a>asize_tableauV0c0ICtaRoota>asize_fo_formula_listV3c0Aa>asize_fo_formulaV2c0Aa>asize_tableauV1c0aNodeVVVV0ACtaRoota<anat_to_intanat_size_tableauV4anat_to_intanat_size_tableauV0Aa<=c0anat_to_intanat_size_tableauV0aNodeVVVV0F
VC for size_positive_lemma_tableau
a>asize_tableauV0c0F
a=arename_tableauarename_tableauV1V2V3V4V5arename_tableauV1arcomposeV2V4arcomposeV3V5ICtaRoota=arename_fo_formula_listarename_fo_formula_listV8V2V3V4V5arename_fo_formula_listV8arcomposeV2V4arcomposeV3V5Aa=arename_fo_formulaarename_fo_formulaV7V2V3V4V5arename_fo_formulaV7arcomposeV2V4arcomposeV3V5Aa=arename_tableauarename_tableauV6V2V3V4V5arename_tableauV6arcomposeV2V4arcomposeV3V5aNodeVVVV1ACtaRoota<asize_tableauV9asize_tableauV1Aa<=c0asize_tableauV1aNodeVVVV1F
VC for renaming_composition_lemma_tableau
a=arename_tableauarename_tableauV1V2V3V4V5arename_tableauV1arcomposeV2V4arcomposeV3V5F
a=arename_tableauV6aidentityaidentityV6ICtaRoota=arename_fo_formula_listV9aidentityaidentityV9Aa=arename_fo_formulaV8aidentityaidentityV8Aa=arename_tableauV7aidentityaidentityV7aNodeVVVV6ACtaRoota<asize_tableauV10asize_tableauV6Aa<=c0asize_tableauV6aNodeVVVV6F
VC for renaming_identity_lemma_tableau
a=arename_tableauV6aidentityaidentityV6F
a=asubst_tableauarename_tableauV7V8V9V10V11asubst_tableauV7arcomposeV8V10arcomposeV9V11ICtaRoota=asubst_fo_formula_listarename_fo_formula_listV14V8V9V20V19asubst_fo_formula_listV14arcomposeV8V20arcomposeV9V19Larename_subst_symbolV10aidentityLarename_subst_fo_termV11aidentityaidentityAa=asubst_fo_formulaarename_fo_formulaV13V8V9V18V17asubst_fo_formulaV13arcomposeV8V18arcomposeV9V17Larename_subst_symbolV10aidentityLarename_subst_fo_termV11aidentityaidentityAa=asubst_tableauarename_tableauV12V8V9V16V15asubst_tableauV12arcomposeV8V16arcomposeV9V15Larename_subst_symbolV10aidentityLarename_subst_fo_termV11aidentityaidentityaNodeVVVV7ACtaRoota<asize_tableauV21asize_tableauV7Aa<=c0asize_tableauV7aNodeVVVV7F
VC for rename_then_subst_composition_lemma_tableau
a=asubst_tableauarename_tableauV7V8V9V10V11asubst_tableauV7arcomposeV8V10arcomposeV9V11F
a=arename_tableauasubst_tableauV12V13V14V15V16asubst_tableauV12arename_subst_symbolV13V15arename_subst_fo_termV14V15V16ICtaRoota=arename_fo_formula_listasubst_fo_formula_listV19V25V24V15V16asubst_fo_formula_listV19arename_subst_symbolV25V15arename_subst_fo_termV24V15V16Larename_subst_symbolV13aidentityLarename_subst_fo_termV14aidentityaidentityAa=arename_fo_formulaasubst_fo_formulaV18V23V22V15V16asubst_fo_formulaV18arename_subst_symbolV23V15arename_subst_fo_termV22V15V16Larename_subst_symbolV13aidentityLarename_subst_fo_termV14aidentityaidentityAa=arename_tableauasubst_tableauV17V21V20V15V16asubst_tableauV17arename_subst_symbolV21V15arename_subst_fo_termV20V15V16Larename_subst_symbolV13aidentityLarename_subst_fo_termV14aidentityaidentityaNodeVVVV12ACtaRoota<asize_tableauV26asize_tableauV12Aa<=c0asize_tableauV12aNodeVVVV12F
VC for subst_then_rename_composition_lemma_tableau
a=arename_tableauasubst_tableauV12V13V14V15V16asubst_tableauV12arename_subst_symbolV13V15arename_subst_fo_termV14V15V16F
a<asize_tableauV22asize_tableauV17Aa<=c0asize_tableauV17Ia=V17aNodeV22V23V24FF
variant decrease
a=asubst_tableauasubst_tableauV17V18V19V20V21asubst_tableauV17asubst_compose_symbolV18V20asubst_compose_fo_termV19V20V21ICtaRoota=asubst_fo_formula_listasubst_fo_formula_listV24V36V35V34V33asubst_fo_formula_listV24asubst_compose_symbolV36V34asubst_compose_fo_termV35V34V33Larename_subst_symbolV18aidentityLarename_subst_fo_termV19aidentityaidentityLarename_subst_symbolV20aidentityLarename_subst_fo_termV21aidentityaidentityAa=asubst_fo_formulaasubst_fo_formulaV23V32V31V30V29asubst_fo_formulaV23asubst_compose_symbolV32V30asubst_compose_fo_termV31V30V29Larename_subst_symbolV18aidentityLarename_subst_fo_termV19aidentityaidentityLarename_subst_symbolV20aidentityLarename_subst_fo_termV21aidentityaidentityAa=asubst_tableauasubst_tableauV22V28V27V26V25asubst_tableauV22asubst_compose_symbolV28V26asubst_compose_fo_termV27V26V25Larename_subst_symbolV18aidentityLarename_subst_fo_termV19aidentityaidentityLarename_subst_symbolV20aidentityLarename_subst_fo_termV21aidentityaidentityaNodeVVVV17F
postcondition
