%----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, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_33, type, vIMP: ($o > $o > $o)).
thf(func_def_34, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_35, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_36, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_37, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_38, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_39, type, vAND: ($o > $o > $o)).
thf(func_def_40, type, vOR: ($o > $o > $o)).
thf(func_def_41, type, vNOT: ($o > $o)).
thf(func_def_42, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_43, type, db6: !>[X0: $tType]:(X0)).
thf(func_def_44, type, db4: !>[X0: $tType]:(X0)).
thf(func_def_45, type, db5: !>[X0: $tType]:(X0)).
thf(func_def_46, type, db7: !>[X0: $tType]:(X0)).
thf(func_def_47, type, db8: !>[X0: $tType]:(X0)).
thf(func_def_48, type, db9: !>[X0: $tType]:(X0)).
thf(func_def_49, type, sK0: ($i > d_unsorted)).
thf(func_def_52, type, sK1: ($i > $i > $o)).
thf(func_def_53, type, sK2: ($i > $o)).
thf(func_def_54, type, sK3: ($i > $o)).
thf(func_def_56, type, sK5: ($i > $i)).
thf(func_def_57, type, sK6: ($i > $i)).
thf(func_def_58, type, sK7: (($i > $i > $o) > $i)).
thf(func_def_59, type, sK8: (($i > $i > $o) > $i)).
thf(func_def_60, type, sK9: (($i > $i > $o) > $i)).
thf(func_def_61, type, sK10: (($i > $i > $o) > $i)).
thf(func_def_62, type, sK11: (($i > $i > $o) > $i)).
thf(func_def_63, type, sK12: (($i > $i > $o) > $i)).
thf(func_def_64, type, sK13: (($i > $i > $o) > $i)).
thf(func_def_65, type, sK14: (($i > $i > $o) > $i)).
thf(func_def_66, type, sK15: (($i > $i > $o) > $i)).
thf(func_def_67, type, sK16: (($i > $i > $o) > $i)).
thf(func_def_68, type, sK17: (($i > $i > $o) > $i)).
thf(func_def_69, type, sK18: (($i > $i > $o) > $i)).
thf(func_def_70, type, sK19: (($i > $i > $o) > $i)).
thf(func_def_71, type, sK20: (($i > $i > $o) > $i)).
thf(func_def_72, type, sK21: (($i > $i > $o) > $i)).
thf(func_def_73, type, sK22: (($i > $i > $o) > $i)).
thf(func_def_74, type, sK23: (($i > $i > $o) > $i)).
thf(func_def_75, type, sK24: (($i > $i > $o) > $i)).
thf(func_def_76, type, sK25: (($i > $i > $o) > $i)).
thf(func_def_77, type, sK26: (($i > $i > $o) > $i)).
thf(func_def_78, type, sK27: (($i > $i > $o) > $i)).
thf(func_def_79, type, sK28: ($i > $i)).
thf(func_def_80, type, sK29: (($i > $i > $o) > $i)).
thf(func_def_81, type, sK30: (($i > $i > $o) > $i)).
thf(func_def_82, type, sK31: (($i > $i > $o) > $i)).
thf(func_def_83, type, sK32: (($i > $i > $o) > $i)).
thf(func_def_84, type, sK33: (($i > $i > $o) > $i)).
thf(func_def_85, type, sK34: (($i > $i > $o) > $i)).
thf(func_def_86, type, sK35: (($i > $i > $o) > $i)).
thf(func_def_87, type, sK36: (($i > $i > $o) > $i)).
thf(func_def_88, type, sK37: (($i > $i > $o) > $i)).
thf(func_def_89, type, sK38: (($i > $i > $o) > $i)).
thf(func_def_91, type, sK40: ($i > $i)).
thf(func_def_92, type, sK41: (($i > $i > $o) > $i)).
thf(func_def_93, type, sK42: (($i > $i > $o) > $i)).
thf(func_def_94, type, sK43: (($i > $i > $o) > $i)).
thf(func_def_95, type, sK44: (($i > $i > $o) > $i)).
thf(func_def_96, type, sK45: (($i > $i > $o) > $i)).
thf(func_def_97, type, sK46: (($i > $o) > $i)).
thf(func_def_98, type, sK47: (($i > $o) > $i)).
thf(func_def_99, type, sK48: ($i > ($i > $o) > $i > $i > $o)).
thf(func_def_100, type, sK49: ($i > ($i > $o) > $i > $i > $o)).
thf(func_def_101, type, sK50: (($i > $o) > $i > $i > $i > $o)).
thf(func_def_102, type, sK51: (($i > $o) > $i > $i > $i > $o)).
thf(func_def_103, type, sK52: (($i > $o) > $i > $i > $i > $o)).
thf(func_def_104, type, sK53: (($i > $o) > $i)).
thf(func_def_105, type, sK54: (($i > $o) > $i > $i > $i > $o)).
thf(f1,conjecture,(
  ((^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X2 : $i] : (X1 @ X2)))) = ind)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',satisfying_the_induction_principle)).
thf(f2,negated_conjecture,(
  ~ ((^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X2 : $i] : (X1 @ X2)))) = ind)),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,axiom,(
  ((^[X2 : ($i > $i > $o)] : (! [X3 : $i] : (X2 @ X3 @ X3))) = refl) & ((^[X5 : (($i > $i > $o) > $i > $i > $o)] : (! [X3 : $i,X4 : $i,X2 : ($i > $i > $o)] : ((X5 @ X2 @ X3 @ X4) | ~(X2 @ X3 @ X4)))) = infl) & (trans = (^[X2 : ($i > $i > $o)] : (! [X9 : $i,X4 : $i,X3 : $i] : ((X2 @ X3 @ X9) | ~(X2 @ X4 @ X9) | ~(X2 @ X3 @ X4))))) & (trsc = (^[X2 : ($i > $i > $o), X10 : $i, X11 : $i] : ((X10 = X11) | ! [X6 : ($i > $i > $o)] : ((X6 @ X11 @ X10) | ~ ! [X12 : $i,X13 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | ~ ! [X9 : $i,X14 : $i,X15 : $i] : ((X6 @ X14 @ X9) | ~(X6 @ X15 @ X9) | ~(X6 @ X14 @ X15))) | ! [X6 : ($i > $i > $o)] : (~ ! [X12 : $i,X13 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | ~ ! [X9 : $i,X15 : $i,X14 : $i] : (~(X6 @ X15 @ X9) | ~(X6 @ X14 @ X15) | (X6 @ X14 @ X9)) | (X6 @ X10 @ X11))))) & ((^[X2 : ($i > $i > $o)] : (! [X3 : $i] : ~(X2 @ X3 @ X3))) = irrefl) & ((^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : (! [X6 : ($i > $i > $o)] : (~ ! [X12 : $i,X13 : $i] : (~(X2 @ X12 @ X13) | (X6 @ X12 @ X13)) | ~ ! [X9 : $i,X14 : $i,X15 : $i] : (~(X6 @ X14 @ X15) | ~(X6 @ X15 @ X9) | (X6 @ X14 @ X9)) | (X6 @ X3 @ X4)))) = tc) & ! [X0 : $i] : ? [X1 : d_unsorted] : (X0 = ((d2unsorted @ X1))) & (sconfl = (^[X2 : ($i > $i > $o)] : (! [X3 : $i,X4 : $i,X9 : $i,X28 : ($i > $i > $o),X29 : ($i > $i > $o)] : (~ ! [X12 : $i,X13 : $i] : ((X28 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | (X4 = X9) | ~ ! [X15 : $i,X14 : $i,X20 : $i] : (~(X28 @ X15 @ X20) | ~(X28 @ X14 @ X15) | (X28 @ X14 @ X20)) | ~ ! [X22 : $i] : (~ ! [X6 : ($i > $i > $o)] : ((X6 @ X4 @ X22) | ~ ! [X13 : $i,X12 : $i] : (~(X2 @ X12 @ X13) | (X6 @ X12 @ X13)) | ~ ! [X14 : $i,X15 : $i,X20 : $i] : (~(X6 @ X15 @ X20) | (X6 @ X14 @ X20) | ~(X6 @ X14 @ X15))) | ~ ! [X6 : ($i > $i > $o)] : (~ ! [X14 : $i,X15 : $i,X21 : $i] : (~(X6 @ X15 @ X21) | (X6 @ X14 @ X21) | ~(X6 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | (X6 @ X9 @ X22))) | (X29 @ X9 @ X4) | ((X3 != X4) & ~ ! [X6 : ($i > $i > $o)] : ((X6 @ X3 @ X4) | ~ ! [X30 : $i,X15 : $i,X14 : $i] : (~(X6 @ X14 @ X15) | (X6 @ X14 @ X30) | ~(X6 @ X15 @ X30)) | ~ ! [X13 : $i,X12 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)))) | (X28 @ X4 @ X9) | ~ ! [X12 : $i,X13 : $i] : ((X29 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | ~(X2 @ X3 @ X9) | ~ ! [X21 : $i,X15 : $i,X14 : $i] : ((X29 @ X14 @ X21) | ~(X29 @ X15 @ X21) | ~(X29 @ X14 @ X15)))))) & (so = (^[X2 : ($i > $i > $o)] : (! [X4 : $i,X3 : $i] : (~(X2 @ X3 @ X4) | ~(X2 @ X4 @ X3)) & ! [X3 : $i,X9 : $i,X4 : $i] : (~(X2 @ X3 @ X4) | (X2 @ X3 @ X9) | ~(X2 @ X4 @ X9))))) & (nfof = (^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : (((X3 = X4) | ! [X6 : ($i > $i > $o)] : ((X6 @ X4 @ X3) | ~ ! [X13 : $i,X12 : $i] : (~(X2 @ X12 @ X13) | (X6 @ X12 @ X13)) | ~ ! [X9 : $i,X14 : $i,X15 : $i] : (~(X6 @ X14 @ X15) | (X6 @ X14 @ X9) | ~(X6 @ X15 @ X9)))) & ! [X35 : $i] : ~(X2 @ X3 @ X35)))) & ! [X37 : d_unsorted,X36 : d_unsorted] : ((((d2unsorted @ X36)) = ((d2unsorted @ X37))) => (X36 = X37)) & (rc = (^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : ((X2 @ X3 @ X4) | (X3 = X4)))) & ((^[X2 : ($i > $i > $o), X6 : ($i > $i > $o)] : (! [X4 : $i,X3 : $i] : ((X6 @ X3 @ X4) | ~(X2 @ X3 @ X4)))) = subrel) & ((^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : ((X2 @ X4 @ X3) | (X2 @ X3 @ X4))) = sc) & (mono = (^[X5 : (($i > $i > $o) > $i > $i > $o)] : (! [X8 : $i,X7 : $i,X2 : ($i > $i > $o),X6 : ($i > $i > $o)] : (~(X5 @ X2 @ X7 @ X8) | ~ ! [X4 : $i,X3 : $i] : ((X6 @ X3 @ X4) | ~(X2 @ X3 @ X4)) | (X5 @ X6 @ X7 @ X8))))) & ((^[X2 : ($i > $i > $o)] : (! [X17 : $i,X16 : ($i > $o)] : (~(X16 @ X17) | ~ ! [X3 : $i] : (~ ! [X4 : $i] : (~(X16 @ X4) | ~(X2 @ X3 @ X4)) | ~(X16 @ X3))))) = term) & ((^[X2 : ($i > $i > $o)] : (! [X3 : $i,X4 : $i,X31 : ($i > $i > $o),X9 : $i,X32 : ($i > $i > $o)] : ((X4 = X9) | (X32 @ X9 @ X4) | ~ ! [X13 : $i,X12 : $i] : ((X32 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | (X31 @ X4 @ X9) | ~ ! [X13 : $i,X12 : $i] : ((X31 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | ~ ! [X15 : $i,X21 : $i,X14 : $i] : (~(X32 @ X15 @ X21) | (X32 @ X14 @ X21) | ~(X32 @ X14 @ X15)) | ~(X2 @ X3 @ X9) | ~ ! [X22 : $i] : (~ ! [X6 : ($i > $i > $o)] : ((X6 @ X9 @ X22) | ~ ! [X13 : $i,X12 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | ~ ! [X15 : $i,X14 : $i,X21 : $i] : ((X6 @ X14 @ X21) | ~(X6 @ X14 @ X15) | ~(X6 @ X15 @ X21))) | ~ ! [X6 : ($i > $i > $o)] : (~ ! [X15 : $i,X14 : $i,X20 : $i] : (~(X6 @ X15 @ X20) | ~(X6 @ X14 @ X15) | (X6 @ X14 @ X20)) | (X6 @ X4 @ X22) | ~ ! [X12 : $i,X13 : $i] : (~(X2 @ X12 @ X13) | (X6 @ X12 @ X13)))) | ~ ! [X15 : $i,X14 : $i,X20 : $i] : (~(X31 @ X14 @ X15) | (X31 @ X14 @ X20) | ~(X31 @ X15 @ X20)) | ~(X2 @ X3 @ X4)))) = lconfl) & ((^[X2 : ($i > $i > $o)] : (! [X19 : $i,X18 : ($i > $o)] : ((X18 @ X19) | ~ ! [X3 : $i] : (~ ! [X4 : $i] : ((X18 @ X4) | ~ ! [X6 : ($i > $i > $o)] : (~ ! [X15 : $i,X14 : $i,X9 : $i] : (~(X6 @ X15 @ X9) | ~(X6 @ X14 @ X15) | (X6 @ X14 @ X9)) | ~ ! [X12 : $i,X13 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | (X6 @ X3 @ X4))) | (X18 @ X3))))) = ind) & ((^[X2 : ($i > $i > $o)] : (! [X4 : $i,X3 : $i] : (~(X2 @ X3 @ X4) | (X2 @ X4 @ X3)))) = symm) & ((^[X2 : ($i > $i > $o)] : (! [X9 : $i,X3 : $i,X24 : ($i > $i > $o),X23 : ($i > $i > $o),X4 : $i] : ((X4 = X9) | ~ ! [X13 : $i,X12 : $i] : (~(X2 @ X12 @ X13) | (X24 @ X12 @ X13)) | (X23 @ X4 @ X9) | ~ ! [X22 : $i] : (~ ! [X6 : ($i > $i > $o)] : (~ ! [X12 : $i,X13 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | (X6 @ X4 @ X22) | ~ ! [X20 : $i,X14 : $i,X15 : $i] : ((X6 @ X14 @ X20) | ~(X6 @ X14 @ X15) | ~(X6 @ X15 @ X20))) | ~ ! [X6 : ($i > $i > $o)] : (~ ! [X21 : $i,X15 : $i,X14 : $i] : (~(X6 @ X14 @ X15) | (X6 @ X14 @ X21) | ~(X6 @ X15 @ X21)) | ~ ! [X12 : $i,X13 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | (X6 @ X9 @ X22))) | (X24 @ X9 @ X4) | ~ ! [X13 : $i,X12 : $i] : ((X23 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | ~ ! [X14 : $i,X20 : $i,X15 : $i] : ((X23 @ X14 @ X20) | ~(X23 @ X15 @ X20) | ~(X23 @ X14 @ X15)) | ~ ! [X15 : $i,X21 : $i,X14 : $i] : (~(X24 @ X15 @ X21) | ~(X24 @ X14 @ X15) | (X24 @ X14 @ X21)) | ((X3 != X9) & ~ ! [X6 : ($i > $i > $o)] : ((X6 @ X3 @ X9) | ~ ! [X21 : $i,X15 : $i,X14 : $i] : ((X6 @ X14 @ X21) | ~(X6 @ X14 @ X15) | ~(X6 @ X15 @ X21)) | ~ ! [X13 : $i,X12 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)))) | (~ ! [X6 : ($i > $i > $o)] : (~ ! [X14 : $i,X25 : $i,X15 : $i] : ((X6 @ X14 @ X25) | ~(X6 @ X15 @ X25) | ~(X6 @ X14 @ X15)) | (X6 @ X3 @ X4) | ~ ! [X12 : $i,X13 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13))) & (X3 != X4))))) = confl) & ((^[X5 : (($i > $i > $o) > $i > $i > $o)] : (! [X2 : ($i > $i > $o)] : (((X5 @ X2)) = ((X5 @ (X5 @ X2)))))) = idem) & ! [X1 : d_unsorted] : (X1 = d_unsorted_0) & ((^[X2 : ($i > $i > $o), X3 : $i] : (! [X4 : $i] : ~(X2 @ X3 @ X4))) = innf) & (antisymm = (^[X2 : ($i > $i > $o)] : (! [X4 : $i,X3 : $i] : (~(X2 @ X3 @ X4) | (X3 = X4) | ~(X2 @ X4 @ X3))))) & (join = (^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : (~((X3 != X4) & ~ ! [X6 : ($i > $i > $o)] : (~ ! [X14 : $i,X21 : $i,X15 : $i] : ((X6 @ X14 @ X21) | ~(X6 @ X14 @ X15) | ~(X6 @ X15 @ X21)) | (X6 @ X3 @ X4) | ~ ! [X12 : $i,X13 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13))) & ~ ! [X6 : ($i > $i > $o)] : (~ ! [X13 : $i,X12 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | (X6 @ X4 @ X3) | ~ ! [X15 : $i,X14 : $i,X20 : $i] : (~(X6 @ X15 @ X20) | ~(X6 @ X14 @ X15) | (X6 @ X14 @ X20))) & ! [X22 : $i] : (~ ! [X6 : ($i > $i > $o)] : (~ ! [X12 : $i,X13 : $i] : (~(X2 @ X12 @ X13) | (X6 @ X12 @ X13)) | ~ ! [X14 : $i,X21 : $i,X15 : $i] : ((X6 @ X14 @ X21) | ~(X6 @ X14 @ X15) | ~(X6 @ X15 @ X21)) | (X6 @ X3 @ X22)) | ~ ! [X6 : ($i > $i > $o)] : (~ ! [X15 : $i,X20 : $i,X14 : $i] : (~(X6 @ X15 @ X20) | ~(X6 @ X14 @ X15) | (X6 @ X14 @ X20)) | ~ ! [X13 : $i,X12 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | (X6 @ X4 @ X22))))))) & ((^[X2 : ($i > $i > $o)] : (! [X3 : $i,X4 : $i] : ((X2 @ X4 @ X3) | (X3 = X4) | (X2 @ X3 @ X4)))) = total) & ((^[X2 : ($i > $i > $o)] : (! [X3 : $i,X26 : ($i > $i > $o),X4 : $i,X27 : ($i > $i > $o)] : (~ ! [X22 : $i] : (~ ! [X6 : ($i > $i > $o)] : (~ ! [X12 : $i,X13 : $i] : (~(X2 @ X12 @ X13) | (X6 @ X12 @ X13)) | (X6 @ X3 @ X22) | ~ ! [X14 : $i,X15 : $i,X21 : $i] : (~(X6 @ X14 @ X15) | (X6 @ X14 @ X21) | ~(X6 @ X15 @ X21))) | ~ ! [X6 : ($i > $i > $o)] : ((X6 @ X4 @ X22) | ~ ! [X20 : $i,X15 : $i,X14 : $i] : (~(X6 @ X15 @ X20) | (X6 @ X14 @ X20) | ~(X6 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i] : (~(X2 @ X12 @ X13) | (X6 @ X12 @ X13)))) | ~ ! [X15 : $i,X14 : $i,X21 : $i] : (~(X27 @ X14 @ X15) | ~(X27 @ X15 @ X21) | (X27 @ X14 @ X21)) | (X27 @ X3 @ X4) | ~ ! [X12 : $i,X13 : $i] : (~(X2 @ X12 @ X13) | (X26 @ X12 @ X13)) | ~ ! [X15 : $i,X14 : $i,X20 : $i] : (~(X26 @ X15 @ X20) | ~(X26 @ X14 @ X15) | (X26 @ X14 @ X20)) | (X26 @ X4 @ X3) | (~ ! [X6 : ($i > $i > $o)] : (~ ! [X14 : $i,X9 : $i,X15 : $i] : (~(X6 @ X15 @ X9) | ~(X6 @ X14 @ X15) | (X6 @ X14 @ X9)) | ~ ! [X13 : $i,X12 : $i] : (~(X2 @ X12 @ X13) | (X6 @ X12 @ X13)) | (X6 @ X3 @ X4)) & ~ ! [X6 : ($i > $i > $o)] : ((X6 @ X4 @ X3) | ~ ! [X15 : $i,X9 : $i,X14 : $i] : ((X6 @ X14 @ X9) | ~(X6 @ X15 @ X9) | ~(X6 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i] : (~(X2 @ X12 @ X13) | (X6 @ X12 @ X13))) & (X3 != X4)) | ~ ! [X12 : $i,X13 : $i] : ((X27 @ X12 @ X13) | ~(X2 @ X12 @ X13)) | (X3 = X4)))) = cr) & ((^[X2 : ($i > $i > $o)] : (! [X4 : $i,X3 : $i] : (~(X2 @ X3 @ X4) | ~(X2 @ X4 @ X3)))) = asymm) & (trc = (^[X2 : ($i > $i > $o), X10 : $i, X11 : $i] : ((X10 = X11) | ! [X6 : ($i > $i > $o)] : (~ ! [X14 : $i,X15 : $i,X9 : $i] : (~(X6 @ X15 @ X9) | (X6 @ X14 @ X9) | ~(X6 @ X14 @ X15)) | (X6 @ X10 @ X11) | ~ ! [X12 : $i,X13 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)))))) & (norm = (^[X2 : ($i > $i > $o)] : (! [X3 : $i,X33 : $i] : (~ ! [X34 : $i] : (~ ! [X35 : $i] : ~(X2 @ X34 @ X35) | ~ ! [X6 : ($i > $i > $o)] : ((X6 @ X3 @ X34) | ~ ! [X9 : $i,X14 : $i,X15 : $i] : (~(X6 @ X14 @ X15) | ~(X6 @ X15 @ X9) | (X6 @ X14 @ X9)) | ~ ! [X12 : $i,X13 : $i] : ((X6 @ X12 @ X13) | ~(X2 @ X12 @ X13)))) | ~(X2 @ X3 @ X33))))) & (inv = (^[X2 : ($i > $i > $o), X3 : $i, X4 : $i] : ((X2 @ X4 @ X3)))) & ((^[X2 : ($i > $i > $o)] : (! [X3 : $i] : (X2 @ X3 @ X3) & ! [X4 : $i,X3 : $i] : ((X3 = X4) | ~(X2 @ X4 @ X3) | ~(X2 @ X3 @ X4)) & ! [X3 : $i,X9 : $i,X4 : $i] : (~(X2 @ X4 @ X9) | (X2 @ X3 @ X9) | ~(X2 @ X3 @ X4)))) = po)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',sev441_1)).
