TSTP Solution File: COM047_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM047_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 : n007.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 10:47:38 EDT 2024
% Result : Theorem 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM047_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 04:58:48 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (19706)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (19709)WARNING: value z3 for option sas not known
% 0.15/0.38 % (19710)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (19707)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (19711)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)
% 0.15/0.38 % (19712)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)
% 0.15/0.38 % (19713)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)
% 0.15/0.38 % (19709)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)
% 0.15/0.38 % (19708)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (19713)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39 % Exception at run slice level% Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.41 % (19715)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)
% 0.21/0.41 % (19714)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.41 % (19716)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)
% 0.21/0.41 % (19715)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.41 % (19714)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.41 % Exception at run slice level
% 0.21/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43 % (19717)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)
% 0.21/0.45 % (19711)First to succeed.
% 0.21/0.47 % (19716)Also succeeded, but the first one will report.
% 0.21/0.47 % (19711)Refutation found. Thanks to Tanya!
% 0.21/0.47 % SZS status Theorem for theBenchmark
% 0.21/0.47 % SZS output start Proof for theBenchmark
% 0.21/0.47 tff(type_def_5, type, bool: $tType).
% 0.21/0.47 tff(type_def_6, type, int: $tType).
% 0.21/0.47 tff(type_def_7, type, list: $tType > $tType).
% 0.21/0.47 tff(type_def_8, type, nat: $tType).
% 0.21/0.47 tff(type_def_9, type, atom: $tType).
% 0.21/0.47 tff(type_def_10, type, fun: ($tType * $tType) > $tType).
% 0.21/0.47 tff(func_def_0, type, combb: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,X1) * fun(X2,X0)) > fun(X2,X1))).
% 0.21/0.47 tff(func_def_1, type, combk: !>[X0: $tType, X1: $tType]:(fun(X0,fun(X1,X0)))).
% 0.21/0.47 tff(func_def_2, type, combs: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * fun(X0,X1)) > fun(X0,X2))).
% 0.21/0.47 tff(func_def_3, type, div_mod: !>[X0: $tType]:((X0 * X0) > X0)).
% 0.21/0.47 tff(func_def_4, type, one_one: !>[X0: $tType]:(X0)).
% 0.21/0.47 tff(func_def_5, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.21/0.47 tff(func_def_6, type, iprod: !>[X0: $tType]:((list(X0) * list(X0)) > X0)).
% 0.21/0.47 tff(func_def_7, type, zipwith0: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * list(X0) * list(X1)) > list(X2))).
% 0.21/0.47 tff(func_def_8, type, insert: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 0.21/0.47 tff(func_def_9, type, cons: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 0.21/0.47 tff(func_def_10, type, nil: !>[X0: $tType]:(list(X0))).
% 0.21/0.47 tff(func_def_11, type, list_case: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(list(X1),X0)) * list(X1)) > X0)).
% 0.21/0.47 tff(func_def_12, type, list_rec: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1)) > X0)).
% 0.21/0.47 tff(func_def_13, type, list_size: !>[X0: $tType]:((fun(X0,nat) * list(X0)) > nat)).
% 0.21/0.47 tff(func_def_14, type, splice: !>[X0: $tType]:((list(X0) * list(X0)) > list(X0))).
% 0.21/0.47 tff(func_def_15, type, sublist: !>[X0: $tType]:((list(X0) * fun(nat,bool)) > list(X0))).
% 0.21/0.47 tff(func_def_16, type, tl: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.21/0.47 tff(func_def_17, type, size_size: !>[X0: $tType]:((X0) > nat)).
% 0.21/0.47 tff(func_def_18, type, asubst: (int * list(int) * atom) > atom).
% 0.21/0.47 tff(func_def_19, type, dvd: (int * int * list(int)) > atom).
% 0.21/0.47 tff(func_def_20, type, c_PresArith_Oatom_OLe: (int * list(int)) > atom).
% 0.21/0.47 tff(func_def_21, type, nDvd: (int * int * list(int)) > atom).
% 0.21/0.47 tff(func_def_22, type, atom_case: !>[X0: $tType]:((fun(int,fun(list(int),X0)) * fun(int,fun(int,fun(list(int),X0))) * fun(int,fun(int,fun(list(int),X0))) * atom) > X0)).
% 0.21/0.47 tff(func_def_23, type, atom_rec: !>[X0: $tType]:((fun(int,fun(list(int),X0)) * fun(int,fun(int,fun(list(int),X0))) * fun(int,fun(int,fun(list(int),X0))) * atom) > X0)).
% 0.21/0.47 tff(func_def_24, type, atom_size: atom > nat).
% 0.21/0.47 tff(func_def_25, type, decr_Z: atom > atom).
% 0.21/0.47 tff(func_def_26, type, divisor: atom > int).
% 0.21/0.47 tff(func_def_27, type, hd_coeff: atom > int).
% 0.21/0.47 tff(func_def_28, type, hd_coeff1: (int * atom) > atom).
% 0.21/0.47 tff(func_def_29, type, aa: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * X0) > X1)).
% 0.21/0.47 tff(func_def_30, type, fFalse: bool).
% 0.21/0.47 tff(func_def_31, type, fNot: fun(bool,bool)).
% 0.21/0.47 tff(func_def_32, type, fTrue: bool).
% 0.21/0.47 tff(func_def_33, type, fdisj: fun(bool,fun(bool,bool))).
% 0.21/0.47 tff(func_def_34, type, fequal: !>[X0: $tType]:((X0) > fun(X0,bool))).
% 0.21/0.47 tff(func_def_35, type, a: atom).
% 0.21/0.47 tff(func_def_36, type, e: list(int)).
% 0.21/0.47 tff(func_def_37, type, i: int).
% 0.21/0.47 tff(func_def_38, type, int1: int).
% 0.21/0.47 tff(func_def_39, type, j: int).
% 0.21/0.47 tff(func_def_40, type, list1: list(int)).
% 0.21/0.47 tff(func_def_41, type, sK2: atom > int).
% 0.21/0.47 tff(func_def_42, type, sK3: atom > int).
% 0.21/0.47 tff(func_def_43, type, sK4: atom > list(int)).
% 0.21/0.47 tff(func_def_44, type, sK5: atom > int).
% 0.21/0.47 tff(func_def_45, type, sK6: atom > int).
% 0.21/0.47 tff(func_def_46, type, sK7: atom > list(int)).
% 0.21/0.47 tff(func_def_47, type, sK8: atom > int).
% 0.21/0.47 tff(func_def_48, type, sK9: atom > list(int)).
% 0.21/0.47 tff(func_def_49, type, sK10: !>[X0: $tType]:((list(X0)) > X0)).
% 0.21/0.47 tff(func_def_50, type, sK11: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.21/0.47 tff(func_def_51, type, sK12: !>[X0: $tType]:((list(X0)) > X0)).