a=asubst_tableauasubst_tableauV17V18V19V20V21asubst_tableauV17asubst_compose_symbolV18V20asubst_compose_fo_termV19V20V21ICtaRoota=asubst_fo_formula_listasubst_fo_formula_listV24V36V35V34V33asubst_fo_formula_listV24asubst_compose_symbolV36V34asubst_compose_fo_termV35V34V33Larename_subst_symbolV18aidentityLarename_subst_fo_termV19aidentityaidentityLarename_subst_symbolV20aidentityLarename_subst_fo_termV21aidentityaidentityAa=asubst_fo_formulaasubst_fo_formulaV23V32V31V30V29asubst_fo_formulaV23asubst_compose_symbolV32V30asubst_compose_fo_termV31V30V29Larename_subst_symbolV18aidentityLarename_subst_fo_termV19aidentityaidentityLarename_subst_symbolV20aidentityLarename_subst_fo_termV21aidentityaidentityAa=asubst_tableauasubst_tableauV22V28V27V26V25asubst_tableauV22asubst_compose_symbolV28V26asubst_compose_fo_termV27V26V25Larename_subst_symbolV18aidentityLarename_subst_fo_termV19aidentityaidentityLarename_subst_symbolV20aidentityLarename_subst_fo_termV21aidentityaidentityaNodeVVVV17ACtaRoota<asize_tableauV37asize_tableau
VC for subst_composition_lemma_tableau
a=asubst_tableauasubst_tableauV17V18V19V20V21asubst_tableauV17asubst_compose_symbolV18V20asubst_compose_fo_termV19V20V21F
a=asubst_tableauV22asubst_id_symbolasubst_id_fo_termV22ICtaRoota=asubst_fo_formula_listV25asubst_id_symbolasubst_id_fo_termV25Aa=asubst_fo_formulaV24asubst_id_symbolasubst_id_fo_termV24Aa=asubst_tableauV23asubst_id_symbolasubst_id_fo_termV23aNodeVVVV22ACtaRoota<asize_tableauV26asize_tableauV22Aa<=c0asize_tableauV22aNodeVVVV22F
VC for subst_identity_lemma_tableau
a=asubst_tableauV22asubst_id_symbolasubst_id_fo_termV22F
a=asize_tableauarename_tableauV23V24V25asize_tableauV23ICtaRoota=asize_fo_formula_listarename_fo_formula_listV28V24V25asize_fo_formula_listV28Aa=asize_fo_formulaarename_fo_formulaV27V24V25asize_fo_formulaV27Aa=asize_tableauarename_tableauV26V24V25asize_tableauV26aNodeVVVV23ACtaRoota<asize_tableauV29asize_tableauV23Aa<=c0asize_tableauV23aNodeVVVV23F
VC for renaming_preserve_size_tableau
a=asize_tableauarename_tableauV23V24V25asize_tableauV23F
a=a@V28V30V26Aais_symbol_free_var_in_tableauV30V27ICfaRootiia=V30V34Aa=a@V28V34V26Aais_symbol_free_var_in_fo_formula_listV34V33EAais_symbol_free_var_in_fo_formula_listV26arename_fo_formula_listV33V28V29a=V30V35Aa=a@V28V35V26Aais_symbol_free_var_in_fo_formulaV35V32Eais_symbol_free_var_in_fo_formulaV26arename_fo_formulaV32V28V29a=V30V36Aa=a@V28V36V26Aais_symbol_free_var_in_tableauV36V31Eais_symbol_free_var_in_tableauV26arename_tableauV31V28V29aNodeVVVV27FACfaRootiiifais_symbol_free_var_in_fo_formula_listV26arename_fo_formula_listV39V28V29ais_symbol_free_var_in_fo_formula_listV26arename_fo_formula_listV39V28V29ais_symbol_free_var_in_fo_formulaV26arename_fo_formulaV38V28V29ais_symbol_free_var_in_fo_formulaV26arename_fo_formulaV38V28V29ais_symbol_free_var_in_tableauV26arename_tableauV37V28V29Aa<asize_tableauV37asize_tableauV27Aa<=c0asize_tableauV27ais_symbol_free_var_in_tableauV26arename_tableauV37V28V29aNodeVVVV27Iais_symbol_free_var_in_tableauV26arename_tableauV27V28V29F
VC for rename_free_var_constructive_inversion_symbol_tableau
a=a@V28V31V26Aais_symbol_free_var_in_tableauV31V27EIa=a@V28V30V26Aais_symbol_free_var_in_tableauV30V27FAais_symbol_free_var_in_tableauV26arename_tableauV27V28V29Aa<asize_tableauV27a+c1asize_tableauV27Aa<=c0a+c1asize_tableauV27Iais_symbol_free_var_in_tableauV26arename_tableauV27V28V29F
VC for rename_free_var_inversion_symbol_tableau
a=a@V29V30V26Aais_fo_term_free_var_in_tableauV30V27ICfaRootiia=V30V34Aa=a@V29V34V26Aais_fo_term_free_var_in_fo_formula_listV34V33EAais_fo_term_free_var_in_fo_formula_listV26arename_fo_formula_listV33V28V29a=V30V35Aa=a@V29V35V26Aais_fo_term_free_var_in_fo_formulaV35V32Eais_fo_term_free_var_in_fo_formulaV26arename_fo_formulaV32V28V29a=V30V36Aa=a@V29V36V26Aais_fo_term_free_var_in_tableauV36V31Eais_fo_term_free_var_in_tableauV26arename_tableauV31V28V29aNodeVVVV27FACfaRootiiifais_fo_term_free_var_in_fo_formula_listV26arename_fo_formula_listV39V28V29ais_fo_term_free_var_in_fo_formula_listV26arename_fo_formula_listV39V28V29ais_fo_term_free_var_in_fo_formulaV26arename_fo_formulaV38V28V29ais_fo_term_free_var_in_fo_formulaV26arename_fo_formulaV38V28V29ais_fo_term_free_var_in_tableauV26arename_tableauV37V28V29Aa<asize_tableauV37asize_tableauV27Aa<=c0asize_tableauV27ais_fo_term_free_var_in_tableauV26arename_tableauV37V28V29aNodeVVVV27Iais_fo_term_free_var_in_tableauV26arename_tableauV27V28V29F
