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_27p_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27p_29,axiom,![A_27b, A_27c, A_27p]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27p),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27p),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27p),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27p),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27b,A_27p),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27p),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27p_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2CA_27p_29_2Ctyop_2Emin_2Efun_28A_27c_2CA_27p_29_29,axiom,![A_27b, A_27c, A_27p]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27p,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27p,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27p,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p)),X1_2E0))))).
fof(simpleSetCatTheory_2ESpushout__ind,axiom,![A_27a, A_27b, A_27c, A_27d, A_27p]: ![V0P_27_2E0]: (![V1A_2E0, V2B_2E0, V3C_2E0, V4f_2E0, V5g_2E0, V6P_2E0, V7i1_2E0, V8i2_2E0]: p(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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27d),tyop_2Emin_2Ebool))))))),V0P_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2B_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3C_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V5g_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27p,tyop_2Emin_2Ebool),V6P_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27p),V7i1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27p),V8i2_2E0))))))),s(tyop_2Ebool_2Eitself(A_27d),c_2Ebool_2Ethe__value_2E0)))) => ![V9v_2E0, V10v1_2E0, V11v2_2E0, V12v3_2E0, V13v4_2E0, V14v5_2E0, V15v6_2E0, V16v7_2E0, V17v8_2E0]: p(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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),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_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27d),tyop_2Emin_2Ebool))))))),V0P_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V9v_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V10v1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V11v2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V12v3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V13v4_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27p,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27p,tyop_2Emin_2Ebool),V14v5_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,A_27p),tyop_2Emin_2Efun(A_27c,A_27p)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,A_27p),V15v6_2E0),s(tyop_2Emin_2Efun(A_27c,A_27p),V16v7_2E0))))))),s(tyop_2Ebool_2Eitself(A_27d),V17v8_2E0)))))).
