TSTP Solution File: LCL785_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL785_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:49:18 EDT 2024
% Result : Theorem 0.16s 0.51s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LCL785_5 : TPTP v8.1.2. Released v6.0.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n023.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 23:24:10 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % (6021)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.34 % (6024)WARNING: value z3 for option sas not known
% 0.16/0.34 % (6023)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.34 % (6026)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.34 % (6025)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.34 % (6022)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.34 % (6027)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.34 % (6024)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.34 % (6028)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.34 % Exception at run slice level
% 0.16/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.34 % (6028)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.35 % Exception at run slice level
% 0.16/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.35 % Exception at run slice level
% 0.16/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.36 % (6029)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.16/0.36 % (6031)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.16/0.36 % (6030)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.16/0.37 % (6029)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.37 % (6030)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.37 % Exception at run slice level
% 0.16/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.38 % (6033)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.16/0.48 % (6026)First to succeed.
% 0.16/0.51 % (6026)Refutation found. Thanks to Tanya!
% 0.16/0.51 % SZS status Theorem for theBenchmark
% 0.16/0.51 % SZS output start Proof for theBenchmark
% 0.16/0.51 tff(type_def_5, type, bool: $tType).
% 0.16/0.51 tff(type_def_6, type, dB: $tType).
% 0.16/0.51 tff(type_def_7, type, list: $tType > $tType).
% 0.16/0.51 tff(type_def_8, type, nat: $tType).
% 0.16/0.51 tff(type_def_9, type, type: $tType).
% 0.16/0.51 tff(type_def_10, type, fun: ($tType * $tType) > $tType).
% 0.16/0.51 tff(func_def_0, type, combb: !>[X0: $tType, X1: $tType, X2: $tType]:(fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))))).
% 0.16/0.51 tff(func_def_1, type, combc: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2))) > fun(X1,fun(X0,X2)))).
% 0.16/0.51 tff(func_def_2, type, combs: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * fun(X0,X1)) > fun(X0,X2))).
% 0.16/0.51 tff(func_def_3, type, it: fun(dB,bool)).
% 0.16/0.51 tff(func_def_4, type, app: fun(dB,fun(dB,dB))).
% 0.16/0.51 tff(func_def_5, type, var: nat > dB).
% 0.16/0.51 tff(func_def_6, type, dB_case: !>[X0: $tType]:((fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB) > X0)).
% 0.16/0.51 tff(func_def_7, type, subst: (dB * dB * nat) > dB).
% 0.16/0.51 tff(func_def_8, type, append: !>[X0: $tType]:(fun(list(X0),fun(list(X0),list(X0))))).
% 0.16/0.51 tff(func_def_9, type, foldl: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0)) * X0 * list(X1)) > X0)).
% 0.16/0.51 tff(func_def_10, type, foldr: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X1)) * list(X0) * X1) > X1)).
% 0.16/0.51 tff(func_def_11, type, insert: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 0.16/0.51 tff(func_def_12, type, cons: !>[X0: $tType]:(fun(X0,fun(list(X0),list(X0))))).
% 0.16/0.51 tff(func_def_13, type, nil: !>[X0: $tType]:(list(X0))).
% 0.16/0.51 tff(func_def_14, type, list_case: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(list(X1),X0)) * list(X1)) > X0)).
% 0.16/0.51 tff(func_def_15, type, maps: !>[X0: $tType, X1: $tType]:((fun(X0,list(X1)) * list(X0)) > list(X1))).
% 0.16/0.51 tff(func_def_16, type, rotate1: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.16/0.51 tff(func_def_17, type, splice: !>[X0: $tType]:((list(X0) * list(X0)) > list(X0))).
% 0.16/0.51 tff(func_def_18, type, shift: !>[X0: $tType]:((fun(nat,X0) * nat * X0) > fun(nat,X0))).
% 0.16/0.51 tff(func_def_19, type, fun1: fun(type,fun(type,type))).
% 0.16/0.51 tff(func_def_20, type, type_case: !>[X0: $tType]:((fun(nat,X0) * fun(type,fun(type,X0)) * type) > X0)).
% 0.16/0.51 tff(func_def_21, type, typing: (fun(nat,type) * dB) > fun(type,bool)).
% 0.16/0.51 tff(func_def_22, type, typings: (fun(nat,type) * list(dB)) > fun(list(type),bool)).
% 0.16/0.51 tff(func_def_23, type, aa: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * X0) > X1)).
% 0.16/0.51 tff(func_def_24, type, fFalse: bool).
% 0.16/0.51 tff(func_def_25, type, fTrue: bool).
% 0.16/0.51 tff(func_def_26, type, fconj: fun(bool,fun(bool,bool))).
% 0.16/0.51 tff(func_def_27, type, t: type).
% 0.16/0.51 tff(func_def_28, type, t_a: type).
% 0.16/0.51 tff(func_def_29, type, t1: type).
% 0.16/0.51 tff(func_def_30, type, a: dB).
% 0.16/0.51 tff(func_def_31, type, as: list(dB)).
% 0.16/0.51 tff(func_def_32, type, e: fun(nat,type)).
% 0.16/0.51 tff(func_def_33, type, ea: fun(nat,type)).
% 0.16/0.51 tff(func_def_34, type, i: nat).
% 0.16/0.51 tff(func_def_35, type, ia: nat).
% 0.16/0.51 tff(func_def_36, type, n: nat).
% 0.16/0.51 tff(func_def_37, type, rs: list(dB)).
% 0.16/0.51 tff(func_def_38, type, t2: dB).
% 0.16/0.51 tff(func_def_39, type, u: dB).
% 0.16/0.51 tff(func_def_40, type, ua: dB).
% 0.16/0.51 tff(func_def_41, type, sK5: !>[X0: $tType]:((list(X0)) > X0)).
% 0.16/0.51 tff(func_def_42, type, sK6: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.16/0.51 tff(func_def_43, type, sK7: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.16/0.51 tff(func_def_44, type, sK8: !>[X0: $tType]:((list(X0)) > X0)).
% 0.16/0.51 tff(func_def_45, type, sK9: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.16/0.51 tff(func_def_46, type, sK10: !>[X0: $tType]:((list(X0)) > X0)).
% 0.16/0.51 tff(func_def_47, type, sK11: !>[X0: $tType]:((list(X0)) > X0)).
% 0.16/0.51 tff(func_def_48, type, sK12: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.16/0.51 tff(func_def_49, type, sK13: !>[X0: $tType]:((fun(list(X0),bool)) > X0)).
% 0.16/0.51 tff(func_def_50, type, sK14: !>[X0: $tType]:((fun(list(X0),bool)) > list(X0))).
% 0.16/0.51 tff(func_def_51, type, sK15: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > X0)).
% 0.16/0.51 tff(func_def_52, type, sK16: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > list(X0))).
% 0.16/0.51 tff(func_def_53, type, sK17: (type * list(dB) * dB * fun(nat,type)) > list(type)).
% 0.16/0.51 tff(func_def_54, type, sK18: (type * list(dB) * dB * fun(nat,type)) > list(type)).
% 0.16/0.51 tff(func_def_55, type, sK19: (type * list(dB) * nat * fun(nat,type)) > list(type)).
% 0.16/0.51 tff(func_def_56, type, sK20: (type * dB * dB * fun(nat,type)) > type).
% 0.16/0.51 tff(func_def_57, type, sK21: (list(type) * dB * list(dB) * fun(nat,type)) > list(type)).
% 0.16/0.51 tff(func_def_58, type, sK22: (list(type) * dB * list(dB) * fun(nat,type)) > type).
% 0.16/0.51 tff(func_def_59, type, sK23: !>[X0: $tType, X1: $tType]:((fun(X1,X0) * fun(X1,X0)) > X1)).
% 0.16/0.51 tff(func_def_60, type, sK24: (dB * dB * list(dB) * dB) > list(dB)).
% 0.16/0.51 tff(func_def_61, type, sK25: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > list(X0))).
% 0.16/0.51 tff(func_def_62, type, sK26: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > list(X0))).
% 0.16/0.51 tff(func_def_63, type, sK27: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * list(X0)) > list(X0))).
% 0.16/0.51 tff(func_def_64, type, sK28: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 0.16/0.51 tff(func_def_65, type, sK29: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 0.16/0.51 tff(func_def_66, type, sK30: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X0)).
% 0.16/0.51 tff(func_def_67, type, sK31: (type * type * list(dB) * fun(nat,type)) > list(type)).
% 0.16/0.51 tff(pred_def_1, type, listsp: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 0.16/0.51 tff(pred_def_2, type, pp: bool > $o).
% 0.16/0.51 tff(pred_def_3, type, sP0: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 0.16/0.51 tff(pred_def_4, type, sP1: (dB * dB * list(dB) * dB) > $o).
% 0.16/0.51 tff(pred_def_5, type, sP2: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > $o)).
% 0.16/0.51 tff(pred_def_6, type, sP3: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > $o)).
% 0.16/0.51 tff(pred_def_7, type, sP4: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * list(X0)) > $o)).
% 0.16/0.51 tff(f2862,plain,(
% 0.16/0.51 $false),
% 0.16/0.51 inference(avatar_sat_refutation,[],[f635,f640,f644,f648,f653,f658,f663,f667,f678,f683,f687,f693,f697,f702,f706,f710,f714,f718,f722,f738,f742,f746,f753,f761,f765,f769,f776,f780,f784,f794,f798,f802,f806,f813,f818,f824,f828,f832,f836,f840,f844,f848,f860,f873,f877,f882,f887,f899,f911,f915,f919,f923,f932,f937,f942,f946,f950,f954,f958,f965,f969,f973,f981,f986,f990,f994,f998,f1002,f1022,f1026,f1034,f1038,f1042,f1046,f1050,f1054,f1058,f1063,f1067,f1071,f1094,f1135,f1139,f1143,f1180,f1184,f1188,f1192,f1230,f1240,f1244,f1248,f1269,f1273,f1291,f1295,f1319,f1323,f1345,f1349,f1353,f1409,f1413,f1417,f1421,f1462,f1469,f1477,f1481,f1485,f1528,f1532,f1536,f1540,f1544,f1548,f1552,f1556,f1838,f1844,f1859,f1863,f1889,f1893,f1899,f1903,f1909,f1919,f1925,f1929,f1935,f1945,f1950,f1956,f1962,f1967,f1973,f1977,f1988,f1993,f1999,f2004,f2008,f2012,f2018,f2024,f2038,f2043,f2055,f2066,f2070,f2075,f2534,f2540,f2553,f2574,f2580,f2587,f2591,f2597,f2607,f2613,f2623,f2629,f2639,f2715,f2719,f2736,f2742,f2764,f2770,f2786,f2792,f2796,f2811,f2817,f2832,f2838,f2854,f2860,f2861])).
% 0.16/0.51 tff(f2861,plain,(
% 0.16/0.51 ~spl32_2 | spl32_1 | ~spl32_24),
% 0.16/0.51 inference(avatar_split_clause,[],[f2644,f755,f632,f637])).
% 0.16/0.51 tff(f637,plain,(
% 0.16/0.51 spl32_2 <=> pp(fTrue)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_2])])).
% 0.16/0.51 tff(f632,plain,(
% 0.16/0.51 spl32_1 <=> pp(fFalse)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_1])])).
% 0.16/0.51 tff(f755,plain,(
% 0.16/0.51 spl32_24 <=> ! [X0 : bool] : fTrue = X0),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_24])])).
% 0.16/0.51 tff(f2644,plain,(
% 0.16/0.51 ~pp(fTrue) | (spl32_1 | ~spl32_24)),
% 0.16/0.51 inference(superposition,[],[f634,f756])).
% 0.16/0.51 tff(f756,plain,(
% 0.16/0.51 ( ! [X0 : bool] : (fTrue = X0) ) | ~spl32_24),
% 0.16/0.51 inference(avatar_component_clause,[],[f755])).
% 0.16/0.51 tff(f634,plain,(
% 0.16/0.51 ~pp(fFalse) | spl32_1),
% 0.16/0.51 inference(avatar_component_clause,[],[f632])).
% 0.16/0.51 tff(f2860,plain,(
% 0.16/0.51 spl32_179 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_178),
% 0.16/0.51 inference(avatar_split_clause,[],[f2856,f2852,f1538,f979,f744,f2858])).
% 0.16/0.51 tff(f2858,plain,(
% 0.16/0.51 spl32_179 <=> ! [X0 : list(type),X3 : fun(nat,type),X2 : list(dB),X1 : dB] : (foldl(list(type),list(type),append(type),sK21(X0,X1,X2,X3),insert(list(type),insert(type,sK22(X0,X1,X2,X3),nil(type)),nil(list(type)))) = X0 | ~pp(aa(list(type),bool,typings(X3,foldl(list(dB),list(dB),append(dB),X2,insert(list(dB),insert(dB,X1,nil(dB)),nil(list(dB))))),X0)))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_179])])).
% 0.16/0.51 tff(f744,plain,(
% 0.16/0.51 spl32_22 <=> ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X1,fun(X0,X1))] : foldl(X1,X0,X3,X2,nil(X0)) = X2),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_22])])).
% 0.16/0.51 tff(f979,plain,(
% 0.16/0.51 spl32_64 <=> ! [X0 : $tType,X1 : X0] : insert(X0,X1,nil(X0)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_64])])).
% 0.16/0.51 tff(f1538,plain,(
% 0.16/0.51 spl32_115 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X0,X5 : fun(X0,fun(X1,X0)),X2 : list(X1)] : foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_115])])).
% 0.16/0.51 tff(f2852,plain,(
% 0.16/0.51 spl32_178 <=> ! [X0 : list(type),X3 : fun(nat,type),X2 : list(dB),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),insert(dB,X1,nil(dB)))),X0)) | aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),sK21(X0,X1,X2,X3)),insert(type,sK22(X0,X1,X2,X3),nil(type))) = X0)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_178])])).
% 0.16/0.51 tff(f2856,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (foldl(list(type),list(type),append(type),sK21(X0,X1,X2,X3),insert(list(type),insert(type,sK22(X0,X1,X2,X3),nil(type)),nil(list(type)))) = X0 | ~pp(aa(list(type),bool,typings(X3,foldl(list(dB),list(dB),append(dB),X2,insert(list(dB),insert(dB,X1,nil(dB)),nil(list(dB))))),X0))) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_178)),
% 0.16/0.51 inference(forward_demodulation,[],[f2855,f1721])).
% 0.16/0.51 tff(f1721,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X0)),X3 : X0,X4 : X1] : (aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4) = foldl(X0,X1,X2,X3,insert(X1,X4,nil(X1)))) ) | (~spl32_22 | ~spl32_64 | ~spl32_115)),
% 0.16/0.51 inference(forward_demodulation,[],[f1678,f980])).
% 0.16/0.51 tff(f980,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X1 : X0] : (insert(X0,X1,nil(X0)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0))) ) | ~spl32_64),
% 0.16/0.51 inference(avatar_component_clause,[],[f979])).
% 0.16/0.51 tff(f1678,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X0)),X3 : X0,X4 : X1] : (aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4) = foldl(X0,X1,X2,X3,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X4),nil(X1)))) ) | (~spl32_22 | ~spl32_115)),
% 0.16/0.51 inference(superposition,[],[f1539,f745])).
% 0.16/0.51 tff(f745,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X1,fun(X0,X1))] : (foldl(X1,X0,X3,X2,nil(X0)) = X2) ) | ~spl32_22),
% 0.16/0.51 inference(avatar_component_clause,[],[f744])).
% 0.16/0.51 tff(f1539,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : X0,X5 : fun(X0,fun(X1,X0))] : (foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2)) ) | ~spl32_115),
% 0.16/0.51 inference(avatar_component_clause,[],[f1538])).
% 0.16/0.51 tff(f2855,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,foldl(list(dB),list(dB),append(dB),X2,insert(list(dB),insert(dB,X1,nil(dB)),nil(list(dB))))),X0)) | aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),sK21(X0,X1,X2,X3)),insert(type,sK22(X0,X1,X2,X3),nil(type))) = X0) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_178)),
% 0.16/0.51 inference(forward_demodulation,[],[f2853,f1721])).
% 0.16/0.51 tff(f2853,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),insert(dB,X1,nil(dB)))),X0)) | aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),sK21(X0,X1,X2,X3)),insert(type,sK22(X0,X1,X2,X3),nil(type))) = X0) ) | ~spl32_178),
% 0.16/0.51 inference(avatar_component_clause,[],[f2852])).
% 0.16/0.51 tff(f2854,plain,(
% 0.16/0.51 spl32_178),
% 0.16/0.51 inference(avatar_split_clause,[],[f614,f2852])).
% 0.16/0.51 tff(f614,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),insert(dB,X1,nil(dB)))),X0)) | aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),sK21(X0,X1,X2,X3)),insert(type,sK22(X0,X1,X2,X3),nil(type))) = X0) )),
% 0.16/0.51 inference(forward_demodulation,[],[f613,f374])).
% 0.16/0.51 tff(f374,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X1 : X0] : (insert(X0,X1,nil(X0)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f122])).
% 0.16/0.51 tff(f122,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : X0] : insert(X0,X1,nil(X0)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0))),
% 0.16/0.51 inference(rectify,[],[f47])).
% 0.16/0.51 tff(f47,axiom,(
% 0.16/0.51 ! [X2 : $tType,X59 : X2] : insert(X2,X59,nil(X2)) = aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X59),nil(X2))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_insert__Nil)).
% 0.16/0.51 tff(f613,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),sK21(X0,X1,X2,X3)),insert(type,sK22(X0,X1,X2,X3),nil(type))) = X0 | ~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X1),nil(dB)))),X0))) )),
% 0.16/0.51 inference(forward_demodulation,[],[f449,f374])).
% 0.16/0.51 tff(f449,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),sK21(X0,X1,X2,X3)),aa(list(type),list(type),aa(type,fun(list(type),list(type)),cons(type),sK22(X0,X1,X2,X3)),nil(type))) = X0 | ~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X1),nil(dB)))),X0))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f304])).
% 0.16/0.51 tff(f304,plain,(
% 0.16/0.51 ! [X0 : list(type),X1 : dB,X2 : list(dB),X3 : fun(nat,type)] : ((pp(aa(type,bool,typing(X3,X1),sK22(X0,X1,X2,X3))) & pp(aa(list(type),bool,typings(X3,X2),sK21(X0,X1,X2,X3))) & aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),sK21(X0,X1,X2,X3)),aa(list(type),list(type),aa(type,fun(list(type),list(type)),cons(type),sK22(X0,X1,X2,X3)),nil(type))) = X0) | ~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X1),nil(dB)))),X0)))),
% 0.16/0.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f228,f303])).
% 0.16/0.51 tff(f303,plain,(
% 0.16/0.51 ! [X0 : list(type),X1 : dB,X2 : list(dB),X3 : fun(nat,type)] : (? [X4 : list(type),X5 : type] : (pp(aa(type,bool,typing(X3,X1),X5)) & pp(aa(list(type),bool,typings(X3,X2),X4)) & aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),X4),aa(list(type),list(type),aa(type,fun(list(type),list(type)),cons(type),X5),nil(type))) = X0) => (pp(aa(type,bool,typing(X3,X1),sK22(X0,X1,X2,X3))) & pp(aa(list(type),bool,typings(X3,X2),sK21(X0,X1,X2,X3))) & aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),sK21(X0,X1,X2,X3)),aa(list(type),list(type),aa(type,fun(list(type),list(type)),cons(type),sK22(X0,X1,X2,X3)),nil(type))) = X0))),
% 0.16/0.51 introduced(choice_axiom,[])).
% 0.16/0.51 tff(f228,plain,(
% 0.16/0.51 ! [X0 : list(type),X1 : dB,X2 : list(dB),X3 : fun(nat,type)] : (? [X4 : list(type),X5 : type] : (pp(aa(type,bool,typing(X3,X1),X5)) & pp(aa(list(type),bool,typings(X3,X2),X4)) & aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),X4),aa(list(type),list(type),aa(type,fun(list(type),list(type)),cons(type),X5),nil(type))) = X0) | ~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X1),nil(dB)))),X0)))),
% 0.16/0.51 inference(flattening,[],[f227])).
% 0.16/0.51 tff(f227,plain,(
% 0.16/0.51 ! [X0 : list(type),X1 : dB,X2 : list(dB),X3 : fun(nat,type)] : (? [X4 : list(type),X5 : type] : ((pp(aa(type,bool,typing(X3,X1),X5)) & pp(aa(list(type),bool,typings(X3,X2),X4))) & aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),X4),aa(list(type),list(type),aa(type,fun(list(type),list(type)),cons(type),X5),nil(type))) = X0) | ~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X1),nil(dB)))),X0)))),
% 0.16/0.51 inference(ennf_transformation,[],[f170])).
% 0.16/0.51 tff(f170,plain,(
% 0.16/0.51 ! [X0 : list(type),X1 : dB,X2 : list(dB),X3 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X1),nil(dB)))),X0)) => ~! [X4 : list(type),X5 : type] : (aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),X4),aa(list(type),list(type),aa(type,fun(list(type),list(type)),cons(type),X5),nil(type))) = X0 => (pp(aa(list(type),bool,typings(X3,X2),X4)) => ~pp(aa(type,bool,typing(X3,X1),X5)))))),
% 0.16/0.51 inference(rectify,[],[f89])).
% 0.16/0.51 tff(f89,axiom,(
% 0.16/0.51 ! [X87 : list(type),X37 : dB,X14 : list(dB),X12 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X12,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X14),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X37),nil(dB)))),X87)) => ~! [X88 : list(type),X89 : type] : (aa(list(type),list(type),aa(list(type),fun(list(type),list(type)),append(type),X88),aa(list(type),list(type),aa(type,fun(list(type),list(type)),cons(type),X89),nil(type))) = X87 => (pp(aa(list(type),bool,typings(X12,X14),X88)) => ~pp(aa(type,bool,typing(X12,X37),X89)))))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_types__snocE)).
% 0.16/0.51 tff(f2838,plain,(
% 0.16/0.51 spl32_177 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_176),
% 0.16/0.51 inference(avatar_split_clause,[],[f2834,f2830,f1538,f979,f744,f2836])).
% 0.16/0.51 tff(f2836,plain,(
% 0.16/0.51 spl32_177 <=> ! [X2 : $tType,X4 : list(X2),X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (foldl(list(X2),list(X2),append(X2),sK27(X2,X0,X1,X3,X4),insert(list(X2),X0,nil(list(X2)))) = X1 | foldl(list(X2),list(X2),append(X2),sK27(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | ~sP4(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_177])])).
% 0.16/0.51 tff(f2830,plain,(
% 0.16/0.51 spl32_176 <=> ! [X2 : $tType,X4 : list(X2),X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X0) = X1 | ~sP4(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_176])])).
% 0.16/0.51 tff(f2834,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (foldl(list(X2),list(X2),append(X2),sK27(X2,X0,X1,X3,X4),insert(list(X2),X0,nil(list(X2)))) = X1 | foldl(list(X2),list(X2),append(X2),sK27(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | ~sP4(X2,X0,X1,X3,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_176)),
% 0.16/0.51 inference(forward_demodulation,[],[f2833,f1721])).
% 0.16/0.51 tff(f2833,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (foldl(list(X2),list(X2),append(X2),sK27(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X0) = X1 | ~sP4(X2,X0,X1,X3,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_176)),
% 0.16/0.51 inference(forward_demodulation,[],[f2831,f1721])).
% 0.16/0.51 tff(f2831,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X0) = X1 | ~sP4(X2,X0,X1,X3,X4)) ) | ~spl32_176),
% 0.16/0.51 inference(avatar_component_clause,[],[f2830])).
% 0.16/0.51 tff(f2832,plain,(
% 0.16/0.51 spl32_176),
% 0.16/0.51 inference(avatar_split_clause,[],[f514,f2830])).
% 0.16/0.51 tff(f514,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X0) = X1 | ~sP4(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f343])).
% 0.16/0.51 tff(f343,plain,(
% 0.16/0.51 ! [X0 : list(X2),X1 : list(X2),X2 : $tType,X3 : list(X2),X4 : list(X2)] : ((sP4(X2,X0,X1,X3,X4) | ! [X5 : list(X2)] : ((aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1) != X0 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),X5) != X3) & (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X0) != X1 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),X5) != X4))) & (((aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X1) = X0 & aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),sK27(X2,X0,X1,X3,X4)) = X3) | (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X0) = X1 & aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),sK27(X2,X0,X1,X3,X4)) = X4)) | ~sP4(X2,X0,X1,X3,X4)))),
% 0.16/0.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f341,f342])).
% 0.16/0.51 tff(f342,plain,(
% 0.16/0.51 ! [X2 : $tType,X0 : list(X2),X1 : list(X2),X3 : list(X2),X4 : list(X2)] : (? [X6 : list(X2)] : ((aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X6),X1) = X0 & aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),X6) = X3) | (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X6),X0) = X1 & aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),X6) = X4)) => ((aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X1) = X0 & aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),sK27(X2,X0,X1,X3,X4)) = X3) | (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X0) = X1 & aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),sK27(X2,X0,X1,X3,X4)) = X4)))),
% 0.16/0.51 introduced(choice_axiom,[])).
% 0.16/0.51 tff(f341,plain,(
% 0.16/0.51 ! [X0 : list(X2),X1 : list(X2),X2 : $tType,X3 : list(X2),X4 : list(X2)] : ((sP4(X2,X0,X1,X3,X4) | ! [X5 : list(X2)] : ((aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1) != X0 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),X5) != X3) & (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X0) != X1 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),X5) != X4))) & (? [X6 : list(X2)] : ((aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X6),X1) = X0 & aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),X6) = X3) | (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X6),X0) = X1 & aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),X6) = X4)) | ~sP4(X2,X0,X1,X3,X4)))),
% 0.16/0.51 inference(rectify,[],[f340])).
% 0.16/0.51 tff(f340,plain,(
% 0.16/0.51 ! [X3 : list(X0),X1 : list(X0),X0 : $tType,X2 : list(X0),X4 : list(X0)] : ((sP4(X0,X3,X1,X2,X4) | ! [X5 : list(X0)] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X1) != X3 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X5) != X2) & (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X3) != X1 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X5) != X4))) & (? [X5 : list(X0)] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X1) = X3 & aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X5) = X2) | (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X3) = X1 & aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X5) = X4)) | ~sP4(X0,X3,X1,X2,X4)))),
% 0.16/0.51 inference(nnf_transformation,[],[f261])).
% 0.16/0.51 tff(f261,plain,(
% 0.16/0.51 ! [X3 : list(X0),X1 : list(X0),X0 : $tType,X2 : list(X0),X4 : list(X0)] : (sP4(X0,X3,X1,X2,X4) <=> ? [X5 : list(X0)] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X1) = X3 & aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X5) = X2) | (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X3) = X1 & aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X5) = X4)))),
% 0.16/0.51 introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])])).
% 0.16/0.51 tff(f2817,plain,(
% 0.16/0.51 spl32_175 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_174),
% 0.16/0.51 inference(avatar_split_clause,[],[f2813,f2809,f1538,f979,f744,f2815])).
% 0.16/0.51 tff(f2815,plain,(
% 0.16/0.51 spl32_175 <=> ! [X2 : $tType,X4 : list(X2),X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (foldl(list(X2),list(X2),append(X2),X3,insert(list(X2),sK27(X2,X0,X1,X3,X4),nil(list(X2)))) = X4 | foldl(list(X2),list(X2),append(X2),sK27(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | ~sP4(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_175])])).
% 0.16/0.51 tff(f2809,plain,(
% 0.16/0.51 spl32_174 <=> ! [X2 : $tType,X4 : list(X2),X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),sK27(X2,X0,X1,X3,X4)) = X4 | ~sP4(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_174])])).
% 0.16/0.51 tff(f2813,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (foldl(list(X2),list(X2),append(X2),X3,insert(list(X2),sK27(X2,X0,X1,X3,X4),nil(list(X2)))) = X4 | foldl(list(X2),list(X2),append(X2),sK27(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | ~sP4(X2,X0,X1,X3,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_174)),
% 0.16/0.51 inference(forward_demodulation,[],[f2812,f1721])).
% 0.16/0.51 tff(f2812,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (foldl(list(X2),list(X2),append(X2),sK27(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),sK27(X2,X0,X1,X3,X4)) = X4 | ~sP4(X2,X0,X1,X3,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_174)),
% 0.16/0.51 inference(forward_demodulation,[],[f2810,f1721])).
% 0.16/0.51 tff(f2810,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),sK27(X2,X0,X1,X3,X4)) = X4 | ~sP4(X2,X0,X1,X3,X4)) ) | ~spl32_174),
% 0.16/0.51 inference(avatar_component_clause,[],[f2809])).
% 0.16/0.51 tff(f2811,plain,(
% 0.16/0.51 spl32_174),
% 0.16/0.51 inference(avatar_split_clause,[],[f513,f2809])).
% 0.16/0.51 tff(f513,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),sK27(X2,X0,X1,X3,X4)) = X4 | ~sP4(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f343])).
% 0.16/0.51 tff(f2796,plain,(
% 0.16/0.51 spl32_173 | ~spl32_2 | ~spl32_24),
% 0.16/0.51 inference(avatar_split_clause,[],[f2642,f755,f637,f2794])).
% 0.16/0.51 tff(f2794,plain,(
% 0.16/0.51 spl32_173 <=> ! [X0 : bool] : pp(X0)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_173])])).
% 0.16/0.51 tff(f2642,plain,(
% 0.16/0.51 ( ! [X0 : bool] : (pp(X0)) ) | (~spl32_2 | ~spl32_24)),
% 0.16/0.51 inference(superposition,[],[f639,f756])).
% 0.16/0.51 tff(f639,plain,(
% 0.16/0.51 pp(fTrue) | ~spl32_2),
% 0.16/0.51 inference(avatar_component_clause,[],[f637])).
% 0.16/0.51 tff(f2792,plain,(
% 0.16/0.51 spl32_172 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_171),
% 0.16/0.51 inference(avatar_split_clause,[],[f2788,f2784,f1538,f979,f744,f2790])).
% 0.16/0.51 tff(f2790,plain,(
% 0.16/0.51 spl32_172 <=> ! [X2 : $tType,X4 : list(X2),X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (foldl(list(X2),list(X2),append(X2),sK27(X2,X0,X1,X3,X4),insert(list(X2),X0,nil(list(X2)))) = X1 | foldl(list(X2),list(X2),append(X2),X4,insert(list(X2),sK27(X2,X0,X1,X3,X4),nil(list(X2)))) = X3 | ~sP4(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_172])])).
% 0.16/0.51 tff(f2784,plain,(
% 0.16/0.51 spl32_171 <=> ! [X2 : $tType,X4 : list(X2),X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),sK27(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X0) = X1 | ~sP4(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_171])])).
% 0.16/0.51 tff(f2788,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (foldl(list(X2),list(X2),append(X2),sK27(X2,X0,X1,X3,X4),insert(list(X2),X0,nil(list(X2)))) = X1 | foldl(list(X2),list(X2),append(X2),X4,insert(list(X2),sK27(X2,X0,X1,X3,X4),nil(list(X2)))) = X3 | ~sP4(X2,X0,X1,X3,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_171)),
% 0.16/0.51 inference(forward_demodulation,[],[f2787,f1721])).
% 0.16/0.51 tff(f2787,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (foldl(list(X2),list(X2),append(X2),X4,insert(list(X2),sK27(X2,X0,X1,X3,X4),nil(list(X2)))) = X3 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X0) = X1 | ~sP4(X2,X0,X1,X3,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_171)),
% 0.16/0.51 inference(forward_demodulation,[],[f2785,f1721])).
% 0.16/0.51 tff(f2785,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),sK27(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X0) = X1 | ~sP4(X2,X0,X1,X3,X4)) ) | ~spl32_171),
% 0.16/0.51 inference(avatar_component_clause,[],[f2784])).
