%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ITP012_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 : n023.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 04:08:39 EDT 2023 % Result : Theorem 18.91s 3.23s % Output : Proof 25.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : ITP012_1 : TPTP v8.1.2. Bugfixed v7.5.0. % 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n023.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sun Aug 27 14:04:11 EDT 2023 % 0.14/0.35 % CPUTime : % 0.57/0.63 ________ _____ % 0.57/0.63 ___ __ \_________(_)________________________________ % 0.57/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.57/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.57/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.57/0.63 % 0.57/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.57/0.63 (2023-06-19) % 0.57/0.63 % 0.57/0.63 (c) Philipp Rümmer, 2009-2023 % 0.57/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.57/0.63 Amanda Stjerna. % 0.57/0.63 Free software under BSD-3-Clause. % 0.57/0.63 % 0.57/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.57/0.63 % 0.57/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.57/0.64 Running up to 7 provers in parallel. % 0.73/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.73/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.73/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.73/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.73/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.73/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.73/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.23/1.57 Prover 1: Preprocessing ... % 6.23/1.59 Prover 4: Preprocessing ... % 6.23/1.62 Prover 6: Preprocessing ... % 6.23/1.62 Prover 0: Preprocessing ... % 6.23/1.62 Prover 5: Preprocessing ... % 6.23/1.62 Prover 2: Preprocessing ... % 6.23/1.62 Prover 3: Preprocessing ... % 14.30/2.60 Prover 1: Warning: ignoring some quantifiers % 14.30/2.62 Prover 3: Warning: ignoring some quantifiers % 14.80/2.68 Prover 4: Warning: ignoring some quantifiers % 14.80/2.68 Prover 1: Constructing countermodel ... % 14.80/2.69 Prover 3: Constructing countermodel ... % 14.80/2.72 Prover 6: Proving ... % 14.80/2.73 Prover 4: Constructing countermodel ... % 14.80/2.74 Prover 5: Proving ... % 15.49/2.79 Prover 0: Proving ... % 16.65/2.92 Prover 2: Proving ... % 18.33/3.16 Prover 3: gave up % 18.33/3.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 18.91/3.22 Prover 0: proved (2571ms) % 18.91/3.22 % 18.91/3.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.91/3.23 % 18.91/3.24 Prover 6: stopped % 18.91/3.24 Prover 2: stopped % 18.91/3.26 Prover 5: stopped % 18.91/3.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.91/3.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 18.91/3.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.91/3.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 19.37/3.30 Prover 7: Preprocessing ... % 20.66/3.45 Prover 11: Preprocessing ... % 20.66/3.46 Prover 10: Preprocessing ... % 20.66/3.47 Prover 13: Preprocessing ... % 20.66/3.47 Prover 8: Preprocessing ... % 21.22/3.57 Prover 1: gave up % 21.62/3.57 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 21.62/3.62 Prover 7: Warning: ignoring some quantifiers % 21.62/3.64 Prover 7: Constructing countermodel ... % 22.27/3.66 Prover 8: Warning: ignoring some quantifiers % 22.27/3.66 Prover 16: Preprocessing ... % 22.51/3.68 Prover 8: Constructing countermodel ... % 23.09/3.80 Prover 10: Warning: ignoring some quantifiers % 23.09/3.81 Prover 13: Warning: ignoring some quantifiers % 23.56/3.83 Prover 10: Constructing countermodel ... % 23.56/3.85 Prover 13: Constructing countermodel ... % 23.89/3.89 Prover 4: Found proof (size 61) % 23.89/3.89 Prover 4: proved (3239ms) % 23.89/3.90 Prover 7: stopped % 23.89/3.90 Prover 10: stopped % 23.89/3.90 Prover 8: stopped % 23.89/3.90 Prover 13: stopped % 23.89/3.91 Prover 11: Warning: ignoring some quantifiers % 23.89/3.92 Prover 11: Constructing countermodel ... % 23.89/3.93 Prover 16: Warning: ignoring some quantifiers % 23.89/3.93 Prover 11: stopped % 23.89/3.94 Prover 16: Constructing countermodel ... % 24.48/3.95 Prover 16: stopped % 24.48/3.95 % 24.48/3.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 24.48/3.95 % 24.48/3.96 % SZS output start Proof for theBenchmark % 24.48/3.97 Assumptions after simplification: % 24.48/3.97 --------------------------------- % 24.48/3.97 % 24.48/3.97 (arityeq1_2Ec_2Ebool_2E_7E_2E1) % 24.67/4.00 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0) % 24.67/4.00 & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) % 24.67/4.00 | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: mono_2Etyop_2Emin_2Ebool] : % 24.67/4.00 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 24.67/4.00 v0) = v2 & p(v2) = 0 & mono_2Etyop_2Emin_2Ebool(v2))) & ! [v0: % 24.67/4.00 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ( ~ % 24.67/4.00 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 24.67/4.00 v0) = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: any] : ? [v3: % 24.67/4.00 any] : (p(v1) = v3 & p(v0) = v2 & (v3 = 0 | v2 = 0))) & ! [v0: % 24.67/4.00 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ( ~ % 24.67/4.00 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 24.67/4.00 v0) = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: any] : ? [v3: % 24.67/4.00 any] : (p(v1) = v2 & p(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: % 24.67/4.00 mono_2Etyop_2Emin_2Ebool] : ( ~ (p(v0) = 0) | ~ % 24.67/4.00 mono_2Etyop_2Emin_2Ebool(v0) | ? [v1: