fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq2_2Ec_2EsimpleSetCat_2Ecardgt_2E2_2Emono_2EA_27d,axiom,![A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2Ecardgt_2E2(s(tyop_2Ebool_2Eitself(A_27d),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27d),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2EsimpleSetCat_2Ecardgt_2E0),s(tyop_2Ebool_2Eitself(A_27d),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))))).
fof(arityeq2_2Ec_2EsimpleSetCat_2Ecardgt_2E2_2Emono_2EA_27e,axiom,![A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2Ecardgt_2E2(s(tyop_2Ebool_2Eitself(A_27e),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27e),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2EsimpleSetCat_2Ecardgt_2E0),s(tyop_2Ebool_2Eitself(A_27e),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27e_20mono_2EA_27d,axiom,![A_27b, A_27d, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27b,A_27e),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27e))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))))).
fof(arityeq2_2Ec_2EsimpleSetCat_2Erestr_2E2_2Emono_2EA_27b_20mono_2EA_27e,axiom,![A_27b, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27b,A_27e),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27b,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27e))),c_2EsimpleSetCat_2Erestr_2E0),s(tyop_2Emin_2Efun(A_27b,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27e_20mono_2EA_27d,axiom,![A_27c, A_27d, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27c,A_27e),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27e))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X1_2E0))))).
fof(arityeq2_2Ec_2EsimpleSetCat_2Erestr_2E2_2Emono_2EA_27c_20mono_2EA_27e,axiom,![A_27c, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27c,A_27e),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27c,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,A_27e))),c_2EsimpleSetCat_2Erestr_2E0),s(tyop_2Emin_2Efun(A_27c,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27d_20mono_2EA_27e,axiom,![A_27d, A_27e]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),X2_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27d_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29,axiom,![A_27b, A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2CA_27d_29_2Ctyop_2Emin_2Efun_28A_27c_2CA_27d_29_29,axiom,![A_27b, A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),X1_2E0))))).
fof(arityeq7_2Ec_2EsimpleSetCat_2ESpushout_2E7_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27e_20mono_2EA_27d,axiom,![A_27a, A_27b, A_27c, A_27d, A_27e]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0, X4_2E0, X5_2E0, X6_2E0]: (s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2ESpushout_2E7(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X4_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),X5_2E0),s(tyop_2Ebool_2Eitself(A_27e),X6_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27e),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27e),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27e),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27e),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27e),tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27e),tyop_2Emin_2Ebool)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27e),tyop_2Emin_2Ebool))))))),c_2EsimpleSetCat_2ESpushout_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X4_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),X5_2E0))),s(tyop_2Ebool_2Eitself(A_27e),X6_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27e_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27e_29,axiom,![A_27b, A_27c, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27e),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27b,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27e),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27e_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2CA_27e_29_2Ctyop_2Emin_2Efun_28A_27c_2CA_27e_29_29,axiom,![A_27b, A_27c, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e)),X1_2E0))))).
fof(arityeq7_2Ec_2EsimpleSetCat_2ESpushout_2E7_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e,axiom,![A_27a, A_27b, A_27c, A_27d, A_27e]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0, X4_2E0, X5_2E0, X6_2E0]: (s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2ESpushout_2E7(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X4_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),X5_2E0),s(tyop_2Ebool_2Eitself(A_27d),X6_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27d),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27d),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27d),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27d),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27d),tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27d),tyop_2Emin_2Ebool)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27d),tyop_2Emin_2Ebool))))))),c_2EsimpleSetCat_2ESpushout_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X4_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),X5_2E0))),s(tyop_2Ebool_2Eitself(A_27d),X6_2E0))))).
fof(simpleSetCatTheory_2ESpushouts__iso,axiom,![A_27a, A_27b, A_27c, A_27d, A_27e]: ![V0j2_2E0, V1j1_2E0, V2Q_2E0, V3i2_2E0, V4i1_2E0, V5P_2E0, V6g_2E0, V7f_2E0, V8C_2E0, V9B_2E0, V10A_2E0]: ((p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2ESpushout_2E7(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V10A_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V9B_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V8C_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V6g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V5P_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V4i1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V3i2_2E0))))),s(tyop_2Ebool_2Eitself(A_27e),c_2Ebool_2Ethe__value_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2ESpushout_2E7(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V10A_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V9B_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V8C_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V6g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(A_27c,A_27e)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27e),V1j1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27e),V0j2_2E0))))),s(tyop_2Ebool_2Eitself(A_27d),c_2Ebool_2Ethe__value_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2Ecardgt_2E2(s(tyop_2Ebool_2Eitself(A_27d),c_2Ebool_2Ethe__value_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2Ecardgt_2E2(s(tyop_2Ebool_2Eitself(A_27e),c_2Ebool_2Ethe__value_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))) => ?[V11H_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27d,A_27e),V11H_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V5P_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),V2Q_2E0)))) & ((s(tyop_2Emin_2Efun(A_27b,A_27e),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27b,A_27e),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V11H_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4i1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V9B_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27e),V1j1_2E0)) & (s(tyop_2Emin_2Efun(A_27c,A_27e),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27c,A_27e),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V11H_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V3i2_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V8C_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27e),V0j2_2E0)))))).
