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_2EringNorm_2EPconst_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPconst_2E1(s(A_27a,X0_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2EringNorm_2Epolynom(A_27a)),c_2EringNorm_2EPconst_2E0),s(A_27a,X0_2E0))))).
fof(arityeq1_2Ec_2EringNorm_2EPopp_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPopp_2E1(s(tyop_2EringNorm_2Epolynom(A_27a),X0_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2EringNorm_2Epolynom(A_27a)),c_2EringNorm_2EPopp_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),X0_2E0))))).
fof(arityeq1_2Ec_2EringNorm_2EPvar_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPvar_2E1(s(tyop_2Equote_2Eindex,X0_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EringNorm_2Epolynom(A_27a)),c_2EringNorm_2EPvar_2E0),s(tyop_2Equote_2Eindex,X0_2E0))))).
fof(arityeq2_2Ec_2EringNorm_2EPmult_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPmult_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),X0_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),X1_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2EringNorm_2Epolynom(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2EringNorm_2Epolynom(A_27a))),c_2EringNorm_2EPmult_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),X0_2E0))),s(tyop_2EringNorm_2Epolynom(A_27a),X1_2E0))))).
fof(arityeq2_2Ec_2EringNorm_2EPplus_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPplus_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),X0_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),X1_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2EringNorm_2Epolynom(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2EringNorm_2Epolynom(A_27a))),c_2EringNorm_2EPplus_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),X0_2E0))),s(tyop_2EringNorm_2Epolynom(A_27a),X1_2E0))))).
fof(arityeq6_2Ec_2EringNorm_2Epolynom__CASE_2E6_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0, X4_2E0, X5_2E0]: (s(A_27b,c_2EringNorm_2Epolynom__CASE_2E6(s(tyop_2EringNorm_2Epolynom(A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),X3_2E0),s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),X4_2E0),s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),X5_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),A_27b)))))),c_2EringNorm_2Epolynom__CASE_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),X3_2E0))),s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),X4_2E0))),s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),X5_2E0))))).
fof(ringNormTheory_2Epolynom__case__eq,axiom,![A_27a, A_27b]: ![V0v_2E0, V1f4_2E0, V2f3_2E0, V3f2_2E0, V4f1_2E0, V5f_2E0, V6x_2E0]: ((s(A_27b,c_2EringNorm_2Epolynom__CASE_2E6(s(tyop_2EringNorm_2Epolynom(A_27a),V6x_2E0),s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),V5f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f1_2E0),s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),V3f2_2E0),s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),V2f3_2E0),s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V1f4_2E0))) = s(A_27b,V0v_2E0)) <=> (?[V7i_2E0]: ((s(tyop_2EringNorm_2Epolynom(A_27a),V6x_2E0) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPvar_2E1(s(tyop_2Equote_2Eindex,V7i_2E0)))) & (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),V5f_2E0),s(tyop_2Equote_2Eindex,V7i_2E0))) = s(A_27b,V0v_2E0))) | (?[V8a_2E0]: ((s(tyop_2EringNorm_2Epolynom(A_27a),V6x_2E0) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPconst_2E1(s(A_27a,V8a_2E0)))) & (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f1_2E0),s(A_27a,V8a_2E0))) = s(A_27b,V0v_2E0))) | (?[V9p_2E0, V10p0_2E0]: ((s(tyop_2EringNorm_2Epolynom(A_27a),V6x_2E0) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPplus_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V9p_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V10p0_2E0)))) & (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),V3f2_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V9p_2E0))),s(tyop_2EringNorm_2Epolynom(A_27a),V10p0_2E0))) = s(A_27b,V0v_2E0))) | (?[V11p_2E0, V12p0_2E0]: ((s(tyop_2EringNorm_2Epolynom(A_27a),V6x_2E0) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPmult_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V11p_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V12p0_2E0)))) & (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b)),V2f3_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V11p_2E0))),s(tyop_2EringNorm_2Epolynom(A_27a),V12p0_2E0))) = s(A_27b,V0v_2E0))) | ?[V13p_2E0]: ((s(tyop_2EringNorm_2Epolynom(A_27a),V6x_2E0) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPopp_2E1(s(tyop_2EringNorm_2Epolynom(A_27a),V13p_2E0)))) & (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V1f4_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V13p_2E0))) = s(A_27b,V0v_2E0))))))))).