thf(f4,plain,(
  ~ ((^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X4 : $i] : (X1 @ X4)))) = ind)),
  inference(rectify,[],[f2])).
thf(f5,plain,(
  ~ (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
  inference(fool_elimination,[],[f4])).
thf(f6,plain,(
  ((^[X0 : ($i > $i > $o)] : (! [X1 : $i] : (X0 @ X1 @ X1))) = refl) & ((^[X2 : (($i > $i > $o) > $i > $i > $o)] : (! [X3 : $i,X4 : $i,X5 : ($i > $i > $o)] : ((X2 @ X5 @ X3 @ X4) | ~(X5 @ X3 @ X4)))) = infl) & (trans = (^[X6 : ($i > $i > $o)] : (! [X7 : $i,X8 : $i,X9 : $i] : ((X6 @ X9 @ X7) | ~(X6 @ X8 @ X7) | ~(X6 @ X9 @ X8))))) & (trsc = (^[X10 : ($i > $i > $o), X11 : $i, X12 : $i] : ((X11 = X12) | ! [X13 : ($i > $i > $o)] : ((X13 @ X12 @ X11) | ~ ! [X14 : $i,X15 : $i] : ((X13 @ X14 @ X15) | ~(X10 @ X14 @ X15)) | ~ ! [X16 : $i,X17 : $i,X18 : $i] : ((X13 @ X17 @ X16) | ~(X13 @ X18 @ X16) | ~(X13 @ X17 @ X18))) | ! [X19 : ($i > $i > $o)] : (~ ! [X20 : $i,X21 : $i] : ((X19 @ X20 @ X21) | ~(X10 @ X20 @ X21)) | ~ ! [X22 : $i,X23 : $i,X24 : $i] : (~(X19 @ X23 @ X22) | ~(X19 @ X24 @ X23) | (X19 @ X24 @ X22)) | (X19 @ X11 @ X12))))) & ((^[X25 : ($i > $i > $o)] : (! [X26 : $i] : ~(X25 @ X26 @ X26))) = irrefl) & ((^[X27 : ($i > $i > $o), X28 : $i, X29 : $i] : (! [X30 : ($i > $i > $o)] : (~ ! [X31 : $i,X32 : $i] : (~(X27 @ X31 @ X32) | (X30 @ X31 @ X32)) | ~ ! [X33 : $i,X34 : $i,X35 : $i] : (~(X30 @ X34 @ X35) | ~(X30 @ X35 @ X33) | (X30 @ X34 @ X33)) | (X30 @ X28 @ X29)))) = tc) & ! [X36 : $i] : ? [X37 : d_unsorted] : (((d2unsorted @ X37)) = X36) & (sconfl = (^[X38 : ($i > $i > $o)] : (! [X39 : $i,X40 : $i,X41 : $i,X42 : ($i > $i > $o),X43 : ($i > $i > $o)] : (~ ! [X44 : $i,X45 : $i] : ((X42 @ X44 @ X45) | ~(X38 @ X44 @ X45)) | (X40 = X41) | ~ ! [X46 : $i,X47 : $i,X48 : $i] : (~(X42 @ X46 @ X48) | ~(X42 @ X47 @ X46) | (X42 @ X47 @ X48)) | ~ ! [X49 : $i] : (~ ! [X50 : ($i > $i > $o)] : ((X50 @ X40 @ X49) | ~ ! [X51 : $i,X52 : $i] : (~(X38 @ X52 @ X51) | (X50 @ X52 @ X51)) | ~ ! [X53 : $i,X54 : $i,X55 : $i] : (~(X50 @ X54 @ X55) | (X50 @ X53 @ X55) | ~(X50 @ X53 @ X54))) | ~ ! [X56 : ($i > $i > $o)] : (~ ! [X57 : $i,X58 : $i,X59 : $i] : (~(X56 @ X58 @ X59) | (X56 @ X57 @ X59) | ~(X56 @ X57 @ X58)) | ~ ! [X60 : $i,X61 : $i] : ((X56 @ X60 @ X61) | ~(X38 @ X60 @ X61)) | (X56 @ X41 @ X49))) | (X43 @ X41 @ X40) | ((X39 != X40) & ~ ! [X62 : ($i > $i > $o)] : ((X62 @ X39 @ X40) | ~ ! [X63 : $i,X64 : $i,X65 : $i] : (~(X62 @ X65 @ X64) | (X62 @ X65 @ X63) | ~(X62 @ X64 @ X63)) | ~ ! [X66 : $i,X67 : $i] : ((X62 @ X67 @ X66) | ~(X38 @ X67 @ X66)))) | (X42 @ X40 @ X41) | ~ ! [X68 : $i,X69 : $i] : ((X43 @ X68 @ X69) | ~(X38 @ X68 @ X69)) | ~(X38 @ X39 @ X41) | ~ ! [X70 : $i,X71 : $i,X72 : $i] : ((X43 @ X72 @ X70) | ~(X43 @ X71 @ X70) | ~(X43 @ X72 @ X71)))))) & (so = (^[X73 : ($i > $i > $o)] : (! [X74 : $i,X75 : $i] : (~(X73 @ X75 @ X74) | ~(X73 @ X74 @ X75)) & ! [X76 : $i,X77 : $i,X78 : $i] : (~(X73 @ X76 @ X78) | (X73 @ X76 @ X77) | ~(X73 @ X78 @ X77))))) & (nfof = (^[X79 : ($i > $i > $o), X80 : $i, X81 : $i] : (((X80 = X81) | ! [X82 : ($i > $i > $o)] : ((X82 @ X81 @ X80) | ~ ! [X83 : $i,X84 : $i] : (~(X79 @ X84 @ X83) | (X82 @ X84 @ X83)) | ~ ! [X85 : $i,X86 : $i,X87 : $i] : (~(X82 @ X86 @ X87) | (X82 @ X86 @ X85) | ~(X82 @ X87 @ X85)))) & ! [X88 : $i] : ~(X79 @ X80 @ X88)))) & ! [X89 : d_unsorted,X90 : d_unsorted] : ((((d2unsorted @ X90)) = ((d2unsorted @ X89))) => (X89 = X90)) & (rc = (^[X91 : ($i > $i > $o), X92 : $i, X93 : $i] : ((X91 @ X92 @ X93) | (X92 = X93)))) & ((^[X94 : ($i > $i > $o), X95 : ($i > $i > $o)] : (! [X96 : $i,X97 : $i] : ((X95 @ X97 @ X96) | ~(X94 @ X97 @ X96)))) = subrel) & ((^[X98 : ($i > $i > $o), X99 : $i, X100 : $i] : ((X98 @ X100 @ X99) | (X98 @ X99 @ X100))) = sc) & (mono = (^[X101 : (($i > $i > $o) > $i > $i > $o)] : (! [X102 : $i,X103 : $i,X104 : ($i > $i > $o),X105 : ($i > $i > $o)] : (~(X101 @ X104 @ X103 @ X102) | ~ ! [X106 : $i,X107 : $i] : ((X105 @ X107 @ X106) | ~(X104 @ X107 @ X106)) | (X101 @ X105 @ X103 @ X102))))) & ((^[X108 : ($i > $i > $o)] : (! [X109 : $i,X110 : ($i > $o)] : (~(X110 @ X109) | ~ ! [X111 : $i] : (~ ! [X112 : $i] : (~(X110 @ X112) | ~(X108 @ X111 @ X112)) | ~(X110 @ X111))))) = term) & ((^[X113 : ($i > $i > $o)] : (! [X114 : $i,X115 : $i,X116 : ($i > $i > $o),X117 : $i,X118 : ($i > $i > $o)] : ((X115 = X117) | (X118 @ X117 @ X115) | ~ ! [X119 : $i,X120 : $i] : ((X118 @ X120 @ X119) | ~(X113 @ X120 @ X119)) | (X116 @ X115 @ X117) | ~ ! [X121 : $i,X122 : $i] : ((X116 @ X122 @ X121) | ~(X113 @ X122 @ X121)) | ~ ! [X123 : $i,X124 : $i,X125 : $i] : (~(X118 @ X123 @ X124) | (X118 @ X125 @ X124) | ~(X118 @ X125 @ X123)) | ~(X113 @ X114 @ X117) | ~ ! [X126 : $i] : (~ ! [X127 : ($i > $i > $o)] : ((X127 @ X117 @ X126) | ~ ! [X128 : $i,X129 : $i] : ((X127 @ X129 @ X128) | ~(X113 @ X129 @ X128)) | ~ ! [X130 : $i,X131 : $i,X132 : $i] : ((X127 @ X131 @ X132) | ~(X127 @ X131 @ X130) | ~(X127 @ X130 @ X132))) | ~ ! [X133 : ($i > $i > $o)] : (~ ! [X134 : $i,X135 : $i,X136 : $i] : (~(X133 @ X134 @ X136) | ~(X133 @ X135 @ X134) | (X133 @ X135 @ X136)) | (X133 @ X115 @ X126) | ~ ! [X137 : $i,X138 : $i] : (~(X113 @ X137 @ X138) | (X133 @ X137 @ X138)))) | ~ ! [X139 : $i,X140 : $i,X141 : $i] : (~(X116 @ X140 @ X139) | (X116 @ X140 @ X141) | ~(X116 @ X139 @ X141)) | ~(X113 @ X114 @ X115)))) = lconfl) & ((^[X142 : ($i > $i > $o)] : (! [X143 : $i,X144 : ($i > $o)] : ((X144 @ X143) | ~ ! [X145 : $i] : (~ ! [X146 : $i] : ((X144 @ X146) | ~ ! [X147 : ($i > $i > $o)] : (~ ! [X148 : $i,X149 : $i,X150 : $i] : (~(X147 @ X148 @ X150) | ~(X147 @ X149 @ X148) | (X147 @ X149 @ X150)) | ~ ! [X151 : $i,X152 : $i] : ((X147 @ X151 @ X152) | ~(X142 @ X151 @ X152)) | (X147 @ X145 @ X146))) | (X144 @ X145))))) = ind) & ((^[X153 : ($i > $i > $o)] : (! [X154 : $i,X155 : $i] : (~(X153 @ X155 @ X154) | (X153 @ X154 @ X155)))) = symm) & ((^[X156 : ($i > $i > $o)] : (! [X157 : $i,X158 : $i,X159 : ($i > $i > $o),X160 : ($i > $i > $o),X161 : $i] : ((X157 = X161) | ~ ! [X162 : $i,X163 : $i] : (~(X156 @ X163 @ X162) | (X159 @ X163 @ X162)) | (X160 @ X161 @ X157) | ~ ! [X164 : $i] : (~ ! [X165 : ($i > $i > $o)] : (~ ! [X166 : $i,X167 : $i] : ((X165 @ X166 @ X167) | ~(X156 @ X166 @ X167)) | (X165 @ X161 @ X164) | ~ ! [X168 : $i,X169 : $i,X170 : $i] : ((X165 @ X169 @ X168) | ~(X165 @ X169 @ X170) | ~(X165 @ X170 @ X168))) | ~ ! [X171 : ($i > $i > $o)] : (~ ! [X172 : $i,X173 : $i,X174 : $i] : (~(X171 @ X174 @ X173) | (X171 @ X174 @ X172) | ~(X171 @ X173 @ X172)) | ~ ! [X175 : $i,X176 : $i] : ((X171 @ X175 @ X176) | ~(X156 @ X175 @ X176)) | (X171 @ X157 @ X164))) | (X159 @ X157 @ X161) | ~ ! [X177 : $i,X178 : $i] : ((X160 @ X178 @ X177) | ~(X156 @ X178 @ X177)) | ~ ! [X179 : $i,X180 : $i,X181 : $i] : ((X160 @ X179 @ X180) | ~(X160 @ X181 @ X180) | ~(X160 @ X179 @ X181)) | ~ ! [X182 : $i,X183 : $i,X184 : $i] : (~(X159 @ X182 @ X183) | ~(X159 @ X184 @ X182) | (X159 @ X184 @ X183)) | ((X157 != X158) & ~ ! [X185 : ($i > $i > $o)] : ((X185 @ X158 @ X157) | ~ ! [X186 : $i,X187 : $i,X188 : $i] : ((X185 @ X188 @ X186) | ~(X185 @ X188 @ X187) | ~(X185 @ X187 @ X186)) | ~ ! [X189 : $i,X190 : $i] : ((X185 @ X190 @ X189) | ~(X156 @ X190 @ X189)))) | (~ ! [X191 : ($i > $i > $o)] : (~ ! [X192 : $i,X193 : $i,X194 : $i] : ((X191 @ X192 @ X193) | ~(X191 @ X194 @ X193) | ~(X191 @ X192 @ X194)) | (X191 @ X158 @ X161) | ~ ! [X195 : $i,X196 : $i] : ((X191 @ X195 @ X196) | ~(X156 @ X195 @ X196))) & (X158 != X161))))) = confl) & ((^[X197 : (($i > $i > $o) > $i > $i > $o)] : (! [X198 : ($i > $i > $o)] : (((X197 @ X198)) = ((X197 @ (X197 @ X198)))))) = idem) & ! [X199 : d_unsorted] : (d_unsorted_0 = X199) & ((^[X200 : ($i > $i > $o), X201 : $i] : (! [X202 : $i] : ~(X200 @ X201 @ X202))) = innf) & (antisymm = (^[X203 : ($i > $i > $o)] : (! [X204 : $i,X205 : $i] : (~(X203 @ X205 @ X204) | (X204 = X205) | ~(X203 @ X204 @ X205))))) & (join = (^[X206 : ($i > $i > $o), X207 : $i, X208 : $i] : (~((X207 != X208) & ~ ! [X209 : ($i > $i > $o)] : (~ ! [X210 : $i,X211 : $i,X212 : $i] : ((X209 @ X210 @ X211) | ~(X209 @ X210 @ X212) | ~(X209 @ X212 @ X211)) | (X209 @ X207 @ X208) | ~ ! [X213 : $i,X214 : $i] : ((X209 @ X213 @ X214) | ~(X206 @ X213 @ X214))) & ~ ! [X215 : ($i > $i > $o)] : (~ ! [X216 : $i,X217 : $i] : ((X215 @ X217 @ X216) | ~(X206 @ X217 @ X216)) | (X215 @ X208 @ X207) | ~ ! [X218 : $i,X219 : $i,X220 : $i] : (~(X215 @ X218 @ X220) | ~(X215 @ X219 @ X218) | (X215 @ X219 @ X220))) & ! [X221 : $i] : (~ ! [X222 : ($i > $i > $o)] : (~ ! [X223 : $i,X224 : $i] : (~(X206 @ X223 @ X224) | (X222 @ X223 @ X224)) | ~ ! [X225 : $i,X226 : $i,X227 : $i] : ((X222 @ X225 @ X226) | ~(X222 @ X225 @ X227) | ~(X222 @ X227 @ X226)) | (X222 @ X207 @ X221)) | ~ ! [X228 : ($i > $i > $o)] : (~ ! [X229 : $i,X230 : $i,X231 : $i] : (~(X228 @ X229 @ X230) | ~(X228 @ X231 @ X229) | (X228 @ X231 @ X230)) | ~ ! [X232 : $i,X233 : $i] : ((X228 @ X233 @ X232) | ~(X206 @ X233 @ X232)) | (X228 @ X208 @ X221))))))) & ((^[X234 : ($i > $i > $o)] : (! [X235 : $i,X236 : $i] : ((X234 @ X236 @ X235) | (X235 = X236) | (X234 @ X235 @ X236)))) = total) & ((^[X237 : ($i > $i > $o)] : (! [X238 : $i,X239 : ($i > $i > $o),X240 : $i,X241 : ($i > $i > $o)] : (~ ! [X242 : $i] : (~ ! [X243 : ($i > $i > $o)] : (~ ! [X244 : $i,X245 : $i] : (~(X237 @ X244 @ X245) | (X243 @ X244 @ X245)) | (X243 @ X238 @ X242) | ~ ! [X246 : $i,X247 : $i,X248 : $i] : (~(X243 @ X246 @ X247) | (X243 @ X246 @ X248) | ~(X243 @ X247 @ X248))) | ~ ! [X249 : ($i > $i > $o)] : ((X249 @ X240 @ X242) | ~ ! [X250 : $i,X251 : $i,X252 : $i] : (~(X249 @ X251 @ X250) | (X249 @ X252 @ X250) | ~(X249 @ X252 @ X251)) | ~ ! [X253 : $i,X254 : $i] : (~(X237 @ X253 @ X254) | (X249 @ X253 @ X254)))) | ~ ! [X255 : $i,X256 : $i,X257 : $i] : (~(X241 @ X256 @ X255) | ~(X241 @ X255 @ X257) | (X241 @ X256 @ X257)) | (X241 @ X238 @ X240) | ~ ! [X258 : $i,X259 : $i] : (~(X237 @ X258 @ X259) | (X239 @ X258 @ X259)) | ~ ! [X260 : $i,X261 : $i,X262 : $i] : (~(X239 @ X260 @ X262) | ~(X239 @ X261 @ X260) | (X239 @ X261 @ X262)) | (X239 @ X240 @ X238) | (~ ! [X263 : ($i > $i > $o)] : (~ ! [X264 : $i,X265 : $i,X266 : $i] : (~(X263 @ X266 @ X265) | ~(X263 @ X264 @ X266) | (X263 @ X264 @ X265)) | ~ ! [X267 : $i,X268 : $i] : (~(X237 @ X268 @ X267) | (X263 @ X268 @ X267)) | (X263 @ X238 @ X240)) & ~ ! [X269 : ($i > $i > $o)] : ((X269 @ X240 @ X238) | ~ ! [X270 : $i,X271 : $i,X272 : $i] : ((X269 @ X272 @ X271) | ~(X269 @ X270 @ X271) | ~(X269 @ X272 @ X270)) | ~ ! [X273 : $i,X274 : $i] : (~(X237 @ X273 @ X274) | (X269 @ X273 @ X274))) & (X238 != X240)) | ~ ! [X275 : $i,X276 : $i] : ((X241 @ X275 @ X276) | ~(X237 @ X275 @ X276)) | (X238 = X240)))) = cr) & ((^[X277 : ($i > $i > $o)] : (! [X278 : $i,X279 : $i] : (~(X277 @ X279 @ X278) | ~(X277 @ X278 @ X279)))) = asymm) & (trc = (^[X280 : ($i > $i > $o), X281 : $i, X282 : $i] : ((X281 = X282) | ! [X283 : ($i > $i > $o)] : (~ ! [X284 : $i,X285 : $i,X286 : $i] : (~(X283 @ X285 @ X286) | (X283 @ X284 @ X286) | ~(X283 @ X284 @ X285)) | (X283 @ X281 @ X282) | ~ ! [X287 : $i,X288 : $i] : ((X283 @ X287 @ X288) | ~(X280 @ X287 @ X288)))))) & (norm = (^[X289 : ($i > $i > $o)] : (! [X290 : $i,X291 : $i] : (~ ! [X292 : $i] : (~ ! [X293 : $i] : ~(X289 @ X292 @ X293) | ~ ! [X294 : ($i > $i > $o)] : ((X294 @ X290 @ X292) | ~ ! [X295 : $i,X296 : $i,X297 : $i] : (~(X294 @ X296 @ X297) | ~(X294 @ X297 @ X295) | (X294 @ X296 @ X295)) | ~ ! [X298 : $i,X299 : $i] : ((X294 @ X298 @ X299) | ~(X289 @ X298 @ X299)))) | ~(X289 @ X290 @ X291))))) & (inv = (^[X300 : ($i > $i > $o), X301 : $i, X302 : $i] : ((X300 @ X302 @ X301)))) & ((^[X303 : ($i > $i > $o)] : (! [X304 : $i] : (X303 @ X304 @ X304) & ! [X305 : $i,X306 : $i] : ((X305 = X306) | ~(X303 @ X305 @ X306) | ~(X303 @ X306 @ X305)) & ! [X307 : $i,X308 : $i,X309 : $i] : (~(X303 @ X309 @ X308) | (X303 @ X307 @ X308) | ~(X303 @ X307 @ X309)))) = po)),
  inference(rectify,[],[f3])).
