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__Axiom,axiom,![A_27a, A_27b]: ![V0f0_2E0, V1f1_2E0, V2f2_2E0, V3f3_2E0, V4f4_2E0]: ?[V5fn_2E0]: (![V6a_2E0]: (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V5fn_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPvar_2E1(s(tyop_2Equote_2Eindex,V6a_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),V0f0_2E0),s(tyop_2Equote_2Eindex,V6a_2E0)))) & (![V7a_2E0]: (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V5fn_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPconst_2E1(s(A_27a,V7a_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f1_2E0),s(A_27a,V7a_2E0)))) & (![V8a0_2E0, V9a1_2E0]: (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V5fn_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPplus_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V8a0_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V9a1_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))),V2f2_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V8a0_2E0))),s(tyop_2EringNorm_2Epolynom(A_27a),V9a1_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V5fn_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V8a0_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V5fn_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V9a1_2E0)))))) & (![V10a0_2E0, V11a1_2E0]: (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V5fn_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPmult_2E2(s(tyop_2EringNorm_2Epolynom(A_27a),V10a0_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V11a1_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))),V3f3_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V10a0_2E0))),s(tyop_2EringNorm_2Epolynom(A_27a),V11a1_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V5fn_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V10a0_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V5fn_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V11a1_2E0)))))) & ![V12a_2E0]: (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V5fn_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),c_2EringNorm_2EPopp_2E1(s(tyop_2EringNorm_2Epolynom(A_27a),V12a_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),V4f4_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V12a_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2EringNorm_2Epolynom(A_27a),A_27b),V5fn_2E0),s(tyop_2EringNorm_2Epolynom(A_27a),V12a_2E0))))))))))).
