a>asize_fo_formula_listV0c0ICtaFOFNila>asize_fo_formula_listV2c0Aa>asize_fo_formulaV1c0aFOFConsVVV0ACtaFOFNila<anat_to_intanat_size_fo_formula_listV4anat_to_intanat_size_fo_formula_listV0Aa<=c0anat_to_intanat_size_fo_formula_listV0Ia>asize_fo_formulaV3c0aFOFConsVVV0F
VC for size_positive_lemma_fo_formula_list
a>asize_fo_formula_listV0c0F
a=arename_fo_formula_listarename_fo_formula_listV1V2V3V4V5arename_fo_formula_listV1arcomposeV2V4arcomposeV3V5ICtaFOFNila=arename_fo_formula_listarename_fo_formula_listV7V2V3V4V5arename_fo_formula_listV7arcomposeV2V4arcomposeV3V5Aa=arename_fo_formulaarename_fo_formulaV6V2V3V4V5arename_fo_formulaV6arcomposeV2V4arcomposeV3V5aFOFConsVVV1ACtaFOFNila<asize_fo_formula_listV9asize_fo_formula_listV1Aa<=c0asize_fo_formula_listV1Ia=arename_fo_formulaarename_fo_formulaV8V2V3V4V5arename_fo_formulaV8arcomposeV2V4arcomposeV3V5aFOFConsVVV1F
VC for renaming_composition_lemma_fo_formula_list
a=arename_fo_formula_listarename_fo_formula_listV1V2V3V4V5arename_fo_formula_listV1arcomposeV2V4arcomposeV3V5F
a=arename_fo_formula_listV6aidentityaidentityV6ICtaFOFNila=arename_fo_formula_listV8aidentityaidentityV8Aa=arename_fo_formulaV7aidentityaidentityV7aFOFConsVVV6ACtaFOFNila<asize_fo_formula_listV10asize_fo_formula_listV6Aa<=c0asize_fo_formula_listV6Ia=arename_fo_formulaV9aidentityaidentityV9aFOFConsVVV6F
VC for renaming_identity_lemma_fo_formula_list
a=arename_fo_formula_listV6aidentityaidentityV6F
a=asubst_fo_formula_listarename_fo_formula_listV7V8V9V10V11asubst_fo_formula_listV7arcomposeV8V10arcomposeV9V11ICtaFOFNila=asubst_fo_formula_listarename_fo_formula_listV13V8V9V17V16asubst_fo_formula_listV13arcomposeV8V17arcomposeV9V16Larename_subst_symbolV10aidentityLarename_subst_fo_termV11aidentityaidentityAa=asubst_fo_formulaarename_fo_formulaV12V8V9V15V14asubst_fo_formulaV12arcomposeV8V15arcomposeV9V14Larename_subst_symbolV10aidentityLarename_subst_fo_termV11aidentityaidentityaFOFConsVVV7ACtaFOFNila<asize_fo_formula_listV19asize_fo_formula_listV7Aa<=c0asize_fo_formula_listV7Ia=asubst_fo_formulaarename_fo_formulaV18V8V9V21V20asubst_fo_formulaV18arcomposeV8V21arcomposeV9V20Larename_subst_symbolV10aidentityLarename_subst_fo_termV11aidentityaidentityaFOFConsVVV7F
VC for rename_then_subst_composition_lemma_fo_formula_list
a=asubst_fo_formula_listarename_fo_formula_listV7V8V9V10V11asubst_fo_formula_listV7arcomposeV8V10arcomposeV9V11F
a=arename_fo_formula_listasubst_fo_formula_listV12V13V14V15V16asubst_fo_formula_listV12arename_subst_symbolV13V15arename_subst_fo_termV14V15V16ICtaFOFNila=arename_fo_formula_listasubst_fo_formula_listV18V22V21V15V16asubst_fo_formula_listV18arename_subst_symbolV22V15arename_subst_fo_termV21V15V16Larename_subst_symbolV13aidentityLarename_subst_fo_termV14aidentityaidentityAa=arename_fo_formulaasubst_fo_formulaV17V20V19V15V16asubst_fo_formulaV17arename_subst_symbolV20V15arename_subst_fo_termV19V15V16Larename_subst_symbolV13aidentityLarename_subst_fo_termV14aidentityaidentityaFOFConsVVV12ACtaFOFNila<asize_fo_formula_listV24asize_fo_formula_listV12Aa<=c0asize_fo_formula_listV12Ia=arename_fo_formulaasubst_fo_formulaV23V26V25V15V16asubst_fo_formulaV23arename_subst_symbolV26V15arename_subst_fo_termV25V15V16Larename_subst_symbolV13aidentityLarename_subst_fo_termV14aidentityaidentityaFOFConsVVV12F
VC for subst_then_rename_composition_lemma_fo_formula_list
a=arename_fo_formula_listasubst_fo_formula_listV12V13V14V15V16asubst_fo_formula_listV12arename_subst_symbolV13V15arename_subst_fo_termV14V15V16F
a<asize_fo_formula_listV23asize_fo_formula_listV17Aa<=c0asize_fo_formula_listV17Ia=asubst_fo_formulaasubst_fo_formulaV22V27V26V25V24asubst_fo_formulaV22asubst_compose_symbolV27V25asubst_compose_fo_termV26V25V24Larename_subst_symbolV18aidentityLarename_subst_fo_termV19aidentityaidentityLarename_subst_symbolV20aidentityLarename_subst_fo_termV21aidentityaidentityIa=V17aFOFConsV22V23FF
variant decrease