VC for rename_free_var_constructive_inversion_fo_term_tableau
a=a@V29V31V26Aais_fo_term_free_var_in_tableauV31V27EIa=a@V29V30V26Aais_fo_term_free_var_in_tableauV30V27FAais_fo_term_free_var_in_tableauV26arename_tableauV27V28V29Aa<asize_tableauV27a+c1asize_tableauV27Aa<=c0a+c1asize_tableauV27Iais_fo_term_free_var_in_tableauV26arename_tableauV27V28V29F
VC for rename_free_var_inversion_fo_term_tableau
a=a@V28V30V26Aais_symbol_free_var_in_tableauV30V27EIais_symbol_free_var_in_tableauV26arename_tableauV27V28V29F
a=a@V34V35V31Aais_fo_term_free_var_in_tableauV35V32EIais_fo_term_free_var_in_tableauV31arename_tableauV32V33V34F
ais_symbol_free_var_in_tableaua@V38V36arename_tableauV37V38V39Iais_symbol_free_var_in_tableauV36V37ICtaRootais_symbol_free_var_in_fo_formula_lista@V38V36arename_fo_formula_listV42V38V39Iais_symbol_free_var_in_fo_formula_listV36V42Aais_symbol_free_var_in_fo_formulaa@V38V36arename_fo_formulaV41V38V39Iais_symbol_free_var_in_fo_formulaV36V41Aais_symbol_free_var_in_tableaua@V38V36arename_tableauV40V38V39Iais_symbol_free_var_in_tableauV36V40aNodeVVVV37ACtaRoota<asize_tableauV43asize_tableauV37Aa<=c0asize_tableauV37aNodeVVVV37F
VC for rename_free_var_propagation_symbol_tableau
ais_fo_term_free_var_in_tableaua@V39V36arename_tableauV37V38V39Iais_fo_term_free_var_in_tableauV36V37ICtaRootais_fo_term_free_var_in_fo_formula_lista@V39V36arename_fo_formula_listV42V38V39Iais_fo_term_free_var_in_fo_formula_listV36V42Aais_fo_term_free_var_in_fo_formulaa@V39V36arename_fo_formulaV41V38V39Iais_fo_term_free_var_in_fo_formulaV36V41Aais_fo_term_free_var_in_tableaua@V39V36arename_tableauV40V38V39Iais_fo_term_free_var_in_tableauV36V40aNodeVVVV37ACtaRoota<asize_tableauV43asize_tableauV37Aa<=c0asize_tableauV37aNodeVVVV37F
VC for rename_free_var_propagation_fo_term_tableau
ais_symbol_free_var_in_tableaua@V38V36arename_tableauV37V38V39Iais_symbol_free_var_in_tableauV36V37F
ais_fo_term_free_var_in_tableaua@V43V40arename_tableauV41V42V43Iais_fo_term_free_var_in_tableauV40V41F
Cais_symbol_free_var_in_symbolV44a@V46V49Aais_symbol_free_var_in_tableauV49V45aLeftVais_symbol_free_var_in_fo_termV44a@V47V50Aais_fo_term_free_var_in_tableauV50V45aRightVV48ICfaRootiiCa=V48aLeftV55Aa=V56V44Aa=a@aidentityV56V44Aais_symbol_free_var_in_symbolV56aevalV46V55EaLeftVa=V48aRightV57Aa=V58V44Aa=a@aidentityV58V44Aais_symbol_free_var_in_fo_termV58aevalV47V57EaRightVV54ACais_symbol_free_var_in_symbolV44a@arename_subst_symbolV46aidentityV59Aais_symbol_free_var_in_fo_formula_listV59V53aLeftVais_symbol_free_var_in_fo_termV44a@arename_subst_fo_termV47aidentityaidentityV60Aais_fo_term_free_var_in_fo_formula_listV60V53aRightVV54EAais_symbol_free_var_in_fo_formula_listV44asubst_fo_formula_listV53arename_subst_symbolV46aidentityarename_subst_fo_termV47aidentityaidentityCa=V48aLeftV62Aa=V63V44Aa=a@aidentityV63V44Aais_symbol_free_var_in_symbolV63aevalV46V62EaLeftVa=V48aRightV64Aa=V65V44Aa=a@aidentityV65V44Aais_symbol_free_var_in_fo_termV65aevalV47V64EaRightVV61ACais_symbol_free_var_in_symbolV44a@arename_subst_symbol
VC for subst_free_var_constructive_inversion_symbol_tableau
ais_symbol_free_var_in_fo_termV44a@V47V49Aais_fo_term_free_var_in_tableauV49V45EOais_symbol_free_var_in_symbolV44a@V46V50Aais_symbol_free_var_in_tableauV50V45EICtaLeftVtaRightVV48ICais_symbol_free_var_in_symbolV44a@V46V53Aais_symbol_free_var_in_tableauV53V45aLeftVais_symbol_free_var_in_fo_termV44a@V47V54Aais_fo_term_free_var_in_tableauV54V45aRightVV48FAais_symbol_free_var_in_tableauV44asubst_tableauV45V46V47Aa<asize_tableauV45a+c1asize_tableauV45Aa<=c0a+c1asize_tableauV45Iais_symbol_free_var_in_tableauV44asubst_tableauV45V46V47F
VC for subst_free_var_inversion_symbol_tableau
ais_fo_term_free_var_in_fo_termV44a@V47V48Aais_fo_term_free_var_in_tableauV48V45ICfaRootiia=V48V52Aa=V53V44Aa=a@aidentityV53V44Aais_fo_term_free_var_in_fo_termV53aevalV47V52EAais_fo_term_free_var_in_fo_termV44a@arename_subst_fo_termV47aidentityaidentityV52Aais_fo_term_free_var_in_fo_formula_listV52V51EAais_fo_term_free_var_in_fo_formula_listV44asubst_fo_formula_listV51arename_subst_symbolV46aidentityarename_subst_fo_termV47aidentityaidentitya=V48V54Aa=V55V44Aa=a@aidentityV55V44Aais_fo_term_free_var_in_fo_termV55aevalV47V54EAais_fo_term_free_var_in_fo_termV44a@arename_subst_fo_termV47aidentityaidentityV54Aais_fo_term_free_var_in_fo_formulaV54V50Eais_fo_term_free_var_in_fo_formulaV44asubst_fo_formulaV50arename_subst_symbolV46aidentityarename_subst_fo_termV47aidentityaidentitya=V48V56Aa=V57V44Aa=a@aidentityV57V44Aais_fo_term_free_var_in_fo_termV57aevalV47V56EAais_fo_term_free_var_in_fo_termV44a@arename_subst_fo_termV47aidentityaidentityV56Aais_fo_term_free_var_in_tableauV56V49Eais_fo_term_free_var_in_tableauV44a