% 0.16/0.51 tff(f2786,plain,(
% 0.16/0.51 spl32_171),
% 0.16/0.51 inference(avatar_split_clause,[],[f512,f2784])).
% 0.16/0.51 tff(f512,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),sK27(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK27(X2,X0,X1,X3,X4)),X0) = X1 | ~sP4(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f343])).
% 0.16/0.51 tff(f2770,plain,(
% 0.16/0.51 spl32_170 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_169),
% 0.16/0.51 inference(avatar_split_clause,[],[f2766,f2762,f1538,f979,f744,f2768])).
% 0.16/0.51 tff(f2768,plain,(
% 0.16/0.51 spl32_170 <=> ! [X2 : $tType,X4 : list(X2),X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (foldl(list(X2),list(X2),append(X2),X3,insert(list(X2),sK27(X2,X0,X1,X3,X4),nil(list(X2)))) = X4 | foldl(list(X2),list(X2),append(X2),X4,insert(list(X2),sK27(X2,X0,X1,X3,X4),nil(list(X2)))) = X3 | ~sP4(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_170])])).
% 0.16/0.51 tff(f2762,plain,(
% 0.16/0.51 spl32_169 <=> ! [X2 : $tType,X4 : list(X2),X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),sK27(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),sK27(X2,X0,X1,X3,X4)) = X4 | ~sP4(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_169])])).
% 0.16/0.51 tff(f2766,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (foldl(list(X2),list(X2),append(X2),X3,insert(list(X2),sK27(X2,X0,X1,X3,X4),nil(list(X2)))) = X4 | foldl(list(X2),list(X2),append(X2),X4,insert(list(X2),sK27(X2,X0,X1,X3,X4),nil(list(X2)))) = X3 | ~sP4(X2,X0,X1,X3,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_169)),
% 0.16/0.51 inference(forward_demodulation,[],[f2765,f1721])).
% 0.16/0.51 tff(f2765,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (foldl(list(X2),list(X2),append(X2),X4,insert(list(X2),sK27(X2,X0,X1,X3,X4),nil(list(X2)))) = X3 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),sK27(X2,X0,X1,X3,X4)) = X4 | ~sP4(X2,X0,X1,X3,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_169)),
% 0.16/0.51 inference(forward_demodulation,[],[f2763,f1721])).
% 0.16/0.51 tff(f2763,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),sK27(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),sK27(X2,X0,X1,X3,X4)) = X4 | ~sP4(X2,X0,X1,X3,X4)) ) | ~spl32_169),
% 0.16/0.51 inference(avatar_component_clause,[],[f2762])).
% 0.16/0.51 tff(f2764,plain,(
% 0.16/0.51 spl32_169),
% 0.16/0.51 inference(avatar_split_clause,[],[f511,f2762])).
% 0.16/0.51 tff(f511,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),sK27(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),sK27(X2,X0,X1,X3,X4)) = X4 | ~sP4(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f343])).
% 0.16/0.51 tff(f2742,plain,(
% 0.16/0.51 spl32_168 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_167),
% 0.16/0.51 inference(avatar_split_clause,[],[f2738,f2734,f1538,f979,f744,f2740])).
% 0.16/0.51 tff(f2740,plain,(
% 0.16/0.51 spl32_168 <=> ! [X4 : list(dB),X1 : dB,X3 : dB] : (sP1(foldl(dB,dB,app,X1,X4),X1,foldl(list(dB),list(dB),append(dB),X4,insert(list(dB),insert(dB,X3,nil(dB)),nil(list(dB)))),X3) | nil(dB) = foldl(list(dB),list(dB),append(dB),X4,insert(list(dB),insert(dB,X3,nil(dB)),nil(list(dB)))))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_168])])).
% 0.16/0.51 tff(f2734,plain,(
% 0.16/0.51 spl32_167 <=> ! [X4 : list(dB),X1 : dB,X3 : dB] : (nil(dB) = aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),insert(dB,X3,nil(dB))) | sP1(foldl(dB,dB,app,X1,X4),X1,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),insert(dB,X3,nil(dB))),X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_167])])).
% 0.16/0.51 tff(f2738,plain,(
% 0.16/0.51 ( ! [X3 : dB,X1 : dB,X4 : list(dB)] : (sP1(foldl(dB,dB,app,X1,X4),X1,foldl(list(dB),list(dB),append(dB),X4,insert(list(dB),insert(dB,X3,nil(dB)),nil(list(dB)))),X3) | nil(dB) = foldl(list(dB),list(dB),append(dB),X4,insert(list(dB),insert(dB,X3,nil(dB)),nil(list(dB))))) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_167)),
% 0.16/0.51 inference(forward_demodulation,[],[f2737,f1721])).
% 0.16/0.51 tff(f2737,plain,(
% 0.16/0.51 ( ! [X3 : dB,X1 : dB,X4 : list(dB)] : (nil(dB) = foldl(list(dB),list(dB),append(dB),X4,insert(list(dB),insert(dB,X3,nil(dB)),nil(list(dB)))) | sP1(foldl(dB,dB,app,X1,X4),X1,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),insert(dB,X3,nil(dB))),X3)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_167)),
% 0.16/0.51 inference(forward_demodulation,[],[f2735,f1721])).
% 0.16/0.51 tff(f2735,plain,(
% 0.16/0.51 ( ! [X3 : dB,X1 : dB,X4 : list(dB)] : (nil(dB) = aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),insert(dB,X3,nil(dB))) | sP1(foldl(dB,dB,app,X1,X4),X1,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),insert(dB,X3,nil(dB))),X3)) ) | ~spl32_167),
% 0.16/0.51 inference(avatar_component_clause,[],[f2734])).
% 0.16/0.51 tff(f2736,plain,(
% 0.16/0.51 spl32_167),
% 0.16/0.51 inference(avatar_split_clause,[],[f617,f2734])).
% 0.16/0.51 tff(f617,plain,(
% 0.16/0.51 ( ! [X3 : dB,X1 : dB,X4 : list(dB)] : (nil(dB) = aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),insert(dB,X3,nil(dB))) | sP1(foldl(dB,dB,app,X1,X4),X1,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),insert(dB,X3,nil(dB))),X3)) )),
% 0.16/0.51 inference(forward_demodulation,[],[f616,f374])).
% 0.16/0.51 tff(f616,plain,(
% 0.16/0.51 ( ! [X3 : dB,X1 : dB,X4 : list(dB)] : (sP1(foldl(dB,dB,app,X1,X4),X1,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),insert(dB,X3,nil(dB))),X3) | nil(dB) = aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB)))) )),
% 0.16/0.51 inference(forward_demodulation,[],[f573,f374])).
% 0.16/0.51 tff(f573,plain,(
% 0.16/0.51 ( ! [X3 : dB,X1 : dB,X4 : list(dB)] : (sP1(foldl(dB,dB,app,X1,X4),X1,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))),X3) | nil(dB) = aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB)))) )),
% 0.16/0.51 inference(equality_resolution,[],[f572])).
% 0.16/0.51 tff(f572,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : dB,X1 : dB,X4 : list(dB)] : (sP1(foldl(dB,dB,app,X1,X4),X1,X2,X3) | aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))) != X2 | nil(dB) = X2) )),
% 0.16/0.51 inference(equality_resolution,[],[f461])).
% 0.16/0.51 tff(f461,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB,X4 : list(dB)] : (sP1(X0,X1,X2,X3) | foldl(dB,dB,app,X1,X4) != X0 | aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))) != X2 | nil(dB) = X2) )),
% 0.16/0.51 inference(cnf_transformation,[],[f313])).
% 0.16/0.51 tff(f313,plain,(
% 0.16/0.51 ! [X0 : dB,X1 : dB,X2 : list(dB),X3 : dB] : ((sP1(X0,X1,X2,X3) | (! [X4 : list(dB)] : (foldl(dB,dB,app,X1,X4) != X0 | aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))) != X2) & nil(dB) != X2) | (aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3) != X1 & nil(dB) = X2)) & ((((foldl(dB,dB,app,X1,sK24(X0,X1,X2,X3)) = X0 & aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),sK24(X0,X1,X2,X3)),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))) = X2) | nil(dB) = X2) & (aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3) = X1 | nil(dB) != X2)) | ~sP1(X0,X1,X2,X3)))),
% 0.16/0.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f311,f312])).
% 0.16/0.51 tff(f312,plain,(
% 0.16/0.51 ! [X0 : dB,X1 : dB,X2 : list(dB),X3 : dB] : (? [X5 : list(dB)] : (foldl(dB,dB,app,X1,X5) = X0 & aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X5),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))) = X2) => (foldl(dB,dB,app,X1,sK24(X0,X1,X2,X3)) = X0 & aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),sK24(X0,X1,X2,X3)),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))) = X2))),
% 0.16/0.51 introduced(choice_axiom,[])).
% 0.16/0.51 tff(f311,plain,(
% 0.16/0.51 ! [X0 : dB,X1 : dB,X2 : list(dB),X3 : dB] : ((sP1(X0,X1,X2,X3) | (! [X4 : list(dB)] : (foldl(dB,dB,app,X1,X4) != X0 | aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))) != X2) & nil(dB) != X2) | (aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3) != X1 & nil(dB) = X2)) & (((? [X5 : list(dB)] : (foldl(dB,dB,app,X1,X5) = X0 & aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X5),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))) = X2) | nil(dB) = X2) & (aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3) = X1 | nil(dB) != X2)) | ~sP1(X0,X1,X2,X3)))),
% 0.16/0.51 inference(rectify,[],[f310])).
% 0.16/0.51 tff(f310,plain,(
% 0.16/0.51 ! [X3 : dB,X1 : dB,X0 : list(dB),X2 : dB] : ((sP1(X3,X1,X0,X2) | (! [X4 : list(dB)] : (foldl(dB,dB,app,X1,X4) != X3 | aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),nil(dB))) != X0) & nil(dB) != X0) | (aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) != X1 & nil(dB) = X0)) & (((? [X4 : list(dB)] : (foldl(dB,dB,app,X1,X4) = X3 & aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),nil(dB))) = X0) | nil(dB) = X0) & (aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) = X1 | nil(dB) != X0)) | ~sP1(X3,X1,X0,X2)))),
% 0.16/0.51 inference(flattening,[],[f309])).
% 0.16/0.51 tff(f309,plain,(
% 0.16/0.51 ! [X3 : dB,X1 : dB,X0 : list(dB),X2 : dB] : ((sP1(X3,X1,X0,X2) | ((! [X4 : list(dB)] : (foldl(dB,dB,app,X1,X4) != X3 | aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),nil(dB))) != X0) & nil(dB) != X0) | (aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) != X1 & nil(dB) = X0))) & (((? [X4 : list(dB)] : (foldl(dB,dB,app,X1,X4) = X3 & aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),nil(dB))) = X0) | nil(dB) = X0) & (aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) = X1 | nil(dB) != X0)) | ~sP1(X3,X1,X0,X2)))),
% 0.16/0.51 inference(nnf_transformation,[],[f255])).
% 0.16/0.51 tff(f255,plain,(
% 0.16/0.51 ! [X3 : dB,X1 : dB,X0 : list(dB),X2 : dB] : (sP1(X3,X1,X0,X2) <=> ((? [X4 : list(dB)] : (foldl(dB,dB,app,X1,X4) = X3 & aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),nil(dB))) = X0) | nil(dB) = X0) & (aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) = X1 | nil(dB) != X0)))),
% 0.16/0.51 introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])])).
% 0.16/0.51 tff(f2719,plain,(
% 0.16/0.51 spl32_166),
% 0.16/0.51 inference(avatar_split_clause,[],[f540,f2717])).
% 0.16/0.51 tff(f2717,plain,(
% 0.16/0.51 spl32_166 <=> ! [X5 : nat,X3 : list(dB),X4 : list(dB),X0 : type,X6 : fun(nat,type),X2 : type,X1 : list(type)] : (foldr(type,type,fun1,sK31(X0,X2,X3,X6),X2) = X0 | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) | ~pp(aa(list(type),bool,typings(X6,X4),X1)) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_166])])).
% 0.16/0.51 tff(f540,plain,(
% 0.16/0.51 ( ! [X2 : type,X3 : list(dB),X0 : type,X1 : list(type),X6 : fun(nat,type),X4 : list(dB),X5 : nat] : (foldr(type,type,fun1,sK31(X0,X2,X3,X6),X2) = X0 | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) | ~pp(aa(list(type),bool,typings(X6,X4),X1)) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f352])).
% 0.16/0.51 tff(f352,plain,(
% 0.16/0.51 ! [X0 : type,X1 : list(type),X2 : type,X3 : list(dB),X4 : list(dB),X5 : nat,X6 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X6,X3),sK31(X0,X2,X3,X6))) & foldr(type,type,fun1,sK31(X0,X2,X3,X6),X2) = X0) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) | ~pp(aa(list(type),bool,typings(X6,X4),X1)) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)))),
% 0.16/0.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f252,f351])).
% 0.16/0.51 tff(f351,plain,(
% 0.16/0.51 ! [X0 : type,X2 : type,X3 : list(dB),X6 : fun(nat,type)] : (? [X7 : list(type)] : (pp(aa(list(type),bool,typings(X6,X3),X7)) & foldr(type,type,fun1,X7,X2) = X0) => (pp(aa(list(type),bool,typings(X6,X3),sK31(X0,X2,X3,X6))) & foldr(type,type,fun1,sK31(X0,X2,X3,X6),X2) = X0))),
% 0.16/0.51 introduced(choice_axiom,[])).
% 0.16/0.51 tff(f252,plain,(
% 0.16/0.51 ! [X0 : type,X1 : list(type),X2 : type,X3 : list(dB),X4 : list(dB),X5 : nat,X6 : fun(nat,type)] : (? [X7 : list(type)] : (pp(aa(list(type),bool,typings(X6,X3),X7)) & foldr(type,type,fun1,X7,X2) = X0) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) | ~pp(aa(list(type),bool,typings(X6,X4),X1)) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)))),
% 0.16/0.51 inference(flattening,[],[f251])).
% 0.16/0.51 tff(f251,plain,(
% 0.16/0.51 ! [X0 : type,X1 : list(type),X2 : type,X3 : list(dB),X4 : list(dB),X5 : nat,X6 : fun(nat,type)] : (((? [X7 : list(type)] : (pp(aa(list(type),bool,typings(X6,X3),X7)) & foldr(type,type,fun1,X7,X2) = X0) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0))) | ~pp(aa(list(type),bool,typings(X6,X4),X1))) | ~pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)))),
% 0.16/0.51 inference(ennf_transformation,[],[f211])).
% 0.16/0.51 tff(f211,plain,(
% 0.16/0.51 ! [X0 : type,X1 : list(type),X2 : type,X3 : list(dB),X4 : list(dB),X5 : nat,X6 : fun(nat,type)] : (pp(aa(type,bool,typing(X6,foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) => (pp(aa(list(type),bool,typings(X6,X4),X1)) => (pp(aa(type,bool,typing(X6,foldl(dB,dB,app,var(X5),X4)),X0)) => ? [X7 : list(type)] : (pp(aa(list(type),bool,typings(X6,X3),X7)) & foldr(type,type,fun1,X7,X2) = X0))))),
% 0.16/0.51 inference(rectify,[],[f92])).
% 0.16/0.51 tff(f92,axiom,(
% 0.16/0.51 ! [X16 : type,X87 : list(type),X8 : type,X90 : list(dB),X14 : list(dB),X11 : nat,X12 : fun(nat,type)] : (pp(aa(type,bool,typing(X12,foldl(dB,dB,app,foldl(dB,dB,app,var(X11),X14),X90)),X8)) => (pp(aa(list(type),bool,typings(X12,X14),X87)) => (pp(aa(type,bool,typing(X12,foldl(dB,dB,app,var(X11),X14)),X16)) => ? [X88 : list(type)] : (pp(aa(list(type),bool,typings(X12,X90),X88)) & foldr(type,type,fun1,X88,X8) = X16))))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_var__app__types)).
% 0.16/0.51 tff(f2715,plain,(
% 0.16/0.51 ~spl32_24 | spl32_25),
% 0.16/0.51 inference(avatar_contradiction_clause,[],[f2714])).
% 0.16/0.51 tff(f2714,plain,(
% 0.16/0.51 $false | (~spl32_24 | spl32_25)),
% 0.16/0.51 inference(trivial_inequality_removal,[],[f2643])).
% 0.16/0.51 tff(f2643,plain,(
% 0.16/0.51 fTrue != fTrue | (~spl32_24 | spl32_25)),
% 0.16/0.51 inference(superposition,[],[f760,f756])).
% 0.16/0.51 tff(f760,plain,(
% 0.16/0.51 fFalse != fTrue | spl32_25),
% 0.16/0.51 inference(avatar_component_clause,[],[f758])).
% 0.16/0.51 tff(f758,plain,(
% 0.16/0.51 spl32_25 <=> fFalse = fTrue),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_25])])).
% 0.16/0.51 tff(f2639,plain,(
% 0.16/0.51 spl32_165),
% 0.16/0.51 inference(avatar_split_clause,[],[f538,f2637])).
% 0.16/0.51 tff(f2637,plain,(
% 0.16/0.51 spl32_165 <=> ! [X3 : fun(nat,type),X4 : dB,X0 : dB,X6 : type,X5 : type,X2 : nat,X1 : type] : (pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X5)) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) | ~pp(aa(dB,bool,it,X4)) | t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_165])])).
% 0.16/0.51 tff(f538,plain,(
% 0.16/0.51 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type,X6 : type,X4 : dB,X5 : type] : (pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X5)) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) | ~pp(aa(dB,bool,it,X4)) | t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f248])).
% 0.16/0.51 tff(f248,plain,(
% 0.16/0.51 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X5)) | ~pp(aa(dB,bool,it,X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) | ~pp(aa(dB,bool,it,X4)) | t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 0.16/0.51 inference(flattening,[],[f247])).
% 0.16/0.51 tff(f247,plain,(
% 0.16/0.51 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (((((pp(aa(dB,bool,it,subst(X4,X0,X2))) | ~pp(aa(type,bool,typing(X3,X0),X5))) | ~pp(aa(dB,bool,it,X0))) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1))) | ~pp(aa(dB,bool,it,X4))) | t1 != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 0.16/0.51 inference(ennf_transformation,[],[f209])).
% 0.16/0.51 tff(f209,plain,(
% 0.16/0.51 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (t1 = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) => (pp(aa(dB,bool,it,X4)) => (pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) => (pp(aa(dB,bool,it,X0)) => (pp(aa(type,bool,typing(X3,X0),X5)) => pp(aa(dB,bool,it,subst(X4,X0,X2))))))))),
% 0.16/0.51 inference(rectify,[],[f24])).
% 0.16/0.51 tff(f24,axiom,(
% 0.16/0.51 ! [X36 : dB,X8 : type,X11 : nat,X12 : fun(nat,type),X37 : dB,X38 : type,X39 : type] : (t1 = aa(type,type,aa(type,fun(type,type),fun1,X39),X38) => (pp(aa(dB,bool,it,X37)) => (pp(aa(type,bool,typing(shift(type,X12,X11,X38),X37),X8)) => (pp(aa(dB,bool,it,X36)) => (pp(aa(type,bool,typing(X12,X36),X38)) => pp(aa(dB,bool,it,subst(X37,X36,X11))))))))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_MI2)).
% 0.16/0.51 tff(f2629,plain,(
% 0.16/0.51 spl32_164 | ~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_163),
% 0.16/0.51 inference(avatar_split_clause,[],[f2625,f2621,f1538,f1534,f979,f744,f740,f2627])).
% 0.16/0.51 tff(f2627,plain,(
% 0.16/0.51 spl32_164 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),X0) = X1 | foldl(list(X2),list(X2),append(X2),sK26(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | ~sP3(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_164])])).
% 0.16/0.51 tff(f740,plain,(
% 0.16/0.51 spl32_21 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,fun(X1,X1)),X2 : X1] : foldr(X0,X1,X3,nil(X0),X2) = X2),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_21])])).
% 0.16/0.51 tff(f1534,plain,(
% 0.16/0.51 spl32_114 <=> ! [X1 : $tType,X0 : $tType,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X1,X1)),X2 : X1] : foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_114])])).
% 0.16/0.51 tff(f2621,plain,(
% 0.16/0.51 spl32_163 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK26(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP3(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_163])])).
% 0.16/0.51 tff(f2625,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),X0) = X1 | foldl(list(X2),list(X2),append(X2),sK26(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | ~sP3(X2,X0,X1,X3,X4)) ) | (~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_163)),
% 0.16/0.51 inference(forward_demodulation,[],[f2624,f1608])).
% 0.16/0.51 tff(f1608,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : $tType,X3 : fun(X0,fun(X2,X2)),X1 : X0,X4 : X2] : (foldr(X0,X2,X3,insert(X0,X1,nil(X0)),X4) = aa(X2,X2,aa(X0,fun(X2,X2),X3,X1),X4)) ) | (~spl32_21 | ~spl32_64 | ~spl32_114)),
% 0.16/0.51 inference(forward_demodulation,[],[f1569,f741])).
% 0.16/0.51 tff(f741,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1))] : (foldr(X0,X1,X3,nil(X0),X2) = X2) ) | ~spl32_21),
% 0.16/0.51 inference(avatar_component_clause,[],[f740])).
% 0.16/0.51 tff(f1569,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : $tType,X3 : fun(X0,fun(X2,X2)),X1 : X0,X4 : X2] : (aa(X2,X2,aa(X0,fun(X2,X2),X3,X1),foldr(X0,X2,X3,nil(X0),X4)) = foldr(X0,X2,X3,insert(X0,X1,nil(X0)),X4)) ) | (~spl32_64 | ~spl32_114)),
% 0.16/0.51 inference(superposition,[],[f1535,f980])).
% 0.16/0.51 tff(f1535,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X1,X1))] : (foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2))) ) | ~spl32_114),
% 0.16/0.51 inference(avatar_component_clause,[],[f1534])).
% 0.16/0.51 tff(f2624,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (foldl(list(X2),list(X2),append(X2),sK26(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP3(X2,X0,X1,X3,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_163)),
% 0.16/0.51 inference(forward_demodulation,[],[f2622,f1721])).
% 0.16/0.51 tff(f2622,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK26(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP3(X2,X0,X1,X3,X4)) ) | ~spl32_163),
% 0.16/0.51 inference(avatar_component_clause,[],[f2621])).
% 0.16/0.51 tff(f2623,plain,(
% 0.16/0.51 spl32_163),
% 0.16/0.51 inference(avatar_split_clause,[],[f506,f2621])).
% 0.16/0.51 tff(f506,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK26(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP3(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f338])).
% 0.16/0.51 tff(f338,plain,(
% 0.16/0.51 ! [X0 : list(X2),X1 : list(X2),X2 : $tType,X3 : list(X2),X4 : X2] : ((sP3(X2,X0,X1,X3,X4) | (! [X5 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1) != X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5) != X3) & (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) != X1 | nil(X2) != X3))) & ((aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK26(X2,X0,X1,X3,X4)),X1) = X0 & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK26(X2,X0,X1,X3,X4)) = X3) | (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 & nil(X2) = X3) | ~sP3(X2,X0,X1,X3,X4)))),
% 0.16/0.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f336,f337])).
% 0.16/0.51 tff(f337,plain,(
% 0.16/0.51 ! [X2 : $tType,X0 : list(X2),X1 : list(X2),X3 : list(X2),X4 : X2] : (? [X6 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X6),X1) = X0 & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X6) = X3) => (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK26(X2,X0,X1,X3,X4)),X1) = X0 & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK26(X2,X0,X1,X3,X4)) = X3))),
% 0.16/0.51 introduced(choice_axiom,[])).
% 0.16/0.51 tff(f336,plain,(
% 0.16/0.51 ! [X0 : list(X2),X1 : list(X2),X2 : $tType,X3 : list(X2),X4 : X2] : ((sP3(X2,X0,X1,X3,X4) | (! [X5 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1) != X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5) != X3) & (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) != X1 | nil(X2) != X3))) & (? [X6 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X6),X1) = X0 & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X6) = X3) | (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 & nil(X2) = X3) | ~sP3(X2,X0,X1,X3,X4)))),
% 0.16/0.51 inference(rectify,[],[f335])).
% 0.16/0.51 tff(f335,plain,(
% 0.16/0.51 ! [X1 : list(X0),X3 : list(X0),X0 : $tType,X4 : list(X0),X2 : X0] : ((sP3(X0,X1,X3,X4,X2) | (! [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X3) != X1 | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X5) != X4) & (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X3 | nil(X0) != X4))) & (? [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X3) = X1 & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X5) = X4) | (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = X3 & nil(X0) = X4) | ~sP3(X0,X1,X3,X4,X2)))),
% 0.16/0.51 inference(flattening,[],[f334])).
% 0.16/0.51 tff(f334,plain,(
% 0.16/0.51 ! [X1 : list(X0),X3 : list(X0),X0 : $tType,X4 : list(X0),X2 : X0] : ((sP3(X0,X1,X3,X4,X2) | (! [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X3) != X1 | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X5) != X4) & (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X3 | nil(X0) != X4))) & ((? [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X3) = X1 & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X5) = X4) | (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = X3 & nil(X0) = X4)) | ~sP3(X0,X1,X3,X4,X2)))),
% 0.16/0.51 inference(nnf_transformation,[],[f259])).
% 0.16/0.51 tff(f259,plain,(
% 0.16/0.51 ! [X1 : list(X0),X3 : list(X0),X0 : $tType,X4 : list(X0),X2 : X0] : (sP3(X0,X1,X3,X4,X2) <=> (? [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X3) = X1 & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X5) = X4) | (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = X3 & nil(X0) = X4)))),
% 0.16/0.51 introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])])).
% 0.16/0.51 tff(f2613,plain,(
% 0.16/0.51 spl32_162 | ~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_161),
% 0.16/0.51 inference(avatar_split_clause,[],[f2609,f2605,f1538,f1534,f979,f744,f740,f2611])).
% 0.16/0.51 tff(f2611,plain,(
% 0.16/0.51 spl32_162 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),X0) = X1 | foldl(list(X2),list(X2),append(X2),sK25(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | ~sP2(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_162])])).
% 0.16/0.51 tff(f2605,plain,(
% 0.16/0.51 spl32_161 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK25(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP2(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_161])])).
% 0.16/0.51 tff(f2609,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),X0) = X1 | foldl(list(X2),list(X2),append(X2),sK25(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | ~sP2(X2,X0,X1,X3,X4)) ) | (~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_161)),
% 0.16/0.51 inference(forward_demodulation,[],[f2608,f1608])).
% 0.16/0.51 tff(f2608,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (foldl(list(X2),list(X2),append(X2),sK25(X2,X0,X1,X3,X4),insert(list(X2),X1,nil(list(X2)))) = X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP2(X2,X0,X1,X3,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_161)),
% 0.16/0.51 inference(forward_demodulation,[],[f2606,f1721])).
% 0.16/0.51 tff(f2606,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK25(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP2(X2,X0,X1,X3,X4)) ) | ~spl32_161),
% 0.16/0.51 inference(avatar_component_clause,[],[f2605])).
% 0.16/0.51 tff(f2607,plain,(
% 0.16/0.51 spl32_161),
% 0.16/0.51 inference(avatar_split_clause,[],[f498,f2605])).
% 0.16/0.51 tff(f498,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK25(X2,X0,X1,X3,X4)),X1) = X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP2(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f332])).
% 0.16/0.51 tff(f332,plain,(
% 0.16/0.51 ! [X0 : list(X2),X1 : list(X2),X2 : $tType,X3 : list(X2),X4 : X2] : ((sP2(X2,X0,X1,X3,X4) | (! [X5 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1) != X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5) != X3) & (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) != X1 | nil(X2) != X3))) & ((aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK25(X2,X0,X1,X3,X4)),X1) = X0 & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK25(X2,X0,X1,X3,X4)) = X3) | (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 & nil(X2) = X3) | ~sP2(X2,X0,X1,X3,X4)))),
% 0.16/0.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f330,f331])).
% 0.16/0.51 tff(f331,plain,(
% 0.16/0.51 ! [X2 : $tType,X0 : list(X2),X1 : list(X2),X3 : list(X2),X4 : X2] : (? [X6 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X6),X1) = X0 & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X6) = X3) => (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK25(X2,X0,X1,X3,X4)),X1) = X0 & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK25(X2,X0,X1,X3,X4)) = X3))),
% 0.16/0.51 introduced(choice_axiom,[])).
% 0.16/0.51 tff(f330,plain,(
% 0.16/0.51 ! [X0 : list(X2),X1 : list(X2),X2 : $tType,X3 : list(X2),X4 : X2] : ((sP2(X2,X0,X1,X3,X4) | (! [X5 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1) != X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5) != X3) & (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) != X1 | nil(X2) != X3))) & (? [X6 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X6),X1) = X0 & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X6) = X3) | (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 & nil(X2) = X3) | ~sP2(X2,X0,X1,X3,X4)))),
% 0.16/0.51 inference(rectify,[],[f329])).
% 0.16/0.51 tff(f329,plain,(
% 0.16/0.51 ! [X3 : list(X0),X1 : list(X0),X0 : $tType,X2 : list(X0),X4 : X0] : ((sP2(X0,X3,X1,X2,X4) | (! [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X1) != X3 | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) != X2) & (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) != X1 | nil(X0) != X2))) & (? [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X1) = X3 & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) = X2) | (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) = X1 & nil(X0) = X2) | ~sP2(X0,X3,X1,X2,X4)))),
% 0.16/0.51 inference(flattening,[],[f328])).
% 0.16/0.51 tff(f328,plain,(
% 0.16/0.51 ! [X3 : list(X0),X1 : list(X0),X0 : $tType,X2 : list(X0),X4 : X0] : ((sP2(X0,X3,X1,X2,X4) | (! [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X1) != X3 | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) != X2) & (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) != X1 | nil(X0) != X2))) & ((? [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X1) = X3 & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) = X2) | (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) = X1 & nil(X0) = X2)) | ~sP2(X0,X3,X1,X2,X4)))),
% 0.16/0.51 inference(nnf_transformation,[],[f257])).
% 0.16/0.51 tff(f257,plain,(
% 0.16/0.51 ! [X3 : list(X0),X1 : list(X0),X0 : $tType,X2 : list(X0),X4 : X0] : (sP2(X0,X3,X1,X2,X4) <=> (? [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X1) = X3 & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) = X2) | (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) = X1 & nil(X0) = X2)))),
% 0.16/0.51 introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])])).
% 0.16/0.51 tff(f2597,plain,(
% 0.16/0.51 spl32_160 | ~spl32_21 | ~spl32_64 | ~spl32_114 | ~spl32_159),
% 0.16/0.51 inference(avatar_split_clause,[],[f2593,f2589,f1534,f979,f740,f2595])).
% 0.16/0.51 tff(f2595,plain,(
% 0.16/0.51 spl32_160 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),X0) = X1 | foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),sK26(X2,X0,X1,X3,X4)) = X3 | ~sP3(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_160])])).
% 0.16/0.51 tff(f2589,plain,(
% 0.16/0.51 spl32_159 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK26(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP3(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_159])])).
% 0.16/0.51 tff(f2593,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),X0) = X1 | foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),sK26(X2,X0,X1,X3,X4)) = X3 | ~sP3(X2,X0,X1,X3,X4)) ) | (~spl32_21 | ~spl32_64 | ~spl32_114 | ~spl32_159)),
% 0.16/0.51 inference(forward_demodulation,[],[f2592,f1608])).
% 0.16/0.51 tff(f2592,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),sK26(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP3(X2,X0,X1,X3,X4)) ) | (~spl32_21 | ~spl32_64 | ~spl32_114 | ~spl32_159)),
% 0.16/0.51 inference(forward_demodulation,[],[f2590,f1608])).
