%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, unsorted: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(type_def_7, type, d_unsorted: $tType).
thf(func_def_0, type, subrel: (($i > $i > $o) > ($i > $i > $o) > $o)).
thf(func_def_1, type, inv: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_2, type, idem: ((($i > $i > $o) > $i > $i > $o) > $o)).
thf(func_def_3, type, infl: ((($i > $i > $o) > $i > $i > $o) > $o)).
thf(func_def_4, type, mono: ((($i > $i > $o) > $i > $i > $o) > $o)).
thf(func_def_5, type, refl: (($i > $i > $o) > $o)).
thf(func_def_6, type, irrefl: (($i > $i > $o) > $o)).
thf(func_def_7, type, rc: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_8, type, symm: (($i > $i > $o) > $o)).
thf(func_def_9, type, antisymm: (($i > $i > $o) > $o)).
thf(func_def_10, type, asymm: (($i > $i > $o) > $o)).
thf(func_def_11, type, sc: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_12, type, trans: (($i > $i > $o) > $o)).
thf(func_def_13, type, tc: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_14, type, trc: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_15, type, trsc: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_16, type, po: (($i > $i > $o) > $o)).
thf(func_def_17, type, so: (($i > $i > $o) > $o)).
thf(func_def_18, type, total: (($i > $i > $o) > $o)).
thf(func_def_19, type, term: (($i > $i > $o) > $o)).
thf(func_def_20, type, ind: (($i > $i > $o) > $o)).
thf(func_def_21, type, innf: (($i > $i > $o) > $i > $o)).
thf(func_def_22, type, nfof: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_23, type, norm: (($i > $i > $o) > $o)).
thf(func_def_24, type, join: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_25, type, lconfl: (($i > $i > $o) > $o)).
thf(func_def_26, type, sconfl: (($i > $i > $o) > $o)).
thf(func_def_27, type, confl: (($i > $i > $o) > $o)).
thf(func_def_28, type, cr: (($i > $i > $o) > $o)).
thf(func_def_29, type, d2unsorted: (d_unsorted > $i)).
thf(func_def_30, type, d_unsorted_0: d_unsorted).
thf(func_def_32, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_33, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_34, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_35, type, vOR: ($o > $o > $o)).
thf(func_def_36, type, vNOT: ($o > $o)).
thf(func_def_37, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_38, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_39, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_40, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_41, type, db5: !>[X0: $tType]:(X0)).
thf(func_def_42, type, vAND: ($o > $o > $o)).
thf(func_def_43, type, db6: !>[X0: $tType]:(X0)).
thf(func_def_44, type, db7: !>[X0: $tType]:(X0)).
thf(func_def_45, type, db8: !>[X0: $tType]:(X0)).
thf(func_def_46, type, db4: !>[X0: $tType]:(X0)).
thf(func_def_47, type, db9: !>[X0: $tType]:(X0)).
thf(func_def_48, type, sK0: ($i > d_unsorted)).
thf(func_def_52, type, sK2: ($i > $i > $o)).
thf(func_def_55, type, sK5: ($i > $i)).
thf(func_def_56, type, sK6: ($i > $i > $o)).
thf(func_def_57, type, sK7: ($i > ($i > $i > $o) > $i > $i > $i > $o)).
thf(func_def_58, type, sK8: (($i > $i > $o) > $i)).
thf(func_def_59, type, sK9: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_60, type, sK10: (($i > $i > $o) > $i)).
thf(func_def_61, type, sK11: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_62, type, sK12: (($i > $i > $o) > $i)).
thf(func_def_63, type, sK13: (($i > $i > $o) > $i)).
thf(func_def_65, type, sK15: (($i > $i > $o) > $i)).
thf(func_def_66, type, sK16: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_67, type, sK17: (($i > $i > $o) > $i)).
thf(func_def_68, type, sK18: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_69, type, sK19: (($i > $i > $o) > $i)).
thf(func_def_70, type, sK20: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_71, type, sK21: (($i > $i > $o) > $i)).
thf(func_def_72, type, sK22: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_73, type, sK23: (($i > $i > $o) > $i)).
thf(func_def_74, type, sK24: (($i > $i > $o) > $i)).
thf(func_def_75, type, sK25: (($i > $i > $o) > $i)).
thf(func_def_76, type, sK26: (($i > $i > $o) > $i)).
thf(func_def_77, type, sK27: ($i > ($i > $i > $o) > $i > $i > $i > $o)).
thf(func_def_78, type, sK28: ($i > ($i > $i > $o) > $i > $i > $i > $o)).
thf(func_def_80, type, sK30: ($i > $i > $o)).
thf(func_def_81, type, sK31: ($i > $i > $o)).
thf(func_def_82, type, sK32: (($i > $i > $o) > $i)).
thf(func_def_83, type, sK33: (($i > $i > $o) > $i)).
thf(func_def_84, type, sK34: (($i > $i > $o) > $i)).
thf(func_def_85, type, sK35: (($i > $i > $o) > $i)).
thf(func_def_86, type, sK36: (($i > $i > $o) > $i)).
thf(func_def_87, type, sK37: (($i > $i > $o) > $i)).
thf(func_def_88, type, sK38: (($i > $i > $o) > $i)).
thf(func_def_89, type, sK39: (($i > $i > $o) > $i)).
thf(func_def_90, type, sK40: (($i > $i > $o) > $i)).
thf(func_def_91, type, sK41: (($i > $i > $o) > $i)).
thf(func_def_92, type, sK42: (($i > $i > $o) > $i)).
thf(func_def_93, type, sK43: (($i > $i > $o) > $i)).
thf(func_def_94, type, sK44: (($i > $i > $o) > $i)).
thf(f1,axiom,(