a=asubst_fo_formula_listasubst_fo_formula_listV17V18V19V20V21asubst_fo_formula_listV17asubst_compose_symbolV18V20asubst_compose_fo_termV19V20V21ICtaFOFNila=asubst_fo_formula_listasubst_fo_formula_listV23V31V30V29V28asubst_fo_formula_listV23asubst_compose_symbolV31V29asubst_compose_fo_termV30V29V28Larename_subst_symbolV18aidentityLarename_subst_fo_termV19aidentityaidentityLarename_subst_symbolV20aidentityLarename_subst_fo_termV21aidentityaidentityAa=asubst_fo_formulaasubst_fo_formulaV22V27V26V25V24asubst_fo_formulaV22asubst_compose_symbolV27V25asubst_compose_fo_termV26V25V24Larename_subst_symbolV18aidentityLarename_subst_fo_termV19aidentityaidentityLarename_subst_symbolV20aidentityLarename_subst_fo_termV21aidentityaidentityaFOFConsVVV17F
postcondition
a=asubst_fo_formula_listasubst_fo_formula_listV17V18V19V20V21asubst_fo_formula_listV17asubst_compose_symbolV18V20asubst_compose_fo_termV19V20V21ICtaFOFNila=asubst_fo_formula_listasubst_fo_formula_listV23V31V30V29V28asubst_fo_formula_listV23asubst_compose_symbolV31V29asubst_compose_fo_termV30V29V28Larename_subst_symbolV18aidentityLarename_subst_fo_termV19aidentityaidentityLarename_subst_symbolV20aidentityLarename_subst_fo_termV21aidentityaidentityAa=asubst_fo_formulaasubst_fo_formulaV22V27V26V25V24asubst_fo_formulaV22asubst_compose_symbolV27V25asubst_compose_fo_termV26V25V24Larename_subst_symbolV18aidentityLarename_subst_fo_termV19aidentityaidentityLarename_subst_symbolV20aidentityLarename_subst_fo_termV21aidentityaidentityaFOFConsVVV17ACtaFOFNila<asize_fo_formula_listV33asize_fo_formula_listV17Aa<=c0asize_fo_formula_listV17Ia=asubst_fo_formulaasubst_fo_formulaV32V37V36V35V34asubst_fo_formulaV32asubst_compose_symbolV37V35asubst_compose_fo_termV36V35V34Larename_subst_symbolV18aidentityLarename_subst_fo_termV19a
VC for subst_composition_lemma_fo_formula_list
a=asubst_fo_formula_listasubst_fo_formula_listV17V18V19V20V21asubst_fo_formula_listV17asubst_compose_symbolV18V20asubst_compose_fo_termV19V20V21F
a=asubst_fo_formula_listV22asubst_id_symbolasubst_id_fo_termV22ICtaFOFNila=asubst_fo_formula_listV24asubst_id_symbolasubst_id_fo_termV24Aa=asubst_fo_formulaV23asubst_id_symbolasubst_id_fo_termV23aFOFConsVVV22ACtaFOFNila<asize_fo_formula_listV26asize_fo_formula_listV22Aa<=c0asize_fo_formula_listV22Ia=asubst_fo_formulaV25asubst_id_symbolasubst_id_fo_termV25aFOFConsVVV22F
VC for subst_identity_lemma_fo_formula_list
a=asubst_fo_formula_listV22asubst_id_symbolasubst_id_fo_termV22F
a=asize_fo_formula_listarename_fo_formula_listV23V24V25asize_fo_formula_listV23ICtaFOFNila=asize_fo_formula_listarename_fo_formula_listV27V24V25asize_fo_formula_listV27Aa=asize_fo_formulaarename_fo_formulaV26V24V25asize_fo_formulaV26aFOFConsVVV23ACtaFOFNila<asize_fo_formula_listV29asize_fo_formula_listV23Aa<=c0asize_fo_formula_listV23Ia=asize_fo_formulaarename_fo_formulaV28V24V25asize_fo_formulaV28aFOFConsVVV23F
VC for renaming_preserve_size_fo_formula_list
a=asize_fo_formula_listarename_fo_formula_listV23V24V25asize_fo_formula_listV23F
a=a@V28V30V26Aais_symbol_free_var_in_fo_formula_listV30V27ICfaFOFNilia=V30V33Aa=a@V28V33V26Aais_symbol_free_var_in_fo_formula_listV33V32EAais_symbol_free_var_in_fo_formula_listV26arename_fo_formula_listV32V28V29a=V30V34Aa=a@V28V34V26Aais_symbol_free_var_in_fo_formulaV34V31Eais_symbol_free_var_in_fo_formulaV26arename_fo_formulaV31V28V29aFOFConsVVV27FACfaFOFNiliifais_symbol_free_var_in_fo_formula_listV26arename_fo_formula_listV36V28V29Aa<asize_fo_formula_listV36asize_fo_formula_listV27Aa<=c0asize_fo_formula_listV27ais_symbol_free_var_in_fo_formula_listV26arename_fo_formula_listV36V28V29ais_symbol_free_var_in_fo_formulaV26arename_fo_formulaV35V28V29ais_symbol_free_var_in_fo_formulaV26arename_fo_formulaV35V28V29aFOFConsVVV27Iais_symbol_free_var_in_fo_formula_listV26arename_fo_formula_listV27V28V29F
VC for rename_free_var_constructive_inversion_symbol_fo_formula_list
a=a@V28V31V26Aais_symbol_free_var_in_fo_formula_listV31V27EIa=a@V28V30V26Aais_symbol_free_var_in_fo_formula_listV30V27FAais_symbol_free_var_in_fo_formula_listV26arename_fo_formula_listV27V28V29Aa<asize_fo_formula_listV27a+c1asize_fo_formula_listV27Aa<=c0a+c1asize_fo_formula_listV27Iais_symbol_free_var_in_fo_formula_listV26arename_fo_formula_listV27V28V29F
VC for rename_free_var_inversion_symbol_fo_formula_list