% 0.16/0.51 tff(f2590,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK26(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP3(X2,X0,X1,X3,X4)) ) | ~spl32_159),
% 0.16/0.51 inference(avatar_component_clause,[],[f2589])).
% 0.16/0.51 tff(f2591,plain,(
% 0.16/0.51 spl32_159),
% 0.16/0.51 inference(avatar_split_clause,[],[f504,f2589])).
% 0.16/0.51 tff(f504,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK26(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP3(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f338])).
% 0.16/0.51 tff(f2587,plain,(
% 0.16/0.51 ~spl32_2 | spl32_24 | spl32_9 | ~spl32_13 | ~spl32_48 | ~spl32_50 | ~spl32_115 | ~spl32_139),
% 0.16/0.51 inference(avatar_split_clause,[],[f2443,f1975,f1538,f908,f884,f695,f675,f755,f637])).
% 0.16/0.51 tff(f675,plain,(
% 0.16/0.51 spl32_9 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_9])])).
% 0.16/0.51 tff(f695,plain,(
% 0.16/0.51 spl32_13 <=> ! [X0 : bool] : (~pp(X0) | fTrue = X0)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_13])])).
% 0.16/0.51 tff(f884,plain,(
% 0.16/0.51 spl32_48 <=> pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(i),rs)),t))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_48])])).
% 0.16/0.51 tff(f908,plain,(
% 0.16/0.51 spl32_50 <=> rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_50])])).
% 0.16/0.51 tff(f1975,plain,(
% 0.16/0.51 spl32_139 <=> ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_139])])).
% 0.16/0.51 tff(f2443,plain,(
% 0.16/0.51 ( ! [X0 : bool] : (fTrue = X0 | ~pp(fTrue)) ) | (spl32_9 | ~spl32_13 | ~spl32_48 | ~spl32_50 | ~spl32_115 | ~spl32_139)),
% 0.16/0.51 inference(duplicate_literal_removal,[],[f2442])).
% 0.16/0.51 tff(f2442,plain,(
% 0.16/0.51 ( ! [X0 : bool] : (fTrue = X0 | ~pp(fTrue) | fTrue = X0) ) | (spl32_9 | ~spl32_13 | ~spl32_48 | ~spl32_50 | ~spl32_115 | ~spl32_139)),
% 0.16/0.51 inference(forward_demodulation,[],[f2441,f905])).
% 0.16/0.51 tff(f905,plain,(
% 0.16/0.51 fTrue = aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(i),rs)),t) | (~spl32_13 | ~spl32_48)),
% 0.16/0.51 inference(resolution,[],[f886,f696])).
% 0.16/0.51 tff(f696,plain,(
% 0.16/0.51 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | ~spl32_13),
% 0.16/0.51 inference(avatar_component_clause,[],[f695])).
% 0.16/0.51 tff(f886,plain,(
% 0.16/0.51 pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(i),rs)),t)) | ~spl32_48),
% 0.16/0.51 inference(avatar_component_clause,[],[f884])).
% 0.16/0.51 tff(f2441,plain,(
% 0.16/0.51 ( ! [X0 : bool] : (aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(i),rs)),t) = X0 | ~pp(fTrue) | fTrue = X0) ) | (spl32_9 | ~spl32_50 | ~spl32_115 | ~spl32_139)),
% 0.16/0.51 inference(forward_demodulation,[],[f2273,f1659])).
% 0.16/0.51 tff(f1659,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,fun(dB,X0))] : (foldl(X0,dB,X1,aa(dB,X0,aa(X0,fun(dB,X0),X1,X2),a),as) = foldl(X0,dB,X1,X2,rs)) ) | (~spl32_50 | ~spl32_115)),
% 0.16/0.51 inference(superposition,[],[f1539,f910])).
% 0.16/0.51 tff(f910,plain,(
% 0.16/0.51 rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) | ~spl32_50),
% 0.16/0.51 inference(avatar_component_clause,[],[f908])).
% 0.16/0.51 tff(f2273,plain,(
% 0.16/0.51 ( ! [X0 : bool] : (~pp(fTrue) | aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t) = X0 | fTrue = X0) ) | (spl32_9 | ~spl32_139)),
% 0.16/0.51 inference(superposition,[],[f677,f1976])).
% 0.16/0.51 tff(f1976,plain,(
% 0.16/0.51 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl32_139),
% 0.16/0.51 inference(avatar_component_clause,[],[f1975])).
% 0.16/0.51 tff(f677,plain,(
% 0.16/0.51 ~pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t)) | spl32_9),
% 0.16/0.51 inference(avatar_component_clause,[],[f675])).
% 0.16/0.51 tff(f2580,plain,(
% 0.16/0.51 spl32_158 | ~spl32_21 | ~spl32_64 | ~spl32_114 | ~spl32_157),
% 0.16/0.51 inference(avatar_split_clause,[],[f2576,f2572,f1534,f979,f740,f2578])).
% 0.16/0.51 tff(f2578,plain,(
% 0.16/0.51 spl32_158 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),X0) = X1 | foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),sK25(X2,X0,X1,X3,X4)) = X3 | ~sP2(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_158])])).
% 0.16/0.51 tff(f2572,plain,(
% 0.16/0.51 spl32_157 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK25(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP2(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_157])])).
% 0.16/0.51 tff(f2576,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),X0) = X1 | foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),sK25(X2,X0,X1,X3,X4)) = X3 | ~sP2(X2,X0,X1,X3,X4)) ) | (~spl32_21 | ~spl32_64 | ~spl32_114 | ~spl32_157)),
% 0.16/0.51 inference(forward_demodulation,[],[f2575,f1608])).
% 0.16/0.51 tff(f2575,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (foldr(X2,list(X2),cons(X2),insert(X2,X4,nil(X2)),sK25(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP2(X2,X0,X1,X3,X4)) ) | (~spl32_21 | ~spl32_64 | ~spl32_114 | ~spl32_157)),
% 0.16/0.51 inference(forward_demodulation,[],[f2573,f1608])).
% 0.16/0.51 tff(f2573,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK25(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP2(X2,X0,X1,X3,X4)) ) | ~spl32_157),
% 0.16/0.51 inference(avatar_component_clause,[],[f2572])).
% 0.16/0.51 tff(f2574,plain,(
% 0.16/0.51 spl32_157),
% 0.16/0.51 inference(avatar_split_clause,[],[f496,f2572])).
% 0.16/0.51 tff(f496,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK25(X2,X0,X1,X3,X4)) = X3 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) = X1 | ~sP2(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f332])).
% 0.16/0.51 tff(f2553,plain,(
% 0.16/0.51 spl32_156),
% 0.16/0.51 inference(avatar_split_clause,[],[f624,f2551])).
% 0.16/0.51 tff(f2551,plain,(
% 0.16/0.51 spl32_156 <=> ! [X0 : $tType,X2 : list(X0),X4 : list(X0),X3 : X0,X1 : X0] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),insert(X0,X1,nil(X0))) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),insert(X0,X3,nil(X0))) | X2 = X4)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_156])])).
% 0.16/0.51 tff(f624,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : X0,X1 : X0,X4 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),insert(X0,X1,nil(X0))) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),insert(X0,X3,nil(X0))) | X2 = X4) )),
% 0.16/0.51 inference(forward_demodulation,[],[f623,f374])).
% 0.16/0.51 tff(f623,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : X0,X1 : X0,X4 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),insert(X0,X1,nil(X0))) | X2 = X4) )),
% 0.16/0.51 inference(forward_demodulation,[],[f519,f374])).
% 0.16/0.51 tff(f519,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : X0,X1 : X0,X4 : list(X0)] : (X2 = X4 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f346])).
% 0.16/0.51 tff(f346,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : X0,X2 : list(X0),X3 : X0,X4 : list(X0)] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0))) | X1 != X3 | X2 != X4) & ((X1 = X3 & X2 = X4) | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)))))),
% 0.16/0.51 inference(flattening,[],[f345])).
% 0.16/0.51 tff(f345,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : X0,X2 : list(X0),X3 : X0,X4 : list(X0)] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0))) | (X1 != X3 | X2 != X4)) & ((X1 = X3 & X2 = X4) | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)))))),
% 0.16/0.51 inference(nnf_transformation,[],[f194])).
% 0.16/0.51 tff(f194,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : X0,X2 : list(X0),X3 : X0,X4 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0))) <=> (X1 = X3 & X2 = X4))),
% 0.16/0.51 inference(rectify,[],[f66])).
% 0.16/0.51 tff(f66,axiom,(
% 0.16/0.51 ! [X2 : $tType,X78 : X2,X77 : list(X2),X9 : X2,X34 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X34),aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X9),nil(X2))) = aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X77),aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X78),nil(X2))) <=> (X9 = X78 & X34 = X77))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_append1__eq__conv)).
% 0.16/0.51 tff(f2540,plain,(
% 0.16/0.51 spl32_155 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_154),
% 0.16/0.51 inference(avatar_split_clause,[],[f2536,f2532,f1538,f979,f744,f2538])).
% 0.16/0.51 tff(f2538,plain,(
% 0.16/0.51 spl32_155 <=> ! [X4 : list(dB),X1 : dB,X3 : dB] : (foldl(dB,dB,app,foldl(dB,dB,app,X1,X4),insert(dB,X3,nil(dB))) != X1 | sP1(foldl(dB,dB,app,X1,X4),X1,foldl(list(dB),list(dB),append(dB),X4,insert(list(dB),insert(dB,X3,nil(dB)),nil(list(dB)))),X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_155])])).
% 0.16/0.51 tff(f2532,plain,(
% 0.16/0.51 spl32_154 <=> ! [X4 : list(dB),X1 : dB,X3 : dB] : (sP1(foldl(dB,dB,app,X1,X4),X1,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),insert(dB,X3,nil(dB))),X3) | aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X1,X4)),X3) != X1)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_154])])).
% 0.16/0.51 tff(f2536,plain,(
% 0.16/0.51 ( ! [X3 : dB,X1 : dB,X4 : list(dB)] : (foldl(dB,dB,app,foldl(dB,dB,app,X1,X4),insert(dB,X3,nil(dB))) != X1 | sP1(foldl(dB,dB,app,X1,X4),X1,foldl(list(dB),list(dB),append(dB),X4,insert(list(dB),insert(dB,X3,nil(dB)),nil(list(dB)))),X3)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_154)),
% 0.16/0.51 inference(forward_demodulation,[],[f2535,f1721])).
% 0.16/0.51 tff(f2535,plain,(
% 0.16/0.51 ( ! [X3 : dB,X1 : dB,X4 : list(dB)] : (sP1(foldl(dB,dB,app,X1,X4),X1,foldl(list(dB),list(dB),append(dB),X4,insert(list(dB),insert(dB,X3,nil(dB)),nil(list(dB)))),X3) | aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X1,X4)),X3) != X1) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_154)),
% 0.16/0.51 inference(forward_demodulation,[],[f2533,f1721])).
% 0.16/0.51 tff(f2533,plain,(
% 0.16/0.51 ( ! [X3 : dB,X1 : dB,X4 : list(dB)] : (sP1(foldl(dB,dB,app,X1,X4),X1,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),insert(dB,X3,nil(dB))),X3) | aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X1,X4)),X3) != X1) ) | ~spl32_154),
% 0.16/0.51 inference(avatar_component_clause,[],[f2532])).
% 0.16/0.51 tff(f2534,plain,(
% 0.16/0.51 spl32_154),
% 0.16/0.51 inference(avatar_split_clause,[],[f615,f2532])).
% 0.16/0.51 tff(f615,plain,(
% 0.16/0.51 ( ! [X3 : dB,X1 : dB,X4 : list(dB)] : (sP1(foldl(dB,dB,app,X1,X4),X1,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),insert(dB,X3,nil(dB))),X3) | aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X1,X4)),X3) != X1) )),
% 0.16/0.51 inference(forward_demodulation,[],[f571,f374])).
% 0.16/0.51 tff(f571,plain,(
% 0.16/0.51 ( ! [X3 : dB,X1 : dB,X4 : list(dB)] : (sP1(foldl(dB,dB,app,X1,X4),X1,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))),X3) | aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X1,X4)),X3) != X1) )),
% 0.16/0.51 inference(equality_resolution,[],[f570])).
% 0.16/0.51 tff(f570,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : dB,X1 : dB,X4 : list(dB)] : (sP1(foldl(dB,dB,app,X1,X4),X1,X2,X3) | aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))) != X2 | aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X1,X4)),X3) != X1) )),
% 0.16/0.51 inference(equality_resolution,[],[f462])).
% 0.16/0.51 tff(f462,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB,X4 : list(dB)] : (sP1(X0,X1,X2,X3) | foldl(dB,dB,app,X1,X4) != X0 | aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))) != X2 | aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3) != X1) )),
% 0.16/0.51 inference(cnf_transformation,[],[f313])).
% 0.16/0.51 tff(f2075,plain,(
% 0.16/0.51 spl32_153 | ~spl32_21 | ~spl32_64 | ~spl32_114 | ~spl32_152),
% 0.16/0.51 inference(avatar_split_clause,[],[f2071,f2068,f1534,f979,f740,f2073])).
% 0.16/0.51 tff(f2073,plain,(
% 0.16/0.51 spl32_153 <=> ! [X1 : $tType,X0 : $tType,X4 : fun(X1,list(X0)),X3 : X1,X2 : list(X1)] : aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),aa(X1,list(X0),X4,X3)),maps(X1,X0,X4,X2)) = maps(X1,X0,X4,foldr(X1,list(X1),cons(X1),insert(X1,X3,nil(X1)),X2))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_153])])).
% 0.16/0.51 tff(f2068,plain,(
% 0.16/0.51 spl32_152 <=> ! [X1 : $tType,X0 : $tType,X4 : fun(X1,list(X0)),X3 : X1,X2 : list(X1)] : maps(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),aa(X1,list(X0),X4,X3)),maps(X1,X0,X4,X2))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_152])])).
% 0.16/0.51 tff(f2071,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,list(X0))] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),aa(X1,list(X0),X4,X3)),maps(X1,X0,X4,X2)) = maps(X1,X0,X4,foldr(X1,list(X1),cons(X1),insert(X1,X3,nil(X1)),X2))) ) | (~spl32_21 | ~spl32_64 | ~spl32_114 | ~spl32_152)),
% 0.16/0.51 inference(forward_demodulation,[],[f2069,f1608])).
% 0.16/0.51 tff(f2069,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,list(X0))] : (maps(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),aa(X1,list(X0),X4,X3)),maps(X1,X0,X4,X2))) ) | ~spl32_152),
% 0.16/0.51 inference(avatar_component_clause,[],[f2068])).
% 0.16/0.51 tff(f2070,plain,(
% 0.16/0.51 spl32_152),
% 0.16/0.51 inference(avatar_split_clause,[],[f485,f2068])).
% 0.16/0.51 tff(f485,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,list(X0))] : (maps(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),aa(X1,list(X0),X4,X3)),maps(X1,X0,X4,X2))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f183])).
% 0.16/0.51 tff(f183,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,list(X0))] : maps(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),aa(X1,list(X0),X4,X3)),maps(X1,X0,X4,X2))),
% 0.16/0.51 inference(rectify,[],[f99])).
% 0.16/0.51 tff(f99,axiom,(
% 0.16/0.51 ! [X2 : $tType,X0 : $tType,X34 : list(X0),X9 : X0,X35 : fun(X0,list(X2))] : maps(X0,X2,X35,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X9),X34)) = aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),aa(X0,list(X2),X35,X9)),maps(X0,X2,X35,X34))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_maps__simps_I1_J)).
% 0.16/0.51 tff(f2066,plain,(
% 0.16/0.51 spl32_151),
% 0.16/0.51 inference(avatar_split_clause,[],[f482,f2064])).
% 0.16/0.51 tff(f2064,plain,(
% 0.16/0.51 spl32_151 <=> ! [X0 : $tType,X3 : list(X0),X2 : fun(X0,bool),X1 : fun(X0,bool)] : (listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) | ~listsp(X0,X1,X3) | ~listsp(X0,X2,X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_151])])).
% 0.16/0.51 tff(f482,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : list(X0),X1 : fun(X0,bool)] : (listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) | ~listsp(X0,X1,X3) | ~listsp(X0,X2,X3)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f325])).
% 0.16/0.51 tff(f325,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : list(X0)] : ((listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) | ~listsp(X0,X1,X3) | ~listsp(X0,X2,X3)) & ((listsp(X0,X1,X3) & listsp(X0,X2,X3)) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)))),
% 0.16/0.51 inference(flattening,[],[f324])).
% 0.16/0.51 tff(f324,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : list(X0)] : ((listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) | (~listsp(X0,X1,X3) | ~listsp(X0,X2,X3))) & ((listsp(X0,X1,X3) & listsp(X0,X2,X3)) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)))),
% 0.16/0.51 inference(nnf_transformation,[],[f180])).
% 0.16/0.51 tff(f180,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : list(X0)] : (listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3) <=> (listsp(X0,X1,X3) & listsp(X0,X2,X3)))),
% 0.16/0.51 inference(rectify,[],[f31])).
% 0.16/0.51 tff(f31,axiom,(
% 0.16/0.51 ! [X2 : $tType,X47 : fun(X2,bool),X48 : fun(X2,bool),X49 : list(X2)] : (listsp(X2,combs(X2,bool,bool,aa(fun(X2,bool),fun(X2,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),X48),X47),X49) <=> (listsp(X2,X47,X49) & listsp(X2,X48,X49)))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_listsp__conj__eq)).
% 0.16/0.51 tff(f2055,plain,(
% 0.16/0.51 spl32_150),
% 0.16/0.51 inference(avatar_split_clause,[],[f622,f2053])).
% 0.16/0.51 tff(f2053,plain,(
% 0.16/0.51 spl32_150 <=> ! [X0 : $tType,X2 : list(X0),X4 : list(X0),X3 : X0,X1 : X0] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),insert(X0,X1,nil(X0))) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),insert(X0,X3,nil(X0))) | X1 = X3)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_150])])).
% 0.16/0.51 tff(f622,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : X0,X1 : X0,X4 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),insert(X0,X1,nil(X0))) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),insert(X0,X3,nil(X0))) | X1 = X3) )),
% 0.16/0.51 inference(forward_demodulation,[],[f621,f374])).
% 0.16/0.51 tff(f621,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : X0,X1 : X0,X4 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),insert(X0,X1,nil(X0))) | X1 = X3) )),
% 0.16/0.51 inference(forward_demodulation,[],[f520,f374])).
% 0.16/0.51 tff(f520,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : X0,X1 : X0,X4 : list(X0)] : (X1 = X3 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0)))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f346])).
% 0.16/0.51 tff(f2043,plain,(
% 0.16/0.51 spl32_149 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_148),
% 0.16/0.51 inference(avatar_split_clause,[],[f2039,f2036,f1538,f979,f744,f2041])).
% 0.16/0.51 tff(f2041,plain,(
% 0.16/0.51 spl32_149 <=> ! [X0 : $tType,X2 : fun(list(X0),bool),X1 : list(X0)] : (~pp(aa(list(X0),bool,X2,foldl(list(X0),list(X0),append(X0),sK14(X0,X2),insert(list(X0),insert(X0,sK13(X0,X2),nil(X0)),nil(list(X0)))))) | pp(aa(list(X0),bool,X2,X1)) | ~pp(aa(list(X0),bool,X2,nil(X0))))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_149])])).
% 0.16/0.51 tff(f2036,plain,(
% 0.16/0.51 spl32_148 <=> ! [X0 : $tType,X2 : fun(list(X0),bool),X1 : list(X0)] : (~pp(aa(list(X0),bool,X2,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK14(X0,X2)),insert(X0,sK13(X0,X2),nil(X0))))) | pp(aa(list(X0),bool,X2,X1)) | ~pp(aa(list(X0),bool,X2,nil(X0))))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_148])])).
% 0.16/0.51 tff(f2039,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : fun(list(X0),bool),X1 : list(X0)] : (~pp(aa(list(X0),bool,X2,foldl(list(X0),list(X0),append(X0),sK14(X0,X2),insert(list(X0),insert(X0,sK13(X0,X2),nil(X0)),nil(list(X0)))))) | pp(aa(list(X0),bool,X2,X1)) | ~pp(aa(list(X0),bool,X2,nil(X0)))) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_148)),
% 0.16/0.51 inference(forward_demodulation,[],[f2037,f1721])).
% 0.16/0.51 tff(f2037,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : fun(list(X0),bool),X1 : list(X0)] : (~pp(aa(list(X0),bool,X2,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK14(X0,X2)),insert(X0,sK13(X0,X2),nil(X0))))) | pp(aa(list(X0),bool,X2,X1)) | ~pp(aa(list(X0),bool,X2,nil(X0)))) ) | ~spl32_148),
% 0.16/0.51 inference(avatar_component_clause,[],[f2036])).
% 0.16/0.51 tff(f2038,plain,(
% 0.16/0.51 spl32_148),
% 0.16/0.51 inference(avatar_split_clause,[],[f609,f2036])).
% 0.16/0.51 tff(f609,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : fun(list(X0),bool),X1 : list(X0)] : (~pp(aa(list(X0),bool,X2,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK14(X0,X2)),insert(X0,sK13(X0,X2),nil(X0))))) | pp(aa(list(X0),bool,X2,X1)) | ~pp(aa(list(X0),bool,X2,nil(X0)))) )),
% 0.16/0.51 inference(forward_demodulation,[],[f405,f374])).
% 0.16/0.51 tff(f405,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : fun(list(X0),bool),X1 : list(X0)] : (pp(aa(list(X0),bool,X2,X1)) | ~pp(aa(list(X0),bool,X2,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK14(X0,X2)),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK13(X0,X2)),nil(X0))))) | ~pp(aa(list(X0),bool,X2,nil(X0)))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f277])).
% 0.16/0.51 tff(f277,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : fun(list(X0),bool)] : (pp(aa(list(X0),bool,X2,X1)) | (~pp(aa(list(X0),bool,X2,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK14(X0,X2)),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK13(X0,X2)),nil(X0))))) & pp(aa(list(X0),bool,X2,sK14(X0,X2)))) | ~pp(aa(list(X0),bool,X2,nil(X0))))),
% 0.16/0.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f221,f276])).
% 0.16/0.51 tff(f276,plain,(
% 0.16/0.51 ! [X0 : $tType,X2 : fun(list(X0),bool)] : (? [X3 : X0,X4 : list(X0)] : (~pp(aa(list(X0),bool,X2,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))))) & pp(aa(list(X0),bool,X2,X4))) => (~pp(aa(list(X0),bool,X2,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK14(X0,X2)),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK13(X0,X2)),nil(X0))))) & pp(aa(list(X0),bool,X2,sK14(X0,X2)))))),
% 0.16/0.51 introduced(choice_axiom,[])).
% 0.16/0.51 tff(f221,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : fun(list(X0),bool)] : (pp(aa(list(X0),bool,X2,X1)) | ? [X3 : X0,X4 : list(X0)] : (~pp(aa(list(X0),bool,X2,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))))) & pp(aa(list(X0),bool,X2,X4))) | ~pp(aa(list(X0),bool,X2,nil(X0))))),
% 0.16/0.51 inference(flattening,[],[f220])).
% 0.16/0.51 tff(f220,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : fun(list(X0),bool)] : ((pp(aa(list(X0),bool,X2,X1)) | ? [X3 : X0,X4 : list(X0)] : (~pp(aa(list(X0),bool,X2,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))))) & pp(aa(list(X0),bool,X2,X4)))) | ~pp(aa(list(X0),bool,X2,nil(X0))))),
% 0.16/0.51 inference(ennf_transformation,[],[f148])).
% 0.16/0.51 tff(f148,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : fun(list(X0),bool)] : (pp(aa(list(X0),bool,X2,nil(X0))) => (! [X3 : X0,X4 : list(X0)] : (pp(aa(list(X0),bool,X2,X4)) => pp(aa(list(X0),bool,X2,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0)))))) => pp(aa(list(X0),bool,X2,X1))))),
% 0.16/0.51 inference(rectify,[],[f78])).
% 0.16/0.51 tff(f78,axiom,(
% 0.16/0.51 ! [X2 : $tType,X34 : list(X2),X84 : fun(list(X2),bool)] : (pp(aa(list(X2),bool,X84,nil(X2))) => (! [X68 : X2,X85 : list(X2)] : (pp(aa(list(X2),bool,X84,X85)) => pp(aa(list(X2),bool,X84,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X85),aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X68),nil(X2)))))) => pp(aa(list(X2),bool,X84,X34))))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rev__induct)).
% 0.16/0.51 tff(f2024,plain,(
% 0.16/0.51 spl32_147 | ~spl32_55 | ~spl32_64),
% 0.16/0.51 inference(avatar_split_clause,[],[f1005,f979,f935,f2022])).
% 0.16/0.51 tff(f2022,plain,(
% 0.16/0.51 spl32_147 <=> ! [X0 : $tType,X1 : X0] : nil(X0) != insert(X0,X1,nil(X0))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_147])])).
% 0.16/0.51 tff(f935,plain,(
% 0.16/0.51 spl32_55 <=> ! [X0 : $tType,X2 : X0,X3 : list(X0)] : nil(X0) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_55])])).
% 0.16/0.51 tff(f1005,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X1 : X0] : (nil(X0) != insert(X0,X1,nil(X0))) ) | (~spl32_55 | ~spl32_64)),
% 0.16/0.51 inference(superposition,[],[f936,f980])).
% 0.16/0.51 tff(f936,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X3 : list(X0)] : (nil(X0) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3)) ) | ~spl32_55),
% 0.16/0.51 inference(avatar_component_clause,[],[f935])).
% 0.16/0.51 tff(f2018,plain,(
% 0.16/0.51 spl32_146 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_145),
% 0.16/0.51 inference(avatar_split_clause,[],[f2014,f2010,f1538,f979,f744,f2016])).
% 0.16/0.51 tff(f2016,plain,(
% 0.16/0.51 spl32_146 <=> ! [X4 : fun(nat,type),X0 : dB,X3 : dB,X2 : type,X1 : type] : (~pp(aa(type,bool,typing(X4,X3),foldl(type,type,fun1,X2,insert(type,X1,nil(type))))) | pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,insert(dB,X0,nil(dB)))),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_146])])).
% 0.16/0.51 tff(f2010,plain,(
% 0.16/0.51 spl32_145 <=> ! [X2 : type,X4 : fun(nat,type),X0 : dB,X3 : dB,X1 : type] : (pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_145])])).
% 0.16/0.51 tff(f2014,plain,(
% 0.16/0.51 ( ! [X2 : type,X3 : dB,X0 : dB,X1 : type,X4 : fun(nat,type)] : (~pp(aa(type,bool,typing(X4,X3),foldl(type,type,fun1,X2,insert(type,X1,nil(type))))) | pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,insert(dB,X0,nil(dB)))),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2))) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_145)),
% 0.16/0.51 inference(forward_demodulation,[],[f2013,f1721])).
% 0.16/0.51 tff(f2013,plain,(
% 0.16/0.51 ( ! [X2 : type,X3 : dB,X0 : dB,X1 : type,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,insert(dB,X0,nil(dB)))),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)))) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_145)),
% 0.16/0.51 inference(forward_demodulation,[],[f2011,f1721])).
% 0.16/0.51 tff(f2011,plain,(
% 0.16/0.51 ( ! [X2 : type,X3 : dB,X0 : dB,X1 : type,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)))) ) | ~spl32_145),
% 0.16/0.51 inference(avatar_component_clause,[],[f2010])).
% 0.16/0.51 tff(f2012,plain,(
% 0.16/0.51 spl32_145),
% 0.16/0.51 inference(avatar_split_clause,[],[f491,f2010])).
% 0.16/0.51 tff(f491,plain,(
% 0.16/0.51 ( ! [X2 : type,X3 : dB,X0 : dB,X1 : type,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f239])).
% 0.16/0.51 tff(f239,plain,(
% 0.16/0.51 ! [X0 : dB,X1 : type,X2 : type,X3 : dB,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))))),
% 0.16/0.51 inference(flattening,[],[f238])).
% 0.16/0.51 tff(f238,plain,(
% 0.16/0.51 ! [X0 : dB,X1 : type,X2 : type,X3 : dB,X4 : fun(nat,type)] : ((pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X0),X2))) | ~pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))))),
% 0.16/0.51 inference(ennf_transformation,[],[f189])).
% 0.16/0.51 tff(f189,plain,(
% 0.16/0.51 ! [X0 : dB,X1 : type,X2 : type,X3 : dB,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) => (pp(aa(type,bool,typing(X4,X0),X2)) => pp(aa(type,bool,typing(X4,aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))))),
% 0.16/0.51 inference(rectify,[],[f29])).
% 0.16/0.51 tff(f29,axiom,(
% 0.16/0.51 ! [X37 : dB,X16 : type,X8 : type,X13 : dB,X10 : fun(nat,type)] : (pp(aa(type,bool,typing(X10,X13),aa(type,type,aa(type,fun(type,type),fun1,X8),X16))) => (pp(aa(type,bool,typing(X10,X37),X8)) => pp(aa(type,bool,typing(X10,aa(dB,dB,aa(dB,fun(dB,dB),app,X13),X37)),X16))))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_App)).
% 0.16/0.51 tff(f2008,plain,(
% 0.16/0.51 spl32_144),
% 0.16/0.51 inference(avatar_split_clause,[],[f481,f2006])).
% 0.16/0.51 tff(f2006,plain,(
% 0.16/0.51 spl32_144 <=> ! [X0 : $tType,X3 : list(X0),X2 : fun(X0,bool),X1 : fun(X0,bool)] : (listsp(X0,X1,X3) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_144])])).
% 0.16/0.51 tff(f481,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : list(X0),X1 : fun(X0,bool)] : (listsp(X0,X1,X3) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f325])).
% 0.16/0.51 tff(f2004,plain,(
% 0.16/0.51 spl32_143),
% 0.16/0.51 inference(avatar_split_clause,[],[f480,f2002])).
% 0.16/0.51 tff(f2002,plain,(
% 0.16/0.51 spl32_143 <=> ! [X0 : $tType,X3 : list(X0),X2 : fun(X0,bool),X1 : fun(X0,bool)] : (listsp(X0,X2,X3) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_143])])).
% 0.16/0.51 tff(f480,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : list(X0),X1 : fun(X0,bool)] : (listsp(X0,X2,X3) | ~listsp(X0,combs(X0,bool,bool,aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2),X1),X3)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f325])).
% 0.16/0.51 tff(f1999,plain,(
% 0.16/0.51 spl32_142),
% 0.16/0.51 inference(avatar_split_clause,[],[f608,f1997])).
% 0.16/0.51 tff(f1997,plain,(
% 0.16/0.51 spl32_142 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X1),insert(dB,X0,nil(dB))))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_142])])).
% 0.16/0.51 tff(f608,plain,(
% 0.16/0.51 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X1),insert(dB,X0,nil(dB))))) )),
% 0.16/0.51 inference(forward_demodulation,[],[f400,f374])).
% 0.16/0.51 tff(f400,plain,(
% 0.16/0.51 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X1),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),nil(dB))))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f144])).
% 0.16/0.51 tff(f144,plain,(
% 0.16/0.51 ! [X0 : dB,X1 : list(dB),X2 : dB] : aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X1),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),nil(dB))))),
% 0.16/0.51 inference(rectify,[],[f51])).
% 0.16/0.51 tff(f51,axiom,(
% 0.16/0.51 ! [X36 : dB,X14 : list(dB),X37 : dB] : aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X37,X14)),X36) = foldl(dB,dB,app,X37,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X14),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X36),nil(dB))))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_app__last)).
% 0.16/0.51 tff(f1993,plain,(
% 0.16/0.51 spl32_141 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_140),
% 0.16/0.51 inference(avatar_split_clause,[],[f1989,f1986,f1538,f979,f744,f1991])).