% 0.21/0.47 tff(func_def_52, type, sK13: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.21/0.47 tff(func_def_53, type, sK14: !>[X0: $tType]:((fun(list(X0),bool)) > X0)).
% 0.21/0.47 tff(func_def_54, type, sK15: !>[X0: $tType]:((fun(list(X0),bool)) > list(X0))).
% 0.21/0.47 tff(func_def_55, type, sK16: !>[X0: $tType]:((fun(list(X0),bool)) > X0)).
% 0.21/0.47 tff(func_def_56, type, sK17: !>[X0: $tType]:((list(X0) * X0) > X0)).
% 0.21/0.47 tff(func_def_57, type, sK18: !>[X0: $tType]:((list(X0) * X0) > list(X0))).
% 0.21/0.47 tff(func_def_58, type, sK19: !>[X0: $tType]:((list(X0) * X0) > X0)).
% 0.21/0.47 tff(func_def_59, type, sK20: !>[X0: $tType]:((list(X0) * X0) > X0)).
% 0.21/0.47 tff(func_def_60, type, sK21: !>[X0: $tType]:((list(X0) * X0) > list(X0))).
% 0.21/0.47 tff(pred_def_1, type, one: !>[X0: $tType]:($o)).
% 0.21/0.47 tff(pred_def_2, type, ring: !>[X0: $tType]:($o)).
% 0.21/0.47 tff(pred_def_3, type, zero: !>[X0: $tType]:($o)).
% 0.21/0.47 tff(pred_def_4, type, zero_neq_one: !>[X0: $tType]:($o)).
% 0.21/0.47 tff(pred_def_5, type, semiring_div: !>[X0: $tType]:($o)).
% 0.21/0.47 tff(pred_def_6, type, equal_equal: !>[X0: $tType]:((X0 * X0) > $o)).
% 0.21/0.47 tff(pred_def_7, type, listMem: !>[X0: $tType]:((X0 * list(X0)) > $o)).
% 0.21/0.47 tff(pred_def_8, type, list_all: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 0.21/0.47 tff(pred_def_9, type, list_ex1: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 0.21/0.47 tff(pred_def_10, type, member1: !>[X0: $tType]:((list(X0) * X0) > $o)).
% 0.21/0.47 tff(pred_def_11, type, null: !>[X0: $tType]:((list(X0)) > $o)).
% 0.21/0.47 tff(pred_def_12, type, i_Z: (atom * list(int)) > $o).
% 0.21/0.47 tff(pred_def_13, type, member: !>[X0: $tType]:((X0 * fun(X0,bool)) > $o)).
% 0.21/0.47 tff(pred_def_14, type, pp: bool > $o).
% 0.21/0.47 tff(pred_def_15, type, sP0: !>[X0: $tType]:((list(X0) * X0) > $o)).
% 0.21/0.47 tff(pred_def_16, type, sP1: !>[X0: $tType]:((list(X0) * fun(X0,bool) * X0) > $o)).
% 0.21/0.47 tff(f1754,plain,(
% 0.21/0.47 $false),
% 0.21/0.47 inference(avatar_sat_refutation,[],[f512,f517,f522,f527,f532,f537,f542,f547,f552,f557,f562,f571,f575,f580,f585,f589,f593,f597,f601,f605,f609,f616,f620,f624,f628,f632,f636,f640,f644,f648,f652,f660,f664,f668,f672,f677,f681,f686,f691,f695,f699,f703,f708,f713,f717,f721,f726,f730,f734,f738,f746,f750,f756,f760,f766,f770,f774,f778,f782,f786,f795,f799,f804,f808,f812,f816,f820,f833,f837,f846,f850,f854,f858,f862,f866,f870,f874,f878,f882,f916,f922,f926,f930,f934,f938,f942,f946,f950,f963,f969,f973,f977,f981,f985,f989,f993,f997,f1001,f1005,f1009,f1052,f1056,f1060,f1064,f1068,f1072,f1087,f1091,f1095,f1099,f1103,f1107,f1111,f1115,f1132,f1139,f1143,f1147,f1151,f1155,f1159,f1169,f1183,f1187,f1191,f1195,f1199,f1203,f1207,f1273,f1277,f1281,f1285,f1292,f1302,f1306,f1310,f1332,f1338,f1345,f1349,f1353,f1412,f1440,f1456,f1496,f1500,f1504,f1508,f1512,f1516,f1636,f1640,f1644,f1670,f1705,f1709,f1713,f1717,f1729,f1749,f1753])).
% 0.21/0.47 tff(f1753,plain,(
% 0.21/0.47 spl22_1 | ~spl22_15 | ~spl22_121 | ~spl22_143 | ~spl22_163),
% 0.21/0.47 inference(avatar_split_clause,[],[f1752,f1746,f1347,f1149,f577,f509])).
% 0.21/0.47 tff(f509,plain,(
% 0.21/0.47 spl22_1 <=> pp(fFalse)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_1])])).
% 0.21/0.47 tff(f577,plain,(
% 0.21/0.47 spl22_15 <=> a = c_PresArith_Oatom_OLe(int1,list1)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_15])])).
% 0.21/0.47 tff(f1149,plain,(
% 0.21/0.47 spl22_121 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : X0] : aa(X0,X1,aa(X1,fun(X0,X1),combk(X1,X0),X3),X2) = X3),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_121])])).
% 0.21/0.47 tff(f1347,plain,(
% 0.21/0.47 spl22_143 <=> ! [X0 : $tType,X3 : fun(int,fun(int,fun(list(int),X0))),X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(list(int),X0)),X2 : int,X1 : list(int)] : atom_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_143])])).
% 0.21/0.47 tff(f1746,plain,(
% 0.21/0.47 spl22_163 <=> pp(atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),a))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_163])])).
% 0.21/0.47 tff(f1752,plain,(
% 0.21/0.47 pp(fFalse) | (~spl22_15 | ~spl22_121 | ~spl22_143 | ~spl22_163)),
% 0.21/0.47 inference(forward_demodulation,[],[f1751,f1150])).
% 0.21/0.47 tff(f1150,plain,(
% 0.21/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : (aa(X0,X1,aa(X1,fun(X0,X1),combk(X1,X0),X3),X2) = X3) ) | ~spl22_121),
% 0.21/0.47 inference(avatar_component_clause,[],[f1149])).
% 0.21/0.47 tff(f1751,plain,(
% 0.21/0.47 pp(aa(list(int),bool,aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse),list1)) | (~spl22_15 | ~spl22_121 | ~spl22_143 | ~spl22_163)),
% 0.21/0.47 inference(forward_demodulation,[],[f1750,f1150])).