  ((^[X2 : ($i > $i > $o)] : (! [X30 : $i,X3 : $i] : (~ ! [X31 : $i] : (~ ! [X32 : $i] : ~(X2 @ X31 @ X32) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X3 @ X31) | ~ ! [X8 : $i,X7 : $i,X6 : $i] : (~(X5 @ X6 @ X7) | ~(X5 @ X7 @ X8) | (X5 @ X6 @ X8)) | ~ ! [X10 : $i,X9 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10)))) | ~(X2 @ X3 @ X30)))) = norm) & ! [X0 : $i] : ? [X1 : d_unsorted] : (X0 = ((d2unsorted @ X1))) & ! [X1 : d_unsorted] : (X1 = d_unsorted_0) & (so = (^[X2 : ($i > $i > $o)] : (! [X3 : $i,X4 : $i] : (~(X2 @ X4 @ X3) | ~(X2 @ X3 @ X4)) & ! [X4 : $i,X3 : $i,X8 : $i] : ((X2 @ X3 @ X8) | ~(X2 @ X3 @ X4) | ~(X2 @ X4 @ X8))))) & ((^[X2 : ($i > $i > $o)] : (! [X20 : ($i > $i > $o),X8 : $i,X4 : $i,X3 : $i,X21 : ($i > $i > $o)] : (~ ! [X6 : $i,X18 : $i,X7 : $i] : (~(X20 @ X7 @ X18) | (X20 @ X6 @ X18) | ~(X20 @ X6 @ X7)) | ~(X2 @ X3 @ X4) | ~(X2 @ X3 @ X8) | ~ ! [X19 : $i,X7 : $i,X6 : $i] : (~(X21 @ X6 @ X7) | (X21 @ X6 @ X19) | ~(X21 @ X7 @ X19)) | (X20 @ X4 @ X8) | (X4 = X8) | (X21 @ X8 @ X4) | ~ ! [X10 : $i,X9 : $i] : ((X21 @ X9 @ X10) | ~(X2 @ X9 @ X10)) | ~ ! [X17 : $i] : (~ ! [X5 : ($i > $i > $o)] : (~ ! [X9 : $i,X10 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10)) | ~ ! [X6 : $i,X7 : $i,X19 : $i] : (~(X5 @ X6 @ X7) | ~(X5 @ X7 @ X19) | (X5 @ X6 @ X19)) | (X5 @ X8 @ X17)) | ~ ! [X5 : ($i > $i > $o)] : (~ ! [X10 : $i,X9 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10)) | ~ ! [X6 : $i,X7 : $i,X18 : $i] : ((X5 @ X6 @ X18) | ~(X5 @ X6 @ X7) | ~(X5 @ X7 @ X18)) | (X5 @ X4 @ X17))) | ~ ! [X9 : $i,X10 : $i] : (~(X2 @ X9 @ X10) | (X20 @ X9 @ X10))))) = lconfl) & ((^[X2 : ($i > $i > $o)] : (! [X25 : ($i > $i > $o),X4 : $i,X3 : $i,X26 : ($i > $i > $o)] : (~ ! [X6 : $i,X7 : $i,X18 : $i] : (~(X25 @ X6 @ X7) | ~(X25 @ X7 @ X18) | (X25 @ X6 @ X18)) | (X3 = X4) | (~ ! [X5 : ($i > $i > $o)] : (~ ! [X10 : $i,X9 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10)) | ~ ! [X7 : $i,X8 : $i,X6 : $i] : ((X5 @ X6 @ X8) | ~(X5 @ X6 @ X7) | ~(X5 @ X7 @ X8)) | (X5 @ X4 @ X3)) & ~ ! [X5 : ($i > $i > $o)] : (~ ! [X10 : $i,X9 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10)) | (X5 @ X3 @ X4) | ~ ! [X7 : $i,X8 : $i,X6 : $i] : ((X5 @ X6 @ X8) | ~(X5 @ X7 @ X8) | ~(X5 @ X6 @ X7))) & (X3 != X4)) | ~ ! [X17 : $i] : (~ ! [X5 : ($i > $i > $o)] : (~ ! [X6 : $i,X19 : $i,X7 : $i] : (~(X5 @ X7 @ X19) | (X5 @ X6 @ X19) | ~(X5 @ X6 @ X7)) | ~ ! [X9 : $i,X10 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10)) | (X5 @ X3 @ X17)) | ~ ! [X5 : ($i > $i > $o)] : (~ ! [X7 : $i,X6 : $i,X18 : $i] : (~(X5 @ X7 @ X18) | (X5 @ X6 @ X18) | ~(X5 @ X6 @ X7)) | ~ ! [X9 : $i,X10 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10)) | (X5 @ X4 @ X17))) | (X26 @ X3 @ X4) | ~ ! [X10 : $i,X9 : $i] : (~(X2 @ X9 @ X10) | (X25 @ X9 @ X10)) | ~ ! [X10 : $i,X9 : $i] : (~(X2 @ X9 @ X10) | (X26 @ X9 @ X10)) | (X25 @ X4 @ X3) | ~ ! [X19 : $i,X7 : $i,X6 : $i] : (~(X26 @ X6 @ X7) | ~(X26 @ X7 @ X19) | (X26 @ X6 @ X19))))) = cr) & ((^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : ((X2 @ X4 @ X3))) = inv) & (symm = (^[X2 : ($i > $i > $o)] : (! [X4 : $i,X3 : $i] : ((X2 @ X4 @ X3) | ~(X2 @ X3 @ X4))))) & ((^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : (! [X32 : $i] : ~(X2 @ X3 @ X32) & ((X3 = X4) | ! [X5 : ($i > $i > $o)] : (~ ! [X6 : $i,X7 : $i,X8 : $i] : (~(X5 @ X7 @ X8) | ~(X5 @ X6 @ X7) | (X5 @ X6 @ X8)) | ~ ! [X10 : $i,X9 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10)) | (X5 @ X4 @ X3))))) = nfof) & (sc = (^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : ((X2 @ X3 @ X4) | (X2 @ X4 @ X3)))) & (subrel = (^[X2 : ($i > $i > $o), X5 : ($i > $i > $o)] : (! [X4 : $i,X3 : $i] : (~(X2 @ X3 @ X4) | (X5 @ X3 @ X4))))) & (mono = (^[X33 : (($i > $i > $o) > $i > $i > $o)] : (! [X5 : ($i > $i > $o),X2 : ($i > $i > $o),X34 : $i,X35 : $i] : ((X33 @ X5 @ X34 @ X35) | ~ ! [X4 : $i,X3 : $i] : ((X5 @ X3 @ X4) | ~(X2 @ X3 @ X4)) | ~(X33 @ X2 @ X34 @ X35))))) & ((^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : ((X3 = X4) | (X2 @ X3 @ X4))) = rc) & ! [X36 : d_unsorted,X37 : d_unsorted] : ((((d2unsorted @ X36)) = ((d2unsorted @ X37))) => (X36 = X37)) & (idem = (^[X33 : (($i > $i > $o) > $i > $i > $o)] : (! [X2 : ($i > $i > $o)] : (((X33 @ X2)) = ((X33 @ (X33 @ X2))))))) & ((^[X2 : ($i > $i > $o)] : (! [X8 : $i,X4 : $i,X28 : ($i > $i > $o),X3 : $i,X27 : ($i > $i > $o)] : (~ ! [X17 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X8 @ X17) | ~ ! [X6 : $i,X19 : $i,X7 : $i] : (~(X5 @ X7 @ X19) | (X5 @ X6 @ X19) | ~(X5 @ X6 @ X7)) | ~ ! [X9 : $i,X10 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10))) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X4 @ X17) | ~ ! [X18 : $i,X6 : $i,X7 : $i] : (~(X5 @ X6 @ X7) | (X5 @ X6 @ X18) | ~(X5 @ X7 @ X18)) | ~ ! [X9 : $i,X10 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10)))) | (X4 = X8) | ~ ! [X7 : $i,X18 : $i,X6 : $i] : (~(X27 @ X6 @ X7) | (X27 @ X6 @ X18) | ~(X27 @ X7 @ X18)) | (X27 @ X4 @ X8) | (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X3 @ X4) | ~ ! [X9 : $i,X10 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10)) | ~ ! [X29 : $i,X6 : $i,X7 : $i] : (~(X5 @ X7 @ X29) | ~(X5 @ X6 @ X7) | (X5 @ X6 @ X29))) & (X3 != X4)) | ~(X2 @ X3 @ X8) | ~ ! [X19 : $i,X7 : $i,X6 : $i] : (~(X28 @ X7 @ X19) | (X28 @ X6 @ X19) | ~(X28 @ X6 @ X7)) | ~ ! [X10 : $i,X9 : $i] : ((X28 @ X9 @ X10) | ~(X2 @ X9 @ X10)) | ~ ! [X10 : $i,X9 : $i] : (~(X2 @ X9 @ X10) | (X27 @ X9 @ X10)) | (X28 @ X8 @ X4)))) = sconfl) & (term = (^[X2 : ($i > $i > $o)] : (! [X14 : $i,X13 : ($i > $o)] : (~(X13 @ X14) | ~ ! [X3 : $i] : (~(X13 @ X3) | ~ ! [X4 : $i] : (~(X13 @ X4) | ~(X2 @ X3 @ X4))))))) & (confl = (^[X2 : ($i > $i > $o)] : (! [X4 : $i,X23 : ($i > $i > $o),X3 : $i,X22 : ($i > $i > $o),X8 : $i] : (~ ! [X17 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X4 @ X17) | ~ ! [X10 : $i,X9 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10)) | ~ ! [X6 : $i,X7 : $i,X18 : $i] : ((X5 @ X6 @ X18) | ~(X5 @ X7 @ X18) | ~(X5 @ X6 @ X7))) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X8 @ X17) | ~ ! [X10 : $i,X9 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10)) | ~ ! [X7 : $i,X6 : $i,X19 : $i] : ((X5 @ X6 @ X19) | ~(X5 @ X6 @ X7) | ~(X5 @ X7 @ X19)))) | (X4 = X8) | ~ ! [X19 : $i,X6 : $i,X7 : $i] : (~(X23 @ X6 @ X7) | ~(X23 @ X7 @ X19) | (X23 @ X6 @ X19)) | ~ ! [X18 : $i,X7 : $i,X6 : $i] : (~(X22 @ X6 @ X7) | ~(X22 @ X7 @ X18) | (X22 @ X6 @ X18)) | ~ ! [X10 : $i,X9 : $i] : ((X23 @ X9 @ X10) | ~(X2 @ X9 @ X10)) | (~ ! [X5 : ($i > $i > $o)] : (~ ! [X9 : $i,X10 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10)) | ~ ! [X6 : $i,X7 : $i,X24 : $i] : (~(X5 @ X6 @ X7) | ~(X5 @ X7 @ X24) | (X5 @ X6 @ X24)) | (X5 @ X3 @ X4)) & (X3 != X4)) | (X23 @ X8 @ X4) | (X22 @ X4 @ X8) | ~ ! [X9 : $i,X10 : $i] : (~(X2 @ X9 @ X10) | (X22 @ X9 @ X10)) | ((X3 != X8) & ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X3 @ X8) | ~ ! [X9 : $i,X10 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10)) | ~ ! [X19 : $i,X6 : $i,X7 : $i] : ((X5 @ X6 @ X19) | ~(X5 @ X6 @ X7) | ~(X5 @ X7 @ X19)))))))) & ((^[X2 : ($i > $i > $o)] : (! [X3 : $i] : ~(X2 @ X3 @ X3))) = irrefl) & ((^[X2 : ($i > $i > $o), X11 : $i, X12 : $i] : ((X11 = X12) | ! [X5 : ($i > $i > $o)] : (~ ! [X7 : $i,X6 : $i,X8 : $i] : (~(X5 @ X7 @ X8) | ~(X5 @ X6 @ X7) | (X5 @ X6 @ X8)) | (X5 @ X11 @ X12) | ~ ! [X9 : $i,X10 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10))))) = trc) & ((^[X2 : ($i > $i > $o)] : (! [X3 : $i] : (X2 @ X3 @ X3))) = refl) & ((^[X2 : ($i > $i > $o)] : (! [X16 : $i,X15 : ($i > $o)] : ((X15 @ X16) | ~ ! [X3 : $i] : (~ ! [X4 : $i] : ((X15 @ X4) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X3 @ X4) | ~ ! [X7 : $i,X8 : $i,X6 : $i] : ((X5 @ X6 @ X8) | ~(X5 @ X7 @ X8) | ~(X5 @ X6 @ X7)) | ~ ! [X10 : $i,X9 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10)))) | (X15 @ X3))))) = ind) & (join = (^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : (~(~ ! [X5 : ($i > $i > $o)] : ((X5 @ X3 @ X4) | ~ ! [X19 : $i,X7 : $i,X6 : $i] : (~(X5 @ X7 @ X19) | ~(X5 @ X6 @ X7) | (X5 @ X6 @ X19)) | ~ ! [X9 : $i,X10 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10))) & ! [X17 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X3 @ X17) | ~ ! [X10 : $i,X9 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10)) | ~ ! [X19 : $i,X7 : $i,X6 : $i] : (~(X5 @ X6 @ X7) | ~(X5 @ X7 @ X19) | (X5 @ X6 @ X19))) | ~ ! [X5 : ($i > $i > $o)] : (~ ! [X10 : $i,X9 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10)) | (X5 @ X4 @ X17) | ~ ! [X18 : $i,X6 : $i,X7 : $i] : (~(X5 @ X6 @ X7) | ~(X5 @ X7 @ X18) | (X5 @ X6 @ X18)))) & (X3 != X4) & ~ ! [X5 : ($i > $i > $o)] : (~ ! [X10 : $i,X9 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10)) | ~ ! [X18 : $i,X6 : $i,X7 : $i] : (~(X5 @ X6 @ X7) | ~(X5 @ X7 @ X18) | (X5 @ X6 @ X18)) | (X5 @ X4 @ X3)))))) & ((^[X2 : ($i > $i > $o)] : (! [X3 : $i,X4 : $i] : (~(X2 @ X4 @ X3) | ~(X2 @ X3 @ X4)))) = asymm) & ((^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : (! [X5 : ($i > $i > $o)] : (~ ! [X9 : $i,X10 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10)) | (X5 @ X3 @ X4) | ~ ! [X6 : $i,X8 : $i,X7 : $i] : (~(X5 @ X6 @ X7) | (X5 @ X6 @ X8) | ~(X5 @ X7 @ X8))))) = tc) & ((^[X2 : ($i > $i > $o)] : (! [X3 : $i,X4 : $i,X8 : $i] : (~(X2 @ X4 @ X8) | (X2 @ X3 @ X8) | ~(X2 @ X3 @ X4)))) = trans) & ((^[X2 : ($i > $i > $o)] : (! [X3 : $i] : (X2 @ X3 @ X3) & ! [X4 : $i,X3 : $i] : ((X3 = X4) | ~(X2 @ X4 @ X3) | ~(X2 @ X3 @ X4)) & ! [X8 : $i,X4 : $i,X3 : $i] : (~(X2 @ X4 @ X8) | (X2 @ X3 @ X8) | ~(X2 @ X3 @ X4)))) = po) & ((^[X2 : ($i > $i > $o), X11 : $i, X12 : $i] : ((X11 = X12) | ! [X5 : ($i > $i > $o)] : ((X5 @ X12 @ X11) | ~ ! [X9 : $i,X10 : $i] : ((X5 @ X9 @ X10) | ~(X2 @ X9 @ X10)) | ~ ! [X6 : $i,X8 : $i,X7 : $i] : ((X5 @ X6 @ X8) | ~(X5 @ X6 @ X7) | ~(X5 @ X7 @ X8))) | ! [X5 : ($i > $i > $o)] : ((X5 @ X11 @ X12) | ~ ! [X9 : $i,X10 : $i] : (~(X2 @ X9 @ X10) | (X5 @ X9 @ X10)) | ~ ! [X8 : $i,X6 : $i,X7 : $i] : (~(X5 @ X7 @ X8) | ~(X5 @ X6 @ X7) | (X5 @ X6 @ X8))))) = trsc) & (innf = (^[X2 : ($i > $i > $o), X3 : $i] : (! [X4 : $i] : ~(X2 @ X3 @ X4)))) & ((^[X2 : ($i > $i > $o)] : (! [X3 : $i,X4 : $i] : ((X3 = X4) | (X2 @ X3 @ X4) | (X2 @ X4 @ X3)))) = total) & (infl = (^[X33 : (($i > $i > $o) > $i > $i > $o)] : (! [X4 : $i,X2 : ($i > $i > $o),X3 : $i] : ((X33 @ X2 @ X3 @ X4) | ~(X2 @ X3 @ X4))))) & (antisymm = (^[X2 : ($i > $i > $o)] : (! [X4 : $i,X3 : $i] : ((X3 = X4) | ~(X2 @ X4 @ X3) | ~(X2 @ X3 @ X4)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',sev441_1)).
thf(f2,conjecture,(
  (trsc = (^[X0 : ($i > $i > $o)] : ((sc @ (rc @ (tc @ X0))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure)).
thf(f3,negated_conjecture,(
  ~ (trsc = (^[X0 : ($i > $i > $o)] : ((sc @ (rc @ (tc @ X0))))))),
  inference(negated_conjecture,[status(cth)],[f2])).