VC for subst_free_var_constructive_inversion_fo_term_tableau
ais_fo_term_free_var_in_fo_termV44a@V47V49Aais_fo_term_free_var_in_tableauV49V45EIais_fo_term_free_var_in_fo_termV44a@V47V48Aais_fo_term_free_var_in_tableauV48V45FAais_fo_term_free_var_in_tableauV44asubst_tableauV45V46V47Aa<asize_tableauV45a+c1asize_tableauV45Aa<=c0a+c1asize_tableauV45Iais_fo_term_free_var_in_tableauV44asubst_tableauV45V46V47F
VC for subst_free_var_inversion_fo_term_tableau
ais_symbol_free_var_in_fo_termV44a@V47V48Aais_fo_term_free_var_in_tableauV48V45EOais_symbol_free_var_in_symbolV44a@V46V49Aais_symbol_free_var_in_tableauV49V45EIais_symbol_free_var_in_tableauV44asubst_tableauV45V46V47F
ais_fo_term_free_var_in_fo_termV50a@V53V54Aais_fo_term_free_var_in_tableauV54V51EIais_fo_term_free_var_in_tableauV50asubst_tableauV51V52V53F
a<asize_tableauV60asize_tableauV57Aa<=c0asize_tableauV57Larename_subst_symbolV58aidentityIa=V57aNodeV60V61V62FF
ais_symbol_free_var_in_symbolV56aevalarename_subst_symbolV58aidentityV55Iais_symbol_free_var_in_symbolV56a@V58V55Iais_symbol_free_var_in_symbola@V64V56arename_symbolV65V64Iais_symbol_free_var_in_symbolV56V65LaevalV58V55LaidentityIais_symbol_free_var_in_tableauV56asubst_tableauV60V63arename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_symbolV56a@V63V55Aais_symbol_free_var_in_tableauV55V60Larename_subst_symbolV58aidentityIa=V57aNodeV60V61V62FF
assertion
ais_symbol_free_var_in_symbolV56aevalarename_subst_symbolV58aidentityV55Iais_symbol_free_var_in_symbolV56a@V58V55Iais_symbol_free_var_in_symbola@V67V56arename_symbolV68V67Iais_symbol_free_var_in_symbolV56V68LaevalV58V55LaidentityIais_symbol_free_var_in_fo_formulaV56asubst_fo_formulaV61V66arename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_symbolV56a@V66V55Aais_symbol_free_var_in_fo_formulaV55V61Larename_subst_symbolV58aidentityIais_symbol_free_var_in_symbolV56aevalarename_subst_symbolV58aidentityV55Iais_symbol_free_var_in_symbolV56a@V58V55Iais_symbol_free_var_in_symbola@V64V56arename_symbolV65V64Iais_symbol_free_var_in_symbolV56V65LaevalV58V55LaidentityIais_symbol_free_var_in_tableauV56asubst_tableauV60V63arename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_symbolV56a@V63V55Aais_symbol_free_var_in_tableauV55V60Larename_subst_symbolV58aidentityIa=V57aNodeV60V61V62FF
ais_symbol_free_var_in_symbolV56aevalarename_subst_symbolV58aidentityV55Iais_symbol_free_var_in_symbolV56a@V58V55Iais_symbol_free_var_in_symbola@V70V56arename_symbolV71V70Iais_symbol_free_var_in_symbolV56V71LaevalV58V55LaidentityIais_symbol_free_var_in_fo_formula_listV56asubst_fo_formula_listV62V69arename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_symbolV56a@V69V55Aais_symbol_free_var_in_fo_formula_listV55V62Larename_subst_symbolV58aidentityIais_symbol_free_var_in_symbolV56aevalarename_subst_symbolV58aidentityV55Iais_symbol_free_var_in_symbolV56a@V58V55Iais_symbol_free_var_in_symbola@V67V56arename_symbolV68V67Iais_symbol_free_var_in_symbolV56V68LaevalV58V55LaidentityIais_symbol_free_var_in_fo_formulaV56asubst_fo_formulaV61V66arename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_symbolV56a@V66V55Aais_symbol_free_var_in_fo_formulaV55V61Larename_subst_symbolV58aidentityIais_symbol_free_var_in_symbolV56aevalarename_subst_symbolV58aidentityV55Iais_symbol_free_var_in_symbolV56a@V58V55Iais_symbol_free_var_in_symbol
ais_symbol_free_var_in_tableauV56asubst_tableauV57V58V59Iais_symbol_free_var_in_symbolV56a@V58V55Aais_symbol_free_var_in_tableauV55V57ICtaRootais_symbol_free_var_in_symbolV56aevalarename_subst_symbolV58aidentityV55Iais_symbol_free_var_in_symbolV56a@V58V55Aais_symbol_free_var_in_symbola@V70V56arename_symbolV71V70Iais_symbol_free_var_in_symbolV56V71LaevalV58V55LaidentityAais_symbol_free_var_in_fo_formula_listV56asubst_fo_formula_listV62V69arename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_symbolV56a@V69V55Aais_symbol_free_var_in_fo_formula_listV55V62Larename_subst_symbolV58aidentityAais_symbol_free_var_in_symbolV56aevalarename_subst_symbolV58aidentityV55Iais_symbol_free_var_in_symbolV56a@V58V55Aais_symbol_free_var_in_symbola@V67V56arename_symbolV68V67Iais_symbol_free_var_in_symbolV56V68LaevalV58V55LaidentityAais_symbol_free_var_in_fo_formulaV56asubst_fo_formulaV61V66arename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_symbolV56a@V66V55Aais_symbol_free_var_in_fo_formulaV55V61Larename_subst_symbol