% 0.21/0.47 tff(f1750,plain,(
% 0.21/0.47 pp(aa(list(int),bool,aa(int,fun(list(int),bool),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),int1),list1)) | (~spl22_15 | ~spl22_143 | ~spl22_163)),
% 0.21/0.47 inference(forward_demodulation,[],[f1748,f1377])).
% 0.21/0.47 tff(f1377,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : fun(int,fun(int,fun(list(int),X0))),X3 : fun(int,fun(int,fun(list(int),X0))),X1 : fun(int,fun(list(int),X0))] : (aa(list(int),X0,aa(int,fun(list(int),X0),X1,int1),list1) = atom_case(X0,X1,X2,X3,a)) ) | (~spl22_15 | ~spl22_143)),
% 0.21/0.47 inference(superposition,[],[f1348,f579])).
% 0.21/0.47 tff(f579,plain,(
% 0.21/0.47 a = c_PresArith_Oatom_OLe(int1,list1) | ~spl22_15),
% 0.21/0.47 inference(avatar_component_clause,[],[f577])).
% 0.21/0.47 tff(f1348,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : int,X3 : fun(int,fun(int,fun(list(int),X0))),X1 : list(int),X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(list(int),X0))] : (atom_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1)) ) | ~spl22_143),
% 0.21/0.47 inference(avatar_component_clause,[],[f1347])).
% 0.21/0.47 tff(f1748,plain,(
% 0.21/0.47 pp(atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),a)) | ~spl22_163),
% 0.21/0.47 inference(avatar_component_clause,[],[f1746])).
% 0.21/0.47 tff(f1749,plain,(
% 0.21/0.47 spl22_163),
% 0.21/0.47 inference(avatar_split_clause,[],[f331,f1746])).
% 0.21/0.47 tff(f331,plain,(
% 0.21/0.47 pp(atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),a))),
% 0.21/0.47 inference(cnf_transformation,[],[f4])).
% 0.21/0.47 tff(f4,axiom,(
% 0.21/0.47 pp(atom_case(bool,aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fFalse)),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),aa(fun(int,fun(list(int),bool)),fun(int,fun(int,fun(list(int),bool))),combk(fun(int,fun(list(int),bool)),int),aa(fun(list(int),bool),fun(int,fun(list(int),bool)),combk(fun(list(int),bool),int),aa(bool,fun(list(int),bool),combk(bool,list(int)),fTrue))),a))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I1_J)).
% 0.21/0.47 tff(f1729,plain,(
% 0.21/0.47 ~spl22_5 | ~spl22_162 | ~spl22_24 | ~spl22_37),
% 0.21/0.47 inference(avatar_split_clause,[],[f751,f674,f618,f1726,f529])).
% 0.21/0.47 tff(f529,plain,(
% 0.21/0.47 spl22_5 <=> zero_neq_one(nat)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_5])])).
% 0.21/0.47 tff(f1726,plain,(
% 0.21/0.47 spl22_162 <=> atom_size(a) = one_one(nat)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_162])])).
% 0.21/0.47 tff(f618,plain,(
% 0.21/0.47 spl22_24 <=> ! [X0 : $tType] : (one_one(X0) != zero_zero(X0) | ~zero_neq_one(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_24])])).
% 0.21/0.47 tff(f674,plain,(
% 0.21/0.47 spl22_37 <=> zero_zero(nat) = atom_size(a)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_37])])).
% 0.21/0.47 tff(f751,plain,(
% 0.21/0.47 atom_size(a) != one_one(nat) | ~zero_neq_one(nat) | (~spl22_24 | ~spl22_37)),
% 0.21/0.47 inference(superposition,[],[f619,f676])).
% 0.21/0.47 tff(f676,plain,(
% 0.21/0.47 zero_zero(nat) = atom_size(a) | ~spl22_37),
% 0.21/0.47 inference(avatar_component_clause,[],[f674])).
% 0.21/0.47 tff(f619,plain,(
% 0.21/0.47 ( ! [X0 : $tType] : (one_one(X0) != zero_zero(X0) | ~zero_neq_one(X0)) ) | ~spl22_24),
% 0.21/0.47 inference(avatar_component_clause,[],[f618])).
% 0.21/0.47 tff(f1717,plain,(
% 0.21/0.47 spl22_161),
% 0.21/0.47 inference(avatar_split_clause,[],[f505,f1715])).
% 0.21/0.47 tff(f1715,plain,(
% 0.21/0.47 spl22_161 <=> ! [X0 : $tType,X2 : list(X0),X1 : fun(list(X0),bool)] : (~pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0)))) | pp(aa(list(X0),bool,X1,X2)) | ~pp(aa(list(X0),bool,X1,cons(X0,sK14(X0,X1),sK15(X0,X1)))) | nil(X0) = X2)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_161])])).
% 0.21/0.47 tff(f505,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X1 : fun(list(X0),bool)] : (~pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0)))) | pp(aa(list(X0),bool,X1,X2)) | ~pp(aa(list(X0),bool,X1,cons(X0,sK14(X0,X1),sK15(X0,X1)))) | nil(X0) = X2) )),
% 0.21/0.47 inference(forward_demodulation,[],[f409,f367])).
% 0.21/0.47 tff(f367,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : X0] : (insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f156])).
% 0.21/0.47 tff(f156,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0] : insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0))),
% 0.21/0.47 inference(rectify,[],[f36])).
% 0.21/0.47 tff(f36,axiom,(
% 0.21/0.47 ! [X0 : $tType,X8 : X0] : insert(X0,X8,nil(X0)) = cons(X0,X8,nil(X0))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_insert__Nil)).
% 0.21/0.47 tff(f409,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X1 : fun(list(X0),bool)] : (pp(aa(list(X0),bool,X1,X2)) | ~pp(aa(list(X0),bool,X1,cons(X0,sK14(X0,X1),sK15(X0,X1)))) | ~pp(aa(list(X0),bool,X1,cons(X0,sK16(X0,X1),nil(X0)))) | nil(X0) = X2) )),
% 0.21/0.47 inference(cnf_transformation,[],[f284])).
% 0.21/0.47 tff(f284,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(list(X0),bool),X2 : list(X0)] : (pp(aa(list(X0),bool,X1,X2)) | (~pp(aa(list(X0),bool,X1,cons(X0,sK14(X0,X1),sK15(X0,X1)))) & pp(aa(list(X0),bool,X1,sK15(X0,X1))) & nil(X0) != sK15(X0,X1)) | ~pp(aa(list(X0),bool,X1,cons(X0,sK16(X0,X1),nil(X0)))) | nil(X0) = X2)),
% 0.21/0.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f281,f283,f282])).
