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_2Ecanonical_2ECons__varlist_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X1_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))),c_2Ecanonical_2ECons__varlist_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X1_2E0))))).
fof(arityeq3_2Ec_2Ecanonical_2ECons__monom_2E3_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)))),c_2Ecanonical_2ECons__monom_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X2_2E0))))).
fof(arityeq3_2Ec_2Ecanonical_2Ecanonical__sum__merge_2E3_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X2_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)))),c_2Ecanonical_2Ecanonical__sum__merge_2E0),s(tyop_2Esemi__ring_2Esemi__ring(A_27a),X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X2_2E0))))).
fof(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex,axiom,![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))) = s(tyop_2EternaryComparisons_2Eordering,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2EternaryComparisons_2Eordering),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2EternaryComparisons_2Eordering)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2EternaryComparisons_2Eordering))),c_2EternaryComparisons_2Elist__compare_2E0),s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0))))).
fof(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Ecanonical_2Ecanonical__sum_28A_27a_29,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0]: (s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,X0_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X3_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Ecanonical__sum(A_27a),tyop_2Ecanonical_2Ecanonical__sum(A_27a))))),c_2EternaryComparisons_2Eordering__CASE_2E0),s(tyop_2EternaryComparisons_2Eordering,X0_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),X3_2E0))))).
fof(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SR1_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(A_27a,c_2Esemi__ring_2Esemi__ring__SR1_2E1(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),A_27a),c_2Esemi__ring_2Esemi__ring__SR1_2E0),s(tyop_2Esemi__ring_2Esemi__ring(A_27a),X0_2E0))))).
fof(arityeq3_2Ec_2Esemi__ring_2Esemi__ring__SRP_2E3_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(A_27a,c_2Esemi__ring_2Esemi__ring__SRP_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Esemi__ring_2Esemi__ring__SRP_2E0),s(tyop_2Esemi__ring_2Esemi__ring(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))))).
fof(canonicalTheory_2Ecanonical__sum__merge__def,axiom,![A_27a]: (![V0t2_2E0, V1t1_2E0, V2sr_2E0, V3l2_2E0, V4l1_2E0, V5c2_2E0, V6c1_2E0]: (s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V2sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V6c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V4l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V1t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V5c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V3l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V0t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V4l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V3l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V6c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V4l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V2sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V1t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V5c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V3l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V0t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,c_2Esemi__ring_2Esemi__ring__SRP_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V2sr_2E0),s(A_27a,V6c1_2E0),s(A_27a,V5c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V4l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V2sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V1t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V0t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V5c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V3l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V2sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V6c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V4l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V1t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V0t2_2E0)))))))) & (![V7t2_2E0, V8t1_2E0, V9sr_2E0, V10l2_2E0, V11l1_2E0, V12c1_2E0]: (s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V9sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V12c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V11l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V8t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V10l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V7t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V11l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V10l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V12c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V11l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V9sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V8t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V10l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V7t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,c_2Esemi__ring_2Esemi__ring__SRP_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V9sr_2E0),s(A_27a,V12c1_2E0),s(A_27a,c_2Esemi__ring_2Esemi__ring__SR1_2E1(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V9sr_2E0))))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V11l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V9sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V8t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V7t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V10l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V9sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V12c1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V11l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V8t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V7t2_2E0)))))))) & (![V13t2_2E0, V14t1_2E0, V15sr_2E0, V16l2_2E0, V17l1_2E0, V18c2_2E0]: (s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V15sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V17l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V14t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V18c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V16l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V13t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V17l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V16l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V17l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V15sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V14t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V18c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V16l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V13t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,c_2Esemi__ring_2Esemi__ring__SRP_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V15sr_2E0),s(A_27a,c_2Esemi__ring_2Esemi__ring__SR1_2E1(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V15sr_2E0))),s(A_27a,V18c2_2E0))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V17l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V15sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V14t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V13t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V18c2_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V16l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V15sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V17l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V14t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V13t2_2E0)))))))) & (![V19t2_2E0, V20t1_2E0, V21sr_2E0, V22l2_2E0, V23l1_2E0]: (s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V21sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V23l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V20t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V22l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V19t2_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2EternaryComparisons_2Eordering__CASE_2E4(s(tyop_2EternaryComparisons_2Eordering,c_2EternaryComparisons_2Elist__compare_2E3(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),c_2Equote_2Eindex__compare_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V23l1_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V22l2_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V23l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V21sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V20t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V22l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V19t2_2E0))))))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,c_2Esemi__ring_2Esemi__ring__SRP_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V21sr_2E0),s(A_27a,c_2Esemi__ring_2Esemi__ring__SR1_2E1(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V21sr_2E0))),s(A_27a,c_2Esemi__ring_2Esemi__ring__SR1_2E1(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V21sr_2E0))))),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V23l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V21sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V20t1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V19t2_2E0))))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V22l2_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V21sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V23l1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V20t1_2E0))),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V19t2_2E0)))))))) & (![V24sr_2E0, V25s1_2E0]: (s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V24sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V25s1_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ENil__monom_2E0))) = s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V25s1_2E0)) & (![V26v6_2E0, V27v5_2E0, V28v4_2E0, V29sr_2E0]: (s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V29sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ENil__monom_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V28v4_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V27v5_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V26v6_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__monom_2E3(s(A_27a,V28v4_2E0),s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V27v5_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V26v6_2E0)))) & ![V30v8_2E0, V31v7_2E0, V32sr_2E0]: (s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2Ecanonical__sum__merge_2E3(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),V32sr_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ENil__monom_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V31v7_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V30v8_2E0))))) = s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),c_2Ecanonical_2ECons__varlist_2E2(s(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V31v7_2E0),s(tyop_2Ecanonical_2Ecanonical__sum(A_27a),V30v8_2E0))))))))))).