VC for subst_free_var_propagation_symbol_symbol_tableau
a<asize_tableauV60asize_tableauV57Aa<=c0asize_tableauV57Larename_subst_fo_termV59aidentityaidentityIa=V57aNodeV60V61V62FF
ais_symbol_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_symbol_free_var_in_fo_termV56a@V59V55Iais_symbol_free_var_in_fo_terma@V64V56arename_fo_termV65V64aidentityIais_symbol_free_var_in_fo_termV56V65LaevalV59V55LaidentityIais_symbol_free_var_in_tableauV56asubst_tableauV60arename_subst_symbolV58aidentityV63Iais_symbol_free_var_in_fo_termV56a@V63V55Aais_fo_term_free_var_in_tableauV55V60Larename_subst_fo_termV59aidentityaidentityIa=V57aNodeV60V61V62FF
ais_symbol_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_symbol_free_var_in_fo_termV56a@V59V55Iais_symbol_free_var_in_fo_terma@V67V56arename_fo_termV68V67aidentityIais_symbol_free_var_in_fo_termV56V68LaevalV59V55LaidentityIais_symbol_free_var_in_fo_formulaV56asubst_fo_formulaV61arename_subst_symbolV58aidentityV66Iais_symbol_free_var_in_fo_termV56a@V66V55Aais_fo_term_free_var_in_fo_formulaV55V61Larename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_symbol_free_var_in_fo_termV56a@V59V55Iais_symbol_free_var_in_fo_terma@V64V56arename_fo_termV65V64aidentityIais_symbol_free_var_in_fo_termV56V65LaevalV59V55LaidentityIais_symbol_free_var_in_tableauV56asubst_tableauV60arename_subst_symbolV58aidentityV63Iais_symbol_free_var_in_fo_termV56a@V63V55Aais_fo_term_free_var_in_tableauV55V60Larename_subst_fo_termV59aidentityaidentityIa=V57aNodeV60V61V62FF
ais_symbol_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_symbol_free_var_in_fo_termV56a@V59V55Iais_symbol_free_var_in_fo_terma@V70V56arename_fo_termV71V70aidentityIais_symbol_free_var_in_fo_termV56V71LaevalV59V55LaidentityIais_symbol_free_var_in_fo_formula_listV56asubst_fo_formula_listV62arename_subst_symbolV58aidentityV69Iais_symbol_free_var_in_fo_termV56a@V69V55Aais_fo_term_free_var_in_fo_formula_listV55V62Larename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_symbol_free_var_in_fo_termV56a@V59V55Iais_symbol_free_var_in_fo_terma@V67V56arename_fo_termV68V67aidentityIais_symbol_free_var_in_fo_termV56V68LaevalV59V55LaidentityIais_symbol_free_var_in_fo_formulaV56asubst_fo_formulaV61arename_subst_symbolV58aidentityV66Iais_symbol_free_var_in_fo_termV56a@V66V55Aais_fo_term_free_var_in_fo_formulaV55V61Larename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentity
ais_symbol_free_var_in_tableauV56asubst_tableauV57V58V59Iais_symbol_free_var_in_fo_termV56a@V59V55Aais_fo_term_free_var_in_tableauV55V57ICtaRootais_symbol_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_symbol_free_var_in_fo_termV56a@V59V55Aais_symbol_free_var_in_fo_terma@V70V56arename_fo_termV71V70aidentityIais_symbol_free_var_in_fo_termV56V71LaevalV59V55LaidentityAais_symbol_free_var_in_fo_formula_listV56asubst_fo_formula_listV62arename_subst_symbolV58aidentityV69Iais_symbol_free_var_in_fo_termV56a@V69V55Aais_fo_term_free_var_in_fo_formula_listV55V62Larename_subst_fo_termV59aidentityaidentityAais_symbol_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_symbol_free_var_in_fo_termV56a@V59V55Aais_symbol_free_var_in_fo_terma@V67V56arename_fo_termV68V67aidentityIais_symbol_free_var_in_fo_termV56V68LaevalV59V55LaidentityAais_symbol_free_var_in_fo_formulaV56asubst_fo_formulaV61arename_subst_symbolV58aidentityV66Iais_symbol_free_var_in_fo_termV56a@V66V55Aais_fo_term_free_var_in_fo_formula
VC for subst_free_var_propagation_fo_term_symbol_tableau
ais_fo_term_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_fo_term_free_var_in_fo_termV56a@V59V55Iais_fo_term_free_var_in_fo_terma@V64V56arename_fo_termV65aidentityV64Iais_fo_term_free_var_in_fo_termV56V65LaevalV59V55LaidentityIais_fo_term_free_var_in_tableauV56asubst_tableauV60arename_subst_symbolV58aidentityV63Iais_fo_term_free_var_in_fo_termV56a@V63V55Aais_fo_term_free_var_in_tableauV55V60Larename_subst_fo_termV59aidentityaidentityIa=V57aNodeV60V61V62FF
