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(arityeq3_2Ec_2EsimpleSetCat_2Eshom_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2Eshom_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),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_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2EsimpleSetCat_2Eshom_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))))).
fof(arityeq3_2Ec_2EsimpleSetCat_2Eshom_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,![A_27a, A_27c]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2Eshom_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2EsimpleSetCat_2Eshom_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eone_2Eone_29,axiom,![A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28A_27c_2Ctyop_2Eone_2Eone_29_29,axiom,![A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone)),X1_2E0))))).
fof(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Eone_2Eone,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Eone_2Eone,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27b,axiom,![A_27b]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),c_2Ecombin_2EK_2E1(s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E0),s(tyop_2Eone_2Eone,X0_2E0))))).
fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27c,axiom,![A_27c]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),c_2Ecombin_2EK_2E1(s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E0),s(tyop_2Eone_2Eone,X0_2E0))))).
fof(arityeq7_2Ec_2EsimpleSetCat_2ESpushout_2E7_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eone_2Eone,axiom,![A_27a, A_27b, A_27c]: ![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(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),X5_2E0),s(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),X6_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),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(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),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(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),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(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),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(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),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(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),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(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),X5_2E0))),s(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),X6_2E0))))).
fof(arityeq2_2Ec_2EsimpleSetCat_2Erestr_2E2_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,![A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone))),c_2EsimpleSetCat_2Erestr_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2EsimpleSetCat_2Erestr_2E2_2Emono_2EA_27c_20mono_2Etyop_2Eone_2Eone,axiom,![A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),c_2EsimpleSetCat_2Erestr_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))))).
fof(simpleSetCatTheory_2Eunit__pushout,axiom,![A_27a, A_27b, A_27c]: ![V0C_2E0, V1g_2E0, V2B_2E0, V3A_2E0, V4f_2E0]: ((p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2Eshom_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3A_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2B_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2Eshom_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3A_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V0C_2E0)))) & ~ ((s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3A_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) => p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2ESpushout_2E7(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3A_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2B_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V0C_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),c_2Ecombin_2EK_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2B_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eone_2Eone),c_2Ecombin_2EK_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V0C_2E0))))))),s(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),c_2Ebool_2Ethe__value_2E0)))))).