thf(f7,plain,(
  (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y3 @ Y2)))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y1 @ Y3)))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & ! [X36 : $i] : ? [X37 : d_unsorted] : (((d2unsorted @ X37)) = X36) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y7 @ Y8))) | (Y1 @ Y6 @ Y8))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (Y6 @ Y5 @ Y4))))) & (~ (Y5 = Y4)))) | (Y1 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y7 @ Y6) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y8 @ Y6))))))))))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))))))))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2))))))))) & ! [X89 : d_unsorted,X90 : d_unsorted] : ((((d2unsorted @ X90)) = ((d2unsorted @ X89))) => (X89 = X90)) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y0 @ Y1 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y2 @ Y5 @ Y6)) | (Y1 @ Y5 @ Y6)))))))) | (~ (Y0 @ Y2 @ Y3 @ Y4))))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2))))))))) & (lconfl = (^[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]: ((((((((((~ (Y0 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (Y3 @ Y7 @ Y6)) | (~ (Y3 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y8) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($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 @ Y2 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (Y1 @ Y2 @ Y4)) | (Y4 = 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]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6)))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (symm = (^[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 > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (Y6 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y7 @ Y9)))))))))) | (Y6 @ Y4 @ Y5))))) & (~ (Y5 = Y4)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y6 @ Y7) | (~ (Y3 @ Y6 @ Y8))) | (~ (Y3 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y6)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y7)))))))) | (Y3 @ Y5 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y9 @ Y10))))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))))))))))) | (Y2 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 = Y1)))))))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & ! [X199 : d_unsorted] : (d_unsorted_0 = X199) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y6) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y7 @ Y6)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y5))) | (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5)))))))))))))) & (~ (Y1 = Y2)))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2)))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y4 = Y2) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (((~ (Y4 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y2 @ Y4)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))))))))) | (Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y6 @ Y5) | (~ (Y3 @ Y6 @ Y7))) | (~ (Y3 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y1 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y6 @ Y5) | (~ (Y1 @ Y7 @ Y5))) | (~ (Y1 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9))))))))))) | (Y6 @ Y2 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))))))))))))))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5))))))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y1 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))),
  inference(fool_elimination,[],[f6])).
thf(f8,plain,(
  (ind != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
  inference(flattening,[],[f5])).
thf(f9,plain,(
  (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y6) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y7 @ Y6)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y5))) | (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5)))))))))))))) & (~ (Y1 = Y2)))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y1 @ Y3)))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y0 @ Y1 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y2 @ Y5 @ Y6)) | (Y1 @ Y5 @ Y6)))))))) | (~ (Y0 @ Y2 @ Y3 @ Y4))))))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y1 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2)))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (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]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6)))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5))))))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (Y6 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y7 @ Y9)))))))))) | (Y6 @ Y4 @ Y5))))) & (~ (Y5 = Y4)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y6 @ Y7) | (~ (Y3 @ Y6 @ Y8))) | (~ (Y3 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y6)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y7)))))))) | (Y3 @ Y5 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y9 @ Y10))))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))))))))))) | (Y2 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 = Y1)))))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $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)))))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X3)) = ((d2unsorted @ X2))) => (X2 = X3)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y3 @ Y2)))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y4 = Y2) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (((~ (Y4 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y2 @ Y4)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))))))))) | (Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y6 @ Y5) | (~ (Y3 @ Y6 @ Y7))) | (~ (Y3 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y1 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y6 @ Y5) | (~ (Y1 @ Y7 @ Y5))) | (~ (Y1 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9))))))))))) | (Y6 @ Y2 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))))))))))))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y7 @ Y8))) | (Y1 @ Y6 @ Y8))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (Y6 @ Y5 @ Y4))))) & (~ (Y5 = Y4)))) | (Y1 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y7 @ Y6) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y8 @ Y6))))))))))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))))))))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (lconfl = (^[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]: ((((((((((~ (Y0 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (Y3 @ Y7 @ Y6)) | (~ (Y3 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y8) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($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 @ Y2 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (Y1 @ Y2 @ Y4)) | (Y4 = Y2))))))))))))))),
  inference(rectify,[],[f7])).
thf(f10,plain,(
  (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (Y6 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y7 @ Y9)))))))))) | (Y6 @ Y4 @ Y5))))) & (~ (Y5 = Y4)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y6 @ Y7) | (~ (Y3 @ Y6 @ Y8))) | (~ (Y3 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y6)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y7)))))))) | (Y3 @ Y5 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y9 @ Y10))))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))))))))))) | (Y2 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 = Y1)))))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y1 @ Y3)))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2))))))))) & (lconfl = (^[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]: ((((((((((~ (Y0 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (Y3 @ Y7 @ Y6)) | (~ (Y3 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y8) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($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 @ Y2 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (Y1 @ Y2 @ Y4)) | (Y4 = Y2)))))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2))))))))) & (irrefl = (^[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]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6)))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y7 @ Y8))) | (Y1 @ Y6 @ Y8))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (Y6 @ Y5 @ Y4))))) & (~ (Y5 = Y4)))) | (Y1 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y7 @ Y6) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y8 @ Y6))))))))))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))))))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y3 @ Y2)))))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5))))))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y1 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((X2 = X3) | (((d2unsorted @ X3)) != ((d2unsorted @ X2)))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y0 @ Y1 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y2 @ Y5 @ Y6)) | (Y1 @ Y5 @ Y6)))))))) | (~ (Y0 @ Y2 @ Y3 @ Y4))))))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y4 = Y2) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (((~ (Y4 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y2 @ Y4)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))))))))) | (Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y6 @ Y5) | (~ (Y3 @ Y6 @ Y7))) | (~ (Y3 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y1 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y6 @ Y5) | (~ (Y1 @ Y7 @ Y5))) | (~ (Y1 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9))))))))))) | (Y6 @ Y2 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))))))))))))))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2)))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y6) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y7 @ Y6)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y5))) | (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5)))))))))))))) & (~ (Y1 = Y2))))))))))),
  inference(ennf_transformation,[],[f9])).
thf(f11,plain,(
  (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (Y6 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y7 @ Y9)))))))))) | (Y6 @ Y4 @ Y5))))) & (~ (Y5 = Y4)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y6 @ Y7) | (~ (Y3 @ Y6 @ Y8))) | (~ (Y3 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y6)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y7)))))))) | (Y3 @ Y5 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y9 @ Y10))))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))))))))))) | (Y2 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 = Y1)))))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y1 @ Y3)))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2))))))))) & (lconfl = (^[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]: ((((((((((~ (Y0 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (Y3 @ Y7 @ Y6)) | (~ (Y3 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y8) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($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 @ Y2 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (Y1 @ Y2 @ Y4)) | (Y4 = Y2)))))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2))))))))) & (irrefl = (^[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]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6)))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y7 @ Y8))) | (Y1 @ Y6 @ Y8))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (Y6 @ Y5 @ Y4))))) & (~ (Y5 = Y4)))) | (Y1 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y7 @ Y6) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y8 @ Y6))))))))))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))))))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y3 @ Y2)))))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5))))))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y1 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & ! [X1 : d_unsorted,X2 : d_unsorted] : ((X1 = X2) | (((d2unsorted @ X1)) != ((d2unsorted @ X2)))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y0 @ Y1 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y2 @ Y5 @ Y6)) | (Y1 @ Y5 @ Y6)))))))) | (~ (Y0 @ Y2 @ Y3 @ Y4))))))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y4 = Y2) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (((~ (Y4 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y2 @ Y4)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))))))))) | (Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y6 @ Y5) | (~ (Y3 @ Y6 @ Y7))) | (~ (Y3 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y1 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y6 @ Y5) | (~ (Y1 @ Y7 @ Y5))) | (~ (Y1 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9))))))))))) | (Y6 @ Y2 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))))))))))))))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2)))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y6) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y7 @ Y6)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y5))) | (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5)))))))))))))) & (~ (Y1 = Y2))))))))))),
  inference(rectify,[],[f10])).
thf(f12,plain,(
  (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) | (Y1 = Y2)))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (Y6 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y7 @ Y9)))))))))) | (Y6 @ Y4 @ Y5))))) & (~ (Y5 = Y4)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y6 @ Y7) | (~ (Y3 @ Y6 @ Y8))) | (~ (Y3 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y8 @ Y6)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y7)))))))) | (Y3 @ Y5 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y8))) | (Y7 @ Y9 @ Y10))))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))))))))))) | (Y2 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 = Y1)))))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y4))))))))))))) | (Y1 = Y2)))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y1 @ Y3)))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2))))))))) & (lconfl = (^[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]: ((((((((((~ (Y0 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (Y3 @ Y7 @ Y6)) | (~ (Y3 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y8) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($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 @ Y2 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y1 @ Y6 @ Y7)))))))) | (Y1 @ Y2 @ Y4)) | (Y4 = Y2)))))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2))))))))) & (irrefl = (^[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]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6)))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y7)) | (~ (Y1 @ Y7 @ Y8))) | (Y1 @ Y6 @ Y8))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y2 @ Y4 @ Y3)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y9)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (Y6 @ Y5 @ Y4))))) & (~ (Y5 = Y4)))) | (Y1 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y7 @ Y6) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y8 @ Y6))))))))))) | (Y4 = Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))))))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y3 @ Y2)))))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5))))))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y1 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & ! [X1 : d_unsorted,X2 : d_unsorted] : ((X1 = X2) | (((d2unsorted @ X1)) != ((d2unsorted @ X2)))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y0 @ Y1 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y2 @ Y5 @ Y6)) | (Y1 @ Y5 @ Y6)))))))) | (~ (Y0 @ Y2 @ Y3 @ Y4))))))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y4 = Y2) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (((~ (Y4 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y2 @ Y4)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))))))))) | (Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y6 @ Y5) | (~ (Y3 @ Y6 @ Y7))) | (~ (Y3 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y1 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y6 @ Y5) | (~ (Y1 @ Y7 @ Y5))) | (~ (Y1 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9))))))))))) | (Y6 @ Y2 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))))))))))))))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2)))))))) & ! [X3 : $i] : (((d2unsorted @ (sK0 @ X3))) = X3) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y6) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y7 @ Y6)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y5))) | (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5)))))))))))))) & (~ (Y1 = Y2))))))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,$thf(sK0 @ X3))],[f11])).
thf(f13,plain,(
  (ind != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
  inference(cnf_transformation,[],[f8])).
thf(f15,plain,(
  ( ! [X3 : $i] : ((((d2unsorted @ (sK0 @ X3))) = X3)) )),
  inference(cnf_transformation,[],[f12])).
thf(f21,plain,(
  ( ! [X0 : d_unsorted] : ((d_unsorted_0 = X0)) )),
  inference(cnf_transformation,[],[f12])).
thf(f28,plain,(
  (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f34,plain,(
  (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]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6)))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f48,plain,(
  ((^[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]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6)))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2))))))) != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y4 @ Y9 @ Y8)))))))))))))))) @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
  inference(definition_unfolding,[],[f13,f34,f28])).
thf(f49,plain,(
  ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) != (^[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]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6)))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2))))))))),
  inference(beta-eta_normalization,[],[f48])).
thf(f51,plain,(
  ( ! [X3 : $i] : ((((d2unsorted @ d_unsorted_0)) = X3)) )),
  inference(forward_demodulation,[],[f15,f21])).
thf(f60,plain,(
  ((((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) @ sK1)) != (((^[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]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6)))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2))))))) @ sK1)))),
  inference(negative_extensionality,[],[f49])).
thf(f61,plain,(
  ($true = (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) @ sK1))) | ($true = (((^[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]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6)))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2))))))) @ sK1)))),
  inference(xor_proxy_clausification,[],[f60])).
thf(f62,plain,(
  ((((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) | (~ (Y4 @ Y5 @ Y7))) | (~ (Y4 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) @ sK1)) = $false) | ($false = (((^[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]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6)))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2))))))) @ sK1)))),
  inference(xor_proxy_clausification,[],[f60])).
thf(f63,plain,(
  ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (sK1 @ Y5 @ Y4))))))))))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))))) | (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y7 @ Y5)))))))))))))) | (Y0 @ Y3))))))))) | (Y0 @ Y1))))))) = $false)),
  inference(beta-eta_normalization,[],[f62])).
thf(f64,plain,(
  (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y7 @ Y5)))))))))))))) | (Y0 @ Y3))))))))) | (Y0 @ Y1))))))) = $false) | ($false = (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (sK1 @ Y5 @ Y4))))))))))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ sK2)))),
  inference(sigma_proxy_clausification,[],[f63])).
thf(f65,plain,(
  ($false = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y7 @ Y5)))))))))))))) | (Y0 @ Y3))))))))) | (Y0 @ Y1))))) @ sK3))) | ($false = (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (sK1 @ Y5 @ Y4))))))))))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ sK2)))),
  inference(sigma_proxy_clausification,[],[f64])).
thf(f66,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))))))) | (sK3 @ Y2))))))))) | (sK3 @ Y0)))))) | ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) | (~ (Y2 @ Y3 @ Y5))) | (~ (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK1 @ Y4 @ Y3))))))))))) => (sK2 @ Y1)))) => (sK2 @ Y0)))) => (!! @ $i @ sK2))) = $false)),
  inference(beta-eta_normalization,[],[f65])).
thf(f67,plain,(
  ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) | (~ (Y2 @ Y3 @ Y5))) | (~ (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK1 @ Y4 @ Y3))))))))))) => (sK2 @ Y1)))) => (sK2 @ Y0)))) => (!! @ $i @ sK2))) = $false) | ($false = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))))))) | (sK3 @ Y2))))))))) | (sK3 @ Y0))) @ sK4)))),
  inference(sigma_proxy_clausification,[],[f66])).
thf(f68,plain,(
  ($false = ((!! @ $i @ sK2))) | ($false = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))))))) | (sK3 @ Y2))))))))) | (sK3 @ Y0))) @ sK4)))),
  inference(imp_proxy_clausification,[],[f67])).
thf(f69,plain,(
  ($false = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))))))) | (sK3 @ Y2))))))))) | (sK3 @ Y0))) @ sK4))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) | (~ (Y2 @ Y3 @ Y5))) | (~ (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK1 @ Y4 @ Y3))))))))))) => (sK2 @ Y1)))) => (sK2 @ Y0))))))),
  inference(imp_proxy_clausification,[],[f67])).
thf(f70,plain,(
  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) | (~ (Y2 @ Y3 @ Y5))) | (~ (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK1 @ Y4 @ Y3))))))))))) => (sK2 @ Y1)))) => (sK2 @ Y0))) @ X1))) | ($false = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))))))) | (sK3 @ Y2))))))))) | (sK3 @ Y0))) @ sK4)))) )),
  inference(pi_proxy_clausification,[],[f69])).
thf(f71,plain,(
  ( ! [X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (sK2 @ Y0)))) => (sK2 @ X1)))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (sK3 @ Y1))))))))) | (sK3 @ sK4))))) )),
  inference(beta-eta_normalization,[],[f70])).
thf(f72,plain,(
  ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (sK2 @ Y0))))) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (sK3 @ Y1))))))))) | (sK3 @ sK4)))) | ($true = ((sK2 @ X1)))) )),
  inference(imp_proxy_clausification,[],[f71])).
thf(f73,plain,(
  ( ! [X1 : $i] : (($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (sK3 @ Y1))))))))) | (sK3 @ sK4)))) | ($false = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (sK2 @ Y0))) @ (sK5 @ X1)))) | ($true = ((sK2 @ X1)))) )),
  inference(sigma_proxy_clausification,[],[f72])).
thf(f74,plain,(
  ( ! [X1 : $i] : ((((sK3 @ sK4)) = $false) | ($true = ((sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (sK2 @ Y0))) @ (sK5 @ X1))))) )),
  inference(or_proxy_clausification,[],[f73])).
thf(f75,plain,(
  ( ! [X1 : $i] : (($true = ((sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (sK2 @ Y0))) @ (sK5 @ X1)))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (sK3 @ Y1)))))))))))) )),
  inference(or_proxy_clausification,[],[f73])).
thf(f76,plain,(
  ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (sK3 @ Y1)))))))))) | ($true = ((sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (sK2 @ Y0))) @ (sK5 @ X1))))) )),
  inference(not_proxy_clausification,[],[f75])).
thf(f77,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X1))) | ($true = (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (sK3 @ Y1))))))) @ X2))) | ($false = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (sK2 @ Y0))) @ (sK5 @ X1))))) )),
  inference(pi_proxy_clausification,[],[f76])).
thf(f78,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = (((sK3 @ X2) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (sK3 @ Y0)))))))) | ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1))))))))))) => (sK2 @ (sK5 @ X1)))) = $false) | ($true = ((sK2 @ X1)))) )),
  inference(beta-eta_normalization,[],[f77])).
thf(f79,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1))))))))))) => (sK2 @ (sK5 @ X1)))) = $false) | ($true = ((sK2 @ X1))) | ($true = ((sK3 @ X2))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (sK3 @ Y0)))))))) )),
  inference(or_proxy_clausification,[],[f78])).
thf(f81,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK3 @ X2))) | ($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1))))))))))))) | ($true = ((sK2 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (sK3 @ Y0)))))))) )),
  inference(imp_proxy_clausification,[],[f79])).
thf(f82,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (sK3 @ Y0))))))) | ($true = ((sK2 @ X1))) | ($true = ((sK3 @ X2))) | ($true = (((^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1)))))))))) @ X3)))) )),
  inference(pi_proxy_clausification,[],[f81])).
thf(f83,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1)))))))))) @ X3))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (sK3 @ Y0))))) = $false) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1)))) )),
  inference(not_proxy_clausification,[],[f82])).
thf(f84,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1))) | ($true = (((^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1)))))))))) @ X3))) | ($false = (((^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (sK3 @ Y0))) @ (sK6 @ X2))))) )),
  inference(sigma_proxy_clausification,[],[f83])).
thf(f85,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ X1))) | ($true = ((((X3 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X3 @ Y1 @ Y2) | (~ (X3 @ Y0 @ Y2))) | (~ (X3 @ Y1 @ Y0))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0))))))))))) | ($false = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))) | (sK3 @ (sK6 @ X2))))) | ($true = ((sK3 @ X2)))) )),
  inference(beta-eta_normalization,[],[f84])).
thf(f86,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))))))) | ($false = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))) | (sK3 @ (sK6 @ X2))))) | ($true = ((sK3 @ X2))) | ($true = (((X3 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X3 @ Y1 @ Y2) | (~ (X3 @ Y0 @ Y2))) | (~ (X3 @ Y1 @ Y0)))))))))))))) )),
  inference(or_proxy_clausification,[],[f85])).
thf(f87,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X2))) | ($false = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))) | (sK3 @ (sK6 @ X2))))) | ($true = (((X3 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X3 @ Y1 @ Y2) | (~ (X3 @ Y0 @ Y2))) | (~ (X3 @ Y1 @ Y0))))))))))))) | ($true = ((sK2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))))))) )),
  inference(not_proxy_clausification,[],[f86])).
thf(f89,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X2))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0))))))))) | ($true = (((X3 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X3 @ Y1 @ Y2) | (~ (X3 @ Y0 @ Y2))) | (~ (X3 @ Y1 @ Y0))))))))))))) | ($true = ((sK2 @ X1))) | ($false = ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1))))))))))))))))) )),
  inference(or_proxy_clausification,[],[f87])).
thf(f90,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($false = ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))) @ (sK7 @ X3))) = $false) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1))) | ($true = (((X3 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X3 @ Y1 @ Y2) | (~ (X3 @ Y0 @ Y2))) | (~ (X3 @ Y1 @ Y0)))))))))))))) )),
  inference(sigma_proxy_clausification,[],[f89])).
thf(f91,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i] : (($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1))))))))))))))) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))) @ (sK7 @ X3))) = $false) | ($true = (((X3 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X3 @ Y1 @ Y2) | (~ (X3 @ Y0 @ Y2))) | (~ (X3 @ Y1 @ Y0)))))))))))))) )),
  inference(not_proxy_clausification,[],[f90])).
thf(f92,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = (((X3 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X3 @ Y1 @ Y2) | (~ (X3 @ Y0 @ Y2))) | (~ (X3 @ Y1 @ Y0))))))))))))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))) @ (sK7 @ X3))) = $false) | ($true = ((sK2 @ X1))) | ($true = (((^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))) @ X4))) | ($true = ((sK3 @ X2)))) )),
  inference(pi_proxy_clausification,[],[f91])).
thf(f93,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X3 @ Y1 @ Y2) | (~ (X3 @ Y0 @ Y2))) | (~ (X3 @ Y1 @ Y0)))))))))))) | ($true = (((^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))) @ X4))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))) @ (sK7 @ X3))) = $false) | ($true = ((sK3 @ X2)))) )),
  inference(or_proxy_clausification,[],[f92])).