% 0.21/0.47 tff(f282,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(list(X0),bool)] : (? [X3 : X0,X4 : list(X0)] : (~pp(aa(list(X0),bool,X1,cons(X0,X3,X4))) & pp(aa(list(X0),bool,X1,X4)) & nil(X0) != X4) => (~pp(aa(list(X0),bool,X1,cons(X0,sK14(X0,X1),sK15(X0,X1)))) & pp(aa(list(X0),bool,X1,sK15(X0,X1))) & nil(X0) != sK15(X0,X1)))),
% 0.21/0.47 introduced(choice_axiom,[])).
% 0.21/0.47 tff(f283,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(list(X0),bool)] : (? [X5 : X0] : ~pp(aa(list(X0),bool,X1,cons(X0,X5,nil(X0)))) => ~pp(aa(list(X0),bool,X1,cons(X0,sK16(X0,X1),nil(X0)))))),
% 0.21/0.47 introduced(choice_axiom,[])).
% 0.21/0.47 tff(f281,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(list(X0),bool),X2 : list(X0)] : (pp(aa(list(X0),bool,X1,X2)) | ? [X3 : X0,X4 : list(X0)] : (~pp(aa(list(X0),bool,X1,cons(X0,X3,X4))) & pp(aa(list(X0),bool,X1,X4)) & nil(X0) != X4) | ? [X5 : X0] : ~pp(aa(list(X0),bool,X1,cons(X0,X5,nil(X0)))) | nil(X0) = X2)),
% 0.21/0.47 inference(rectify,[],[f248])).
% 0.21/0.47 tff(f248,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(list(X0),bool),X2 : list(X0)] : (pp(aa(list(X0),bool,X1,X2)) | ? [X4 : X0,X5 : list(X0)] : (~pp(aa(list(X0),bool,X1,cons(X0,X4,X5))) & pp(aa(list(X0),bool,X1,X5)) & nil(X0) != X5) | ? [X3 : X0] : ~pp(aa(list(X0),bool,X1,cons(X0,X3,nil(X0)))) | nil(X0) = X2)),
% 0.21/0.47 inference(flattening,[],[f247])).
% 0.21/0.47 tff(f247,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(list(X0),bool),X2 : list(X0)] : (((pp(aa(list(X0),bool,X1,X2)) | ? [X4 : X0,X5 : list(X0)] : ((~pp(aa(list(X0),bool,X1,cons(X0,X4,X5))) & pp(aa(list(X0),bool,X1,X5))) & nil(X0) != X5)) | ? [X3 : X0] : ~pp(aa(list(X0),bool,X1,cons(X0,X3,nil(X0))))) | nil(X0) = X2)),
% 0.21/0.47 inference(ennf_transformation,[],[f191])).
% 0.21/0.47 tff(f191,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(list(X0),bool),X2 : list(X0)] : (nil(X0) != X2 => (! [X3 : X0] : pp(aa(list(X0),bool,X1,cons(X0,X3,nil(X0)))) => (! [X4 : X0,X5 : list(X0)] : (nil(X0) != X5 => (pp(aa(list(X0),bool,X1,X5)) => pp(aa(list(X0),bool,X1,cons(X0,X4,X5))))) => pp(aa(list(X0),bool,X1,X2)))))),
% 0.21/0.47 inference(rectify,[],[f87])).
% 0.21/0.47 tff(f87,axiom,(
% 0.21/0.47 ! [X0 : $tType,X38 : fun(list(X0),bool),X16 : list(X0)] : (nil(X0) != X16 => (! [X58 : X0] : pp(aa(list(X0),bool,X38,cons(X0,X58,nil(X0)))) => (! [X58 : X0,X59 : list(X0)] : (nil(X0) != X59 => (pp(aa(list(X0),bool,X38,X59)) => pp(aa(list(X0),bool,X38,cons(X0,X58,X59))))) => pp(aa(list(X0),bool,X38,X16)))))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_list__nonempty__induct)).
% 0.21/0.47 tff(f1713,plain,(
% 0.21/0.47 spl22_160),
% 0.21/0.47 inference(avatar_split_clause,[],[f415,f1711])).
% 0.21/0.47 tff(f1711,plain,(
% 0.21/0.47 spl22_160 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : list(X2),X4 : X2,X7 : fun(X0,fun(X2,X1)),X6 : X0,X5 : list(X0)] : (zipwith0(X0,X2,X1,X7,cons(X0,X6,X5),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X7,X6),X4),zipwith0(X0,X2,X1,X7,X5,X3)) | ~zero(X0) | ~zero(X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_160])])).
% 0.21/0.47 tff(f415,plain,(
% 0.21/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : list(X2),X6 : X0,X7 : fun(X0,fun(X2,X1)),X4 : X2,X5 : list(X0)] : (zipwith0(X0,X2,X1,X7,cons(X0,X6,X5),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X7,X6),X4),zipwith0(X0,X2,X1,X7,X5,X3)) | ~zero(X0) | ~zero(X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f257])).
% 0.21/0.47 tff(f257,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : list(X2),X4 : X2,X5 : list(X0),X6 : X0,X7 : fun(X0,fun(X2,X1))] : zipwith0(X0,X2,X1,X7,cons(X0,X6,X5),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X7,X6),X4),zipwith0(X0,X2,X1,X7,X5,X3)) | ~zero(X0) | ~zero(X2))),
% 0.21/0.47 inference(flattening,[],[f256])).
% 0.21/0.47 tff(f256,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : list(X2),X4 : X2,X5 : list(X0),X6 : X0,X7 : fun(X0,fun(X2,X1))] : zipwith0(X0,X2,X1,X7,cons(X0,X6,X5),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X7,X6),X4),zipwith0(X0,X2,X1,X7,X5,X3)) | (~zero(X0) | ~zero(X2)))),
% 0.21/0.47 inference(ennf_transformation,[],[f196])).
% 0.21/0.47 tff(f196,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((zero(X0) & zero(X2)) => ! [X3 : list(X2),X4 : X2,X5 : list(X0),X6 : X0,X7 : fun(X0,fun(X2,X1))] : zipwith0(X0,X2,X1,X7,cons(X0,X6,X5),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X7,X6),X4),zipwith0(X0,X2,X1,X7,X5,X3)))),
% 0.21/0.47 inference(rectify,[],[f12])).
% 0.21/0.47 tff(f12,axiom,(
% 0.21/0.47 ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((zero(X1) & zero(X2)) => ! [X14 : list(X2),X15 : X2,X16 : list(X1),X17 : X1,X18 : fun(X1,fun(X2,X0))] : zipwith0(X1,X2,X0,X18,cons(X1,X17,X16),cons(X2,X15,X14)) = cons(X0,aa(X2,X0,aa(X1,fun(X2,X0),X18,X17),X15),zipwith0(X1,X2,X0,X18,X16,X14)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zipwith0_Osimps_I2_J)).