mono_2Etyop_2Emin_2Ebool] : ? [v2: % 24.67/4.00 int] : ( ~ (v2 = 0) & % 24.67/4.00 mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 24.67/4.00 v0) = v1 & p(v1) = v2 & mono_2Etyop_2Emin_2Ebool(v1))) % 24.67/4.00 % 24.67/4.00 (thm_2Ebool_2EEQ__CLAUSES) % 24.67/4.00 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0) & % 24.67/4.00 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ~ % 24.67/4.00 (p(mono_2Ec_2Ebool_2EF_2E0) = 0) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: % 24.67/4.00 int] : (v1 = 0 | v0 = mono_2Ec_2Ebool_2EF_2E0 | ~ (p(v0) = v1) | ~ % 24.67/4.00 mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : (v0 = % 24.67/4.00 mono_2Ec_2Ebool_2ET_2E0 | ~ (p(v0) = 0) | ~ mono_2Etyop_2Emin_2Ebool(v0)) % 24.67/4.00 & ! [v0: int] : (v0 = 0 | ~ (p(mono_2Ec_2Ebool_2ET_2E0) = v0)) % 24.67/4.00 % 24.67/4.00 (thm_2Ebool_2EIMP__CLAUSES) % 24.67/4.01 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0) & % 24.67/4.01 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: any] : ? [v1: % 24.67/4.01 any] : (p(mono_2Ec_2Ebool_2ET_2E0) = v0 & p(mono_2Ec_2Ebool_2EF_2E0) = v1 & % 24.67/4.01 ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: int] : ( ~ (v1 = 0) | ~ (v0 = 0) % 24.67/4.01 | v3 = 0 | ~ (p(v2) = v3) | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: % 24.67/4.01 mono_2Etyop_2Emin_2Ebool] : ! [v3: int] : (v3 = 0 | v0 = 0 | ~ (p(v2) = % 24.67/4.01 v3) | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: % 24.67/4.01 mono_2Etyop_2Emin_2Ebool] : ! [v3: MultipleValueBool] : (v1 = 0 | v0 = 0 % 24.67/4.01 | ~ (p(v2) = v3) | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: % 24.67/4.01 mono_2Etyop_2Emin_2Ebool] : ( ~ (v1 = 0) | ~ (p(v2) = 0) | ~ % 24.67/4.01 mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: mono_2Etyop_2Emin_2Ebool] : (v0 = % 24.67/4.01 0 | ~ (p(v2) = 0) | ~ mono_2Etyop_2Emin_2Ebool(v2))) % 24.67/4.01 % 24.67/4.01 (thm_2Ebool_2ENOT__CLAUSES) % 24.67/4.01 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0) & % 24.67/4.01 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: any] : ? [v1: % 24.67/4.01 any] : (p(mono_2Ec_2Ebool_2ET_2E0) = v0 & p(mono_2Ec_2Ebool_2EF_2E0) = v1 & % 24.67/4.01 ((v1 = 0 & ~ (v0 = 0)) | (v0 = 0 & ~ (v1 = 0)))) % 24.67/4.01 % 24.67/4.01 (thm_2Einteger_2EINT__DIVIDES__NEG) % 24.67/4.01 ! [v0: mono_2Etyop_2Einteger_2Eint] : ! [v1: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.01 ! [v2: mono_2Etyop_2Einteger_2Eint] : ! [v3: mono_2Etyop_2Emin_2Ebool] : ( ~ % 24.67/4.01 (mono_2Ec_2Einteger_2Eint__neg_2E1(v1) = v2) | ~ % 24.67/4.01 (mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v2) = v3) | ~ % 24.67/4.01 mono_2Etyop_2Einteger_2Eint(v1) | ~ mono_2Etyop_2Einteger_2Eint(v0) | % 24.67/4.01 (mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v1) = v3 & % 24.67/4.01 mono_2Etyop_2Emin_2Ebool(v3))) & ! [v0: mono_2Etyop_2Einteger_2Eint] : ! % 24.67/4.01 [v1: mono_2Etyop_2Einteger_2Eint] : ! [v2: mono_2Etyop_2Einteger_2Eint] : ! % 24.67/4.01 [v3: mono_2Etyop_2Emin_2Ebool] : ( ~ (mono_2Ec_2Einteger_2Eint__neg_2E1(v0) = % 24.67/4.01 v2) | ~ (mono_2Ec_2Einteger_2Eint__divides_2E2(v2, v1) = v3) | ~ % 24.67/4.01 mono_2Etyop_2Einteger_2Eint(v1) | ~ mono_2Etyop_2Einteger_2Eint(v0) | % 24.67/4.01 (mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v1) = v3 & % 24.67/4.01 mono_2Etyop_2Emin_2Ebool(v3))) & ! [v0: mono_2Etyop_2Einteger_2Eint] : ! % 24.67/4.01 [v1: mono_2Etyop_2Einteger_2Eint] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ( ~ % 24.67/4.01 (mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v1) = v2) | ~ % 24.67/4.01 mono_2Etyop_2Einteger_2Eint(v1) | ~ mono_2Etyop_2Einteger_2Eint(v0) | ? % 24.67/4.01 [v3: mono_2Etyop_2Einteger_2Eint] : (mono_2Ec_2Einteger_2Eint__neg_2E1(v1) = % 24.67/4.01 v3 & mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v3) = v2 & % 24.67/4.01 mono_2Etyop_2Einteger_2Eint(v3) & mono_2Etyop_2Emin_2Ebool(v2))) & ! [v0: % 24.67/4.01 mono_2Etyop_2Einteger_2Eint] : ! [v1: mono_2Etyop_2Einteger_2Eint] : ! % 24.67/4.01 [v2: mono_2Etyop_2Emin_2Ebool] : ( ~ % 24.67/4.01 (mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v1) = v2) | ~ % 24.67/4.01 mono_2Etyop_2Einteger_2Eint(v1) | ~ mono_2Etyop_2Einteger_2Eint(v0) | ? % 24.67/4.01 [v3: mono_2Etyop_2Einteger_2Eint] : (mono_2Ec_2Einteger_2Eint__neg_2E1(v0) = % 24.67/4.01 v3 & mono_2Ec_2Einteger_2Eint__divides_2E2(v3, v1) = v2 & % 24.67/4.01 mono_2Etyop_2Einteger_2Eint(v3) & mono_2Etyop_2Emin_2Ebool(v2))) % 24.67/4.01 % 24.67/4.01 (thm_2Einteger_2EINT__DIVIDES__RADD) % 24.67/4.02 ! [v0: mono_2Etyop_2Einteger_2Eint] : ! [v1: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.02 ! [v2: mono_2Etyop_2Einteger_2Eint] : ! [v3: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.02 ! [v4: mono_2Etyop_2Emin_2Ebool] : ( ~ % 24.67/4.02 (mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v3) = v4) | ~ % 24.67/4.02 (mono_2Ec_2Einteger_2Eint__add_2E2(v2, v1) = v3) | ~ % 24.67/4.02 mono_2Etyop_2Einteger_2Eint(v2) | ~ mono_2Etyop_2Einteger_2Eint(v1) | ~ % 24.67/4.02 mono_2Etyop_2Einteger_2Eint(v0) | ? [v5: mono_2Etyop_2Emin_2Ebool] : ? % 24.67/4.02 [v6: any] : ? [v7: mono_2Etyop_2Emin_2Ebool] : % 24.67/4.02 (mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v2) = v7 & % 24.67/4.02 mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v1) = v5 & p(v5) = v6 & % 24.67/4.02 mono_2Etyop_2Emin_2Ebool(v7) & mono_2Etyop_2Emin_2Ebool(v5) & ( ~ (v6 = 0) % 24.67/4.02 | v7 = v4))) % 24.67/4.02 % 24.67/4.02 (thm_2Einteger_2EINT__DIVIDES__RSUB) % 24.67/4.02 ? [v0: mono_2Etyop_2Einteger_2Eint] : ? [v1: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.02 ? [v2: