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_2Epred__set_2EINJ_2E3_2Emono_2EA_27e_20mono_2EA_27d,axiom,![A_27d, A_27e]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27e,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27e,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X2_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27f_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27f_29,axiom,![A_27b, A_27c, A_27f]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27f),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27f),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27f),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27f),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27b,A_27f),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27f),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27f_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2CA_27f_29_2Ctyop_2Emin_2Efun_28A_27c_2CA_27f_29_29,axiom,![A_27b, A_27c, A_27f]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f)),X1_2E0))))).
fof(arityeq7_2Ec_2EsimpleSetCat_2ESpushout_2E7_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27f,axiom,![A_27a, A_27b, A_27c, A_27d, A_27f]: ![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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),X5_2E0))),s(tyop_2Ebool_2Eitself(A_27d),X6_2E0))))).
fof(arityeq7_2Ec_2EsimpleSetCat_2ESpushout_2E7_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27e_20mono_2EA_27f,axiom,![A_27a, A_27b, A_27c, A_27e, A_27f]: ![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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),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_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),X5_2E0))),s(tyop_2Ebool_2Eitself(A_27e),X6_2E0))))).
fof(simpleSetCatTheory_2ESpushout__transfer,axiom,![A_27a, A_27b, A_27c, A_27d, A_27e, A_27f]: ![V0h_2E0, V1i2_2E0, V2i1_2E0, V3P_2E0, V4g_2E0, V5f_2E0, V6C_2E0, V7B_2E0, V8A_2E0]: ((p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2ESpushout_2E7(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8A_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7B_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V6C_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V4g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27f),V2i1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27f),V1i2_2E0))))),s(tyop_2Ebool_2Eitself(A_27d),c_2Ebool_2Ethe__value_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27e,A_27d),V0h_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) => p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2ESpushout_2E7(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8A_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V7B_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V6C_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V4g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27f),tyop_2Emin_2Efun(A_27c,A_27f)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27f),V2i1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27f),V1i2_2E0))))),s(tyop_2Ebool_2Eitself(A_27e),c_2Ebool_2Ethe__value_2E0)))))).