thf(f94,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = (((^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))) @ X4))) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))) @ (sK7 @ X3))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X3 @ Y1 @ Y2) | (~ (X3 @ Y0 @ Y2))) | (~ (X3 @ Y1 @ Y0)))))))))) = $false)) )),
  inference(not_proxy_clausification,[],[f93])).
thf(f95,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))) @ (sK7 @ X3))) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X3 @ Y1 @ Y2) | (~ (X3 @ Y0 @ Y2))) | (~ (X3 @ Y1 @ Y0)))))))) @ (sK8 @ X3)))) | ($true = (((^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))) @ X4))) | ($true = ((sK3 @ X2))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1)))) )),
  inference(sigma_proxy_clausification,[],[f94])).
thf(f96,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X3 @ Y0 @ Y1) | (~ (X3 @ (sK8 @ X3) @ Y1))) | (~ (X3 @ Y0 @ (sK8 @ X3))))))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0 @ (sK7 @ X3)) | (~ (sK1 @ Y0 @ (sK7 @ X3))))))) = $false) | ($true = ((sK2 @ X1))) | ($true = ((((X4 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X4 @ Y1 @ Y0) | (~ (X4 @ Y1 @ Y2))) | (~ (X4 @ Y2 @ Y0))))))))))))) | ($true = ((X3 @ X1 @ (sK5 @ X1))))) )),
  inference(beta-eta_normalization,[],[f95])).
thf(f97,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ($true = ((((X4 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X4 @ Y1 @ Y0) | (~ (X4 @ Y1 @ Y2))) | (~ (X4 @ Y2 @ Y0))))))))))))) | (((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0 @ (sK7 @ X3)) | (~ (sK1 @ Y0 @ (sK7 @ X3))))))) = $false) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X3 @ Y0 @ Y1) | (~ (X3 @ (sK8 @ X3) @ Y1))) | (~ (X3 @ Y0 @ (sK8 @ X3))))))) @ (sK9 @ X3))) = $false)) )),
  inference(sigma_proxy_clausification,[],[f96])).
thf(f98,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ X1))) | ($true = ((sK3 @ X2))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = (((X4 @ X2 @ (sK6 @ X2)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0)))))))))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X3 @ Y0 @ Y1) | (~ (X3 @ (sK8 @ X3) @ Y1))) | (~ (X3 @ Y0 @ (sK8 @ X3))))))) @ (sK9 @ X3))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0 @ (sK7 @ X3)) | (~ (sK1 @ Y0 @ (sK7 @ X3))))))) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X4 @ Y1 @ Y0) | (~ (X4 @ Y1 @ Y2))) | (~ (X4 @ Y2 @ Y0))))))))))))) )),
  inference(or_proxy_clausification,[],[f97])).
thf(f99,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X3 @ Y0 @ Y1) | (~ (X3 @ (sK8 @ X3) @ Y1))) | (~ (X3 @ Y0 @ (sK8 @ X3))))))) @ (sK9 @ X3))) = $false) | ($true = ((sK2 @ X1))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X4 @ Y1 @ Y0) | (~ (X4 @ Y1 @ Y2))) | (~ (X4 @ Y2 @ Y0)))))))))))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0))))))))) | (((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0 @ (sK7 @ X3)) | (~ (sK1 @ Y0 @ (sK7 @ X3))))))) = $false)) )),
  inference(or_proxy_clausification,[],[f98])).
thf(f100,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0))))))))) | ($true = ((sK2 @ X1))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X3 @ Y0 @ Y1) | (~ (X3 @ (sK8 @ X3) @ Y1))) | (~ (X3 @ Y0 @ (sK8 @ X3))))))) @ (sK9 @ X3))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X4 @ Y1 @ Y0) | (~ (X4 @ Y1 @ Y2))) | (~ (X4 @ Y2 @ Y0))))))))))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK3 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0 @ (sK7 @ X3)) | (~ (sK1 @ Y0 @ (sK7 @ X3))))))) = $false)) )),
  inference(not_proxy_clausification,[],[f99])).
thf(f101,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X4 @ Y1 @ Y0) | (~ (X4 @ Y1 @ Y2))) | (~ (X4 @ Y2 @ Y0))))))))))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1))) | (((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0 @ (sK7 @ X3)) | (~ (sK1 @ Y0 @ (sK7 @ X3))))))) = $false) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X3 @ Y0 @ Y1) | (~ (X3 @ (sK8 @ X3) @ Y1))) | (~ (X3 @ Y0 @ (sK8 @ X3))))))) @ (sK9 @ X3))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0)))))))) | ($true = ((X4 @ X2 @ (sK6 @ X2))))) )),
  inference(not_proxy_clausification,[],[f100])).
thf(f102,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0 @ (sK7 @ X3)) | (~ (sK1 @ Y0 @ (sK7 @ X3))))))) = $false) | ($true = ((sK2 @ X1))) | ($true = ((sK3 @ X2))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X3 @ Y0 @ Y1) | (~ (X3 @ (sK8 @ X3) @ Y1))) | (~ (X3 @ Y0 @ (sK8 @ X3))))))) @ (sK9 @ X3))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0)))))))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X4 @ Y1 @ Y0) | (~ (X4 @ Y1 @ Y2))) | (~ (X4 @ Y2 @ Y0)))))))) @ (sK10 @ X4)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((X3 @ X1 @ (sK5 @ X1))))) )),
  inference(sigma_proxy_clausification,[],[f101])).
thf(f103,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X4 @ Y1 @ Y0) | (~ (X4 @ Y1 @ Y2))) | (~ (X4 @ Y2 @ Y0)))))))) @ (sK10 @ X4)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0)))))))) | ($true = ((sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((X3 @ Y0 @ (sK7 @ X3)) | (~ (sK1 @ Y0 @ (sK7 @ X3))))) @ (sK11 @ X3)))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK3 @ X2))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X3 @ Y0 @ Y1) | (~ (X3 @ (sK8 @ X3) @ Y1))) | (~ (X3 @ Y0 @ (sK8 @ X3))))))) @ (sK9 @ X3))) = $false)) )),
  inference(sigma_proxy_clausification,[],[f102])).
thf(f104,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = (((^[Y0 : $i]: ((X3 @ Y0 @ (sK7 @ X3)) | (~ (sK1 @ Y0 @ (sK7 @ X3))))) @ (sK11 @ X3)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X4 @ Y1 @ Y0))))) @ (sK12 @ X4))) = $false) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X4 @ Y1 @ Y0) | (~ (X4 @ Y1 @ Y2))) | (~ (X4 @ Y2 @ Y0)))))))) @ (sK10 @ X4)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X3 @ Y0 @ Y1) | (~ (X3 @ (sK8 @ X3) @ Y1))) | (~ (X3 @ Y0 @ (sK8 @ X3))))))) @ (sK9 @ X3))) = $false)) )),
  inference(sigma_proxy_clausification,[],[f103])).
thf(f105,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK12 @ X4))) | (X4 @ Y0 @ (sK12 @ X4)))))) = $false) | ((((X3 @ (sK11 @ X3) @ (sK7 @ X3)) | (~ (sK1 @ (sK11 @ X3) @ (sK7 @ X3))))) = $false) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | (((!! @ $i @ (^[Y0 : $i]: (((X3 @ (sK9 @ X3) @ Y0) | (~ (X3 @ (sK8 @ X3) @ Y0))) | (~ (X3 @ (sK9 @ X3) @ (sK8 @ X3))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X4 @ Y0 @ (sK10 @ X4)) | (~ (X4 @ Y0 @ Y1))) | (~ (X4 @ Y1 @ (sK10 @ X4)))))))))) | ($true = ((X3 @ X1 @ (sK5 @ X1))))) )),
  inference(beta-eta_normalization,[],[f104])).
thf(f106,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ((((X3 @ (sK11 @ X3) @ (sK7 @ X3)) | (~ (sK1 @ (sK11 @ X3) @ (sK7 @ X3))))) = $false) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X4 @ Y0 @ (sK10 @ X4)) | (~ (X4 @ Y0 @ Y1))) | (~ (X4 @ Y1 @ (sK10 @ X4)))))))))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | (((!! @ $i @ (^[Y0 : $i]: (((X3 @ (sK9 @ X3) @ Y0) | (~ (X3 @ (sK8 @ X3) @ Y0))) | (~ (X3 @ (sK9 @ X3) @ (sK8 @ X3))))))) = $false) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK12 @ X4))) | (X4 @ Y0 @ (sK12 @ X4)))) @ (sK13 @ X4)))) | ($true = ((sK2 @ X1)))) )),
  inference(sigma_proxy_clausification,[],[f105])).
thf(f107,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK12 @ X4))) | (X4 @ Y0 @ (sK12 @ X4)))) @ (sK13 @ X4)))) | ($true = ((sK3 @ X2))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X4 @ Y0 @ (sK10 @ X4)) | (~ (X4 @ Y0 @ Y1))) | (~ (X4 @ Y1 @ (sK10 @ X4)))))))))) | ($true = ((sK2 @ X1))) | ($false = ((~ (sK1 @ (sK11 @ X3) @ (sK7 @ X3))))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | (((!! @ $i @ (^[Y0 : $i]: (((X3 @ (sK9 @ X3) @ Y0) | (~ (X3 @ (sK8 @ X3) @ Y0))) | (~ (X3 @ (sK9 @ X3) @ (sK8 @ X3))))))) = $false)) )),
  inference(or_proxy_clausification,[],[f106])).
thf(f171,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = ((~ (sK1 @ (sK11 @ X3) @ (sK7 @ X3))))) | (((!! @ $i @ (^[Y0 : $i]: (((X3 @ (sK9 @ X3) @ Y0) | (~ (X3 @ (sK8 @ X3) @ Y0))) | (~ (X3 @ (sK9 @ X3) @ (sK8 @ X3))))))) = $false) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK12 @ X4))) | (X4 @ Y0 @ (sK12 @ X4)))) @ (sK13 @ X4)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X4 @ Y0 @ (sK10 @ X4)) | (~ (X4 @ Y0 @ Y1))) | (~ (X4 @ Y1 @ (sK10 @ X4))))))) @ (sK17 @ X4))))) )),
  inference(sigma_proxy_clausification,[],[f107])).
thf(f172,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X4 @ Y0 @ (sK10 @ X4)) | (~ (X4 @ Y0 @ Y1))) | (~ (X4 @ Y1 @ (sK10 @ X4))))))) @ (sK17 @ X4)))) | ($true = ((sK3 @ X2))) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK12 @ X4))) | (X4 @ Y0 @ (sK12 @ X4)))) @ (sK13 @ X4)))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1))) | (((!! @ $i @ (^[Y0 : $i]: (((X3 @ (sK9 @ X3) @ Y0) | (~ (X3 @ (sK8 @ X3) @ Y0))) | (~ (X3 @ (sK9 @ X3) @ (sK8 @ X3))))))) = $false)) )),
  inference(not_proxy_clausification,[],[f171])).
thf(f173,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($false = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK12 @ X4))) | (X4 @ Y0 @ (sK12 @ X4)))) @ (sK13 @ X4)))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X4 @ Y0 @ (sK10 @ X4)) | (~ (X4 @ Y0 @ Y1))) | (~ (X4 @ Y1 @ (sK10 @ X4))))))) @ (sK17 @ X4)))) | ((((^[Y0 : $i]: (((X3 @ (sK9 @ X3) @ Y0) | (~ (X3 @ (sK8 @ X3) @ Y0))) | (~ (X3 @ (sK9 @ X3) @ (sK8 @ X3))))) @ (sK18 @ X3))) = $false) | ($true = ((X4 @ X2 @ (sK6 @ X2))))) )),
  inference(sigma_proxy_clausification,[],[f172])).
thf(f174,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ X1))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK3 @ X2))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($false = ((((X3 @ (sK9 @ X3) @ (sK18 @ X3)) | (~ (X3 @ (sK8 @ X3) @ (sK18 @ X3)))) | (~ (X3 @ (sK9 @ X3) @ (sK8 @ X3)))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ Y0))) | (~ (X4 @ Y0 @ (sK10 @ X4)))))))) | ((((~ (sK1 @ (sK13 @ X4) @ (sK12 @ X4))) | (X4 @ (sK13 @ X4) @ (sK12 @ X4)))) = $false)) )),
  inference(beta-eta_normalization,[],[f173])).
thf(f175,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ Y0))) | (~ (X4 @ Y0 @ (sK10 @ X4)))))))) | ((((~ (sK1 @ (sK13 @ X4) @ (sK12 @ X4))) | (X4 @ (sK13 @ X4) @ (sK12 @ X4)))) = $false) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | (((~ (X3 @ (sK9 @ X3) @ (sK8 @ X3)))) = $false)) )),
  inference(or_proxy_clausification,[],[f174])).
thf(f176,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ((((~ (sK1 @ (sK13 @ X4) @ (sK12 @ X4))) | (X4 @ (sK13 @ X4) @ (sK12 @ X4)))) = $false) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ((((X3 @ (sK9 @ X3) @ (sK18 @ X3)) | (~ (X3 @ (sK8 @ X3) @ (sK18 @ X3))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ Y0))) | (~ (X4 @ Y0 @ (sK10 @ X4)))))))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1)))) )),
  inference(or_proxy_clausification,[],[f174])).
thf(f178,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ X1))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ Y0))) | (~ (X4 @ Y0 @ (sK10 @ X4)))))))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($false = ((~ (sK1 @ (sK13 @ X4) @ (sK12 @ X4))))) | ((((X3 @ (sK9 @ X3) @ (sK18 @ X3)) | (~ (X3 @ (sK8 @ X3) @ (sK18 @ X3))))) = $false) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK3 @ X2)))) )),
  inference(or_proxy_clausification,[],[f176])).
thf(f179,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($false = ((~ (sK1 @ (sK13 @ X4) @ (sK12 @ X4))))) | ($true = ((sK3 @ X2))) | ((((^[Y0 : $i]: (((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ Y0))) | (~ (X4 @ Y0 @ (sK10 @ X4))))) @ (sK19 @ X4))) = $false) | ($true = ((sK2 @ X1))) | ((((X3 @ (sK9 @ X3) @ (sK18 @ X3)) | (~ (X3 @ (sK8 @ X3) @ (sK18 @ X3))))) = $false) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3))))) )),
  inference(sigma_proxy_clausification,[],[f178])).
thf(f180,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ((((^[Y0 : $i]: (((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ Y0))) | (~ (X4 @ Y0 @ (sK10 @ X4))))) @ (sK19 @ X4))) = $false) | ($true = ((sK2 @ X1))) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK3 @ X2))) | ((((X3 @ (sK9 @ X3) @ (sK18 @ X3)) | (~ (X3 @ (sK8 @ X3) @ (sK18 @ X3))))) = $false) | ($true = ((X4 @ X2 @ (sK6 @ X2))))) )),
  inference(not_proxy_clausification,[],[f179])).
thf(f182,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (((((^[Y0 : $i]: (((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ Y0))) | (~ (X4 @ Y0 @ (sK10 @ X4))))) @ (sK19 @ X4))) = $false) | (((X3 @ (sK9 @ X3) @ (sK18 @ X3))) = $false) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK2 @ X1))) | ($true = ((sK3 @ X2))) | ($true = ((X3 @ X1 @ (sK5 @ X1))))) )),
  inference(or_proxy_clausification,[],[f180])).
thf(f183,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ (sK19 @ X4)))) | (~ (X4 @ (sK19 @ X4) @ (sK10 @ X4))))) = $false) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK3 @ X2))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((sK2 @ X1))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | (((X3 @ (sK9 @ X3) @ (sK18 @ X3))) = $false) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4))))) )),
  inference(beta-eta_normalization,[],[f182])).
thf(f184,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | (((~ (X4 @ (sK19 @ X4) @ (sK10 @ X4)))) = $false) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | (((X3 @ (sK9 @ X3) @ (sK18 @ X3))) = $false) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1)))) )),
  inference(or_proxy_clausification,[],[f183])).
thf(f189,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X3 @ X1 @ (sK5 @ X1)))) | (((X3 @ (sK9 @ X3) @ (sK18 @ X3))) = $false) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK2 @ X1))) | ($true = ((X4 @ (sK19 @ X4) @ (sK10 @ X4))))) )),
  inference(not_proxy_clausification,[],[f184])).
thf(f217,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ X1))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK3 @ X2))) | ((((^[Y0 : $i]: (((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ Y0))) | (~ (X4 @ Y0 @ (sK10 @ X4))))) @ (sK22 @ X4))) = $false) | (((~ (X3 @ (sK9 @ X3) @ (sK8 @ X3)))) = $false) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ((((~ (sK1 @ (sK13 @ X4) @ (sK12 @ X4))) | (X4 @ (sK13 @ X4) @ (sK12 @ X4)))) = $false) | ($true = ((X3 @ X1 @ (sK5 @ X1))))) )),
  inference(sigma_proxy_clausification,[],[f175])).
thf(f218,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ X1))) | ((((^[Y0 : $i]: (((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ Y0))) | (~ (X4 @ Y0 @ (sK10 @ X4))))) @ (sK22 @ X4))) = $false) | ((((~ (sK1 @ (sK13 @ X4) @ (sK12 @ X4))) | (X4 @ (sK13 @ X4) @ (sK12 @ X4)))) = $false) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((X3 @ (sK9 @ X3) @ (sK8 @ X3))))) )),
  inference(not_proxy_clausification,[],[f217])).
thf(f220,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($false = ((~ (sK1 @ (sK13 @ X4) @ (sK12 @ X4))))) | ($true = ((sK2 @ X1))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((X3 @ (sK9 @ X3) @ (sK8 @ X3)))) | ((((^[Y0 : $i]: (((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ Y0))) | (~ (X4 @ Y0 @ (sK10 @ X4))))) @ (sK22 @ X4))) = $false) | ($true = ((sK3 @ X2))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3))))) )),
  inference(or_proxy_clausification,[],[f218])).
thf(f221,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (((((^[Y0 : $i]: (((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ Y0))) | (~ (X4 @ Y0 @ (sK10 @ X4))))) @ (sK22 @ X4))) = $false) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((sK2 @ X1))) | ($true = ((X3 @ (sK9 @ X3) @ (sK8 @ X3))))) )),
  inference(not_proxy_clausification,[],[f220])).
thf(f222,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($false = ((((X4 @ (sK17 @ X4) @ (sK10 @ X4)) | (~ (X4 @ (sK17 @ X4) @ (sK22 @ X4)))) | (~ (X4 @ (sK22 @ X4) @ (sK10 @ X4)))))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((X3 @ (sK9 @ X3) @ (sK8 @ X3)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1))) | ($true = ((sK3 @ X2))) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4))))) )),
  inference(beta-eta_normalization,[],[f221])).
thf(f223,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK3 @ X2))) | (((~ (X4 @ (sK22 @ X4) @ (sK10 @ X4)))) = $false) | ($true = ((sK2 @ X1))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((X3 @ (sK9 @ X3) @ (sK8 @ X3)))) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4))))) )),
  inference(or_proxy_clausification,[],[f222])).
thf(f228,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X3 @ (sK9 @ X3) @ (sK8 @ X3)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((sK2 @ X1))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK3 @ X2))) | ($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((X4 @ (sK22 @ X4) @ (sK10 @ X4)))) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4))))) )),
  inference(not_proxy_clausification,[],[f223])).
thf(f298,plain,(
  ( ! [X1 : $i] : ((((sK3 @ sK4)) = $false) | ($true = ((sK2 @ X1))) | ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1))))))))))) => (sK2 @ (sK5 @ X1)))) = $false)) )),
  inference(beta-eta_normalization,[],[f74])).
thf(f300,plain,(
  ( ! [X1 : $i] : (($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1))))))))))))) | ($true = ((sK2 @ X1))) | (((sK3 @ sK4)) = $false)) )),
  inference(imp_proxy_clausification,[],[f298])).
thf(f301,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ X1))) | (((sK3 @ sK4)) = $false) | ($true = (((^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1)))))))))) @ X2)))) )),
  inference(pi_proxy_clausification,[],[f300])).
thf(f302,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((((X2 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y2) | (~ (X2 @ Y0 @ Y2))) | (~ (X2 @ Y1 @ Y0))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0))))))))))) | (((sK3 @ sK4)) = $false) | ($true = ((sK2 @ X1)))) )),
  inference(beta-eta_normalization,[],[f301])).
thf(f303,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = (((X2 @ X1 @ (sK5 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y2) | (~ (X2 @ Y0 @ Y2))) | (~ (X2 @ Y1 @ Y0))))))))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))))))) | ($true = ((sK2 @ X1))) | (((sK3 @ sK4)) = $false)) )),
  inference(or_proxy_clausification,[],[f302])).
thf(f304,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y2) | (~ (X2 @ Y0 @ Y2))) | (~ (X2 @ Y1 @ Y0)))))))))))) | (((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1)))) )),
  inference(or_proxy_clausification,[],[f303])).
thf(f305,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))))) = $false) | ($true = ((sK2 @ X1))) | (((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y2) | (~ (X2 @ Y0 @ Y2))) | (~ (X2 @ Y1 @ Y0))))))))))))) )),
  inference(not_proxy_clausification,[],[f304])).
