mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v3) % 28.37/4.80 & mono_2Etyop_2Emin_2Ebool(v4)) % 28.37/4.80 % 28.37/4.80 (thm_2Ereal__topology_2EBOUNDED__CBALL) % 28.37/4.80 ! [v0: mono_2Etyop_2Erealax_2Ereal] : ! [v1: mono_2Etyop_2Erealax_2Ereal] : % 28.37/4.80 ! [v2: % 28.37/4.80 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.37/4.80 : ( ~ % 28.37/4.80 (mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(v0, % 28.37/4.80 v1) = v2) | ~ mono_2Etyop_2Erealax_2Ereal(v1) | ~ % 28.37/4.80 mono_2Etyop_2Erealax_2Ereal(v0) | ? [v3: % 28.37/4.80 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : % 28.37/4.80 ? [v4: mono_2Etyop_2Emin_2Ebool] : % 28.37/4.80 (mono_2Ec_2Ereal__topology_2Ecball_2E1(v2) = v3 & % 28.37/4.80 mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(v3) = v4 & p(v4) = 0 & % 28.37/4.80 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v3) % 28.37/4.80 & mono_2Etyop_2Emin_2Ebool(v4))) % 28.37/4.80 % 28.37/4.80 (thm_2Ereal__topology_2EBOUNDED__SUBSET) % 28.37/4.80 ! [v0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] % 28.37/4.80 : ! [v1: % 28.37/4.80 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ! % 28.37/4.80 [v2: mono_2Etyop_2Emin_2Ebool] : ( ~ % 28.37/4.80 (mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(v0, v1) = % 28.37/4.80 v2) | ~ % 28.37/4.80 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v1) | % 28.37/4.80 ~ mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v0) % 28.37/4.80 | ? [v3: mono_2Etyop_2Emin_2Ebool] : ? [v4: any] : ? [v5: any] : ? [v6: % 28.37/4.80 mono_2Etyop_2Emin_2Ebool] : ? [v7: any] : % 28.37/4.80 (mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(v1) = v3 & % 28.37/4.80 mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(v0) = v6 & p(v6) = v7 & p(v3) % 28.37/4.80 = v4 & p(v2) = v5 & mono_2Etyop_2Emin_2Ebool(v6) & % 28.37/4.80 mono_2Etyop_2Emin_2Ebool(v3) & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0))) % 28.37/4.80 % 28.37/4.80 (thm_2Esat_2EAND__INV2) % 28.37/4.80 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: MultipleValueBool] % 28.37/4.80 : (p(mono_2Ec_2Ebool_2EF_2E0) = v0) % 28.37/4.80 % 28.37/4.80 (thm_2Esat_2EAND__INV__IMP) % 28.37/4.80 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: MultipleValueBool] % 28.37/4.80 : (p(mono_2Ec_2Ebool_2EF_2E0) = v0) % 28.37/4.80 % 28.37/4.80 (thm_2Esat_2EOR__DUAL2) % 28.37/4.80 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: MultipleValueBool] % 28.37/4.80 : (p(mono_2Ec_2Ebool_2EF_2E0) = v0) % 28.37/4.80 % 28.37/4.80 (thm_2Esat_2EOR__DUAL3) % 28.37/4.80 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: MultipleValueBool] % 28.37/4.80 : (p(mono_2Ec_2Ebool_2EF_2E0) = v0) % 28.37/4.80 % 28.37/4.80 (thm_2Esat_2Edc__eq) % 28.37/4.81 ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! % 28.37/4.81 [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: int] : ! [v4: int] : ! [v5: int] : % 28.37/4.81 (v5 = 0 | v4 = 0 | v3 = 0 | v1 = v0 | ~ (p(v2) = v3) | ~ (p(v1) = v4) | ~ % 28.37/4.81 (p(v0) = v5) | ~ mono_2Etyop_2Emin_2Ebool(v2) | ~ % 28.37/4.81 mono_2Etyop_2Emin_2Ebool(v1) | ~ mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: % 28.37/4.81 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: % 28.37/4.81 mono_2Etyop_2Emin_2Ebool] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | % 28.37/4.81 v1 = v0 | ~ (p(v2) = 0) | ~ (p(v1) = v3) | ~ (p(v0) = v4) | ~ % 28.37/4.81 mono_2Etyop_2Emin_2Ebool(v2) | ~ mono_2Etyop_2Emin_2Ebool(v1) | ~ % 28.37/4.81 mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: % 28.37/4.81 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: int] % 28.37/4.81 : (v3 = 0 | v1 = v0 | ~ (p(v2) = v3) | ~ (p(v1) = 0) | ~ (p(v0) = 0) | ~ % 28.37/4.81 mono_2Etyop_2Emin_2Ebool(v2) | ~ mono_2Etyop_2Emin_2Ebool(v1) | ~ % 28.37/4.81 mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: % 28.37/4.81 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | % 28.37/4.81 ~ (p(v2) = 0) | ~ (p(v1) = 0) | ~ (p(v0) = 0) | ~ % 28.37/4.81 mono_2Etyop_2Emin_2Ebool(v2) | ~ mono_2Etyop_2Emin_2Ebool(v1) | ~ % 28.37/4.81 mono_2Etyop_2Emin_2Ebool(v0)) % 28.37/4.81 % 28.37/4.81 (function-axioms) % 28.49/4.82 ! [v0: u] : ! [v1: u] : ! [v2: du] : ! [v3: du] : (v1 = v0 | ~ % 28.49/4.82 (c_2Epred__set_2ESUBSET_2E2(v3, v2) = v1) | ~ % 28.49/4.82 (c_2Epred__set_2ESUBSET_2E2(v3, v2) = v0)) & ! [v0: u] : ! [v1: u] : ! % 28.49/4.82 [v2: du] : ! [v3: du] : (v1 = v0 | ~ (c_2Epair_2E_2C_2E2(v3, v2) = v1) | ~ % 28.49/4.82 (c_2Epair_2E_2C_2E2(v3, v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ! % 28.49/4.82 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : % 28.49/4.82 ! [v2: % 28.49/4.82 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.82 : ! [v3: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.82 : (v1 = v0 | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v3, % 28.49/4.82 v2) = v1) | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v3, % 28.49/4.82 v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: % 28.49/4.82 mono_2Etyop_2Emin_2Ebool] : ! [v2: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ! % 28.49/4.82 [v3: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : % 28.49/4.82 (v1 = v0 | ~ % 28.49/4.82 (mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(v3, v2) = % 28.49/4.82 v1) | ~ % 28.49/4.82 (mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(v3, v2) = % 28.49/4.82 v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29] % 28.49/4.82 : ! [v1: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29] % 28.49/4.82 : ! [v2: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ! % 28.49/4.82 [v3: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.82 : (v1 = v0 | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(v3, % 28.49/4.82 v2) = v1) | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(v3, % 28.49/4.82 v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: % 28.49/4.82 mono_2Etyop_2Emin_2Ebool] : ! [v2: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ! % 28.49/4.82 [v3: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29] % 28.49/4.82 : (v1 = v0 | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(v3, % 28.49/4.82 v2) = v1) | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(v3, % 28.49/4.82 v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 28.49/4.82 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 28.49/4.82 [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.82 : (v1 = v0 | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3, % 28.49/4.82 v2) = v1) | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3, % 28.49/4.82 v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: % 28.49/4.82 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 = % 28.49/4.82 v0 | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3, % 28.49/4.82 v2) = v1) | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3, % 28.49/4.82 v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.82 : ! [v1: % 28.49/4.82 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.82 : ! [v2: mono_2Etyop_2Erealax_2Ereal] : ! [v3: mono_2Etyop_2Erealax_2Ereal] % 28.49/4.82 : (v1 = v0 | ~ % 28.49/4.82 (mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(v3, % 28.49/4.82 v2) = v1) | ~ % 28.49/4.82 (mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(v3, % 28.49/4.82 v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 28.49/4.82 : ! [v1: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 28.49/4.82 : ! [v2: mono_2Etyop_2Erealax_2Ereal] : ! [v3: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29] % 28.49/4.82 : (v1 = v0 | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v3, % 28.49/4.82 v2) = v1) | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v3, % 28.49/4.82 v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.82 : ! [v1: % 28.49/4.82 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.82 : ! [v2: mono_2Etyop_2Erealax_2Ereal] : ! [v3: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 28.49/4.82 : (v1 = v0 | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v3, % 28.49/4.82 v2) = v1) | ~ % 28.49/4.82 (mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v3, % 28.49/4.82 v2) = v0)) & ! [v0: d] : ! [v1: d] : ! [v2: d] : ! [v3: d] : (v1 = % 28.49/4.82 v0 | ~ (tyop_2Epair_2Eprod(v3, v2) = v1) | ~ (tyop_2Epair_2Eprod(v3, v2) = % 28.49/4.82 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : ! [v3: du] : (v1 = v0 | ~ % 28.49/4.82 (c_2Emin_2E_3D_2E2(v3, v2) = v1) | ~ (c_2Emin_2E_3D_2E2(v3, v2) = v0)) & ! % 28.49/4.82 [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: % 28.49/4.82 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | % 28.49/4.82 ~ (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v1) | ~ % 28.49/4.82 (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: % 28.49/4.82 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | % 28.49/4.82 ~ (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v1) | ~ % 28.49/4.82 (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: % 28.49/4.82 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | % 28.49/4.82 ~ (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v1) | ~ % 28.49/4.82 (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v0)) & ! [v0: d] : ! [v1: d] : ! % 28.49/4.82 [v2: d] : ! [v3: d] : (v1 = v0 | ~ (tyop_2Emin_2Efun(v3, v2) = v1) | ~ % 28.49/4.82 (tyop_2Emin_2Efun(v3, v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : % 28.49/4.82 ! [v3: du] : (v1 = v0 | ~ (app_2E2(v3, v2) = v1) | ~ (app_2E2(v3, v2) = v0)) % 28.49/4.82 & ! [v0: du] : ! [v1: du] : ! [v2: u] : ! [v3: d] : (v1 = v0 | ~ (s(v3, % 28.49/4.82 v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ! % 28.49/4.82 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : % 28.49/4.82 ! [v2: % 28.49/4.82 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.82 : (v1 = v0 | ~ (mono_2Ec_2Ereal__topology_2Ecball_2E1(v2) = v1) | ~ % 28.49/4.82 (mono_2Ec_2Ereal__topology_2Ecball_2E1(v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (v1 % 28.49/4.82 = v0 | ~ (mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(v2) = v1) | ~ % 28.49/4.82 (mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ! % 28.49/4.82 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : % 28.49/4.82 ! [v2: % 28.49/4.82 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.82 : (v1 = v0 | ~ (mono_2Ec_2Ereal__topology_2Eball_2E1(v2) = v1) | ~ % 28.49/4.82 (mono_2Ec_2Ereal__topology_2Eball_2E1(v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Erealax_2Ereal] : ! [v1: