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(arityeq2_2Ec_2Ellist_2ELAPPEND_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELAPPEND_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))))).
fof(arityeq3_2Ec_2Ellist_2Ellist__upto_2E3_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Ebool,c_2Ellist_2Ellist__upto_2E3(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0),s(tyop_2Ellist_2Ellist(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool))),c_2Ellist_2Ellist__upto_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X2_2E0))))).
fof(llistTheory_2Ellist__upto__ind,axiom,![A_27a]: ![V0R_2E0, V1llist__upto_27_2E0]: ((![V2x_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V1llist__upto_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2x_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V2x_2E0)))) & (![V3x_2E0, V4y_2E0]: (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3x_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V4y_2E0)))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V1llist__upto_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3x_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V4y_2E0))))) & (![V5x_2E0, V6y_2E0, V7z_2E0]: ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V1llist__upto_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5x_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V1llist__upto_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6y_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V7z_2E0))))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V1llist__upto_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5x_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V7z_2E0))))) & ![V8x_2E0, V9y_2E0, V10z_2E0]: (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V1llist__upto_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V8x_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V9y_2E0)))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V1llist__upto_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V10z_2E0),s(tyop_2Ellist_2Ellist(A_27a),V8x_2E0))))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V10z_2E0),s(tyop_2Ellist_2Ellist(A_27a),V9y_2E0)))))))))) => ![V11a0_2E0, V12a1_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellist__upto_2E3(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Ellist_2Ellist(A_27a),V11a0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V12a1_2E0)))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V1llist__upto_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V11a0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V12a1_2E0))))))).