thf(f306,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y2) | (~ (X2 @ Y0 @ Y2))) | (~ (X2 @ Y1 @ Y0)))))))))))) | (((sK3 @ sK4)) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))) @ (sK34 @ X2))))) )),
  inference(sigma_proxy_clausification,[],[f305])).
thf(f307,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y2) | (~ (X2 @ Y0 @ Y2))) | (~ (X2 @ Y1 @ Y0))))))))))) | (((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))) @ (sK34 @ X2)))) | ($true = ((sK2 @ X1)))) )),
  inference(not_proxy_clausification,[],[f306])).
thf(f308,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y2) | (~ (X2 @ Y0 @ Y2))) | (~ (X2 @ Y1 @ Y0)))))))) @ (sK35 @ X2))) = $false) | (((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))) @ (sK34 @ X2))))) )),
  inference(sigma_proxy_clausification,[],[f307])).
thf(f309,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X2 @ Y0 @ Y1) | (~ (X2 @ (sK35 @ X2) @ Y1))) | (~ (X2 @ Y0 @ (sK35 @ X2)))))))))) | (((sK3 @ sK4)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0 @ (sK34 @ X2)) | (~ (sK1 @ Y0 @ (sK34 @ X2))))))) = $false) | ($true = ((sK2 @ X1))) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
  inference(beta-eta_normalization,[],[f308])).
thf(f310,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0 @ (sK34 @ X2)) | (~ (sK1 @ Y0 @ (sK34 @ X2))))))) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X2 @ Y0 @ Y1) | (~ (X2 @ (sK35 @ X2) @ Y1))) | (~ (X2 @ Y0 @ (sK35 @ X2))))))) @ (sK36 @ X2)))) | ($true = ((sK2 @ X1))) | (((sK3 @ sK4)) = $false)) )),
  inference(sigma_proxy_clausification,[],[f309])).
thf(f311,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK3 @ sK4)) = $false) | ($false = (((^[Y0 : $i]: ((X2 @ Y0 @ (sK34 @ X2)) | (~ (sK1 @ Y0 @ (sK34 @ X2))))) @ (sK37 @ X2)))) | ($true = ((sK2 @ X1))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X2 @ Y0 @ Y1) | (~ (X2 @ (sK35 @ X2) @ Y1))) | (~ (X2 @ Y0 @ (sK35 @ X2))))))) @ (sK36 @ X2))))) )),
  inference(sigma_proxy_clausification,[],[f310])).
thf(f312,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: (((X2 @ (sK36 @ X2) @ Y0) | (~ (X2 @ (sK35 @ X2) @ Y0))) | (~ (X2 @ (sK36 @ X2) @ (sK35 @ X2)))))))) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ((((X2 @ (sK37 @ X2) @ (sK34 @ X2)) | (~ (sK1 @ (sK37 @ X2) @ (sK34 @ X2))))) = $false) | (((sK3 @ sK4)) = $false) | ($true = ((sK2 @ X1)))) )),
  inference(beta-eta_normalization,[],[f311])).
thf(f313,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ X1))) | (((sK3 @ sK4)) = $false) | ($false = (((^[Y0 : $i]: (((X2 @ (sK36 @ X2) @ Y0) | (~ (X2 @ (sK35 @ X2) @ Y0))) | (~ (X2 @ (sK36 @ X2) @ (sK35 @ X2))))) @ (sK38 @ X2)))) | ((((X2 @ (sK37 @ X2) @ (sK34 @ X2)) | (~ (sK1 @ (sK37 @ X2) @ (sK34 @ X2))))) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
  inference(sigma_proxy_clausification,[],[f312])).
thf(f314,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ X1))) | ($false = ((~ (sK1 @ (sK37 @ X2) @ (sK34 @ X2))))) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($false = (((^[Y0 : $i]: (((X2 @ (sK36 @ X2) @ Y0) | (~ (X2 @ (sK35 @ X2) @ Y0))) | (~ (X2 @ (sK36 @ X2) @ (sK35 @ X2))))) @ (sK38 @ X2)))) | (((sK3 @ sK4)) = $false)) )),
  inference(or_proxy_clausification,[],[f313])).
thf(f315,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: (((X2 @ (sK36 @ X2) @ Y0) | (~ (X2 @ (sK35 @ X2) @ Y0))) | (~ (X2 @ (sK36 @ X2) @ (sK35 @ X2))))) @ (sK38 @ X2)))) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK3 @ sK4)) = $false) | ($false = ((X2 @ (sK37 @ X2) @ (sK34 @ X2)))) | ($true = ((sK2 @ X1)))) )),
  inference(or_proxy_clausification,[],[f313])).
thf(f316,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK3 @ sK4)) = $false) | ($false = ((X2 @ (sK37 @ X2) @ (sK34 @ X2)))) | ($false = ((((X2 @ (sK36 @ X2) @ (sK38 @ X2)) | (~ (X2 @ (sK35 @ X2) @ (sK38 @ X2)))) | (~ (X2 @ (sK36 @ X2) @ (sK35 @ X2)))))) | ($true = ((sK2 @ X1))) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
  inference(beta-eta_normalization,[],[f315])).
thf(f318,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ X1))) | ($false = (((X2 @ (sK36 @ X2) @ (sK38 @ X2)) | (~ (X2 @ (sK35 @ X2) @ (sK38 @ X2)))))) | (((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($false = ((X2 @ (sK37 @ X2) @ (sK34 @ X2))))) )),
  inference(or_proxy_clausification,[],[f316])).
thf(f320,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($false = ((X2 @ (sK37 @ X2) @ (sK34 @ X2)))) | ($true = ((sK2 @ X1))) | (((sK3 @ sK4)) = $false) | ($false = ((X2 @ (sK36 @ X2) @ (sK38 @ X2))))) )),
  inference(or_proxy_clausification,[],[f318])).
thf(f323,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK5 @ X1)))) | (((sK3 @ sK4)) = $false) | ($true = ((sK2 @ X1))) | ($false = (((^[Y0 : $i]: (((X2 @ (sK36 @ X2) @ Y0) | (~ (X2 @ (sK35 @ X2) @ Y0))) | (~ (X2 @ (sK36 @ X2) @ (sK35 @ X2))))) @ (sK38 @ X2)))) | ($true = ((sK1 @ (sK37 @ X2) @ (sK34 @ X2))))) )),
  inference(not_proxy_clausification,[],[f314])).
thf(f324,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($false = ((((X2 @ (sK36 @ X2) @ (sK38 @ X2)) | (~ (X2 @ (sK35 @ X2) @ (sK38 @ X2)))) | (~ (X2 @ (sK36 @ X2) @ (sK35 @ X2)))))) | ($true = ((sK1 @ (sK37 @ X2) @ (sK34 @ X2)))) | ($true = ((sK2 @ X1)))) )),
  inference(beta-eta_normalization,[],[f323])).
thf(f325,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($true = ((sK1 @ (sK37 @ X2) @ (sK34 @ X2)))) | ($true = ((sK2 @ X1))) | ($false = ((~ (X2 @ (sK36 @ X2) @ (sK35 @ X2)))))) )),
  inference(or_proxy_clausification,[],[f324])).
thf(f330,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (sK36 @ X2) @ (sK35 @ X2)))) | (((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1))) | ($true = ((sK1 @ (sK37 @ X2) @ (sK34 @ X2))))) )),
  inference(not_proxy_clausification,[],[f325])).
thf(f331,plain,(
  (((sK2 @ sK39)) = $false) | ($false = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))))))) | (sK3 @ Y2))))))))) | (sK3 @ Y0))) @ sK4)))),
  inference(sigma_proxy_clausification,[],[f68])).
thf(f332,plain,(
  ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (sK3 @ Y1))))))))) | (sK3 @ sK4)))) | (((sK2 @ sK39)) = $false)),
  inference(beta-eta_normalization,[],[f331])).
thf(f333,plain,(
  (((sK3 @ sK4)) = $false) | (((sK2 @ sK39)) = $false)),
  inference(or_proxy_clausification,[],[f332])).
thf(f334,plain,(
  (((sK2 @ sK39)) = $false) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (sK3 @ Y1)))))))))))),
  inference(or_proxy_clausification,[],[f332])).
thf(f335,plain,(
  ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (sK3 @ Y1)))))))))) | (((sK2 @ sK39)) = $false)),
  inference(not_proxy_clausification,[],[f334])).
thf(f336,plain,(
  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (sK3 @ Y1))))))) @ X1))) | (((sK2 @ sK39)) = $false)) )),
  inference(pi_proxy_clausification,[],[f335])).
thf(f337,plain,(
  ( ! [X1 : $i] : (($true = (((sK3 @ X1) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (sK3 @ Y0)))))))) | (((sK2 @ sK39)) = $false)) )),
  inference(beta-eta_normalization,[],[f336])).
thf(f338,plain,(
  ( ! [X1 : $i] : (($true = ((sK3 @ X1))) | (((sK2 @ sK39)) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (sK3 @ Y0)))))))) )),
  inference(or_proxy_clausification,[],[f337])).
thf(f339,plain,(
  ( ! [X1 : $i] : ((((sK2 @ sK39)) = $false) | ($true = ((sK3 @ X1))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (sK3 @ Y0))))) = $false)) )),
  inference(not_proxy_clausification,[],[f338])).
thf(f340,plain,(
  ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (sK3 @ Y0))) @ (sK40 @ X1)))) | (((sK2 @ sK39)) = $false) | ($true = ((sK3 @ X1)))) )),
  inference(sigma_proxy_clausification,[],[f339])).
thf(f341,plain,(
  ( ! [X1 : $i] : (($false = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK40 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))) | (sK3 @ (sK40 @ X1))))) | ($true = ((sK3 @ X1))) | (((sK2 @ sK39)) = $false)) )),
  inference(beta-eta_normalization,[],[f340])).
thf(f343,plain,(
  ( ! [X1 : $i] : ((((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK40 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1))))))))))))))) = $false) | ($true = ((sK3 @ X1))) | (((sK2 @ sK39)) = $false)) )),
  inference(or_proxy_clausification,[],[f341])).
thf(f344,plain,(
  ( ! [X1 : $i] : (($true = ((sK3 @ X1))) | ($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK40 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1))))))))))))))) | (((sK2 @ sK39)) = $false)) )),
  inference(not_proxy_clausification,[],[f343])).
thf(f345,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $i > $o]: (((Y0 @ X1 @ (sK40 @ X1)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))) @ X2))) | ($true = ((sK3 @ X1))) | (((sK2 @ sK39)) = $false)) )),
  inference(pi_proxy_clausification,[],[f344])).
thf(f346,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | (((sK2 @ sK39)) = $false) | ($true = ((((X2 @ X1 @ (sK40 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y0) | (~ (X2 @ Y1 @ Y2))) | (~ (X2 @ Y2 @ Y0)))))))))))))) )),
  inference(beta-eta_normalization,[],[f345])).
thf(f347,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y0) | (~ (X2 @ Y1 @ Y2))) | (~ (X2 @ Y2 @ Y0)))))))))))) | (((sK2 @ sK39)) = $false) | ($true = (((X2 @ X1 @ (sK40 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0)))))))))) | ($true = ((sK3 @ X1)))) )),
  inference(or_proxy_clausification,[],[f346])).
thf(f348,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = (((X2 @ X1 @ (sK40 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0)))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y0) | (~ (X2 @ Y1 @ Y2))) | (~ (X2 @ Y2 @ Y0))))))))))) | (((sK2 @ sK39)) = $false) | ($true = ((sK3 @ X1)))) )),
  inference(not_proxy_clausification,[],[f347])).
thf(f349,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y0) | (~ (X2 @ Y1 @ Y2))) | (~ (X2 @ Y2 @ Y0))))))))))) | ($true = ((sK3 @ X1))) | ($true = ((X2 @ X1 @ (sK40 @ X1)))) | (((sK2 @ sK39)) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0)))))))))) )),
  inference(or_proxy_clausification,[],[f348])).
thf(f350,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y0) | (~ (X2 @ Y1 @ Y2))) | (~ (X2 @ Y2 @ Y0)))))))) @ (sK41 @ X2))) = $false) | ($true = ((X2 @ X1 @ (sK40 @ X1)))) | (((sK2 @ sK39)) = $false) | ($true = ((sK3 @ X1))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0)))))))))) )),
  inference(sigma_proxy_clausification,[],[f349])).
thf(f351,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | ($true = ((X2 @ X1 @ (sK40 @ X1)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y0) | (~ (X2 @ Y1 @ Y2))) | (~ (X2 @ Y2 @ Y0)))))))) @ (sK41 @ X2))) = $false) | (((sK2 @ sK39)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0))))))))) )),
  inference(not_proxy_clausification,[],[f350])).
thf(f352,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | (((sK2 @ sK39)) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (X2 @ Y1 @ Y0))))) @ (sK42 @ X2)))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X2 @ Y1 @ Y0) | (~ (X2 @ Y1 @ Y2))) | (~ (X2 @ Y2 @ Y0)))))))) @ (sK41 @ X2))) = $false) | ($true = ((X2 @ X1 @ (sK40 @ X1))))) )),
  inference(sigma_proxy_clausification,[],[f351])).
thf(f353,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK40 @ X1)))) | ($true = ((sK3 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK42 @ X2))) | (X2 @ Y0 @ (sK42 @ X2))))))) | (((sK2 @ sK39)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X2 @ Y0 @ (sK41 @ X2)) | (~ (X2 @ Y0 @ Y1))) | (~ (X2 @ Y1 @ (sK41 @ X2))))))))))) )),
  inference(beta-eta_normalization,[],[f352])).
thf(f354,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | (((sK2 @ sK39)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X2 @ Y0 @ (sK41 @ X2)) | (~ (X2 @ Y0 @ Y1))) | (~ (X2 @ Y1 @ (sK41 @ X2)))))))))) | ($true = ((X2 @ X1 @ (sK40 @ X1)))) | ((((^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK42 @ X2))) | (X2 @ Y0 @ (sK42 @ X2)))) @ (sK43 @ X2))) = $false)) )),
  inference(sigma_proxy_clausification,[],[f353])).
thf(f355,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (((((^[Y0 : $i]: ((~ (sK1 @ Y0 @ (sK42 @ X2))) | (X2 @ Y0 @ (sK42 @ X2)))) @ (sK43 @ X2))) = $false) | ($true = ((sK3 @ X1))) | (((sK2 @ sK39)) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X2 @ Y0 @ (sK41 @ X2)) | (~ (X2 @ Y0 @ Y1))) | (~ (X2 @ Y1 @ (sK41 @ X2))))))) @ (sK44 @ X2)))) | ($true = ((X2 @ X1 @ (sK40 @ X1))))) )),
  inference(sigma_proxy_clausification,[],[f354])).
thf(f356,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK40 @ X1)))) | (((!! @ $i @ (^[Y0 : $i]: (((X2 @ (sK44 @ X2) @ (sK41 @ X2)) | (~ (X2 @ (sK44 @ X2) @ Y0))) | (~ (X2 @ Y0 @ (sK41 @ X2))))))) = $false) | ($true = ((sK3 @ X1))) | (((sK2 @ sK39)) = $false) | ($false = (((~ (sK1 @ (sK43 @ X2) @ (sK42 @ X2))) | (X2 @ (sK43 @ X2) @ (sK42 @ X2)))))) )),
  inference(beta-eta_normalization,[],[f355])).
thf(f357,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK40 @ X1)))) | ($true = ((sK3 @ X1))) | ((((^[Y0 : $i]: (((X2 @ (sK44 @ X2) @ (sK41 @ X2)) | (~ (X2 @ (sK44 @ X2) @ Y0))) | (~ (X2 @ Y0 @ (sK41 @ X2))))) @ (sK45 @ X2))) = $false) | (((sK2 @ sK39)) = $false) | ($false = (((~ (sK1 @ (sK43 @ X2) @ (sK42 @ X2))) | (X2 @ (sK43 @ X2) @ (sK42 @ X2)))))) )),
  inference(sigma_proxy_clausification,[],[f356])).
thf(f359,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (((((^[Y0 : $i]: (((X2 @ (sK44 @ X2) @ (sK41 @ X2)) | (~ (X2 @ (sK44 @ X2) @ Y0))) | (~ (X2 @ Y0 @ (sK41 @ X2))))) @ (sK45 @ X2))) = $false) | ($true = ((sK3 @ X1))) | (((~ (sK1 @ (sK43 @ X2) @ (sK42 @ X2)))) = $false) | ($true = ((X2 @ X1 @ (sK40 @ X1)))) | (((sK2 @ sK39)) = $false)) )),
  inference(or_proxy_clausification,[],[f357])).
thf(f360,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (sK40 @ X1)))) | ($true = ((sK1 @ (sK43 @ X2) @ (sK42 @ X2)))) | (((sK2 @ sK39)) = $false) | ((((^[Y0 : $i]: (((X2 @ (sK44 @ X2) @ (sK41 @ X2)) | (~ (X2 @ (sK44 @ X2) @ Y0))) | (~ (X2 @ Y0 @ (sK41 @ X2))))) @ (sK45 @ X2))) = $false) | ($true = ((sK3 @ X1)))) )),
  inference(not_proxy_clausification,[],[f359])).
thf(f361,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | ($true = ((sK1 @ (sK43 @ X2) @ (sK42 @ X2)))) | ($true = ((X2 @ X1 @ (sK40 @ X1)))) | ($false = ((((X2 @ (sK44 @ X2) @ (sK41 @ X2)) | (~ (X2 @ (sK44 @ X2) @ (sK45 @ X2)))) | (~ (X2 @ (sK45 @ X2) @ (sK41 @ X2)))))) | (((sK2 @ sK39)) = $false)) )),
  inference(beta-eta_normalization,[],[f360])).
thf(f362,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | (((sK2 @ sK39)) = $false) | ($true = ((X2 @ X1 @ (sK40 @ X1)))) | ($true = ((sK1 @ (sK43 @ X2) @ (sK42 @ X2)))) | ($false = ((~ (X2 @ (sK45 @ X2) @ (sK41 @ X2)))))) )),
  inference(or_proxy_clausification,[],[f361])).
thf(f367,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | ($true = ((X2 @ (sK45 @ X2) @ (sK41 @ X2)))) | ($true = ((sK1 @ (sK43 @ X2) @ (sK42 @ X2)))) | ($true = ((X2 @ X1 @ (sK40 @ X1)))) | (((sK2 @ sK39)) = $false)) )),
  inference(not_proxy_clausification,[],[f362])).
thf(f375,plain,(
  ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y7 @ Y5)))))))))))))) | (Y0 @ Y3))))))))) | (Y0 @ Y1)))))))) | ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (sK1 @ Y5 @ Y4))))))))))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))))))),
  inference(beta-eta_normalization,[],[f61])).
thf(f376,plain,(
  ( ! [X1 : ($i > $o)] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (sK1 @ Y5 @ Y4))))))))))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))))) | ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y7 @ Y5)))))))))))))) | (Y0 @ Y3))))))))) | (Y0 @ Y1))))) @ X1)))) )),
  inference(pi_proxy_clausification,[],[f375])).
thf(f377,plain,(
  ( ! [X2 : ($i > $o),X1 : ($i > $o)] : (($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (sK1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y7 @ Y5)))))))))))))) | (Y0 @ Y3))))))))) | (Y0 @ Y1))))) @ X1))) | ($true = (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $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 @ Y5 @ Y4) | (~ (sK1 @ Y5 @ Y4))))))))))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ X2)))) )),
  inference(pi_proxy_clausification,[],[f376])).
thf(f378,plain,(
  ( ! [X2 : ($i > $o),X1 : ($i > $o)] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) | (~ (Y2 @ Y3 @ Y5))) | (~ (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK1 @ Y4 @ Y3))))))))))) => (X2 @ Y1)))) => (X2 @ Y0)))) => (!! @ $i @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))))))) | (X1 @ Y2))))))))) | (X1 @ Y0))))))) )),
  inference(beta-eta_normalization,[],[f377])).
thf(f379,plain,(
  ( ! [X2 : ($i > $o),X1 : ($i > $o)] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))))))) | (X1 @ Y2))))))))) | (X1 @ Y0)))))) | ($true = ((!! @ $i @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) | (~ (Y2 @ Y3 @ Y5))) | (~ (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK1 @ Y4 @ Y3))))))))))) => (X2 @ Y1)))) => (X2 @ Y0))))) = $false)) )),
  inference(imp_proxy_clausification,[],[f378])).
thf(f380,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) | (~ (Y2 @ Y3 @ Y5))) | (~ (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK1 @ Y4 @ Y3))))))))))) => (X2 @ Y1)))) => (X2 @ Y0))))) = $false) | ($true = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))))))) | (X1 @ Y2))))))))) | (X1 @ Y0))) @ X3))) | ($true = ((!! @ $i @ X2)))) )),
  inference(pi_proxy_clausification,[],[f379])).
thf(f381,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : (($true = ((!! @ $i @ X2))) | ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) | (~ (Y2 @ Y3 @ Y5))) | (~ (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK1 @ Y4 @ Y3))))))))))) => (X2 @ Y1)))) => (X2 @ Y0))) @ (sK46 @ X2))) = $false) | ($true = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))))))) | (X1 @ Y2))))))))) | (X1 @ Y0))) @ X3)))) )),
  inference(sigma_proxy_clausification,[],[f380])).