ais_fo_term_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_fo_term_free_var_in_fo_termV56a@V59V55Iais_fo_term_free_var_in_fo_terma@V67V56arename_fo_termV68aidentityV67Iais_fo_term_free_var_in_fo_termV56V68LaevalV59V55LaidentityIais_fo_term_free_var_in_fo_formulaV56asubst_fo_formulaV61arename_subst_symbolV58aidentityV66Iais_fo_term_free_var_in_fo_termV56a@V66V55Aais_fo_term_free_var_in_fo_formulaV55V61Larename_subst_fo_termV59aidentityaidentityIais_fo_term_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_fo_term_free_var_in_fo_termV56a@V59V55Iais_fo_term_free_var_in_fo_terma@V64V56arename_fo_termV65aidentityV64Iais_fo_term_free_var_in_fo_termV56V65LaevalV59V55LaidentityIais_fo_term_free_var_in_tableauV56asubst_tableauV60arename_subst_symbolV58aidentityV63Iais_fo_term_free_var_in_fo_termV56a@V63V55Aais_fo_term_free_var_in_tableauV55V60Larename_subst_fo_termV59aidentityaidentityIa=V57aNodeV60V61V62FF
ais_fo_term_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_fo_term_free_var_in_fo_termV56a@V59V55Iais_fo_term_free_var_in_fo_terma@V70V56arename_fo_termV71aidentityV70Iais_fo_term_free_var_in_fo_termV56V71LaevalV59V55LaidentityIais_fo_term_free_var_in_fo_formula_listV56asubst_fo_formula_listV62arename_subst_symbolV58aidentityV69Iais_fo_term_free_var_in_fo_termV56a@V69V55Aais_fo_term_free_var_in_fo_formula_listV55V62Larename_subst_fo_termV59aidentityaidentityIais_fo_term_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_fo_term_free_var_in_fo_termV56a@V59V55Iais_fo_term_free_var_in_fo_terma@V67V56arename_fo_termV68aidentityV67Iais_fo_term_free_var_in_fo_termV56V68LaevalV59V55LaidentityIais_fo_term_free_var_in_fo_formulaV56asubst_fo_formulaV61arename_subst_symbolV58aidentityV66Iais_fo_term_free_var_in_fo_termV56a@V66V55Aais_fo_term_free_var_in_fo_formulaV55V61Larename_subst_fo_termV59aidentityaidentityIais_fo_term_free_var_in_fo_termV56aevalarename_subst_fo_term
ais_fo_term_free_var_in_tableauV56asubst_tableauV57V58V59Iais_fo_term_free_var_in_fo_termV56a@V59V55Aais_fo_term_free_var_in_tableauV55V57ICtaRootais_fo_term_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_fo_term_free_var_in_fo_termV56a@V59V55Aais_fo_term_free_var_in_fo_terma@V70V56arename_fo_termV71aidentityV70Iais_fo_term_free_var_in_fo_termV56V71LaevalV59V55LaidentityAais_fo_term_free_var_in_fo_formula_listV56asubst_fo_formula_listV62arename_subst_symbolV58aidentityV69Iais_fo_term_free_var_in_fo_termV56a@V69V55Aais_fo_term_free_var_in_fo_formula_listV55V62Larename_subst_fo_termV59aidentityaidentityAais_fo_term_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_fo_term_free_var_in_fo_termV56a@V59V55Aais_fo_term_free_var_in_fo_terma@V67V56arename_fo_termV68aidentityV67Iais_fo_term_free_var_in_fo_termV56V68LaevalV59V55LaidentityAais_fo_term_free_var_in_fo_formulaV56asubst_fo_formulaV61arename_subst_symbolV58aidentityV66Iais_fo_term_free_var_in_fo_termV56
VC for subst_free_var_propagation_fo_term_fo_term_tableau
ais_symbol_free_var_in_tableauV56asubst_tableauV57V58V59Iais_symbol_free_var_in_symbolV56a@V58V55Aais_symbol_free_var_in_tableauV55V57F
ais_symbol_free_var_in_tableauV61asubst_tableauV62V63V64Iais_symbol_free_var_in_fo_termV61a@V64V60Aais_fo_term_free_var_in_tableauV60V62F
ais_fo_term_free_var_in_tableauV66asubst_tableauV67V68V69Iais_fo_term_free_var_in_fo_termV66a@V69V65Aais_fo_term_free_var_in_tableauV65V67F
a=asubst_tableauV70V71V73asubst_tableauV70V72V74ICtaRoota=asubst_fo_formula_listV77arename_subst_symbolV71aidentityarename_subst_fo_termV73aidentityaidentityasubst_fo_formula_listV77arename_subst_symbolV72aidentityarename_subst_fo_termV74aidentityaidentityAais_fo_term_free_var_in_tableauV78V70Iais_fo_term_free_var_in_fo_formula_listV78V77FAais_symbol_free_var_in_tableauV79V70Iais_symbol_free_var_in_fo_formula_listV79V77FAa=asubst_fo_formulaV76arename_subst_symbolV71aidentityarename_subst_fo_termV73aidentityaidentityasubst_fo_formulaV76arename_subst_symbolV72aidentityarename_subst_fo_termV74aidentityaidentityAais_fo_term_free_var_in_tableauV80V70Iais_fo_term_free_var_in_fo_formulaV80V76FAais_symbol_free_var_in_tableauV81V70Iais_symbol_free_var_in_fo_formulaV81V76FAa=asubst_tableauV75arename_subst_symbolV71aidentityarename_subst_fo_termV73aidentityaidentityasubst_tableauV75arename_subst_symbolV72aidentityarename_subst_fo_termV74aidentityaidentityAais_fo_term_free_var_in_tableauV82V70Iais_fo_term_free_var_in_tableau