% 0.21/0.47 tff(f1709,plain,(
% 0.21/0.47 spl22_159),
% 0.21/0.47 inference(avatar_split_clause,[],[f414,f1707])).
% 0.21/0.47 tff(f1707,plain,(
% 0.21/0.47 spl22_159 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X2,X1))] : (zipwith0(X0,X2,X1,X5,cons(X0,X4,X3),nil(X2)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2)),zipwith0(X0,X2,X1,X5,X3,nil(X2))) | ~zero(X0) | ~zero(X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_159])])).
% 0.21/0.47 tff(f414,plain,(
% 0.21/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X2,X1))] : (zipwith0(X0,X2,X1,X5,cons(X0,X4,X3),nil(X2)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2)),zipwith0(X0,X2,X1,X5,X3,nil(X2))) | ~zero(X0) | ~zero(X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f255])).
% 0.21/0.47 tff(f255,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X2,X1))] : zipwith0(X0,X2,X1,X5,cons(X0,X4,X3),nil(X2)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2)),zipwith0(X0,X2,X1,X5,X3,nil(X2))) | ~zero(X0) | ~zero(X2))),
% 0.21/0.47 inference(flattening,[],[f254])).
% 0.21/0.47 tff(f254,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X2,X1))] : zipwith0(X0,X2,X1,X5,cons(X0,X4,X3),nil(X2)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2)),zipwith0(X0,X2,X1,X5,X3,nil(X2))) | (~zero(X0) | ~zero(X2)))),
% 0.21/0.47 inference(ennf_transformation,[],[f195])).
% 0.21/0.47 tff(f195,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((zero(X0) & zero(X2)) => ! [X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X2,X1))] : zipwith0(X0,X2,X1,X5,cons(X0,X4,X3),nil(X2)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),zero_zero(X2)),zipwith0(X0,X2,X1,X5,X3,nil(X2))))),
% 0.21/0.47 inference(rectify,[],[f38])).
% 0.21/0.47 tff(f38,axiom,(
% 0.21/0.47 ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((zero(X1) & zero(X2)) => ! [X16 : list(X1),X17 : X1,X18 : fun(X1,fun(X2,X0))] : zipwith0(X1,X2,X0,X18,cons(X1,X17,X16),nil(X2)) = cons(X0,aa(X2,X0,aa(X1,fun(X2,X0),X18,X17),zero_zero(X2)),zipwith0(X1,X2,X0,X18,X16,nil(X2))))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zipwith0_Osimps_I3_J)).
% 0.21/0.47 tff(f1705,plain,(
% 0.21/0.47 spl22_158),
% 0.21/0.47 inference(avatar_split_clause,[],[f413,f1703])).
% 0.21/0.47 tff(f1703,plain,(
% 0.21/0.47 spl22_158 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : list(X2),X4 : X2,X5 : fun(X0,fun(X2,X1))] : (zipwith0(X0,X2,X1,X5,nil(X0),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4),zipwith0(X0,X2,X1,X5,nil(X0),X3)) | ~zero(X0) | ~zero(X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_158])])).
% 0.21/0.47 tff(f413,plain,(
% 0.21/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : list(X2),X4 : X2,X5 : fun(X0,fun(X2,X1))] : (zipwith0(X0,X2,X1,X5,nil(X0),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4),zipwith0(X0,X2,X1,X5,nil(X0),X3)) | ~zero(X0) | ~zero(X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f253])).
% 0.21/0.47 tff(f253,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : list(X2),X4 : X2,X5 : fun(X0,fun(X2,X1))] : zipwith0(X0,X2,X1,X5,nil(X0),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4),zipwith0(X0,X2,X1,X5,nil(X0),X3)) | ~zero(X0) | ~zero(X2))),
% 0.21/0.47 inference(flattening,[],[f252])).
% 0.21/0.47 tff(f252,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : list(X2),X4 : X2,X5 : fun(X0,fun(X2,X1))] : zipwith0(X0,X2,X1,X5,nil(X0),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4),zipwith0(X0,X2,X1,X5,nil(X0),X3)) | (~zero(X0) | ~zero(X2)))),
% 0.21/0.47 inference(ennf_transformation,[],[f194])).
% 0.21/0.47 tff(f194,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((zero(X0) & zero(X2)) => ! [X3 : list(X2),X4 : X2,X5 : fun(X0,fun(X2,X1))] : zipwith0(X0,X2,X1,X5,nil(X0),cons(X2,X4,X3)) = cons(X1,aa(X2,X1,aa(X0,fun(X2,X1),X5,zero_zero(X0)),X4),zipwith0(X0,X2,X1,X5,nil(X0),X3)))),
% 0.21/0.47 inference(rectify,[],[f39])).
% 0.21/0.47 tff(f39,axiom,(
% 0.21/0.47 ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((zero(X1) & zero(X2)) => ! [X14 : list(X2),X15 : X2,X18 : fun(X1,fun(X2,X0))] : zipwith0(X1,X2,X0,X18,nil(X1),cons(X2,X15,X14)) = cons(X0,aa(X2,X0,aa(X1,fun(X2,X0),X18,zero_zero(X1)),X15),zipwith0(X1,X2,X0,X18,nil(X1),X14)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zipwith0_Osimps_I4_J)).
% 0.21/0.47 tff(f1670,plain,(
% 0.21/0.47 spl22_157),
% 0.21/0.47 inference(avatar_split_clause,[],[f465,f1668])).
% 0.21/0.47 tff(f1668,plain,(
% 0.21/0.47 spl22_157 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : fun(X1,fun(list(X1),fun(X0,X0))),X5 : X0,X2 : list(X1)] : list_rec(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_157])])).
% 0.21/0.47 tff(f465,plain,(
% 0.21/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,fun(list(X1),fun(X0,X0))),X5 : X0] : (list_rec(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f222])).
% 0.21/0.47 tff(f222,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,fun(list(X1),fun(X0,X0))),X5 : X0] : list_rec(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X4,X3),X2),list_rec(X0,X1,X5,X4,X2))),
% 0.21/0.47 inference(rectify,[],[f10])).
% 0.21/0.47 tff(f10,axiom,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X6 : list(X1),X7 : X1,X10 : fun(X1,fun(list(X1),fun(X0,X0))),X11 : X0] : list_rec(X0,X1,X11,X10,cons(X1,X7,X6)) = aa(X0,X0,aa(list(X1),fun(X0,X0),aa(X1,fun(list(X1),fun(X0,X0)),X10,X7),X6),list_rec(X0,X1,X11,X10,X6))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_list_Orecs_I2_J)).
% 0.21/0.47 tff(f1644,plain,(
% 0.21/0.47 spl22_156),
% 0.21/0.47 inference(avatar_split_clause,[],[f506,f1642])).