% 0.16/0.51 tff(f1991,plain,(
% 0.16/0.51 spl32_141 <=> ! [X0 : list(type),X3 : fun(nat,type),X2 : list(dB),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,foldl(list(dB),list(dB),append(dB),X2,insert(list(dB),insert(dB,X1,nil(dB)),nil(list(dB))))),X0)) | pp(aa(list(type),bool,typings(X3,X2),sK21(X0,X1,X2,X3))))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_141])])).
% 0.16/0.51 tff(f1986,plain,(
% 0.16/0.51 spl32_140 <=> ! [X0 : list(type),X3 : fun(nat,type),X2 : list(dB),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),insert(dB,X1,nil(dB)))),X0)) | pp(aa(list(type),bool,typings(X3,X2),sK21(X0,X1,X2,X3))))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_140])])).
% 0.16/0.51 tff(f1989,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,foldl(list(dB),list(dB),append(dB),X2,insert(list(dB),insert(dB,X1,nil(dB)),nil(list(dB))))),X0)) | pp(aa(list(type),bool,typings(X3,X2),sK21(X0,X1,X2,X3)))) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_140)),
% 0.16/0.51 inference(forward_demodulation,[],[f1987,f1721])).
% 0.16/0.51 tff(f1987,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),insert(dB,X1,nil(dB)))),X0)) | pp(aa(list(type),bool,typings(X3,X2),sK21(X0,X1,X2,X3)))) ) | ~spl32_140),
% 0.16/0.51 inference(avatar_component_clause,[],[f1986])).
% 0.16/0.51 tff(f1988,plain,(
% 0.16/0.51 spl32_140),
% 0.16/0.51 inference(avatar_split_clause,[],[f612,f1986])).
% 0.16/0.51 tff(f612,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),insert(dB,X1,nil(dB)))),X0)) | pp(aa(list(type),bool,typings(X3,X2),sK21(X0,X1,X2,X3)))) )),
% 0.16/0.51 inference(forward_demodulation,[],[f450,f374])).
% 0.16/0.51 tff(f450,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (pp(aa(list(type),bool,typings(X3,X2),sK21(X0,X1,X2,X3))) | ~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X1),nil(dB)))),X0))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f304])).
% 0.16/0.51 tff(f1977,plain,(
% 0.16/0.51 spl32_139 | ~spl32_8),
% 0.16/0.51 inference(avatar_split_clause,[],[f668,f665,f1975])).
% 0.16/0.51 tff(f665,plain,(
% 0.16/0.51 spl32_8 <=> ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_8])])).
% 0.16/0.51 tff(f668,plain,(
% 0.16/0.51 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl32_8),
% 0.16/0.51 inference(superposition,[],[f666,f666])).
% 0.16/0.51 tff(f666,plain,(
% 0.16/0.51 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) ) | ~spl32_8),
% 0.16/0.51 inference(avatar_component_clause,[],[f665])).
% 0.16/0.51 tff(f1973,plain,(
% 0.16/0.51 spl32_138 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_137),
% 0.16/0.51 inference(avatar_split_clause,[],[f1969,f1965,f1538,f979,f744,f1971])).
% 0.16/0.51 tff(f1971,plain,(
% 0.16/0.51 spl32_138 <=> ! [X0 : $tType,X2 : list(X0),X4 : list(X0),X3 : list(X0),X1 : list(X0)] : (foldl(list(X0),list(X0),append(X0),X2,insert(list(X0),X1,nil(list(X0)))) = foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) | ~sP4(X0,X3,X1,X2,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_138])])).
% 0.16/0.51 tff(f1965,plain,(
% 0.16/0.51 spl32_137 <=> ! [X0 : $tType,X2 : list(X0),X4 : list(X0),X3 : list(X0),X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) | ~sP4(X0,X3,X1,X2,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_137])])).
% 0.16/0.51 tff(f1969,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (foldl(list(X0),list(X0),append(X0),X2,insert(list(X0),X1,nil(list(X0)))) = foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) | ~sP4(X0,X3,X1,X2,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_137)),
% 0.16/0.51 inference(forward_demodulation,[],[f1968,f1721])).
% 0.16/0.51 tff(f1968,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) | ~sP4(X0,X3,X1,X2,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_137)),
% 0.16/0.51 inference(forward_demodulation,[],[f1966,f1721])).
% 0.16/0.51 tff(f1966,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) | ~sP4(X0,X3,X1,X2,X4)) ) | ~spl32_137),
% 0.16/0.51 inference(avatar_component_clause,[],[f1965])).
% 0.16/0.51 tff(f1967,plain,(
% 0.16/0.51 spl32_137),
% 0.16/0.51 inference(avatar_split_clause,[],[f518,f1965])).
% 0.16/0.51 tff(f518,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) | ~sP4(X0,X3,X1,X2,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f344])).
% 0.16/0.51 tff(f344,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : list(X0),X4 : list(X0)] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) | ~sP4(X0,X3,X1,X2,X4)) & (sP4(X0,X3,X1,X2,X4) | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3)))),
% 0.16/0.51 inference(nnf_transformation,[],[f262])).
% 0.16/0.51 tff(f262,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) <=> sP4(X0,X3,X1,X2,X4))),
% 0.16/0.51 inference(definition_folding,[],[f193,f261])).
% 0.16/0.51 tff(f193,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) <=> ? [X5 : list(X0)] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X1) = X3 & aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X5) = X2) | (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X3) = X1 & aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X5) = X4)))),
% 0.16/0.51 inference(rectify,[],[f71])).
% 0.16/0.51 tff(f71,axiom,(
% 0.16/0.51 ! [X2 : $tType,X14 : list(X2),X76 : list(X2),X77 : list(X2),X34 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X34),X77) = aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X76),X14) <=> ? [X80 : list(X2)] : ((aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X80),X14) = X77 & aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X34),X80) = X76) | (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X80),X77) = X14 & aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X76),X80) = X34)))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_append__eq__append__conv2)).
% 0.16/0.51 tff(f1962,plain,(
% 0.16/0.51 spl32_136 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_135),
% 0.16/0.51 inference(avatar_split_clause,[],[f1958,f1954,f1538,f979,f744,f1960])).
% 0.16/0.51 tff(f1960,plain,(
% 0.16/0.51 spl32_136 <=> ! [X0 : $tType,X2 : list(X0),X4 : list(X0),X3 : list(X0),X1 : list(X0)] : (foldl(list(X0),list(X0),append(X0),X2,insert(list(X0),X1,nil(list(X0)))) != foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) | sP4(X0,X3,X1,X2,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_136])])).
% 0.16/0.51 tff(f1954,plain,(
% 0.16/0.51 spl32_135 <=> ! [X0 : $tType,X4 : list(X0),X3 : list(X0),X2 : list(X0),X1 : list(X0)] : (sP4(X0,X3,X1,X2,X4) | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_135])])).
% 0.16/0.51 tff(f1958,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (foldl(list(X0),list(X0),append(X0),X2,insert(list(X0),X1,nil(list(X0)))) != foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) | sP4(X0,X3,X1,X2,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_135)),
% 0.16/0.51 inference(forward_demodulation,[],[f1957,f1721])).
% 0.16/0.51 tff(f1957,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) | sP4(X0,X3,X1,X2,X4)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_135)),
% 0.16/0.51 inference(forward_demodulation,[],[f1955,f1721])).
% 0.16/0.51 tff(f1955,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (sP4(X0,X3,X1,X2,X4) | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3)) ) | ~spl32_135),
% 0.16/0.51 inference(avatar_component_clause,[],[f1954])).
% 0.16/0.51 tff(f1956,plain,(
% 0.16/0.51 spl32_135),
% 0.16/0.51 inference(avatar_split_clause,[],[f517,f1954])).
% 0.16/0.51 tff(f517,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (sP4(X0,X3,X1,X2,X4) | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f344])).
% 0.16/0.51 tff(f1950,plain,(
% 0.16/0.51 spl32_134 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_133),
% 0.16/0.51 inference(avatar_split_clause,[],[f1946,f1943,f1538,f979,f744,f1948])).
% 0.16/0.51 tff(f1948,plain,(
% 0.16/0.51 spl32_134 <=> ! [X0 : list(type),X3 : fun(nat,type),X2 : list(dB),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,foldl(list(dB),list(dB),append(dB),X2,insert(list(dB),insert(dB,X1,nil(dB)),nil(list(dB))))),X0)) | pp(aa(type,bool,typing(X3,X1),sK22(X0,X1,X2,X3))))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_134])])).
% 0.16/0.51 tff(f1943,plain,(
% 0.16/0.51 spl32_133 <=> ! [X0 : list(type),X3 : fun(nat,type),X2 : list(dB),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),insert(dB,X1,nil(dB)))),X0)) | pp(aa(type,bool,typing(X3,X1),sK22(X0,X1,X2,X3))))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_133])])).
% 0.16/0.51 tff(f1946,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,foldl(list(dB),list(dB),append(dB),X2,insert(list(dB),insert(dB,X1,nil(dB)),nil(list(dB))))),X0)) | pp(aa(type,bool,typing(X3,X1),sK22(X0,X1,X2,X3)))) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_133)),
% 0.16/0.51 inference(forward_demodulation,[],[f1944,f1721])).
% 0.16/0.51 tff(f1944,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),insert(dB,X1,nil(dB)))),X0)) | pp(aa(type,bool,typing(X3,X1),sK22(X0,X1,X2,X3)))) ) | ~spl32_133),
% 0.16/0.51 inference(avatar_component_clause,[],[f1943])).
% 0.16/0.51 tff(f1945,plain,(
% 0.16/0.51 spl32_133),
% 0.16/0.51 inference(avatar_split_clause,[],[f611,f1943])).
% 0.16/0.51 tff(f611,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),insert(dB,X1,nil(dB)))),X0)) | pp(aa(type,bool,typing(X3,X1),sK22(X0,X1,X2,X3)))) )),
% 0.16/0.51 inference(forward_demodulation,[],[f451,f374])).
% 0.16/0.51 tff(f451,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : list(type),X1 : dB] : (pp(aa(type,bool,typing(X3,X1),sK22(X0,X1,X2,X3))) | ~pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X2),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X1),nil(dB)))),X0))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f304])).
% 0.16/0.51 tff(f1935,plain,(
% 0.16/0.51 spl32_132 | ~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_131),
% 0.16/0.51 inference(avatar_split_clause,[],[f1931,f1927,f1538,f1534,f979,f744,f740,f1933])).
% 0.16/0.51 tff(f1933,plain,(
% 0.16/0.51 spl32_132 <=> ! [X0 : $tType,X4 : list(X0),X3 : list(X0),X2 : X0,X1 : list(X0)] : (foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) = foldr(X0,list(X0),cons(X0),insert(X0,X2,nil(X0)),X1) | ~sP3(X0,X1,X3,X4,X2))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_132])])).
% 0.16/0.51 tff(f1927,plain,(
% 0.16/0.51 spl32_131 <=> ! [X0 : $tType,X2 : X0,X4 : list(X0),X3 : list(X0),X1 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) | ~sP3(X0,X1,X3,X4,X2))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_131])])).
% 0.16/0.51 tff(f1931,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) = foldr(X0,list(X0),cons(X0),insert(X0,X2,nil(X0)),X1) | ~sP3(X0,X1,X3,X4,X2)) ) | (~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_131)),
% 0.16/0.51 inference(forward_demodulation,[],[f1930,f1608])).
% 0.16/0.51 tff(f1930,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) | ~sP3(X0,X1,X3,X4,X2)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_131)),
% 0.16/0.51 inference(forward_demodulation,[],[f1928,f1721])).
% 0.16/0.51 tff(f1928,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) | ~sP3(X0,X1,X3,X4,X2)) ) | ~spl32_131),
% 0.16/0.51 inference(avatar_component_clause,[],[f1927])).
% 0.16/0.51 tff(f1929,plain,(
% 0.16/0.51 spl32_131),
% 0.16/0.51 inference(avatar_split_clause,[],[f510,f1927])).
% 0.16/0.51 tff(f510,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) | ~sP3(X0,X1,X3,X4,X2)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f339])).
% 0.16/0.51 tff(f339,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : list(X0)] : ((aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) | ~sP3(X0,X1,X3,X4,X2)) & (sP3(X0,X1,X3,X4,X2) | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3)))),
% 0.16/0.51 inference(nnf_transformation,[],[f260])).
% 0.16/0.51 tff(f260,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) <=> sP3(X0,X1,X3,X4,X2))),
% 0.16/0.51 inference(definition_folding,[],[f192,f259])).
% 0.16/0.51 tff(f192,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3) <=> (? [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X3) = X1 & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X5) = X4) | (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = X3 & nil(X0) = X4)))),
% 0.16/0.51 inference(rectify,[],[f73])).
% 0.16/0.51 tff(f73,axiom,(
% 0.16/0.51 ! [X2 : $tType,X34 : list(X2),X9 : X2,X76 : list(X2),X77 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X77),X76) = aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X9),X34) <=> (? [X82 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X82),X76) = X34 & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X9),X82) = X77) | (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X9),X34) = X76 & nil(X2) = X77)))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_append__eq__Cons__conv)).
% 0.16/0.51 tff(f1925,plain,(
% 0.16/0.51 spl32_130 | ~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_129),
% 0.16/0.51 inference(avatar_split_clause,[],[f1921,f1917,f1538,f1534,f979,f744,f740,f1923])).
% 0.16/0.51 tff(f1923,plain,(
% 0.16/0.51 spl32_130 <=> ! [X0 : $tType,X4 : list(X0),X3 : list(X0),X2 : X0,X1 : list(X0)] : (foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) != foldr(X0,list(X0),cons(X0),insert(X0,X2,nil(X0)),X1) | sP3(X0,X1,X3,X4,X2))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_130])])).
% 0.16/0.51 tff(f1917,plain,(
% 0.16/0.51 spl32_129 <=> ! [X0 : $tType,X4 : list(X0),X3 : list(X0),X2 : X0,X1 : list(X0)] : (sP3(X0,X1,X3,X4,X2) | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_129])])).
% 0.16/0.51 tff(f1921,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) != foldr(X0,list(X0),cons(X0),insert(X0,X2,nil(X0)),X1) | sP3(X0,X1,X3,X4,X2)) ) | (~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_129)),
% 0.16/0.51 inference(forward_demodulation,[],[f1920,f1608])).
% 0.16/0.51 tff(f1920,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != foldl(list(X0),list(X0),append(X0),X4,insert(list(X0),X3,nil(list(X0)))) | sP3(X0,X1,X3,X4,X2)) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_129)),
% 0.16/0.51 inference(forward_demodulation,[],[f1918,f1721])).
% 0.16/0.51 tff(f1918,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (sP3(X0,X1,X3,X4,X2) | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3)) ) | ~spl32_129),
% 0.16/0.51 inference(avatar_component_clause,[],[f1917])).
% 0.16/0.51 tff(f1919,plain,(
% 0.16/0.51 spl32_129),
% 0.16/0.51 inference(avatar_split_clause,[],[f509,f1917])).
% 0.16/0.51 tff(f509,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : list(X0)] : (sP3(X0,X1,X3,X4,X2) | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f339])).
% 0.16/0.51 tff(f1909,plain,(
% 0.16/0.51 spl32_128 | ~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_127),
% 0.16/0.51 inference(avatar_split_clause,[],[f1905,f1901,f1538,f1534,f979,f744,f740,f1907])).
% 0.16/0.51 tff(f1907,plain,(
% 0.16/0.51 spl32_128 <=> ! [X0 : $tType,X2 : list(X0),X4 : X0,X3 : list(X0),X1 : list(X0)] : (foldl(list(X0),list(X0),append(X0),X2,insert(list(X0),X1,nil(list(X0)))) = foldr(X0,list(X0),cons(X0),insert(X0,X4,nil(X0)),X3) | ~sP2(X0,X3,X1,X2,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_128])])).
% 0.16/0.51 tff(f1901,plain,(
% 0.16/0.51 spl32_127 <=> ! [X0 : $tType,X2 : list(X0),X4 : X0,X3 : list(X0),X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) | ~sP2(X0,X3,X1,X2,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_127])])).
% 0.16/0.51 tff(f1905,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : X0] : (foldl(list(X0),list(X0),append(X0),X2,insert(list(X0),X1,nil(list(X0)))) = foldr(X0,list(X0),cons(X0),insert(X0,X4,nil(X0)),X3) | ~sP2(X0,X3,X1,X2,X4)) ) | (~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_127)),
% 0.16/0.51 inference(forward_demodulation,[],[f1904,f1721])).
% 0.16/0.51 tff(f1904,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : X0] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = foldr(X0,list(X0),cons(X0),insert(X0,X4,nil(X0)),X3) | ~sP2(X0,X3,X1,X2,X4)) ) | (~spl32_21 | ~spl32_64 | ~spl32_114 | ~spl32_127)),
% 0.16/0.51 inference(forward_demodulation,[],[f1902,f1608])).
% 0.16/0.51 tff(f1902,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : X0] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) | ~sP2(X0,X3,X1,X2,X4)) ) | ~spl32_127),
% 0.16/0.51 inference(avatar_component_clause,[],[f1901])).
% 0.16/0.51 tff(f1903,plain,(
% 0.16/0.51 spl32_127),
% 0.16/0.51 inference(avatar_split_clause,[],[f502,f1901])).
% 0.16/0.51 tff(f502,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : X0] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) | ~sP2(X0,X3,X1,X2,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f333])).
% 0.16/0.51 tff(f333,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : list(X0),X4 : X0] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) | ~sP2(X0,X3,X1,X2,X4)) & (sP2(X0,X3,X1,X2,X4) | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3)))),
% 0.16/0.51 inference(nnf_transformation,[],[f258])).
% 0.16/0.51 tff(f258,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : list(X0),X4 : X0] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) <=> sP2(X0,X3,X1,X2,X4))),
% 0.16/0.51 inference(definition_folding,[],[f191,f257])).
% 0.16/0.51 tff(f191,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : list(X0),X4 : X0] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) <=> (? [X5 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X5),X1) = X3 & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) = X2) | (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) = X1 & nil(X0) = X2)))),
% 0.16/0.51 inference(rectify,[],[f74])).
% 0.16/0.51 tff(f74,axiom,(
% 0.16/0.51 ! [X2 : $tType,X76 : list(X2),X77 : list(X2),X34 : list(X2),X9 : X2] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X77),X76) = aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X9),X34) <=> (? [X82 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X82),X76) = X34 & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X9),X82) = X77) | (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X9),X34) = X76 & nil(X2) = X77)))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Cons__eq__append__conv)).
% 0.16/0.51 tff(f1899,plain,(
% 0.16/0.51 spl32_126 | ~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_125),
% 0.16/0.51 inference(avatar_split_clause,[],[f1895,f1891,f1538,f1534,f979,f744,f740,f1897])).
% 0.16/0.51 tff(f1897,plain,(
% 0.16/0.51 spl32_126 <=> ! [X0 : $tType,X2 : list(X0),X4 : X0,X3 : list(X0),X1 : list(X0)] : (foldl(list(X0),list(X0),append(X0),X2,insert(list(X0),X1,nil(list(X0)))) != foldr(X0,list(X0),cons(X0),insert(X0,X4,nil(X0)),X3) | sP2(X0,X3,X1,X2,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_126])])).
% 0.16/0.51 tff(f1891,plain,(
% 0.16/0.51 spl32_125 <=> ! [X0 : $tType,X4 : X0,X3 : list(X0),X2 : list(X0),X1 : list(X0)] : (sP2(X0,X3,X1,X2,X4) | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_125])])).
% 0.16/0.51 tff(f1895,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : X0] : (foldl(list(X0),list(X0),append(X0),X2,insert(list(X0),X1,nil(list(X0)))) != foldr(X0,list(X0),cons(X0),insert(X0,X4,nil(X0)),X3) | sP2(X0,X3,X1,X2,X4)) ) | (~spl32_21 | ~spl32_22 | ~spl32_64 | ~spl32_114 | ~spl32_115 | ~spl32_125)),
% 0.16/0.51 inference(forward_demodulation,[],[f1894,f1721])).
% 0.16/0.51 tff(f1894,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : X0] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != foldr(X0,list(X0),cons(X0),insert(X0,X4,nil(X0)),X3) | sP2(X0,X3,X1,X2,X4)) ) | (~spl32_21 | ~spl32_64 | ~spl32_114 | ~spl32_125)),
% 0.16/0.51 inference(forward_demodulation,[],[f1892,f1608])).
% 0.16/0.51 tff(f1892,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : X0] : (sP2(X0,X3,X1,X2,X4) | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3)) ) | ~spl32_125),
% 0.16/0.51 inference(avatar_component_clause,[],[f1891])).
% 0.16/0.51 tff(f1893,plain,(
% 0.16/0.51 spl32_125),
% 0.16/0.51 inference(avatar_split_clause,[],[f501,f1891])).
% 0.16/0.51 tff(f501,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0),X4 : X0] : (sP2(X0,X3,X1,X2,X4) | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f333])).
% 0.16/0.51 tff(f1889,plain,(
% 0.16/0.51 spl32_124 | ~spl32_56 | ~spl32_57 | ~spl32_117),
% 0.16/0.51 inference(avatar_split_clause,[],[f1805,f1546,f944,f940,f1887])).
% 0.16/0.51 tff(f1887,plain,(
% 0.16/0.51 spl32_124 <=> ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : sP4(X0,X1,X1,X2,X2)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_124])])).
% 0.16/0.51 tff(f940,plain,(
% 0.16/0.51 spl32_56 <=> ! [X0 : $tType,X1 : list(X0)] : aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X1),nil(X0)) = X1),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_56])])).
% 0.16/0.51 tff(f944,plain,(
% 0.16/0.51 spl32_57 <=> ! [X0 : $tType,X1 : list(X0)] : aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),nil(X0)),X1) = X1),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_57])])).
% 0.16/0.51 tff(f1546,plain,(
% 0.16/0.51 spl32_117 <=> ! [X2 : $tType,X4 : list(X2),X5 : list(X2),X1 : list(X2)] : sP4(X2,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1),X1,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),X5),X4)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_117])])).
% 0.16/0.51 tff(f1805,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (sP4(X0,X1,X1,X2,X2)) ) | (~spl32_56 | ~spl32_57 | ~spl32_117)),
% 0.16/0.51 inference(forward_demodulation,[],[f1795,f941])).
% 0.16/0.51 tff(f941,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X1),nil(X0)) = X1) ) | ~spl32_56),
% 0.16/0.51 inference(avatar_component_clause,[],[f940])).
% 0.16/0.51 tff(f1795,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (sP4(X0,X1,X1,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),nil(X0)),X2)) ) | (~spl32_57 | ~spl32_117)),
% 0.16/0.51 inference(superposition,[],[f1547,f945])).
% 0.16/0.51 tff(f945,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),nil(X0)),X1) = X1) ) | ~spl32_57),
% 0.16/0.51 inference(avatar_component_clause,[],[f944])).
% 0.16/0.51 tff(f1547,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X1 : list(X2),X4 : list(X2),X5 : list(X2)] : (sP4(X2,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1),X1,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),X5),X4)) ) | ~spl32_117),
% 0.16/0.51 inference(avatar_component_clause,[],[f1546])).
% 0.16/0.51 tff(f1863,plain,(
% 0.16/0.51 spl32_123),
% 0.16/0.51 inference(avatar_split_clause,[],[f478,f1861])).
% 0.16/0.51 tff(f1861,plain,(
% 0.16/0.51 spl32_123 <=> ! [X0 : $tType,X3 : list(X0),X2 : list(X0),X1 : list(X0)] : (X1 = X3 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X1),X2) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X2))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_123])])).
% 0.16/0.51 tff(f478,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0)] : (X1 = X3 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X1),X2) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X2)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f323])).
% 0.16/0.51 tff(f323,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : list(X0)] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X1),X2) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X2) | X1 != X3) & (X1 = X3 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X1),X2) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X2)))),
% 0.16/0.51 inference(nnf_transformation,[],[f179])).
% 0.16/0.51 tff(f179,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X1),X2) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X2) <=> X1 = X3)),
% 0.16/0.51 inference(rectify,[],[f55])).
% 0.16/0.51 tff(f55,axiom,(
% 0.16/0.51 ! [X2 : $tType,X76 : list(X2),X34 : list(X2),X77 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X77),X34) = aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X76),X34) <=> X76 = X77)),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_append__same__eq)).
% 0.16/0.51 tff(f1859,plain,(
% 0.16/0.51 spl32_122),
% 0.16/0.51 inference(avatar_split_clause,[],[f476,f1857])).
% 0.16/0.51 tff(f1857,plain,(
% 0.16/0.51 spl32_122 <=> ! [X0 : $tType,X3 : list(X0),X2 : list(X0),X1 : list(X0)] : (X1 = X2 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X2) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X1))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_122])])).
% 0.16/0.51 tff(f476,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : list(X0)] : (X1 = X2 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X2) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X1)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f322])).
% 0.16/0.51 tff(f322,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : list(X0)] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X2) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X1) | X1 != X2) & (X1 = X2 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X2) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X1)))),
% 0.16/0.51 inference(nnf_transformation,[],[f178])).
% 0.16/0.51 tff(f178,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X2) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X3),X1) <=> X1 = X2)),
% 0.16/0.51 inference(rectify,[],[f54])).
% 0.16/0.51 tff(f54,axiom,(
% 0.16/0.51 ! [X2 : $tType,X76 : list(X2),X77 : list(X2),X34 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X34),X77) = aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X34),X76) <=> X76 = X77)),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_same__append__eq)).
% 0.16/0.51 tff(f1844,plain,(
% 0.16/0.51 spl32_121 | ~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_120),
% 0.16/0.51 inference(avatar_split_clause,[],[f1840,f1836,f1538,f979,f744,f1842])).
% 0.16/0.51 tff(f1842,plain,(
% 0.16/0.51 spl32_121 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : dB] : (~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,insert(dB,X1,nil(dB)))),X0)) | pp(aa(type,bool,typing(X3,X2),foldl(type,type,fun1,sK20(X0,X1,X2,X3),insert(type,X0,nil(type))))))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_121])])).
% 0.16/0.51 tff(f1836,plain,(
% 0.16/0.51 spl32_120 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : dB] : (pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK20(X0,X1,X2,X3)),X0))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_120])])).
% 0.16/0.51 tff(f1840,plain,(
% 0.16/0.51 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,insert(dB,X1,nil(dB)))),X0)) | pp(aa(type,bool,typing(X3,X2),foldl(type,type,fun1,sK20(X0,X1,X2,X3),insert(type,X0,nil(type)))))) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_120)),
% 0.16/0.51 inference(forward_demodulation,[],[f1839,f1721])).
% 0.16/0.51 tff(f1839,plain,(
% 0.16/0.51 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X2),foldl(type,type,fun1,sK20(X0,X1,X2,X3),insert(type,X0,nil(type))))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | (~spl32_22 | ~spl32_64 | ~spl32_115 | ~spl32_120)),
% 0.16/0.51 inference(forward_demodulation,[],[f1837,f1721])).
% 0.16/0.51 tff(f1837,plain,(
% 0.16/0.51 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK20(X0,X1,X2,X3)),X0))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | ~spl32_120),
% 0.16/0.51 inference(avatar_component_clause,[],[f1836])).
% 0.16/0.51 tff(f1838,plain,(
% 0.16/0.51 spl32_120),
% 0.16/0.51 inference(avatar_split_clause,[],[f447,f1836])).
% 0.16/0.51 tff(f447,plain,(
% 0.16/0.51 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK20(X0,X1,X2,X3)),X0))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f302])).
% 0.16/0.51 tff(f302,plain,(
% 0.16/0.51 ! [X0 : type,X1 : dB,X2 : dB,X3 : fun(nat,type)] : ((pp(aa(type,bool,typing(X3,X1),sK20(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK20(X0,X1,X2,X3)),X0)))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 0.16/0.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f226,f301])).
% 0.16/0.51 tff(f301,plain,(
% 0.16/0.51 ! [X0 : type,X1 : dB,X2 : dB,X3 : fun(nat,type)] : (? [X4 : type] : (pp(aa(type,bool,typing(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0)))) => (pp(aa(type,bool,typing(X3,X1),sK20(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK20(X0,X1,X2,X3)),X0)))))),
% 0.16/0.51 introduced(choice_axiom,[])).
% 0.16/0.51 tff(f226,plain,(
% 0.16/0.51 ! [X0 : type,X1 : dB,X2 : dB,X3 : fun(nat,type)] : (? [X4 : type] : (pp(aa(type,bool,typing(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0)))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 0.16/0.51 inference(ennf_transformation,[],[f169])).
% 0.16/0.51 tff(f169,plain,(
% 0.16/0.51 ! [X0 : type,X1 : dB,X2 : dB,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) => ~! [X4 : type] : (pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0))) => ~pp(aa(type,bool,typing(X3,X1),X4))))),
% 0.16/0.51 inference(rectify,[],[f43])).
% 0.16/0.51 tff(f43,axiom,(
% 0.16/0.51 ! [X8 : type,X36 : dB,X37 : dB,X12 : fun(nat,type)] : (pp(aa(type,bool,typing(X12,aa(dB,dB,aa(dB,fun(dB,dB),app,X37),X36)),X8)) => ~! [X60 : type] : (pp(aa(type,bool,typing(X12,X37),aa(type,type,aa(type,fun(type,type),fun1,X60),X8))) => ~pp(aa(type,bool,typing(X12,X36),X60))))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_typing__elims_I2_J)).
% 0.16/0.51 tff(f1556,plain,(
% 0.16/0.51 spl32_119),
% 0.16/0.51 inference(avatar_split_clause,[],[f618,f1554])).
% 0.16/0.51 tff(f1554,plain,(
% 0.16/0.51 spl32_119 <=> ! [X0 : dB,X3 : dB,X2 : list(dB),X1 : dB] : (aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),sK24(X0,X1,X2,X3)),insert(dB,X3,nil(dB))) = X2 | nil(dB) = X2 | ~sP1(X0,X1,X2,X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_119])])).
% 0.16/0.51 tff(f618,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),sK24(X0,X1,X2,X3)),insert(dB,X3,nil(dB))) = X2 | nil(dB) = X2 | ~sP1(X0,X1,X2,X3)) )),
% 0.16/0.51 inference(forward_demodulation,[],[f457,f374])).
% 0.16/0.51 tff(f457,plain,(
% 0.16/0.51 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),sK24(X0,X1,X2,X3)),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X3),nil(dB))) = X2 | nil(dB) = X2 | ~sP1(X0,X1,X2,X3)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f313])).
% 0.16/0.51 tff(f1552,plain,(
% 0.16/0.51 spl32_118),
% 0.16/0.51 inference(avatar_split_clause,[],[f598,f1550])).
% 0.16/0.51 tff(f1550,plain,(
% 0.16/0.51 spl32_118 <=> ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X5 : list(X2)] : sP4(X2,X0,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X0),X3,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),X5))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_118])])).
% 0.16/0.51 tff(f598,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X5 : list(X2)] : (sP4(X2,X0,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X0),X3,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),X5))) )),
% 0.16/0.51 inference(equality_resolution,[],[f597])).
% 0.16/0.51 tff(f597,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X4 : list(X2),X5 : list(X2)] : (sP4(X2,X0,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X0),X3,X4) | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),X5) != X4) )),
% 0.16/0.51 inference(equality_resolution,[],[f515])).
% 0.16/0.51 tff(f515,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2),X5 : list(X2)] : (sP4(X2,X0,X1,X3,X4) | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X0) != X1 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X3),X5) != X4) )),
% 0.16/0.51 inference(cnf_transformation,[],[f343])).
% 0.16/0.51 tff(f1548,plain,(
% 0.16/0.51 spl32_117),
% 0.16/0.51 inference(avatar_split_clause,[],[f596,f1546])).