thf(f4,plain,(
  ~ (trsc = (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ((^[X0 : ($i > $i > $o)] : (! [X1 : $i,X2 : $i] : (~ ! [X3 : $i] : (~ ! [X4 : $i] : ~(X0 @ X3 @ X4) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X2 @ X3) | ~ ! [X6 : $i,X7 : $i,X8 : $i] : (~(X5 @ X8 @ X7) | ~(X5 @ X7 @ X6) | (X5 @ X8 @ X6)) | ~ ! [X9 : $i,X10 : $i] : ((X5 @ X10 @ X9) | ~(X0 @ X10 @ X9)))) | ~(X0 @ X2 @ X1)))) = norm) & ! [X11 : $i] : ? [X12 : d_unsorted] : (((d2unsorted @ X12)) = X11) & ! [X13 : d_unsorted] : (d_unsorted_0 = X13) & (so = (^[X14 : ($i > $i > $o)] : (! [X15 : $i,X16 : $i] : (~(X14 @ X16 @ X15) | ~(X14 @ X15 @ X16)) & ! [X17 : $i,X18 : $i,X19 : $i] : ((X14 @ X18 @ X19) | ~(X14 @ X18 @ X17) | ~(X14 @ X17 @ X19))))) & ((^[X20 : ($i > $i > $o)] : (! [X21 : ($i > $i > $o),X22 : $i,X23 : $i,X24 : $i,X25 : ($i > $i > $o)] : (~ ! [X26 : $i,X27 : $i,X28 : $i] : (~(X21 @ X28 @ X27) | (X21 @ X26 @ X27) | ~(X21 @ X26 @ X28)) | ~(X20 @ X24 @ X23) | ~(X20 @ X24 @ X22) | ~ ! [X29 : $i,X30 : $i,X31 : $i] : (~(X25 @ X31 @ X30) | (X25 @ X31 @ X29) | ~(X25 @ X30 @ X29)) | (X21 @ X23 @ X22) | (X22 = X23) | (X25 @ X22 @ X23) | ~ ! [X32 : $i,X33 : $i] : ((X25 @ X33 @ X32) | ~(X20 @ X33 @ X32)) | ~ ! [X34 : $i] : (~ ! [X35 : ($i > $i > $o)] : (~ ! [X36 : $i,X37 : $i] : (~(X20 @ X36 @ X37) | (X35 @ X36 @ X37)) | ~ ! [X38 : $i,X39 : $i,X40 : $i] : (~(X35 @ X38 @ X39) | ~(X35 @ X39 @ X40) | (X35 @ X38 @ X40)) | (X35 @ X22 @ X34)) | ~ ! [X41 : ($i > $i > $o)] : (~ ! [X42 : $i,X43 : $i] : (~(X20 @ X43 @ X42) | (X41 @ X43 @ X42)) | ~ ! [X44 : $i,X45 : $i,X46 : $i] : ((X41 @ X44 @ X46) | ~(X41 @ X44 @ X45) | ~(X41 @ X45 @ X46)) | (X41 @ X23 @ X34))) | ~ ! [X47 : $i,X48 : $i] : (~(X20 @ X47 @ X48) | (X21 @ X47 @ X48))))) = lconfl) & ((^[X49 : ($i > $i > $o)] : (! [X50 : ($i > $i > $o),X51 : $i,X52 : $i,X53 : ($i > $i > $o)] : (~ ! [X54 : $i,X55 : $i,X56 : $i] : (~(X50 @ X54 @ X55) | ~(X50 @ X55 @ X56) | (X50 @ X54 @ X56)) | (X51 = X52) | (~ ! [X57 : ($i > $i > $o)] : (~ ! [X58 : $i,X59 : $i] : (~(X49 @ X59 @ X58) | (X57 @ X59 @ X58)) | ~ ! [X60 : $i,X61 : $i,X62 : $i] : ((X57 @ X62 @ X61) | ~(X57 @ X62 @ X60) | ~(X57 @ X60 @ X61)) | (X57 @ X51 @ X52)) & ~ ! [X63 : ($i > $i > $o)] : (~ ! [X64 : $i,X65 : $i] : ((X63 @ X65 @ X64) | ~(X49 @ X65 @ X64)) | (X63 @ X52 @ X51) | ~ ! [X66 : $i,X67 : $i,X68 : $i] : ((X63 @ X68 @ X67) | ~(X63 @ X66 @ X67) | ~(X63 @ X68 @ X66))) & (X51 != X52)) | ~ ! [X69 : $i] : (~ ! [X70 : ($i > $i > $o)] : (~ ! [X71 : $i,X72 : $i,X73 : $i] : (~(X70 @ X73 @ X72) | (X70 @ X71 @ X72) | ~(X70 @ X71 @ X73)) | ~ ! [X74 : $i,X75 : $i] : (~(X49 @ X74 @ X75) | (X70 @ X74 @ X75)) | (X70 @ X52 @ X69)) | ~ ! [X76 : ($i > $i > $o)] : (~ ! [X77 : $i,X78 : $i,X79 : $i] : (~(X76 @ X77 @ X79) | (X76 @ X78 @ X79) | ~(X76 @ X78 @ X77)) | ~ ! [X80 : $i,X81 : $i] : (~(X49 @ X80 @ X81) | (X76 @ X80 @ X81)) | (X76 @ X51 @ X69))) | (X53 @ X52 @ X51) | ~ ! [X82 : $i,X83 : $i] : (~(X49 @ X83 @ X82) | (X50 @ X83 @ X82)) | ~ ! [X84 : $i,X85 : $i] : (~(X49 @ X85 @ X84) | (X53 @ X85 @ X84)) | (X50 @ X51 @ X52) | ~ ! [X86 : $i,X87 : $i,X88 : $i] : (~(X53 @ X88 @ X87) | ~(X53 @ X87 @ X86) | (X53 @ X88 @ X86))))) = cr) & ((^[X89 : ($i > $i > $o), X90 : $i, X91 : $i] : ((X89 @ X91 @ X90))) = inv) & (symm = (^[X92 : ($i > $i > $o)] : (! [X93 : $i,X94 : $i] : ((X92 @ X93 @ X94) | ~(X92 @ X94 @ X93))))) & ((^[X95 : ($i > $i > $o), X96 : $i, X97 : $i] : (! [X98 : $i] : ~(X95 @ X96 @ X98) & ((X96 = X97) | ! [X99 : ($i > $i > $o)] : (~ ! [X100 : $i,X101 : $i,X102 : $i] : (~(X99 @ X101 @ X102) | ~(X99 @ X100 @ X101) | (X99 @ X100 @ X102)) | ~ ! [X103 : $i,X104 : $i] : (~(X95 @ X104 @ X103) | (X99 @ X104 @ X103)) | (X99 @ X97 @ X96))))) = nfof) & (sc = (^[X105 : ($i > $i > $o), X106 : $i, X107 : $i] : ((X105 @ X106 @ X107) | (X105 @ X107 @ X106)))) & (subrel = (^[X108 : ($i > $i > $o), X109 : ($i > $i > $o)] : (! [X110 : $i,X111 : $i] : (~(X108 @ X111 @ X110) | (X109 @ X111 @ X110))))) & (mono = (^[X112 : (($i > $i > $o) > $i > $i > $o)] : (! [X113 : ($i > $i > $o),X114 : ($i > $i > $o),X115 : $i,X116 : $i] : ((X112 @ X113 @ X115 @ X116) | ~ ! [X117 : $i,X118 : $i] : ((X113 @ X118 @ X117) | ~(X114 @ X118 @ X117)) | ~(X112 @ X114 @ X115 @ X116))))) & ((^[X119 : ($i > $i > $o), X120 : $i, X121 : $i] : ((X120 = X121) | (X119 @ X120 @ X121))) = rc) & ! [X122 : d_unsorted,X123 : d_unsorted] : ((((d2unsorted @ X123)) = ((d2unsorted @ X122))) => (X122 = X123)) & (idem = (^[X124 : (($i > $i > $o) > $i > $i > $o)] : (! [X125 : ($i > $i > $o)] : (((X124 @ X125)) = ((X124 @ (X124 @ X125))))))) & ((^[X126 : ($i > $i > $o)] : (! [X127 : $i,X128 : $i,X129 : ($i > $i > $o),X130 : $i,X131 : ($i > $i > $o)] : (~ ! [X132 : $i] : (~ ! [X133 : ($i > $i > $o)] : ((X133 @ X127 @ X132) | ~ ! [X134 : $i,X135 : $i,X136 : $i] : (~(X133 @ X136 @ X135) | (X133 @ X134 @ X135) | ~(X133 @ X134 @ X136)) | ~ ! [X137 : $i,X138 : $i] : ((X133 @ X137 @ X138) | ~(X126 @ X137 @ X138))) | ~ ! [X139 : ($i > $i > $o)] : ((X139 @ X128 @ X132) | ~ ! [X140 : $i,X141 : $i,X142 : $i] : (~(X139 @ X141 @ X142) | (X139 @ X141 @ X140) | ~(X139 @ X142 @ X140)) | ~ ! [X143 : $i,X144 : $i] : ((X139 @ X143 @ X144) | ~(X126 @ X143 @ X144)))) | (X127 = X128) | ~ ! [X145 : $i,X146 : $i,X147 : $i] : (~(X131 @ X147 @ X145) | (X131 @ X147 @ X146) | ~(X131 @ X145 @ X146)) | (X131 @ X128 @ X127) | (~ ! [X148 : ($i > $i > $o)] : ((X148 @ X130 @ X128) | ~ ! [X149 : $i,X150 : $i] : ((X148 @ X149 @ X150) | ~(X126 @ X149 @ X150)) | ~ ! [X151 : $i,X152 : $i,X153 : $i] : (~(X148 @ X153 @ X151) | ~(X148 @ X152 @ X153) | (X148 @ X152 @ X151))) & (X128 != X130)) | ~(X126 @ X130 @ X127) | ~ ! [X154 : $i,X155 : $i,X156 : $i] : (~(X129 @ X155 @ X154) | (X129 @ X156 @ X154) | ~(X129 @ X156 @ X155)) | ~ ! [X157 : $i,X158 : $i] : ((X129 @ X158 @ X157) | ~(X126 @ X158 @ X157)) | ~ ! [X159 : $i,X160 : $i] : (~(X126 @ X160 @ X159) | (X131 @ X160 @ X159)) | (X129 @ X127 @ X128)))) = sconfl) & (term = (^[X161 : ($i > $i > $o)] : (! [X162 : $i,X163 : ($i > $o)] : (~(X163 @ X162) | ~ ! [X164 : $i] : (~(X163 @ X164) | ~ ! [X165 : $i] : (~(X163 @ X165) | ~(X161 @ X164 @ X165))))))) & (confl = (^[X166 : ($i > $i > $o)] : (! [X167 : $i,X168 : ($i > $i > $o),X169 : $i,X170 : ($i > $i > $o),X171 : $i] : (~ ! [X172 : $i] : (~ ! [X173 : ($i > $i > $o)] : ((X173 @ X167 @ X172) | ~ ! [X174 : $i,X175 : $i] : (~(X166 @ X175 @ X174) | (X173 @ X175 @ X174)) | ~ ! [X176 : $i,X177 : $i,X178 : $i] : ((X173 @ X176 @ X178) | ~(X173 @ X177 @ X178) | ~(X173 @ X176 @ X177))) | ~ ! [X179 : ($i > $i > $o)] : ((X179 @ X171 @ X172) | ~ ! [X180 : $i,X181 : $i] : ((X179 @ X181 @ X180) | ~(X166 @ X181 @ X180)) | ~ ! [X182 : $i,X183 : $i,X184 : $i] : ((X179 @ X183 @ X184) | ~(X179 @ X183 @ X182) | ~(X179 @ X182 @ X184)))) | (X167 = X171) | ~ ! [X185 : $i,X186 : $i,X187 : $i] : (~(X168 @ X186 @ X187) | ~(X168 @ X187 @ X185) | (X168 @ X186 @ X185)) | ~ ! [X188 : $i,X189 : $i,X190 : $i] : (~(X170 @ X190 @ X189) | ~(X170 @ X189 @ X188) | (X170 @ X190 @ X188)) | ~ ! [X191 : $i,X192 : $i] : ((X168 @ X192 @ X191) | ~(X166 @ X192 @ X191)) | (~ ! [X193 : ($i > $i > $o)] : (~ ! [X194 : $i,X195 : $i] : ((X193 @ X194 @ X195) | ~(X166 @ X194 @ X195)) | ~ ! [X196 : $i,X197 : $i,X198 : $i] : (~(X193 @ X196 @ X197) | ~(X193 @ X197 @ X198) | (X193 @ X196 @ X198)) | (X193 @ X169 @ X167)) & (X167 != X169)) | (X168 @ X171 @ X167) | (X170 @ X167 @ X171) | ~ ! [X199 : $i,X200 : $i] : (~(X166 @ X199 @ X200) | (X170 @ X199 @ X200)) | ((X169 != X171) & ~ ! [X201 : ($i > $i > $o)] : ((X201 @ X169 @ X171) | ~ ! [X202 : $i,X203 : $i] : ((X201 @ X202 @ X203) | ~(X166 @ X202 @ X203)) | ~ ! [X204 : $i,X205 : $i,X206 : $i] : ((X201 @ X205 @ X204) | ~(X201 @ X205 @ X206) | ~(X201 @ X206 @ X204)))))))) & ((^[X207 : ($i > $i > $o)] : (! [X208 : $i] : ~(X207 @ X208 @ X208))) = irrefl) & ((^[X209 : ($i > $i > $o), X210 : $i, X211 : $i] : ((X210 = X211) | ! [X212 : ($i > $i > $o)] : (~ ! [X213 : $i,X214 : $i,X215 : $i] : (~(X212 @ X213 @ X215) | ~(X212 @ X214 @ X213) | (X212 @ X214 @ X215)) | (X212 @ X210 @ X211) | ~ ! [X216 : $i,X217 : $i] : (~(X209 @ X216 @ X217) | (X212 @ X216 @ X217))))) = trc) & ((^[X218 : ($i > $i > $o)] : (! [X219 : $i] : (X218 @ X219 @ X219))) = refl) & ((^[X220 : ($i > $i > $o)] : (! [X221 : $i,X222 : ($i > $o)] : ((X222 @ X221) | ~ ! [X223 : $i] : (~ ! [X224 : $i] : ((X222 @ X224) | ~ ! [X225 : ($i > $i > $o)] : ((X225 @ X223 @ X224) | ~ ! [X226 : $i,X227 : $i,X228 : $i] : ((X225 @ X228 @ X227) | ~(X225 @ X226 @ X227) | ~(X225 @ X228 @ X226)) | ~ ! [X229 : $i,X230 : $i] : ((X225 @ X230 @ X229) | ~(X220 @ X230 @ X229)))) | (X222 @ X223))))) = ind) & (join = (^[X231 : ($i > $i > $o), X232 : $i, X233 : $i] : (~(~ ! [X234 : ($i > $i > $o)] : ((X234 @ X232 @ X233) | ~ ! [X235 : $i,X236 : $i,X237 : $i] : (~(X234 @ X236 @ X235) | ~(X234 @ X237 @ X236) | (X234 @ X237 @ X235)) | ~ ! [X238 : $i,X239 : $i] : ((X234 @ X238 @ X239) | ~(X231 @ X238 @ X239))) & ! [X240 : $i] : (~ ! [X241 : ($i > $i > $o)] : ((X241 @ X232 @ X240) | ~ ! [X242 : $i,X243 : $i] : ((X241 @ X243 @ X242) | ~(X231 @ X243 @ X242)) | ~ ! [X244 : $i,X245 : $i,X246 : $i] : (~(X241 @ X246 @ X245) | ~(X241 @ X245 @ X244) | (X241 @ X246 @ X244))) | ~ ! [X247 : ($i > $i > $o)] : (~ ! [X248 : $i,X249 : $i] : (~(X231 @ X249 @ X248) | (X247 @ X249 @ X248)) | (X247 @ X233 @ X240) | ~ ! [X250 : $i,X251 : $i,X252 : $i] : (~(X247 @ X251 @ X252) | ~(X247 @ X252 @ X250) | (X247 @ X251 @ X250)))) & (X232 != X233) & ~ ! [X253 : ($i > $i > $o)] : (~ ! [X254 : $i,X255 : $i] : (~(X231 @ X255 @ X254) | (X253 @ X255 @ X254)) | ~ ! [X256 : $i,X257 : $i,X258 : $i] : (~(X253 @ X257 @ X258) | ~(X253 @ X258 @ X256) | (X253 @ X257 @ X256)) | (X253 @ X233 @ X232)))))) & ((^[X259 : ($i > $i > $o)] : (! [X260 : $i,X261 : $i] : (~(X259 @ X261 @ X260) | ~(X259 @ X260 @ X261)))) = asymm) & ((^[X262 : ($i > $i > $o), X263 : $i, X264 : $i] : (! [X265 : ($i > $i > $o)] : (~ ! [X266 : $i,X267 : $i] : (~(X262 @ X266 @ X267) | (X265 @ X266 @ X267)) | (X265 @ X263 @ X264) | ~ ! [X268 : $i,X269 : $i,X270 : $i] : (~(X265 @ X268 @ X270) | (X265 @ X268 @ X269) | ~(X265 @ X270 @ X269))))) = tc) & ((^[X271 : ($i > $i > $o)] : (! [X272 : $i,X273 : $i,X274 : $i] : (~(X271 @ X273 @ X274) | (X271 @ X272 @ X274) | ~(X271 @ X272 @ X273)))) = trans) & ((^[X275 : ($i > $i > $o)] : (! [X276 : $i] : (X275 @ X276 @ X276) & ! [X277 : $i,X278 : $i] : ((X277 = X278) | ~(X275 @ X277 @ X278) | ~(X275 @ X278 @ X277)) & ! [X279 : $i,X280 : $i,X281 : $i] : (~(X275 @ X280 @ X279) | (X275 @ X281 @ X279) | ~(X275 @ X281 @ X280)))) = po) & ((^[X282 : ($i > $i > $o), X283 : $i, X284 : $i] : ((X283 = X284) | ! [X285 : ($i > $i > $o)] : ((X285 @ X284 @ X283) | ~ ! [X286 : $i,X287 : $i] : ((X285 @ X286 @ X287) | ~(X282 @ X286 @ X287)) | ~ ! [X288 : $i,X289 : $i,X290 : $i] : ((X285 @ X288 @ X289) | ~(X285 @ X288 @ X290) | ~(X285 @ X290 @ X289))) | ! [X291 : ($i > $i > $o)] : ((X291 @ X283 @ X284) | ~ ! [X292 : $i,X293 : $i] : (~(X282 @ X292 @ X293) | (X291 @ X292 @ X293)) | ~ ! [X294 : $i,X295 : $i,X296 : $i] : (~(X291 @ X296 @ X294) | ~(X291 @ X295 @ X296) | (X291 @ X295 @ X294))))) = trsc) & (innf = (^[X297 : ($i > $i > $o), X298 : $i] : (! [X299 : $i] : ~(X297 @ X298 @ X299)))) & ((^[X300 : ($i > $i > $o)] : (! [X301 : $i,X302 : $i] : ((X301 = X302) | (X300 @ X301 @ X302) | (X300 @ X302 @ X301)))) = total) & (infl = (^[X303 : (($i > $i > $o) > $i > $i > $o)] : (! [X304 : $i,X305 : ($i > $i > $o),X306 : $i] : ((X303 @ X305 @ X306 @ X304) | ~(X305 @ X306 @ X304))))) & (antisymm = (^[X307 : ($i > $i > $o)] : (! [X308 : $i,X309 : $i] : ((X308 = X309) | ~(X307 @ X308 @ X309) | ~(X307 @ X309 @ X308)))))),
  inference(rectify,[],[f1])).