% 0.21/0.47 tff(f1642,plain,(
% 0.21/0.47 spl22_156 <=> ! [X0 : $tType,X2 : list(X0),X1 : fun(list(X0),bool)] : (~pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0)))) | pp(aa(list(X0),bool,X1,X2)) | pp(aa(list(X0),bool,X1,sK15(X0,X1))) | nil(X0) = X2)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_156])])).
% 0.21/0.47 tff(f506,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X1 : fun(list(X0),bool)] : (~pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0)))) | pp(aa(list(X0),bool,X1,X2)) | pp(aa(list(X0),bool,X1,sK15(X0,X1))) | nil(X0) = X2) )),
% 0.21/0.47 inference(forward_demodulation,[],[f408,f367])).
% 0.21/0.47 tff(f408,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X1 : fun(list(X0),bool)] : (pp(aa(list(X0),bool,X1,X2)) | pp(aa(list(X0),bool,X1,sK15(X0,X1))) | ~pp(aa(list(X0),bool,X1,cons(X0,sK16(X0,X1),nil(X0)))) | nil(X0) = X2) )),
% 0.21/0.47 inference(cnf_transformation,[],[f284])).
% 0.21/0.47 tff(f1640,plain,(
% 0.21/0.47 spl22_155),
% 0.21/0.47 inference(avatar_split_clause,[],[f439,f1638])).
% 0.21/0.47 tff(f1638,plain,(
% 0.21/0.47 spl22_155 <=> ! [X2 : $tType,X0 : list(X2),X3 : X2,X1 : fun(X2,bool)] : (sP1(X2,X0,X1,X3) | ~pp(aa(X2,bool,X1,X3)) | ~list_all(X2,combs(X2,bool,bool,combb(bool,fun(bool,bool),X2,fdisj,combb(bool,bool,X2,fNot,X1)),fequal(X2,X3)),X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_155])])).
% 0.21/0.47 tff(f439,plain,(
% 0.21/0.47 ( ! [X2 : $tType,X3 : X2,X0 : list(X2),X1 : fun(X2,bool)] : (sP1(X2,X0,X1,X3) | ~pp(aa(X2,bool,X1,X3)) | ~list_all(X2,combs(X2,bool,bool,combb(bool,fun(bool,bool),X2,fdisj,combb(bool,bool,X2,fNot,X1)),fequal(X2,X3)),X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f301])).
% 0.21/0.47 tff(f301,plain,(
% 0.21/0.47 ! [X0 : list(X2),X1 : fun(X2,bool),X2 : $tType,X3 : X2] : ((sP1(X2,X0,X1,X3) | (~list_ex1(X2,X1,X0) & ~pp(aa(X2,bool,X1,X3))) | (~list_all(X2,combs(X2,bool,bool,combb(bool,fun(bool,bool),X2,fdisj,combb(bool,bool,X2,fNot,X1)),fequal(X2,X3)),X0) & pp(aa(X2,bool,X1,X3)))) & (((list_ex1(X2,X1,X0) | pp(aa(X2,bool,X1,X3))) & (list_all(X2,combs(X2,bool,bool,combb(bool,fun(bool,bool),X2,fdisj,combb(bool,bool,X2,fNot,X1)),fequal(X2,X3)),X0) | ~pp(aa(X2,bool,X1,X3)))) | ~sP1(X2,X0,X1,X3)))),
% 0.21/0.47 inference(rectify,[],[f300])).
% 0.21/0.47 tff(f300,plain,(
% 0.21/0.47 ! [X1 : list(X0),X3 : fun(X0,bool),X0 : $tType,X2 : X0] : ((sP1(X0,X1,X3,X2) | (~list_ex1(X0,X3,X1) & ~pp(aa(X0,bool,X3,X2))) | (~list_all(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combb(bool,bool,X0,fNot,X3)),fequal(X0,X2)),X1) & pp(aa(X0,bool,X3,X2)))) & (((list_ex1(X0,X3,X1) | pp(aa(X0,bool,X3,X2))) & (list_all(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combb(bool,bool,X0,fNot,X3)),fequal(X0,X2)),X1) | ~pp(aa(X0,bool,X3,X2)))) | ~sP1(X0,X1,X3,X2)))),
% 0.21/0.47 inference(flattening,[],[f299])).
% 0.21/0.47 tff(f299,plain,(
% 0.21/0.47 ! [X1 : list(X0),X3 : fun(X0,bool),X0 : $tType,X2 : X0] : ((sP1(X0,X1,X3,X2) | ((~list_ex1(X0,X3,X1) & ~pp(aa(X0,bool,X3,X2))) | (~list_all(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combb(bool,bool,X0,fNot,X3)),fequal(X0,X2)),X1) & pp(aa(X0,bool,X3,X2))))) & (((list_ex1(X0,X3,X1) | pp(aa(X0,bool,X3,X2))) & (list_all(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combb(bool,bool,X0,fNot,X3)),fequal(X0,X2)),X1) | ~pp(aa(X0,bool,X3,X2)))) | ~sP1(X0,X1,X3,X2)))),
% 0.21/0.47 inference(nnf_transformation,[],[f262])).
% 0.21/0.47 tff(f262,plain,(
% 0.21/0.47 ! [X1 : list(X0),X3 : fun(X0,bool),X0 : $tType,X2 : X0] : (sP1(X0,X1,X3,X2) <=> ((list_ex1(X0,X3,X1) | pp(aa(X0,bool,X3,X2))) & (list_all(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combb(bool,bool,X0,fNot,X3)),fequal(X0,X2)),X1) | ~pp(aa(X0,bool,X3,X2)))))),
% 0.21/0.47 introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])])).
% 0.21/0.47 tff(f1636,plain,(
% 0.21/0.47 spl22_154),
% 0.21/0.47 inference(avatar_split_clause,[],[f436,f1634])).
% 0.21/0.47 tff(f1634,plain,(
% 0.21/0.47 spl22_154 <=> ! [X2 : $tType,X0 : list(X2),X3 : X2,X1 : fun(X2,bool)] : (list_all(X2,combs(X2,bool,bool,combb(bool,fun(bool,bool),X2,fdisj,combb(bool,bool,X2,fNot,X1)),fequal(X2,X3)),X0) | ~pp(aa(X2,bool,X1,X3)) | ~sP1(X2,X0,X1,X3))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_154])])).
% 0.21/0.47 tff(f436,plain,(
% 0.21/0.47 ( ! [X2 : $tType,X3 : X2,X0 : list(X2),X1 : fun(X2,bool)] : (list_all(X2,combs(X2,bool,bool,combb(bool,fun(bool,bool),X2,fdisj,combb(bool,bool,X2,fNot,X1)),fequal(X2,X3)),X0) | ~pp(aa(X2,bool,X1,X3)) | ~sP1(X2,X0,X1,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f301])).
