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(arityeq1_2Ec_2Eenumeral_2Ezerbl_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Eenumeral_2Ebl(A_27a),c_2Eenumeral_2Ezerbl_2E1(s(tyop_2Eenumeral_2Ebl(A_27a),X0_2E0))) = s(tyop_2Eenumeral_2Ebl(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)),c_2Eenumeral_2Ezerbl_2E0),s(tyop_2Eenumeral_2Ebl(A_27a),X0_2E0))))).
fof(arityeq3_2Ec_2Eenumeral_2Eonebl_2E3_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Eenumeral_2Ebl(A_27a),c_2Eenumeral_2Eonebl_2E3(s(A_27a,X0_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),X1_2E0),s(tyop_2Eenumeral_2Ebl(A_27a),X2_2E0))) = s(tyop_2Eenumeral_2Ebl(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)))),c_2Eenumeral_2Eonebl_2E0),s(A_27a,X0_2E0))),s(tyop_2Eenumeral_2Ebt(A_27a),X1_2E0))),s(tyop_2Eenumeral_2Ebl(A_27a),X2_2E0))))).
fof(arityeq4_2Ec_2Eenumeral_2Ebl__CASE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0]: (s(A_27b,c_2Eenumeral_2Ebl__CASE_2E4(s(tyop_2Eenumeral_2Ebl(A_27a),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),X2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),A_27b)))),c_2Eenumeral_2Ebl__CASE_2E0),s(tyop_2Eenumeral_2Ebl(A_27a),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),X3_2E0))))).
fof(enumeralTheory_2Ebl__case__cong,axiom,![A_27a, A_27b]: ![V0f1_27_2E0, V1f_27_2E0, V2v_27_2E0, V3M_2E0, V4M_27_2E0, V5v_2E0, V6f_2E0, V7f1_2E0]: (((s(tyop_2Eenumeral_2Ebl(A_27a),V3M_2E0) = s(tyop_2Eenumeral_2Ebl(A_27a),V4M_27_2E0)) & (((s(tyop_2Eenumeral_2Ebl(A_27a),V4M_27_2E0) = s(tyop_2Eenumeral_2Ebl(A_27a),c_2Eenumeral_2Enbl_2E0)) => (s(A_27b,V5v_2E0) = s(A_27b,V2v_27_2E0))) & (![V8a_2E0]: ((s(tyop_2Eenumeral_2Ebl(A_27a),V4M_27_2E0) = s(tyop_2Eenumeral_2Ebl(A_27a),c_2Eenumeral_2Ezerbl_2E1(s(tyop_2Eenumeral_2Ebl(A_27a),V8a_2E0)))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),V6f_2E0),s(tyop_2Eenumeral_2Ebl(A_27a),V8a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),V1f_27_2E0),s(tyop_2Eenumeral_2Ebl(A_27a),V8a_2E0))))) & ![V9a0_2E0, V10a1_2E0, V11a2_2E0]: ((s(tyop_2Eenumeral_2Ebl(A_27a),V4M_27_2E0) = s(tyop_2Eenumeral_2Ebl(A_27a),c_2Eenumeral_2Eonebl_2E3(s(A_27a,V9a0_2E0),s(tyop_2Eenumeral_2Ebt(A_27a),V10a1_2E0),s(tyop_2Eenumeral_2Ebl(A_27a),V11a2_2E0)))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),V7f1_2E0),s(A_27a,V9a0_2E0))),s(tyop_2Eenumeral_2Ebt(A_27a),V10a1_2E0))),s(tyop_2Eenumeral_2Ebl(A_27a),V11a2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),V0f1_27_2E0),s(A_27a,V9a0_2E0))),s(tyop_2Eenumeral_2Ebt(A_27a),V10a1_2E0))),s(tyop_2Eenumeral_2Ebl(A_27a),V11a2_2E0)))))))) => (s(A_27b,c_2Eenumeral_2Ebl__CASE_2E4(s(tyop_2Eenumeral_2Ebl(A_27a),V3M_2E0),s(A_27b,V5v_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),V6f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),V7f1_2E0))) = s(A_27b,c_2Eenumeral_2Ebl__CASE_2E4(s(tyop_2Eenumeral_2Ebl(A_27a),V4M_27_2E0),s(A_27b,V2v_27_2E0),s(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b),V1f_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),A_27b))),V0f1_27_2E0)))))).