a=a@V29V30V26Aais_fo_term_free_var_in_fo_formula_listV30V27ICfaFOFNilia=V30V33Aa=a@V29V33V26Aais_fo_term_free_var_in_fo_formula_listV33V32EAais_fo_term_free_var_in_fo_formula_listV26arename_fo_formula_listV32V28V29a=V30V34Aa=a@V29V34V26Aais_fo_term_free_var_in_fo_formulaV34V31Eais_fo_term_free_var_in_fo_formulaV26arename_fo_formulaV31V28V29aFOFConsVVV27FACfaFOFNiliifais_fo_term_free_var_in_fo_formula_listV26arename_fo_formula_listV36V28V29Aa<asize_fo_formula_listV36asize_fo_formula_listV27Aa<=c0asize_fo_formula_listV27ais_fo_term_free_var_in_fo_formula_listV26arename_fo_formula_listV36V28V29ais_fo_term_free_var_in_fo_formulaV26arename_fo_formulaV35V28V29ais_fo_term_free_var_in_fo_formulaV26arename_fo_formulaV35V28V29aFOFConsVVV27Iais_fo_term_free_var_in_fo_formula_listV26arename_fo_formula_listV27V28V29F
VC for rename_free_var_constructive_inversion_fo_term_fo_formula_list
a=a@V29V31V26Aais_fo_term_free_var_in_fo_formula_listV31V27EIa=a@V29V30V26Aais_fo_term_free_var_in_fo_formula_listV30V27FAais_fo_term_free_var_in_fo_formula_listV26arename_fo_formula_listV27V28V29Aa<asize_fo_formula_listV27a+c1asize_fo_formula_listV27Aa<=c0a+c1asize_fo_formula_listV27Iais_fo_term_free_var_in_fo_formula_listV26arename_fo_formula_listV27V28V29F
VC for rename_free_var_inversion_fo_term_fo_formula_list
a=a@V28V30V26Aais_symbol_free_var_in_fo_formula_listV30V27EIais_symbol_free_var_in_fo_formula_listV26arename_fo_formula_listV27V28V29F
a=a@V34V35V31Aais_fo_term_free_var_in_fo_formula_listV35V32EIais_fo_term_free_var_in_fo_formula_listV31arename_fo_formula_listV32V33V34F
ais_symbol_free_var_in_fo_formula_lista@V38V36arename_fo_formula_listV37V38V39Iais_symbol_free_var_in_fo_formula_listV36V37ICtaFOFNilais_symbol_free_var_in_fo_formula_lista@V38V36arename_fo_formula_listV41V38V39Iais_symbol_free_var_in_fo_formula_listV36V41Aais_symbol_free_var_in_fo_formulaa@V38V36arename_fo_formulaV40V38V39Iais_symbol_free_var_in_fo_formulaV36V40aFOFConsVVV37ACtaFOFNila<asize_fo_formula_listV43asize_fo_formula_listV37Aa<=c0asize_fo_formula_listV37Iais_symbol_free_var_in_fo_formulaa@V38V36arename_fo_formulaV42V38V39Iais_symbol_free_var_in_fo_formulaV36V42aFOFConsVVV37F
VC for rename_free_var_propagation_symbol_fo_formula_list
ais_fo_term_free_var_in_fo_formula_lista@V39V36arename_fo_formula_listV37V38V39Iais_fo_term_free_var_in_fo_formula_listV36V37ICtaFOFNilais_fo_term_free_var_in_fo_formula_lista@V39V36arename_fo_formula_listV41V38V39Iais_fo_term_free_var_in_fo_formula_listV36V41Aais_fo_term_free_var_in_fo_formulaa@V39V36arename_fo_formulaV40V38V39Iais_fo_term_free_var_in_fo_formulaV36V40aFOFConsVVV37ACtaFOFNila<asize_fo_formula_listV43asize_fo_formula_listV37Aa<=c0asize_fo_formula_listV37Iais_fo_term_free_var_in_fo_formulaa@V39V36arename_fo_formulaV42V38V39Iais_fo_term_free_var_in_fo_formulaV36V42aFOFConsVVV37F
VC for rename_free_var_propagation_fo_term_fo_formula_list
ais_symbol_free_var_in_fo_formula_lista@V38V36arename_fo_formula_listV37V38V39Iais_symbol_free_var_in_fo_formula_listV36V37F
ais_fo_term_free_var_in_fo_formula_lista@V43V40arename_fo_formula_listV41V42V43Iais_fo_term_free_var_in_fo_formula_listV40V41F
Cais_symbol_free_var_in_symbolV44a@V46V49Aais_symbol_free_var_in_fo_formula_listV49V45aLeftVais_symbol_free_var_in_fo_termV44a@V47V50Aais_fo_term_free_var_in_fo_formula_listV50V45aRightVV48ICfaFOFNiliCa=V48aLeftV54Aa=V55V44Aa=a@aidentityV55V44Aais_symbol_free_var_in_symbolV55aevalV46V54EaLeftVa=V48aRightV56Aa=V57V44Aa=a@aidentityV57V44Aais_symbol_free_var_in_fo_termV57aevalV47V56EaRightVV53ACais_symbol_free_var_in_symbolV44a@arename_subst_symbolV46aidentityV58Aais_symbol_free_var_in_fo_formula_listV58V52aLeftVais_symbol_free_var_in_fo_termV44a@arename_subst_fo_termV47aidentityaidentityV59Aais_fo_term_free_var_in_fo_formula_listV59V52aRightVV53EAais_symbol_free_var_in_fo_formula_listV44asubst_fo_formula_listV52arename_subst_symbolV46aidentityarename_subst_fo_termV47aidentityaidentityCa=V48aLeftV61Aa=V62V44Aa=a@aidentityV62V44Aais_symbol_free_var_in_symbolV62aevalV46V61EaLeftVa=V48aRightV63Aa=V64V44Aa=a@aidentityV64V44Aais_symbol_free_var_in_fo_termV64aevalV47V63EaRightVV60ACais_symbol_free_var_in_symbolV44a@arename_subst_symbol