% 0.21/0.47 tff(f1516,plain,(
% 0.21/0.47 spl22_153),
% 0.21/0.47 inference(avatar_split_clause,[],[f507,f1514])).
% 0.21/0.47 tff(f1514,plain,(
% 0.21/0.47 spl22_153 <=> ! [X0 : $tType,X2 : list(X0),X1 : fun(list(X0),bool)] : (~pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0)))) | pp(aa(list(X0),bool,X1,X2)) | nil(X0) != sK15(X0,X1) | nil(X0) = X2)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_153])])).
% 0.21/0.47 tff(f507,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X1 : fun(list(X0),bool)] : (~pp(aa(list(X0),bool,X1,insert(X0,sK16(X0,X1),nil(X0)))) | pp(aa(list(X0),bool,X1,X2)) | nil(X0) != sK15(X0,X1) | nil(X0) = X2) )),
% 0.21/0.47 inference(forward_demodulation,[],[f407,f367])).
% 0.21/0.47 tff(f407,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X1 : fun(list(X0),bool)] : (pp(aa(list(X0),bool,X1,X2)) | nil(X0) != sK15(X0,X1) | ~pp(aa(list(X0),bool,X1,cons(X0,sK16(X0,X1),nil(X0)))) | nil(X0) = X2) )),
% 0.21/0.47 inference(cnf_transformation,[],[f284])).
% 0.21/0.47 tff(f1512,plain,(
% 0.21/0.47 spl22_152),
% 0.21/0.47 inference(avatar_split_clause,[],[f477,f1510])).
% 0.21/0.47 tff(f1510,plain,(
% 0.21/0.47 spl22_152 <=> ! [X0 : $tType,X5 : fun(int,fun(int,fun(list(int),X0))),X6 : fun(int,fun(list(int),X0)),X4 : fun(int,fun(int,fun(list(int),X0))),X3 : int,X2 : int,X1 : list(int)] : aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X4,X3),X2),X1) = atom_rec(X0,X6,X5,X4,nDvd(X3,X2,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_152])])).
% 0.21/0.47 tff(f477,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : int,X3 : int,X1 : list(int),X6 : fun(int,fun(list(int),X0)),X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(int,fun(list(int),X0)))] : (aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X4,X3),X2),X1) = atom_rec(X0,X6,X5,X4,nDvd(X3,X2,X1))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f228])).
% 0.21/0.47 tff(f228,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(int),X2 : int,X3 : int,X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(int,fun(list(int),X0))),X6 : fun(int,fun(list(int),X0))] : aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X4,X3),X2),X1) = atom_rec(X0,X6,X5,X4,nDvd(X3,X2,X1))),
% 0.21/0.47 inference(rectify,[],[f84])).
% 0.21/0.47 tff(f84,axiom,(
% 0.21/0.47 ! [X0 : $tType,X6 : list(int),X47 : int,X48 : int,X23 : fun(int,fun(int,fun(list(int),X0))),X10 : fun(int,fun(int,fun(list(int),X0))),X11 : fun(int,fun(list(int),X0))] : aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X23,X48),X47),X6) = atom_rec(X0,X11,X10,X23,nDvd(X48,X47,X6))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_atom_Orecs_I3_J)).
% 0.21/0.47 tff(f1508,plain,(
% 0.21/0.47 spl22_151),
% 0.21/0.47 inference(avatar_split_clause,[],[f476,f1506])).
% 0.21/0.47 tff(f1506,plain,(
% 0.21/0.47 spl22_151 <=> ! [X0 : $tType,X5 : fun(int,fun(int,fun(list(int),X0))),X6 : fun(int,fun(list(int),X0)),X4 : fun(int,fun(int,fun(list(int),X0))),X3 : int,X2 : int,X1 : list(int)] : aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1) = atom_rec(X0,X6,X5,X4,dvd(X3,X2,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_151])])).
% 0.21/0.47 tff(f476,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : int,X3 : int,X1 : list(int),X6 : fun(int,fun(list(int),X0)),X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(int,fun(list(int),X0)))] : (aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1) = atom_rec(X0,X6,X5,X4,dvd(X3,X2,X1))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f227])).
% 0.21/0.47 tff(f227,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(int),X2 : int,X3 : int,X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(int,fun(list(int),X0))),X6 : fun(int,fun(list(int),X0))] : aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1) = atom_rec(X0,X6,X5,X4,dvd(X3,X2,X1))),
% 0.21/0.47 inference(rectify,[],[f85])).
% 0.21/0.47 tff(f85,axiom,(
% 0.21/0.47 ! [X0 : $tType,X6 : list(int),X47 : int,X48 : int,X23 : fun(int,fun(int,fun(list(int),X0))),X10 : fun(int,fun(int,fun(list(int),X0))),X11 : fun(int,fun(list(int),X0))] : aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X10,X48),X47),X6) = atom_rec(X0,X11,X10,X23,dvd(X48,X47,X6))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_atom_Orecs_I2_J)).
% 0.21/0.47 tff(f1504,plain,(
% 0.21/0.47 spl22_150),
% 0.21/0.47 inference(avatar_split_clause,[],[f475,f1502])).
% 0.21/0.47 tff(f1502,plain,(
% 0.21/0.47 spl22_150 <=> ! [X0 : $tType,X5 : fun(int,fun(int,fun(list(int),X0))),X6 : fun(int,fun(list(int),X0)),X4 : fun(int,fun(int,fun(list(int),X0))),X3 : int,X2 : int,X1 : list(int)] : atom_case(X0,X6,X5,X4,nDvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X4,X3),X2),X1)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_150])])).
% 0.21/0.47 tff(f475,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : int,X3 : int,X1 : list(int),X6 : fun(int,fun(list(int),X0)),X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(int,fun(list(int),X0)))] : (atom_case(X0,X6,X5,X4,nDvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X4,X3),X2),X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f226])).
% 0.21/0.47 tff(f226,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(int),X2 : int,X3 : int,X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(int,fun(list(int),X0))),X6 : fun(int,fun(list(int),X0))] : atom_case(X0,X6,X5,X4,nDvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X4,X3),X2),X1)),
% 0.21/0.47 inference(rectify,[],[f77])).
% 0.21/0.47 tff(f77,axiom,(
% 0.21/0.47 ! [X0 : $tType,X6 : list(int),X47 : int,X48 : int,X23 : fun(int,fun(int,fun(list(int),X0))),X10 : fun(int,fun(int,fun(list(int),X0))),X11 : fun(int,fun(list(int),X0))] : atom_case(X0,X11,X10,X23,nDvd(X48,X47,X6)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X23,X48),X47),X6)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_atom_Osimps_I12_J)).
% 0.21/0.47 tff(f1500,plain,(
% 0.21/0.47 spl22_149),
% 0.21/0.47 inference(avatar_split_clause,[],[f474,f1498])).
