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(arityeq5_2Ec_2Ering_2Erecordtype_2Ering_2E5_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0, X4_2E0]: (s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X4_2E0))) = s(tyop_2Ering_2Ering(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Ering_2Ering(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Ering_2Ering(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Ering_2Ering(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Ering_2Ering(A_27a)))))),c_2Ering_2Erecordtype_2Ering_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X4_2E0))))).
fof(arityeq1_2Ec_2Ering_2Ering__R0_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),A_27a),c_2Ering_2Ering__R0_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))))).
fof(arityeq1_2Ec_2Ering_2Ering__R1_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),A_27a),c_2Ering_2Ering__R1_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))))).
fof(arityeq1_2Ec_2Ering_2Ering__RM_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ering_2Ering__RM_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))))).
fof(arityeq1_2Ec_2Ering_2Ering__RN_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RN_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))))).
fof(arityeq1_2Ec_2Ering_2Ering__RP_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ering_2Ering__RP_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))))).
fof(ringTheory_2Ering__accessors,axiom,![A_27a]: (![V0a_2E0, V1a0_2E0, V2f_2E0, V3f0_2E0, V4f1_2E0]: (s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V0a_2E0),s(A_27a,V1a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4f1_2E0))))) = s(A_27a,V0a_2E0)) & (![V5a_2E0, V6a0_2E0, V7f_2E0, V8f0_2E0, V9f1_2E0]: (s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V5a_2E0),s(A_27a,V6a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V7f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V8f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V9f1_2E0))))) = s(A_27a,V6a0_2E0)) & (![V10a_2E0, V11a0_2E0, V12f_2E0, V13f0_2E0, V14f1_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V10a_2E0),s(A_27a,V11a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V12f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V13f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V14f1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V12f_2E0)) & (![V15a_2E0, V16a0_2E0, V17f_2E0, V18f0_2E0, V19f1_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V15a_2E0),s(A_27a,V16a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V17f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V18f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V19f1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V18f0_2E0)) & ![V20a_2E0, V21a0_2E0, V22f_2E0, V23f0_2E0, V24f1_2E0]: (s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V20a_2E0),s(A_27a,V21a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V22f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V23f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V24f1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27a),V24f1_2E0))))))).