VC for subst_free_var_constructive_inversion_symbol_fo_formula_list
ais_symbol_free_var_in_fo_termV44a@V47V49Aais_fo_term_free_var_in_fo_formula_listV49V45EOais_symbol_free_var_in_symbolV44a@V46V50Aais_symbol_free_var_in_fo_formula_listV50V45EICtaLeftVtaRightVV48ICais_symbol_free_var_in_symbolV44a@V46V53Aais_symbol_free_var_in_fo_formula_listV53V45aLeftVais_symbol_free_var_in_fo_termV44a@V47V54Aais_fo_term_free_var_in_fo_formula_listV54V45aRightVV48FAais_symbol_free_var_in_fo_formula_listV44asubst_fo_formula_listV45V46V47Aa<asize_fo_formula_listV45a+c1asize_fo_formula_listV45Aa<=c0a+c1asize_fo_formula_listV45Iais_symbol_free_var_in_fo_formula_listV44asubst_fo_formula_listV45V46V47F
VC for subst_free_var_inversion_symbol_fo_formula_list
ais_fo_term_free_var_in_fo_termV44a@V47V48Aais_fo_term_free_var_in_fo_formula_listV48V45ICfaFOFNilia=V48V51Aa=V52V44Aa=a@aidentityV52V44Aais_fo_term_free_var_in_fo_termV52aevalV47V51EAais_fo_term_free_var_in_fo_termV44a@arename_subst_fo_termV47aidentityaidentityV51Aais_fo_term_free_var_in_fo_formula_listV51V50EAais_fo_term_free_var_in_fo_formula_listV44asubst_fo_formula_listV50arename_subst_symbolV46aidentityarename_subst_fo_termV47aidentityaidentitya=V48V53Aa=V54V44Aa=a@aidentityV54V44Aais_fo_term_free_var_in_fo_termV54aevalV47V53EAais_fo_term_free_var_in_fo_termV44a@arename_subst_fo_termV47aidentityaidentityV53Aais_fo_term_free_var_in_fo_formulaV53V49Eais_fo_term_free_var_in_fo_formulaV44asubst_fo_formulaV49arename_subst_symbolV46aidentityarename_subst_fo_termV47aidentityaidentityaFOFConsVVV45FACfaFOFNiliifa=V61V44Ia=a@V59V61V44Aais_fo_term_free_var_in_fo_termV61V60FAais_fo_term_free_var_in_fo_termV44arename_fo_termV60aidentityV59LaevalV47V58LaidentityIais_fo_term_free_var_in_fo_termV44a@V57V58Aais_fo_term_free_var_in_fo_formula_list
VC for subst_free_var_constructive_inversion_fo_term_fo_formula_list
ais_fo_term_free_var_in_fo_termV44a@V47V49Aais_fo_term_free_var_in_fo_formula_listV49V45EIais_fo_term_free_var_in_fo_termV44a@V47V48Aais_fo_term_free_var_in_fo_formula_listV48V45FAais_fo_term_free_var_in_fo_formula_listV44asubst_fo_formula_listV45V46V47Aa<asize_fo_formula_listV45a+c1asize_fo_formula_listV45Aa<=c0a+c1asize_fo_formula_listV45Iais_fo_term_free_var_in_fo_formula_listV44asubst_fo_formula_listV45V46V47F
VC for subst_free_var_inversion_fo_term_fo_formula_list
ais_symbol_free_var_in_fo_termV44a@V47V48Aais_fo_term_free_var_in_fo_formula_listV48V45EOais_symbol_free_var_in_symbolV44a@V46V49Aais_symbol_free_var_in_fo_formula_listV49V45EIais_symbol_free_var_in_fo_formula_listV44asubst_fo_formula_listV45V46V47F
ais_fo_term_free_var_in_fo_termV50a@V53V54Aais_fo_term_free_var_in_fo_formula_listV54V51EIais_fo_term_free_var_in_fo_formula_listV50asubst_fo_formula_listV51V52V53F
ais_symbol_free_var_in_fo_formula_listV56asubst_fo_formula_listV57V58V59Iais_symbol_free_var_in_symbolV56a@V58V55Aais_symbol_free_var_in_fo_formula_listV55V57ICtaFOFNilais_symbol_free_var_in_symbolV56aevalarename_subst_symbolV58aidentityV55Iais_symbol_free_var_in_symbolV56a@V58V55Aais_symbol_free_var_in_symbola@V66V56arename_symbolV67V66Iais_symbol_free_var_in_symbolV56V67LaevalV58V55LaidentityAais_symbol_free_var_in_fo_formula_listV56asubst_fo_formula_listV61V65arename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_symbolV56a@V65V55Aais_symbol_free_var_in_fo_formula_listV55V61Larename_subst_symbolV58aidentityAais_symbol_free_var_in_symbolV56aevalarename_subst_symbolV58aidentityV55Iais_symbol_free_var_in_symbolV56a@V58V55Aais_symbol_free_var_in_symbola@V63V56arename_symbolV64V63Iais_symbol_free_var_in_symbolV56V64LaevalV58V55LaidentityAais_symbol_free_var_in_fo_formulaV56asubst_fo_formulaV60V62arename_subst_fo_termV59aidentityaidentityIais_symbol_free_var_in_symbolV56a@V62V55Aais_symbol_free_var_in_fo_formula
VC for subst_free_var_propagation_symbol_symbol_fo_formula_list
