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(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(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2CA_27e_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27e_29,axiom,![A_27b, A_27c, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27c,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27e),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27c,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,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_27c_2CA_27e_29_2Ctyop_2Emin_2Efun_28A_27b_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_27c,A_27e),tyop_2Emin_2Efun(A_27b,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_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,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_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,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_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e)),X1_2E0))))).
fof(arityeq7_2Ec_2EsimpleSetCat_2ESpushout_2E7_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b_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_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X4_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,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_27c,A_27e),tyop_2Emin_2Efun(A_27b,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_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,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_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,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_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,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_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,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_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X4_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e))),X5_2E0))),s(tyop_2Ebool_2Eitself(A_27d),X6_2E0))))).
fof(simpleSetCatTheory_2ESpushout__sym,axiom,![A_27a, A_27b, A_27c, A_27d, A_27e]: ![V0p2_2E0, V1p1_2E0, V2P_2E0, V3g_2E0, V4f_2E0, V5C_2E0, V6B_2E0, V7A_2E0]: (p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2ESpushout_2E7(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V7A_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V6B_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V5C_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V3g_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),V2P_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),V1p1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27e),V0p2_2E0))))),s(tyop_2Ebool_2Eitself(A_27d),c_2Ebool_2Ethe__value_2E0)))) => p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2ESpushout_2E7(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V7A_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V5C_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V6B_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V3g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,A_27e)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27c,A_27e),V0p2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27e),V1p1_2E0))))),s(tyop_2Ebool_2Eitself(A_27d),c_2Ebool_2Ethe__value_2E0)))))).