% 0.16/0.51 tff(f596,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X1 : list(X2),X4 : list(X2),X5 : list(X2)] : (sP4(X2,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1),X1,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),X5),X4)) )),
% 0.16/0.51 inference(equality_resolution,[],[f595])).
% 0.16/0.51 tff(f595,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X1 : list(X2),X4 : list(X2),X5 : list(X2)] : (sP4(X2,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1),X1,X3,X4) | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),X5) != X3) )),
% 0.16/0.51 inference(equality_resolution,[],[f516])).
% 0.16/0.51 tff(f516,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : list(X2),X5 : list(X2)] : (sP4(X2,X0,X1,X3,X4) | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1) != X0 | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X4),X5) != X3) )),
% 0.16/0.51 inference(cnf_transformation,[],[f343])).
% 0.16/0.51 tff(f1544,plain,(
% 0.16/0.51 spl32_116),
% 0.16/0.51 inference(avatar_split_clause,[],[f533,f1542])).
% 0.16/0.51 tff(f1542,plain,(
% 0.16/0.51 spl32_116 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X5 : fun(X1,X0),X4 : fun(X2,X1),X3 : X2] : aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_116])])).
% 0.16/0.51 tff(f533,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X1,X0)] : (aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f204])).
% 0.16/0.51 tff(f204,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X1,X0)] : aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))),
% 0.16/0.51 inference(rectify,[],[f103])).
% 0.16/0.51 tff(f103,axiom,(
% 0.16/0.51 ! [X1 : $tType,X0 : $tType,X2 : $tType,X92 : X2,X93 : fun(X2,X0),X94 : fun(X0,X1)] : aa(X2,X1,aa(fun(X2,X0),fun(X2,X1),aa(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1)),combb(X0,X1,X2),X94),X93),X92) = aa(X0,X1,X94,aa(X2,X0,X93,X92))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U)).
% 0.16/0.51 tff(f1540,plain,(
% 0.16/0.51 spl32_115),
% 0.16/0.51 inference(avatar_split_clause,[],[f532,f1538])).
% 0.16/0.51 tff(f532,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : X0,X5 : fun(X0,fun(X1,X0))] : (foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f203])).
% 0.16/0.51 tff(f203,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : $tType,X2 : list(X1),X3 : X1,X4 : X0,X5 : fun(X0,fun(X1,X0))] : foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2)),
% 0.16/0.51 inference(rectify,[],[f23])).
% 0.16/0.51 tff(f23,axiom,(
% 0.16/0.51 ! [X2 : $tType,X0 : $tType,X34 : list(X0),X9 : X0,X33 : X2,X35 : fun(X2,fun(X0,X2))] : foldl(X2,X0,X35,X33,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X9),X34)) = foldl(X2,X0,X35,aa(X0,X2,aa(X2,fun(X0,X2),X35,X33),X9),X34)),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_foldl__Cons)).
% 0.16/0.51 tff(f1536,plain,(
% 0.16/0.51 spl32_114),
% 0.16/0.51 inference(avatar_split_clause,[],[f531,f1534])).
% 0.16/0.51 tff(f531,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X1,X1))] : (foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f202])).
% 0.16/0.51 tff(f202,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X1,X1))] : foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2))),
% 0.16/0.51 inference(rectify,[],[f95])).
% 0.16/0.51 tff(f95,axiom,(
% 0.16/0.51 ! [X0 : $tType,X2 : $tType,X33 : X2,X34 : list(X0),X9 : X0,X35 : fun(X0,fun(X2,X2))] : foldr(X0,X2,X35,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X9),X34),X33) = aa(X2,X2,aa(X0,fun(X2,X2),X35,X9),foldr(X0,X2,X35,X34,X33))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_foldr_Osimps_I2_J)).
% 0.16/0.51 tff(f1532,plain,(
% 0.16/0.51 spl32_113 | ~spl32_10 | ~spl32_13),
% 0.16/0.51 inference(avatar_split_clause,[],[f726,f695,f681,f1530])).
% 0.16/0.51 tff(f1530,plain,(
% 0.16/0.51 spl32_113 <=> ! [X0 : nat] : fTrue = aa(dB,bool,it,var(X0))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_113])])).
% 0.16/0.51 tff(f681,plain,(
% 0.16/0.51 spl32_10 <=> ! [X0 : nat] : pp(aa(dB,bool,it,var(X0)))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_10])])).
% 0.16/0.51 tff(f726,plain,(
% 0.16/0.51 ( ! [X0 : nat] : (fTrue = aa(dB,bool,it,var(X0))) ) | (~spl32_10 | ~spl32_13)),
% 0.16/0.51 inference(resolution,[],[f696,f682])).
% 0.16/0.51 tff(f682,plain,(
% 0.16/0.51 ( ! [X0 : nat] : (pp(aa(dB,bool,it,var(X0)))) ) | ~spl32_10),
% 0.16/0.51 inference(avatar_component_clause,[],[f681])).
% 0.16/0.51 tff(f1528,plain,(
% 0.16/0.51 spl32_112),
% 0.16/0.51 inference(avatar_split_clause,[],[f493,f1526])).
% 0.16/0.51 tff(f1526,plain,(
% 0.16/0.51 spl32_112 <=> ! [X0 : $tType,X2 : X0,X4 : X0,X3 : list(X0),X1 : list(X0)] : (X1 = X3 | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_112])])).
% 0.16/0.51 tff(f493,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (X1 = X3 | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f327])).
% 0.16/0.51 tff(f327,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : ((aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) | X1 != X3 | X2 != X4) & ((X1 = X3 & X2 = X4) | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3)))),
% 0.16/0.51 inference(flattening,[],[f326])).
% 0.16/0.51 tff(f326,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : ((aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) | (X1 != X3 | X2 != X4)) & ((X1 = X3 & X2 = X4) | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3)))),
% 0.16/0.51 inference(nnf_transformation,[],[f190])).
% 0.16/0.51 tff(f190,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) <=> (X1 = X3 & X2 = X4))),
% 0.16/0.51 inference(rectify,[],[f22])).
% 0.16/0.51 tff(f22,axiom,(
% 0.16/0.51 ! [X2 : $tType,X30 : list(X2),X31 : X2,X32 : list(X2),X33 : X2] : (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X33),X32) = aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X31),X30) <=> (X30 = X32 & X31 = X33))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_list_Oinject)).
% 0.16/0.51 tff(f1485,plain,(
% 0.16/0.51 spl32_111),
% 0.16/0.51 inference(avatar_split_clause,[],[f592,f1483])).
% 0.16/0.51 tff(f1483,plain,(
% 0.16/0.51 spl32_111 <=> ! [X2 : $tType,X4 : X2,X5 : list(X2),X1 : list(X2)] : sP3(X2,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1),X1,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5),X4)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_111])])).
% 0.16/0.51 tff(f592,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X1 : list(X2),X4 : X2,X5 : list(X2)] : (sP3(X2,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1),X1,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5),X4)) )),
% 0.16/0.51 inference(equality_resolution,[],[f591])).
% 0.16/0.51 tff(f591,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X1 : list(X2),X4 : X2,X5 : list(X2)] : (sP3(X2,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1),X1,X3,X4) | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5) != X3) )),
% 0.16/0.51 inference(equality_resolution,[],[f508])).
% 0.16/0.51 tff(f508,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2,X5 : list(X2)] : (sP3(X2,X0,X1,X3,X4) | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1) != X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5) != X3) )),
% 0.16/0.51 inference(cnf_transformation,[],[f338])).
% 0.16/0.51 tff(f1481,plain,(
% 0.16/0.51 spl32_110),
% 0.16/0.51 inference(avatar_split_clause,[],[f588,f1479])).
% 0.16/0.51 tff(f1479,plain,(
% 0.16/0.51 spl32_110 <=> ! [X2 : $tType,X4 : X2,X5 : list(X2),X1 : list(X2)] : sP2(X2,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1),X1,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5),X4)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_110])])).
% 0.16/0.51 tff(f588,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X1 : list(X2),X4 : X2,X5 : list(X2)] : (sP2(X2,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1),X1,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5),X4)) )),
% 0.16/0.51 inference(equality_resolution,[],[f587])).
% 0.16/0.51 tff(f587,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X1 : list(X2),X4 : X2,X5 : list(X2)] : (sP2(X2,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1),X1,X3,X4) | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5) != X3) )),
% 0.16/0.51 inference(equality_resolution,[],[f500])).
% 0.16/0.51 tff(f500,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2,X5 : list(X2)] : (sP2(X2,X0,X1,X3,X4) | aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X5),X1) != X0 | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X5) != X3) )),
% 0.16/0.51 inference(cnf_transformation,[],[f332])).
% 0.16/0.51 tff(f1477,plain,(
% 0.16/0.51 spl32_109),
% 0.16/0.51 inference(avatar_split_clause,[],[f492,f1475])).
% 0.16/0.51 tff(f1475,plain,(
% 0.16/0.51 spl32_109 <=> ! [X0 : $tType,X4 : X0,X3 : list(X0),X2 : X0,X1 : list(X0)] : (X2 = X4 | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_109])])).
% 0.16/0.51 tff(f492,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (X2 = X4 | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f327])).
% 0.16/0.51 tff(f1469,plain,(
% 0.16/0.51 spl32_108),
% 0.16/0.51 inference(avatar_split_clause,[],[f505,f1467])).
% 0.16/0.51 tff(f1467,plain,(
% 0.16/0.51 spl32_108 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK26(X2,X0,X1,X3,X4)),X1) = X0 | nil(X2) = X3 | ~sP3(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_108])])).
% 0.16/0.51 tff(f505,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK26(X2,X0,X1,X3,X4)),X1) = X0 | nil(X2) = X3 | ~sP3(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f338])).
% 0.16/0.51 tff(f1462,plain,(
% 0.16/0.51 spl32_107),
% 0.16/0.51 inference(avatar_split_clause,[],[f497,f1460])).
% 0.16/0.51 tff(f1460,plain,(
% 0.16/0.51 spl32_107 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK25(X2,X0,X1,X3,X4)),X1) = X0 | nil(X2) = X3 | ~sP2(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_107])])).
% 0.16/0.51 tff(f497,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),sK25(X2,X0,X1,X3,X4)),X1) = X0 | nil(X2) = X3 | ~sP2(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f332])).
% 0.16/0.51 tff(f1421,plain,(
% 0.16/0.51 spl32_106),
% 0.16/0.51 inference(avatar_split_clause,[],[f530,f1419])).
% 0.16/0.51 tff(f1419,plain,(
% 0.16/0.51 spl32_106 <=> ! [X1 : $tType,X0 : $tType,X5 : X0,X4 : fun(X1,fun(list(X1),X0)),X3 : X1,X2 : list(X1)] : list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_106])])).
% 0.16/0.51 tff(f530,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,fun(list(X1),X0)),X5 : X0] : (list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f201])).
% 0.16/0.51 tff(f201,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,fun(list(X1),X0)),X5 : X0] : list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2)),
% 0.16/0.51 inference(rectify,[],[f86])).
% 0.16/0.51 tff(f86,axiom,(
% 0.16/0.51 ! [X2 : $tType,X0 : $tType,X32 : list(X0),X33 : X0,X41 : fun(X0,fun(list(X0),X2)),X42 : X2] : list_case(X2,X0,X42,X41,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X33),X32)) = aa(list(X0),X2,aa(X0,fun(list(X0),X2),X41,X33),X32)),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_list_Osimps_I5_J)).
% 0.16/0.51 tff(f1417,plain,(
% 0.16/0.51 spl32_105),
% 0.16/0.51 inference(avatar_split_clause,[],[f503,f1415])).
% 0.16/0.51 tff(f1415,plain,(
% 0.16/0.51 spl32_105 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK26(X2,X0,X1,X3,X4)) = X3 | nil(X2) = X3 | ~sP3(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_105])])).
% 0.16/0.51 tff(f503,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK26(X2,X0,X1,X3,X4)) = X3 | nil(X2) = X3 | ~sP3(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f338])).
% 0.16/0.51 tff(f1413,plain,(
% 0.16/0.51 spl32_104),
% 0.16/0.51 inference(avatar_split_clause,[],[f495,f1411])).
% 0.16/0.51 tff(f1411,plain,(
% 0.16/0.51 spl32_104 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2),X3 : list(X2),X1 : list(X2)] : (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK25(X2,X0,X1,X3,X4)) = X3 | nil(X2) = X3 | ~sP2(X2,X0,X1,X3,X4))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_104])])).
% 0.16/0.51 tff(f495,plain,(
% 0.16/0.51 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),sK25(X2,X0,X1,X3,X4)) = X3 | nil(X2) = X3 | ~sP2(X2,X0,X1,X3,X4)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f332])).
% 0.16/0.51 tff(f1409,plain,(
% 0.16/0.51 spl32_103),
% 0.16/0.51 inference(avatar_split_clause,[],[f489,f1407])).
% 0.16/0.51 tff(f1407,plain,(
% 0.16/0.51 spl32_103 <=> ! [X2 : list(type),X4 : fun(nat,type),X0 : list(dB),X3 : dB,X1 : type] : (pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,X0)),X1)) | ~pp(aa(list(type),bool,typings(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,X2,X1))))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_103])])).
% 0.16/0.51 tff(f489,plain,(
% 0.16/0.51 ( ! [X2 : list(type),X3 : dB,X0 : list(dB),X1 : type,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,X0)),X1)) | ~pp(aa(list(type),bool,typings(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,X2,X1)))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f235])).
% 0.16/0.51 tff(f235,plain,(
% 0.16/0.51 ! [X0 : list(dB),X1 : type,X2 : list(type),X3 : dB,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,X0)),X1)) | ~pp(aa(list(type),bool,typings(X4,X0),X2)) | ~pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,X2,X1))))),
% 0.16/0.51 inference(flattening,[],[f234])).
% 0.16/0.51 tff(f234,plain,(
% 0.16/0.51 ! [X0 : list(dB),X1 : type,X2 : list(type),X3 : dB,X4 : fun(nat,type)] : ((pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,X0)),X1)) | ~pp(aa(list(type),bool,typings(X4,X0),X2))) | ~pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,X2,X1))))),
% 0.16/0.51 inference(ennf_transformation,[],[f187])).
% 0.16/0.51 tff(f187,plain,(
% 0.16/0.51 ! [X0 : list(dB),X1 : type,X2 : list(type),X3 : dB,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,X2,X1))) => (pp(aa(list(type),bool,typings(X4,X0),X2)) => pp(aa(type,bool,typing(X4,foldl(dB,dB,app,X3,X0)),X1))))),
% 0.16/0.51 inference(rectify,[],[f91])).
% 0.16/0.51 tff(f91,axiom,(
% 0.16/0.51 ! [X14 : list(dB),X8 : type,X87 : list(type),X37 : dB,X12 : fun(nat,type)] : (pp(aa(type,bool,typing(X12,X37),foldr(type,type,fun1,X87,X8))) => (pp(aa(list(type),bool,typings(X12,X14),X87)) => pp(aa(type,bool,typing(X12,foldl(dB,dB,app,X37,X14)),X8))))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_list__app__typeI)).
% 0.16/0.51 tff(f1353,plain,(
% 0.16/0.51 spl32_102),
% 0.16/0.51 inference(avatar_split_clause,[],[f529,f1351])).
% 0.16/0.51 tff(f1351,plain,(
% 0.16/0.51 spl32_102 <=> ! [X1 : $tType,X0 : $tType,X3 : list(X1),X4 : X0,X5 : fun(X0,fun(X1,X0)),X2 : list(X1)] : foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(list(X1),fun(list(X1),list(X1)),append(X1),X3),X2)) = foldl(X0,X1,X5,foldl(X0,X1,X5,X4,X3),X2)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_102])])).
% 0.16/0.51 tff(f529,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : list(X1),X4 : X0,X5 : fun(X0,fun(X1,X0))] : (foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(list(X1),fun(list(X1),list(X1)),append(X1),X3),X2)) = foldl(X0,X1,X5,foldl(X0,X1,X5,X4,X3),X2)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f200])).
% 0.16/0.51 tff(f200,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : $tType,X2 : list(X1),X3 : list(X1),X4 : X0,X5 : fun(X0,fun(X1,X0))] : foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(list(X1),fun(list(X1),list(X1)),append(X1),X3),X2)) = foldl(X0,X1,X5,foldl(X0,X1,X5,X4,X3),X2)),
% 0.16/0.51 inference(rectify,[],[f63])).
% 0.16/0.51 tff(f63,axiom,(
% 0.16/0.51 ! [X2 : $tType,X0 : $tType,X77 : list(X0),X34 : list(X0),X33 : X2,X35 : fun(X2,fun(X0,X2))] : foldl(X2,X0,X35,X33,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X34),X77)) = foldl(X2,X0,X35,foldl(X2,X0,X35,X33,X34),X77)),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_foldl__append)).
% 0.16/0.51 tff(f1349,plain,(
% 0.16/0.51 spl32_101),
% 0.16/0.51 inference(avatar_split_clause,[],[f528,f1347])).
% 0.16/0.51 tff(f1347,plain,(
% 0.16/0.51 spl32_101 <=> ! [X1 : $tType,X0 : $tType,X3 : list(X0),X4 : list(X0),X5 : fun(X0,fun(X1,X1)),X2 : X1] : foldr(X0,X1,X5,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3),X2) = foldr(X0,X1,X5,X4,foldr(X0,X1,X5,X3,X2))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_101])])).
% 0.16/0.51 tff(f528,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : list(X0),X4 : list(X0),X5 : fun(X0,fun(X1,X1))] : (foldr(X0,X1,X5,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3),X2) = foldr(X0,X1,X5,X4,foldr(X0,X1,X5,X3,X2))) )),
% 0.16/0.51 inference(cnf_transformation,[],[f199])).
% 0.16/0.51 tff(f199,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : list(X0),X4 : list(X0),X5 : fun(X0,fun(X1,X1))] : foldr(X0,X1,X5,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X4),X3),X2) = foldr(X0,X1,X5,X4,foldr(X0,X1,X5,X3,X2))),
% 0.16/0.51 inference(rectify,[],[f93])).
% 0.16/0.51 tff(f93,axiom,(
% 0.16/0.51 ! [X0 : $tType,X2 : $tType,X33 : X2,X77 : list(X0),X34 : list(X0),X35 : fun(X0,fun(X2,X2))] : foldr(X0,X2,X35,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X34),X77),X33) = foldr(X0,X2,X35,X34,foldr(X0,X2,X35,X77,X33))),
% 0.16/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_foldr__append)).
% 0.16/0.51 tff(f1345,plain,(
% 0.16/0.51 spl32_100),
% 0.16/0.51 inference(avatar_split_clause,[],[f407,f1343])).
% 0.16/0.51 tff(f1343,plain,(
% 0.16/0.51 spl32_100 <=> ! [X1 : $tType,X2 : list(X1),X0 : fun(X1,bool)] : (aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK15(X1,X0,X2)),sK16(X1,X0,X2)) = X2 | nil(X1) = X2 | ~sP0(X1,X0,X2))),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_100])])).
% 0.16/0.51 tff(f407,plain,(
% 0.16/0.51 ( ! [X1 : $tType,X2 : list(X1),X0 : fun(X1,bool)] : (aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK15(X1,X0,X2)),sK16(X1,X0,X2)) = X2 | nil(X1) = X2 | ~sP0(X1,X0,X2)) )),
% 0.16/0.51 inference(cnf_transformation,[],[f282])).
% 0.16/0.51 tff(f282,plain,(
% 0.16/0.51 ! [X0 : fun(X1,bool),X1 : $tType,X2 : list(X1)] : ((sP0(X1,X0,X2) | (! [X3 : X1,X4 : list(X1)] : (~listsp(X1,X0,X4) | ~pp(aa(X1,bool,X0,X3)) | aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X4) != X2) & nil(X1) != X2)) & ((listsp(X1,X0,sK16(X1,X0,X2)) & pp(aa(X1,bool,X0,sK15(X1,X0,X2))) & aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK15(X1,X0,X2)),sK16(X1,X0,X2)) = X2) | nil(X1) = X2 | ~sP0(X1,X0,X2)))),
% 0.16/0.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f280,f281])).
% 0.16/0.51 tff(f281,plain,(
% 0.16/0.51 ! [X1 : $tType,X0 : fun(X1,bool),X2 : list(X1)] : (? [X5 : X1,X6 : list(X1)] : (listsp(X1,X0,X6) & pp(aa(X1,bool,X0,X5)) & aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X5),X6) = X2) => (listsp(X1,X0,sK16(X1,X0,X2)) & pp(aa(X1,bool,X0,sK15(X1,X0,X2))) & aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK15(X1,X0,X2)),sK16(X1,X0,X2)) = X2))),
% 0.16/0.51 introduced(choice_axiom,[])).
% 0.16/0.51 tff(f280,plain,(
% 0.16/0.51 ! [X0 : fun(X1,bool),X1 : $tType,X2 : list(X1)] : ((sP0(X1,X0,X2) | (! [X3 : X1,X4 : list(X1)] : (~listsp(X1,X0,X4) | ~pp(aa(X1,bool,X0,X3)) | aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X4) != X2) & nil(X1) != X2)) & (? [X5 : X1,X6 : list(X1)] : (listsp(X1,X0,X6) & pp(aa(X1,bool,X0,X5)) & aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X5),X6) = X2) | nil(X1) = X2 | ~sP0(X1,X0,X2)))),
% 0.16/0.51 inference(rectify,[],[f279])).
% 0.16/0.51 tff(f279,plain,(
% 0.16/0.51 ! [X2 : fun(X0,bool),X0 : $tType,X1 : list(X0)] : ((sP0(X0,X2,X1) | (! [X3 : X0,X4 : list(X0)] : (~listsp(X0,X2,X4) | ~pp(aa(X0,bool,X2,X3)) | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1) & nil(X0) != X1)) & (? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) = X1) | nil(X0) = X1 | ~sP0(X0,X2,X1)))),
% 0.16/0.51 inference(flattening,[],[f278])).
% 0.16/0.51 tff(f278,plain,(
% 0.16/0.51 ! [X2 : fun(X0,bool),X0 : $tType,X1 : list(X0)] : ((sP0(X0,X2,X1) | (! [X3 : X0,X4 : list(X0)] : (~listsp(X0,X2,X4) | ~pp(aa(X0,bool,X2,X3)) | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1) & nil(X0) != X1)) & ((? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) = X1) | nil(X0) = X1) | ~sP0(X0,X2,X1)))),
% 0.16/0.51 inference(nnf_transformation,[],[f253])).
% 0.16/0.51 tff(f253,plain,(
% 0.16/0.51 ! [X2 : fun(X0,bool),X0 : $tType,X1 : list(X0)] : (sP0(X0,X2,X1) <=> (? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) = X1) | nil(X0) = X1))),
% 0.16/0.51 introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])).
% 0.16/0.51 tff(f1323,plain,(
% 0.16/0.51 spl32_99),
% 0.16/0.51 inference(avatar_split_clause,[],[f607,f1321])).
% 0.16/0.51 tff(f1321,plain,(
% 0.16/0.51 spl32_99 <=> ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK9(X0,X1)),insert(X0,sK10(X0,X1),nil(X0))) = X1 | nil(X0) = X1)),
% 0.16/0.51 introduced(avatar_definition,[new_symbols(naming,[spl32_99])])).
% 0.16/0.51 tff(f607,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK9(X0,X1)),insert(X0,sK10(X0,X1),nil(X0))) = X1 | nil(X0) = X1) )),
% 0.16/0.51 inference(forward_demodulation,[],[f382,f374])).
% 0.16/0.51 tff(f382,plain,(
% 0.16/0.51 ( ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK9(X0,X1)),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK10(X0,X1)),nil(X0))) = X1 | nil(X0) = X1) )),
% 0.16/0.51 inference(cnf_transformation,[],[f268])).
% 0.16/0.51 tff(f268,plain,(
% 0.16/0.51 ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK9(X0,X1)),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK10(X0,X1)),nil(X0))) = X1 | nil(X0) = X1)),
% 0.16/0.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f215,f267])).
% 0.16/0.51 tff(f267,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (? [X2 : list(X0),X3 : X0] : aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) = X1 => aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK9(X0,X1)),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK10(X0,X1)),nil(X0))) = X1)),
% 0.16/0.52 introduced(choice_axiom,[])).
% 0.16/0.52 tff(f215,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (? [X2 : list(X0),X3 : X0] : aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) = X1 | nil(X0) = X1)),
% 0.16/0.52 inference(ennf_transformation,[],[f130])).
% 0.16/0.52 tff(f130,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (nil(X0) != X1 => ~! [X2 : list(X0),X3 : X0] : aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) != X1)),
% 0.16/0.52 inference(rectify,[],[f80])).
% 0.16/0.52 tff(f80,axiom,(
% 0.16/0.52 ! [X2 : $tType,X58 : list(X2)] : (nil(X2) != X58 => ~! [X86 : list(X2),X69 : X2] : aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X86),aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X69),nil(X2))) != X58)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rev__exhaust2)).
% 0.16/0.52 tff(f1319,plain,(
% 0.16/0.52 spl32_98),
% 0.16/0.52 inference(avatar_split_clause,[],[f606,f1317])).
% 0.16/0.52 tff(f1317,plain,(
% 0.16/0.52 spl32_98 <=> ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK7(X0,X1)),insert(X0,sK8(X0,X1),nil(X0))) = X1 | nil(X0) = X1)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_98])])).
% 0.16/0.52 tff(f606,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK7(X0,X1)),insert(X0,sK8(X0,X1),nil(X0))) = X1 | nil(X0) = X1) )),
% 0.16/0.52 inference(forward_demodulation,[],[f381,f374])).
% 0.16/0.52 tff(f381,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK7(X0,X1)),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK8(X0,X1)),nil(X0))) = X1 | nil(X0) = X1) )),
% 0.16/0.52 inference(cnf_transformation,[],[f266])).
% 0.16/0.52 tff(f266,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK7(X0,X1)),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK8(X0,X1)),nil(X0))) = X1 | nil(X0) = X1)),
% 0.16/0.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f214,f265])).
% 0.16/0.52 tff(f265,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (? [X2 : list(X0),X3 : X0] : aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) = X1 => aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),sK7(X0,X1)),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK8(X0,X1)),nil(X0))) = X1)),
% 0.16/0.52 introduced(choice_axiom,[])).
% 0.16/0.52 tff(f214,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (? [X2 : list(X0),X3 : X0] : aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) = X1 | nil(X0) = X1)),
% 0.16/0.52 inference(ennf_transformation,[],[f129])).
% 0.16/0.52 tff(f129,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (nil(X0) != X1 => ~! [X2 : list(X0),X3 : X0] : aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),nil(X0))) != X1)),
% 0.16/0.52 inference(rectify,[],[f79])).
% 0.16/0.52 tff(f79,axiom,(
% 0.16/0.52 ! [X2 : $tType,X58 : list(X2)] : (nil(X2) != X58 => ~! [X86 : list(X2),X69 : X2] : aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X86),aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X69),nil(X2))) != X58)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_rev__cases)).
% 0.16/0.52 tff(f1295,plain,(
% 0.16/0.52 spl32_97),
% 0.16/0.52 inference(avatar_split_clause,[],[f445,f1293])).
% 0.16/0.52 tff(f1293,plain,(
% 0.16/0.52 spl32_97 <=> ! [X0 : type,X3 : fun(nat,type),X2 : nat,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_97])])).
% 0.16/0.52 tff(f445,plain,(
% 0.16/0.52 ( ! [X2 : nat,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f300])).
% 0.16/0.52 tff(f300,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : nat,X3 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 0.16/0.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f225,f299])).
% 0.16/0.52 tff(f299,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : nat,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,X4,X0)))) => (pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0)))))),
% 0.16/0.52 introduced(choice_axiom,[])).
% 0.16/0.52 tff(f225,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : nat,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,X4,X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 0.16/0.52 inference(ennf_transformation,[],[f168])).
% 0.16/0.52 tff(f168,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : nat,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)) => ~! [X4 : list(type)] : (pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,X4,X0))) => ~pp(aa(list(type),bool,typings(X3,X1),X4))))),
% 0.16/0.52 inference(rectify,[],[f96])).
% 0.16/0.52 tff(f96,axiom,(
% 0.16/0.52 ! [X8 : type,X14 : list(dB),X11 : nat,X12 : fun(nat,type)] : (pp(aa(type,bool,typing(X12,foldl(dB,dB,app,var(X11),X14)),X8)) => ~! [X91 : list(type)] : (pp(aa(type,bool,typing(X12,var(X11)),foldr(type,type,fun1,X91,X8))) => ~pp(aa(list(type),bool,typings(X12,X14),X91))))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_var__app__typesE)).
% 0.16/0.52 tff(f1291,plain,(
% 0.16/0.52 spl32_96),
% 0.16/0.52 inference(avatar_split_clause,[],[f436,f1289])).
% 0.16/0.52 tff(f1289,plain,(
% 0.16/0.52 spl32_96 <=> ! [X0 : nat,X3 : dB,X2 : dB,X1 : dB] : subst(aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X3,X1,X0)),subst(X2,X1,X0))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_96])])).
% 0.16/0.52 tff(f436,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : dB,X0 : nat,X1 : dB] : (subst(aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X3,X1,X0)),subst(X2,X1,X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f162])).
% 0.16/0.52 tff(f162,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : dB,X2 : dB,X3 : dB] : subst(aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X3,X1,X0)),subst(X2,X1,X0))),
% 0.16/0.52 inference(rectify,[],[f33])).
% 0.16/0.52 tff(f33,axiom,(
% 0.16/0.52 ! [X50 : nat,X51 : dB,X52 : dB,X28 : dB] : subst(aa(dB,dB,aa(dB,fun(dB,dB),app,X28),X52),X51,X50) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X28,X51,X50)),subst(X52,X51,X50))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_subst__App)).
% 0.16/0.52 tff(f1273,plain,(
% 0.16/0.52 spl32_95),
% 0.16/0.52 inference(avatar_split_clause,[],[f605,f1271])).
% 0.16/0.52 tff(f1271,plain,(
% 0.16/0.52 spl32_95 <=> ! [X3 : fun(nat,type),X4 : type,X0 : nat,X5 : dB,X2 : dB,X1 : type] : (pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)) | ~pp(aa(type,bool,typing(X3,X2),X1)) | ~pp(aa(type,bool,typing(shift(type,X3,X0,X1),X5),X4)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_95])])).
% 0.16/0.52 tff(f605,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : fun(nat,type),X0 : nat,X1 : type,X4 : type,X5 : dB] : (pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)) | ~pp(aa(type,bool,typing(X3,X2),X1)) | ~pp(aa(type,bool,typing(shift(type,X3,X0,X1),X5),X4))) )),
% 0.16/0.52 inference(equality_resolution,[],[f537])).
% 0.16/0.52 tff(f537,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : fun(nat,type),X0 : nat,X1 : type,X6 : fun(nat,type),X4 : type,X5 : dB] : (pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)) | shift(type,X3,X0,X1) != X6 | ~pp(aa(type,bool,typing(X3,X2),X1)) | ~pp(aa(type,bool,typing(X6,X5),X4))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f246])).
% 0.16/0.52 tff(f246,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : type,X2 : dB,X3 : fun(nat,type),X4 : type,X5 : dB,X6 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)) | shift(type,X3,X0,X1) != X6 | ~pp(aa(type,bool,typing(X3,X2),X1)) | ~pp(aa(type,bool,typing(X6,X5),X4)))),
% 0.16/0.52 inference(flattening,[],[f245])).
% 0.16/0.52 tff(f245,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : type,X2 : dB,X3 : fun(nat,type),X4 : type,X5 : dB,X6 : fun(nat,type)] : (((pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)) | shift(type,X3,X0,X1) != X6) | ~pp(aa(type,bool,typing(X3,X2),X1))) | ~pp(aa(type,bool,typing(X6,X5),X4)))),
% 0.16/0.52 inference(ennf_transformation,[],[f208])).