mono_2Etyop_2Einteger_2Eint] : ? [v3: mono_2Etyop_2Emin_2Ebool] : ? % 24.67/4.02 [v4: mono_2Etyop_2Einteger_2Eint] : ? [v5: mono_2Etyop_2Emin_2Ebool] : ? % 24.67/4.02 [v6: mono_2Etyop_2Emin_2Ebool] : ( ~ (v6 = v5) & % 24.67/4.02 mono_2Ec_2Einteger_2Eint__sub_2E2(v2, v1) = v4 & % 24.67/4.02 mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v4) = v5 & % 24.67/4.02 mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v2) = v6 & % 24.67/4.02 mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v1) = v3 & p(v3) = 0 & % 24.67/4.02 mono_2Etyop_2Einteger_2Eint(v4) & mono_2Etyop_2Einteger_2Eint(v2) & % 24.67/4.02 mono_2Etyop_2Einteger_2Eint(v1) & mono_2Etyop_2Einteger_2Eint(v0) & % 24.67/4.02 mono_2Etyop_2Emin_2Ebool(v6) & mono_2Etyop_2Emin_2Ebool(v5) & % 24.67/4.02 mono_2Etyop_2Emin_2Ebool(v3)) % 24.67/4.02 % 24.67/4.02 (thm_2Einteger_2Eint__sub) % 24.67/4.02 ! [v0: mono_2Etyop_2Einteger_2Eint] : ! [v1: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.02 ! [v2: mono_2Etyop_2Einteger_2Eint] : ! [v3: mono_2Etyop_2Einteger_2Eint] : ( % 24.67/4.02 ~ (mono_2Ec_2Einteger_2Eint__neg_2E1(v1) = v2) | ~ % 24.67/4.02 (mono_2Ec_2Einteger_2Eint__add_2E2(v0, v2) = v3) | ~ % 24.67/4.02 mono_2Etyop_2Einteger_2Eint(v1) | ~ mono_2Etyop_2Einteger_2Eint(v0) | % 24.67/4.02 (mono_2Ec_2Einteger_2Eint__sub_2E2(v0, v1) = v3 & % 24.67/4.02 mono_2Etyop_2Einteger_2Eint(v3))) & ! [v0: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.02 ! [v1: mono_2Etyop_2Einteger_2Eint] : ! [v2: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.02 ( ~ (mono_2Ec_2Einteger_2Eint__sub_2E2(v0, v1) = v2) | ~ % 24.67/4.02 mono_2Etyop_2Einteger_2Eint(v1) | ~ mono_2Etyop_2Einteger_2Eint(v0) | ? % 24.67/4.02 [v3: mono_2Etyop_2Einteger_2Eint] : (mono_2Ec_2Einteger_2Eint__neg_2E1(v1) = % 24.67/4.02 v3 & mono_2Ec_2Einteger_2Eint__add_2E2(v0, v3) = v2 & % 24.67/4.02 mono_2Etyop_2Einteger_2Eint(v3) & mono_2Etyop_2Einteger_2Eint(v2))) % 24.67/4.02 % 24.67/4.02 (function-axioms) % 24.67/4.03 ! [v0: mono_2Etyop_2Einteger_2Eint] : ! [v1: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.03 ! [v2: mono_2Etyop_2Einteger_2Eint] : ! [v3: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.03 (v1 = v0 | ~ (mono_2Ec_2Einteger_2Eint__sub_2E2(v3, v2) = v1) | ~ % 24.67/4.03 (mono_2Ec_2Einteger_2Eint__sub_2E2(v3, v2) = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: % 24.67/4.03 mono_2Etyop_2Einteger_2Eint] : ! [v3: mono_2Etyop_2Einteger_2Eint] : (v1 = % 24.67/4.03 v0 | ~ (mono_2Ec_2Einteger_2Eint__divides_2E2(v3, v2) = v1) | ~ % 24.67/4.03 (mono_2Ec_2Einteger_2Eint__divides_2E2(v3, v2) = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29] : ! % 24.67/4.03 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29] : % 24.67/4.03 ! [v2: mono_2Etyop_2Einteger_2Eint] : ! [v3: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29] % 24.67/4.03 : (v1 = v0 | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(v3, % 24.67/4.03 v2) = v1) | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(v3, % 24.67/4.03 v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: % 24.67/4.03 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Einteger_2Eint] : ! [v3: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29] : (v1 % 24.67/4.03 = v0 | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(v3, % 24.67/4.03 v2) = v1) | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(v3, % 24.67/4.03 v2) = v0)) & ! [v0: mono_2Etyop_2Einteger_2Eint] : ! [v1: % 24.67/4.03 mono_2Etyop_2Einteger_2Eint] : ! [v2: mono_2Etyop_2Einteger_2Eint] : ! % 24.67/4.03 [v3: mono_2Etyop_2Einteger_2Eint] : (v1 = v0 | ~ % 24.67/4.03 (mono_2Ec_2Einteger_2Eint__add_2E2(v3, v2) = v1) | ~ % 24.67/4.03 (mono_2Ec_2Einteger_2Eint__add_2E2(v3, v2) = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] : % 24.67/4.03 ! [v1: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] : % 24.67/4.03 ! [v2: mono_2Etyop_2Einteger_2Eint] : ! [v3: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29] % 24.67/4.03 : (v1 = v0 | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29(v3, % 24.67/4.03 v2) = v1) | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29(v3, % 24.67/4.03 v2) = v0)) & ! [v0: mono_2Etyop_2Einteger_2Eint] : ! [v1: % 24.67/4.03 mono_2Etyop_2Einteger_2Eint] : ! [v2: mono_2Etyop_2Einteger_2Eint] : ! % 24.67/4.03 [v3: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] % 24.67/4.03 : (v1 = v0 | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(v3, % 24.67/4.03 v2) = v1) | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(v3, % 24.67/4.03 v2) = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 24.67/4.03 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 24.67/4.03 [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 24.67/4.03 : (v1 = v0 | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3, % 24.67/4.03 v2) = v1) | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3, % 24.67/4.03 v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: % 24.67/4.03 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 = % 24.67/4.03 v0 | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3, % 24.67/4.03 v2) = v1) | ~ % 24.67/4.03 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3, % 24.67/4.03 v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : ! [v3: du] : (v1 = % 24.67/4.03 v0 | ~ (c_2Emin_2E_3D_2E2(v3, v2) = v1) | ~ (c_2Emin_2E_3D_2E2(v3, v2) = % 24.67/4.03 v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: % 24.67/4.03 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: % 24.67/4.03 mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~ % 24.67/4.03 (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v1) | ~ % 24.67/4.03 (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: % 24.67/4.03 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | % 24.67/4.03 ~ (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v1) | ~ % 24.67/4.03 (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: % 24.67/4.03 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | % 24.67/4.03 ~ (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v1) | ~ % 24.67/4.03 (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v0)) & ! [v0: d] : ! [v1: d] : ! % 24.67/4.03 [v2: d] : ! [v3: d] : (v1 = v0 | ~ (tyop_2Emin_2Efun(v3, v2) = v1) | ~ % 24.67/4.03 (tyop_2Emin_2Efun(v3, v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : % 24.67/4.03 ! [v3: du] : (v1 = v0 | ~ (app_2E2(v3, v2) = v1) | ~ (app_2E2(v3, v2) = v0)) % 24.67/4.03 & ! [v0: du] : ! [v1: du] : ! [v2: u] : ! [v3: d] : (v1 = v0 | ~ (s(v3, % 24.67/4.03 v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0: mono_2Etyop_2Einteger_2Eint] % 24.67/4.03 : ! [v1: mono_2Etyop_2Einteger_2Eint] : ! [v2: mono_2Etyop_2Einteger_2Eint] % 24.67/4.03 : (v1 = v0 | ~ (mono_2Ec_2Einteger_2Eint__neg_2E1(v2) = v1) | ~ % 24.67/4.03 (mono_2Ec_2Einteger_2Eint__neg_2E1(v2) = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Einteger_2Eint] : ! [v1: mono_2Etyop_2Einteger_2Eint] : ! % 24.67/4.03 [v2: du] : (v1 = v0 | ~ (j_mono_2Etyop_2Einteger_2Eint(v2) = v1) | ~ % 24.67/4.03 (j_mono_2Etyop_2Einteger_2Eint(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! % 24.67/4.03 [v2: mono_2Etyop_2Einteger_2Eint] : (v1 = v0 | ~ % 24.67/4.03 (i_mono_2Etyop_2Einteger_2Eint(v2) = v1) | ~ % 24.67/4.03 (i_mono_2Etyop_2Einteger_2Eint(v2) = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] : % 24.67/4.03 ! [v1: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] : % 24.67/4.03 ! [v2: du] : (v1 = v0 | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29(v2) % 24.67/4.03 = v1) | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29(v2) % 24.67/4.03 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] : % 24.67/4.03 (v1 = v0 | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29(v2) % 24.67/4.03 = v1) | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29(v2) % 24.67/4.03 = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29] % 24.67/4.03 : ! [v1: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29] % 24.67/4.03 : ! [v2: du] : (v1 = v0 | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29(v2) % 24.67/4.03 = v1) | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29(v2) % 24.67/4.03 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29] % 24.67/4.03 : (v1 = v0 | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29(v2) % 24.67/4.03 = v1) | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29(v2) % 24.67/4.03 = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29] % 24.67/4.03 : ! [v1: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29] % 24.67/4.03 : ! [v2: du] : (v1 = v0 | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29(v2) % 24.67/4.03 = v1) | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29(v2) % 24.67/4.03 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29] % 24.67/4.03 : (v1 = v0 | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29(v2) % 24.67/4.03 = v1) | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29(v2) % 24.67/4.03 = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29] : ! % 24.67/4.03 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29] : % 24.67/4.03 ! [v2: du] : (v1 = v0 | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(v2) % 24.67/4.03 = v1) | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(v2) % 24.67/4.03 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29] : (v1 % 24.67/4.03 = v0 | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(v2) % 24.67/4.03 = v1) | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(v2) % 24.67/4.03 = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 24.67/4.03 : ! [v1: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 24.67/4.03 : ! [v2: du] : (v1 = v0 | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 24.67/4.03 = v1) | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 24.67/4.03 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 24.67/4.03 : (v1 = v0 | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 24.67/4.03 = v1) | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 24.67/4.03 = v0)) & ! [v0: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 24.67/4.03 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 24.67/4.03 [v2: du] : (v1 = v0 | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 24.67/4.03 v1) | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 24.67/4.03 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 24.67/4.03 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 = % 24.67/4.03 v0 | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 24.67/4.03 v1) | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 24.67/4.03 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = % 24.67/4.03 v0 | ~ (i_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~ % 24.67/4.03 (i_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 24.67/4.03 du] : (v1 = v0 | ~ (c_2Ebool_2E_3F_2E1(v2) = v1) | ~ % 24.67/4.03 (c_2Ebool_2E_3F_2E1(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : (v1 % 24.67/4.03 = v0 | ~ (c_2Ebool_2E_21_2E1(v2) = v1) | ~ (c_2Ebool_2E_21_2E1(v2) = v0)) % 24.67/4.03 & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! % 24.67/4.03 [v2: du] : (v1 = v0 | ~ (j_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~ % 24.67/4.03 (j_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : % 24.67/4.03 ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = % 24.67/4.03 v0 | ~ (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v1) | ~ % 24.67/4.03 (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 24.67/4.03 MultipleValueBool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~ % 24.67/4.03 (p(v2) = v1) | ~ (p(v2) = v0)) % 24.67/4.03 % 24.67/4.03 Further assumptions not needed in the proof: % 24.67/4.03 -------------------------------------------- % 24.67/4.03 arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, % 24.67/4.03 arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, % 24.67/4.03 arityeq1_2Ec_2Einteger_2Eint__neg_2E1, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, % 24.67/4.03 arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, arityeq2_2Ec_2Einteger_2Eint__add_2E2, % 24.67/4.03 arityeq2_2Ec_2Einteger_2Eint__divides_2E2, % 24.67/4.03 arityeq2_2Ec_2Einteger_2Eint__sub_2E2, % 24.67/4.03 arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, % 24.67/4.03 ij_2Emono_2Etyop_2Einteger_2Eint, ij_2Emono_2Etyop_2Emin_2Ebool, % 24.67/4.03 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29, % 24.67/4.03 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29, % 24.67/4.03 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29, % 24.67/4.03 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29, % 24.67/4.03 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, % 24.67/4.03 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, % 24.67/4.03 ji_2Emono_2Etyop_2Einteger_2Eint, ji_2Emono_2Etyop_2Emin_2Ebool, % 24.67/4.03 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29, % 24.67/4.03 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29, % 24.67/4.03 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29, % 24.67/4.03 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29, % 24.67/4.03 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, % 24.67/4.03 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, % 24.67/4.03 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint, % 24.67/4.03 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool, % 24.67/4.03 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29, % 24.67/4.03 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29, % 24.67/4.03 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool, % 24.67/4.03 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, % 24.67/4.03 reserved_2Eho_2Ebool__cases__ax, reserved_2Eho_2Eboolext, % 24.67/4.03 reserved_2Eho_2Eeq__ext, reserved_2Eho_2Ei__thm, reserved_2Eho_2Ek__thm, % 24.67/4.03 reserved_2Eho_2Enotfalse, reserved_2Eho_2Es__thm, reserved_2Eho_2Etruth, % 24.67/4.03 reserved_2Elogic_2E_2F_5C, reserved_2Elogic_2E_3D, reserved_2Elogic_2E_3D_3D_3E, % 24.67/4.03 reserved_2Elogic_2E_5C_2F, reserved_2Elogic_2E_7E, reserved_2Equant_2E_21, % 24.67/4.03 reserved_2Equant_2E_3F, thm_2Ebool_2EDE__MORGAN__THM, thm_2Ebool_2EDISJ__ASSOC, % 24.67/4.03 thm_2Ebool_2EDISJ__SYM, thm_2Ebool_2EFORALL__AND__THM, thm_2Ebool_2EF__IMP, % 24.67/4.03 thm_2Ebool_2EIMP__ANTISYM__AX, thm_2Ebool_2EIMP__F, % 24.67/4.03 thm_2Ebool_2ENOT__FORALL__THM, thm_2Ebool_2ETRUTH, thm_2Esat_2EAND__INV2, % 24.67/4.03 thm_2Esat_2EAND__INV__IMP, thm_2Esat_2ENOT__NOT, thm_2Esat_2EOR__DUAL2, % 24.67/4.03 thm_2Esat_2EOR__DUAL3, thm_2Esat_2Edc__conj, thm_2Esat_2Edc__disj, % 24.67/4.03 thm_2Esat_2Edc__eq, thm_2Esat_2Edc__imp, thm_2Esat_2Edc__neg % 24.67/4.03 % 24.67/4.03 Those formulas are unsatisfiable: % 24.67/4.03 --------------------------------- % 24.67/4.03 % 24.67/4.03 Begin of proof % 24.67/4.04 | % 24.67/4.04 | ALPHA: (arityeq1_2Ec_2Ebool_2E_7E_2E1) implies: % 24.67/4.04 | (1) ! [v0: mono_2Etyop_2Emin_2Ebool] : ( ~ (p(v0) = 0) | ~ % 24.67/4.04 | mono_2Etyop_2Emin_2Ebool(v0) | ? [v1: mono_2Etyop_2Emin_2Ebool] : ? % 24.67/4.04 | [v2: int] : ( ~ (v2 = 0) & % 24.67/4.04 | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 24.67/4.04 | v0) = v1 & p(v1) = v2 & mono_2Etyop_2Emin_2Ebool(v1))) % 24.67/4.04 | (2) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : (v1 = 0 | ~ (p(v0) % 24.67/4.04 | = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: % 24.67/4.04 | mono_2Etyop_2Emin_2Ebool] : % 24.67/4.04 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 24.67/4.04 | v0) = v2 & p(v2) = 0 & mono_2Etyop_2Emin_2Ebool(v2))) % 24.67/4.04 | % 24.67/4.04 | ALPHA: (thm_2Ebool_2EIMP__CLAUSES) implies: % 24.67/4.04 | (3) ? [v0: any] : ? [v1: any] : (p(mono_2Ec_2Ebool_2ET_2E0) = v0 & % 24.67/4.04 | p(mono_2Ec_2Ebool_2EF_2E0) = v1 & ! [v2: mono_2Etyop_2Emin_2Ebool] : % 24.67/4.04 | ! [v3: int] : ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | ~ (p(v2) = v3) % 24.67/4.04 | | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: % 24.67/4.04 | mono_2Etyop_2Emin_2Ebool] : ! [v3: int] : (v3 = 0 | v0 = 0 | ~ % 24.67/4.04 | (p(v2) = v3) | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: % 24.67/4.04 | mono_2Etyop_2Emin_2Ebool] : ! [v3: MultipleValueBool] : (v1 = 0 | % 24.67/4.04 | v0 = 0 | ~ (p(v2) = v3) | ~ mono_2Etyop_2Emin_2Ebool(v2)) & ! % 24.67/4.04 | [v2: mono_2Etyop_2Emin_2Ebool] : ( ~ (v1 = 0) | ~ (p(v2) = 0) | ~ % 24.67/4.04 | mono_2Etyop_2Emin_2Ebool(v2)) & ! [v2: mono_2Etyop_2Emin_2Ebool] : % 24.67/4.04 | (v0 = 0 | ~ (p(v2) = 0) | ~ mono_2Etyop_2Emin_2Ebool(v2))) % 24.67/4.04 | % 24.67/4.04 | ALPHA: (thm_2Ebool_2ENOT__CLAUSES) implies: % 24.67/4.04 | (4) ? [v0: any] : ? [v1: any] : (p(mono_2Ec_2Ebool_2ET_2E0) = v0 & % 24.67/4.04 | p(mono_2Ec_2Ebool_2EF_2E0) = v1 & ((v1 = 0 & ~ (v0 = 0)) | (v0 = 0 & % 24.67/4.04 | ~ (v1 = 0)))) % 24.67/4.04 | % 