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(ringNormTheory_2Epolynom__distinct,axiom,![A_27a]: (![V0a_27_2E0, V1a_2E0]: ~ ((s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPvar_2E1(s(tyop_2Equote_2Eindex,V1a_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPconst_2E1(s(A_27a,V0a_27_2E0))))) & (![V2a1_2E0, V3a0_2E0, V4a_2E0]: ~ ((s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPvar_2E1(s(tyop_2Equote_2Eindex,V4a_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPplus_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V3a0_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V2a1_2E0))))) & (![V5a1_2E0, V6a0_2E0, V7a_2E0]: ~ ((s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPvar_2E1(s(tyop_2Equote_2Eindex,V7a_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPmult_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V6a0_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V5a1_2E0))))) & (![V8a_27_2E0, V9a_2E0]: ~ ((s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPvar_2E1(s(tyop_2Equote_2Eindex,V9a_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPopp_2E1(s(tyop_2EringNorm_2Epolynom(A_27a),V8a_27_2E0))))) & (![V10a1_2E0, V11a0_2E0, V12a_2E0]: ~ ((s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPconst_2E1(s(A_27a,V12a_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPplus_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V11a0_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V10a1_2E0))))) & (![V13a1_2E0, V14a0_2E0, V15a_2E0]: ~ ((s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPconst_2E1(s(A_27a,V15a_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPmult_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V14a0_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V13a1_2E0))))) & (![V16a_27_2E0, V17a_2E0]: ~ ((s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPconst_2E1(s(A_27a,V17a_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPopp_2E1(s(tyop_2EringNorm_2Epolynom(A_27a),V16a_27_2E0))))) & (![V18a1_27_2E0, V19a1_2E0, V20a0_27_2E0, V21a0_2E0]: ~ ((s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPplus_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V21a0_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V19a1_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPmult_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V20a0_27_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V18a1_27_2E0))))) & (![V22a1_2E0, V23a0_2E0, V24a_2E0]: ~ ((s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPplus_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V23a0_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V22a1_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPopp_2E1(s(tyop_2EringNorm_2Epolynom(A_27a),V24a_2E0))))) & ![V25a1_2E0, V26a0_2E0, V27a_2E0]: ~ ((s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPmult_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V26a0_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V25a1_2E0))) = s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPopp_2E1(s(tyop_2EringNorm_2Epolynom(A_27a),V27a_2E0))))))))))))))).