VC for free_var_equivalence_of_subst_tableau
a=asubst_tableauV70V71V73asubst_tableauV70V72V74Ia=a@V73V75a@V74V75Iais_fo_term_free_var_in_tableauV75V70FIa=a@V71V76a@V72V76Iais_symbol_free_var_in_tableauV76V70FF
a=arename_tableauV77V78V80arename_tableauV77V79V81Ia=asubst_tableauV77V85V83asubst_tableauV77V84V82Aa=a@V83V86a@V82V86Iais_fo_term_free_var_in_tableauV86V77FAa=a@V85V87a@V84V87Iais_symbol_free_var_in_tableauV87V77FLasubst_of_rename_symbolV78Lasubst_of_rename_symbolV79Lasubst_of_rename_fo_termV80Lasubst_of_rename_fo_termV81Ia=a@V80V88a@V81V88Iais_fo_term_free_var_in_tableauV88V77FAa=a@V78V89a@V79V89Iais_symbol_free_var_in_tableauV89V77FF
VC for free_var_equivalence_of_rename_tableau
a=arename_tableauV77V78V80arename_tableauV77V79V81Ia=a@V80V82a@V81V82Iais_fo_term_free_var_in_tableauV82V77FIa=a@V78V83a@V79V83Iais_symbol_free_var_in_tableauV83V77FF
a=a@V87V89a@V88V89Iais_fo_term_free_var_in_tableauV89V84FAa=a@V85V90a@V86V90Iais_symbol_free_var_in_tableauV90V84FICtaRoota=a@V87V94a@V88V94Iais_fo_term_free_var_in_fo_formula_listV94V93FAa=a@V87V95a@V88V95Aa=arename_fo_termarename_fo_terma@V88V95aidentityaidentityaidentityaidentitya@V88V95Aa=arename_fo_termarename_fo_terma@V87V95aidentityaidentityaidentityaidentityarename_fo_termarename_fo_terma@V88V95aidentityaidentityaidentityaidentityAa=a@V87V95arename_fo_termarename_fo_terma@V87V95aidentityaidentityaidentityaidentityAa=aevalarename_subst_fo_termV88aidentityaidentityV95arename_fo_terma@V88V95aidentityaidentityAa=aevalarename_subst_fo_termV87aidentityaidentityV95aevalarename_subst_fo_termV88aidentityaidentityV95Aa=arename_fo_terma@V87V95aidentityaidentityaevalarename_subst_fo_termV87aidentityaidentityV95Iais_fo_term_free_var_in_fo_formula_listV95V93FAa=a@V85V96a@V86V96Iais_symbol_free_var_in_fo_formula_listV96V93FAa=a@V85V97a@V86V97Aa=arename_symbolarename_symbola@V86V97aidentityaidentitya@V86V97Aa=arename_symbol
VC for free_var_derive_equivalence_of_subst_tableau
a=a@V87V89a@V88V89Iais_fo_term_free_var_in_tableauV89V84FAa=a@V85V90a@V86V90Iais_symbol_free_var_in_tableauV90V84FIa=asubst_tableauV84V85V87asubst_tableauV84V86V88F
a=asubst_tableauV91V99V97asubst_tableauV91V98V96Lasubst_of_rename_symbolV92Lasubst_of_rename_symbolV93Lasubst_of_rename_fo_termV94Lasubst_of_rename_fo_termV95Ia=arename_tableauV91V92V94arename_tableauV91V93V95F
precondition
a=a@V92V100a@V93V100Aa=a@V92V100a@V93V100Ia=a@asubst_of_rename_symbolV92V100a@asubst_of_rename_symbolV93V100FIa=a@V97V101a@V96V101Iais_fo_term_free_var_in_tableauV101V91FAa=a@V99V102a@V98V102Iais_symbol_free_var_in_tableauV102V91FLasubst_of_rename_symbolV92Lasubst_of_rename_symbolV93Lasubst_of_rename_fo_termV94Lasubst_of_rename_fo_termV95Ia=arename_tableauV91V92V94arename_tableauV91V93V95F
a=a@V94V100a@V95V100Aa=a@V94V100a@V95V100Ia=a@asubst_of_rename_fo_termV94V100a@asubst_of_rename_fo_termV95V100FIa=a@V92V101a@V93V101Aa=a@V92V101a@V93V101Ia=a@asubst_of_rename_symbolV92V101a@asubst_of_rename_symbolV93V101FIa=a@V97V102a@V96V102Iais_fo_term_free_var_in_tableauV102V91FAa=a@V99V103a@V98V103Iais_symbol_free_var_in_tableauV103V91FLasubst_of_rename_symbolV92Lasubst_of_rename_symbolV93Lasubst_of_rename_fo_termV94Lasubst_of_rename_fo_termV95Ia=arename_tableauV91V92V94arename_tableauV91V93V95F
a=a@V92V100a@V93V100Iais_symbol_free_var_in_tableauV100V91FIa=a@V94V101a@V95V101Aa=a@V94V101a@V95V101Ia=a@asubst_of_rename_fo_termV94V101a@asubst_of_rename_fo_termV95V101FIa=a@V92V102a@V93V102Aa=a@V92V102a@V93V102Ia=a@asubst_of_rename_symbolV92V102a@asubst_of_rename_symbolV93V102FIa=a@V97V103a@V96V103Iais_fo_term_free_var_in_tableauV103V91FAa=a@V99V104a@V98V104Iais_symbol_free_var_in_tableauV104V91FLasubst_of_rename_symbolV92Lasubst_of_rename_symbolV93Lasubst_of_rename_fo_termV94Lasubst_of_rename_fo_termV95Ia=arename_tableauV91V92V94arename_tableauV91V93V95F
a=a@V94V100a@V95V100Iais_fo_term_free_var_in_tableauV100V91FIa=a@V92V101a@V93V101Iais_symbol_free_var_in_tableauV101V91FIa=a@V94V102a@V95V102Aa=a@V94V102a@V95V102Ia=a@asubst_of_rename_fo_termV94V102a@asubst_of_rename_fo_termV95V102FIa=a@V92V103a@V93V103Aa=a@V92V103a@V93V103Ia=a@asubst_of_rename_symbolV92V103a@asubst_of_rename_symbolV93V103FIa=a@V97V104a@V96V104Iais_fo_term_free_var_in_tableauV104V91FAa=a@V99V105a@V98V105Iais_symbol_free_var_in_tableauV105V91FLasubst_of_rename_symbolV92Lasubst_of_rename_symbolV93Lasubst_of_rename_fo_termV94Lasubst_of_rename_fo_termV95Ia=arename_tableauV91V92V94arename_tableauV91V93V95F