ais_symbol_free_var_in_fo_formula_listV56asubst_fo_formula_listV57V58V59Iais_symbol_free_var_in_fo_termV56a@V59V55Aais_fo_term_free_var_in_fo_formula_listV55V57ICtaFOFNilais_symbol_free_var_in_fo_termV56aevalarename_subst_fo_termV59aidentityaidentityV55Iais_symbol_free_var_in_fo_termV56a@V59V55Aais_symbol_free_var_in_fo_terma@V66V56arename_fo_termV67V66aidentityIais_symbol_free_var_in_fo_termV56V67LaevalV59V55LaidentityAais_symbol_free_var_in_fo_formula_listV56asubst_fo_formula_listV61arename_subst_symbolV58aidentityV65Iais_symbol_free_var_in_fo_termV56a@V65V55Aais_fo_term_free_var_in_fo_formula_listV55V61Larename_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@V63V56arename_fo_termV64V63aidentityIais_symbol_free_var_in_fo_termV56V64LaevalV59V55LaidentityAais_symbol_free_var_in_fo_formulaV56asubst_fo_formulaV60arename_subst_symbolV58aidentityV62Iais_symbol_free_var_in_fo_term
VC for subst_free_var_propagation_fo_term_symbol_fo_formula_list
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@V63V56arename_fo_termV64aidentityV63Iais_fo_term_free_var_in_fo_termV56V64LaevalV59V55LaidentityIais_fo_term_free_var_in_fo_formulaV56asubst_fo_formulaV60arename_subst_symbolV58aidentityV62Iais_fo_term_free_var_in_fo_termV56a@V62V55Aais_fo_term_free_var_in_fo_formulaV55V60Larename_subst_fo_termV59aidentityaidentityIa=V57aFOFConsV60V61FF
assertion
a<asize_fo_formula_listV61asize_fo_formula_listV57Aa<=c0asize_fo_formula_listV57Larename_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@V63V56arename_fo_termV64aidentityV63Iais_fo_term_free_var_in_fo_termV56V64LaevalV59V55LaidentityIais_fo_term_free_var_in_fo_formulaV56asubst_fo_formulaV60arename_subst_symbolV58aidentityV62Iais_fo_term_free_var_in_fo_termV56a@V62V55Aais_fo_term_free_var_in_fo_formulaV55V60Larename_subst_fo_termV59aidentityaidentityIa=V57aFOFConsV60V61FF
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@V66V56arename_fo_termV67aidentityV66Iais_fo_term_free_var_in_fo_termV56V67LaevalV59V55LaidentityIais_fo_term_free_var_in_fo_formula_listV56asubst_fo_formula_listV61arename_subst_symbolV58aidentityV65Iais_fo_term_free_var_in_fo_termV56a@V65V55Aais_fo_term_free_var_in_fo_formula_listV55V61Larename_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@V63V56arename_fo_termV64aidentityV63Iais_fo_term_free_var_in_fo_termV56V64LaevalV59V55LaidentityIais_fo_term_free_var_in_fo_formulaV56asubst_fo_formulaV60arename_subst_symbolV58aidentityV62Iais_fo_term_free_var_in_fo_termV56a@V62V55Aais_fo_term_free_var_in_fo_formulaV55V60Larename_subst_fo_termV59aidentityaidentityIa=V57aFOFConsV60V61FF
ais_fo_term_free_var_in_fo_formula_listV56asubst_fo_formula_listV57V58V59Iais_fo_term_free_var_in_fo_termV56a@V59V55Aais_fo_term_free_var_in_fo_formula_listV55V57ICtaFOFNilais_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@V66V56arename_fo_termV67aidentityV66Iais_fo_term_free_var_in_fo_termV56V67LaevalV59V55LaidentityAais_fo_term_free_var_in_fo_formula_listV56asubst_fo_formula_listV61arename_subst_symbolV58aidentityV65Iais_fo_term_free_var_in_fo_termV56a@V65V55Aais_fo_term_free_var_in_fo_formula_listV55V61Larename_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@V63V56arename_fo_termV64aidentityV63Iais_fo_term_free_var_in_fo_termV56V64LaevalV59V55LaidentityAais_fo_term_free_var_in_fo_formulaV56asubst_fo_formulaV60arename_subst_symbolV58aidentityV62Iais_fo_term_free_var_in_fo_term
VC for subst_free_var_propagation_fo_term_fo_term_fo_formula_list
ais_symbol_free_var_in_fo_formula_listV56asubst_fo_formula_listV57V58V59Iais_symbol_free_var_in_symbolV56a@V58V55Aais_symbol_free_var_in_fo_formula_listV55V57F
ais_symbol_free_var_in_fo_formula_listV61asubst_fo_formula_listV62V63V64Iais_symbol_free_var_in_fo_termV61a@V64V60Aais_fo_term_free_var_in_fo_formula_listV60V62F
ais_fo_term_free_var_in_fo_formula_listV66asubst_fo_formula_listV67V68V69Iais_fo_term_free_var_in_fo_termV66a@V69V65Aais_fo_term_free_var_in_fo_formula_listV65V67F