thf(f6,plain,(
  (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6))))))))))) | (Y4 @ Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & ! [X11 : $i] : ? [X12 : d_unsorted] : (((d2unsorted @ X12)) = X11) & ! [X13 : d_unsorted] : (d_unsorted_0 = X13) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y8) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (Y1 @ Y4 @ Y3)) | (Y4 = Y3)) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7))))))))))) | (~ (Y0 @ Y2 @ Y4))) | (~ (Y0 @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7))))))))))))))))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y5 @ Y7) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y5 @ Y6)))))))))) | (Y4 @ Y3 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y1 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y7)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))))))))))) | (((~ (Y3 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7))))))))) | (Y5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y8))) | (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) | (~ (Y4 @ Y6 @ Y5))) | (~ (Y4 @ Y7 @ Y6))))))))))))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (Y0 @ Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y0 @ Y4 @ Y2 @ Y1)))))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & ! [X122 : d_unsorted,X123 : d_unsorted] : ((((d2unsorted @ X123)) = ((d2unsorted @ X122))) => (X122 = X123)) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y3 @ Y5 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y8)) | (~ (Y3 @ Y7 @ Y8))))))))))) | (~ (Y0 @ Y2 @ Y5))) | ((~ (Y4 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y2 @ Y4))))))) | (Y1 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (Y5 = Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y4 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (Y7 @ Y5 @ Y6)))))))))))))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))) | (~ (Y1 @ Y3)))))) | (~ (Y1 @ Y2))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y1))))) & (~ (Y3 = Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | ((~ (Y5 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y7 @ Y8) | (~ (Y4 @ Y6 @ Y8))) | (~ (Y4 @ Y7 @ Y6))))))))))) | (Y5 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y5 @ Y6)))))))))))))))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y3 @ Y4))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))) & (~ (Y1 = Y2))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5)))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y1 @ Y2))))))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y1))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)) | (Y2 = Y1)))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y1 @ Y3)) | (Y0 @ Y2 @ Y1 @ Y3)))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))))),
  inference(fool_elimination,[],[f5])).
thf(f7,plain,(
  (trsc != (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
  inference(flattening,[],[f4])).
thf(f8,plain,(
  ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y1 @ Y3)) | (Y0 @ Y2 @ Y1 @ Y3)))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6))))))))))) | (Y4 @ Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y5 @ Y7) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y5 @ Y6)))))))))) | (Y4 @ Y3 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y1 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y7)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))))))))))) | (((~ (Y3 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7))))))))) | (Y5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y8))) | (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) | (~ (Y4 @ Y6 @ Y5))) | (~ (Y4 @ Y7 @ Y6))))))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y3 @ Y4))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y3 @ Y5 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y8)) | (~ (Y3 @ Y7 @ Y8))))))))))) | (~ (Y0 @ Y2 @ Y5))) | ((~ (Y4 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y2 @ Y4))))))) | (Y1 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (Y5 = Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y4 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (Y7 @ Y5 @ Y6)))))))))))))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y1))))) & (~ (Y3 = Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | ((~ (Y5 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y7 @ Y8) | (~ (Y4 @ Y6 @ Y8))) | (~ (Y4 @ Y7 @ Y6))))))))))) | (Y5 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y5 @ Y6)))))))))))))))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (Y0 @ Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y0 @ Y4 @ Y2 @ Y1)))))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & ! [X4 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X3)) = ((d2unsorted @ X4))) => (X3 = X4)) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1)))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y1))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))) | (~ (Y1 @ Y3)))))) | (~ (Y1 @ Y2))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)) | (Y2 = Y1)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y8) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (Y1 @ Y4 @ Y3)) | (Y4 = Y3)) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7))))))))))) | (~ (Y0 @ Y2 @ Y4))) | (~ (Y0 @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7))))))))))))))))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))) & (~ (Y1 = Y2))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5)))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y1 @ Y2))))))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))),
  inference(rectify,[],[f6])).
thf(f9,plain,(
  (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y5 @ Y7) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y5 @ Y6)))))))))) | (Y4 @ Y3 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y1 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y7)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))))))))))) | (((~ (Y3 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7))))))))) | (Y5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y8))) | (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) | (~ (Y4 @ Y6 @ Y5))) | (~ (Y4 @ Y7 @ Y6))))))))))))))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (Y0 @ Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y0 @ Y4 @ Y2 @ Y1)))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y3 @ Y5 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y8)) | (~ (Y3 @ Y7 @ Y8))))))))))) | (~ (Y0 @ Y2 @ Y5))) | ((~ (Y4 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y2 @ Y4))))))) | (Y1 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (Y5 = Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y4 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (Y7 @ Y5 @ Y6)))))))))))))))))))))) & ! 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[X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6))))))))))) | (Y4 @ Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y1))))) & (~ (Y3 = Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | ((~ (Y5 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y7 @ Y8) | (~ (Y4 @ Y6 @ Y8))) | (~ (Y4 @ Y7 @ Y6))))))))))) | (Y5 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y5 @ Y6)))))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | (((d2unsorted @ X3)) != ((d2unsorted @ X4)))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))) | (~ (Y1 @ Y3)))))) | (~ (Y1 @ Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1)))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y8) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (Y1 @ Y4 @ Y3)) | (Y4 = Y3)) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7))))))))))) | (~ (Y0 @ Y2 @ Y4))) | (~ (Y0 @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7))))))))))))))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y1))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))))) | (Y1 = Y2))))))))),
  inference(ennf_transformation,[],[f8])).
thf(f10,plain,(
  (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y5 @ Y7) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y5 @ Y6)))))))))) | (Y4 @ Y3 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y1 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y7)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))))))))))) | (((~ (Y3 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7))))))))) | (Y5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y8))) | (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) | (~ (Y4 @ Y6 @ Y5))) | (~ (Y4 @ Y7 @ Y6))))))))))))))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (Y0 @ Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y0 @ Y4 @ Y2 @ Y1)))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y3 @ Y5 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y8)) | (~ (Y3 @ Y7 @ Y8))))))))))) | (~ (Y0 @ Y2 @ Y5))) | ((~ (Y4 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y2 @ Y4))))))) | (Y1 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (Y5 = Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y4 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (Y7 @ Y5 @ Y6)))))))))))))))))))))) & ! 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[X1 : $i] : ? [X2 : d_unsorted] : (((d2unsorted @ X2)) = X1) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6))))))))))) | (Y4 @ Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y1))))) & (~ (Y3 = Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | ((~ (Y5 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y7 @ Y8) | (~ (Y4 @ Y6 @ Y8))) | (~ (Y4 @ Y7 @ Y6))))))))))) | (Y5 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y5 @ Y6)))))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | (((d2unsorted @ X3)) != ((d2unsorted @ X4)))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))) | (~ (Y1 @ Y3)))))) | (~ (Y1 @ Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1)))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y8) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (Y1 @ Y4 @ Y3)) | (Y4 = Y3)) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7))))))))))) | (~ (Y0 @ Y2 @ Y4))) | (~ (Y0 @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7))))))))))))))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y1))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))))) | (Y1 = Y2))))))))),
  inference(rectify,[],[f9])).