thf(f382,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (($true = ((X2 @ X4))) | ($true = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (sK1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))))))) | (X1 @ Y2))))))))) | (X1 @ Y0))) @ X3))) | ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) | (~ (Y2 @ Y3 @ Y5))) | (~ (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK1 @ Y4 @ Y3))))))))))) => (X2 @ Y1)))) => (X2 @ Y0))) @ (sK46 @ X2))) = $false)) )),
  inference(pi_proxy_clausification,[],[f381])).
thf(f383,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (((((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK46 @ X2) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (X2 @ Y0)))) => (X2 @ (sK46 @ X2)))) = $false) | ($true = ((X2 @ X4))) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (X1 @ Y1))))))))) | (X1 @ X3))))) )),
  inference(beta-eta_normalization,[],[f382])).
thf(f384,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X2 @ (sK46 @ X2))) = $false) | ($true = ((X2 @ X4))) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (X1 @ Y1))))))))) | (X1 @ X3))))) )),
  inference(imp_proxy_clausification,[],[f383])).
thf(f385,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (X1 @ Y1))))))))) | (X1 @ X3)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK46 @ X2) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (X2 @ Y0)))))) | ($true = ((X2 @ X4)))) )),
  inference(imp_proxy_clausification,[],[f383])).
thf(f386,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (X1 @ Y1))))))))))) | (((X1 @ X3)) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK46 @ X2) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (X2 @ Y0)))))) | ($true = ((X2 @ X4)))) )),
  inference(or_proxy_clausification,[],[f385])).
thf(f387,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X1 @ X3)) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK46 @ X2) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (X2 @ Y0)))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (X1 @ Y1)))))))))) | ($true = ((X2 @ X4)))) )),
  inference(not_proxy_clausification,[],[f386])).
thf(f388,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK46 @ X2) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (X2 @ Y0))) @ X5))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (X1 @ Y1))))))))))) )),
  inference(pi_proxy_clausification,[],[f387])).
thf(f389,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (((((^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (X1 @ Y1))))))) @ (sK47 @ X1))) = $false) | (((X1 @ X3)) = $true) | ($true = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK46 @ X2) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) | (~ (Y1 @ Y2 @ Y4))) | (~ (Y1 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK1 @ Y3 @ Y2))))))))))) => (X2 @ Y0))) @ X5))) | ($true = ((X2 @ X4)))) )),
  inference(sigma_proxy_clausification,[],[f388])).
thf(f390,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (($false = (((X1 @ (sK47 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK47 @ X1) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (X1 @ Y0)))))))) | ($true = ((X2 @ X4))) | ($true = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK46 @ X2) @ X5) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1))))))))))) => (X2 @ X5)))) | (((X1 @ X3)) = $true)) )),
  inference(beta-eta_normalization,[],[f389])).
thf(f391,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (($true = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK46 @ X2) @ X5) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1))))))))))) => (X2 @ X5)))) | ($true = ((X2 @ X4))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK47 @ X1) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (X1 @ Y0))))))) | (((X1 @ X3)) = $true)) )),
  inference(or_proxy_clausification,[],[f390])).
thf(f418,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((X2 @ X4))) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | ($false = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK46 @ X2) @ X5) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK47 @ X1) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (X1 @ Y0)))))))) )),
  inference(imp_proxy_clausification,[],[f391])).
thf(f419,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (((((^[Y0 : $i > $i > $o]: (((Y0 @ (sK46 @ X2) @ X5) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1)))))))))) @ (sK49 @ X5 @ X2))) = $false) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X5))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK47 @ X1) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (X1 @ Y0)))))))) )),
  inference(sigma_proxy_clausification,[],[f418])).
thf(f420,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK47 @ X1) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (X1 @ Y0)))))) | ($true = ((X2 @ X4))) | (((X1 @ X3)) = $true) | ((((^[Y0 : $i > $i > $o]: (((Y0 @ (sK46 @ X2) @ X5) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1)))))))))) @ (sK49 @ X5 @ X2))) = $false) | ($true = ((X2 @ X5)))) )),
  inference(not_proxy_clausification,[],[f419])).
thf(f421,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (((((^[Y0 : $i > $i > $o]: (((Y0 @ (sK46 @ X2) @ X5) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y2 @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK1 @ Y2 @ Y1)))))))))) @ (sK49 @ X5 @ X2))) = $false) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | ($true = ((X2 @ X4))) | ($true = (((^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK47 @ X1) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (X1 @ Y0))) @ X6)))) )),
  inference(pi_proxy_clausification,[],[f420])).
thf(f422,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = (((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))) | (X1 @ X6)))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | (((((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK49 @ X5 @ X2 @ Y1 @ Y2) | (~ (sK49 @ X5 @ X2 @ Y0 @ Y2))) | (~ (sK49 @ X5 @ X2 @ Y1 @ Y0))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK49 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))))))) = $false) | ($true = ((X2 @ X5)))) )),
  inference(beta-eta_normalization,[],[f421])).
thf(f423,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK49 @ X5 @ X2 @ Y1 @ Y2) | (~ (sK49 @ X5 @ X2 @ Y0 @ Y2))) | (~ (sK49 @ X5 @ X2 @ Y1 @ Y0))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK49 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))))))) = $false) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | ($true = ((X1 @ X6))) | ($true = ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))))) | ($true = ((X2 @ X4)))) )),
  inference(or_proxy_clausification,[],[f422])).
thf(f424,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X1 @ X6))) | ($true = ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK49 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0))))))))))) )),
  inference(or_proxy_clausification,[],[f423])).
thf(f425,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X5))) | ($true = ((X1 @ X6))) | ($true = ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))))) | (((X1 @ X3)) = $true) | ((((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK49 @ X5 @ X2 @ Y1 @ Y2) | (~ (sK49 @ X5 @ X2 @ Y0 @ Y2))) | (~ (sK49 @ X5 @ X2 @ Y1 @ Y0)))))))))))) = $false) | ($true = ((X2 @ X4)))) )),
  inference(or_proxy_clausification,[],[f423])).
thf(f426,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (((((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK49 @ X5 @ X2 @ Y1 @ Y2) | (~ (sK49 @ X5 @ X2 @ Y0 @ Y2))) | (~ (sK49 @ X5 @ X2 @ Y1 @ Y0)))))))))))) = $false) | ($true = ((X2 @ X5))) | ($true = ((X2 @ X4))) | (((X1 @ X3)) = $true) | ($true = ((X1 @ X6))) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))) = $false)) )),
  inference(not_proxy_clausification,[],[f425])).
thf(f428,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X1 @ X6))) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))) = $false) | (((X1 @ X3)) = $true) | (((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false)) )),
  inference(or_proxy_clausification,[],[f426])).
thf(f429,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false) | ($true = ((X1 @ X6))) | ($true = ((X2 @ X5))) | ((((^[Y0 : $i > $i > $o]: (((Y0 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))) @ (sK50 @ X1 @ X6))) = $false) | ($true = ((X2 @ X4))) | (((X1 @ X3)) = $true)) )),
  inference(sigma_proxy_clausification,[],[f428])).
thf(f430,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X4))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | ($false = ((((sK50 @ X1 @ X6 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK50 @ X1 @ X6 @ Y1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK50 @ X1 @ X6 @ Y1 @ Y0) | (~ (sK50 @ X1 @ X6 @ Y1 @ Y2))) | (~ (sK50 @ X1 @ X6 @ Y2 @ Y0))))))))))))) | ($true = ((X1 @ X6))) | (((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false)) )),
  inference(beta-eta_normalization,[],[f429])).
thf(f432,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = ((X1 @ X6))) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | ((((sK50 @ X1 @ X6 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK50 @ X1 @ X6 @ Y1 @ Y0))))))))) = $false) | (((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false)) )),
  inference(or_proxy_clausification,[],[f430])).
thf(f433,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = ((X1 @ X6))) | (((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false) | ($true = ((X2 @ X4))) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK50 @ X1 @ X6 @ Y1 @ Y0)))))))) = $false) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5)))) )),
  inference(or_proxy_clausification,[],[f432])).
thf(f434,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = ((X1 @ X6))) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X5))) | (((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false) | (((X1 @ X3)) = $true) | ($false = ((sK50 @ X1 @ X6 @ (sK47 @ X1) @ X6)))) )),
  inference(or_proxy_clausification,[],[f432])).
thf(f435,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : ((((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X5))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK50 @ X1 @ X6 @ Y1 @ Y0)))))))) | ($true = ((X1 @ X6))) | (((X1 @ X3)) = $true)) )),
  inference(not_proxy_clausification,[],[f433])).
thf(f436,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | (((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false) | ($true = ((X2 @ X4))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK50 @ X1 @ X6 @ Y1 @ Y0))))) @ X7))) | ($true = ((X2 @ X5))) | ($true = ((X1 @ X6)))) )),
  inference(pi_proxy_clausification,[],[f435])).
thf(f437,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X4))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ X7)) | (sK50 @ X1 @ X6 @ Y0 @ X7)))))) | ($true = ((X1 @ X6))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | (((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false)) )),
  inference(beta-eta_normalization,[],[f436])).
thf(f438,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X1 @ X6))) | ($true = ((X2 @ X4))) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ X7)) | (sK50 @ X1 @ X6 @ Y0 @ X7))) @ X8))) | (((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true)) )),
  inference(pi_proxy_clausification,[],[f437])).
thf(f439,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((~ (sK1 @ X8 @ X7)) | (sK50 @ X1 @ X6 @ X8 @ X7)))) | ($true = ((X2 @ X5))) | (((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false) | (((X1 @ X3)) = $true) | ($true = ((X1 @ X6))) | ($true = ((X2 @ X4)))) )),
  inference(beta-eta_normalization,[],[f438])).
thf(f440,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X4))) | ($true = ((X1 @ X6))) | ($true = ((X2 @ X5))) | ($true = ((sK50 @ X1 @ X6 @ X8 @ X7))) | (((X1 @ X3)) = $true) | ($true = ((~ (sK1 @ X8 @ X7)))) | (((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false)) )),
  inference(or_proxy_clausification,[],[f439])).
thf(f441,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X4))) | ($true = ((sK50 @ X1 @ X6 @ X8 @ X7))) | (((sK1 @ X8 @ X7)) = $false) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | ($true = ((X1 @ X6))) | (((sK49 @ X5 @ X2 @ (sK46 @ X2) @ X5)) = $false)) )),
  inference(not_proxy_clausification,[],[f440])).
thf(f498,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK49 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))))))) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))) = $false) | ($true = ((X2 @ X5))) | ($true = ((X1 @ X6))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4)))) )),
  inference(not_proxy_clausification,[],[f424])).
thf(f499,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK49 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0))))))))) | ($true = ((X1 @ X6))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | ($true = ((X2 @ X4))) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))) = $false)) )),
  inference(not_proxy_clausification,[],[f498])).
thf(f500,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))))) = $false) | ($true = ((X2 @ X4))) | ($true = ((X1 @ X6))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK49 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))) @ X7)))) )),
  inference(pi_proxy_clausification,[],[f499])).
thf(f501,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK49 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK1 @ Y1 @ Y0)))))) @ X7))) | ((((^[Y0 : $i > $i > $o]: (((Y0 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))))) @ (sK52 @ X1 @ X6))) = $false) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | ($true = ((X1 @ X6))) | ($true = ((X2 @ X4)))) )),
  inference(sigma_proxy_clausification,[],[f500])).
thf(f502,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | ($true = ((X1 @ X6))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK49 @ X5 @ X2 @ Y0 @ X7) | (~ (sK1 @ Y0 @ X7))))))) | ($true = ((X2 @ X4))) | (((((sK52 @ X1 @ X6 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK52 @ X1 @ X6 @ Y1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK52 @ X1 @ X6 @ Y1 @ Y0) | (~ (sK52 @ X1 @ X6 @ Y1 @ Y2))) | (~ (sK52 @ X1 @ X6 @ Y2 @ Y0)))))))))))) = $false) | ($true = ((X2 @ X5)))) )),
  inference(beta-eta_normalization,[],[f501])).
thf(f503,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: ((sK49 @ X5 @ X2 @ Y0 @ X7) | (~ (sK1 @ Y0 @ X7)))) @ X8))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | (((((sK52 @ X1 @ X6 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK52 @ X1 @ X6 @ Y1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK52 @ X1 @ X6 @ Y1 @ Y0) | (~ (sK52 @ X1 @ X6 @ Y1 @ Y2))) | (~ (sK52 @ X1 @ X6 @ Y2 @ Y0)))))))))))) = $false) | ($true = ((X2 @ X4))) | ($true = ((X1 @ X6)))) )),
  inference(pi_proxy_clausification,[],[f502])).
thf(f505,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X1 @ X6))) | ($true = ((X2 @ X5))) | ($false = (((sK52 @ X1 @ X6 @ (sK47 @ X1) @ X6) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK52 @ X1 @ X6 @ Y1 @ Y0)))))))))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | ($true = (((^[Y0 : $i]: ((sK49 @ X5 @ X2 @ Y0 @ X7) | (~ (sK1 @ Y0 @ X7)))) @ X8)))) )),
  inference(or_proxy_clausification,[],[f503])).
thf(f506,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X1 @ X6))) | (((X1 @ X3)) = $true) | ($true = (((^[Y0 : $i]: ((sK49 @ X5 @ X2 @ Y0 @ X7) | (~ (sK1 @ Y0 @ X7)))) @ X8))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK52 @ X1 @ X6 @ Y1 @ Y0))))))))) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X5)))) )),
  inference(or_proxy_clausification,[],[f505])).
thf(f507,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X1 @ X6))) | ($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | ($false = ((sK52 @ X1 @ X6 @ (sK47 @ X1) @ X6))) | ($true = (((^[Y0 : $i]: ((sK49 @ X5 @ X2 @ Y0 @ X7) | (~ (sK1 @ Y0 @ X7)))) @ X8)))) )),
  inference(or_proxy_clausification,[],[f505])).
thf(f508,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | ($true = ((X1 @ X6))) | ($true = ((X2 @ X5))) | ($false = ((sK52 @ X1 @ X6 @ (sK47 @ X1) @ X6))) | ($true = (((sK49 @ X5 @ X2 @ X8 @ X7) | (~ (sK1 @ X8 @ X7)))))) )),
  inference(beta-eta_normalization,[],[f507])).
thf(f509,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X1 @ X6))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | ($true = ((~ (sK1 @ X8 @ X7)))) | ($false = ((sK52 @ X1 @ X6 @ (sK47 @ X1) @ X6))) | ($true = ((X2 @ X5))) | ($true = ((sK49 @ X5 @ X2 @ X8 @ X7)))) )),
  inference(or_proxy_clausification,[],[f508])).
thf(f510,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK52 @ X1 @ X6 @ (sK47 @ X1) @ X6))) | ($true = ((X2 @ X5))) | ($true = ((sK49 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X4))) | (((sK1 @ X8 @ X7)) = $false) | (((X1 @ X3)) = $true) | ($true = ((X1 @ X6)))) )),
  inference(not_proxy_clausification,[],[f509])).
thf(f511,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: ((sK49 @ X5 @ X2 @ Y0 @ X7) | (~ (sK1 @ Y0 @ X7)))) @ X8))) | ($true = ((X2 @ X4))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK52 @ X1 @ X6 @ Y1 @ Y0)))))))) | ($true = ((X1 @ X6)))) )),
  inference(not_proxy_clausification,[],[f506])).
thf(f512,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (sK1 @ Y1 @ Y0)) | (sK52 @ X1 @ X6 @ Y1 @ Y0))))) @ X9))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | ($true = ((X1 @ X6))) | ($true = (((^[Y0 : $i]: ((sK49 @ X5 @ X2 @ Y0 @ X7) | (~ (sK1 @ Y0 @ X7)))) @ X8))) | ($true = ((X2 @ X5)))) )),
  inference(pi_proxy_clausification,[],[f511])).
thf(f513,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X4))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (sK1 @ Y0 @ X9)) | (sK52 @ X1 @ X6 @ Y0 @ X9))))) = $true) | ($true = ((X1 @ X6))) | ($true = (((sK49 @ X5 @ X2 @ X8 @ X7) | (~ (sK1 @ X8 @ X7))))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X5)))) )),
  inference(beta-eta_normalization,[],[f512])).
thf(f514,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ X9)) | (sK52 @ X1 @ X6 @ Y0 @ X9))) @ X10))) | ($true = ((X2 @ X5))) | ($true = ((X2 @ X4))) | ($true = ((X1 @ X6))) | ($true = (((sK49 @ X5 @ X2 @ X8 @ X7) | (~ (sK1 @ X8 @ X7)))))) )),
  inference(pi_proxy_clausification,[],[f513])).
thf(f515,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X5))) | ($true = ((~ (sK1 @ X8 @ X7)))) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ X9)) | (sK52 @ X1 @ X6 @ Y0 @ X9))) @ X10))) | ($true = ((X2 @ X4))) | ($true = ((sK49 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X1 @ X6))) | (((X1 @ X3)) = $true)) )),
  inference(or_proxy_clausification,[],[f514])).
thf(f516,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X4))) | (((sK1 @ X8 @ X7)) = $false) | ($true = (((^[Y0 : $i]: ((~ (sK1 @ Y0 @ X9)) | (sK52 @ X1 @ X6 @ Y0 @ X9))) @ X10))) | ($true = ((sK49 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X5))) | ($true = ((X1 @ X6))) | (((X1 @ X3)) = $true)) )),
  inference(not_proxy_clausification,[],[f515])).
thf(f517,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((X1 @ X3)) = $true) | ($true = (((~ (sK1 @ X10 @ X9)) | (sK52 @ X1 @ X6 @ X10 @ X9)))) | ($true = ((X2 @ X5))) | ($true = ((X2 @ X4))) | ($true = ((sK49 @ X5 @ X2 @ X8 @ X7))) | (((sK1 @ X8 @ X7)) = $false) | ($true = ((X1 @ X6)))) )),
  inference(beta-eta_normalization,[],[f516])).
thf(f518,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X1 @ X6))) | ($true = ((sK52 @ X1 @ X6 @ X10 @ X9))) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X5))) | ($true = ((sK49 @ X5 @ X2 @ X8 @ X7))) | ($true = ((~ (sK1 @ X10 @ X9)))) | (((X1 @ X3)) = $true) | (((sK1 @ X8 @ X7)) = $false)) )),
  inference(or_proxy_clausification,[],[f517])).
thf(f519,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X10 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((sK52 @ X1 @ X6 @ X10 @ X9))) | (((sK1 @ X8 @ X7)) = $false) | (((sK1 @ X10 @ X9)) = $false) | ($true = ((X2 @ X5))) | ($true = ((sK49 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X4))) | ($true = ((X1 @ X6))) | (((X1 @ X3)) = $true)) )),
  inference(not_proxy_clausification,[],[f518])).
thf(f533,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X1 @ X3)) = $true) | (((X2 @ (sK46 @ X2))) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (X1 @ Y1))))))))))) | ($true = ((X2 @ X4)))) )),
  inference(or_proxy_clausification,[],[f384])).
thf(f534,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | (((X2 @ (sK46 @ X2))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (X1 @ Y1))))))))))) )),
  inference(not_proxy_clausification,[],[f533])).
thf(f535,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : ((((X1 @ X3)) = $true) | ($false = (((^[Y0 : $i]: ((X1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))))))) | (X1 @ Y1))))))) @ (sK53 @ X1)))) | (((X2 @ (sK46 @ X2))) = $false) | ($true = ((X2 @ X4)))) )),
  inference(sigma_proxy_clausification,[],[f534])).
thf(f536,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (($false = (((X1 @ (sK53 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ (sK53 @ X1) @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))))))) | (X1 @ Y0)))))))) | ($true = ((X2 @ X4))) | (((X2 @ (sK46 @ X2))) = $false) | (((X1 @ X3)) = $true)) )),
  inference(beta-eta_normalization,[],[f535])).
thf(f538,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (($false = ((X1 @ (sK53 @ X1)))) | ($true = ((X2 @ X4))) | (((X1 @ X3)) = $true) | (((X2 @ (sK46 @ X2))) = $false)) )),
  inference(or_proxy_clausification,[],[f536])).
thf(f588,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK2 @ X1))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | (((X3 @ (sK9 @ X3) @ (sK18 @ X3))) = $false) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((X4 @ (sK19 @ X4) @ (sK10 @ X4))))) )),
  inference(forward_demodulation,[],[f189,f51])).
thf(f600,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X3 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK8 @ X3)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ (sK22 @ X4) @ (sK10 @ X4)))) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | ($true = ((X4 @ X2 @ (sK6 @ X2))))) )),
  inference(forward_demodulation,[],[f228,f51])).
thf(f617,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ X1))) | ($true = ((X2 @ X1 @ (d2unsorted @ d_unsorted_0)))) | (((sK3 @ sK4)) = $false) | ($false = ((X2 @ (sK37 @ X2) @ (sK34 @ X2)))) | ($false = ((X2 @ (sK36 @ X2) @ (sK38 @ X2))))) )),
  inference(forward_demodulation,[],[f320,f51])).