mono_2Etyop_2Erealax_2Ereal] : ! % 28.49/4.82 [v2: du] : (v1 = v0 | ~ (j_mono_2Etyop_2Erealax_2Ereal(v2) = v1) | ~ % 28.49/4.82 (j_mono_2Etyop_2Erealax_2Ereal(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! % 28.49/4.82 [v2: mono_2Etyop_2Erealax_2Ereal] : (v1 = v0 | ~ % 28.49/4.82 (i_mono_2Etyop_2Erealax_2Ereal(v2) = v1) | ~ % 28.49/4.82 (i_mono_2Etyop_2Erealax_2Ereal(v2) = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.82 : ! [v1: % 28.49/4.82 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.82 : ! [v2: du] : (v1 = v0 | ~ % 28.49/4.82 (j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2) % 28.49/4.82 = v1) | ~ % 28.49/4.82 (j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2) % 28.49/4.82 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 28.49/4.82 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.82 : (v1 = v0 | ~ % 28.49/4.82 (i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2) % 28.49/4.82 = v1) | ~ % 28.49/4.82 (i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2) % 28.49/4.82 = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 28.49/4.82 : ! [v1: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 28.49/4.82 : ! [v2: du] : (v1 = v0 | ~ % 28.49/4.82 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 28.49/4.82 = v1) | ~ % 28.49/4.82 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 28.49/4.82 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 28.49/4.82 : (v1 = v0 | ~ % 28.49/4.82 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 28.49/4.82 = v1) | ~ % 28.49/4.82 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 28.49/4.82 = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29] % 28.49/4.82 : ! [v1: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29] % 28.49/4.82 : ! [v2: du] : (v1 = v0 | ~ % 28.49/4.82 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(v2) % 28.49/4.82 = v1) | ~ % 28.49/4.82 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(v2) % 28.49/4.82 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29] % 28.49/4.82 : (v1 = v0 | ~ % 28.49/4.82 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(v2) % 28.49/4.82 = v1) | ~ % 28.49/4.82 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(v2) % 28.49/4.82 = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ! % 28.49/4.82 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : % 28.49/4.82 ! [v2: du] : (v1 = v0 | ~ % 28.49/4.82 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v2) % 28.49/4.82 = v1) | ~ % 28.49/4.82 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v2) % 28.49/4.82 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (v1 % 28.49/4.82 = v0 | ~ % 28.49/4.82 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v2) % 28.49/4.82 = v1) | ~ % 28.49/4.82 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v2) % 28.49/4.82 = v0)) & ! [v0: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.82 : ! [v1: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.82 : ! [v2: du] : (v1 = v0 | ~ % 28.49/4.82 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.82 = v1) | ~ % 28.49/4.82 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.82 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 28.49/4.82 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.82 : (v1 = v0 | ~ % 28.49/4.82 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.82 = v1) | ~ % 28.49/4.83 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.83 = v0)) & ! [v0: % 28.49/4.83 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.83 : ! [v1: % 28.49/4.83 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.83 : ! [v2: du] : (v1 = v0 | ~ % 28.49/4.83 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.83 = v1) | ~ % 28.49/4.83 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.83 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 28.49/4.83 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.83 : (v1 = v0 | ~ % 28.49/4.83 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.83 = v1) | ~ % 28.49/4.83 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.83 = v0)) & ! [v0: % 28.49/4.83 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29] % 28.49/4.83 : ! [v1: % 28.49/4.83 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29] % 28.49/4.83 : ! [v2: du] : (v1 = v0 | ~ % 28.49/4.83 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(v2) % 28.49/4.83 = v1) | ~ % 28.49/4.83 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(v2) % 28.49/4.83 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 28.49/4.83 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29] % 28.49/4.83 : (v1 = v0 | ~ % 28.49/4.83 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(v2) % 28.49/4.83 = v1) | ~ % 28.49/4.83 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(v2) % 28.49/4.83 = v0)) & ! [v0: % 28.49/4.83 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.83 : ! [v1: % 28.49/4.83 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.83 : ! [v2: du] : (v1 = v0 | ~ % 28.49/4.83 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.83 = v1) | ~ % 28.49/4.83 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.83 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 28.49/4.83 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 28.49/4.83 : (v1 = v0 | ~ % 28.49/4.83 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.83 = v1) | ~ % 28.49/4.83 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 28.49/4.83 = v0)) & ! [v0: % 28.49/4.83 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 28.49/4.83 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 28.49/4.83 [v2: du] : (v1 = v0 | ~ % 28.49/4.83 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 28.49/4.83 v1) | ~ % 28.49/4.83 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 28.49/4.83 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 28.49/4.83 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 = % 28.49/4.83 v0 | ~ % 28.49/4.83 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 28.49/4.83 v1) | ~ % 28.49/4.83 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 28.49/4.83 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = % 28.49/4.83 v0 | ~ (i_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~ % 28.49/4.83 (i_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 28.49/4.83 du] : (v1 = v0 | ~ (c_2Ebool_2E_3F_2E1(v2) = v1) | ~ % 28.49/4.83 (c_2Ebool_2E_3F_2E1(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : (v1 % 28.49/4.83 = v0 | ~ (c_2Ebool_2E_21_2E1(v2) = v1) | ~ (c_2Ebool_2E_21_2E1(v2) = v0)) % 28.49/4.83 & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! % 28.49/4.83 [v2: du] : (v1 = v0 | ~ (j_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~ % 28.49/4.83 (j_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.83 ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = % 28.49/4.83 v0 | ~ (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v1) | ~ % 28.49/4.83 (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.49/4.83 MultipleValueBool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~ % 28.49/4.83 (p(v2) = v1) | ~ (p(v2) = v0)) % 28.49/4.83 % 28.49/4.83 Further assumptions not needed in the proof: % 28.49/4.83 -------------------------------------------- % 28.49/4.83 arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, % 28.49/4.83 arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, % 28.49/4.83 arityeq1_2Ec_2Ereal__topology_2Eball_2E1, % 28.49/4.83 arityeq1_2Ec_2Ereal__topology_2Ebounded__def_2E1, % 28.49/4.83 arityeq1_2Ec_2Ereal__topology_2Ecball_2E1, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, % 28.49/4.83 arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, % 28.49/4.83 arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, % 28.49/4.83 arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal, % 28.49/4.83 arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal, % 28.49/4.83 ij_2Emono_2Etyop_2Emin_2Ebool, % 28.49/4.83 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, % 28.49/4.83 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, % 28.49/4.83 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29, % 28.49/4.83 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29, % 28.49/4.83 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29, % 28.49/4.83 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, % 28.49/4.83 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29, % 28.49/4.83 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29, % 28.49/4.83 ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, % 28.49/4.83 ij_2Emono_2Etyop_2Erealax_2Ereal, ji_2Emono_2Etyop_2Emin_2Ebool, % 28.49/4.83 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, % 28.49/4.83 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, % 28.49/4.83 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29, % 28.49/4.83 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29, % 28.49/4.83 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29, % 28.49/4.83 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, % 28.49/4.83 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29, % 28.49/4.83 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29, % 28.49/4.83 ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, % 28.49/4.83 ji_2Emono_2Etyop_2Erealax_2Ereal, % 28.49/4.83 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool, % 28.49/4.83 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, % 28.49/4.83 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool, % 28.49/4.83 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29, % 28.49/4.83 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, % 28.49/4.83 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29, % 28.49/4.83 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, % 28.49/4.83 monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal, % 28.49/4.83 monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal, % 28.49/4.83 monoeq_2Emono_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Erealax_2Ereal, % 28.49/4.83 monoeq_2Emono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal, % 28.49/4.83 reserved_2Eho_2Ebool__cases__ax, reserved_2Eho_2Eboolext, % 28.49/4.83 reserved_2Eho_2Eeq__ext, reserved_2Eho_2Ei__thm, reserved_2Eho_2Ek__thm, % 28.49/4.83 reserved_2Eho_2Es__thm, reserved_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, % 28.49/4.83 reserved_2Elogic_2E_3D, reserved_2Elogic_2E_3D_3D_3E, reserved_2Elogic_2E_5C_2F, % 28.49/4.83 