thf(f11,plain,(
  (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y5 @ Y7) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y5 @ Y6)))))))))) | (Y4 @ Y3 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y1 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y7)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))))))))))) | (((~ (Y3 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7))))))))) | (Y5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y8))) | (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))) | (Y3 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) | (~ (Y4 @ Y6 @ Y5))) | (~ (Y4 @ Y7 @ Y6))))))))))))))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (Y0 @ Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y0 @ Y4 @ Y2 @ Y1)))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y3 @ Y5 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y8)) | (~ (Y3 @ Y7 @ Y8))))))))))) | (~ (Y0 @ Y2 @ Y5))) | ((~ (Y4 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y2 @ Y4))))))) | (Y1 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y7)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (Y5 = Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y4 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (Y7 @ Y5 @ Y6)))))))))))))))))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))) & (~ (Y1 = Y2))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5)))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y1 @ Y2))))))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y1 @ Y3)) | (Y0 @ Y2 @ Y1 @ Y3)))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)) | (Y2 = Y1)))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y3 @ Y4))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & ! [X1 : $i] : (((d2unsorted @ (sK0 @ X1))) = X1) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6))))))))))) | (Y4 @ Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y1))))) & (~ (Y3 = Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | ((~ (Y5 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y7 @ Y8) | (~ (Y4 @ Y6 @ Y8))) | (~ (Y4 @ Y7 @ Y6))))))))))) | (Y5 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y10 @ Y8))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y5 @ Y6)))))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | (((d2unsorted @ X3)) != ((d2unsorted @ X4)))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y2 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))) | (~ (Y1 @ Y3)))))) | (~ (Y1 @ Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1)))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y8) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (Y1 @ Y4 @ Y3)) | (Y4 = Y3)) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7))))))))))) | (~ (Y0 @ Y2 @ Y4))) | (~ (Y0 @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7))))))))))))))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y1))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))))) | (Y1 = Y2))))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,$thf(sK0 @ X1))],[f10])).
thf(f12,plain,(
  (trsc != (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
  inference(cnf_transformation,[],[f7])).
thf(f21,plain,(
  (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2))))))))),
  inference(cnf_transformation,[],[f11])).
thf(f26,plain,(
  (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))),
  inference(cnf_transformation,[],[f11])).
thf(f27,plain,(
  (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))),
  inference(cnf_transformation,[],[f11])).
thf(f33,plain,(
  ( ! [X1 : $i] : ((((d2unsorted @ (sK0 @ X1))) = X1)) )),
  inference(cnf_transformation,[],[f11])).
thf(f41,plain,(
  ( ! [X0 : d_unsorted] : ((d_unsorted_0 = X0)) )),
  inference(cnf_transformation,[],[f11])).
thf(f48,definition,(
  spl1_1 <=> (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))),
  introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
thf(f50,plain,(
  (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)))))))) | ~spl1_1),
  inference(avatar_component_clause,[],[f48])).
thf(f51,plain,(
  spl1_1),
  inference(avatar_split_clause,[],[f27,f48])).
thf(f53,definition,(
  spl1_2 <=> (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2))))))))),
  introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
thf(f55,plain,(
  (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) | ~spl1_2),
  inference(avatar_component_clause,[],[f53])).
thf(f56,plain,(
  spl1_2),
  inference(avatar_split_clause,[],[f21,f53])).
thf(f58,definition,(
  spl1_3 <=> (trsc = (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
  introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
thf(f60,plain,(
  (trsc != (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0))))) | spl1_3),
  inference(avatar_component_clause,[],[f58])).
thf(f61,plain,(
  ~spl1_3),
  inference(avatar_split_clause,[],[f12,f58])).
thf(f63,definition,(
  spl1_4 <=> (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))),
  introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
thf(f65,plain,(
  (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) | ~spl1_4),
  inference(avatar_component_clause,[],[f63])).
thf(f66,plain,(
  spl1_4),
  inference(avatar_split_clause,[],[f26,f63])).
thf(f72,plain,(
  (((trsc @ sK2)) != (((^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))) @ sK2))) | spl1_3),
  inference(negative_extensionality,[],[f60])).
thf(f73,plain,(
  (((trsc @ sK2)) != ((sc @ (rc @ (tc @ sK2))))) | spl1_3),
  inference(beta-eta_normalization,[],[f72])).
thf(f75,definition,(
  spl1_6 <=> (((trsc @ sK2)) = ((sc @ (rc @ (tc @ sK2)))))),
  introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition])).
thf(f77,plain,(
  (((trsc @ sK2)) != ((sc @ (rc @ (tc @ sK2))))) | spl1_6),
  inference(avatar_component_clause,[],[f75])).
thf(f78,plain,(
  ~spl1_6 | spl1_3),
  inference(avatar_split_clause,[],[f73,f58,f75])).
thf(f80,plain,(
  ( ! [X0 : $i] : ((((d2unsorted @ d_unsorted_0)) = X0)) )),
  inference(superposition,[],[f33,f41])).
thf(f86,plain,(
  ( ! [X1 : ($i > $i > $o)] : (((((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))) @ X1)) = ((rc @ X1)))) ) | ~spl1_4),
  inference(argument_congruence,[],[f65])).
thf(f87,plain,(
  ( ! [X1 : ($i > $i > $o)] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((X1 @ Y0 @ Y1) | (Y0 = Y1))))) = ((rc @ X1)))) ) | ~spl1_4),
  inference(beta-eta_normalization,[],[f86])).
thf(f88,plain,(
  (((sc @ (rc @ (tc @ sK2)) @ sK3)) != ((trsc @ sK2 @ sK3))) | spl1_6),
  inference(negative_extensionality,[],[f77])).
thf(f90,definition,(
  spl1_7 <=> (((sc @ (rc @ (tc @ sK2)) @ sK3)) = ((trsc @ sK2 @ sK3)))),
  introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition])).
thf(f92,plain,(
  (((sc @ (rc @ (tc @ sK2)) @ sK3)) != ((trsc @ sK2 @ sK3))) | spl1_7),
  inference(avatar_component_clause,[],[f90])).
thf(f93,plain,(
  ~spl1_7 | spl1_6),
  inference(avatar_split_clause,[],[f88,f75,f90])).
thf(f104,plain,(
  ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
  inference(superposition,[],[f80,f80])).
thf(f117,plain,(
  (((sc @ (rc @ (tc @ sK2)) @ sK3 @ sK4)) != ((trsc @ sK2 @ sK3 @ sK4))) | spl1_7),
  inference(negative_extensionality,[],[f92])).
thf(f122,plain,(
  (((trsc @ sK2 @ sK3 @ sK4)) = $false) | (((sc @ (rc @ (tc @ sK2)) @ sK3 @ sK4)) = $false) | spl1_7),
  inference(xor_proxy_clausification,[],[f117])).
thf(f129,definition,(
  spl1_9 <=> (((trsc @ sK2 @ sK3 @ sK4)) = $false)),
  introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition])).
thf(f131,plain,(
  (((trsc @ sK2 @ sK3 @ sK4)) = $false) | ~spl1_9),
  inference(avatar_component_clause,[],[f129])).
thf(f133,definition,(
  spl1_10 <=> (((sc @ (rc @ (tc @ sK2)) @ sK3 @ sK4)) = $false)),
  introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition])).
thf(f135,plain,(
  (((sc @ (rc @ (tc @ sK2)) @ sK3 @ sK4)) = $false) | ~spl1_10),
  inference(avatar_component_clause,[],[f133])).
thf(f136,plain,(
  spl1_9 | spl1_10 | spl1_7),
  inference(avatar_split_clause,[],[f122,f90,f133,f129])).
thf(f182,plain,(
  ( ! [X0 : $i] : ((((trsc @ sK2 @ sK3 @ X0)) = $false)) ) | ~spl1_9),
  inference(superposition,[],[f131,f104])).
thf(f266,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((trsc @ sK2 @ X0 @ X1)) = $false)) ) | ~spl1_9),
  inference(superposition,[],[f182,f104])).
thf(f287,plain,(
  ( ! [X1 : ($i > $i > $o)] : (((((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))) @ X1)) = ((sc @ X1)))) ) | ~spl1_1),
  inference(argument_congruence,[],[f50])).
thf(f288,plain,(
  ( ! [X1 : ($i > $i > $o)] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((X1 @ Y1 @ Y0) | (X1 @ Y0 @ Y1))))) = ((sc @ X1)))) ) | ~spl1_1),
  inference(beta-eta_normalization,[],[f287])).
thf(f292,plain,(
  ( ! [X1 : ($i > $i > $o)] : (((((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y4))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2))))))) @ X1)) = ((trsc @ X1)))) ) | ~spl1_2),
  inference(argument_congruence,[],[f55])).
thf(f293,plain,(
  ( ! [X1 : ($i > $i > $o)] : (((^[Y0 : $i]: ((^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) | (~ (Y2 @ Y4 @ Y3))) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y5 @ Y3))) | (Y2 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y1 @ Y0))))) | (Y0 = Y1))))) = ((trsc @ X1)))) ) | ~spl1_2),
  inference(beta-eta_normalization,[],[f292])).
thf(f299,plain,(
  ( ! [X2 : $i,X1 : ($i > $i > $o)] : ((((sc @ X1 @ X2)) = (((^[Y0 : $i]: ((^[Y1 : $i]: ((X1 @ Y1 @ Y0) | (X1 @ Y0 @ Y1))))) @ X2)))) ) | ~spl1_1),
  inference(argument_congruence,[],[f288])).