a=asubst_fo_formula_listV70V71V73asubst_fo_formula_listV70V72V74ICtaFOFNila=asubst_fo_formula_listV76arename_subst_symbolV71aidentityarename_subst_fo_termV73aidentityaidentityasubst_fo_formula_listV76arename_subst_symbolV72aidentityarename_subst_fo_termV74aidentityaidentityAais_fo_term_free_var_in_fo_formula_listV77V70Iais_fo_term_free_var_in_fo_formula_listV77V76FAais_symbol_free_var_in_fo_formula_listV78V70Iais_symbol_free_var_in_fo_formula_listV78V76FAa=asubst_fo_formulaV75arename_subst_symbolV71aidentityarename_subst_fo_termV73aidentityaidentityasubst_fo_formulaV75arename_subst_symbolV72aidentityarename_subst_fo_termV74aidentityaidentityAais_fo_term_free_var_in_fo_formula_listV79V70Iais_fo_term_free_var_in_fo_formulaV79V75FAais_symbol_free_var_in_fo_formula_listV80V70Iais_symbol_free_var_in_fo_formulaV80V75FaFOFConsVVV70ACtaFOFNila=a@arename_subst_fo_termV73aidentityaidentityV87a@arename_subst_fo_termV74aidentityaidentityV87Iais_fo_term_free_var_in_fo_formula_listV87V82FAa=a@arename_subst_symbolV71aidentity
VC for free_var_equivalence_of_subst_fo_formula_list
a=asubst_fo_formula_listV70V71V73asubst_fo_formula_listV70V72V74Ia=a@V73V75a@V74V75Iais_fo_term_free_var_in_fo_formula_listV75V70FIa=a@V71V76a@V72V76Iais_symbol_free_var_in_fo_formula_listV76V70FF
a=arename_fo_formula_listV77V78V80arename_fo_formula_listV77V79V81Ia=asubst_fo_formula_listV77V85V83asubst_fo_formula_listV77V84V82Aa=a@V83V86a@V82V86Iais_fo_term_free_var_in_fo_formula_listV86V77FAa=a@V85V87a@V84V87Iais_symbol_free_var_in_fo_formula_listV87V77FLasubst_of_rename_symbolV78Lasubst_of_rename_symbolV79Lasubst_of_rename_fo_termV80Lasubst_of_rename_fo_termV81Ia=a@V80V88a@V81V88Iais_fo_term_free_var_in_fo_formula_listV88V77FAa=a@V78V89a@V79V89Iais_symbol_free_var_in_fo_formula_listV89V77FF
VC for free_var_equivalence_of_rename_fo_formula_list
a=arename_fo_formula_listV77V78V80arename_fo_formula_listV77V79V81Ia=a@V80V82a@V81V82Iais_fo_term_free_var_in_fo_formula_listV82V77FIa=a@V78V83a@V79V83Iais_symbol_free_var_in_fo_formula_listV83V77FF
a=asubst_fo_formulaV89V94V92asubst_fo_formulaV89V93V91Larename_subst_symbolV85aidentityLarename_subst_symbolV86aidentityLarename_subst_fo_termV87aidentityaidentityLarename_subst_fo_termV88aidentityaidentityIa=V84aFOFConsV89V90FIa=asubst_fo_formula_listV84V85V87asubst_fo_formula_listV84V86V88F
precondition
a=a@V85V95a@V86V95Iais_symbol_free_var_in_fo_formulaV95V89FAa=a@V85V96a@V86V96Aa=arename_symbolarename_symbola@V86V96aidentityaidentitya@V86V96Aa=arename_symbolarename_symbola@V85V96aidentityaidentityarename_symbolarename_symbola@V86V96aidentityaidentityAa=a@V85V96arename_symbolarename_symbola@V85V96aidentityaidentityAa=aevalarename_subst_symbolV86aidentityV96arename_symbola@V86V96aidentityAa=aevalarename_subst_symbolV85aidentityV96aevalarename_subst_symbolV86aidentityV96Aa=arename_symbola@V85V96aidentityaevalarename_subst_symbolV85aidentityV96Iais_symbol_free_var_in_fo_formulaV96V89FIa=a@V92V97a@V91V97Iais_fo_term_free_var_in_fo_formulaV97V89FAa=a@V94V98a@V93V98Iais_symbol_free_var_in_fo_formulaV98V89FLarename_subst_symbolV85aidentityLarename_subst_symbolV86aidentityLarename_subst_fo_termV87aidentityaidentityLarename_subst_fo_termV88aidentityaidentityIa=V84aFOFConsV89V90FIa=asubst_fo_formula_listV84V85V87asubst_fo_formula_listV84V86V88F
a=a@V87V95a@V88V95Iais_fo_term_free_var_in_fo_formulaV95V89FAa=a@V87V96a@V88V96Aa=arename_fo_termarename_fo_terma@V88V96aidentityaidentityaidentityaidentitya@V88V96Aa=arename_fo_termarename_fo_terma@V87V96aidentityaidentityaidentityaidentityarename_fo_termarename_fo_terma@V88V96aidentityaidentityaidentityaidentityAa=a@V87V96arename_fo_termarename_fo_terma@V87V96aidentityaidentityaidentityaidentityAa=aevalarename_subst_fo_termV88aidentityaidentityV96arename_fo_terma@V88V96aidentityaidentityAa=aevalarename_subst_fo_termV87aidentityaidentityV96aevalarename_subst_fo_termV88aidentityaidentityV96Aa=arename_fo_terma@V87V96aidentityaidentityaevalarename_subst_fo_termV87aidentityaidentityV96Iais_fo_term_free_var_in_fo_formulaV96V89FIa=a@V85V97a@V86V97Iais_symbol_free_var_in_fo_formulaV97V89FAa=a@V85V98a@V86V98Aa=arename_symbolarename_symbola@V86V98aidentityaidentitya@V86V98Aa=arename_symbolarename_symbola@V85V98aidentityaidentityarename_symbolarename_symbola@V86V98aidentityaidentityAa=a@V85V98arename_symbolarename_symbol