24.67/4.04 | ALPHA: (thm_2Ebool_2EEQ__CLAUSES) implies: % 24.67/4.04 | (5) mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0) % 24.67/4.04 | (6) ! [v0: int] : (v0 = 0 | ~ (p(mono_2Ec_2Ebool_2ET_2E0) = v0)) % 24.67/4.04 | (7) ! [v0: mono_2Etyop_2Emin_2Ebool] : (v0 = mono_2Ec_2Ebool_2ET_2E0 | ~ % 24.67/4.04 | (p(v0) = 0) | ~ mono_2Etyop_2Emin_2Ebool(v0)) % 24.67/4.04 | % 24.67/4.04 | ALPHA: (thm_2Einteger_2Eint__sub) implies: % 24.67/4.04 | (8) ! [v0: mono_2Etyop_2Einteger_2Eint] : ! [v1: % 24.67/4.04 | mono_2Etyop_2Einteger_2Eint] : ! [v2: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.04 | ( ~ (mono_2Ec_2Einteger_2Eint__sub_2E2(v0, v1) = v2) | ~ % 24.67/4.04 | mono_2Etyop_2Einteger_2Eint(v1) | ~ mono_2Etyop_2Einteger_2Eint(v0) % 24.67/4.04 | | ? [v3: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.04 | (mono_2Ec_2Einteger_2Eint__neg_2E1(v1) = v3 & % 24.67/4.04 | mono_2Ec_2Einteger_2Eint__add_2E2(v0, v3) = v2 & % 24.67/4.04 | mono_2Etyop_2Einteger_2Eint(v3) & mono_2Etyop_2Einteger_2Eint(v2))) % 24.67/4.04 | % 24.67/4.04 | ALPHA: (thm_2Einteger_2EINT__DIVIDES__NEG) implies: % 24.67/4.04 | (9) ! [v0: mono_2Etyop_2Einteger_2Eint] : ! [v1: % 24.67/4.04 | mono_2Etyop_2Einteger_2Eint] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ( % 24.67/4.04 | ~ (mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v1) = v2) | ~ % 24.67/4.04 | mono_2Etyop_2Einteger_2Eint(v1) | ~ mono_2Etyop_2Einteger_2Eint(v0) % 24.67/4.04 | | ? [v3: mono_2Etyop_2Einteger_2Eint] : % 24.67/4.04 | (mono_2Ec_2Einteger_2Eint__neg_2E1(v1) = v3 & % 24.67/4.04 | mono_2Ec_2Einteger_2Eint__divides_2E2(v0, v3) = v2 & % 24.67/4.04 | mono_2Etyop_2Einteger_2Eint(v3) & mono_2Etyop_2Emin_2Ebool(v2))) % 24.67/4.04 | % 24.67/4.04 | ALPHA: (function-axioms) implies: % 24.67/4.04 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 24.67/4.04 | mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = % 24.67/4.04 | v0)) % 24.67/4.04 | (11) ! [v0: mono_2Etyop_2Einteger_2Eint] : ! [v1: % 24.67/4.04 | mono_2Etyop_2Einteger_2Eint] : ! [v2: mono_2Etyop_2Einteger_2Eint] % 24.67/4.04 | : (v1 = v0 | ~ (mono_2Ec_2Einteger_2Eint__neg_2E1(v2) = v1) | ~ % 24.67/4.04 | (mono_2Ec_2Einteger_2Eint__neg_2E1(v2) = v0)) % 24.67/4.04 | (12) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] % 24.67/4.04 | : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: % 24.67/4.04 | mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] % 24.67/4.04 | : (v1 = v0 | ~ % 24.67/4.04 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3, % 24.67/4.04 | v2) = v1) | ~ % 24.67/4.04 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3, % 24.67/4.04 | v2) = v0)) % 24.67/4.05 | (13) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] % 24.67/4.05 | : ! [v2: mono_2Etyop_2Einteger_2Eint] : ! [v3: % 24.67/4.05 | mono_2Etyop_2Einteger_2Eint] : (v1 = v0 | ~ % 24.67/4.05 | (mono_2Ec_2Einteger_2Eint__divides_2E2(v3, v2) = v1) | ~ % 24.67/4.05 | (mono_2Ec_2Einteger_2Eint__divides_2E2(v3, v2) = v0)) % 24.67/4.05 | % 24.67/4.05 | DELTA: instantiating (4) with fresh symbols all_77_0, all_77_1 gives: % 24.67/4.05 | (14) p(mono_2Ec_2Ebool_2ET_2E0) = all_77_1 & p(mono_2Ec_2Ebool_2EF_2E0) = % 24.67/4.05 | all_77_0 & ((all_77_0 = 0 & ~ (all_77_1 = 0)) | (all_77_1 = 0 & ~ % 24.67/4.05 | (all_77_0 = 0))) % 24.67/4.05 | % 24.67/4.05 | ALPHA: (14) implies: % 24.67/4.05 | (15) p(mono_2Ec_2Ebool_2ET_2E0) = all_77_1 % 24.67/4.05 | % 24.67/4.05 | DELTA: instantiating (thm_2Einteger_2EINT__DIVIDES__RSUB) with fresh symbols % 24.67/4.05 | all_115_0, all_115_1, all_115_2, all_115_3, all_115_4, all_115_5, % 24.67/4.05 | all_115_6 gives: % 24.95/4.05 | (16) ~ (all_115_0 = all_115_1) & % 24.95/4.05 | mono_2Ec_2Einteger_2Eint__sub_2E2(all_115_4, all_115_5) = all_115_2 & % 24.95/4.05 | mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_115_2) = % 24.95/4.05 | all_115_1 & mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, % 24.95/4.05 | all_115_4) = all_115_0 & % 24.95/4.05 | mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_115_5) = % 24.95/4.05 | all_115_3 & p(all_115_3) = 0 & mono_2Etyop_2Einteger_2Eint(all_115_2) % 24.95/4.05 | & mono_2Etyop_2Einteger_2Eint(all_115_4) & % 24.95/4.05 | mono_2Etyop_2Einteger_2Eint(all_115_5) & % 24.95/4.05 | mono_2Etyop_2Einteger_2Eint(all_115_6) & % 24.95/4.05 | mono_2Etyop_2Emin_2Ebool(all_115_0) & % 24.95/4.05 | mono_2Etyop_2Emin_2Ebool(all_115_1) & % 24.95/4.05 | mono_2Etyop_2Emin_2Ebool(all_115_3) % 24.95/4.05 | % 24.95/4.05 | ALPHA: (16) implies: % 24.95/4.05 | (17) ~ (all_115_0 = all_115_1) % 24.95/4.05 | (18) mono_2Etyop_2Emin_2Ebool(all_115_3) % 24.95/4.05 | (19) mono_2Etyop_2Einteger_2Eint(all_115_6) % 24.95/4.05 | (20) mono_2Etyop_2Einteger_2Eint(all_115_5) % 24.95/4.05 | (21) mono_2Etyop_2Einteger_2Eint(all_115_4) % 24.95/4.05 | (22) p(all_115_3) = 0 % 24.95/4.05 | (23) mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_115_5) = % 24.95/4.05 | all_115_3 % 24.95/4.05 | (24) mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_115_4) = % 24.95/4.05 | all_115_0 % 24.95/4.05 | (25) mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_115_2) = % 24.95/4.05 | all_115_1 % 24.95/4.05 | (26) mono_2Ec_2Einteger_2Eint__sub_2E2(all_115_4, all_115_5) = all_115_2 % 24.95/4.05 | % 24.95/4.05 | DELTA: instantiating (3) with fresh symbols all_117_0, all_117_1 gives: % 24.95/4.05 | (27) p(mono_2Ec_2Ebool_2ET_2E0) = all_117_1 & p(mono_2Ec_2Ebool_2EF_2E0) = % 24.95/4.05 | all_117_0 & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : ( ~ % 24.95/4.05 | (all_117_0 = 0) | ~ (all_117_1 = 0) | v1 = 0 | ~ (p(v0) = v1) | ~ % 24.95/4.05 | mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : % 24.95/4.05 | ! [v1: int] : (v1 = 0 | all_117_1 = 0 | ~ (p(v0) = v1) | ~ % 24.95/4.05 | mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : % 24.95/4.05 | ! [v1: MultipleValueBool] : (all_117_0 = 0 | all_117_1 = 0 | ~ (p(v0) % 24.95/4.05 | = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: % 24.95/4.05 | mono_2Etyop_2Emin_2Ebool] : ( ~ (all_117_0 = 0) | ~ (p(v0) = 0) | % 24.95/4.05 | ~ mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] % 24.95/4.05 | : (all_117_1 = 0 | ~ (p(v0) = 0) | ~ mono_2Etyop_2Emin_2Ebool(v0)) % 24.95/4.05 | % 24.95/4.05 | ALPHA: (27) implies: % 24.95/4.05 | (28) p(mono_2Ec_2Ebool_2ET_2E0) = all_117_1 % 24.95/4.05 | % 24.95/4.05 | GROUND_INST: instantiating (10) with all_77_1, all_117_1, % 24.95/4.05 | mono_2Ec_2Ebool_2ET_2E0, simplifying with (15), (28) gives: % 24.95/4.05 | (29) all_117_1 = all_77_1 % 24.95/4.05 | % 24.95/4.05 | GROUND_INST: instantiating (6) with all_117_1, simplifying with (28) gives: % 24.95/4.05 | (30) all_117_1 = 0 % 24.95/4.05 | % 24.95/4.05 | COMBINE_EQS: (29), (30) imply: % 24.95/4.05 | (31) all_77_1 = 0 % 24.95/4.05 | % 24.95/4.05 | REDUCE: (15), (31) imply: % 24.95/4.05 | (32) p(mono_2Ec_2Ebool_2ET_2E0) = 0 % 24.95/4.05 | % 24.95/4.05 | GROUND_INST: instantiating (1) with mono_2Ec_2Ebool_2ET_2E0, simplifying with % 24.95/4.05 | (5), (32) gives: % 25.00/4.05 | (33) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 = 0) & % 25.00/4.05 | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 25.00/4.05 | mono_2Ec_2Ebool_2ET_2E0) = v0 & p(v0) = v1 & % 25.00/4.05 | mono_2Etyop_2Emin_2Ebool(v0)) % 25.00/4.05 | % 25.00/4.06 | GROUND_INST: instantiating (7) with all_115_3, simplifying with (18), (22) % 25.00/4.06 | gives: % 25.00/4.06 | (34) all_115_3 = mono_2Ec_2Ebool_2ET_2E0 % 25.00/4.06 | % 25.00/4.06 | GROUND_INST: instantiating (1) with all_115_3, simplifying with (18), (22) % 25.00/4.06 | gives: % 25.00/4.06 | (35) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 = 0) & % 25.00/4.06 | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 25.00/4.06 | all_115_3) = v0 & p(v0) = v1 & mono_2Etyop_2Emin_2Ebool(v0)) % 25.00/4.06 | % 25.00/4.06 | GROUND_INST: instantiating (9) with all_115_6, all_115_5, all_115_3, % 25.00/4.06 | simplifying with (19), (20), (23) gives: % 25.00/4.06 | (36) ? [v0: mono_2Etyop_2Einteger_2Eint] : % 25.00/4.06 | (mono_2Ec_2Einteger_2Eint__neg_2E1(all_115_5) = v0 & % 25.00/4.06 | mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, v0) = all_115_3 & % 25.00/4.06 | mono_2Etyop_2Einteger_2Eint(v0) & % 25.00/4.06 | mono_2Etyop_2Emin_2Ebool(all_115_3)) % 25.00/4.06 | % 25.00/4.06 | GROUND_INST: instantiating (8) with all_115_4, all_115_5, all_115_2, % 25.00/4.06 | simplifying with (20), (21), (26) gives: % 25.00/4.06 | (37) ? [v0: mono_2Etyop_2Einteger_2Eint] : % 25.00/4.06 | (mono_2Ec_2Einteger_2Eint__neg_2E1(all_115_5) = v0 & % 25.00/4.06 | mono_2Ec_2Einteger_2Eint__add_2E2(all_115_4, v0) = all_115_2 & % 25.00/4.06 | mono_2Etyop_2Einteger_2Eint(v0) & % 25.00/4.06 | mono_2Etyop_2Einteger_2Eint(all_115_2)) % 25.00/4.06 | % 25.00/4.06 | DELTA: instantiating (37) with fresh symbol all_154_0 gives: % 25.00/4.06 | (38) mono_2Ec_2Einteger_2Eint__neg_2E1(all_115_5) = all_154_0 & % 25.00/4.06 | mono_2Ec_2Einteger_2Eint__add_2E2(all_115_4, all_154_0) = all_115_2 & % 25.00/4.06 | mono_2Etyop_2Einteger_2Eint(all_154_0) & % 25.00/4.06 | mono_2Etyop_2Einteger_2Eint(all_115_2) % 25.00/4.06 | % 25.00/4.06 | ALPHA: (38) implies: % 25.00/4.06 | (39) mono_2Ec_2Einteger_2Eint__add_2E2(all_115_4, all_154_0) = all_115_2 % 25.00/4.06 | (40) mono_2Ec_2Einteger_2Eint__neg_2E1(all_115_5) = all_154_0 % 25.00/4.06 | % 25.00/4.06 | DELTA: instantiating (33) with fresh symbols all_158_0, all_158_1 gives: % 25.00/4.06 | (41) ~ (all_158_0 = 0) & % 25.00/4.06 | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 25.00/4.06 | mono_2Ec_2Ebool_2ET_2E0) = all_158_1 & p(all_158_1) = all_158_0 & % 25.00/4.06 | mono_2Etyop_2Emin_2Ebool(all_158_1) % 25.00/4.06 | % 25.00/4.06 | ALPHA: (41) implies: % 25.00/4.06 | (42) p(all_158_1) = all_158_0 % 25.00/4.06 | (43) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 25.00/4.06 | mono_2Ec_2Ebool_2ET_2E0) = all_158_1 % 25.00/4.06 | % 25.00/4.06 | DELTA: instantiating (35) with fresh symbols all_168_0, all_168_1 gives: % 25.00/4.06 | (44) ~ (all_168_0 = 0) & % 25.00/4.06 | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 25.00/4.06 | all_115_3) = all_168_1 & p(all_168_1) = all_168_0 & % 25.00/4.06 | mono_2Etyop_2Emin_2Ebool(all_168_1) % 25.00/4.06 | % 25.00/4.06 | ALPHA: (44) implies: % 25.00/4.06 | (45) ~ (all_168_0 = 0) % 25.00/4.06 | (46) mono_2Etyop_2Emin_2Ebool(all_168_1) % 25.00/4.06 | (47) p(all_168_1) = all_168_0 % 25.00/4.06 | (48) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 25.00/4.06 | all_115_3) = all_168_1 % 25.00/4.06 | % 25.00/4.06 | DELTA: instantiating (36) with fresh symbol all_176_0 gives: % 25.00/4.06 | (49) mono_2Ec_2Einteger_2Eint__neg_2E1(all_115_5) = all_176_0 & % 25.00/4.06 | mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_176_0) = % 25.00/4.06 | all_115_3 & mono_2Etyop_2Einteger_2Eint(all_176_0) & % 25.00/4.06 | mono_2Etyop_2Emin_2Ebool(all_115_3) % 25.00/4.06 | % 25.00/4.06 | ALPHA: (49) implies: % 25.00/4.06 | (50) mono_2Etyop_2Einteger_2Eint(all_176_0) % 25.00/4.06 | (51) mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_176_0) = % 25.00/4.06 | all_115_3 % 25.00/4.06 | (52) mono_2Ec_2Einteger_2Eint__neg_2E1(all_115_5) = all_176_0 % 25.00/4.06 | % 25.00/4.06 | REDUCE: (34), (51) imply: % 25.00/4.06 | (53) mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_176_0) = % 