thf(f300,plain,(
  ( ! [X2 : $i,X1 : ($i > $i > $o)] : (((^[Y0 : $i]: ((X1 @ Y0 @ X2) | (X1 @ X2 @ Y0))) = ((sc @ X1 @ X2)))) ) | ~spl1_1),
  inference(beta-eta_normalization,[],[f299])).
thf(f301,plain,(
  ( ! [X2 : $i,X1 : ($i > $i > $o)] : ((((rc @ X1 @ X2)) = (((^[Y0 : $i]: ((^[Y1 : $i]: ((X1 @ Y0 @ Y1) | (Y0 = Y1))))) @ X2)))) ) | ~spl1_4),
  inference(argument_congruence,[],[f87])).
thf(f302,plain,(
  ( ! [X2 : $i,X1 : ($i > $i > $o)] : ((((rc @ X1 @ X2)) = (^[Y0 : $i]: ((X1 @ X2 @ Y0) | (X2 = Y0))))) ) | ~spl1_4),
  inference(beta-eta_normalization,[],[f301])).
thf(f305,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : (((((^[Y0 : $i]: ((X1 @ Y0 @ X2) | (X1 @ X2 @ Y0))) @ X3)) = ((sc @ X1 @ X2 @ X3)))) ) | ~spl1_1),
  inference(argument_congruence,[],[f300])).
thf(f307,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : (($true = ((sc @ X1 @ X2 @ X3))) | ((((^[Y0 : $i]: ((X1 @ Y0 @ X2) | (X1 @ X2 @ Y0))) @ X3)) = $false)) ) | ~spl1_1),
  inference(iff_proxy_clausification,[],[f305])).
thf(f308,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : (($true = ((sc @ X1 @ X2 @ X3))) | ((((X1 @ X3 @ X2) | (X1 @ X2 @ X3))) = $false)) ) | ~spl1_1),
  inference(beta-eta_normalization,[],[f307])).
thf(f309,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : (($true = ((sc @ X1 @ X2 @ X3))) | (((X1 @ X2 @ X3)) = $false)) ) | ~spl1_1),
  inference(or_proxy_clausification,[],[f308])).
thf(f320,plain,(
  ( ! [X2 : $i,X1 : ($i > $i > $o)] : (((((^[Y0 : $i]: ((^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) | (~ (Y2 @ Y4 @ Y3))) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y5 @ Y3))) | (Y2 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (Y2 @ Y1 @ Y0))))) | (Y0 = Y1))))) @ X2)) = ((trsc @ X1 @ X2)))) ) | ~spl1_2),
  inference(argument_congruence,[],[f293])).
thf(f321,plain,(
  ( ! [X2 : $i,X1 : ($i > $i > $o)] : (((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y3 @ Y2))) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2))))))))) | (Y1 @ X2 @ Y0)))) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y4 @ Y2))) | (Y1 @ Y4 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ Y0 @ X2))))) | (X2 = Y0))) = ((trsc @ X1 @ X2)))) ) | ~spl1_2),
  inference(beta-eta_normalization,[],[f320])).
thf(f322,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : (((((^[Y0 : $i]: ((X1 @ X2 @ Y0) | (X2 = Y0))) @ X3)) = ((rc @ X1 @ X2 @ X3)))) ) | ~spl1_4),
  inference(argument_congruence,[],[f302])).
thf(f324,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((rc @ X1 @ X2 @ X3)) = $true) | ((((^[Y0 : $i]: ((X1 @ X2 @ Y0) | (X2 = Y0))) @ X3)) = $false)) ) | ~spl1_4),
  inference(iff_proxy_clausification,[],[f322])).
thf(f325,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : (((((X1 @ X2 @ X3) | (X2 = X3))) = $false) | (((rc @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_4),
  inference(beta-eta_normalization,[],[f324])).
thf(f326,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((X2 = X3)) = $false) | (((rc @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_4),
  inference(or_proxy_clausification,[],[f325])).
thf(f328,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((X2 != X3) | (((rc @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_4),
  inference(equality_proxy_clausification,[],[f326])).
thf(f332,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((rc @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_4),
  inference(forward_subsumption_resolution,[],[f328,f104])).
thf(f400,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((trsc @ X1 @ X2 @ X3)) = (((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y3 @ Y2))) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2))))))))) | (Y1 @ X2 @ Y0)))) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y4 @ Y2))) | (Y1 @ Y4 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ Y0 @ X2))))) | (X2 = Y0))) @ X3)))) ) | ~spl1_2),
  inference(argument_congruence,[],[f321])).
thf(f401,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : (($false = (((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y3 @ Y2))) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2))))))))) | (Y1 @ X2 @ Y0)))) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y4 @ Y2))) | (Y1 @ Y4 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (Y1 @ Y0 @ X2))))) | (X2 = Y0))) @ X3))) | (((trsc @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_2),
  inference(iff_proxy_clausification,[],[f400])).
thf(f552,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (X1 @ Y2 @ Y1))))))))) | (Y0 @ X2 @ X3)))) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (Y0 @ X3 @ X2))))) | (X2 = X3))) = $false) | (((trsc @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_2),
  inference(beta-eta_normalization,[],[f401])).
thf(f553,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((trsc @ X1 @ X2 @ X3)) = $true) | (((X2 = X3)) = $false)) ) | ~spl1_2),
  inference(or_proxy_clausification,[],[f552])).
thf(f605,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((trsc @ X1 @ X2 @ X3)) = $true) | (X2 != X3)) ) | ~spl1_2),
  inference(equality_proxy_clausification,[],[f553])).
thf(f606,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((trsc @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_2),
  inference(forward_subsumption_resolution,[],[f605,f104])).
thf(f843,plain,(
  ($true = $false) | (~spl1_2 | ~spl1_9)),
  inference(backward_demodulation,[],[f266,f606])).
thf(f844,plain,(
  $false | (~spl1_2 | ~spl1_9)),
  inference(trivial_inequality_removal,[],[f843])).
thf(f845,plain,(
  ~spl1_2 | ~spl1_9),
  inference(avatar_contradiction_clause,[],[f844])).
thf(f869,plain,(
  (((rc @ (tc @ sK2) @ sK3 @ sK4)) = $false) | ($true = $false) | (~spl1_1 | ~spl1_10)),
  inference(superposition,[],[f135,f309])).
thf(f872,plain,(
  (((rc @ (tc @ sK2) @ sK3 @ sK4)) = $false) | (~spl1_1 | ~spl1_10)),
  inference(trivial_inequality_removal,[],[f869])).
thf(f876,plain,(
  ($true = $false) | (~spl1_1 | ~spl1_4 | ~spl1_10)),
  inference(forward_demodulation,[],[f872,f332])).
thf(f877,plain,(
  $false | (~spl1_1 | ~spl1_4 | ~spl1_10)),
  inference(trivial_inequality_removal,[],[f876])).
thf(f878,plain,(
  ~spl1_1 | ~spl1_4 | ~spl1_10),
  inference(avatar_contradiction_clause,[],[f877])).
cnf(s1, plain, spl1_1, inference(sat_conversion,[],[f51])).
cnf(s2, plain, spl1_2, inference(sat_conversion,[],[f56])).
cnf(s3, plain, ~spl1_3, inference(sat_conversion,[],[f61])).
cnf(s4, plain, spl1_4, inference(sat_conversion,[],[f66])).
cnf(s6, plain, spl1_3 | ~spl1_6, inference(sat_conversion,[],[f78])).
cnf(s7, plain, spl1_6 | ~spl1_7, inference(sat_conversion,[],[f93])).
cnf(s9, plain, spl1_7 | spl1_9 | spl1_10, inference(sat_conversion,[],[f136])).
cnf(s58, plain, ~spl1_2 | ~spl1_9, inference(sat_conversion,[],[f845])).
cnf(s77, plain, ~spl1_1 | ~spl1_4 | ~spl1_10, inference(sat_conversion,[],[f878])).
cnf(s79, plain, ~spl1_6, inference(rat,[],[s6,s3])).
cnf(s80, plain, ~spl1_7, inference(rat,[],[s7,s79])).
cnf(s82, plain, ~spl1_9, inference(rat,[],[s58,s2])).
cnf(s84, plain, spl1_10, inference(rat,[],[s9,s80,s82])).
cnf(s89, plain, ~spl1_1, inference(rat,[],[s77,s4,s84])).
cnf(s100, plain, $false, inference(rat,[],[s1,s89])).
thf(f879,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s100])).
% SZS output end Proof for theBenchmark