thf(f622,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ X1))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (sK35 @ X2)))) | (((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($true = ((sK1 @ (sK37 @ X2) @ (sK34 @ X2))))) )),
  inference(forward_demodulation,[],[f330,f51])).
thf(f626,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (sK41 @ X2)))) | ($true = ((sK3 @ X1))) | ($true = ((sK1 @ (sK43 @ X2) @ (sK42 @ X2)))) | ($true = ((X2 @ X1 @ (sK40 @ X1)))) | (((sK2 @ sK39)) = $false)) )),
  inference(forward_demodulation,[],[f367,f51])).
thf(f631,plain,(
  (((sK2 @ sK39)) = $false) | ($false = ((sK3 @ (d2unsorted @ d_unsorted_0))))),
  inference(forward_demodulation,[],[f333,f51])).
thf(f635,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = ((X2 @ X5))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | (((sK49 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5)) = $false) | ($false = ((sK50 @ X1 @ X6 @ (sK47 @ X1) @ X6))) | ($true = ((X1 @ X6)))) )),
  inference(forward_demodulation,[],[f434,f51])).
thf(f636,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((X1 @ X6))) | (((X1 @ X3)) = $true) | (((sK1 @ X8 @ X7)) = $false) | (((sK49 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5)) = $false) | ($true = ((X2 @ X5))) | ($true = ((X2 @ X4))) | ($true = ((sK50 @ X1 @ X6 @ X8 @ X7)))) )),
  inference(forward_demodulation,[],[f441,f51])).
thf(f650,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK52 @ X1 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6)) = $false) | ($true = ((X1 @ X6))) | (((sK1 @ X8 @ X7)) = $false) | ($true = ((X2 @ X5))) | ($true = ((sK49 @ X5 @ X2 @ X8 @ X7))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4)))) )),
  inference(forward_demodulation,[],[f510,f51])).
thf(f652,definition,(
  spl55_4 <=> ! [X4 : $i,X7 : $i,X8 : $i,X5 : $i,X2 : ($i > $o)] : ((((sK1 @ X8 @ X7)) = $false) | ($true = ((X2 @ X4))) | ($true = ((sK49 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X5))))),
  introduced(definition,[new_symbols(definition,[spl55_4])],[avatar_definition])).
thf(f653,plain,(
  ( ! [X2 : ($i > $o),X8 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((sK49 @ X5 @ X2 @ X8 @ X7))) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X5))) | (((sK1 @ X8 @ X7)) = $false)) ) | ~spl55_4),
  inference(avatar_component_clause,[],[f652])).
thf(f655,definition,(
  spl55_5 <=> ! [X3 : $i,X9 : $i,X10 : $i,X6 : $i,X1 : ($i > $o)] : (($true = ((sK52 @ X1 @ X6 @ X10 @ X9))) | (((X1 @ X3)) = $true) | ($true = ((X1 @ X6))) | (((sK1 @ X10 @ X9)) = $false))),
  introduced(definition,[new_symbols(definition,[spl55_5])],[avatar_definition])).
thf(f656,plain,(
  ( ! [X3 : $i,X10 : $i,X1 : ($i > $o),X6 : $i,X9 : $i] : (($true = ((sK52 @ X1 @ X6 @ X10 @ X9))) | ($true = ((X1 @ X6))) | (((sK1 @ X10 @ X9)) = $false) | (((X1 @ X3)) = $true)) ) | ~spl55_5),
  inference(avatar_component_clause,[],[f655])).
thf(f657,plain,(
  spl55_4 | spl55_5),
  inference(avatar_split_clause,[],[f519,f655,f652])).
thf(f662,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (($false = ((X1 @ (d2unsorted @ d_unsorted_0)))) | (((X1 @ X3)) = $true) | ($true = ((X2 @ X4))) | (((X2 @ (sK46 @ X2))) = $false)) )),
  inference(forward_demodulation,[],[f538,f51])).
thf(f686,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((X3 @ (sK9 @ X3) @ (sK18 @ X3))) = $false) | ($true = ((X4 @ (sK19 @ X4) @ (sK10 @ X4)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK3 @ X2))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK7 @ X3)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | ($true = ((sK2 @ X1)))) )),
  inference(forward_demodulation,[],[f588,f51])).
thf(f698,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ (sK22 @ X4) @ (sK10 @ X4)))) | ($true = ((sK3 @ X2))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK8 @ X3)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | ($true = ((sK2 @ X1))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3))))) )),
  inference(forward_demodulation,[],[f600,f51])).
thf(f715,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((X2 @ (sK37 @ X2) @ (sK34 @ X2)))) | ($false = ((sK3 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((X2 @ (sK36 @ X2) @ (sK38 @ X2)))) | ($true = ((sK2 @ X1)))) )),
  inference(forward_demodulation,[],[f617,f51])).
thf(f720,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK1 @ (sK37 @ X2) @ (sK34 @ X2)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ X1))) | (((sK3 @ sK4)) = $false) | ($true = ((X2 @ X1 @ (sK5 @ X1))))) )),
  inference(forward_demodulation,[],[f622,f51])).
thf(f724,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((sK2 @ sK39)) = $false) | ($true = ((sK1 @ (sK43 @ X2) @ (sK42 @ X2)))) | ($true = ((X2 @ X1 @ (sK40 @ X1))))) )),
  inference(forward_demodulation,[],[f626,f51])).
thf(f729,plain,(
  ($false = ((sK3 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0))))),
  inference(forward_demodulation,[],[f631,f51])).
thf(f732,definition,(
  spl55_7 <=> ! [X1 : ($i > $o),X3 : $i] : (($false = ((X1 @ (d2unsorted @ d_unsorted_0)))) | (((X1 @ X3)) = $true))),
  introduced(definition,[new_symbols(definition,[spl55_7])],[avatar_definition])).
thf(f733,plain,(
  ( ! [X3 : $i,X1 : ($i > $o)] : (($false = ((X1 @ (d2unsorted @ d_unsorted_0)))) | (((X1 @ X3)) = $true)) ) | ~spl55_7),
  inference(avatar_component_clause,[],[f732])).
thf(f742,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X6 : $i,X4 : $i,X5 : $i] : (($true = ((X1 @ X6))) | (((X1 @ X3)) = $true) | (((sK49 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5)) = $false) | ($false = ((sK50 @ X1 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6))) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X5)))) )),
  inference(forward_demodulation,[],[f635,f51])).
thf(f744,definition,(
  spl55_10 <=> ! [X2 : ($i > $o),X5 : $i,X4 : $i] : ((((sK49 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5)) = $false) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X5))))),
  introduced(definition,[new_symbols(definition,[spl55_10])],[avatar_definition])).
thf(f745,plain,(
  ( ! [X2 : ($i > $o),X4 : $i,X5 : $i] : ((((sK49 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5)) = $false) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X5)))) ) | ~spl55_10),
  inference(avatar_component_clause,[],[f744])).
thf(f747,definition,(
  spl55_11 <=> ! [X3 : $i,X7 : $i,X8 : $i,X6 : $i,X1 : ($i > $o)] : (($true = ((X1 @ X6))) | ($true = ((sK50 @ X1 @ X6 @ X8 @ X7))) | (((sK1 @ X8 @ X7)) = $false) | (((X1 @ X3)) = $true))),
  introduced(definition,[new_symbols(definition,[spl55_11])],[avatar_definition])).
thf(f748,plain,(
  ( ! [X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i] : (($true = ((X1 @ X6))) | ($true = ((sK50 @ X1 @ X6 @ X8 @ X7))) | (((sK1 @ X8 @ X7)) = $false) | (((X1 @ X3)) = $true)) ) | ~spl55_11),
  inference(avatar_component_clause,[],[f747])).
thf(f749,plain,(
  spl55_10 | spl55_11),
  inference(avatar_split_clause,[],[f636,f747,f744])).
thf(f759,definition,(
  spl55_14 <=> ! [X6 : $i,X1 : ($i > $o),X3 : $i] : ((((sK52 @ X1 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6)) = $false) | (((X1 @ X3)) = $true) | ($true = ((X1 @ X6))))),
  introduced(definition,[new_symbols(definition,[spl55_14])],[avatar_definition])).
thf(f760,plain,(
  ( ! [X3 : $i,X1 : ($i > $o),X6 : $i] : ((((sK52 @ X1 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6)) = $false) | (((X1 @ X3)) = $true) | ($true = ((X1 @ X6)))) ) | ~spl55_14),
  inference(avatar_component_clause,[],[f759])).
thf(f761,plain,(
  spl55_4 | spl55_14),
  inference(avatar_split_clause,[],[f650,f759,f652])).
thf(f762,plain,(
  ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o),X4 : $i] : (($true = ((X2 @ X4))) | (((X2 @ (d2unsorted @ d_unsorted_0))) = $false) | (((X1 @ X3)) = $true) | ($false = ((X1 @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f662,f51])).
thf(f792,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ (sK19 @ X4) @ (sK10 @ X4)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($false = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK18 @ X3)))) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK7 @ X3)))) | ($true = ((sK2 @ X1))) | ($true = ((sK3 @ X2)))) )),
  inference(forward_demodulation,[],[f686,f51])).
thf(f804,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((sK2 @ X1))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK8 @ X3)))) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (sK10 @ X4))))) )),
  inference(forward_demodulation,[],[f698,f51])).
thf(f821,definition,(
  spl55_17 <=> ($false = ((sK3 @ (d2unsorted @ d_unsorted_0))))),
  introduced(definition,[new_symbols(definition,[spl55_17])],[avatar_definition])).
thf(f823,plain,(
  ($false = ((sK3 @ (d2unsorted @ d_unsorted_0)))) | ~spl55_17),
  inference(avatar_component_clause,[],[f821])).
thf(f825,definition,(
  spl55_18 <=> ($false = ((sK2 @ (d2unsorted @ d_unsorted_0))))),
  introduced(definition,[new_symbols(definition,[spl55_18])],[avatar_definition])).
thf(f827,plain,(
  ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | ~spl55_18),
  inference(avatar_component_clause,[],[f825])).
thf(f829,definition,(
  spl55_19 <=> ! [X2 : $i] : ($true = ((sK3 @ X2)))),
  introduced(definition,[new_symbols(definition,[spl55_19])],[avatar_definition])).
thf(f830,plain,(
  ( ! [X2 : $i] : (($true = ((sK3 @ X2)))) ) | ~spl55_19),
  inference(avatar_component_clause,[],[f829])).
thf(f835,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((X2 @ (d2unsorted @ d_unsorted_0) @ (sK34 @ X2))) = $false) | ($false = ((sK3 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((X2 @ (sK36 @ X2) @ (sK38 @ X2)))) | ($true = ((sK2 @ X1)))) )),
  inference(forward_demodulation,[],[f715,f51])).
thf(f840,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : ((((sK3 @ sK4)) = $false) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK34 @ X2)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($true = ((sK2 @ X1)))) )),
  inference(forward_demodulation,[],[f720,f51])).
thf(f844,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK1 @ (sK43 @ X2) @ (sK42 @ X2)))) | ($true = ((X2 @ X1 @ (sK40 @ X1)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f724,f51])).
thf(f849,plain,(
  spl55_18 | spl55_17),
  inference(avatar_split_clause,[],[f729,f821,f825])).
thf(f855,definition,(
  spl55_22 <=> ! [X6 : $i,X1 : ($i > $o),X3 : $i] : (($true = ((X1 @ X6))) | ($false = ((sK50 @ X1 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6))) | (((X1 @ X3)) = $true))),
  introduced(definition,[new_symbols(definition,[spl55_22])],[avatar_definition])).
thf(f856,plain,(
  ( ! [X3 : $i,X1 : ($i > $o),X6 : $i] : (($false = ((sK50 @ X1 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6))) | (((X1 @ X3)) = $true) | ($true = ((X1 @ X6)))) ) | ~spl55_22),
  inference(avatar_component_clause,[],[f855])).
thf(f857,plain,(
  spl55_10 | spl55_22),
  inference(avatar_split_clause,[],[f742,f855,f744])).
thf(f858,plain,(
  spl55_7 | spl55_7),
  inference(avatar_split_clause,[],[f762,f732,f732])).
thf(f883,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ($true = ((sK1 @ (sK13 @ X4) @ (sK12 @ X4)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK7 @ X3)))) | ($false = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK18 @ X3)))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (sK10 @ X4)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK2 @ X1))) | ($true = ((X4 @ X2 @ (sK6 @ X2))))) )),
  inference(forward_demodulation,[],[f792,f51])).
thf(f895,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK12 @ X4)))) | ($true = ((sK2 @ X1))) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (sK10 @ X4)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK8 @ X3))))) )),
  inference(forward_demodulation,[],[f804,f51])).
thf(f911,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ X1))) | ($false = ((X2 @ (sK36 @ X2) @ (sK38 @ X2)))) | ($false = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($false = ((sK3 @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f835,f51])).
thf(f916,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($false = ((sK3 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (sK5 @ X1)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK34 @ X2)))) | ($true = ((sK2 @ X1)))) )),
  inference(forward_demodulation,[],[f840,f51])).
thf(f919,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK3 @ X1))) | ($true = ((X2 @ X1 @ (sK40 @ X1)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK42 @ X2)))) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f844,f51])).
thf(f943,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (sK10 @ X4)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK12 @ X4)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK7 @ X3)))) | ($false = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK18 @ X3)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK2 @ X1)))) )),
  inference(forward_demodulation,[],[f883,f51])).
thf(f955,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (sK10 @ X4)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK8 @ X3)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK2 @ X1))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK6 @ X2))))) )),
  inference(forward_demodulation,[],[f895,f51])).
thf(f971,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($false = ((X2 @ (d2unsorted @ d_unsorted_0) @ (sK38 @ X2)))) | ($false = ((sK3 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ X1)))) )),
  inference(forward_demodulation,[],[f911,f51])).
thf(f976,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK34 @ X2)))) | ($true = ((sK2 @ X1))) | ($true = ((X2 @ X1 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((sK3 @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f916,f51])).
thf(f979,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK42 @ X2)))) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X1))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f919,f51])).
thf(f1005,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK12 @ X4)))) | ($false = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK18 @ X3)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK7 @ X3)))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ X2 @ (sK6 @ X2)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1)))) )),
  inference(forward_demodulation,[],[f943,f51])).
thf(f1017,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK2 @ X1))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK8 @ X3)))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X2))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true)) )),
  inference(forward_demodulation,[],[f955,f51])).
thf(f1034,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ X1))) | ($false = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((sK3 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f971,f51])).
thf(f1035,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($false = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ X1))) | ($false = ((sK3 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (d2unsorted @ d_unsorted_0))))) )),
  inference(duplicate_literal_removal,[],[f1034])).
thf(f1040,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ X1))) | ($false = ((sK3 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ X1 @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f976,f51])).
thf(f1043,plain,(
  ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((X2 @ X1 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X1))) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f979,f51])).
thf(f1068,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ X2 @ (sK6 @ X2)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK3 @ X2))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK7 @ X3)))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ X1))) | ($false = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK18 @ X3))))) )),
  inference(forward_demodulation,[],[f1005,f51])).
thf(f1080,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK8 @ X3)))) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((X4 @ X2 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK2 @ X1))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK3 @ X2))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f1017,f51])).
thf(f1085,definition,(
  spl55_24 <=> ! [X1 : $i,X3 : ($i > $i > $o)] : (($true = ((sK2 @ X1))) | (((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $false) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true))),
  introduced(definition,[new_symbols(definition,[spl55_24])],[avatar_definition])).
thf(f1086,plain,(
  ( ! [X3 : ($i > $i > $o),X1 : $i] : ((((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $false) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK2 @ X1)))) ) | ~spl55_24),
  inference(avatar_component_clause,[],[f1085])).
thf(f1089,definition,(
  spl55_25 <=> ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))),
  introduced(definition,[new_symbols(definition,[spl55_25])],[avatar_definition])).
thf(f1090,plain,(
  ($true != ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | spl55_25),
  inference(avatar_component_clause,[],[f1089])).
thf(f1091,plain,(
  ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ~spl55_25),
  inference(avatar_component_clause,[],[f1089])).
thf(f1094,definition,(
  spl55_26 <=> ! [X1 : $i,X3 : ($i > $i > $o)] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK2 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl55_26])],[avatar_definition])).
thf(f1095,plain,(
  ( ! [X3 : ($i > $i > $o),X1 : $i] : (($true = ((sK2 @ X1))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) ) | ~spl55_26),
  inference(avatar_component_clause,[],[f1094])).
thf(f1103,definition,(
  spl55_28 <=> ! [X2 : $i,X3 : ($i > $i > $o)] : (($true = ((X3 @ X2 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X2))))),
  introduced(definition,[new_symbols(definition,[spl55_28])],[avatar_definition])).
thf(f1104,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ X2 @ (d2unsorted @ d_unsorted_0))))) ) | ~spl55_28),
  inference(avatar_component_clause,[],[f1103])).
thf(f1108,plain,(
  spl55_17 | spl55_24),
  inference(avatar_split_clause,[],[f1035,f1085,f821])).
thf(f1111,plain,(
  spl55_26 | spl55_25 | spl55_17),
  inference(avatar_split_clause,[],[f1040,f821,f1089,f1094])).
thf(f1114,plain,(
  spl55_25 | spl55_18 | spl55_28),
  inference(avatar_split_clause,[],[f1043,f1103,f825,f1089])).
thf(f1135,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ X1))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK7 @ X3)))) | (((X4 @ X2 @ (d2unsorted @ d_unsorted_0))) = $true) | ($false = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK18 @ X3)))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f1068,f51])).
thf(f1146,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK1 @ (sK11 @ X3) @ (sK7 @ X3)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ X1))) | ($true = ((sK3 @ X2))) | (((X4 @ X2 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f1080,f51])).
thf(f1166,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($false = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK18 @ X3)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X2))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ X1))) | (((X4 @ X2 @ (d2unsorted @ d_unsorted_0))) = $true)) )),
  inference(forward_demodulation,[],[f1135,f51])).
thf(f1167,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK3 @ X2))) | ($false = ((X3 @ (d2unsorted @ d_unsorted_0) @ (sK18 @ X3)))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | (((X4 @ X2 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK2 @ X1))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
  inference(duplicate_literal_removal,[],[f1166])).
thf(f1179,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((X4 @ X2 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK3 @ X2))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK2 @ X1))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (sK7 @ X3)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f1146,f51])).
thf(f1195,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((X4 @ X2 @ (d2unsorted @ d_unsorted_0))) = $true) | (((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $false) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1)))) )),
  inference(forward_demodulation,[],[f1167,f51])).
thf(f1207,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : (($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X2))) | ($true = ((sK2 @ X1))) | (((X4 @ X2 @ (d2unsorted @ d_unsorted_0))) = $true)) )),
  inference(forward_demodulation,[],[f1179,f51])).
thf(f1208,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o),X1 : $i,X4 : ($i > $i > $o)] : ((((X4 @ X2 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((sK2 @ X1))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK3 @ X2))) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) )),
  inference(duplicate_literal_removal,[],[f1207])).
thf(f1217,plain,(
  spl55_25 | spl55_24 | spl55_28),
  inference(avatar_split_clause,[],[f1195,f1103,f1085,f1089])).
thf(f1225,plain,(
  spl55_28 | spl55_26 | spl55_25),
  inference(avatar_split_clause,[],[f1208,f1089,f1094,f1103])).
thf(f1230,plain,(
  ( ! [X0 : $i] : (($false = ((sK2 @ X0)))) ) | ~spl55_18),
  inference(superposition,[],[f827,f51])).
thf(f1236,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : ($i > $o)] : (($false = ((X1 @ X0))) | (((X1 @ X2)) = $true)) ) | ~spl55_7),
  inference(superposition,[],[f733,f51])).
thf(f1244,plain,(
  ( ! [X0 : $i] : (($true = ((sK1 @ X0 @ X0)))) ) | ~spl55_25),
  inference(superposition,[],[f1091,f51])).
thf(f1256,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((sK1 @ X0 @ X1))) | ($true = $false)) ) | (~spl55_7 | ~spl55_25)),
  inference(superposition,[],[f1244,f1236])).
thf(f1260,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((sK1 @ X0 @ X1)))) ) | (~spl55_7 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1256])).
thf(f1285,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : ((((X1 @ X2)) = $true) | (((X1 @ X3)) = $true) | ($false = ((sK1 @ (d2unsorted @ d_unsorted_0) @ X0))) | ($true = ((X1 @ X0))) | ($true = ((X1 @ X0))) | ($true = $false)) ) | (~spl55_4 | ~spl55_10)),
  inference(superposition,[],[f745,f653])).
thf(f1287,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : (($true = ((X1 @ X0))) | (((X1 @ X2)) = $true) | ($false = ((sK1 @ (d2unsorted @ d_unsorted_0) @ X0))) | ($true = $false) | (((X1 @ X3)) = $true)) ) | (~spl55_4 | ~spl55_10)),
  inference(duplicate_literal_removal,[],[f1285])).
thf(f1288,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : (($false = ((sK1 @ (d2unsorted @ d_unsorted_0) @ X0))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true) | ($true = ((X1 @ X0)))) ) | (~spl55_4 | ~spl55_10)),
  inference(trivial_inequality_removal,[],[f1287])).