% 0.16/0.52 tff(f208,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : type,X2 : dB,X3 : fun(nat,type),X4 : type,X5 : dB,X6 : fun(nat,type)] : (pp(aa(type,bool,typing(X6,X5),X4)) => (pp(aa(type,bool,typing(X3,X2),X1)) => (shift(type,X3,X0,X1) = X6 => pp(aa(type,bool,typing(X3,subst(X5,X2,X0)),X4)))))),
% 0.16/0.52 inference(rectify,[],[f39])).
% 0.16/0.52 tff(f39,axiom,(
% 0.16/0.52 ! [X11 : nat,X16 : type,X36 : dB,X57 : fun(nat,type),X8 : type,X37 : dB,X12 : fun(nat,type)] : (pp(aa(type,bool,typing(X12,X37),X8)) => (pp(aa(type,bool,typing(X57,X36),X16)) => (shift(type,X57,X11,X16) = X12 => pp(aa(type,bool,typing(X57,subst(X37,X36,X11)),X8)))))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_subst__lemma)).
% 0.16/0.52 tff(f1269,plain,(
% 0.16/0.52 spl32_94),
% 0.16/0.52 inference(avatar_split_clause,[],[f490,f1267])).
% 0.16/0.52 tff(f1267,plain,(
% 0.16/0.52 spl32_94 <=> ! [X4 : fun(nat,type),X0 : type,X3 : nat,X2 : list(dB),X1 : type] : (X0 = X1 | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X0)) | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X1)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_94])])).
% 0.16/0.52 tff(f490,plain,(
% 0.16/0.52 ( ! [X2 : list(dB),X3 : nat,X0 : type,X1 : type,X4 : fun(nat,type)] : (X0 = X1 | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X0)) | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X1))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f237])).
% 0.16/0.52 tff(f237,plain,(
% 0.16/0.52 ! [X0 : type,X1 : type,X2 : list(dB),X3 : nat,X4 : fun(nat,type)] : (X0 = X1 | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X0)) | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X1)))),
% 0.16/0.52 inference(flattening,[],[f236])).
% 0.16/0.52 tff(f236,plain,(
% 0.16/0.52 ! [X0 : type,X1 : type,X2 : list(dB),X3 : nat,X4 : fun(nat,type)] : ((X0 = X1 | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X0))) | ~pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X1)))),
% 0.16/0.52 inference(ennf_transformation,[],[f188])).
% 0.16/0.52 tff(f188,plain,(
% 0.16/0.52 ! [X0 : type,X1 : type,X2 : list(dB),X3 : nat,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X1)) => (pp(aa(type,bool,typing(X4,foldl(dB,dB,app,var(X3),X2)),X0)) => X0 = X1))),
% 0.16/0.52 inference(rectify,[],[f10])).
% 0.16/0.52 tff(f10,axiom,(
% 0.16/0.52 ! [X16 : type,X8 : type,X14 : list(dB),X11 : nat,X12 : fun(nat,type)] : (pp(aa(type,bool,typing(X12,foldl(dB,dB,app,var(X11),X14)),X8)) => (pp(aa(type,bool,typing(X12,foldl(dB,dB,app,var(X11),X14)),X16)) => X8 = X16))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_var__app__type__eq)).
% 0.16/0.52 tff(f1248,plain,(
% 0.16/0.52 spl32_93),
% 0.16/0.52 inference(avatar_split_clause,[],[f448,f1246])).
% 0.16/0.52 tff(f1246,plain,(
% 0.16/0.52 spl32_93 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : dB] : (pp(aa(type,bool,typing(X3,X1),sK20(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_93])])).
% 0.16/0.52 tff(f448,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X1),sK20(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f302])).
% 0.16/0.52 tff(f1244,plain,(
% 0.16/0.52 spl32_92),
% 0.16/0.52 inference(avatar_split_clause,[],[f443,f1242])).
% 0.16/0.52 tff(f1242,plain,(
% 0.16/0.52 spl32_92 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK18(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_92])])).
% 0.16/0.52 tff(f443,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK18(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f298])).
% 0.16/0.52 tff(f298,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X3,X1),sK18(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK18(X0,X1,X2,X3),X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 0.16/0.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f224,f297])).
% 0.16/0.52 tff(f297,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0)))) => (pp(aa(list(type),bool,typings(X3,X1),sK18(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK18(X0,X1,X2,X3),X0)))))),
% 0.16/0.52 introduced(choice_axiom,[])).
% 0.16/0.52 tff(f224,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 0.16/0.52 inference(ennf_transformation,[],[f167])).
% 0.16/0.52 tff(f167,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)) => ? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0)))))),
% 0.16/0.52 inference(rectify,[],[f98])).
% 0.16/0.52 tff(f98,axiom,(
% 0.16/0.52 ! [X8 : type,X14 : list(dB),X37 : dB,X12 : fun(nat,type)] : (pp(aa(type,bool,typing(X12,foldl(dB,dB,app,X37,X14)),X8)) => ? [X91 : list(type)] : (pp(aa(list(type),bool,typings(X12,X14),X91)) & pp(aa(type,bool,typing(X12,X37),foldr(type,type,fun1,X91,X8)))))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_list__app__typeD)).
% 0.16/0.52 tff(f1240,plain,(
% 0.16/0.52 spl32_91),
% 0.16/0.52 inference(avatar_split_clause,[],[f441,f1238])).
% 0.16/0.52 tff(f1238,plain,(
% 0.16/0.52 spl32_91 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK17(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_91])])).
% 0.16/0.52 tff(f441,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK17(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f296])).
% 0.16/0.52 tff(f296,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK17(X0,X1,X2,X3),X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 0.16/0.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f223,f295])).
% 0.16/0.52 tff(f295,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0)))) => (pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK17(X0,X1,X2,X3),X0)))))),
% 0.16/0.52 introduced(choice_axiom,[])).
% 0.16/0.52 tff(f223,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (? [X4 : list(type)] : (pp(aa(list(type),bool,typings(X3,X1),X4)) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 0.16/0.52 inference(ennf_transformation,[],[f166])).
% 0.16/0.52 tff(f166,plain,(
% 0.16/0.52 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)) => ~! [X4 : list(type)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,X4,X0))) => ~pp(aa(list(type),bool,typings(X3,X1),X4))))),
% 0.16/0.52 inference(rectify,[],[f97])).
% 0.16/0.52 tff(f97,axiom,(
% 0.16/0.52 ! [X8 : type,X14 : list(dB),X37 : dB,X12 : fun(nat,type)] : (pp(aa(type,bool,typing(X12,foldl(dB,dB,app,X37,X14)),X8)) => ~! [X91 : list(type)] : (pp(aa(type,bool,typing(X12,X37),foldr(type,type,fun1,X91,X8))) => ~pp(aa(list(type),bool,typings(X12,X14),X91))))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_list__app__typeE)).
% 0.16/0.52 tff(f1230,plain,(
% 0.16/0.52 spl32_90),
% 0.16/0.52 inference(avatar_split_clause,[],[f555,f1228])).
% 0.16/0.52 tff(f1228,plain,(
% 0.16/0.52 spl32_90 <=> ! [X1 : $tType,X4 : list(X1),X0 : fun(X1,bool),X3 : X1] : (sP0(X1,X0,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X4)) | ~listsp(X1,X0,X4) | ~pp(aa(X1,bool,X0,X3)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_90])])).
% 0.16/0.52 tff(f555,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X3 : X1,X0 : fun(X1,bool),X4 : list(X1)] : (sP0(X1,X0,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X4)) | ~listsp(X1,X0,X4) | ~pp(aa(X1,bool,X0,X3))) )),
% 0.16/0.52 inference(equality_resolution,[],[f411])).
% 0.16/0.52 tff(f411,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X2 : list(X1),X3 : X1,X0 : fun(X1,bool),X4 : list(X1)] : (sP0(X1,X0,X2) | ~listsp(X1,X0,X4) | ~pp(aa(X1,bool,X0,X3)) | aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X4) != X2) )),
% 0.16/0.52 inference(cnf_transformation,[],[f282])).
% 0.16/0.52 tff(f1192,plain,(
% 0.16/0.52 spl32_89),
% 0.16/0.52 inference(avatar_split_clause,[],[f527,f1190])).
% 0.16/0.52 tff(f1190,plain,(
% 0.16/0.52 spl32_89 <=> ! [X0 : $tType,X5 : fun(nat,X0),X4 : fun(dB,fun(dB,X0)),X3 : fun(dB,X0),X2 : dB,X1 : dB] : dB_case(X0,X5,X4,X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) = aa(dB,X0,aa(dB,fun(dB,X0),X4,X2),X1)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_89])])).
% 0.16/0.52 tff(f527,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : dB,X3 : fun(dB,X0),X1 : dB,X4 : fun(dB,fun(dB,X0)),X5 : fun(nat,X0)] : (dB_case(X0,X5,X4,X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) = aa(dB,X0,aa(dB,fun(dB,X0),X4,X2),X1)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f198])).
% 0.16/0.52 tff(f198,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : dB,X2 : dB,X3 : fun(dB,X0),X4 : fun(dB,fun(dB,X0)),X5 : fun(nat,X0)] : dB_case(X0,X5,X4,X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) = aa(dB,X0,aa(dB,fun(dB,X0),X4,X2),X1)),
% 0.16/0.52 inference(rectify,[],[f42])).
% 0.16/0.52 tff(f42,axiom,(
% 0.16/0.52 ! [X2 : $tType,X21 : dB,X22 : dB,X40 : fun(dB,X2),X41 : fun(dB,fun(dB,X2)),X42 : fun(nat,X2)] : dB_case(X2,X42,X41,X40,aa(dB,dB,aa(dB,fun(dB,dB),app,X22),X21)) = aa(dB,X2,aa(dB,fun(dB,X2),X41,X22),X21)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_dB_Osimps_I11_J)).
% 0.16/0.52 tff(f1188,plain,(
% 0.16/0.52 spl32_88),
% 0.16/0.52 inference(avatar_split_clause,[],[f467,f1186])).
% 0.16/0.52 tff(f1186,plain,(
% 0.16/0.52 spl32_88 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : list(X0),X1 : list(X0)] : (listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) | ~listsp(X0,X3,X1) | ~listsp(X0,X3,X2))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_88])])).
% 0.16/0.52 tff(f467,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : list(X0),X3 : fun(X0,bool),X1 : list(X0)] : (listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) | ~listsp(X0,X3,X1) | ~listsp(X0,X3,X2)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f316])).
% 0.16/0.52 tff(f316,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : fun(X0,bool)] : ((listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) | ~listsp(X0,X3,X1) | ~listsp(X0,X3,X2)) & ((listsp(X0,X3,X1) & listsp(X0,X3,X2)) | ~listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))))),
% 0.16/0.52 inference(flattening,[],[f315])).
% 0.16/0.52 tff(f315,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : fun(X0,bool)] : ((listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) | (~listsp(X0,X3,X1) | ~listsp(X0,X3,X2))) & ((listsp(X0,X3,X1) & listsp(X0,X3,X2)) | ~listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))))),
% 0.16/0.52 inference(nnf_transformation,[],[f174])).
% 0.16/0.52 tff(f174,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : fun(X0,bool)] : (listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) <=> (listsp(X0,X3,X1) & listsp(X0,X3,X2)))),
% 0.16/0.52 inference(rectify,[],[f64])).
% 0.16/0.52 tff(f64,axiom,(
% 0.16/0.52 ! [X2 : $tType,X77 : list(X2),X34 : list(X2),X48 : fun(X2,bool)] : (listsp(X2,X48,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X34),X77)) <=> (listsp(X2,X48,X77) & listsp(X2,X48,X34)))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_append__in__listsp__conv)).
% 0.16/0.52 tff(f1184,plain,(
% 0.16/0.52 spl32_87),
% 0.16/0.52 inference(avatar_split_clause,[],[f384,f1182])).
% 0.16/0.52 tff(f1182,plain,(
% 0.16/0.52 spl32_87 <=> ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK11(X0,X1)),sK12(X0,X1)) = X1 | nil(X0) = X1)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_87])])).
% 0.16/0.52 tff(f384,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK11(X0,X1)),sK12(X0,X1)) = X1 | nil(X0) = X1) )),
% 0.16/0.52 inference(cnf_transformation,[],[f272])).
% 0.16/0.52 tff(f272,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : ((nil(X0) != X1 | ! [X2 : X0,X3 : list(X0)] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1) & (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK11(X0,X1)),sK12(X0,X1)) = X1 | nil(X0) = X1))),
% 0.16/0.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f270,f271])).
% 0.16/0.52 tff(f271,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (? [X4 : X0,X5 : list(X0)] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) = X1 => aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK11(X0,X1)),sK12(X0,X1)) = X1)),
% 0.16/0.52 introduced(choice_axiom,[])).
% 0.16/0.52 tff(f270,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : ((nil(X0) != X1 | ! [X2 : X0,X3 : list(X0)] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1) & (? [X4 : X0,X5 : list(X0)] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X5) = X1 | nil(X0) = X1))),
% 0.16/0.52 inference(rectify,[],[f269])).
% 0.16/0.52 tff(f269,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : ((nil(X0) != X1 | ! [X2 : X0,X3 : list(X0)] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1) & (? [X2 : X0,X3 : list(X0)] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) = X1 | nil(X0) = X1))),
% 0.16/0.52 inference(nnf_transformation,[],[f132])).
% 0.16/0.52 tff(f132,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (nil(X0) != X1 <=> ? [X2 : X0,X3 : list(X0)] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) = X1)),
% 0.16/0.52 inference(rectify,[],[f45])).
% 0.16/0.52 tff(f45,axiom,(
% 0.16/0.52 ! [X2 : $tType,X34 : list(X2)] : (nil(X2) != X34 <=> ? [X63 : X2,X64 : list(X2)] : aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X63),X64) = X34)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_neq__Nil__conv)).
% 0.16/0.52 tff(f1180,plain,(
% 0.16/0.52 spl32_86),
% 0.16/0.52 inference(avatar_split_clause,[],[f380,f1178])).
% 0.16/0.52 tff(f1178,plain,(
% 0.16/0.52 spl32_86 <=> ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK5(X0,X1)),sK6(X0,X1)) = X1 | nil(X0) = X1)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_86])])).
% 0.16/0.52 tff(f380,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK5(X0,X1)),sK6(X0,X1)) = X1 | nil(X0) = X1) )),
% 0.16/0.52 inference(cnf_transformation,[],[f264])).
% 0.16/0.52 tff(f264,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK5(X0,X1)),sK6(X0,X1)) = X1 | nil(X0) = X1)),
% 0.16/0.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f213,f263])).
% 0.16/0.52 tff(f263,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (? [X2 : X0,X3 : list(X0)] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) = X1 => aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK5(X0,X1)),sK6(X0,X1)) = X1)),
% 0.16/0.52 introduced(choice_axiom,[])).
% 0.16/0.52 tff(f213,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (? [X2 : X0,X3 : list(X0)] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) = X1 | nil(X0) = X1)),
% 0.16/0.52 inference(ennf_transformation,[],[f128])).
% 0.16/0.52 tff(f128,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : (nil(X0) != X1 => ~! [X2 : X0,X3 : list(X0)] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1)),
% 0.16/0.52 inference(rectify,[],[f46])).
% 0.16/0.52 tff(f46,axiom,(
% 0.16/0.52 ! [X2 : $tType,X65 : list(X2)] : (nil(X2) != X65 => ~! [X66 : X2,X67 : list(X2)] : aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X66),X67) != X65)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_list_Oexhaust)).
% 0.16/0.52 tff(f1143,plain,(
% 0.16/0.52 spl32_85),
% 0.16/0.52 inference(avatar_split_clause,[],[f526,f1141])).
% 0.16/0.52 tff(f1141,plain,(
% 0.16/0.52 spl32_85 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : aa(X0,X1,aa(X2,fun(X0,X1),combc(X0,X2,X1,X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_85])])).
% 0.16/0.52 tff(f526,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : (aa(X0,X1,aa(X2,fun(X0,X1),combc(X0,X2,X1,X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f197])).
% 0.16/0.52 tff(f197,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun(X0,fun(X2,X1))] : aa(X0,X1,aa(X2,fun(X0,X1),combc(X0,X2,X1,X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4)),
% 0.16/0.52 inference(rectify,[],[f104])).
% 0.16/0.52 tff(f104,axiom,(
% 0.16/0.52 ! [X2 : $tType,X1 : $tType,X0 : $tType,X92 : X2,X93 : X0,X94 : fun(X2,fun(X0,X1))] : aa(X2,X1,aa(X0,fun(X2,X1),combc(X2,X0,X1,X94),X93),X92) = aa(X0,X1,aa(X2,fun(X0,X1),X94,X92),X93)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U)).
% 0.16/0.52 tff(f1139,plain,(
% 0.16/0.52 spl32_84),
% 0.16/0.52 inference(avatar_split_clause,[],[f484,f1137])).
% 0.16/0.52 tff(f1137,plain,(
% 0.16/0.52 spl32_84 <=> ! [X0 : $tType,X4 : fun(nat,X0),X3 : fun(type,fun(type,X0)),X2 : type,X1 : type] : type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_84])])).
% 0.16/0.52 tff(f484,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : type,X3 : fun(type,fun(type,X0)),X1 : type,X4 : fun(nat,X0)] : (type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f182])).
% 0.16/0.52 tff(f182,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : type,X2 : type,X3 : fun(type,fun(type,X0)),X4 : fun(nat,X0)] : type_case(X0,X4,X3,aa(type,type,aa(type,fun(type,type),fun1,X2),X1)) = aa(type,X0,aa(type,fun(type,X0),X3,X2),X1)),
% 0.16/0.52 inference(rectify,[],[f48])).
% 0.16/0.52 tff(f48,axiom,(
% 0.16/0.52 ! [X2 : $tType,X45 : type,X46 : type,X41 : fun(type,fun(type,X2)),X42 : fun(nat,X2)] : type_case(X2,X42,X41,aa(type,type,aa(type,fun(type,type),fun1,X46),X45)) = aa(type,X2,aa(type,fun(type,X2),X41,X46),X45)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_type_Osimps_I6_J)).
% 0.16/0.52 tff(f1135,plain,(
% 0.16/0.52 spl32_83),
% 0.16/0.52 inference(avatar_split_clause,[],[f446,f1133])).
% 0.16/0.52 tff(f1133,plain,(
% 0.16/0.52 spl32_83 <=> ! [X0 : type,X3 : fun(nat,type),X2 : nat,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_83])])).
% 0.16/0.52 tff(f446,plain,(
% 0.16/0.52 ( ! [X2 : nat,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f300])).
% 0.16/0.52 tff(f1094,plain,(
% 0.16/0.52 spl32_82 | ~spl32_50 | ~spl32_60),
% 0.16/0.52 inference(avatar_split_clause,[],[f961,f956,f908,f1091])).
% 0.16/0.52 tff(f1091,plain,(
% 0.16/0.52 spl32_82 <=> sP3(dB,as,rs,nil(dB),a)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_82])])).
% 0.16/0.52 tff(f956,plain,(
% 0.16/0.52 spl32_60 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2)] : sP3(X2,X0,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0),nil(X2),X4)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_60])])).
% 0.16/0.52 tff(f961,plain,(
% 0.16/0.52 sP3(dB,as,rs,nil(dB),a) | (~spl32_50 | ~spl32_60)),
% 0.16/0.52 inference(superposition,[],[f957,f910])).
% 0.16/0.52 tff(f957,plain,(
% 0.16/0.52 ( ! [X2 : $tType,X0 : list(X2),X4 : X2] : (sP3(X2,X0,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0),nil(X2),X4)) ) | ~spl32_60),
% 0.16/0.52 inference(avatar_component_clause,[],[f956])).
% 0.16/0.52 tff(f1071,plain,(
% 0.16/0.52 spl32_81),
% 0.16/0.52 inference(avatar_split_clause,[],[f525,f1069])).
% 0.16/0.52 tff(f1069,plain,(
% 0.16/0.52 spl32_81 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X5 : fun(X2,fun(X1,X0)),X4 : fun(X2,X1),X3 : X2] : aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_81])])).
% 0.16/0.52 tff(f525,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X2,fun(X1,X0))] : (aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f196])).
% 0.16/0.52 tff(f196,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X2,fun(X1,X0))] : aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3))),
% 0.16/0.52 inference(rectify,[],[f105])).
% 0.16/0.52 tff(f105,axiom,(
% 0.16/0.52 ! [X1 : $tType,X0 : $tType,X2 : $tType,X92 : X2,X93 : fun(X2,X0),X94 : fun(X2,fun(X0,X1))] : aa(X2,X1,combs(X2,X0,X1,X94,X93),X92) = aa(X0,X1,aa(X2,fun(X0,X1),X94,X92),aa(X2,X0,X93,X92))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U)).
% 0.16/0.52 tff(f1067,plain,(
% 0.16/0.52 spl32_80),
% 0.16/0.52 inference(avatar_split_clause,[],[f472,f1065])).
% 0.16/0.52 tff(f1065,plain,(
% 0.16/0.52 spl32_80 <=> ! [X2 : dB,X0 : dB,X1 : dB,X3 : dB] : (X0 = X2 | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_80])])).
% 0.16/0.52 tff(f472,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : dB] : (X0 = X2 | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f320])).
% 0.16/0.52 tff(f320,plain,(
% 0.16/0.52 ! [X0 : dB,X1 : dB,X2 : dB,X3 : dB] : ((aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) | X0 != X2 | X1 != X3) & ((X0 = X2 & X1 = X3) | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)))),
% 0.16/0.52 inference(flattening,[],[f319])).
% 0.16/0.52 tff(f319,plain,(
% 0.16/0.52 ! [X0 : dB,X1 : dB,X2 : dB,X3 : dB] : ((aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) | (X0 != X2 | X1 != X3)) & ((X0 = X2 & X1 = X3) | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)))),
% 0.16/0.52 inference(nnf_transformation,[],[f176])).
% 0.16/0.52 tff(f176,plain,(
% 0.16/0.52 ! [X0 : dB,X1 : dB,X2 : dB,X3 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) <=> (X0 = X2 & X1 = X3))),
% 0.16/0.52 inference(rectify,[],[f14])).
% 0.16/0.52 tff(f14,axiom,(
% 0.16/0.52 ! [X19 : dB,X20 : dB,X21 : dB,X22 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X22),X21) = aa(dB,dB,aa(dB,fun(dB,dB),app,X20),X19) <=> (X19 = X21 & X20 = X22))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_dB_Osimps_I2_J)).
% 0.16/0.52 tff(f1063,plain,(
% 0.16/0.52 spl32_79 | ~spl32_50 | ~spl32_59),
% 0.16/0.52 inference(avatar_split_clause,[],[f960,f952,f908,f1060])).
% 0.16/0.52 tff(f1060,plain,(
% 0.16/0.52 spl32_79 <=> sP2(dB,as,rs,nil(dB),a)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_79])])).
% 0.16/0.52 tff(f952,plain,(
% 0.16/0.52 spl32_59 <=> ! [X2 : $tType,X4 : X2,X0 : list(X2)] : sP2(X2,X0,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0),nil(X2),X4)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_59])])).
% 0.16/0.52 tff(f960,plain,(
% 0.16/0.52 sP2(dB,as,rs,nil(dB),a) | (~spl32_50 | ~spl32_59)),
% 0.16/0.52 inference(superposition,[],[f953,f910])).
% 0.16/0.52 tff(f953,plain,(
% 0.16/0.52 ( ! [X2 : $tType,X0 : list(X2),X4 : X2] : (sP2(X2,X0,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0),nil(X2),X4)) ) | ~spl32_59),
% 0.16/0.52 inference(avatar_component_clause,[],[f952])).
% 0.16/0.52 tff(f1058,plain,(
% 0.16/0.52 spl32_78),
% 0.16/0.52 inference(avatar_split_clause,[],[f471,f1056])).
% 0.16/0.52 tff(f1056,plain,(
% 0.16/0.52 spl32_78 <=> ! [X0 : dB,X3 : dB,X2 : dB,X1 : dB] : (X1 = X3 | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_78])])).
% 0.16/0.52 tff(f471,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : dB] : (X1 = X3 | aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f320])).
% 0.16/0.52 tff(f1054,plain,(
% 0.16/0.52 spl32_77),
% 0.16/0.52 inference(avatar_split_clause,[],[f469,f1052])).
% 0.16/0.52 tff(f1052,plain,(
% 0.16/0.52 spl32_77 <=> ! [X2 : type,X0 : type,X1 : type,X3 : type] : (X0 = X2 | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_77])])).
% 0.16/0.52 tff(f469,plain,(
% 0.16/0.52 ( ! [X2 : type,X3 : type,X0 : type,X1 : type] : (X0 = X2 | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f318])).
% 0.16/0.52 tff(f318,plain,(
% 0.16/0.52 ! [X0 : type,X1 : type,X2 : type,X3 : type] : ((aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) | X0 != X2 | X1 != X3) & ((X0 = X2 & X1 = X3) | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0)))),
% 0.16/0.52 inference(flattening,[],[f317])).
% 0.16/0.52 tff(f317,plain,(
% 0.16/0.52 ! [X0 : type,X1 : type,X2 : type,X3 : type] : ((aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) | (X0 != X2 | X1 != X3)) & ((X0 = X2 & X1 = X3) | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0)))),
% 0.16/0.52 inference(nnf_transformation,[],[f175])).
% 0.16/0.52 tff(f175,plain,(
% 0.16/0.52 ! [X0 : type,X1 : type,X2 : type,X3 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) <=> (X0 = X2 & X1 = X3))),
% 0.16/0.52 inference(rectify,[],[f30])).
% 0.16/0.52 tff(f30,axiom,(
% 0.16/0.52 ! [X43 : type,X44 : type,X45 : type,X46 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X46),X45) = aa(type,type,aa(type,fun(type,type),fun1,X44),X43) <=> (X43 = X45 & X44 = X46))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_type_Osimps_I2_J)).
% 0.16/0.52 tff(f1050,plain,(
% 0.16/0.52 spl32_76),
% 0.16/0.52 inference(avatar_split_clause,[],[f468,f1048])).
% 0.16/0.52 tff(f1048,plain,(
% 0.16/0.52 spl32_76 <=> ! [X0 : type,X3 : type,X2 : type,X1 : type] : (X1 = X3 | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_76])])).
% 0.16/0.52 tff(f468,plain,(
% 0.16/0.52 ( ! [X2 : type,X3 : type,X0 : type,X1 : type] : (X1 = X3 | aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f318])).
% 0.16/0.52 tff(f1046,plain,(
% 0.16/0.52 spl32_75),
% 0.16/0.52 inference(avatar_split_clause,[],[f444,f1044])).
% 0.16/0.52 tff(f1044,plain,(
% 0.16/0.52 spl32_75 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK18(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_75])])).
% 0.16/0.52 tff(f444,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK18(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f298])).
% 0.16/0.52 tff(f1042,plain,(
% 0.16/0.52 spl32_74),
% 0.16/0.52 inference(avatar_split_clause,[],[f442,f1040])).
% 0.16/0.52 tff(f1040,plain,(
% 0.16/0.52 spl32_74 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_74])])).
% 0.16/0.52 tff(f442,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK17(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f296])).
% 0.16/0.52 tff(f1038,plain,(
% 0.16/0.52 spl32_73),
% 0.16/0.52 inference(avatar_split_clause,[],[f428,f1036])).
% 0.16/0.52 tff(f1036,plain,(
% 0.16/0.52 spl32_73 <=> ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (nil(X0) = X1 | nil(X0) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_73])])).
% 0.16/0.52 tff(f428,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (nil(X0) = X1 | nil(X0) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f292])).
% 0.16/0.52 tff(f292,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : list(X0)] : ((nil(X0) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) | nil(X0) != X1 | nil(X0) != X2) & ((nil(X0) = X1 & nil(X0) = X2) | nil(X0) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)))),
% 0.16/0.52 inference(flattening,[],[f291])).
% 0.16/0.52 tff(f291,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : list(X0)] : ((nil(X0) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) | (nil(X0) != X1 | nil(X0) != X2)) & ((nil(X0) = X1 & nil(X0) = X2) | nil(X0) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)))),
% 0.16/0.52 inference(nnf_transformation,[],[f157])).
% 0.16/0.52 tff(f157,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : list(X0)] : (nil(X0) = aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) <=> (nil(X0) = X1 & nil(X0) = X2))),
% 0.16/0.52 inference(rectify,[],[f57])).
% 0.16/0.52 tff(f57,axiom,(
% 0.16/0.52 ! [X2 : $tType,X77 : list(X2),X34 : list(X2)] : (nil(X2) = aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X34),X77) <=> (nil(X2) = X77 & nil(X2) = X34))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Nil__is__append__conv)).
% 0.16/0.52 tff(f1034,plain,(
% 0.16/0.52 spl32_72),
% 0.16/0.52 inference(avatar_split_clause,[],[f427,f1032])).
% 0.16/0.52 tff(f1032,plain,(
% 0.16/0.52 spl32_72 <=> ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (nil(X0) = X2 | nil(X0) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_72])])).
% 0.16/0.52 tff(f427,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (nil(X0) = X2 | nil(X0) != aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f292])).
% 0.16/0.52 tff(f1026,plain,(
% 0.16/0.52 spl32_71),
% 0.16/0.52 inference(avatar_split_clause,[],[f421,f1024])).
% 0.16/0.52 tff(f1024,plain,(
% 0.16/0.52 spl32_71 <=> ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (nil(X0) = X1 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != X2)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_71])])).
% 0.16/0.52 tff(f421,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (nil(X0) = X1 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != X2) )),
% 0.16/0.52 inference(cnf_transformation,[],[f288])).
% 0.16/0.52 tff(f288,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : list(X0)] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = X2 | nil(X0) != X1) & (nil(X0) = X1 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != X2))),
% 0.16/0.52 inference(nnf_transformation,[],[f154])).
% 0.16/0.52 tff(f154,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = X2 <=> nil(X0) = X1)),
% 0.16/0.52 inference(rectify,[],[f61])).
% 0.16/0.52 tff(f61,axiom,(
% 0.16/0.52 ! [X2 : $tType,X77 : list(X2),X34 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X34),X77) = X34 <=> nil(X2) = X77)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_append__self__conv)).
% 0.16/0.52 tff(f1022,plain,(
% 0.16/0.52 spl32_70),
% 0.16/0.52 inference(avatar_split_clause,[],[f419,f1020])).
% 0.16/0.52 tff(f1020,plain,(
% 0.16/0.52 spl32_70 <=> ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (nil(X0) = X2 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != X1)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_70])])).
% 0.16/0.52 tff(f419,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (nil(X0) = X2 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != X1) )),
% 0.16/0.52 inference(cnf_transformation,[],[f287])).
% 0.16/0.52 tff(f287,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : list(X0)] : ((aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = X1 | nil(X0) != X2) & (nil(X0) = X2 | aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) != X1))),
% 0.16/0.52 inference(nnf_transformation,[],[f153])).
% 0.16/0.52 tff(f153,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1) = X1 <=> nil(X0) = X2)),
% 0.16/0.52 inference(rectify,[],[f62])).
% 0.16/0.52 tff(f62,axiom,(
% 0.16/0.52 ! [X2 : $tType,X77 : list(X2),X34 : list(X2)] : (aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X34),X77) = X77 <=> nil(X2) = X34)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_append__self__conv2)).
% 0.16/0.52 tff(f1002,plain,(
% 0.16/0.52 spl32_69),
% 0.16/0.52 inference(avatar_split_clause,[],[f466,f1000])).
% 0.16/0.52 tff(f1000,plain,(
% 0.16/0.52 spl32_69 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : list(X0),X1 : list(X0)] : (listsp(X0,X3,X1) | ~listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_69])])).