reserved_2Equant_2E_21, reserved_2Equant_2E_3F, thm_2Ebool_2EDE__MORGAN__THM, % 28.49/4.83 thm_2Ebool_2EDISJ__ASSOC, thm_2Ebool_2EDISJ__SYM, thm_2Ebool_2EEQ__SYM__EQ, % 28.49/4.83 thm_2Ebool_2EIMP__ANTISYM__AX, thm_2Ebool_2ENOT__FORALL__THM, % 28.49/4.83 thm_2Ebool_2ETRUTH, thm_2Esat_2ENOT__NOT, thm_2Esat_2Edc__conj, % 28.49/4.83 thm_2Esat_2Edc__disj, thm_2Esat_2Edc__imp, thm_2Esat_2Edc__neg % 28.49/4.83 % 28.49/4.83 Those formulas are unsatisfiable: % 28.49/4.83 --------------------------------- % 28.49/4.83 % 28.49/4.83 Begin of proof % 28.49/4.83 | % 28.49/4.83 | ALPHA: (reserved_2Eho_2Enotfalse) implies: % 28.49/4.83 | (1) ? [v0: int] : ( ~ (v0 = 0) & p(mono_2Ec_2Ebool_2EF_2E0) = v0) % 28.49/4.83 | % 28.49/4.83 | ALPHA: (reserved_2Elogic_2E_7E) implies: % 28.49/4.83 | (2) ! [v0: mono_2Etyop_2Emin_2Ebool] : ( ~ (p(v0) = 0) | ~ % 28.49/4.83 | mono_2Etyop_2Emin_2Ebool(v0) | ? [v1: mono_2Etyop_2Emin_2Ebool] : ? % 28.49/4.83 | [v2: int] : ( ~ (v2 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(v0) = v1 & p(v1) % 28.49/4.83 | = v2 & mono_2Etyop_2Emin_2Ebool(v1))) % 28.49/4.83 | (3) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : (v1 = 0 | ~ (p(v0) % 28.49/4.83 | = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: % 28.49/4.83 | mono_2Etyop_2Emin_2Ebool] : (mono_2Ec_2Ebool_2E_7E_2E1(v0) = v2 & % 28.49/4.83 | p(v2) = 0 & mono_2Etyop_2Emin_2Ebool(v2))) % 28.49/4.83 | % 28.49/4.83 | ALPHA: (arityeq1_2Ec_2Ebool_2E_7E_2E1) implies: % 28.49/4.83 | (4) ! [v0: mono_2Etyop_2Emin_2Ebool] : ( ~ (p(v0) = 0) | ~ % 28.49/4.83 | mono_2Etyop_2Emin_2Ebool(v0) | ? [v1: mono_2Etyop_2Emin_2Ebool] : ? % 28.49/4.83 | [v2: int] : ( ~ (v2 = 0) & % 28.49/4.83 | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.83 | v0) = v1 & p(v1) = v2 & mono_2Etyop_2Emin_2Ebool(v1))) % 28.49/4.83 | (5) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : (v1 = 0 | ~ (p(v0) % 28.49/4.83 | = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: % 28.49/4.83 | mono_2Etyop_2Emin_2Ebool] : % 28.49/4.83 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.83 | v0) = v2 & p(v2) = 0 & mono_2Etyop_2Emin_2Ebool(v2))) % 28.49/4.84 | % 28.49/4.84 | ALPHA: (thm_2Ebool_2EIMP__F) implies: % 28.49/4.84 | (6) ? [v0: any] : (p(mono_2Ec_2Ebool_2EF_2E0) = v0 & ! [v1: % 28.49/4.84 | mono_2Etyop_2Emin_2Ebool] : ( ~ (v0 = 0) | ~ (p(v1) = 0) | ~ % 28.49/4.84 | mono_2Etyop_2Emin_2Ebool(v1))) % 28.49/4.84 | % 28.49/4.84 | ALPHA: (thm_2Ebool_2EIMP__CLAUSES) implies: % 28.49/4.84 | (7) ? [v0: any] : ? [v1: any] : (p(mono_2Ec_2Ebool_2ET_2E0) = v0 & % 28.49/4.84 | p(mono_2Ec_2Ebool_2EF_2E0) = v1 & ! [v2: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.84 | ! [v3: int] : ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | ~ (p(v2) = v3) % 28.49/4.84 | | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: % 28.49/4.84 | mono_2Etyop_2Emin_2Ebool] : ! [v3: int] : (v3 = 0 | v0 = 0 | ~ % 28.49/4.84 | (p(v2) = v3) | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: % 28.49/4.84 | mono_2Etyop_2Emin_2Ebool] : ! [v3: MultipleValueBool] : (v1 = 0 | % 28.49/4.84 | v0 = 0 | ~ (p(v2) = v3) | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! % 28.49/4.84 | [v2: mono_2Etyop_2Emin_2Ebool] : ( ~ (v1 = 0) | ~ (p(v2) = 0) | ~ % 28.49/4.84 | mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.84 | (v0 = 0 | ~ (p(v2) = 0) | ~ mono_2Etyop_2Emin_2Ebool(v2))) % 28.49/4.84 | % 28.49/4.84 | ALPHA: (thm_2Ebool_2ENOT__CLAUSES) implies: % 28.49/4.84 | (8) ? [v0: any] : ? [v1: any] : (p(mono_2Ec_2Ebool_2ET_2E0) = v0 & % 28.49/4.84 | p(mono_2Ec_2Ebool_2EF_2E0) = v1 & ((v1 = 0 & ~ (v0 = 0)) | (v0 = 0 & % 28.49/4.84 | ~ (v1 = 0)))) % 28.49/4.84 | % 28.49/4.84 | ALPHA: (thm_2Ebool_2EEQ__CLAUSES) implies: % 28.49/4.84 | (9) mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0) % 28.49/4.84 | (10) ! [v0: int] : (v0 = 0 | ~ (p(mono_2Ec_2Ebool_2ET_2E0) = v0)) % 28.49/4.84 | (11) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : (v1 = 0 | v0 = % 28.49/4.84 | mono_2Ec_2Ebool_2EF_2E0 | ~ (p(v0) = v1) | ~ % 28.49/4.84 | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.84 | % 28.49/4.84 | ALPHA: (thm_2Esat_2EOR__DUAL3) implies: % 28.49/4.84 | (12) mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) % 28.49/4.84 | (13) ? [v0: MultipleValueBool] : (p(mono_2Ec_2Ebool_2EF_2E0) = v0) % 28.49/4.84 | % 28.49/4.84 | ALPHA: (thm_2Esat_2Edc__eq) implies: % 28.49/4.84 | (14) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] % 28.49/4.84 | : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~ (p(v2) = 0) | ~ % 28.49/4.84 | (p(v1) = 0) | ~ (p(v0) = 0) | ~ mono_2Etyop_2Emin_2Ebool(v2) | ~ % 28.49/4.84 | mono_2Etyop_2Emin_2Ebool(v1) | ~ mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.84 | % 28.49/4.84 | ALPHA: (function-axioms) implies: % 28.49/4.84 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 28.49/4.84 | mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = % 28.49/4.84 | v0)) % 28.49/4.84 | (16) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] % 28.49/4.84 | : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~ % 28.49/4.84 | (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v1) | ~ % 28.49/4.84 | (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v0)) % 28.49/4.84 | (17) ! [v0: % 28.49/4.84 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] % 28.49/4.84 | : ! [v1: % 28.49/4.84 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] % 28.49/4.84 | : ! [v2: % 28.49/4.84 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.84 | : (v1 = v0 | ~ (mono_2Ec_2Ereal__topology_2Eball_2E1(v2) = v1) | ~ % 28.49/4.84 | (mono_2Ec_2Ereal__topology_2Eball_2E1(v2) = v0)) % 28.49/4.84 | (18) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] % 28.49/4.84 | : ! [v2: % 28.49/4.84 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] % 28.49/4.84 | : (v1 = v0 | ~ (mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(v2) = % 28.49/4.84 | v1) | ~ (mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(v2) = v0)) % 28.49/4.84 | (19) ! [v0: % 28.49/4.84 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] % 28.49/4.84 | : ! [v1: % 28.49/4.84 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] % 28.49/4.84 | : ! [v2: % 28.49/4.84 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 28.49/4.84 | : (v1 = v0 | ~ (mono_2Ec_2Ereal__topology_2Ecball_2E1(v2) = v1) | ~ % 28.49/4.84 | (mono_2Ec_2Ereal__topology_2Ecball_2E1(v2) = v0)) % 28.49/4.84 | (20) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] % 28.49/4.84 | : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: % 28.49/4.84 | mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] % 28.49/4.85 | : (v1 = v0 | ~ % 28.49/4.85 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3, % 28.49/4.85 | v2) = v1) | ~ % 28.49/4.85 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3, % 28.49/4.85 | v2) = v0)) % 28.49/4.85 | % 28.49/4.85 | DELTA: instantiating (13) with fresh symbol all_37_0 gives: % 28.49/4.85 | (21) p(mono_2Ec_2Ebool_2EF_2E0) = all_37_0 % 28.49/4.85 | % 28.49/4.85 | DELTA: instantiating (13) with fresh symbol all_47_0 gives: % 28.49/4.85 | (22) p(mono_2Ec_2Ebool_2EF_2E0) = all_47_0 % 28.49/4.85 | % 28.49/4.85 | DELTA: instantiating (13) with fresh symbol all_59_0 gives: % 28.49/4.85 | (23) p(mono_2Ec_2Ebool_2EF_2E0) = all_59_0 % 28.49/4.85 | % 28.49/4.85 | DELTA: instantiating (13) with fresh symbol all_61_0 gives: % 28.49/4.85 | (24) p(mono_2Ec_2Ebool_2EF_2E0) = all_61_0 % 28.49/4.85 | % 28.49/4.85 | DELTA: instantiating (13) with fresh symbol all_63_0 gives: % 28.49/4.85 | (25) p(mono_2Ec_2Ebool_2EF_2E0) = all_63_0 % 28.49/4.85 | % 28.49/4.85 | DELTA: instantiating (1) with fresh symbol all_77_0 gives: % 28.49/4.85 | (26) ~ (all_77_0 = 0) & p(mono_2Ec_2Ebool_2EF_2E0) = all_77_0 % 28.49/4.85 | % 28.49/4.85 | ALPHA: (26) implies: % 28.49/4.85 | (27) ~ (all_77_0 = 0) % 28.49/4.85 | (28) p(mono_2Ec_2Ebool_2EF_2E0) = all_77_0 % 28.49/4.85 | % 28.49/4.85 | DELTA: instantiating (6) with fresh symbol all_80_0 gives: % 28.49/4.85 | (29) p(mono_2Ec_2Ebool_2EF_2E0) = all_80_0 & ! [v0: % 28.49/4.85 | mono_2Etyop_2Emin_2Ebool] : ( ~ (all_80_0 = 0) | ~ (p(v0) = 0) | ~ % 28.49/4.85 | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.85 | % 28.49/4.85 | ALPHA: (29) implies: % 28.49/4.85 | (30) p(mono_2Ec_2Ebool_2EF_2E0) = all_80_0 % 28.49/4.85 | % 28.49/4.85 | DELTA: instantiating (8) with fresh symbols all_83_0, all_83_1 gives: % 28.49/4.85 | (31) p(mono_2Ec_2Ebool_2ET_2E0) = all_83_1 & p(mono_2Ec_2Ebool_2EF_2E0) = % 28.49/4.85 | all_83_0 & ((all_83_0 = 0 & ~ (all_83_1 = 0)) | (all_83_1 = 0 & ~ % 28.49/4.85 | (all_83_0 = 0))) % 28.49/4.85 | % 28.49/4.85 | ALPHA: (31) implies: % 28.49/4.85 | (32) p(mono_2Ec_2Ebool_2EF_2E0) = all_83_0 % 28.49/4.85 | (33) p(mono_2Ec_2Ebool_2ET_2E0) = all_83_1 % 28.49/4.85 | % 28.49/4.85 | DELTA: instantiating (thm_2Ereal__topology_2EBOUNDED__BALL) with fresh symbols % 28.49/4.85 | all_112_0, all_112_1, all_112_2, all_112_3, all_112_4, all_112_5 gives: % 28.49/4.85 | (34) ~ (all_112_0 = 0) & % 28.49/4.85 | mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_112_2) = all_112_1 & % 28.49/4.85 | mono_2Ec_2Ereal__topology_2Eball_2E1(all_112_3) = all_112_2 & % 28.49/4.85 | mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(all_112_5, % 28.49/4.85 | all_112_4) = all_112_3 & p(all_112_1) = all_112_0 & % 28.49/4.85 | mono_2Etyop_2Erealax_2Ereal(all_112_4) & % 28.49/4.85 | mono_2Etyop_2Erealax_2Ereal(all_112_5) & % 28.49/4.85 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(all_112_3) % 28.49/4.85 | & % 28.49/4.85 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(all_112_2) % 28.49/4.85 | & mono_2Etyop_2Emin_2Ebool(all_112_1) % 28.49/4.85 | % 28.49/4.85 | ALPHA: (34) implies: % 28.49/4.85 | (35) ~ (all_112_0 = 0) % 28.49/4.85 | (36) mono_2Etyop_2Emin_2Ebool(all_112_1) % 28.49/4.85 | (37) mono_2Etyop_2Erealax_2Ereal(all_112_5) % 28.49/4.85 | (38) mono_2Etyop_2Erealax_2Ereal(all_112_4) % 28.49/4.85 | (39) p(all_112_1) = all_112_0 % 28.49/4.85 | (40) mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(all_112_5, % 28.49/4.85 | all_112_4) = all_112_3 % 28.49/4.85 | (41) mono_2Ec_2Ereal__topology_2Eball_2E1(all_112_3) = all_112_2 % 28.49/4.85 | (42) mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_112_2) = all_112_1 % 28.49/4.85 | % 28.49/4.85 | DELTA: instantiating (7) with fresh symbols all_145_0, all_145_1 gives: % 28.49/4.85 | (43) p(mono_2Ec_2Ebool_2ET_2E0) = all_145_1 & p(mono_2Ec_2Ebool_2EF_2E0) = % 28.49/4.85 | all_145_0 & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : ( ~ % 28.49/4.85 | (all_145_0 = 0) | ~ (all_145_1 = 0) | v1 = 0 | ~ (p(v0) = v1) | ~ % 28.49/4.85 | mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.85 | ! [v1: int] : (v1 = 0 | all_145_1 = 0 | ~ (p(v0) = v1) | ~ % 28.49/4.85 | mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.85 | ! [v1: MultipleValueBool] : (all_145_0 = 0 | all_145_1 = 0 | ~ (p(v0) % 28.49/4.85 | = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: % 28.49/4.85 | mono_2Etyop_2Emin_2Ebool] : ( ~ (all_145_0 = 0) | ~ (p(v0) = 0) | % 28.49/4.85 | ~ mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] % 28.49/4.85 | : (all_145_1 = 0 | ~ (p(v0) = 0) | ~ mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.85 | % 28.49/4.85 | ALPHA: (43) implies: % 28.49/4.85 | (44) p(mono_2Ec_2Ebool_2EF_2E0) = all_145_0 % 28.49/4.85 | (45) p(mono_2Ec_2Ebool_2ET_2E0) = all_145_1 % 28.49/4.85 | % 28.49/4.85 | GROUND_INST: instantiating (15) with all_37_0, all_59_0, % 28.49/4.85 | mono_2Ec_2Ebool_2EF_2E0, simplifying with (21), (23) gives: % 28.49/4.85 | (46) all_59_0 = all_37_0 % 28.49/4.85 | % 28.49/4.85 | GROUND_INST: instantiating (15) with all_59_0, all_61_0, % 28.49/4.85 | mono_2Ec_2Ebool_2EF_2E0, simplifying with (23), (24) gives: % 28.49/4.85 | (47) all_61_0 = all_59_0 % 28.49/4.85 | % 28.49/4.85 | GROUND_INST: instantiating (15) with all_77_0, all_80_0, % 28.49/4.85 | mono_2Ec_2Ebool_2EF_2E0, simplifying with (28), (30) gives: % 28.49/4.86 | (48) all_80_0 = all_77_0 % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (15) with all_63_0, all_80_0, % 28.49/4.86 | mono_2Ec_2Ebool_2EF_2E0, simplifying with (25), (30) gives: % 28.49/4.86 | (49) all_80_0 = all_63_0 % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (15) with all_61_0, all_80_0, % 28.49/4.86 | mono_2Ec_2Ebool_2EF_2E0, simplifying with (24), (30) gives: % 28.49/4.86 | (50) all_80_0 = all_61_0 % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (15) with all_83_0, all_145_0, % 28.49/4.86 | mono_2Ec_2Ebool_2EF_2E0, simplifying with (32), (44) gives: % 28.49/4.86 | (51) all_145_0 = all_83_0 % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (15) with all_77_0, all_145_0, % 28.49/4.86 | mono_2Ec_2Ebool_2EF_2E0, simplifying with (28), (44) gives: % 28.49/4.86 | (52) all_145_0 = all_77_0 % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (15) with all_47_0, all_145_0, % 28.49/4.86 | mono_2Ec_2Ebool_2EF_2E0, simplifying with (22), (44) gives: % 28.49/4.86 | (53) all_145_0 = all_47_0 % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (15) with all_83_1, all_145_1, % 28.49/4.86 | mono_2Ec_2Ebool_2ET_2E0, simplifying with (33), (45) gives: % 28.49/4.86 | (54) all_145_1 = all_83_1 % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (10) with all_145_1, simplifying with (45) gives: % 28.49/4.86 | (55) all_145_1 = 0 % 28.49/4.86 | % 28.49/4.86 | COMBINE_EQS: (51), (52) imply: % 28.49/4.86 | (56) all_83_0 = all_77_0 % 28.49/4.86 | % 28.49/4.86 | COMBINE_EQS: (51), (53) imply: % 28.49/4.86 | (57) all_83_0 = all_47_0 % 28.49/4.86 | % 28.49/4.86 | COMBINE_EQS: (54), (55) imply: % 28.49/4.86 | (58) all_83_1 = 0 % 28.49/4.86 | % 28.49/4.86 | SIMP: (58) implies: % 28.49/4.86 | (59) all_83_1 = 0 % 28.49/4.86 | % 28.49/4.86 | COMBINE_EQS: (56), (57) imply: % 28.49/4.86 | (60) all_77_0 = all_47_0 % 28.49/4.86 | % 28.49/4.86 | SIMP: (60) implies: % 28.49/4.86 | (61) all_77_0 = all_47_0 % 28.49/4.86 | % 28.49/4.86 | COMBINE_EQS: (49), (50) imply: % 28.49/4.86 | (62) all_63_0 = all_61_0 % 28.49/4.86 | % 28.49/4.86 | COMBINE_EQS: (48), (49) imply: % 28.49/4.86 | (63) all_77_0 = all_63_0 % 28.49/4.86 | % 28.49/4.86 | SIMP: (63) implies: % 28.49/4.86 | (64) all_77_0 = all_63_0 % 28.49/4.86 | % 28.49/4.86 | COMBINE_EQS: (61), (64) imply: % 28.49/4.86 | (65) all_63_0 = all_47_0 % 28.49/4.86 | % 28.49/4.86 | SIMP: (65) implies: % 28.49/4.86 | (66) all_63_0 = all_47_0 % 28.49/4.86 | % 28.49/4.86 | COMBINE_EQS: (62), (66) imply: % 28.49/4.86 | (67) all_61_0 = all_47_0 % 28.49/4.86 | % 28.49/4.86 | SIMP: (67) implies: % 28.49/4.86 | (68) all_61_0 = all_47_0 % 28.49/4.86 | % 28.49/4.86 | COMBINE_EQS: (47), (68) imply: % 28.49/4.86 | (69) all_59_0 = all_47_0 % 28.49/4.86 | % 28.49/4.86 | SIMP: (69) implies: % 28.49/4.86 | (70) all_59_0 = all_47_0 % 28.49/4.86 | % 28.49/4.86 | COMBINE_EQS: (46), (70) imply: % 28.49/4.86 | (71) all_47_0 = all_37_0 % 28.49/4.86 | % 28.49/4.86 | COMBINE_EQS: (61), (71) imply: % 28.49/4.86 | (72) all_77_0 = all_37_0 % 28.49/4.86 | % 28.49/4.86 | REDUCE: (27), (72) imply: % 28.49/4.86 | (73) ~ (all_37_0 = 0) % 28.49/4.86 | % 28.49/4.86 | REDUCE: (33), (59) imply: % 28.49/4.86 | (74) p(mono_2Ec_2Ebool_2ET_2E0) = 0 % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (5) with mono_2Ec_2Ebool_2EF_2E0, all_37_0, % 28.49/4.86 | simplifying with (12), (21) gives: % 28.49/4.86 | (75) all_37_0 = 0 | ? [v0: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.86 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.86 | mono_2Ec_2Ebool_2EF_2E0) = v0 & p(v0) = 0 & % 28.49/4.86 | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (3) with mono_2Ec_2Ebool_2EF_2E0, all_37_0, % 28.49/4.86 | simplifying with (12), (21) gives: % 28.49/4.86 | (76) all_37_0 = 0 | ? [v0: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.86 | (mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2EF_2E0) = v0 & p(v0) = 0 & % 28.49/4.86 | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (4) with mono_2Ec_2Ebool_2ET_2E0, simplifying with % 28.49/4.86 | (9), (74) gives: % 28.49/4.86 | (77) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 = 0) & % 28.49/4.86 | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.86 | mono_2Ec_2Ebool_2ET_2E0) = v0 & p(v0) = v1 & % 28.49/4.86 | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (2) with mono_2Ec_2Ebool_2ET_2E0, simplifying with % 28.49/4.86 | (9), (74) gives: % 28.49/4.86 | (78) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 = 0) & % 28.49/4.86 | mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) = v0 & p(v0) = v1 % 28.49/4.86 | & mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (11) with all_112_1, all_112_0, simplifying with % 28.49/4.86 | (36), (39) gives: % 28.49/4.86 | (79) all_112_0 = 0 | all_112_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (5) with all_112_1, all_112_0, simplifying with % 28.49/4.86 | (36), (39) gives: % 28.49/4.86 | (80) all_112_0 = 0 | ? [v0: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.86 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.86 | all_112_1) = v0 & p(v0) = 0 & mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (3) with all_112_1, all_112_0, simplifying with % 28.49/4.86 | (36), (39) gives: % 28.49/4.86 | (81) all_112_0 = 0 | ? [v0: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.86 | (mono_2Ec_2Ebool_2E_7E_2E1(all_112_1) = v0 & p(v0) = 0 & % 28.49/4.86 | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.86 | % 28.49/4.86 | GROUND_INST: instantiating (thm_2Ereal__topology_2EBALL__SUBSET__CBALL) with % 28.49/4.86 | all_112_5, all_112_4, all_112_3, simplifying with (37), (38), % 28.49/4.86 | (40) gives: % 28.49/4.86 | (82) ? [v0: % 28.49/4.86 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] % 28.49/4.86 | : ? [v1: % 28.49/4.86 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] % 28.49/4.86 | : ? [v2: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.86 | (mono_2Ec_2Ereal__topology_2Ecball_2E1(all_112_3) = v1 & % 28.49/4.86 | mono_2Ec_2Ereal__topology_2Eball_2E1(all_112_3) = v0 & % 28.49/4.86 | mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(v0, % 28.49/4.86 | v1) = v2 & p(v2) = 0 & % 28.49/4.86 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v1) % 28.49/4.86 | & % 28.49/4.86 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v0) % 28.49/4.86 | & mono_2Etyop_2Emin_2Ebool(v2)) % 28.49/4.86 | % 28.49/4.87 | GROUND_INST: instantiating (thm_2Ereal__topology_2EBOUNDED__CBALL) with % 28.49/4.87 | all_112_5, all_112_4, all_112_3, simplifying with (37), (38), % 28.49/4.87 | (40) gives: % 28.49/4.87 | (83) ? [v0: % 28.49/4.87 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] % 28.49/4.87 | : ? [v1: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.87 | (mono_2Ec_2Ereal__topology_2Ecball_2E1(all_112_3) = v0 & % 28.49/4.87 | mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(v0) = v1 & p(v1) = 0 & % 28.49/4.87 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(v0) % 28.49/4.87 | & mono_2Etyop_2Emin_2Ebool(v1)) % 28.49/4.87 | % 28.49/4.87 | DELTA: instantiating (78) with fresh symbols all_197_0, all_197_1 gives: % 28.49/4.87 | (84) ~ (all_197_0 = 0) & % 28.49/4.87 | mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) = all_197_1 & % 28.49/4.87 | p(all_197_1) = all_197_0 & mono_2Etyop_2Emin_2Ebool(all_197_1) % 28.49/4.87 | % 28.49/4.87 | ALPHA: (84) implies: % 28.49/4.87 | (85) ~ (all_197_0 = 0) % 28.49/4.87 | (86) mono_2Etyop_2Emin_2Ebool(all_197_1) % 28.49/4.87 | (87) p(all_197_1) = all_197_0 % 28.49/4.87 | (88) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) = all_197_1 % 28.49/4.87 | % 28.49/4.87 | DELTA: instantiating (77) with fresh symbols all_199_0, all_199_1 gives: % 28.49/4.87 | (89) ~ (all_199_0 = 0) & % 28.49/4.87 | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.87 | mono_2Ec_2Ebool_2ET_2E0) = all_199_1 & p(all_199_1) = all_199_0 & % 28.49/4.87 | mono_2Etyop_2Emin_2Ebool(all_199_1) % 28.49/4.87 | % 28.49/4.87 | ALPHA: (89) implies: % 28.49/4.87 | (90) ~ (all_199_0 = 0) % 28.49/4.87 | (91) mono_2Etyop_2Emin_2Ebool(all_199_1) % 28.49/4.87 | (92) p(all_199_1) = all_199_0 % 28.49/4.87 | (93) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.87 | mono_2Ec_2Ebool_2ET_2E0) = all_199_1 % 28.49/4.87 | % 28.49/4.87 | DELTA: instantiating (83) with fresh symbols all_203_0, all_203_1 gives: % 28.49/4.87 | (94) mono_2Ec_2Ereal__topology_2Ecball_2E1(all_112_3) = all_203_1 & % 28.49/4.87 | mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_203_1) = all_203_0 & % 28.49/4.87 | p(all_203_0) = 0 & % 28.49/4.87 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(all_203_1) % 28.49/4.87 | & mono_2Etyop_2Emin_2Ebool(all_203_0) % 28.49/4.87 | % 28.49/4.87 | ALPHA: (94) implies: % 28.49/4.87 | (95) mono_2Etyop_2Emin_2Ebool(all_203_0) % 28.49/4.87 | (96) p(all_203_0) = 0 % 28.49/4.87 | (97) mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_203_1) = all_203_0 % 28.49/4.87 | (98) mono_2Ec_2Ereal__topology_2Ecball_2E1(all_112_3) = all_203_1 % 28.49/4.87 | % 28.49/4.87 | DELTA: instantiating (82) with fresh symbols all_205_0, all_205_1, all_205_2 % 28.49/4.87 | gives: % 28.49/4.87 | (99) mono_2Ec_2Ereal__topology_2Ecball_2E1(all_112_3) = all_205_1 & % 28.49/4.87 | mono_2Ec_2Ereal__topology_2Eball_2E1(all_112_3) = all_205_2 & % 28.49/4.87 | mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(all_205_2, % 28.49/4.87 | all_205_1) = all_205_0 & p(all_205_0) = 0 & % 28.49/4.87 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(all_205_1) % 28.49/4.87 | & % 28.49/4.87 | mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(all_205_2) % 28.49/4.87 | & mono_2Etyop_2Emin_2Ebool(all_205_0) % 28.49/4.87 | % 28.49/4.87 | ALPHA: (99) implies: % 28.49/4.87 | (100) mono_2Etyop_2Emin_2Ebool(all_205_0) % 28.49/4.87 | (101) mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(all_205_2) % 28.49/4.87 | (102) mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(all_205_1) % 28.49/4.87 | (103) p(all_205_0) = 0 % 28.49/4.87 | (104) mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(all_205_2, % 28.49/4.87 | all_205_1) = all_205_0 % 28.49/4.87 | (105) mono_2Ec_2Ereal__topology_2Eball_2E1(all_112_3) = all_205_2 % 28.49/4.87 | (106) mono_2Ec_2Ereal__topology_2Ecball_2E1(all_112_3) = all_205_1 % 28.49/4.87 | % 28.49/4.87 | BETA: splitting (79) gives: % 28.49/4.87 | % 28.49/4.87 | Case 1: % 28.49/4.87 | | % 28.49/4.87 | | (107) all_112_0 = 0 % 28.49/4.87 | | % 28.49/4.87 | | REDUCE: (35), (107) imply: % 28.49/4.87 | | (108) $false % 28.49/4.87 | | % 28.49/4.87 | | CLOSE: (108) is inconsistent. % 28.49/4.87 | | % 28.49/4.87 | Case 2: % 28.49/4.87 | | % 28.49/4.87 | | (109) all_112_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.49/4.87 | | % 28.49/4.87 | | REDUCE: (42), (109) imply: % 28.49/4.87 | | (110) mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_112_2) = % 28.49/4.87 | | mono_2Ec_2Ebool_2EF_2E0 % 28.49/4.87 | | % 28.49/4.87 | | REDUCE: (39), (109) imply: % 28.49/4.87 | | (111) p(mono_2Ec_2Ebool_2EF_2E0) = all_112_0 % 28.49/4.87 | | % 28.49/4.87 | | BETA: splitting (75) gives: % 28.49/4.87 | | % 28.49/4.87 | | Case 1: % 28.49/4.87 | | | % 28.49/4.87 | | | (112) all_37_0 = 0 % 28.49/4.87 | | | % 28.49/4.87 | | | REDUCE: (73), (112) imply: % 28.49/4.87 | | | (113) $false % 28.49/4.87 | | | % 28.49/4.87 | | | CLOSE: (113) is inconsistent. % 28.49/4.87 | | | % 28.49/4.87 | | Case 2: % 28.49/4.87 | | | % 28.49/4.87 | | | (114) ? [v0: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.87 | | | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.87 | | | mono_2Ec_2Ebool_2EF_2E0) = v0 & p(v0) = 0 & % 28.49/4.87 | | | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.87 | | | % 28.49/4.87 | | | DELTA: instantiating (114) with fresh symbol all_220_0 gives: % 28.49/4.87 | | | (115) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.87 | | | mono_2Ec_2Ebool_2EF_2E0) = all_220_0 & p(all_220_0) = 0 & % 28.49/4.87 | | | mono_2Etyop_2Emin_2Ebool(all_220_0) % 28.49/4.87 | | | % 28.49/4.87 | | | ALPHA: (115) implies: % 28.49/4.87 | | | (116) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.87 | | | mono_2Ec_2Ebool_2EF_2E0) = all_220_0 % 28.49/4.87 | | | % 28.49/4.87 | | | BETA: splitting (80) gives: % 28.49/4.87 | | | % 28.49/4.87 | | | Case 1: % 28.49/4.87 | | | | % 28.49/4.87 | | | | (117) all_112_0 = 0 % 28.49/4.87 | | | | % 28.49/4.87 | | | | REDUCE: (35), (117) imply: % 28.49/4.87 | | | | (118) $false % 28.49/4.87 | | | | % 28.49/4.87 | | | | CLOSE: (118) is inconsistent. % 28.49/4.87 | | | | % 28.49/4.87 | | | Case 2: % 28.49/4.87 | | | | % 28.49/4.87 | | | | (119) ? [v0: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.87 | | | | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.87 | | | | all_112_1) = v0 & p(v0) = 0 & mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.87 | | | | % 28.49/4.87 | | | | DELTA: instantiating (119) with fresh symbol all_225_0 gives: % 28.49/4.87 | | | | (120) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.87 | | | | all_112_1) = all_225_0 & p(all_225_0) = 0 & % 28.49/4.87 | | | | mono_2Etyop_2Emin_2Ebool(all_225_0) % 28.49/4.87 | | | | % 28.49/4.87 | | | | ALPHA: (120) implies: % 28.49/4.87 | | | | (121) mono_2Etyop_2Emin_2Ebool(all_225_0) % 28.49/4.87 | | | | (122) p(all_225_0) = 0 % 28.49/4.87 | | | | (123) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.87 | | | | all_112_1) = all_225_0 % 28.49/4.87 | | | | % 28.49/4.87 | | | | REDUCE: (109), (123) imply: % 28.49/4.87 | | | | (124) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.87 | | | | mono_2Ec_2Ebool_2EF_2E0) = all_225_0 % 28.49/4.87 | | | | % 28.49/4.87 | | | | BETA: splitting (76) gives: % 28.49/4.87 | | | | % 28.49/4.87 | | | | Case 1: % 28.49/4.87 | | | | | % 28.49/4.87 | | | | | (125) all_37_0 = 0 % 28.49/4.87 | | | | | % 28.49/4.87 | | | | | REDUCE: (73), (125) imply: % 28.49/4.88 | | | | | (126) $false % 28.49/4.88 | | | | | % 28.49/4.88 | | | | | CLOSE: (126) is inconsistent. % 28.49/4.88 | | | | | % 28.49/4.88 | | | | Case 2: % 28.49/4.88 | | | | | % 28.49/4.88 | | | | | (127) ? [v0: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.88 | | | | | (mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2EF_2E0) = v0 & % 28.49/4.88 | | | | | p(v0) = 0 & mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.88 | | | | | % 28.49/4.88 | | | | | DELTA: instantiating (127) with fresh symbol all_231_0 gives: % 28.49/4.88 | | | | | (128) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2EF_2E0) = % 28.49/4.88 | | | | | all_231_0 & p(all_231_0) = 0 & % 28.49/4.88 | | | | | mono_2Etyop_2Emin_2Ebool(all_231_0) % 28.49/4.88 | | | | | % 28.49/4.88 | | | | | ALPHA: (128) implies: % 28.49/4.88 | | | | | (129) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2EF_2E0) = % 28.49/4.88 | | | | | all_231_0 % 28.49/4.88 | | | | | % 28.49/4.88 | | | | | BETA: splitting (81) gives: % 28.49/4.88 | | | | | % 28.49/4.88 | | | | | Case 1: % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | (130) all_112_0 = 0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | REDUCE: (35), (130) imply: % 28.49/4.88 | | | | | | (131) $false % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | CLOSE: (131) is inconsistent. % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | Case 2: % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | (132) ? [v0: mono_2Etyop_2Emin_2Ebool] : % 28.49/4.88 | | | | | | (mono_2Ec_2Ebool_2E_7E_2E1(all_112_1) = v0 & p(v0) = 0 & % 28.49/4.88 | | | | | | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | DELTA: instantiating (132) with fresh symbol all_236_0 gives: % 28.49/4.88 | | | | | | (133) mono_2Ec_2Ebool_2E_7E_2E1(all_112_1) = all_236_0 & % 28.49/4.88 | | | | | | p(all_236_0) = 0 & mono_2Etyop_2Emin_2Ebool(all_236_0) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | ALPHA: (133) implies: % 28.49/4.88 | | | | | | (134) mono_2Etyop_2Emin_2Ebool(all_236_0) % 28.49/4.88 | | | | | | (135) p(all_236_0) = 0 % 28.49/4.88 | | | | | | (136) mono_2Ec_2Ebool_2E_7E_2E1(all_112_1) = all_236_0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | REDUCE: (109), (136) imply: % 28.49/4.88 | | | | | | (137) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2EF_2E0) = % 28.49/4.88 | | | | | | all_236_0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (15) with all_37_0, all_112_0, % 28.49/4.88 | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (21), (111) % 28.49/4.88 | | | | | | gives: % 28.49/4.88 | | | | | | (138) all_112_0 = all_37_0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (16) with all_231_0, all_236_0, % 28.49/4.88 | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (129), (137) % 28.49/4.88 | | | | | | gives: % 28.49/4.88 | | | | | | (139) all_236_0 = all_231_0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (20) with all_220_0, all_225_0, % 28.49/4.88 | | | | | | mono_2Ec_2Ebool_2EF_2E0, mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.88 | | | | | | simplifying with (116), (124) gives: % 28.49/4.88 | | | | | | (140) all_225_0 = all_220_0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (17) with all_112_2, all_205_2, % 28.49/4.88 | | | | | | all_112_3, simplifying with (41), (105) gives: % 28.49/4.88 | | | | | | (141) all_205_2 = all_112_2 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (19) with all_203_1, all_205_1, % 28.49/4.88 | | | | | | all_112_3, simplifying with (98), (106) gives: % 28.49/4.88 | | | | | | (142) all_205_1 = all_203_1 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | REDUCE: (104), (141), (142) imply: % 28.49/4.88 | | | | | | (143) mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(all_112_2, % 28.49/4.88 | | | | | | all_203_1) = all_205_0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | REDUCE: (135), (139) imply: % 28.49/4.88 | | | | | | (144) p(all_231_0) = 0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | REDUCE: (122), (140) imply: % 28.49/4.88 | | | | | | (145) p(all_220_0) = 0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | REDUCE: (102), (142) imply: % 28.49/4.88 | | | | | | (146) mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(all_203_1) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | REDUCE: (101), (141) imply: % 28.49/4.88 | | | | | | (147) mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(all_112_2) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | REDUCE: (134), (139) imply: % 28.49/4.88 | | | | | | (148) mono_2Etyop_2Emin_2Ebool(all_231_0) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | REDUCE: (121), (140) imply: % 28.49/4.88 | | | | | | (149) mono_2Etyop_2Emin_2Ebool(all_220_0) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (11) with all_197_1, all_197_0, % 28.49/4.88 | | | | | | simplifying with (86), (87) gives: % 28.49/4.88 | | | | | | (150) all_197_0 = 0 | all_197_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (11) with all_199_1, all_199_0, % 28.49/4.88 | | | | | | simplifying with (91), (92) gives: % 28.49/4.88 | | | | | | (151) all_199_0 = 0 | all_199_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (4) with all_203_0, simplifying with % 28.49/4.88 | | | | | | (95), (96) gives: % 28.49/4.88 | | | | | | (152) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 % 28.49/4.88 | | | | | | = 0) & % 28.49/4.88 | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.88 | | | | | | all_203_0) = v0 & p(v0) = v1 & % 28.49/4.88 | | | | | | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (2) with all_203_0, simplifying with % 28.49/4.88 | | | | | | (95), (96) gives: % 28.49/4.88 | | | | | | (153) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 % 28.49/4.88 | | | | | | = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_203_0) = v0 & % 28.49/4.88 | | | | | | p(v0) = v1 & mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (4) with all_205_0, simplifying with % 28.49/4.88 | | | | | | (100), (103) gives: % 28.49/4.88 | | | | | | (154) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 % 28.49/4.88 | | | | | | = 0) & % 28.49/4.88 | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.88 | | | | | | all_205_0) = v0 & p(v0) = v1 & % 28.49/4.88 | | | | | | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (2) with all_205_0, simplifying with % 28.49/4.88 | | | | | | (100), (103) gives: % 28.49/4.88 | | | | | | (155) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 % 28.49/4.88 | | | | | | = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_205_0) = v0 & % 28.49/4.88 | | | | | | p(v0) = v1 & mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (4) with all_220_0, simplifying with % 28.49/4.88 | | | | | | (145), (149) gives: % 28.49/4.88 | | | | | | (156) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 % 28.49/4.88 | | | | | | = 0) & % 28.49/4.88 | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.88 | | | | | | all_220_0) = v0 & p(v0) = v1 & % 28.49/4.88 | | | | | | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (2) with all_220_0, simplifying with % 28.49/4.88 | | | | | | (145), (149) gives: % 28.49/4.88 | | | | | | (157) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 % 28.49/4.88 | | | | | | = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_220_0) = v0 & % 28.49/4.88 | | | | | | p(v0) = v1 & mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (14) with all_220_0, % 28.49/4.88 | | | | | | mono_2Ec_2Ebool_2ET_2E0, all_231_0, simplifying with % 28.49/4.88 | | | | | | (9), (74), (144), (145), (148), (149) gives: % 28.49/4.88 | | | | | | (158) all_220_0 = mono_2Ec_2Ebool_2ET_2E0 % 28.49/4.88 | | | | | | % 28.49/4.88 | | | | | | GROUND_INST: instantiating (14) with all_205_0, all_220_0, % 28.49/4.88 | | | | | | all_231_0, simplifying with (100), (103), (144), (145), % 28.49/4.88 | | | | | | (148), (149) gives: % 28.49/4.88 | | | | | | (159) all_220_0 = all_205_0 % 28.49/4.88 | | | | | | % 28.49/4.89 | | | | | | GROUND_INST: instantiating (14) with all_203_0, all_231_0, % 28.49/4.89 | | | | | | all_205_0, simplifying with (95), (96), (100), (103), % 28.49/4.89 | | | | | | (144), (148) gives: % 28.49/4.89 | | | | | | (160) all_231_0 = all_203_0 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | GROUND_INST: instantiating (14) with all_220_0, all_231_0, % 28.49/4.89 | | | | | | all_203_0, simplifying with (95), (96), (144), (145), % 28.49/4.89 | | | | | | (148), (149) gives: % 28.49/4.89 | | | | | | (161) all_231_0 = all_220_0 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | GROUND_INST: instantiating (4) with all_231_0, simplifying with % 28.49/4.89 | | | | | | (144), (148) gives: % 28.49/4.89 | | | | | | (162) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 % 28.49/4.89 | | | | | | = 0) & % 28.49/4.89 | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.89 | | | | | | all_231_0) = v0 & p(v0) = v1 & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | GROUND_INST: instantiating (2) with all_231_0, simplifying with % 28.49/4.89 | | | | | | (144), (148) gives: % 28.49/4.89 | | | | | | (163) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 % 28.49/4.89 | | | | | | = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_231_0) = v0 & % 28.49/4.89 | | | | | | p(v0) = v1 & mono_2Etyop_2Emin_2Ebool(v0)) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | GROUND_INST: instantiating (thm_2Ereal__topology_2EBOUNDED__SUBSET) % 28.49/4.89 | | | | | | with all_112_2, all_203_1, all_205_0, simplifying with % 28.49/4.89 | | | | | | (143), (146), (147) gives: % 28.49/4.89 | | | | | | (164) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: any] : ? [v2: % 28.49/4.89 | | | | | | any] : ? [v3: mono_2Etyop_2Emin_2Ebool] : ? [v4: any] : % 28.49/4.89 | | | | | | (mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_203_1) = % 28.49/4.89 | | | | | | v0 & % 28.49/4.89 | | | | | | mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_112_2) = % 28.49/4.89 | | | | | | v3 & p(v3) = v4 & p(v0) = v1 & p(all_205_0) = v2 & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(v3) & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(v0) & ( ~ (v2 = 0) | ~ (v1 = 0) % 28.49/4.89 | | | | | | | v4 = 0)) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | COMBINE_EQS: (160), (161) imply: % 28.49/4.89 | | | | | | (165) all_220_0 = all_203_0 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | SIMP: (165) implies: % 28.49/4.89 | | | | | | (166) all_220_0 = all_203_0 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | COMBINE_EQS: (158), (159) imply: % 28.49/4.89 | | | | | | (167) all_205_0 = mono_2Ec_2Ebool_2ET_2E0 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | COMBINE_EQS: (159), (166) imply: % 28.49/4.89 | | | | | | (168) all_205_0 = all_203_0 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | COMBINE_EQS: (167), (168) imply: % 28.49/4.89 | | | | | | (169) all_203_0 = mono_2Ec_2Ebool_2ET_2E0 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | COMBINE_EQS: (160), (169) imply: % 28.49/4.89 | | | | | | (170) all_231_0 = mono_2Ec_2Ebool_2ET_2E0 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | DELTA: instantiating (154) with fresh symbols all_260_0, all_260_1 % 28.49/4.89 | | | | | | gives: % 28.49/4.89 | | | | | | (171) ~ (all_260_0 = 0) & % 28.49/4.89 | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.89 | | | | | | all_205_0) = all_260_1 & p(all_260_1) = all_260_0 & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(all_260_1) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | ALPHA: (171) implies: % 28.49/4.89 | | | | | | (172) ~ (all_260_0 = 0) % 28.49/4.89 | | | | | | (173) p(all_260_1) = all_260_0 % 28.49/4.89 | | | | | | (174) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.89 | | | | | | all_205_0) = all_260_1 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | DELTA: instantiating (156) with fresh symbols all_262_0, all_262_1 % 28.49/4.89 | | | | | | gives: % 28.49/4.89 | | | | | | (175) ~ (all_262_0 = 0) & % 28.49/4.89 | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.89 | | | | | | all_220_0) = all_262_1 & p(all_262_1) = all_262_0 & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(all_262_1) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | ALPHA: (175) implies: % 28.49/4.89 | | | | | | (176) p(all_262_1) = all_262_0 % 28.49/4.89 | | | | | | (177) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.89 | | | | | | all_220_0) = all_262_1 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | DELTA: instantiating (157) with fresh symbols all_264_0, all_264_1 % 28.49/4.89 | | | | | | gives: % 28.49/4.89 | | | | | | (178) ~ (all_264_0 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_220_0) = % 28.49/4.89 | | | | | | all_264_1 & p(all_264_1) = all_264_0 & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(all_264_1) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | ALPHA: (178) implies: % 28.49/4.89 | | | | | | (179) p(all_264_1) = all_264_0 % 28.49/4.89 | | | | | | (180) mono_2Ec_2Ebool_2E_7E_2E1(all_220_0) = all_264_1 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | DELTA: instantiating (153) with fresh symbols all_266_0, all_266_1 % 28.49/4.89 | | | | | | gives: % 28.49/4.89 | | | | | | (181) ~ (all_266_0 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_203_0) = % 28.49/4.89 | | | | | | all_266_1 & p(all_266_1) = all_266_0 & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(all_266_1) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | ALPHA: (181) implies: % 28.49/4.89 | | | | | | (182) p(all_266_1) = all_266_0 % 28.49/4.89 | | | | | | (183) mono_2Ec_2Ebool_2E_7E_2E1(all_203_0) = all_266_1 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | DELTA: instantiating (163) with fresh symbols all_268_0, all_268_1 % 28.49/4.89 | | | | | | gives: % 28.49/4.89 | | | | | | (184) ~ (all_268_0 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_231_0) = % 28.49/4.89 | | | | | | all_268_1 & p(all_268_1) = all_268_0 & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(all_268_1) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | ALPHA: (184) implies: % 28.49/4.89 | | | | | | (185) p(all_268_1) = all_268_0 % 28.49/4.89 | | | | | | (186) mono_2Ec_2Ebool_2E_7E_2E1(all_231_0) = all_268_1 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | DELTA: instantiating (155) with fresh symbols all_270_0, all_270_1 % 28.49/4.89 | | | | | | gives: % 28.49/4.89 | | | | | | (187) ~ (all_270_0 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_205_0) = % 28.49/4.89 | | | | | | all_270_1 & p(all_270_1) = all_270_0 & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(all_270_1) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | ALPHA: (187) implies: % 28.49/4.89 | | | | | | (188) p(all_270_1) = all_270_0 % 28.49/4.89 | | | | | | (189) mono_2Ec_2Ebool_2E_7E_2E1(all_205_0) = all_270_1 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | DELTA: instantiating (152) with fresh symbols all_272_0, all_272_1 % 28.49/4.89 | | | | | | gives: % 28.49/4.89 | | | | | | (190) ~ (all_272_0 = 0) & % 28.49/4.89 | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.89 | | | | | | all_203_0) = all_272_1 & p(all_272_1) = all_272_0 & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(all_272_1) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | ALPHA: (190) implies: % 28.49/4.89 | | | | | | (191) p(all_272_1) = all_272_0 % 28.49/4.89 | | | | | | (192) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.89 | | | | | | all_203_0) = all_272_1 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | DELTA: instantiating (162) with fresh symbols all_276_0, all_276_1 % 28.49/4.89 | | | | | | gives: % 28.49/4.89 | | | | | | (193) ~ (all_276_0 = 0) & % 28.49/4.89 | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.89 | | | | | | all_231_0) = all_276_1 & p(all_276_1) = all_276_0 & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(all_276_1) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | ALPHA: (193) implies: % 28.49/4.89 | | | | | | (194) p(all_276_1) = all_276_0 % 28.49/4.89 | | | | | | (195) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.89 | | | | | | all_231_0) = all_276_1 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | DELTA: instantiating (164) with fresh symbols all_292_0, all_292_1, % 28.49/4.89 | | | | | | all_292_2, all_292_3, all_292_4 gives: % 28.49/4.89 | | | | | | (196) mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_203_1) = % 28.49/4.89 | | | | | | all_292_4 & % 28.49/4.89 | | | | | | mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_112_2) = % 28.49/4.89 | | | | | | all_292_1 & p(all_292_1) = all_292_0 & p(all_292_4) = % 28.49/4.89 | | | | | | all_292_3 & p(all_205_0) = all_292_2 & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(all_292_1) & % 28.49/4.89 | | | | | | mono_2Etyop_2Emin_2Ebool(all_292_4) & ( ~ (all_292_2 = 0) | % 28.49/4.89 | | | | | | ~ (all_292_3 = 0) | all_292_0 = 0) % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | ALPHA: (196) implies: % 28.49/4.89 | | | | | | (197) p(all_205_0) = all_292_2 % 28.49/4.89 | | | | | | (198) p(all_292_4) = all_292_3 % 28.49/4.89 | | | | | | (199) p(all_292_1) = all_292_0 % 28.49/4.89 | | | | | | (200) mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_112_2) = % 28.49/4.89 | | | | | | all_292_1 % 28.49/4.89 | | | | | | (201) mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_203_1) = % 28.49/4.89 | | | | | | all_292_4 % 28.49/4.89 | | | | | | (202) ~ (all_292_2 = 0) | ~ (all_292_3 = 0) | all_292_0 = 0 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | REDUCE: (97), (169) imply: % 28.49/4.89 | | | | | | (203) mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(all_203_1) = % 28.49/4.89 | | | | | | mono_2Ec_2Ebool_2ET_2E0 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | REDUCE: (170), (195) imply: % 28.49/4.89 | | | | | | (204) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.89 | | | | | | mono_2Ec_2Ebool_2ET_2E0) = all_276_1 % 28.49/4.89 | | | | | | % 28.49/4.89 | | | | | | REDUCE: (158), (177) imply: % 28.49/4.90 | | | | | | (205) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.90 | | | | | | mono_2Ec_2Ebool_2ET_2E0) = all_262_1 % 28.49/4.90 | | | | | | % 28.49/4.90 | | | | | | REDUCE: (167), (174) imply: % 28.49/4.90 | | | | | | (206) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.90 | | | | | | mono_2Ec_2Ebool_2ET_2E0) = all_260_1 % 28.49/4.90 | | | | | | % 28.49/4.90 | | | | | | REDUCE: (169), (192) imply: % 28.49/4.90 | | | | | | (207) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.90 | | | | | | mono_2Ec_2Ebool_2ET_2E0) = all_272_1 % 28.49/4.90 | | | | | | % 28.49/4.90 | | | | | | REDUCE: (170), (186) imply: % 28.49/4.90 | | | | | | (208) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) = % 28.49/4.90 | | | | | | all_268_1 % 28.49/4.90 | | | | | | % 28.49/4.90 | | | | | | REDUCE: (158), (180) imply: % 28.49/4.90 | | | | | | (209) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) = % 28.49/4.90 | | | | | | all_264_1 % 28.49/4.90 | | | | | | % 28.49/4.90 | | | | | | REDUCE: (167), (189) imply: % 28.49/4.90 | | | | | | (210) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) = % 28.49/4.90 | | | | | | all_270_1 % 28.49/4.90 | | | | | | % 28.49/4.90 | | | | | | REDUCE: (169), (183) imply: % 28.49/4.90 | | | | | | (211) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) = % 28.49/4.90 | | | | | | all_266_1 % 28.49/4.90 | | | | | | % 28.49/4.90 | | | | | | REDUCE: (167), (197) imply: % 28.49/4.90 | | | | | | (212) p(mono_2Ec_2Ebool_2ET_2E0) = all_292_2 % 28.49/4.90 | | | | | | % 28.49/4.90 | | | | | | BETA: splitting (151) gives: % 28.49/4.90 | | | | | | % 28.49/4.90 | | | | | | Case 1: % 28.49/4.90 | | | | | | | % 28.49/4.90 | | | | | | | (213) all_199_0 = 0 % 28.49/4.90 | | | | | | | % 28.49/4.90 | | | | | | | REDUCE: (90), (213) imply: % 28.49/4.90 | | | | | | | (214) $false % 28.49/4.90 | | | | | | | % 28.49/4.90 | | | | | | | CLOSE: (214) is inconsistent. % 28.49/4.90 | | | | | | | % 28.49/4.90 | | | | | | Case 2: % 28.49/4.90 | | | | | | | % 28.49/4.90 | | | | | | | (215) all_199_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.49/4.90 | | | | | | | % 28.49/4.90 | | | | | | | REDUCE: (93), (215) imply: % 28.49/4.90 | | | | | | | (216) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 28.49/4.90 | | | | | | | mono_2Ec_2Ebool_2ET_2E0) = mono_2Ec_2Ebool_2EF_2E0 % 28.49/4.90 | | | | | | | % 28.49/4.90 | | | | | | | REDUCE: (92), (215) imply: % 28.49/4.90 | | | | | | | (217) p(mono_2Ec_2Ebool_2EF_2E0) = all_199_0 % 28.49/4.90 | | | | | | | % 28.49/4.90 | | | | | | | BETA: splitting (150) gives: % 28.49/4.90 | | | | | | | % 28.49/4.90 | | | | | | | Case 1: % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | (218) all_197_0 = 0 % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | REDUCE: (85), (218) imply: % 28.49/4.90 | | | | | | | | (219) $false % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | CLOSE: (219) is inconsistent. % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | Case 2: % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | (220) all_197_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | REDUCE: (88), (220) imply: % 28.49/4.90 | | | | | | | | (221) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) = % 28.49/4.90 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0 % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | REDUCE: (87), (220) imply: % 28.49/4.90 | | | | | | | | (222) p(mono_2Ec_2Ebool_2EF_2E0) = all_197_0 % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | GROUND_INST: instantiating (15) with all_37_0, all_199_0, % 28.49/4.90 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (21), % 28.49/4.90 | | | | | | | | (217) gives: % 28.49/4.90 | | | | | | | | (223) all_199_0 = all_37_0 % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | GROUND_INST: instantiating (15) with all_197_0, all_199_0, % 28.49/4.90 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (217), % 28.49/4.90 | | | | | | | | (222) gives: % 28.49/4.90 | | | | | | | | (224) all_199_0 = all_197_0 % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | GROUND_INST: instantiating (10) with all_292_2, simplifying with % 28.49/4.90 | | | | | | | | (212) gives: % 28.49/4.90 | | | | | | | | (225) all_292_2 = 0 % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | GROUND_INST: instantiating (16) with mono_2Ec_2Ebool_2EF_2E0, % 28.49/4.90 | | | | | | | | all_266_1, mono_2Ec_2Ebool_2ET_2E0, simplifying % 28.49/4.90 | | | | | | | | with (211), (221) gives: % 28.49/4.90 | | | | | | | | (226) all_266_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | GROUND_INST: instantiating (16) with all_266_1, all_268_1, % 28.49/4.90 | | | | | | | | mono_2Ec_2Ebool_2ET_2E0, simplifying with (208), % 28.49/4.90 | | | | | | | | (211) gives: % 28.49/4.90 | | | | | | | | (227) all_268_1 = all_266_1 % 28.49/4.90 | | | | | | | | % 28.49/4.90 | | | | | | | | GROUND_INST: instantiating (16) with all_268_1, all_270_1, % 28.49/4.90 | | | | | | | | mono_2Ec_2Ebool_2ET_2E0, simplifying with (208), % 28.49/4.90 | | | | | | | | (210) gives: % 28.89/4.90 | | | | | | | | (228) all_270_1 = all_268_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | GROUND_INST: instantiating (16) with all_264_1, all_270_1, % 28.89/4.90 | | | | | | | | mono_2Ec_2Ebool_2ET_2E0, simplifying with (209), % 28.89/4.90 | | | | | | | | (210) gives: % 28.89/4.90 | | | | | | | | (229) all_270_1 = all_264_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | GROUND_INST: instantiating (20) with mono_2Ec_2Ebool_2EF_2E0, % 28.89/4.90 | | | | | | | | all_262_1, mono_2Ec_2Ebool_2ET_2E0, % 28.89/4.90 | | | | | | | | mono_2Ec_2Ebool_2E_7E_2E0, simplifying with (205), % 28.89/4.90 | | | | | | | | (216) gives: % 28.89/4.90 | | | | | | | | (230) all_262_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | GROUND_INST: instantiating (20) with all_262_1, all_272_1, % 28.89/4.90 | | | | | | | | mono_2Ec_2Ebool_2ET_2E0, mono_2Ec_2Ebool_2E_7E_2E0, % 28.89/4.90 | | | | | | | | simplifying with (205), (207) gives: % 28.89/4.90 | | | | | | | | (231) all_272_1 = all_262_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | GROUND_INST: instantiating (20) with all_272_1, all_276_1, % 28.89/4.90 | | | | | | | | mono_2Ec_2Ebool_2ET_2E0, mono_2Ec_2Ebool_2E_7E_2E0, % 28.89/4.90 | | | | | | | | simplifying with (204), (207) gives: % 28.89/4.90 | | | | | | | | (232) all_276_1 = all_272_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | GROUND_INST: instantiating (20) with all_260_1, all_276_1, % 28.89/4.90 | | | | | | | | mono_2Ec_2Ebool_2ET_2E0, mono_2Ec_2Ebool_2E_7E_2E0, % 28.89/4.90 | | | | | | | | simplifying with (204), (206) gives: % 28.89/4.90 | | | | | | | | (233) all_276_1 = all_260_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | GROUND_INST: instantiating (18) with mono_2Ec_2Ebool_2EF_2E0, % 28.89/4.90 | | | | | | | | all_292_1, all_112_2, simplifying with (110), (200) % 28.89/4.90 | | | | | | | | gives: % 28.89/4.90 | | | | | | | | (234) all_292_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | GROUND_INST: instantiating (18) with mono_2Ec_2Ebool_2ET_2E0, % 28.89/4.90 | | | | | | | | all_292_4, all_203_1, simplifying with (201), (203) % 28.89/4.90 | | | | | | | | gives: % 28.89/4.90 | | | | | | | | (235) all_292_4 = mono_2Ec_2Ebool_2ET_2E0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | COMBINE_EQS: (232), (233) imply: % 28.89/4.90 | | | | | | | | (236) all_272_1 = all_260_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | SIMP: (236) implies: % 28.89/4.90 | | | | | | | | (237) all_272_1 = all_260_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | COMBINE_EQS: (231), (237) imply: % 28.89/4.90 | | | | | | | | (238) all_262_1 = all_260_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | SIMP: (238) implies: % 28.89/4.90 | | | | | | | | (239) all_262_1 = all_260_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | COMBINE_EQS: (228), (229) imply: % 28.89/4.90 | | | | | | | | (240) all_268_1 = all_264_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | SIMP: (240) implies: % 28.89/4.90 | | | | | | | | (241) all_268_1 = all_264_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | COMBINE_EQS: (227), (241) imply: % 28.89/4.90 | | | | | | | | (242) all_266_1 = all_264_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | SIMP: (242) implies: % 28.89/4.90 | | | | | | | | (243) all_266_1 = all_264_1 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | COMBINE_EQS: (226), (243) imply: % 28.89/4.90 | | | | | | | | (244) all_264_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | SIMP: (244) implies: % 28.89/4.90 | | | | | | | | (245) all_264_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | COMBINE_EQS: (230), (239) imply: % 28.89/4.90 | | | | | | | | (246) all_260_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | SIMP: (246) implies: % 28.89/4.90 | | | | | | | | (247) all_260_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | COMBINE_EQS: (223), (224) imply: % 28.89/4.90 | | | | | | | | (248) all_197_0 = all_37_0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | SIMP: (248) implies: % 28.89/4.90 | | | | | | | | (249) all_197_0 = all_37_0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | COMBINE_EQS: (241), (245) imply: % 28.89/4.90 | | | | | | | | (250) all_268_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | COMBINE_EQS: (229), (245) imply: % 28.89/4.90 | | | | | | | | (251) all_270_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | COMBINE_EQS: (237), (247) imply: % 28.89/4.90 | | | | | | | | (252) all_272_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | COMBINE_EQS: (233), (247) imply: % 28.89/4.90 | | | | | | | | (253) all_276_1 = mono_2Ec_2Ebool_2EF_2E0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | REDUCE: (199), (234) imply: % 28.89/4.90 | | | | | | | | (254) p(mono_2Ec_2Ebool_2EF_2E0) = all_292_0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | REDUCE: (198), (235) imply: % 28.89/4.90 | | | | | | | | (255) p(mono_2Ec_2Ebool_2ET_2E0) = all_292_3 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | REDUCE: (194), (253) imply: % 28.89/4.90 | | | | | | | | (256) p(mono_2Ec_2Ebool_2EF_2E0) = all_276_0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | REDUCE: (191), (252) imply: % 28.89/4.90 | | | | | | | | (257) p(mono_2Ec_2Ebool_2EF_2E0) = all_272_0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | REDUCE: (188), (251) imply: % 28.89/4.90 | | | | | | | | (258) p(mono_2Ec_2Ebool_2EF_2E0) = all_270_0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | REDUCE: (185), (250) imply: % 28.89/4.90 | | | | | | | | (259) p(mono_2Ec_2Ebool_2EF_2E0) = all_268_0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | REDUCE: (182), (226) imply: % 28.89/4.90 | | | | | | | | (260) p(mono_2Ec_2Ebool_2EF_2E0) = all_266_0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | REDUCE: (179), (245) imply: % 28.89/4.90 | | | | | | | | (261) p(mono_2Ec_2Ebool_2EF_2E0) = all_264_0 % 28.89/4.90 | | | | | | | | % 28.89/4.90 | | | | | | | | REDUCE: (176), (230) imply: % 28.89/4.91 | | | | | | | | (262) p(mono_2Ec_2Ebool_2EF_2E0) = all_262_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | REDUCE: (173), (247) imply: % 28.89/4.91 | | | | | | | | (263) p(mono_2Ec_2Ebool_2EF_2E0) = all_260_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | GROUND_INST: instantiating (15) with all_37_0, all_266_0, % 28.89/4.91 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (21), % 28.89/4.91 | | | | | | | | (260) gives: % 28.89/4.91 | | | | | | | | (264) all_266_0 = all_37_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | GROUND_INST: instantiating (15) with all_264_0, all_266_0, % 28.89/4.91 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (260), % 28.89/4.91 | | | | | | | | (261) gives: % 28.89/4.91 | | | | | | | | (265) all_266_0 = all_264_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | GROUND_INST: instantiating (15) with all_268_0, all_270_0, % 28.89/4.91 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (258), % 28.89/4.91 | | | | | | | | (259) gives: % 28.89/4.91 | | | | | | | | (266) all_270_0 = all_268_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | GROUND_INST: instantiating (15) with all_264_0, all_270_0, % 28.89/4.91 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (258), % 28.89/4.91 | | | | | | | | (261) gives: % 28.89/4.91 | | | | | | | | (267) all_270_0 = all_264_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | GROUND_INST: instantiating (15) with all_270_0, all_272_0, % 28.89/4.91 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (257), % 28.89/4.91 | | | | | | | | (258) gives: % 28.89/4.91 | | | | | | | | (268) all_272_0 = all_270_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | GROUND_INST: instantiating (15) with all_272_0, all_276_0, % 28.89/4.91 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (256), % 28.89/4.91 | | | | | | | | (257) gives: % 28.89/4.91 | | | | | | | | (269) all_276_0 = all_272_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | GROUND_INST: instantiating (15) with all_260_0, all_276_0, % 28.89/4.91 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (256), % 28.89/4.91 | | | | | | | | (263) gives: % 28.89/4.91 | | | | | | | | (270) all_276_0 = all_260_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | GROUND_INST: instantiating (15) with all_270_0, all_292_0, % 28.89/4.91 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (254), % 28.89/4.91 | | | | | | | | (258) gives: % 28.89/4.91 | | | | | | | | (271) all_292_0 = all_270_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | GROUND_INST: instantiating (15) with all_262_0, all_292_0, % 28.89/4.91 | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (254), % 28.89/4.91 | | | | | | | | (262) gives: % 28.89/4.91 | | | | | | | | (272) all_292_0 = all_262_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | GROUND_INST: instantiating (10) with all_292_3, simplifying with % 28.89/4.91 | | | | | | | | (255) gives: % 28.89/4.91 | | | | | | | | (273) all_292_3 = 0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (271), (272) imply: % 28.89/4.91 | | | | | | | | (274) all_270_0 = all_262_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | SIMP: (274) implies: % 28.89/4.91 | | | | | | | | (275) all_270_0 = all_262_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (269), (270) imply: % 28.89/4.91 | | | | | | | | (276) all_272_0 = all_260_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | SIMP: (276) implies: % 28.89/4.91 | | | | | | | | (277) all_272_0 = all_260_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (268), (277) imply: % 28.89/4.91 | | | | | | | | (278) all_270_0 = all_260_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | SIMP: (278) implies: % 28.89/4.91 | | | | | | | | (279) all_270_0 = all_260_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (266), (267) imply: % 28.89/4.91 | | | | | | | | (280) all_268_0 = all_264_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (266), (275) imply: % 28.89/4.91 | | | | | | | | (281) all_268_0 = all_262_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (266), (279) imply: % 28.89/4.91 | | | | | | | | (282) all_268_0 = all_260_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (280), (281) imply: % 28.89/4.91 | | | | | | | | (283) all_264_0 = all_262_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | SIMP: (283) implies: % 28.89/4.91 | | | | | | | | (284) all_264_0 = all_262_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (281), (282) imply: % 28.89/4.91 | | | | | | | | (285) all_262_0 = all_260_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (264), (265) imply: % 28.89/4.91 | | | | | | | | (286) all_264_0 = all_37_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | SIMP: (286) implies: % 28.89/4.91 | | | | | | | | (287) all_264_0 = all_37_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (284), (287) imply: % 28.89/4.91 | | | | | | | | (288) all_262_0 = all_37_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | SIMP: (288) implies: % 28.89/4.91 | | | | | | | | (289) all_262_0 = all_37_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (285), (289) imply: % 28.89/4.91 | | | | | | | | (290) all_260_0 = all_37_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | SIMP: (290) implies: % 28.89/4.91 | | | | | | | | (291) all_260_0 = all_37_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | COMBINE_EQS: (272), (289) imply: % 28.89/4.91 | | | | | | | | (292) all_292_0 = all_37_0 % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | BETA: splitting (202) gives: % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | | Case 1: % 28.89/4.91 | | | | | | | | | % 28.89/4.91 | | | | | | | | | (293) ~ (all_292_2 = 0) % 28.89/4.91 | | | | | | | | | % 28.89/4.91 | | | | | | | | | REDUCE: (225), (293) imply: % 28.89/4.91 | | | | | | | | | (294) $false % 28.89/4.91 | | | | | | | | | % 28.89/4.91 | | | | | | | | | CLOSE: (294) is inconsistent. % 28.89/4.91 | | | | | | | | | % 28.89/4.91 | | | | | | | | Case 2: % 28.89/4.91 | | | | | | | | | % 28.89/4.91 | | | | | | | | | (295) ~ (all_292_3 = 0) | all_292_0 = 0 % 28.89/4.91 | | | | | | | | | % 28.89/4.91 | | | | | | | | | BETA: splitting (295) gives: % 28.89/4.91 | | | | | | | | | % 28.89/4.91 | | | | | | | | | Case 1: % 28.89/4.91 | | | | | | | | | | % 28.89/4.91 | | | | | | | | | | (296) ~ (all_292_3 = 0) % 28.89/4.91 | | | | | | | | | | % 28.89/4.91 | | | | | | | | | | REDUCE: (273), (296) imply: % 28.89/4.91 | | | | | | | | | | (297) $false % 28.89/4.91 | | | | | | | | | | % 28.89/4.91 | | | | | | | | | | CLOSE: (297) is inconsistent. % 28.89/4.91 | | | | | | | | | | % 28.89/4.91 | | | | | | | | | Case 2: % 28.89/4.91 | | | | | | | | | | % 28.89/4.91 | | | | | | | | | | (298) all_292_0 = 0 % 28.89/4.91 | | | | | | | | | | % 28.89/4.91 | | | | | | | | | | COMBINE_EQS: (292), (298) imply: % 28.89/4.91 | | | | | | | | | | (299) all_37_0 = 0 % 28.89/4.91 | | | | | | | | | | % 28.89/4.91 | | | | | | | | | | SIMP: (299) implies: % 28.89/4.91 | | | | | | | | | | (300) all_37_0 = 0 % 28.89/4.91 | | | | | | | | | | % 28.89/4.91 | | | | | | | | | | REDUCE: (73), (300) imply: % 28.89/4.91 | | | | | | | | | | (301) $false % 28.89/4.91 | | | | | | | | | | % 28.89/4.91 | | | | | | | | | | CLOSE: (301) is inconsistent. % 28.89/4.91 | | | | | | | | | | % 28.89/4.91 | | | | | | | | | End of split % 28.89/4.91 | | | | | | | | | % 28.89/4.91 | | | | | | | | End of split % 28.89/4.91 | | | | | | | | % 28.89/4.91 | | | | | | | End of split % 28.89/4.91 | | | | | | | % 28.89/4.91 | | | | | | End of split % 28.89/4.91 | | | | | | % 28.89/4.91 | | | | | End of split % 28.89/4.91 | | | | | % 28.89/4.91 | | | | End of split % 28.89/4.91 | | | | % 28.89/4.91 | | | End of split % 28.89/4.91 | | | % 28.89/4.91 | | End of split % 28.89/4.91 | | % 28.89/4.91 | End of split % 28.89/4.91 | % 28.89/4.91 End of proof % 28.89/4.91 % SZS output end Proof for theBenchmark % 28.89/4.91 % 28.89/4.91 4289ms %------------------------------------------------------------------------------