a<asize_fo_formula_listV90asize_fo_formula_listV84Aa<=c0asize_fo_formula_listV84Larename_subst_symbolV85aidentityLarename_subst_symbolV86aidentityLarename_subst_fo_termV87aidentityaidentityLarename_subst_fo_termV88aidentityaidentityIa=a@V87V99a@V88V99Iais_fo_term_free_var_in_fo_formulaV99V89FAa=a@V87V100a@V88V100Aa=arename_fo_termarename_fo_terma@V88V100aidentityaidentityaidentityaidentitya@V88V100Aa=arename_fo_termarename_fo_terma@V87V100aidentityaidentityaidentityaidentityarename_fo_termarename_fo_terma@V88V100aidentityaidentityaidentityaidentityAa=a@V87V100arename_fo_termarename_fo_terma@V87V100aidentityaidentityaidentityaidentityAa=aevalarename_subst_fo_termV88aidentityaidentityV100arename_fo_terma@V88V100aidentityaidentityAa=aevalarename_subst_fo_termV87aidentityaidentityV100aevalarename_subst_fo_termV88aidentityaidentityV100Aa=arename_fo_terma@V87V100aidentityaidentityaevalarename_subst_fo_termV87aidentityaidentityV100Iais_fo_term_free_var_in_fo_formulaV100V89FIa=a@V85V101a@V86V101Iais_symbol_free_var_in_fo_formula
a=asubst_fo_formula_listV90V98V96asubst_fo_formula_listV90V97V95Larename_subst_symbolV85aidentityLarename_subst_symbolV86aidentityLarename_subst_fo_termV87aidentityaidentityLarename_subst_fo_termV88aidentityaidentityIa=a@V87V99a@V88V99Iais_fo_term_free_var_in_fo_formulaV99V89FAa=a@V87V100a@V88V100Aa=arename_fo_termarename_fo_terma@V88V100aidentityaidentityaidentityaidentitya@V88V100Aa=arename_fo_termarename_fo_terma@V87V100aidentityaidentityaidentityaidentityarename_fo_termarename_fo_terma@V88V100aidentityaidentityaidentityaidentityAa=a@V87V100arename_fo_termarename_fo_terma@V87V100aidentityaidentityaidentityaidentityAa=aevalarename_subst_fo_termV88aidentityaidentityV100arename_fo_terma@V88V100aidentityaidentityAa=aevalarename_subst_fo_termV87aidentityaidentityV100aevalarename_subst_fo_termV88aidentityaidentityV100Aa=arename_fo_terma@V87V100aidentityaidentityaevalarename_subst_fo_termV87aidentityaidentityV100Iais_fo_term_free_var_in_fo_formulaV100V89FIa=a@V85V101a@V86V101Iais_symbol_free_var_in_fo_formulaV101
a=a@V85V99a@V86V99Iais_symbol_free_var_in_fo_formula_listV99V90FAa=a@V85V100a@V86V100Aa=arename_symbolarename_symbola@V86V100aidentityaidentitya@V86V100Aa=arename_symbolarename_symbola@V85V100aidentityaidentityarename_symbolarename_symbola@V86V100aidentityaidentityAa=a@V85V100arename_symbolarename_symbola@V85V100aidentityaidentityAa=aevalarename_subst_symbolV86aidentityV100arename_symbola@V86V100aidentityAa=aevalarename_subst_symbolV85aidentityV100aevalarename_subst_symbolV86aidentityV100Aa=arename_symbola@V85V100aidentityaevalarename_subst_symbolV85aidentityV100Iais_symbol_free_var_in_fo_formula_listV100V90FIa=a@V96V101a@V95V101Iais_fo_term_free_var_in_fo_formula_listV101V90FAa=a@V98V102a@V97V102Iais_symbol_free_var_in_fo_formula_listV102V90FLarename_subst_symbolV85aidentityLarename_subst_symbolV86aidentityLarename_subst_fo_termV87aidentityaidentityLarename_subst_fo_termV88aidentityaidentityIa=a@V87V103a@V88V103Iais_fo_term_free_var_in_fo_formulaV103V89FAa=a@V87V104a@V88V104Aa=arename_fo_termarename_fo_terma
a=a@V87V99a@V88V99Iais_fo_term_free_var_in_fo_formula_listV99V90FAa=a@V87V100a@V88V100Aa=arename_fo_termarename_fo_terma@V88V100aidentityaidentityaidentityaidentitya@V88V100Aa=arename_fo_termarename_fo_terma@V87V100aidentityaidentityaidentityaidentityarename_fo_termarename_fo_terma@V88V100aidentityaidentityaidentityaidentityAa=a@V87V100arename_fo_termarename_fo_terma@V87V100aidentityaidentityaidentityaidentityAa=aevalarename_subst_fo_termV88aidentityaidentityV100arename_fo_terma@V88V100aidentityaidentityAa=aevalarename_subst_fo_termV87aidentityaidentityV100aevalarename_subst_fo_termV88aidentityaidentityV100Aa=arename_fo_terma@V87V100aidentityaidentityaevalarename_subst_fo_termV87aidentityaidentityV100Iais_fo_term_free_var_in_fo_formula_listV100V90FIa=a@V85V101a@V86V101Iais_symbol_free_var_in_fo_formula_listV101V90FAa=a@V85V102a@V86V102Aa=arename_symbolarename_symbola@V86V102aidentityaidentitya@V86V102Aa=arename_symbolarename_symbola@V85V102aidentityaidentityarename_symbolarename_symbola@V86V102aidentityaidentity