% 0.16/0.52 tff(f466,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : list(X0),X3 : fun(X0,bool),X1 : list(X0)] : (listsp(X0,X3,X1) | ~listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f316])).
% 0.16/0.52 tff(f998,plain,(
% 0.16/0.52 spl32_68),
% 0.16/0.52 inference(avatar_split_clause,[],[f465,f996])).
% 0.16/0.52 tff(f996,plain,(
% 0.16/0.52 spl32_68 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : list(X0),X1 : list(X0)] : (listsp(X0,X3,X2) | ~listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_68])])).
% 0.16/0.52 tff(f465,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : list(X0),X3 : fun(X0,bool),X1 : list(X0)] : (listsp(X0,X3,X2) | ~listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f316])).
% 0.16/0.52 tff(f994,plain,(
% 0.16/0.52 spl32_67),
% 0.16/0.52 inference(avatar_split_clause,[],[f452,f992])).
% 0.16/0.52 tff(f992,plain,(
% 0.16/0.52 spl32_67 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X1,X0),X2 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_67])])).
% 0.16/0.52 tff(f452,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f306])).
% 0.16/0.52 tff(f306,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)))),
% 0.16/0.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f229,f305])).
% 0.16/0.52 tff(f305,plain,(
% 0.16/0.52 ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (? [X4 : X1] : aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) => aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)))),
% 0.16/0.52 introduced(choice_axiom,[])).
% 0.16/0.52 tff(f229,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | ? [X4 : X1] : aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4))),
% 0.16/0.52 inference(ennf_transformation,[],[f171])).
% 0.16/0.52 tff(f171,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (! [X4 : X1] : aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) => X2 = X3)),
% 0.16/0.52 inference(rectify,[],[f76])).
% 0.16/0.52 tff(f76,axiom,(
% 0.16/0.52 ! [X0 : $tType,X2 : $tType,X83 : fun(X2,X0),X35 : fun(X2,X0)] : (! [X68 : X2] : aa(X2,X0,X35,X68) = aa(X2,X0,X83,X68) => X35 = X83)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext)).
% 0.16/0.52 tff(f990,plain,(
% 0.16/0.52 spl32_66),
% 0.16/0.52 inference(avatar_split_clause,[],[f404,f988])).
% 0.16/0.52 tff(f988,plain,(
% 0.16/0.52 spl32_66 <=> ! [X0 : $tType,X2 : fun(list(X0),bool),X1 : list(X0)] : (pp(aa(list(X0),bool,X2,X1)) | pp(aa(list(X0),bool,X2,sK14(X0,X2))) | ~pp(aa(list(X0),bool,X2,nil(X0))))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_66])])).
% 0.16/0.52 tff(f404,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : fun(list(X0),bool),X1 : list(X0)] : (pp(aa(list(X0),bool,X2,X1)) | pp(aa(list(X0),bool,X2,sK14(X0,X2))) | ~pp(aa(list(X0),bool,X2,nil(X0)))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f277])).
% 0.16/0.52 tff(f986,plain,(
% 0.16/0.52 ~spl32_65 | ~spl32_50 | ~spl32_55),
% 0.16/0.52 inference(avatar_split_clause,[],[f938,f935,f908,f983])).
% 0.16/0.52 tff(f983,plain,(
% 0.16/0.52 spl32_65 <=> rs = nil(dB)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_65])])).
% 0.16/0.52 tff(f938,plain,(
% 0.16/0.52 rs != nil(dB) | (~spl32_50 | ~spl32_55)),
% 0.16/0.52 inference(superposition,[],[f936,f910])).
% 0.16/0.52 tff(f981,plain,(
% 0.16/0.52 spl32_64),
% 0.16/0.52 inference(avatar_split_clause,[],[f374,f979])).
% 0.16/0.52 tff(f973,plain,(
% 0.16/0.52 spl32_63),
% 0.16/0.52 inference(avatar_split_clause,[],[f464,f971])).
% 0.16/0.52 tff(f971,plain,(
% 0.16/0.52 spl32_63 <=> ! [X0 : list(dB),X3 : dB,X2 : dB,X1 : dB] : (foldl(dB,dB,app,X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) | ~sP1(X3,X1,X0,X2))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_63])])).
% 0.16/0.52 tff(f464,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : dB,X0 : list(dB),X1 : dB] : (foldl(dB,dB,app,X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) | ~sP1(X3,X1,X0,X2)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f314])).
% 0.16/0.52 tff(f314,plain,(
% 0.16/0.52 ! [X0 : list(dB),X1 : dB,X2 : dB,X3 : dB] : ((foldl(dB,dB,app,X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) | ~sP1(X3,X1,X0,X2)) & (sP1(X3,X1,X0,X2) | foldl(dB,dB,app,X1,X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)))),
% 0.16/0.52 inference(nnf_transformation,[],[f256])).
% 0.16/0.52 tff(f256,plain,(
% 0.16/0.52 ! [X0 : list(dB),X1 : dB,X2 : dB,X3 : dB] : (foldl(dB,dB,app,X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) <=> sP1(X3,X1,X0,X2))),
% 0.16/0.52 inference(definition_folding,[],[f230,f255])).
% 0.16/0.52 tff(f230,plain,(
% 0.16/0.52 ! [X0 : list(dB),X1 : dB,X2 : dB,X3 : dB] : (foldl(dB,dB,app,X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) <=> ((? [X4 : list(dB)] : (foldl(dB,dB,app,X1,X4) = X3 & aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),nil(dB))) = X0) | nil(dB) = X0) & (aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) = X1 | nil(dB) != X0)))),
% 0.16/0.52 inference(ennf_transformation,[],[f173])).
% 0.16/0.52 tff(f173,plain,(
% 0.16/0.52 ! [X0 : list(dB),X1 : dB,X2 : dB,X3 : dB] : (foldl(dB,dB,app,X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) <=> ((nil(dB) != X0 => ? [X4 : list(dB)] : (foldl(dB,dB,app,X1,X4) = X3 & aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X4),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),nil(dB))) = X0)) & (nil(dB) = X0 => aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) = X1)))),
% 0.16/0.52 inference(rectify,[],[f52])).
% 0.16/0.52 tff(f52,axiom,(
% 0.16/0.52 ! [X14 : list(dB),X37 : dB,X13 : dB,X15 : dB] : (foldl(dB,dB,app,X37,X14) = aa(dB,dB,aa(dB,fun(dB,dB),app,X15),X13) <=> ((nil(dB) != X14 => ? [X73 : list(dB)] : (foldl(dB,dB,app,X37,X73) = X15 & aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X73),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X13),nil(dB))) = X14)) & (nil(dB) = X14 => aa(dB,dB,aa(dB,fun(dB,dB),app,X15),X13) = X37)))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_App__eq__foldl__conv)).
% 0.16/0.52 tff(f969,plain,(
% 0.16/0.52 spl32_62),
% 0.16/0.52 inference(avatar_split_clause,[],[f463,f967])).
% 0.16/0.52 tff(f967,plain,(
% 0.16/0.52 spl32_62 <=> ! [X0 : list(dB),X3 : dB,X2 : dB,X1 : dB] : (sP1(X3,X1,X0,X2) | foldl(dB,dB,app,X1,X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_62])])).
% 0.16/0.52 tff(f463,plain,(
% 0.16/0.52 ( ! [X2 : dB,X3 : dB,X0 : list(dB),X1 : dB] : (sP1(X3,X1,X0,X2) | foldl(dB,dB,app,X1,X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f314])).
% 0.16/0.52 tff(f965,plain,(
% 0.16/0.52 spl32_61),
% 0.16/0.52 inference(avatar_split_clause,[],[f383,f963])).
% 0.16/0.52 tff(f963,plain,(
% 0.16/0.52 spl32_61 <=> ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) | ~pp(aa(dB,bool,it,X1)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_61])])).
% 0.16/0.52 tff(f383,plain,(
% 0.16/0.52 ( ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) | ~pp(aa(dB,bool,it,X1))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f216])).
% 0.16/0.52 tff(f216,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) | ~pp(aa(dB,bool,it,X1)))),
% 0.16/0.52 inference(ennf_transformation,[],[f131])).
% 0.16/0.52 tff(f131,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : dB] : (pp(aa(dB,bool,it,X1)) => pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))))),
% 0.16/0.52 inference(rectify,[],[f20])).
% 0.16/0.52 tff(f20,axiom,(
% 0.16/0.52 ! [X27 : nat,X28 : dB] : (pp(aa(dB,bool,it,X28)) => pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X28),var(X27)))))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_app__Var__IT)).
% 0.16/0.52 tff(f958,plain,(
% 0.16/0.52 spl32_60),
% 0.16/0.52 inference(avatar_split_clause,[],[f594,f956])).
% 0.16/0.52 tff(f594,plain,(
% 0.16/0.52 ( ! [X2 : $tType,X0 : list(X2),X4 : X2] : (sP3(X2,X0,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0),nil(X2),X4)) )),
% 0.16/0.52 inference(equality_resolution,[],[f593])).
% 0.16/0.52 tff(f593,plain,(
% 0.16/0.52 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X4 : X2] : (sP3(X2,X0,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0),X3,X4) | nil(X2) != X3) )),
% 0.16/0.52 inference(equality_resolution,[],[f507])).
% 0.16/0.52 tff(f507,plain,(
% 0.16/0.52 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (sP3(X2,X0,X1,X3,X4) | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) != X1 | nil(X2) != X3) )),
% 0.16/0.52 inference(cnf_transformation,[],[f338])).
% 0.16/0.52 tff(f954,plain,(
% 0.16/0.52 spl32_59),
% 0.16/0.52 inference(avatar_split_clause,[],[f590,f952])).
% 0.16/0.52 tff(f590,plain,(
% 0.16/0.52 ( ! [X2 : $tType,X0 : list(X2),X4 : X2] : (sP2(X2,X0,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0),nil(X2),X4)) )),
% 0.16/0.52 inference(equality_resolution,[],[f589])).
% 0.16/0.52 tff(f589,plain,(
% 0.16/0.52 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X4 : X2] : (sP2(X2,X0,aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0),X3,X4) | nil(X2) != X3) )),
% 0.16/0.52 inference(equality_resolution,[],[f499])).
% 0.16/0.52 tff(f499,plain,(
% 0.16/0.52 ( ! [X2 : $tType,X3 : list(X2),X0 : list(X2),X1 : list(X2),X4 : X2] : (sP2(X2,X0,X1,X3,X4) | aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X4),X0) != X1 | nil(X2) != X3) )),
% 0.16/0.52 inference(cnf_transformation,[],[f332])).
% 0.16/0.52 tff(f950,plain,(
% 0.16/0.52 spl32_58),
% 0.16/0.52 inference(avatar_split_clause,[],[f458,f948])).
% 0.16/0.52 tff(f948,plain,(
% 0.16/0.52 spl32_58 <=> ! [X0 : dB,X3 : dB,X2 : list(dB),X1 : dB] : (foldl(dB,dB,app,X1,sK24(X0,X1,X2,X3)) = X0 | nil(dB) = X2 | ~sP1(X0,X1,X2,X3))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_58])])).
% 0.16/0.52 tff(f458,plain,(
% 0.16/0.52 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (foldl(dB,dB,app,X1,sK24(X0,X1,X2,X3)) = X0 | nil(dB) = X2 | ~sP1(X0,X1,X2,X3)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f313])).
% 0.16/0.52 tff(f946,plain,(
% 0.16/0.52 spl32_57),
% 0.16/0.52 inference(avatar_split_clause,[],[f373,f944])).
% 0.16/0.52 tff(f373,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),nil(X0)),X1) = X1) )),
% 0.16/0.52 inference(cnf_transformation,[],[f121])).
% 0.16/0.52 tff(f121,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),nil(X0)),X1) = X1),
% 0.16/0.52 inference(rectify,[],[f68])).
% 0.16/0.52 tff(f68,axiom,(
% 0.16/0.52 ! [X2 : $tType,X75 : list(X2)] : aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),nil(X2)),X75) = X75),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_append__Nil)).
% 0.16/0.52 tff(f942,plain,(
% 0.16/0.52 spl32_56),
% 0.16/0.52 inference(avatar_split_clause,[],[f372,f940])).
% 0.16/0.52 tff(f372,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X1 : list(X0)] : (aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X1),nil(X0)) = X1) )),
% 0.16/0.52 inference(cnf_transformation,[],[f120])).
% 0.16/0.52 tff(f120,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X1),nil(X0)) = X1),
% 0.16/0.52 inference(rectify,[],[f69])).
% 0.16/0.52 tff(f69,axiom,(
% 0.16/0.52 ! [X2 : $tType,X58 : list(X2)] : aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X58),nil(X2)) = X58),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_append__Nil2)).
% 0.16/0.52 tff(f937,plain,(
% 0.16/0.52 spl32_55),
% 0.16/0.52 inference(avatar_split_clause,[],[f549,f935])).
% 0.16/0.52 tff(f549,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : X0,X3 : list(X0)] : (nil(X0) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3)) )),
% 0.16/0.52 inference(equality_resolution,[],[f385])).
% 0.16/0.52 tff(f385,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0)] : (nil(X0) != X1 | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X3) != X1) )),
% 0.16/0.52 inference(cnf_transformation,[],[f272])).
% 0.16/0.52 tff(f932,plain,(
% 0.16/0.52 ~spl32_54 | ~spl32_50 | ~spl32_51),
% 0.16/0.52 inference(avatar_split_clause,[],[f924,f913,f908,f929])).
% 0.16/0.52 tff(f929,plain,(
% 0.16/0.52 spl32_54 <=> rs = as),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_54])])).
% 0.16/0.52 tff(f913,plain,(
% 0.16/0.52 spl32_51 <=> ! [X0 : $tType,X2 : X0,X1 : list(X0)] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_51])])).
% 0.16/0.52 tff(f924,plain,(
% 0.16/0.52 rs != as | (~spl32_50 | ~spl32_51)),
% 0.16/0.52 inference(superposition,[],[f914,f910])).
% 0.16/0.52 tff(f914,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1) ) | ~spl32_51),
% 0.16/0.52 inference(avatar_component_clause,[],[f913])).
% 0.16/0.52 tff(f923,plain,(
% 0.16/0.52 spl32_53),
% 0.16/0.52 inference(avatar_split_clause,[],[f577,f921])).
% 0.16/0.52 tff(f921,plain,(
% 0.16/0.52 spl32_53 <=> ! [X0 : dB,X1 : dB,X3 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3) = X1 | ~sP1(X0,X1,nil(dB),X3))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_53])])).
% 0.16/0.52 tff(f577,plain,(
% 0.16/0.52 ( ! [X3 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3) = X1 | ~sP1(X0,X1,nil(dB),X3)) )),
% 0.16/0.52 inference(equality_resolution,[],[f456])).
% 0.16/0.52 tff(f456,plain,(
% 0.16/0.52 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3) = X1 | nil(dB) != X2 | ~sP1(X0,X1,X2,X3)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f313])).
% 0.16/0.52 tff(f919,plain,(
% 0.16/0.52 spl32_52),
% 0.16/0.52 inference(avatar_split_clause,[],[f454,f917])).
% 0.16/0.52 tff(f917,plain,(
% 0.16/0.52 spl32_52 <=> ! [X2 : list(dB),X0 : list(dB),X1 : nat,X3 : nat] : (X0 = X2 | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_52])])).
% 0.16/0.52 tff(f454,plain,(
% 0.16/0.52 ( ! [X2 : list(dB),X3 : nat,X0 : list(dB),X1 : nat] : (X0 = X2 | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f308])).
% 0.16/0.52 tff(f308,plain,(
% 0.16/0.52 ! [X0 : list(dB),X1 : nat,X2 : list(dB),X3 : nat] : ((foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) | X0 != X2 | X1 != X3) & ((X0 = X2 & X1 = X3) | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0)))),
% 0.16/0.52 inference(flattening,[],[f307])).
% 0.16/0.52 tff(f307,plain,(
% 0.16/0.52 ! [X0 : list(dB),X1 : nat,X2 : list(dB),X3 : nat] : ((foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) | (X0 != X2 | X1 != X3)) & ((X0 = X2 & X1 = X3) | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0)))),
% 0.16/0.52 inference(nnf_transformation,[],[f172])).
% 0.16/0.52 tff(f172,plain,(
% 0.16/0.52 ! [X0 : list(dB),X1 : nat,X2 : list(dB),X3 : nat] : (foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) <=> (X0 = X2 & X1 = X3))),
% 0.16/0.52 inference(rectify,[],[f6])).
% 0.16/0.52 tff(f6,axiom,(
% 0.16/0.52 ! [X4 : list(dB),X5 : nat,X6 : list(dB),X7 : nat] : (foldl(dB,dB,app,var(X7),X6) = foldl(dB,dB,app,var(X5),X4) <=> (X4 = X6 & X5 = X7))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Var__apps__eq__Var__apps__conv)).
% 0.16/0.52 tff(f915,plain,(
% 0.16/0.52 spl32_51),
% 0.16/0.52 inference(avatar_split_clause,[],[f395,f913])).
% 0.16/0.52 tff(f395,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1) )),
% 0.16/0.52 inference(cnf_transformation,[],[f139])).
% 0.16/0.52 tff(f139,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : X0] : aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1),
% 0.16/0.52 inference(rectify,[],[f40])).
% 0.16/0.52 tff(f40,axiom,(
% 0.16/0.52 ! [X2 : $tType,X58 : list(X2),X59 : X2] : aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X59),X58) != X58),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_not__Cons__self2)).
% 0.16/0.52 tff(f911,plain,(
% 0.16/0.52 spl32_50),
% 0.16/0.52 inference(avatar_split_clause,[],[f365,f908])).
% 0.16/0.52 tff(f365,plain,(
% 0.16/0.52 rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as)),
% 0.16/0.52 inference(cnf_transformation,[],[f3])).
% 0.16/0.52 tff(f3,axiom,(
% 0.16/0.52 rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Cons)).
% 0.16/0.52 tff(f899,plain,(
% 0.16/0.52 spl32_49 | ~spl32_6 | ~spl32_13),
% 0.16/0.52 inference(avatar_split_clause,[],[f729,f695,f655,f896])).
% 0.16/0.52 tff(f896,plain,(
% 0.16/0.52 spl32_49 <=> aa(dB,bool,it,ua) = fTrue),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_49])])).
% 0.16/0.52 tff(f655,plain,(
% 0.16/0.52 spl32_6 <=> pp(aa(dB,bool,it,ua))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_6])])).
% 0.16/0.52 tff(f729,plain,(
% 0.16/0.52 aa(dB,bool,it,ua) = fTrue | (~spl32_6 | ~spl32_13)),
% 0.16/0.52 inference(resolution,[],[f696,f657])).
% 0.16/0.52 tff(f657,plain,(
% 0.16/0.52 pp(aa(dB,bool,it,ua)) | ~spl32_6),
% 0.16/0.52 inference(avatar_component_clause,[],[f655])).
% 0.16/0.52 tff(f887,plain,(
% 0.16/0.52 spl32_48),
% 0.16/0.52 inference(avatar_split_clause,[],[f544,f884])).
% 0.16/0.52 tff(f544,plain,(
% 0.16/0.52 pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(i),rs)),t))),
% 0.16/0.52 inference(definition_unfolding,[],[f364,f357])).
% 0.16/0.52 tff(f357,plain,(
% 0.16/0.52 n = i),
% 0.16/0.52 inference(cnf_transformation,[],[f2])).
% 0.16/0.52 tff(f2,axiom,(
% 0.16/0.52 n = i),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_True)).
% 0.16/0.52 tff(f364,plain,(
% 0.16/0.52 pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(n),rs)),t))),
% 0.16/0.52 inference(cnf_transformation,[],[f5])).
% 0.16/0.52 tff(f5,axiom,(
% 0.16/0.52 pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(n),rs)),t))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nT)).
% 0.16/0.52 tff(f882,plain,(
% 0.16/0.52 spl32_47),
% 0.16/0.52 inference(avatar_split_clause,[],[f543,f879])).
% 0.16/0.52 tff(f879,plain,(
% 0.16/0.52 spl32_47 <=> pp(aa(type,bool,typing(shift(type,ea,ia,t1),foldl(dB,dB,app,var(i),rs)),t_a))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_47])])).
% 0.16/0.52 tff(f543,plain,(
% 0.16/0.52 pp(aa(type,bool,typing(shift(type,ea,ia,t1),foldl(dB,dB,app,var(i),rs)),t_a))),
% 0.16/0.52 inference(definition_unfolding,[],[f363,f357])).
% 0.16/0.52 tff(f363,plain,(
% 0.16/0.52 pp(aa(type,bool,typing(shift(type,ea,ia,t1),foldl(dB,dB,app,var(n),rs)),t_a))),
% 0.16/0.52 inference(cnf_transformation,[],[f17])).
% 0.16/0.52 tff(f17,axiom,(
% 0.16/0.52 pp(aa(type,bool,typing(shift(type,ea,ia,t1),foldl(dB,dB,app,var(n),rs)),t_a))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Var_I2_J)).
% 0.16/0.52 tff(f877,plain,(
% 0.16/0.52 spl32_46),
% 0.16/0.52 inference(avatar_split_clause,[],[f453,f875])).
% 0.16/0.52 tff(f875,plain,(
% 0.16/0.52 spl32_46 <=> ! [X0 : list(dB),X3 : nat,X2 : list(dB),X1 : nat] : (X1 = X3 | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_46])])).
% 0.16/0.52 tff(f453,plain,(
% 0.16/0.52 ( ! [X2 : list(dB),X3 : nat,X0 : list(dB),X1 : nat] : (X1 = X3 | foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f308])).
% 0.16/0.52 tff(f873,plain,(
% 0.16/0.52 spl32_45),
% 0.16/0.52 inference(avatar_split_clause,[],[f408,f871])).
% 0.16/0.52 tff(f871,plain,(
% 0.16/0.52 spl32_45 <=> ! [X1 : $tType,X2 : list(X1),X0 : fun(X1,bool)] : (pp(aa(X1,bool,X0,sK15(X1,X0,X2))) | nil(X1) = X2 | ~sP0(X1,X0,X2))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_45])])).
% 0.16/0.52 tff(f408,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X2 : list(X1),X0 : fun(X1,bool)] : (pp(aa(X1,bool,X0,sK15(X1,X0,X2))) | nil(X1) = X2 | ~sP0(X1,X0,X2)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f282])).
% 0.16/0.52 tff(f860,plain,(
% 0.16/0.52 spl32_44 | ~spl32_7 | ~spl32_13),
% 0.16/0.52 inference(avatar_split_clause,[],[f728,f695,f660,f857])).
% 0.16/0.52 tff(f857,plain,(
% 0.16/0.52 spl32_44 <=> aa(dB,bool,it,u) = fTrue),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_44])])).
% 0.16/0.52 tff(f660,plain,(
% 0.16/0.52 spl32_7 <=> pp(aa(dB,bool,it,u))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_7])])).
% 0.16/0.52 tff(f728,plain,(
% 0.16/0.52 aa(dB,bool,it,u) = fTrue | (~spl32_7 | ~spl32_13)),
% 0.16/0.52 inference(resolution,[],[f696,f662])).
% 0.16/0.52 tff(f662,plain,(
% 0.16/0.52 pp(aa(dB,bool,it,u)) | ~spl32_7),
% 0.16/0.52 inference(avatar_component_clause,[],[f660])).
% 0.16/0.52 tff(f848,plain,(
% 0.16/0.52 spl32_43),
% 0.16/0.52 inference(avatar_split_clause,[],[f575,f846])).
% 0.16/0.52 tff(f846,plain,(
% 0.16/0.52 spl32_43 <=> ! [X0 : dB,X3 : dB] : sP1(X0,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3),nil(dB),X3)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_43])])).
% 0.16/0.52 tff(f575,plain,(
% 0.16/0.52 ( ! [X3 : dB,X0 : dB] : (sP1(X0,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3),nil(dB),X3)) )),
% 0.16/0.52 inference(equality_resolution,[],[f574])).
% 0.16/0.52 tff(f574,plain,(
% 0.16/0.52 ( ! [X3 : dB,X0 : dB,X1 : dB] : (sP1(X0,X1,nil(dB),X3) | aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3) != X1) )),
% 0.16/0.52 inference(equality_resolution,[],[f460])).
% 0.16/0.52 tff(f460,plain,(
% 0.16/0.52 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (sP1(X0,X1,X2,X3) | nil(dB) != X2 | aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X3) != X1) )),
% 0.16/0.52 inference(cnf_transformation,[],[f313])).
% 0.16/0.52 tff(f844,plain,(
% 0.16/0.52 spl32_42),
% 0.16/0.52 inference(avatar_split_clause,[],[f417,f842])).
% 0.16/0.52 tff(f842,plain,(
% 0.16/0.52 spl32_42 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (X0 = X2 | foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_42])])).
% 0.16/0.52 tff(f417,plain,(
% 0.16/0.52 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (X0 = X2 | foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f286])).
% 0.16/0.52 tff(f286,plain,(
% 0.16/0.52 ! [X0 : dB,X1 : list(dB),X2 : dB] : ((foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) | X0 != X2) & (X0 = X2 | foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1)))),
% 0.16/0.52 inference(nnf_transformation,[],[f152])).
% 0.16/0.52 tff(f152,plain,(
% 0.16/0.52 ! [X0 : dB,X1 : list(dB),X2 : dB] : (foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) <=> X0 = X2)),
% 0.16/0.52 inference(rectify,[],[f9])).
% 0.16/0.52 tff(f9,axiom,(
% 0.16/0.52 ! [X13 : dB,X14 : list(dB),X15 : dB] : (foldl(dB,dB,app,X15,X14) = foldl(dB,dB,app,X13,X14) <=> X13 = X15)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_apps__eq__tail__conv)).
% 0.16/0.52 tff(f840,plain,(
% 0.16/0.52 spl32_41),
% 0.16/0.52 inference(avatar_split_clause,[],[f409,f838])).
% 0.16/0.52 tff(f838,plain,(
% 0.16/0.52 spl32_41 <=> ! [X1 : $tType,X2 : list(X1),X0 : fun(X1,bool)] : (listsp(X1,X0,sK16(X1,X0,X2)) | nil(X1) = X2 | ~sP0(X1,X0,X2))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_41])])).
% 0.16/0.52 tff(f409,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X2 : list(X1),X0 : fun(X1,bool)] : (listsp(X1,X0,sK16(X1,X0,X2)) | nil(X1) = X2 | ~sP0(X1,X0,X2)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f282])).
% 0.16/0.52 tff(f836,plain,(
% 0.16/0.52 spl32_40),
% 0.16/0.52 inference(avatar_split_clause,[],[f406,f834])).
% 0.16/0.52 tff(f834,plain,(
% 0.16/0.52 spl32_40 <=> ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_40])])).
% 0.16/0.52 tff(f406,plain,(
% 0.16/0.52 ( ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f222])).
% 0.16/0.52 tff(f222,plain,(
% 0.16/0.52 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 0.16/0.52 inference(ennf_transformation,[],[f149])).
% 0.16/0.52 tff(f149,plain,(
% 0.16/0.52 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) => aa(nat,type,X2,X1) = X0)),
% 0.16/0.52 inference(rectify,[],[f8])).
% 0.16/0.52 tff(f8,axiom,(
% 0.16/0.52 ! [X8 : type,X11 : nat,X12 : fun(nat,type)] : (pp(aa(type,bool,typing(X12,var(X11)),X8)) => aa(nat,type,X12,X11) = X8)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_typing__elims_I1_J)).
% 0.16/0.52 tff(f832,plain,(
% 0.16/0.52 spl32_39),
% 0.16/0.52 inference(avatar_split_clause,[],[f402,f830])).
% 0.16/0.52 tff(f830,plain,(
% 0.16/0.52 spl32_39 <=> ! [X2 : dB,X0 : nat,X1 : nat] : (pp(aa(dB,bool,it,subst(X2,var(X1),X0))) | ~pp(aa(dB,bool,it,X2)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_39])])).
% 0.16/0.52 tff(f402,plain,(
% 0.16/0.52 ( ! [X2 : dB,X0 : nat,X1 : nat] : (pp(aa(dB,bool,it,subst(X2,var(X1),X0))) | ~pp(aa(dB,bool,it,X2))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f218])).
% 0.16/0.52 tff(f218,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : nat,X2 : dB] : (pp(aa(dB,bool,it,subst(X2,var(X1),X0))) | ~pp(aa(dB,bool,it,X2)))),
% 0.16/0.52 inference(ennf_transformation,[],[f146])).
% 0.16/0.52 tff(f146,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : nat,X2 : dB] : (pp(aa(dB,bool,it,X2)) => pp(aa(dB,bool,it,subst(X2,var(X1),X0))))),
% 0.16/0.52 inference(rectify,[],[f38])).
% 0.16/0.52 tff(f38,axiom,(
% 0.16/0.52 ! [X55 : nat,X27 : nat,X56 : dB] : (pp(aa(dB,bool,it,X56)) => pp(aa(dB,bool,it,subst(X56,var(X27),X55))))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_subst__Var__IT)).
% 0.16/0.52 tff(f828,plain,(
% 0.16/0.52 spl32_38),
% 0.16/0.52 inference(avatar_split_clause,[],[f379,f826])).
% 0.16/0.52 tff(f826,plain,(
% 0.16/0.52 spl32_38 <=> ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_38])])).
% 0.16/0.52 tff(f379,plain,(
% 0.16/0.52 ( ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f212])).
% 0.16/0.52 tff(f212,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1))),
% 0.16/0.52 inference(ennf_transformation,[],[f127])).
% 0.16/0.52 tff(f127,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : list(dB)] : (listsp(dB,it,X1) => pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))))),
% 0.16/0.52 inference(rectify,[],[f26])).
% 0.16/0.52 tff(f26,axiom,(
% 0.16/0.52 ! [X5 : nat,X6 : list(dB)] : (listsp(dB,it,X6) => pp(aa(dB,bool,it,foldl(dB,dB,app,var(X5),X6))))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_IT_OVar)).
% 0.16/0.52 tff(f824,plain,(
% 0.16/0.52 spl32_37),
% 0.16/0.52 inference(avatar_split_clause,[],[f376,f822])).
% 0.16/0.52 tff(f822,plain,(
% 0.16/0.52 spl32_37 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_37])])).
% 0.16/0.52 tff(f376,plain,(
% 0.16/0.52 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f124])).
% 0.16/0.52 tff(f124,plain,(
% 0.16/0.52 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 0.16/0.52 inference(rectify,[],[f106])).
% 0.16/0.52 tff(f106,axiom,(
% 0.16/0.52 ! [X93 : bool,X94 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X94),X93)) | ~pp(X93) | ~pp(X94))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U)).
% 0.16/0.52 tff(f818,plain,(
% 0.16/0.52 spl32_36 | ~spl32_5 | ~spl32_13),
% 0.16/0.52 inference(avatar_split_clause,[],[f727,f695,f650,f815])).
% 0.16/0.52 tff(f815,plain,(
% 0.16/0.52 spl32_36 <=> aa(dB,bool,it,t2) = fTrue),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_36])])).
% 0.16/0.52 tff(f650,plain,(
% 0.16/0.52 spl32_5 <=> pp(aa(dB,bool,it,t2))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_5])])).
% 0.16/0.52 tff(f727,plain,(
% 0.16/0.52 aa(dB,bool,it,t2) = fTrue | (~spl32_5 | ~spl32_13)),
% 0.16/0.52 inference(resolution,[],[f696,f652])).
% 0.16/0.52 tff(f652,plain,(
% 0.16/0.52 pp(aa(dB,bool,it,t2)) | ~spl32_5),
% 0.16/0.52 inference(avatar_component_clause,[],[f650])).
% 0.16/0.52 tff(f813,plain,(
% 0.16/0.52 spl32_35),
% 0.16/0.52 inference(avatar_split_clause,[],[f390,f811])).
