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_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2EcoalgAxioms_2EF_28A_27a_29_29,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a)),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2EcoalgAxioms_2EF_28A_27b_29_29,axiom,![A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b)),X1_2E0))))).
fof(arityeq4_2Ec_2EcoalgAxioms_2Eepi_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,![A_27a, A_27b, A_27c]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0]: (s(tyop_2Emin_2Ebool,c_2EcoalgAxioms_2Eepi_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),X2_2E0),s(tyop_2Ebool_2Eitself(A_27c),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),tyop_2Emin_2Ebool)))),c_2EcoalgAxioms_2Eepi_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),X2_2E0))),s(tyop_2Ebool_2Eitself(A_27c),X3_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27b_29,axiom,![A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2EcoalgAxioms_2EF_28A_27b_29_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2CA_27b_29_2Ctyop_2Emin_2Efun_28A_27b_2CA_27b_29_29,axiom,![A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0))))).
fof(arityeq7_2Ec_2EcoalgAxioms_2EFpushout_2E7_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27b,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_2EcoalgAxioms_2EFpushout_2E7(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X4_2E0),s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),X5_2E0),s(tyop_2Ebool_2Eitself(A_27c),X6_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),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_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),tyop_2Emin_2Ebool)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),tyop_2Emin_2Ebool))))))),c_2EcoalgAxioms_2EFpushout_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X4_2E0))),s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),X5_2E0))),s(tyop_2Ebool_2Eitself(A_27c),X6_2E0))))).
fof(arityeq2_2Ec_2EsimpleSetCat_2Erestr_2E2_2Emono_2EA_27b_20mono_2EA_27b,axiom,![A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27b,A_27b),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b))),c_2EsimpleSetCat_2Erestr_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))))).
fof(coalgAxiomsTheory_2Eepi__Fpushout,axiom,![A_27a, A_27b, A_27c]: ![F0_2E0]: (![V5x_2E0]: (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),F0_2E0),s(A_27b,V5x_2E0))) = s(A_27b,V5x_2E0)) => ![V0bf_2E0, V1B_2E0, V2af_2E0, V3A_2E0, V4f_2E0]: (s(tyop_2Emin_2Ebool,c_2EcoalgAxioms_2Eepi_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a)),V2af_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1B_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b)),V0bf_2E0))),s(tyop_2Ebool_2Eitself(A_27c),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Emin_2Ebool,c_2EcoalgAxioms_2EFpushout_2E7(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2EcoalgAxioms_2EF(A_27a)),V2af_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1B_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b)),V0bf_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1B_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b)),V0bf_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1B_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2EcoalgAxioms_2EF(A_27b)),V0bf_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1B_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27b),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1B_2E0))))))),s(tyop_2Ebool_2Eitself(A_27c),c_2Ebool_2Ethe__value_2E0)))))).