25.00/4.06 | mono_2Ec_2Ebool_2ET_2E0 % 25.00/4.06 | % 25.00/4.06 | REDUCE: (34), (48) imply: % 25.00/4.06 | (54) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 25.00/4.06 | mono_2Ec_2Ebool_2ET_2E0) = all_168_1 % 25.00/4.06 | % 25.00/4.06 | GROUND_INST: instantiating (12) with all_158_1, all_168_1, % 25.00/4.06 | mono_2Ec_2Ebool_2ET_2E0, mono_2Ec_2Ebool_2E_7E_2E0, simplifying % 25.00/4.06 | with (43), (54) gives: % 25.00/4.06 | (55) all_168_1 = all_158_1 % 25.00/4.06 | % 25.00/4.06 | GROUND_INST: instantiating (11) with all_154_0, all_176_0, all_115_5, % 25.00/4.06 | simplifying with (40), (52) gives: % 25.00/4.06 | (56) all_176_0 = all_154_0 % 25.00/4.06 | % 25.00/4.06 | REDUCE: (53), (56) imply: % 25.00/4.06 | (57) mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_154_0) = % 25.00/4.06 | mono_2Ec_2Ebool_2ET_2E0 % 25.00/4.06 | % 25.00/4.06 | REDUCE: (47), (55) imply: % 25.00/4.06 | (58) p(all_158_1) = all_168_0 % 25.00/4.06 | % 25.00/4.06 | REDUCE: (50), (56) imply: % 25.00/4.06 | (59) mono_2Etyop_2Einteger_2Eint(all_154_0) % 25.00/4.06 | % 25.00/4.06 | REDUCE: (46), (55) imply: % 25.00/4.06 | (60) mono_2Etyop_2Emin_2Ebool(all_158_1) % 25.00/4.06 | % 25.00/4.06 | GROUND_INST: instantiating (10) with all_158_0, all_168_0, all_158_1, % 25.00/4.06 | simplifying with (42), (58) gives: % 25.00/4.07 | (61) all_168_0 = all_158_0 % 25.00/4.07 | % 25.00/4.07 | REDUCE: (45), (61) imply: % 25.00/4.07 | (62) ~ (all_158_0 = 0) % 25.00/4.07 | % 25.00/4.07 | GROUND_INST: instantiating (2) with all_158_1, all_158_0, simplifying with % 25.00/4.07 | (42), (60) gives: % 25.00/4.07 | (63) all_158_0 = 0 | ? [v0: mono_2Etyop_2Emin_2Ebool] : % 25.00/4.07 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0, % 25.00/4.07 | all_158_1) = v0 & p(v0) = 0 & mono_2Etyop_2Emin_2Ebool(v0)) % 25.00/4.07 | % 25.00/4.07 | GROUND_INST: instantiating (thm_2Einteger_2EINT__DIVIDES__RADD) with % 25.00/4.07 | all_115_6, all_154_0, all_115_4, all_115_2, all_115_1, % 25.00/4.07 | simplifying with (19), (21), (25), (39), (59) gives: % 25.00/4.07 | (64) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: any] : ? [v2: % 25.00/4.07 | mono_2Etyop_2Emin_2Ebool] : % 25.00/4.07 | (mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_154_0) = v0 & % 25.00/4.07 | mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_115_4) = v2 & % 25.00/4.07 | p(v0) = v1 & mono_2Etyop_2Emin_2Ebool(v2) & % 25.00/4.07 | mono_2Etyop_2Emin_2Ebool(v0) & ( ~ (v1 = 0) | v2 = all_115_1)) % 25.00/4.07 | % 25.00/4.07 | DELTA: instantiating (64) with fresh symbols all_255_0, all_255_1, all_255_2 % 25.00/4.07 | gives: % 25.00/4.07 | (65) mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_154_0) = % 25.00/4.07 | all_255_2 & mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, % 25.00/4.07 | all_115_4) = all_255_0 & p(all_255_2) = all_255_1 & % 25.00/4.07 | mono_2Etyop_2Emin_2Ebool(all_255_0) & % 25.00/4.07 | mono_2Etyop_2Emin_2Ebool(all_255_2) & ( ~ (all_255_1 = 0) | all_255_0 % 25.00/4.07 | = all_115_1) % 25.00/4.07 | % 25.00/4.07 | ALPHA: (65) implies: % 25.00/4.07 | (66) p(all_255_2) = all_255_1 % 25.00/4.07 | (67) mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_115_4) = % 25.00/4.07 | all_255_0 % 25.00/4.07 | (68) mono_2Ec_2Einteger_2Eint__divides_2E2(all_115_6, all_154_0) = % 25.00/4.07 | all_255_2 % 25.00/4.07 | (69) ~ (all_255_1 = 0) | all_255_0 = all_115_1 % 25.00/4.07 | % 25.00/4.07 | BETA: splitting (63) gives: % 25.00/4.07 | % 25.00/4.07 | Case 1: % 25.00/4.07 | | % 25.00/4.07 | | (70) all_158_0 = 0 % 25.00/4.07 | | % 25.00/4.07 | | REDUCE: (62), (70) imply: % 25.00/4.07 | | (71) $false % 25.00/4.07 | | % 25.00/4.07 | | CLOSE: (71) is inconsistent. % 25.00/4.07 | | % 25.00/4.07 | Case 2: % 25.00/4.07 | | % 25.00/4.07 | | % 25.00/4.07 | | GROUND_INST: instantiating (13) with all_115_0, all_255_0, all_115_4, % 25.00/4.07 | | all_115_6, simplifying with (24), (67) gives: % 25.00/4.07 | | (72) all_255_0 = all_115_0 % 25.00/4.07 | | % 25.00/4.07 | | GROUND_INST: instantiating (13) with mono_2Ec_2Ebool_2ET_2E0, all_255_2, % 25.00/4.07 | | all_154_0, all_115_6, simplifying with (57), (68) gives: % 25.00/4.07 | | (73) all_255_2 = mono_2Ec_2Ebool_2ET_2E0 % 25.00/4.07 | | % 25.00/4.07 | | REDUCE: (66), (73) imply: % 25.00/4.07 | | (74) p(mono_2Ec_2Ebool_2ET_2E0) = all_255_1 % 25.00/4.07 | | % 25.00/4.07 | | BETA: splitting (69) gives: % 25.00/4.07 | | % 25.00/4.07 | | Case 1: % 25.00/4.07 | | | % 25.00/4.07 | | | (75) ~ (all_255_1 = 0) % 25.00/4.07 | | | % 25.00/4.07 | | | GROUND_INST: instantiating (6) with all_255_1, simplifying with (74) % 25.00/4.07 | | | gives: % 25.00/4.07 | | | (76) all_255_1 = 0 % 25.00/4.07 | | | % 25.00/4.07 | | | REDUCE: (75), (76) imply: % 25.00/4.07 | | | (77) $false % 25.00/4.07 | | | % 25.00/4.07 | | | CLOSE: (77) is inconsistent. % 25.00/4.07 | | | % 25.00/4.07 | | Case 2: % 25.00/4.07 | | | % 25.00/4.07 | | | (78) all_255_0 = all_115_1 % 25.00/4.07 | | | % 25.00/4.07 | | | COMBINE_EQS: (72), (78) imply: % 25.00/4.07 | | | (79) all_115_0 = all_115_1 % 25.00/4.07 | | | % 25.00/4.07 | | | SIMP: (79) implies: % 25.00/4.07 | | | (80) all_115_0 = all_115_1 % 25.00/4.07 | | | % 25.00/4.07 | | | REDUCE: (17), (80) imply: % 25.00/4.07 | | | (81) $false % 25.00/4.07 | | | % 25.00/4.07 | | | CLOSE: (81) is inconsistent. % 25.00/4.07 | | | % 25.00/4.07 | | End of split % 25.00/4.07 | | % 25.00/4.07 | End of split % 25.00/4.07 | % 25.00/4.07 End of proof % 25.00/4.07 % SZS output end Proof for theBenchmark % 25.00/4.07 % 25.00/4.07 3442ms %------------------------------------------------------------------------------