% 0.16/0.52 tff(f811,plain,(
% 0.16/0.52 spl32_35 <=> ! [X0 : list(type),X1 : fun(nat,type)] : (nil(type) = X0 | ~pp(aa(list(type),bool,typings(X1,nil(dB)),X0)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_35])])).
% 0.16/0.52 tff(f390,plain,(
% 0.16/0.52 ( ! [X0 : list(type),X1 : fun(nat,type)] : (nil(type) = X0 | ~pp(aa(list(type),bool,typings(X1,nil(dB)),X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f275])).
% 0.16/0.52 tff(f275,plain,(
% 0.16/0.52 ! [X0 : list(type),X1 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X1,nil(dB)),X0)) | nil(type) != X0) & (nil(type) = X0 | ~pp(aa(list(type),bool,typings(X1,nil(dB)),X0))))),
% 0.16/0.52 inference(nnf_transformation,[],[f135])).
% 0.16/0.52 tff(f135,plain,(
% 0.16/0.52 ! [X0 : list(type),X1 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X1,nil(dB)),X0)) <=> nil(type) = X0)),
% 0.16/0.52 inference(rectify,[],[f85])).
% 0.16/0.52 tff(f85,axiom,(
% 0.16/0.52 ! [X87 : list(type),X12 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X12,nil(dB)),X87)) <=> nil(type) = X87)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_typings_Osimps_I1_J)).
% 0.16/0.52 tff(f806,plain,(
% 0.16/0.52 spl32_34),
% 0.16/0.52 inference(avatar_split_clause,[],[f415,f804])).
% 0.16/0.52 tff(f804,plain,(
% 0.16/0.52 spl32_34 <=> ! [X2 : nat,X0 : list(dB),X1 : dB] : (nil(dB) = X0 | var(X2) != foldl(dB,dB,app,X1,X0))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_34])])).
% 0.16/0.52 tff(f415,plain,(
% 0.16/0.52 ( ! [X2 : nat,X0 : list(dB),X1 : dB] : (nil(dB) = X0 | var(X2) != foldl(dB,dB,app,X1,X0)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f285])).
% 0.16/0.52 tff(f285,plain,(
% 0.16/0.52 ! [X0 : list(dB),X1 : dB,X2 : nat] : ((var(X2) = foldl(dB,dB,app,X1,X0) | nil(dB) != X0 | var(X2) != X1) & ((nil(dB) = X0 & var(X2) = X1) | var(X2) != foldl(dB,dB,app,X1,X0)))),
% 0.16/0.52 inference(flattening,[],[f284])).
% 0.16/0.52 tff(f284,plain,(
% 0.16/0.52 ! [X0 : list(dB),X1 : dB,X2 : nat] : ((var(X2) = foldl(dB,dB,app,X1,X0) | (nil(dB) != X0 | var(X2) != X1)) & ((nil(dB) = X0 & var(X2) = X1) | var(X2) != foldl(dB,dB,app,X1,X0)))),
% 0.16/0.52 inference(nnf_transformation,[],[f151])).
% 0.16/0.52 tff(f151,plain,(
% 0.16/0.52 ! [X0 : list(dB),X1 : dB,X2 : nat] : (var(X2) = foldl(dB,dB,app,X1,X0) <=> (nil(dB) = X0 & var(X2) = X1))),
% 0.16/0.52 inference(rectify,[],[f27])).
% 0.16/0.52 tff(f27,axiom,(
% 0.16/0.52 ! [X4 : list(dB),X13 : dB,X7 : nat] : (var(X7) = foldl(dB,dB,app,X13,X4) <=> (nil(dB) = X4 & var(X7) = X13))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Var__eq__apps__conv)).
% 0.16/0.52 tff(f802,plain,(
% 0.16/0.52 spl32_33),
% 0.16/0.52 inference(avatar_split_clause,[],[f393,f800])).
% 0.16/0.52 tff(f800,plain,(
% 0.16/0.52 spl32_33 <=> ! [X2 : nat,X0 : dB,X1 : dB] : var(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_33])])).
% 0.16/0.52 tff(f393,plain,(
% 0.16/0.52 ( ! [X2 : nat,X0 : dB,X1 : dB] : (var(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f137])).
% 0.16/0.52 tff(f137,plain,(
% 0.16/0.52 ! [X0 : dB,X1 : dB,X2 : nat] : var(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0)),
% 0.16/0.52 inference(rectify,[],[f15])).
% 0.16/0.52 tff(f15,axiom,(
% 0.16/0.52 ! [X23 : dB,X24 : dB,X25 : nat] : var(X25) != aa(dB,dB,aa(dB,fun(dB,dB),app,X24),X23)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_dB_Osimps_I4_J)).
% 0.16/0.52 tff(f798,plain,(
% 0.16/0.52 spl32_32),
% 0.16/0.52 inference(avatar_split_clause,[],[f378,f796])).
% 0.16/0.52 tff(f796,plain,(
% 0.16/0.52 spl32_32 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_32])])).
% 0.16/0.52 tff(f378,plain,(
% 0.16/0.52 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f126])).
% 0.16/0.52 tff(f126,plain,(
% 0.16/0.52 ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 0.16/0.52 inference(rectify,[],[f108])).
% 0.16/0.52 tff(f108,axiom,(
% 0.16/0.52 ! [X93 : bool,X94 : bool] : (pp(X93) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X94),X93)))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U)).
% 0.16/0.52 tff(f794,plain,(
% 0.16/0.52 spl32_31),
% 0.16/0.52 inference(avatar_split_clause,[],[f377,f792])).
% 0.16/0.52 tff(f792,plain,(
% 0.16/0.52 spl32_31 <=> ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_31])])).
% 0.16/0.52 tff(f377,plain,(
% 0.16/0.52 ( ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f125])).
% 0.16/0.52 tff(f125,plain,(
% 0.16/0.52 ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 0.16/0.52 inference(rectify,[],[f107])).
% 0.16/0.52 tff(f107,axiom,(
% 0.16/0.52 ! [X93 : bool,X94 : bool] : (pp(X94) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X94),X93)))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U)).
% 0.16/0.52 tff(f784,plain,(
% 0.16/0.52 spl32_30),
% 0.16/0.52 inference(avatar_split_clause,[],[f554,f782])).
% 0.16/0.52 tff(f782,plain,(
% 0.16/0.52 spl32_30 <=> ! [X2 : fun(nat,type),X1 : nat] : pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_30])])).
% 0.16/0.52 tff(f554,plain,(
% 0.16/0.52 ( ! [X2 : fun(nat,type),X1 : nat] : (pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1)))) )),
% 0.16/0.52 inference(equality_resolution,[],[f403])).
% 0.16/0.52 tff(f403,plain,(
% 0.16/0.52 ( ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) | aa(nat,type,X2,X1) != X0) )),
% 0.16/0.52 inference(cnf_transformation,[],[f219])).
% 0.16/0.52 tff(f219,plain,(
% 0.16/0.52 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) | aa(nat,type,X2,X1) != X0)),
% 0.16/0.52 inference(ennf_transformation,[],[f147])).
% 0.16/0.52 tff(f147,plain,(
% 0.16/0.52 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (aa(nat,type,X2,X1) = X0 => pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 0.16/0.52 inference(rectify,[],[f7])).
% 0.16/0.52 tff(f7,axiom,(
% 0.16/0.52 ! [X8 : type,X9 : nat,X10 : fun(nat,type)] : (aa(nat,type,X10,X9) = X8 => pp(aa(type,bool,typing(X10,var(X9)),X8)))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_typing_OVar)).
% 0.16/0.52 tff(f780,plain,(
% 0.16/0.52 spl32_29),
% 0.16/0.52 inference(avatar_split_clause,[],[f483,f778])).
% 0.16/0.52 tff(f778,plain,(
% 0.16/0.52 spl32_29 <=> ! [X0 : $tType,X2 : fun(dB,X0),X4 : fun(nat,X0),X3 : fun(dB,fun(dB,X0)),X1 : nat] : dB_case(X0,X4,X3,X2,var(X1)) = aa(nat,X0,X4,X1)),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_29])])).
% 0.16/0.52 tff(f483,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : fun(dB,X0),X3 : fun(dB,fun(dB,X0)),X1 : nat,X4 : fun(nat,X0)] : (dB_case(X0,X4,X3,X2,var(X1)) = aa(nat,X0,X4,X1)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f181])).
% 0.16/0.52 tff(f181,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : nat,X2 : fun(dB,X0),X3 : fun(dB,fun(dB,X0)),X4 : fun(nat,X0)] : dB_case(X0,X4,X3,X2,var(X1)) = aa(nat,X0,X4,X1)),
% 0.16/0.52 inference(rectify,[],[f28])).
% 0.16/0.52 tff(f28,axiom,(
% 0.16/0.52 ! [X2 : $tType,X18 : nat,X40 : fun(dB,X2),X41 : fun(dB,fun(dB,X2)),X42 : fun(nat,X2)] : dB_case(X2,X42,X41,X40,var(X18)) = aa(nat,X2,X42,X18)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_dB_Osimps_I10_J)).
% 0.16/0.52 tff(f776,plain,(
% 0.16/0.52 spl32_28),
% 0.16/0.52 inference(avatar_split_clause,[],[f414,f774])).
% 0.16/0.52 tff(f774,plain,(
% 0.16/0.52 spl32_28 <=> ! [X2 : nat,X0 : list(dB),X1 : dB] : (var(X2) = X1 | var(X2) != foldl(dB,dB,app,X1,X0))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_28])])).
% 0.16/0.52 tff(f414,plain,(
% 0.16/0.52 ( ! [X2 : nat,X0 : list(dB),X1 : dB] : (var(X2) = X1 | var(X2) != foldl(dB,dB,app,X1,X0)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f285])).
% 0.16/0.52 tff(f769,plain,(
% 0.16/0.52 spl32_27),
% 0.16/0.52 inference(avatar_split_clause,[],[f584,f767])).
% 0.16/0.52 tff(f767,plain,(
% 0.16/0.52 spl32_27 <=> ! [X0 : $tType,X2 : fun(nat,X0),X4 : nat,X1 : X0] : aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_27])])).
% 0.16/0.52 tff(f584,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : fun(nat,X0),X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1) )),
% 0.16/0.52 inference(equality_resolution,[],[f487])).
% 0.16/0.52 tff(f487,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : fun(nat,X0),X3 : nat,X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 | X3 != X4) )),
% 0.16/0.52 inference(cnf_transformation,[],[f231])).
% 0.16/0.52 tff(f231,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : X0,X2 : fun(nat,X0),X3 : nat,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 | X3 != X4)),
% 0.16/0.52 inference(ennf_transformation,[],[f185])).
% 0.16/0.52 tff(f185,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : X0,X2 : fun(nat,X0),X3 : nat,X4 : nat] : (X3 = X4 => aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1)),
% 0.16/0.52 inference(rectify,[],[f21])).
% 0.16/0.52 tff(f21,axiom,(
% 0.16/0.52 ! [X2 : $tType,X8 : X2,X12 : fun(nat,X2),X29 : nat,X11 : nat] : (X11 = X29 => aa(nat,X2,shift(X2,X12,X11,X8),X29) = X8)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_shift__eq)).
% 0.16/0.52 tff(f765,plain,(
% 0.16/0.52 spl32_26),
% 0.16/0.52 inference(avatar_split_clause,[],[f552,f763])).
% 0.16/0.52 tff(f763,plain,(
% 0.16/0.52 spl32_26 <=> ! [X1 : fun(nat,type)] : pp(aa(list(type),bool,typings(X1,nil(dB)),nil(type)))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_26])])).
% 0.16/0.52 tff(f552,plain,(
% 0.16/0.52 ( ! [X1 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X1,nil(dB)),nil(type)))) )),
% 0.16/0.52 inference(equality_resolution,[],[f391])).
% 0.16/0.52 tff(f391,plain,(
% 0.16/0.52 ( ! [X0 : list(type),X1 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X1,nil(dB)),X0)) | nil(type) != X0) )),
% 0.16/0.52 inference(cnf_transformation,[],[f275])).
% 0.16/0.52 tff(f761,plain,(
% 0.16/0.52 spl32_24 | ~spl32_25 | ~spl32_8),
% 0.16/0.52 inference(avatar_split_clause,[],[f673,f665,f758,f755])).
% 0.16/0.52 tff(f673,plain,(
% 0.16/0.52 ( ! [X0 : bool] : (fFalse != fTrue | fTrue = X0) ) | ~spl32_8),
% 0.16/0.52 inference(equality_factoring,[],[f666])).
% 0.16/0.52 tff(f753,plain,(
% 0.16/0.52 spl32_23),
% 0.16/0.52 inference(avatar_split_clause,[],[f392,f751])).
% 0.16/0.52 tff(f751,plain,(
% 0.16/0.52 spl32_23 <=> ! [X1 : $tType,X0 : $tType,X2 : fun(X0,list(X1))] : nil(X1) = maps(X0,X1,X2,nil(X0))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_23])])).
% 0.16/0.52 tff(f392,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,list(X1))] : (nil(X1) = maps(X0,X1,X2,nil(X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f136])).
% 0.16/0.52 tff(f136,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : $tType,X2 : fun(X0,list(X1))] : nil(X1) = maps(X0,X1,X2,nil(X0))),
% 0.16/0.52 inference(rectify,[],[f100])).
% 0.16/0.52 tff(f100,axiom,(
% 0.16/0.52 ! [X0 : $tType,X2 : $tType,X35 : fun(X0,list(X2))] : nil(X2) = maps(X0,X2,X35,nil(X0))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_maps__simps_I2_J)).
% 0.16/0.52 tff(f746,plain,(
% 0.16/0.52 spl32_22),
% 0.16/0.52 inference(avatar_split_clause,[],[f435,f744])).
% 0.16/0.52 tff(f435,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X1,fun(X0,X1))] : (foldl(X1,X0,X3,X2,nil(X0)) = X2) )),
% 0.16/0.52 inference(cnf_transformation,[],[f161])).
% 0.16/0.52 tff(f161,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X1,fun(X0,X1))] : foldl(X1,X0,X3,X2,nil(X0)) = X2),
% 0.16/0.52 inference(rectify,[],[f36])).
% 0.16/0.52 tff(f36,axiom,(
% 0.16/0.52 ! [X0 : $tType,X2 : $tType,X33 : X2,X35 : fun(X2,fun(X0,X2))] : foldl(X2,X0,X35,X33,nil(X0)) = X33),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_foldl__Nil)).
% 0.16/0.52 tff(f742,plain,(
% 0.16/0.52 spl32_21),
% 0.16/0.52 inference(avatar_split_clause,[],[f434,f740])).
% 0.16/0.52 tff(f434,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1))] : (foldr(X0,X1,X3,nil(X0),X2) = X2) )),
% 0.16/0.52 inference(cnf_transformation,[],[f160])).
% 0.16/0.52 tff(f160,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1))] : foldr(X0,X1,X3,nil(X0),X2) = X2),
% 0.16/0.52 inference(rectify,[],[f94])).
% 0.16/0.52 tff(f94,axiom,(
% 0.16/0.52 ! [X0 : $tType,X2 : $tType,X33 : X2,X35 : fun(X0,fun(X2,X2))] : foldr(X0,X2,X35,nil(X0),X33) = X33),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_foldr_Osimps_I1_J)).
% 0.16/0.52 tff(f738,plain,(
% 0.16/0.52 spl32_20),
% 0.16/0.52 inference(avatar_split_clause,[],[f433,f736])).
% 0.16/0.52 tff(f736,plain,(
% 0.16/0.52 spl32_20 <=> ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X1] : list_case(X1,X0,X3,X2,nil(X0)) = X3),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_20])])).
% 0.16/0.52 tff(f433,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X1] : (list_case(X1,X0,X3,X2,nil(X0)) = X3) )),
% 0.16/0.52 inference(cnf_transformation,[],[f159])).
% 0.16/0.52 tff(f159,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X1] : list_case(X1,X0,X3,X2,nil(X0)) = X3),
% 0.16/0.52 inference(rectify,[],[f87])).
% 0.16/0.52 tff(f87,axiom,(
% 0.16/0.52 ! [X0 : $tType,X2 : $tType,X41 : fun(X0,fun(list(X0),X2)),X42 : X2] : list_case(X2,X0,X42,X41,nil(X0)) = X42),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_list_Osimps_I4_J)).
% 0.16/0.52 tff(f722,plain,(
% 0.16/0.52 spl32_19),
% 0.16/0.52 inference(avatar_split_clause,[],[f413,f720])).
% 0.16/0.52 tff(f720,plain,(
% 0.16/0.52 spl32_19 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : list(X0)] : (listsp(X0,X2,X1) | ~sP0(X0,X2,X1))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_19])])).
% 0.16/0.52 tff(f413,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : list(X0)] : (listsp(X0,X2,X1) | ~sP0(X0,X2,X1)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f283])).
% 0.16/0.52 tff(f283,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : fun(X0,bool)] : ((listsp(X0,X2,X1) | ~sP0(X0,X2,X1)) & (sP0(X0,X2,X1) | ~listsp(X0,X2,X1)))),
% 0.16/0.52 inference(nnf_transformation,[],[f254])).
% 0.16/0.52 tff(f254,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : fun(X0,bool)] : (listsp(X0,X2,X1) <=> sP0(X0,X2,X1))),
% 0.16/0.52 inference(definition_folding,[],[f150,f253])).
% 0.16/0.52 tff(f150,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0),X2 : fun(X0,bool)] : (listsp(X0,X2,X1) <=> (? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) = X1) | nil(X0) = X1))),
% 0.16/0.52 inference(rectify,[],[f44])).
% 0.16/0.52 tff(f44,axiom,(
% 0.16/0.52 ! [X2 : $tType,X33 : list(X2),X48 : fun(X2,bool)] : (listsp(X2,X48,X33) <=> (? [X61 : X2,X62 : list(X2)] : (listsp(X2,X48,X62) & pp(aa(X2,bool,X48,X61)) & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X61),X62) = X33) | nil(X2) = X33))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_listsp_Osimps)).
% 0.16/0.52 tff(f718,plain,(
% 0.16/0.52 spl32_18),
% 0.16/0.52 inference(avatar_split_clause,[],[f412,f716])).
% 0.16/0.52 tff(f716,plain,(
% 0.16/0.52 spl32_18 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : list(X0)] : (sP0(X0,X2,X1) | ~listsp(X0,X2,X1))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_18])])).
% 0.16/0.52 tff(f412,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : list(X0)] : (sP0(X0,X2,X1) | ~listsp(X0,X2,X1)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f283])).
% 0.16/0.52 tff(f714,plain,(
% 0.16/0.52 spl32_17),
% 0.16/0.52 inference(avatar_split_clause,[],[f386,f712])).
% 0.16/0.52 tff(f712,plain,(
% 0.16/0.52 spl32_17 <=> ! [X0 : nat,X1 : nat] : (X0 = X1 | var(X0) != var(X1))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_17])])).
% 0.16/0.52 tff(f386,plain,(
% 0.16/0.52 ( ! [X0 : nat,X1 : nat] : (X0 = X1 | var(X0) != var(X1)) )),
% 0.16/0.52 inference(cnf_transformation,[],[f273])).
% 0.16/0.52 tff(f273,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : nat] : ((var(X0) = var(X1) | X0 != X1) & (X0 = X1 | var(X0) != var(X1)))),
% 0.16/0.52 inference(nnf_transformation,[],[f133])).
% 0.16/0.52 tff(f133,plain,(
% 0.16/0.52 ! [X0 : nat,X1 : nat] : (var(X0) = var(X1) <=> X0 = X1)),
% 0.16/0.52 inference(rectify,[],[f13])).
% 0.16/0.52 tff(f13,axiom,(
% 0.16/0.52 ! [X17 : nat,X18 : nat] : (var(X18) = var(X17) <=> X17 = X18)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_dB_Osimps_I1_J)).
% 0.16/0.52 tff(f710,plain,(
% 0.16/0.52 spl32_16),
% 0.16/0.52 inference(avatar_split_clause,[],[f371,f708])).
% 0.16/0.52 tff(f708,plain,(
% 0.16/0.52 spl32_16 <=> ! [X0 : $tType,X1 : list(X0)] : splice(X0,nil(X0),X1) = X1),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_16])])).
% 0.16/0.52 tff(f371,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X1 : list(X0)] : (splice(X0,nil(X0),X1) = X1) )),
% 0.16/0.52 inference(cnf_transformation,[],[f119])).
% 0.16/0.52 tff(f119,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : splice(X0,nil(X0),X1) = X1),
% 0.16/0.52 inference(rectify,[],[f77])).
% 0.16/0.52 tff(f77,axiom,(
% 0.16/0.52 ! [X2 : $tType,X75 : list(X2)] : splice(X2,nil(X2),X75) = X75),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_splice_Osimps_I1_J)).
% 0.16/0.52 tff(f706,plain,(
% 0.16/0.52 spl32_15),
% 0.16/0.52 inference(avatar_split_clause,[],[f370,f704])).
% 0.16/0.52 tff(f704,plain,(
% 0.16/0.52 spl32_15 <=> ! [X0 : $tType,X1 : list(X0)] : splice(X0,X1,nil(X0)) = X1),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_15])])).
% 0.16/0.52 tff(f370,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X1 : list(X0)] : (splice(X0,X1,nil(X0)) = X1) )),
% 0.16/0.52 inference(cnf_transformation,[],[f118])).
% 0.16/0.52 tff(f118,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : list(X0)] : splice(X0,X1,nil(X0)) = X1),
% 0.16/0.52 inference(rectify,[],[f75])).
% 0.16/0.52 tff(f75,axiom,(
% 0.16/0.52 ! [X2 : $tType,X58 : list(X2)] : splice(X2,X58,nil(X2)) = X58),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_splice__Nil2)).
% 0.16/0.52 tff(f702,plain,(
% 0.16/0.52 spl32_14),
% 0.16/0.52 inference(avatar_split_clause,[],[f362,f699])).
% 0.16/0.52 tff(f699,plain,(
% 0.16/0.52 spl32_14 <=> pp(aa(type,bool,typing(e,u),t1))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_14])])).
% 0.16/0.52 tff(f362,plain,(
% 0.16/0.52 pp(aa(type,bool,typing(e,u),t1))),
% 0.16/0.52 inference(cnf_transformation,[],[f4])).
% 0.16/0.52 tff(f4,axiom,(
% 0.16/0.52 pp(aa(type,bool,typing(e,u),t1))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_uT)).
% 0.16/0.52 tff(f697,plain,(
% 0.16/0.52 spl32_13 | spl32_1 | ~spl32_8),
% 0.16/0.52 inference(avatar_split_clause,[],[f669,f665,f632,f695])).
% 0.16/0.52 tff(f669,plain,(
% 0.16/0.52 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | (spl32_1 | ~spl32_8)),
% 0.16/0.52 inference(superposition,[],[f634,f666])).
% 0.16/0.52 tff(f693,plain,(
% 0.16/0.52 spl32_12),
% 0.16/0.52 inference(avatar_split_clause,[],[f361,f690])).
% 0.16/0.52 tff(f690,plain,(
% 0.16/0.52 spl32_12 <=> pp(aa(type,bool,typing(ea,ua),t1))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_12])])).
% 0.16/0.52 tff(f361,plain,(
% 0.16/0.52 pp(aa(type,bool,typing(ea,ua),t1))),
% 0.16/0.52 inference(cnf_transformation,[],[f18])).
% 0.16/0.52 tff(f18,axiom,(
% 0.16/0.52 pp(aa(type,bool,typing(ea,ua),t1))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Var_I4_J)).
% 0.16/0.52 tff(f687,plain,(
% 0.16/0.52 spl32_11),
% 0.16/0.52 inference(avatar_split_clause,[],[f369,f685])).
% 0.16/0.52 tff(f685,plain,(
% 0.16/0.52 spl32_11 <=> ! [X0 : dB,X1 : nat] : subst(var(X1),X0,X1) = X0),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_11])])).
% 0.16/0.52 tff(f369,plain,(
% 0.16/0.52 ( ! [X0 : dB,X1 : nat] : (subst(var(X1),X0,X1) = X0) )),
% 0.16/0.52 inference(cnf_transformation,[],[f117])).
% 0.16/0.52 tff(f117,plain,(
% 0.16/0.52 ! [X0 : dB,X1 : nat] : subst(var(X1),X0,X1) = X0),
% 0.16/0.52 inference(rectify,[],[f37])).
% 0.16/0.52 tff(f37,axiom,(
% 0.16/0.52 ! [X52 : dB,X50 : nat] : subst(var(X50),X52,X50) = X52),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_subst__eq)).
% 0.16/0.52 tff(f683,plain,(
% 0.16/0.52 spl32_10),
% 0.16/0.52 inference(avatar_split_clause,[],[f366,f681])).
% 0.16/0.52 tff(f366,plain,(
% 0.16/0.52 ( ! [X0 : nat] : (pp(aa(dB,bool,it,var(X0)))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f114])).
% 0.16/0.52 tff(f114,plain,(
% 0.16/0.52 ! [X0 : nat] : pp(aa(dB,bool,it,var(X0)))),
% 0.16/0.52 inference(rectify,[],[f19])).
% 0.16/0.52 tff(f19,axiom,(
% 0.16/0.52 ! [X26 : nat] : pp(aa(dB,bool,it,var(X26)))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Var__IT)).
% 0.16/0.52 tff(f678,plain,(
% 0.16/0.52 ~spl32_9),
% 0.16/0.52 inference(avatar_split_clause,[],[f542,f675])).
% 0.16/0.52 tff(f542,plain,(
% 0.16/0.52 ~pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t))),
% 0.16/0.52 inference(definition_unfolding,[],[f353,f357])).
% 0.16/0.52 tff(f353,plain,(
% 0.16/0.52 ~pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t))),
% 0.16/0.52 inference(cnf_transformation,[],[f113])).
% 0.16/0.52 tff(f113,plain,(
% 0.16/0.52 ~pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t))),
% 0.16/0.52 inference(flattening,[],[f112])).
% 0.16/0.52 tff(f112,negated_conjecture,(
% 0.16/0.52 ~pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t))),
% 0.16/0.52 inference(negated_conjecture,[],[f111])).
% 0.16/0.52 tff(f111,conjecture,(
% 0.16/0.52 pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.16/0.52 tff(f667,plain,(
% 0.16/0.52 spl32_8),
% 0.16/0.52 inference(avatar_split_clause,[],[f367,f665])).
% 0.16/0.52 tff(f367,plain,(
% 0.16/0.52 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) )),
% 0.16/0.52 inference(cnf_transformation,[],[f115])).
% 0.16/0.52 tff(f115,plain,(
% 0.16/0.52 ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 0.16/0.52 inference(rectify,[],[f110])).
% 0.16/0.52 tff(f110,axiom,(
% 0.16/0.52 ! [X94 : bool] : (fFalse = X94 | fTrue = X94)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T)).
% 0.16/0.52 tff(f663,plain,(
% 0.16/0.52 spl32_7),
% 0.16/0.52 inference(avatar_split_clause,[],[f360,f660])).
% 0.16/0.52 tff(f360,plain,(
% 0.16/0.52 pp(aa(dB,bool,it,u))),
% 0.16/0.52 inference(cnf_transformation,[],[f11])).
% 0.16/0.52 tff(f11,axiom,(
% 0.16/0.52 pp(aa(dB,bool,it,u))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_uIT)).
% 0.16/0.52 tff(f658,plain,(
% 0.16/0.52 spl32_6),
% 0.16/0.52 inference(avatar_split_clause,[],[f359,f655])).
% 0.16/0.52 tff(f359,plain,(
% 0.16/0.52 pp(aa(dB,bool,it,ua))),
% 0.16/0.52 inference(cnf_transformation,[],[f12])).
% 0.16/0.52 tff(f12,axiom,(
% 0.16/0.52 pp(aa(dB,bool,it,ua))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Var_I3_J)).
% 0.16/0.52 tff(f653,plain,(
% 0.16/0.52 spl32_5),
% 0.16/0.52 inference(avatar_split_clause,[],[f358,f650])).
% 0.16/0.52 tff(f358,plain,(
% 0.16/0.52 pp(aa(dB,bool,it,t2))),
% 0.16/0.52 inference(cnf_transformation,[],[f1])).
% 0.16/0.52 tff(f1,axiom,(
% 0.16/0.52 pp(aa(dB,bool,it,t2))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096)).
% 0.16/0.52 tff(f648,plain,(
% 0.16/0.52 spl32_4),
% 0.16/0.52 inference(avatar_split_clause,[],[f556,f646])).
% 0.16/0.52 tff(f646,plain,(
% 0.16/0.52 spl32_4 <=> ! [X1 : $tType,X0 : fun(X1,bool)] : sP0(X1,X0,nil(X1))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_4])])).
% 0.16/0.52 tff(f556,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X0 : fun(X1,bool)] : (sP0(X1,X0,nil(X1))) )),
% 0.16/0.52 inference(equality_resolution,[],[f410])).
% 0.16/0.52 tff(f410,plain,(
% 0.16/0.52 ( ! [X1 : $tType,X2 : list(X1),X0 : fun(X1,bool)] : (sP0(X1,X0,X2) | nil(X1) != X2) )),
% 0.16/0.52 inference(cnf_transformation,[],[f282])).
% 0.16/0.52 tff(f644,plain,(
% 0.16/0.52 spl32_3),
% 0.16/0.52 inference(avatar_split_clause,[],[f368,f642])).
% 0.16/0.52 tff(f642,plain,(
% 0.16/0.52 spl32_3 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : listsp(X0,X1,nil(X0))),
% 0.16/0.52 introduced(avatar_definition,[new_symbols(naming,[spl32_3])])).
% 0.16/0.52 tff(f368,plain,(
% 0.16/0.52 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (listsp(X0,X1,nil(X0))) )),
% 0.16/0.52 inference(cnf_transformation,[],[f116])).
% 0.16/0.52 tff(f116,plain,(
% 0.16/0.52 ! [X0 : $tType,X1 : fun(X0,bool)] : listsp(X0,X1,nil(X0))),
% 0.16/0.52 inference(rectify,[],[f32])).
% 0.16/0.52 tff(f32,axiom,(
% 0.16/0.52 ! [X2 : $tType,X48 : fun(X2,bool)] : listsp(X2,X48,nil(X2))),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_listsp_ONil)).
% 0.16/0.52 tff(f640,plain,(
% 0.16/0.52 spl32_2),
% 0.16/0.52 inference(avatar_split_clause,[],[f356,f637])).
% 0.16/0.52 tff(f356,plain,(
% 0.16/0.52 pp(fTrue)),
% 0.16/0.52 inference(cnf_transformation,[],[f102])).
% 0.16/0.52 tff(f102,axiom,(
% 0.16/0.52 pp(fTrue)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U)).
% 0.16/0.52 tff(f635,plain,(
% 0.16/0.52 ~spl32_1),
% 0.16/0.52 inference(avatar_split_clause,[],[f354,f632])).
% 0.16/0.52 tff(f354,plain,(
% 0.16/0.52 ~pp(fFalse)),
% 0.16/0.52 inference(cnf_transformation,[],[f101])).
% 0.16/0.52 tff(f101,axiom,(
% 0.16/0.52 ~pp(fFalse)),
% 0.16/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U)).
% 0.16/0.52 % SZS output end Proof for theBenchmark
% 0.16/0.52 % (6026)------------------------------
% 0.16/0.52 % (6026)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.52 % (6026)Termination reason: Refutation
% 0.16/0.52
% 0.16/0.52 % (6026)Memory used [KB]: 2633
% 0.16/0.52 % (6026)Time elapsed: 0.173 s
% 0.16/0.52 % (6026)Instructions burned: 340 (million)
% 0.16/0.52 % (6026)------------------------------
% 0.16/0.52 % (6026)------------------------------
% 0.16/0.52 % (6021)Success in time 0.199 s
%------------------------------------------------------------------------------