a=a@V94V100a@V95V100Iais_fo_term_free_var_in_tableauV100V91FAa=a@V92V101a@V93V101Iais_symbol_free_var_in_tableauV101V91FAa=a@V94V102a@V95V102Aa=a@V94V102a@V95V102Ia=a@asubst_of_rename_fo_termV94V102a@asubst_of_rename_fo_termV95V102FAa=a@V92V103a@V93V103Aa=a@V92V103a@V93V103Ia=a@asubst_of_rename_symbolV92V103a@asubst_of_rename_symbolV93V103FIa=a@V97V104a@V96V104Iais_fo_term_free_var_in_tableauV104V91FAa=a@V99V105a@V98V105Iais_symbol_free_var_in_tableauV105V91FAa=asubst_tableauV91V99V97asubst_tableauV91V98V96Lasubst_of_rename_symbolV92Lasubst_of_rename_symbolV93Lasubst_of_rename_fo_termV94Lasubst_of_rename_fo_termV95Ia=arename_tableauV91V92V94arename_tableauV91V93V95F
VC for free_var_derive_equivalence_of_rename_tableau

bdebf009ee61f9a387d9cc732cc17c6a 1H0
acd329fcb587dc6460e21ce4044f1b4d 4H3H2
ac2044402c61b35515f2f2616f0b89dc 7H6H5H2
fca8e3d19d3c371a09689beed8d0a9f2 10H9H8H5H2
4de1e7669c5e45f12ca36b21ee16564a 13H12H11H8H5H2
9d88d18c60291364ccf2657c4e993dcf 20H19H14H11H8H5H2
a51ad5d49cfedc3b8fd78e8bf0651fee 16H15H14H11H8H5H2
212a984213598d7aef67be234360dab8 18H17H14H11H8H5H2
1f6f7720f683d2db480c884d4a3e7487 23H22H21H14H11H8H5H2
2e8717cab0b3d314670019f727102248 26H25H24H21H14H11H8H5H2
e82253639d13fd0867b30ee8824214e1 29H28H27H24H21H14H11H8H5H2
e81649580e20937ea98b5a874fbba511 31H30H27H24H21H14H11H8H5H2
afc4792e112bab953e0a924b4c712696 33H32H27H24H21H14H11H8H5H2
d04ec05d4388b912a9dd59576f44ebbd 35H34H27H24H21H14H11H8H5H2
2e9f6afc22afa49e4794a82f7cefa52c 39H38H37H36H27H24H21H14H11H8H5H2
52f4ee08985a323632aac08b67456524 41H40H37H36H27H24H21H14H11H8H5H2
c5eec686b913dd28a2b6c981a28ac68f 45H44H43H42H37H36H27H24H21H14H11H8H5H2
6cb87d1ba4fe2b749bca6c25c24b4e44 47H46H43H42H37H36H27H24H21H14H11H8H5H2
7b64ed92a599581fe0163b6fef703229 49H48H43H42H37H36H27H24H21H14H11H8H5H2
2bd085138e082ba85179b0791a48d147 51H50H43H42H37H36H27H24H21H14H11H8H5H2
994de7c202d65653075d7f7cdd559f94 60H59H53H52H43H42H37H36H27H24H21H14H11H8H5H2
4ab0e5e23fae1ad8885b5e8200b99ba8 16H54H53H52H43H42H37H36H27H24H21H14H11H8H5H2
6f2e92b9f41c02a4a06e6bc0900a2018 56H55H53H52H43H42H37H36H27H24H21H14H11H8H5H2
c13d45af6a6359cd3f82b85c89ce1911 56H57H53H52H43H42H37H36H27H24H21H14H11H8H5H2
f71cddc983845a64ef3651860f7f085a 56H58H53H52H43H42H37H36H27H24H21H14H11H8H5H2
c7de0bba934258d7ba5d81c585a9152c 18H59H53H52H43H42H37H36H27H24H21H14H11H8H5H2
6b181f740ef338f6243aa36a32256b4e 66H65H53H52H43H42H37H36H27H24H21H14H11H8H5H2
6ceae1fabc2a930fd4307401e1e45751 16H61H53H52H43H42H37H36H27H24H21H14H11H8H5H2
77cb3ce8c423cf6ccead8aa799726a6e 56H62H53H52H43H42H37H36H27H24H21H14H11H8H5H2
05683352b1946bcb4e7610fca02baab4 56H63H53H52H43H42H37H36H27H24H21H14H11H8H5H2
e092f027df253ca0e6a582a2bfc6a945 56H64H53H52H43H42H37H36H27H24H21H14H11H8H5H2
d9bdefd54bc3bbef14515e131484130c 18H65H53H52H43H42H37H36H27H24H21H14H11H8H5H2
047c426a4e4f0d29ee55be6752b91667 71H70H53H52H43H42H37H36H27H24H21H14H11H8H5H2
743012c7f0ed3334ede166d55de8fcfc 16H61H53H52H43H42H37H36H27H24H21H14H11H8H5H2
7a2a83abdab8857945ca34405435a67d 56H67H53H52H43H42H37H36H27H24H21H14H11H8H5H2
f1d71b84aa747f9ff9b7b8d35d1cfb8e 56H68H53H52H43H42H37H36H27H24H21H14H11H8H5H2
9f091581d188343dd999c34f00966ce0 56H69H53H52H43H42H37H36H27H24H21H14H11H8H5H2
71cf3e90f4bd68499cd52edde6ef7856 18H70H53H52H43H42H37H36H27H24H21H14H11H8H5H2
ee95a231fa79110ec61cae8322c59d22 76H75H74H73H72H53H52H43H42H37H36H27H24H21H14H11H8H5H2
d2e36114010ac82e04e3a7551e9547e0 79H78H77H74H73H72H53H52H43H42H37H36H27H24H21H14H11H8H5H2
0f7ccbaa0a8b6bef26a88b94c80ef9cb 82H81H80H77H74H73H72H53H52H43H42H37H36H27H24H21H14H11H8H5H2
73afe619777da719c6ef81f97ff3720d 91H90H83H80H77H74H73H72H53H52H43H42H37H36H27H24H21H14H11H8H5H2
bc614713811bc445610cc7fb000e9072 85H84H83H80H77H74H73H72H53H52H43H42H37H36H27H24H21H14H11H8H5H2
ce5a358ba57ecd6142f6f4e857d39df0 56H86H83H80H77H74H73H72H53H52H43H42H37H36H27H24H21H14H11H8H5H2
604bc1ed1d7ac430eacc9ea6bc000efb 56H87H83H80H77H74H73H72H53H52H43H42H37H36H27H24H21H14H11H8H5H2
eb10fe0641e2cd9b54bb0b32db7dd028 18H88H83H80H77H74H73H72H53H52H43H42H37H36H27H24H21H14H11H8H5H2
95650541f9772b9edab140f19afc98e6 18H89H83H80H77H74H73H72H53H52H43H42H37H36H27H24H21H14H11H8H5H2