thf(f1291,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : (($true = ((X1 @ X0))) | ($true = $false) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) ) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_25)),
  inference(forward_demodulation,[],[f1288,f1260])).
thf(f1292,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : (($true = ((X1 @ X0))) | (((X1 @ X3)) = $true) | (((X1 @ X2)) = $true)) ) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1291])).
thf(f1300,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((sK2 @ X1))) | ($true = ((sK2 @ X0))) | ($true = $false)) ) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_18 | ~spl55_25)),
  inference(superposition,[],[f827,f1292])).
thf(f1305,plain,(
  ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ X1))) | ($true != $true) | ($true = ((X0 @ X2)))) ) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_25)),
  inference(equality_factoring,[],[f1292])).
thf(f1311,plain,(
  ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ X2))) | ($true = ((X0 @ X1)))) ) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1305])).
thf(f1318,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((sK2 @ X0))) | ($true = ((sK2 @ X1)))) ) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_18 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1300])).
thf(f1325,plain,(
  ( ! [X1 : $i] : (($true = ((sK2 @ X1))) | ($true = $false)) ) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_18 | ~spl55_25)),
  inference(forward_demodulation,[],[f1318,f1230])).
thf(f1326,plain,(
  ( ! [X1 : $i] : (($true = ((sK2 @ X1)))) ) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_18 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1325])).
thf(f1336,plain,(
  ($true = $false) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_18 | ~spl55_25)),
  inference(forward_demodulation,[],[f1326,f1230])).
thf(f1337,plain,(
  $false | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_18 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1336])).
thf(f1338,plain,(
  ~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_18 | ~spl55_25),
  inference(avatar_contradiction_clause,[],[f1337])).
thf(f1339,plain,(
  ( ! [X3 : $i,X10 : $i,X1 : ($i > $o),X6 : $i,X9 : $i] : ((((X1 @ X3)) = $true) | ($true = $false) | ($true = ((X1 @ X6))) | ($true = ((sK52 @ X1 @ X6 @ X10 @ X9)))) ) | (~spl55_5 | ~spl55_7 | ~spl55_25)),
  inference(forward_demodulation,[],[f656,f1260])).
thf(f1340,plain,(
  ( ! [X3 : $i,X10 : $i,X1 : ($i > $o),X6 : $i,X9 : $i] : (($true = ((sK52 @ X1 @ X6 @ X10 @ X9))) | ($true = ((X1 @ X6))) | (((X1 @ X3)) = $true)) ) | (~spl55_5 | ~spl55_7 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1339])).
thf(f1341,plain,(
  ( ! [X3 : ($i > $i > $o),X1 : $i] : ((((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $false) | ($true = $false) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true)) ) | (~spl55_18 | ~spl55_24)),
  inference(forward_demodulation,[],[f1086,f1230])).
thf(f1342,plain,(
  ( ! [X3 : ($i > $i > $o),X1 : $i] : ((((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $false) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true)) ) | (~spl55_18 | ~spl55_24)),
  inference(trivial_inequality_removal,[],[f1341])).
thf(f1346,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : ($i > $i > $o)] : ((((X1 @ X2 @ X0)) = $true) | (((X1 @ X0 @ X0)) = $false)) ) | (~spl55_18 | ~spl55_24)),
  inference(superposition,[],[f1342,f51])).
thf(f1412,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ X1))) | ($true = ((X0 @ X2))) | ($true = ((X0 @ X1))) | ($true = $false) | ($true = ((X0 @ X3)))) ) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_25)),
  inference(superposition,[],[f760,f1340])).
thf(f1418,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ X2))) | ($true = $false) | ($true = ((X0 @ X3))) | ($true = ((X0 @ X1)))) ) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_25)),
  inference(duplicate_literal_removal,[],[f1412])).
thf(f1419,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ X3))) | ($true = ((X0 @ X1))) | ($true = ((X0 @ X2)))) ) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1418])).
thf(f1426,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((sK2 @ X1))) | ($true = $false) | ($true = ((sK2 @ X0)))) ) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_18 | ~spl55_25)),
  inference(superposition,[],[f1419,f827])).
thf(f1440,plain,(
  ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ X1))) | ($true != $true) | ($true = ((X0 @ X2)))) ) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_25)),
  inference(equality_factoring,[],[f1419])).
thf(f1444,plain,(
  ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ X2))) | ($true = ((X0 @ X1)))) ) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1440])).
thf(f1453,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((sK2 @ X0))) | ($true = ((sK2 @ X1)))) ) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_18 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1426])).
thf(f1464,plain,(
  ( ! [X1 : $i] : (($true = $false) | ($true = ((sK2 @ X1)))) ) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_18 | ~spl55_25)),
  inference(forward_demodulation,[],[f1453,f1230])).
thf(f1465,plain,(
  ( ! [X1 : $i] : (($true = ((sK2 @ X1)))) ) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_18 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1464])).
thf(f1475,plain,(
  ($true = $false) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_18 | ~spl55_25)),
  inference(forward_demodulation,[],[f1465,f1230])).
thf(f1476,plain,(
  $false | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_18 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1475])).
thf(f1477,plain,(
  ~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_18 | ~spl55_25),
  inference(avatar_contradiction_clause,[],[f1476])).
thf(f1480,plain,(
  ( ! [X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i] : (($true = ((X1 @ X6))) | ($true = $false) | (((X1 @ X3)) = $true) | ($true = ((sK50 @ X1 @ X6 @ X8 @ X7)))) ) | (~spl55_7 | ~spl55_11 | ~spl55_25)),
  inference(forward_demodulation,[],[f748,f1260])).
thf(f1481,plain,(
  ( ! [X3 : $i,X1 : ($i > $o),X8 : $i,X6 : $i,X7 : $i] : (($true = ((sK50 @ X1 @ X6 @ X8 @ X7))) | (((X1 @ X3)) = $true) | ($true = ((X1 @ X6)))) ) | (~spl55_7 | ~spl55_11 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1480])).
thf(f1533,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i] : (($true = $false) | ($true = ((X0 @ X1))) | ($true = ((X0 @ X2))) | ($true = ((X0 @ X1))) | ($true = ((X0 @ X3)))) ) | (~spl55_7 | ~spl55_11 | ~spl55_22 | ~spl55_25)),
  inference(superposition,[],[f1481,f856])).
thf(f1538,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ X3))) | ($true = ((X0 @ X2))) | ($true = $false) | ($true = ((X0 @ X1)))) ) | (~spl55_7 | ~spl55_11 | ~spl55_22 | ~spl55_25)),
  inference(duplicate_literal_removal,[],[f1533])).
thf(f1539,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ X3))) | ($true = ((X0 @ X1))) | ($true = ((X0 @ X2)))) ) | (~spl55_7 | ~spl55_11 | ~spl55_22 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1538])).
thf(f1544,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((sK2 @ X1))) | ($true = $false) | ($true = ((sK2 @ X0)))) ) | (~spl55_7 | ~spl55_11 | ~spl55_18 | ~spl55_22 | ~spl55_25)),
  inference(superposition,[],[f1539,f827])).
thf(f1578,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((sK2 @ X0))) | ($true = ((sK2 @ X1)))) ) | (~spl55_7 | ~spl55_11 | ~spl55_18 | ~spl55_22 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1544])).
thf(f1590,plain,(
  ( ! [X1 : $i] : (($true = ((sK2 @ X1))) | ($true = $false)) ) | (~spl55_7 | ~spl55_11 | ~spl55_18 | ~spl55_22 | ~spl55_25)),
  inference(forward_demodulation,[],[f1578,f1230])).
thf(f1591,plain,(
  ( ! [X1 : $i] : (($true = ((sK2 @ X1)))) ) | (~spl55_7 | ~spl55_11 | ~spl55_18 | ~spl55_22 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1590])).
thf(f1601,plain,(
  ($true = $false) | (~spl55_7 | ~spl55_11 | ~spl55_18 | ~spl55_22 | ~spl55_25)),
  inference(forward_demodulation,[],[f1591,f1230])).
thf(f1602,plain,(
  $false | (~spl55_7 | ~spl55_11 | ~spl55_18 | ~spl55_22 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1601])).
thf(f1603,plain,(
  ~spl55_7 | ~spl55_11 | ~spl55_18 | ~spl55_22 | ~spl55_25),
  inference(avatar_contradiction_clause,[],[f1602])).
thf(f1607,plain,(
  ( ! [X0 : $i] : (($false = ((sK3 @ X0)))) ) | ~spl55_17),
  inference(superposition,[],[f823,f51])).
thf(f1610,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = ((sK3 @ X1))) | ($true = ((sK3 @ X0)))) ) | (~spl55_7 | ~spl55_11 | ~spl55_17 | ~spl55_22 | ~spl55_25)),
  inference(superposition,[],[f823,f1539])).
thf(f1613,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((sK3 @ X1))) | ($true = ((sK3 @ X0)))) ) | (~spl55_7 | ~spl55_11 | ~spl55_17 | ~spl55_22 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1610])).
thf(f1615,plain,(
  spl55_19 | spl55_19 | ~spl55_7 | ~spl55_11 | ~spl55_17 | ~spl55_22 | ~spl55_25),
  inference(avatar_split_clause,[],[f1613,f1089,f855,f821,f747,f732,f829,f829])).
thf(f1619,plain,(
  ($true = $false) | (~spl55_17 | ~spl55_19)),
  inference(superposition,[],[f823,f830])).
thf(f1627,plain,(
  $false | (~spl55_17 | ~spl55_19)),
  inference(trivial_inequality_removal,[],[f1619])).
thf(f1628,plain,(
  ~spl55_17 | ~spl55_19),
  inference(avatar_contradiction_clause,[],[f1627])).
thf(f1693,plain,(
  ( ! [X0 : $i] : (($true = ((sK3 @ X0))) | ($true = $false)) ) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_17 | ~spl55_25)),
  inference(superposition,[],[f823,f1311])).
thf(f1704,plain,(
  ( ! [X0 : $i] : (($true = ((sK3 @ X0)))) ) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_17 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1693])).
thf(f1718,plain,(
  ($true = $false) | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_17 | ~spl55_25)),
  inference(forward_demodulation,[],[f1704,f1607])).
thf(f1719,plain,(
  $false | (~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_17 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1718])).
thf(f1720,plain,(
  ~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_17 | ~spl55_25),
  inference(avatar_contradiction_clause,[],[f1719])).
thf(f1721,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o)] : (($true = ((X3 @ X2 @ (d2unsorted @ d_unsorted_0)))) | ($true = $false) | ($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) ) | (~spl55_17 | ~spl55_28)),
  inference(forward_demodulation,[],[f1104,f1607])).
thf(f1722,plain,(
  ( ! [X2 : $i,X3 : ($i > $i > $o)] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | ($true = ((X3 @ X2 @ (d2unsorted @ d_unsorted_0))))) ) | (~spl55_17 | ~spl55_28)),
  inference(trivial_inequality_removal,[],[f1721])).
thf(f1726,plain,(
  ( ! [X0 : $i] : (($true != ((sK1 @ X0 @ X0)))) ) | spl55_25),
  inference(superposition,[],[f1090,f51])).
thf(f1753,plain,(
  ( ! [X0 : $i] : (($true = ((sK1 @ X0 @ (d2unsorted @ d_unsorted_0)))) | ($true != $true)) ) | (~spl55_17 | spl55_25 | ~spl55_28)),
  inference(superposition,[],[f1090,f1722])).
thf(f1760,plain,(
  ( ! [X0 : $i] : (($true = ((sK1 @ X0 @ (d2unsorted @ d_unsorted_0))))) ) | (~spl55_17 | spl55_25 | ~spl55_28)),
  inference(trivial_inequality_removal,[],[f1753])).
thf(f1778,plain,(
  ($true != $true) | (~spl55_17 | spl55_25 | ~spl55_28)),
  inference(superposition,[],[f1726,f1760])).
thf(f1786,plain,(
  $false | (~spl55_17 | spl55_25 | ~spl55_28)),
  inference(trivial_inequality_removal,[],[f1778])).
thf(f1787,plain,(
  ~spl55_17 | spl55_25 | ~spl55_28),
  inference(avatar_contradiction_clause,[],[f1786])).
thf(f1858,plain,(
  ( ! [X0 : $i] : (($true = ((sK3 @ X0))) | ($true = $false)) ) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_17 | ~spl55_25)),
  inference(superposition,[],[f1444,f823])).
thf(f1878,plain,(
  ( ! [X0 : $i] : (($true = ((sK3 @ X0)))) ) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_17 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1858])).
thf(f1890,plain,(
  ($true = $false) | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_17 | ~spl55_25)),
  inference(forward_demodulation,[],[f1878,f1607])).
thf(f1891,plain,(
  $false | (~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_17 | ~spl55_25)),
  inference(trivial_inequality_removal,[],[f1890])).
thf(f1892,plain,(
  ~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_17 | ~spl55_25),
  inference(avatar_contradiction_clause,[],[f1891])).
thf(f1935,plain,(
  ( ! [X0 : $i] : (($true != $true) | ($false = ((sK1 @ X0 @ X0)))) ) | (~spl55_18 | ~spl55_24 | spl55_25)),
  inference(superposition,[],[f1726,f1346])).
thf(f1944,plain,(
  ( ! [X0 : $i] : (($false = ((sK1 @ X0 @ X0)))) ) | (~spl55_18 | ~spl55_24 | spl55_25)),
  inference(trivial_inequality_removal,[],[f1935])).
thf(f2042,plain,(
  ( ! [X3 : ($i > $i > $o),X1 : $i] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true) | ($true = $false)) ) | (~spl55_18 | ~spl55_26)),
  inference(forward_demodulation,[],[f1095,f1230])).
thf(f2043,plain,(
  ( ! [X3 : ($i > $i > $o),X1 : $i] : (($true = ((X3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) | (((X3 @ X1 @ (d2unsorted @ d_unsorted_0))) = $true)) ) | (~spl55_18 | ~spl55_26)),
  inference(trivial_inequality_removal,[],[f2042])).
thf(f2062,plain,(
  ( ! [X0 : $i] : (($true = ((sK1 @ X0 @ (d2unsorted @ d_unsorted_0)))) | ($true = $false)) ) | (~spl55_18 | ~spl55_24 | spl55_25 | ~spl55_26)),
  inference(superposition,[],[f1944,f2043])).
thf(f2063,plain,(
  ( ! [X0 : $i] : (($true = ((sK1 @ X0 @ (d2unsorted @ d_unsorted_0)))) | ($true != $true)) ) | (~spl55_18 | spl55_25 | ~spl55_26)),
  inference(superposition,[],[f1726,f2043])).
thf(f2069,plain,(
  ( ! [X0 : $i] : (($true = ((sK1 @ X0 @ (d2unsorted @ d_unsorted_0))))) ) | (~spl55_18 | ~spl55_24 | spl55_25 | ~spl55_26)),
  inference(trivial_inequality_removal,[],[f2062])).
thf(f2080,plain,(
  ( ! [X0 : $i] : (($true = ((sK1 @ X0 @ (d2unsorted @ d_unsorted_0))))) ) | (~spl55_18 | spl55_25 | ~spl55_26)),
  inference(trivial_inequality_removal,[],[f2063])).
thf(f2087,definition,(
  spl55_29 <=> ! [X3 : $i] : ($true = ((sK1 @ X3 @ (d2unsorted @ d_unsorted_0))))),
  introduced(definition,[new_symbols(definition,[spl55_29])],[avatar_definition])).
thf(f2088,plain,(
  ( ! [X3 : $i] : (($true = ((sK1 @ X3 @ (d2unsorted @ d_unsorted_0))))) ) | ~spl55_29),
  inference(avatar_component_clause,[],[f2087])).
thf(f2093,plain,(
  spl55_29 | ~spl55_18 | ~spl55_24 | spl55_25 | ~spl55_26),
  inference(avatar_split_clause,[],[f2069,f1094,f1089,f1085,f825,f2087])).
thf(f2097,plain,(
  spl55_29 | ~spl55_18 | spl55_25 | ~spl55_26),
  inference(avatar_split_clause,[],[f2080,f1094,f1089,f825,f2087])).
thf(f2110,plain,(
  ($true != $true) | (spl55_25 | ~spl55_29)),
  inference(superposition,[],[f1726,f2088])).
thf(f2122,plain,(
  $false | (spl55_25 | ~spl55_29)),
  inference(trivial_inequality_removal,[],[f2110])).
thf(f2123,plain,(
  spl55_25 | ~spl55_29),
  inference(avatar_contradiction_clause,[],[f2122])).
cnf(s3, plain, spl55_4 | spl55_5, inference(sat_conversion,[],[f657])).
cnf(s7, plain, spl55_10 | spl55_11, inference(sat_conversion,[],[f749])).
cnf(s10, plain, spl55_4 | spl55_14, inference(sat_conversion,[],[f761])).
cnf(s16, plain, spl55_17 | spl55_18, inference(sat_conversion,[],[f849])).
cnf(s18, plain, spl55_10 | spl55_22, inference(sat_conversion,[],[f857])).
cnf(s19, plain, spl55_7 | spl55_7, inference(sat_conversion,[],[f858])).
cnf(s20, plain, spl55_7, inference(rat,[],[s19])).
cnf(s30, plain, spl55_17 | spl55_24, inference(sat_conversion,[],[f1108])).
cnf(s33, plain, spl55_17 | spl55_25 | spl55_26, inference(sat_conversion,[],[f1111])).
cnf(s36, plain, spl55_18 | spl55_25 | spl55_28, inference(sat_conversion,[],[f1114])).
cnf(s44, plain, spl55_24 | spl55_25 | spl55_28, inference(sat_conversion,[],[f1217])).
cnf(s52, plain, spl55_25 | spl55_26 | spl55_28, inference(sat_conversion,[],[f1225])).
cnf(s57, plain, ~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_18 | ~spl55_25, inference(sat_conversion,[],[f1338])).
cnf(s61, plain, ~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_18 | ~spl55_25, inference(sat_conversion,[],[f1477])).
cnf(s65, plain, ~spl55_7 | ~spl55_11 | ~spl55_18 | ~spl55_22 | ~spl55_25, inference(sat_conversion,[],[f1603])).
cnf(s68, plain, spl55_19 | ~spl55_11 | ~spl55_17 | ~spl55_7 | spl55_19 | ~spl55_22 | ~spl55_25, inference(sat_conversion,[],[f1615])).
cnf(s69, plain, ~spl55_7 | ~spl55_11 | ~spl55_17 | spl55_19 | ~spl55_22 | ~spl55_25, inference(rat,[],[s68])).
cnf(s71, plain, ~spl55_17 | ~spl55_19, inference(sat_conversion,[],[f1628])).
cnf(s77, plain, ~spl55_4 | ~spl55_7 | ~spl55_10 | ~spl55_17 | ~spl55_25, inference(sat_conversion,[],[f1720])).
cnf(s79, plain, ~spl55_17 | spl55_25 | ~spl55_28, inference(sat_conversion,[],[f1787])).
cnf(s83, plain, ~spl55_5 | ~spl55_7 | ~spl55_14 | ~spl55_17 | ~spl55_25, inference(sat_conversion,[],[f1892])).
cnf(s86, plain, ~spl55_18 | ~spl55_24 | spl55_25 | ~spl55_26 | spl55_29, inference(sat_conversion,[],[f2093])).
cnf(s90, plain, ~spl55_18 | spl55_25 | ~spl55_26 | spl55_29, inference(sat_conversion,[],[f2097])).
cnf(s94, plain, spl55_25 | ~spl55_29, inference(sat_conversion,[],[f2123])).
cnf(s99, plain, spl55_17 | spl55_10, inference(rat,[],[s86,s33,s94,s65,s16,s30,s18,s7,s20])).
cnf(s100, plain, ~spl55_17 | ~spl55_5 | ~spl55_14, inference(rat,[],[s90,s36,s52,s79,s94,s83,s20])).
cnf(s101, plain, ~spl55_5 | ~spl55_14, inference(rat,[],[s86,s33,s94,s61,s16,s30,s100,s20])).
cnf(s102, plain, spl55_4, inference(rat,[],[s101,s3,s10])).
cnf(s103, plain, spl55_17, inference(rat,[],[s86,s33,s94,s57,s99,s16,s30,s20,s102])).
cnf(s104, plain, ~spl55_19, inference(rat,[],[s71,s103])).
cnf(s105, plain, spl55_25 | ~spl55_18, inference(rat,[],[s52,s86,s44,s79,s94,s103])).
cnf(s106, plain, ~spl55_25 | ~spl55_18, inference(rat,[],[s69,s7,s18,s57,s102,s103,s104,s20])).
cnf(s107, plain, ~spl55_18, inference(rat,[],[s106,s105])).
cnf(s110, plain, spl55_25, inference(rat,[],[s36,s79,s107,s103])).
cnf(s111, plain, ~spl55_10, inference(rat,[],[s77,s103,s102,s20,s110])).
cnf(s112, plain, spl55_22, inference(rat,[],[s18,s111])).
cnf(s114, plain, spl55_11, inference(rat,[],[s7,s111])).
cnf(s115, plain, $false, inference(rat,[],[s69,s103,s110,s104,s20,s114,s112])).
thf(f2130,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s115])).
% SZS output end Proof for theBenchmark