a=a@V85V89a@V86V89Iais_symbol_free_var_in_fo_formula_listV89V84FICtaFOFNila=a@V87V92a@V88V92Iais_fo_term_free_var_in_fo_formula_listV92V91FAa=a@V87V93a@V88V93Aa=arename_fo_termarename_fo_terma@V88V93aidentityaidentityaidentityaidentitya@V88V93Aa=arename_fo_termarename_fo_terma@V87V93aidentityaidentityaidentityaidentityarename_fo_termarename_fo_terma@V88V93aidentityaidentityaidentityaidentityAa=a@V87V93arename_fo_termarename_fo_terma@V87V93aidentityaidentityaidentityaidentityAa=aevalarename_subst_fo_termV88aidentityaidentityV93arename_fo_terma@V88V93aidentityaidentityAa=aevalarename_subst_fo_termV87aidentityaidentityV93aevalarename_subst_fo_termV88aidentityaidentityV93Aa=arename_fo_terma@V87V93aidentityaidentityaevalarename_subst_fo_termV87aidentityaidentityV93Iais_fo_term_free_var_in_fo_formula_listV93V91FAa=a@V85V94a@V86V94Iais_symbol_free_var_in_fo_formula_listV94V91FAa=a@V85V95a@V86V95Aa=arename_symbolarename_symbola@V86V95aidentityaidentitya@V86V95Aa=arename_symbolarename_symbola@V85V95aidentityaidentitya
a=a@V87V89a@V88V89Iais_fo_term_free_var_in_fo_formula_listV89V84FIa=a@V85V90a@V86V90Iais_symbol_free_var_in_fo_formula_listV90V84FICtaFOFNila=a@V87V93a@V88V93Iais_fo_term_free_var_in_fo_formula_listV93V92FAa=a@V87V94a@V88V94Aa=arename_fo_termarename_fo_terma@V88V94aidentityaidentityaidentityaidentitya@V88V94Aa=arename_fo_termarename_fo_terma@V87V94aidentityaidentityaidentityaidentityarename_fo_termarename_fo_terma@V88V94aidentityaidentityaidentityaidentityAa=a@V87V94arename_fo_termarename_fo_terma@V87V94aidentityaidentityaidentityaidentityAa=aevalarename_subst_fo_termV88aidentityaidentityV94arename_fo_terma@V88V94aidentityaidentityAa=aevalarename_subst_fo_termV87aidentityaidentityV94aevalarename_subst_fo_termV88aidentityaidentityV94Aa=arename_fo_terma@V87V94aidentityaidentityaevalarename_subst_fo_termV87aidentityaidentityV94Iais_fo_term_free_var_in_fo_formula_listV94V92FAa=a@V85V95a@V86V95Iais_symbol_free_var_in_fo_formula_listV95V92FAa=a@V85V96a@V86V96Aa=arename_symbolarename_symbola@V86V96aidentityaidentity
a=a@V87V89a@V88V89Iais_fo_term_free_var_in_fo_formula_listV89V84FAa=a@V85V90a@V86V90Iais_symbol_free_var_in_fo_formula_listV90V84FICtaFOFNila=a@V87V93a@V88V93Iais_fo_term_free_var_in_fo_formula_listV93V92FAa=a@V87V94a@V88V94Aa=arename_fo_termarename_fo_terma@V88V94aidentityaidentityaidentityaidentitya@V88V94Aa=arename_fo_termarename_fo_terma@V87V94aidentityaidentityaidentityaidentityarename_fo_termarename_fo_terma@V88V94aidentityaidentityaidentityaidentityAa=a@V87V94arename_fo_termarename_fo_terma@V87V94aidentityaidentityaidentityaidentityAa=aevalarename_subst_fo_termV88aidentityaidentityV94arename_fo_terma@V88V94aidentityaidentityAa=aevalarename_subst_fo_termV87aidentityaidentityV94aevalarename_subst_fo_termV88aidentityaidentityV94Aa=arename_fo_terma@V87V94aidentityaidentityaevalarename_subst_fo_termV87aidentityaidentityV94Iais_fo_term_free_var_in_fo_formula_listV94V92FAa=a@V85V95a@V86V95Iais_symbol_free_var_in_fo_formula_listV95V92FAa=a@V85V96a@V86V96Aa=arename_symbolarename_symbola@V86V96aidentityaidentity
VC for free_var_derive_equivalence_of_subst_fo_formula_list
a=a@V87V89a@V88V89Iais_fo_term_free_var_in_fo_formula_listV89V84FAa=a@V85V90a@V86V90Iais_symbol_free_var_in_fo_formula_listV90V84FIa=asubst_fo_formula_listV84V85V87asubst_fo_formula_listV84V86V88F
a=asubst_fo_formula_listV91V99V97asubst_fo_formula_listV91V98V96Lasubst_of_rename_symbolV92Lasubst_of_rename_symbolV93Lasubst_of_rename_fo_termV94Lasubst_of_rename_fo_termV95Ia=arename_fo_formula_listV91V92V94arename_fo_formula_listV91V93V95F
a=a@V92V100a@V93V100Aa=a@V92V100a@V93V100Ia=a@asubst_of_rename_symbolV92V100a@asubst_of_rename_symbolV93V100FIa=a@V97V101a@V96V101Iais_fo_term_free_var_in_fo_formula_listV101V91FAa=a@V99V102a@V98V102Iais_symbol_free_var_in_fo_formula_listV102V91FLasubst_of_rename_symbolV92Lasubst_of_rename_symbolV93Lasubst_of_rename_fo_termV94Lasubst_of_rename_fo_termV95Ia=arename_fo_formula_listV91V92V94arename_fo_formula_listV91V93V95F
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_fo_formula_listV102V91FAa=a@V99V103a@V98V103Iais_symbol_free_var_in_fo_formula_listV103V91FLasubst_of_rename_symbolV92Lasubst_of_rename_symbolV93Lasubst_of_rename_fo_termV94Lasubst_of_rename_fo_termV95Ia=arename_fo_formula_listV91V92V94arename_fo_formula_listV91V93V95F
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