% 0.21/0.47 tff(f1498,plain,(
% 0.21/0.47 spl22_149 <=> ! [X0 : $tType,X3 : int,X4 : fun(int,fun(int,fun(list(int),X0))),X6 : fun(int,fun(list(int),X0)),X5 : fun(int,fun(int,fun(list(int),X0))),X2 : int,X1 : list(int)] : atom_case(X0,X6,X5,X4,dvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_149])])).
% 0.21/0.47 tff(f474,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : int,X3 : int,X1 : list(int),X6 : fun(int,fun(list(int),X0)),X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(int,fun(list(int),X0)))] : (atom_case(X0,X6,X5,X4,dvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f225])).
% 0.21/0.47 tff(f225,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(int),X2 : int,X3 : int,X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(int,fun(list(int),X0))),X6 : fun(int,fun(list(int),X0))] : atom_case(X0,X6,X5,X4,dvd(X3,X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X5,X3),X2),X1)),
% 0.21/0.47 inference(rectify,[],[f76])).
% 0.21/0.47 tff(f76,axiom,(
% 0.21/0.47 ! [X0 : $tType,X6 : list(int),X47 : int,X48 : int,X23 : fun(int,fun(int,fun(list(int),X0))),X10 : fun(int,fun(int,fun(list(int),X0))),X11 : fun(int,fun(list(int),X0))] : atom_case(X0,X11,X10,X23,dvd(X48,X47,X6)) = aa(list(int),X0,aa(int,fun(list(int),X0),aa(int,fun(int,fun(list(int),X0)),X10,X48),X47),X6)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_atom_Osimps_I11_J)).
% 0.21/0.47 tff(f1496,plain,(
% 0.21/0.47 spl22_148),
% 0.21/0.47 inference(avatar_split_clause,[],[f441,f1494])).
% 0.21/0.47 tff(f1494,plain,(
% 0.21/0.47 spl22_148 <=> ! [X2 : $tType,X0 : list(X2),X3 : X2,X1 : fun(X2,bool)] : (sP1(X2,X0,X1,X3) | ~list_ex1(X2,X1,X0) | ~list_all(X2,combs(X2,bool,bool,combb(bool,fun(bool,bool),X2,fdisj,combb(bool,bool,X2,fNot,X1)),fequal(X2,X3)),X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_148])])).
% 0.21/0.47 tff(f441,plain,(
% 0.21/0.47 ( ! [X2 : $tType,X3 : X2,X0 : list(X2),X1 : fun(X2,bool)] : (sP1(X2,X0,X1,X3) | ~list_ex1(X2,X1,X0) | ~list_all(X2,combs(X2,bool,bool,combb(bool,fun(bool,bool),X2,fdisj,combb(bool,bool,X2,fNot,X1)),fequal(X2,X3)),X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f301])).
% 0.21/0.47 tff(f1456,plain,(
% 0.21/0.47 spl22_147),
% 0.21/0.47 inference(avatar_split_clause,[],[f464,f1454])).
% 0.21/0.47 tff(f1454,plain,(
% 0.21/0.47 spl22_147 <=> ! [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))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_147])])).
% 0.21/0.47 tff(f464,plain,(
% 0.21/0.47 ( ! [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))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f221])).
% 0.21/0.47 tff(f221,plain,(
% 0.21/0.47 ! [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))),
% 0.21/0.47 inference(rectify,[],[f114])).
% 0.21/0.47 tff(f114,axiom,(
% 0.21/0.47 ! [X2 : $tType,X1 : $tType,X0 : $tType,X64 : X0,X65 : fun(X0,X1),X63 : fun(X0,fun(X1,X2))] : aa(X0,X2,combs(X0,X1,X2,X63,X65),X64) = aa(X1,X2,aa(X0,fun(X1,X2),X63,X64),aa(X0,X1,X65,X64))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U)).
% 0.21/0.47 tff(f1440,plain,(
% 0.21/0.47 spl22_146),
% 0.21/0.47 inference(avatar_split_clause,[],[f354,f1438])).
% 0.21/0.47 tff(f1438,plain,(
% 0.21/0.47 spl22_146 <=> ! [X0 : atom] : (nDvd(sK2(X0),sK3(X0),sK4(X0)) = X0 | dvd(sK5(X0),sK6(X0),sK7(X0)) = X0 | c_PresArith_Oatom_OLe(sK8(X0),sK9(X0)) = X0)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_146])])).
% 0.21/0.47 tff(f354,plain,(
% 0.21/0.47 ( ! [X0 : atom] : (nDvd(sK2(X0),sK3(X0),sK4(X0)) = X0 | dvd(sK5(X0),sK6(X0),sK7(X0)) = X0 | c_PresArith_Oatom_OLe(sK8(X0),sK9(X0)) = X0) )),
% 0.21/0.47 inference(cnf_transformation,[],[f271])).
% 0.21/0.47 tff(f271,plain,(
% 0.21/0.47 ! [X0 : atom] : (nDvd(sK2(X0),sK3(X0),sK4(X0)) = X0 | dvd(sK5(X0),sK6(X0),sK7(X0)) = X0 | c_PresArith_Oatom_OLe(sK8(X0),sK9(X0)) = X0)),
% 0.21/0.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9])],[f267,f270,f269,f268])).
% 0.21/0.47 tff(f268,plain,(
% 0.21/0.47 ! [X0 : atom] : (? [X1 : int,X2 : int,X3 : list(int)] : nDvd(X1,X2,X3) = X0 => nDvd(sK2(X0),sK3(X0),sK4(X0)) = X0)),
% 0.21/0.47 introduced(choice_axiom,[])).
% 0.21/0.47 tff(f269,plain,(
% 0.21/0.47 ! [X0 : atom] : (? [X4 : int,X5 : int,X6 : list(int)] : dvd(X4,X5,X6) = X0 => dvd(sK5(X0),sK6(X0),sK7(X0)) = X0)),
% 0.21/0.47 introduced(choice_axiom,[])).
% 0.21/0.47 tff(f270,plain,(
% 0.21/0.47 ! [X0 : atom] : (? [X7 : int,X8 : list(int)] : c_PresArith_Oatom_OLe(X7,X8) = X0 => c_PresArith_Oatom_OLe(sK8(X0),sK9(X0)) = X0)),
% 0.21/0.47 introduced(choice_axiom,[])).
% 0.21/0.47 tff(f267,plain,(
% 0.21/0.47 ! [X0 : atom] : (? [X1 : int,X2 : int,X3 : list(int)] : nDvd(X1,X2,X3) = X0 | ? [X4 : int,X5 : int,X6 : list(int)] : dvd(X4,X5,X6) = X0 | ? [X7 : int,X8 : list(int)] : c_PresArith_Oatom_OLe(X7,X8) = X0)),
% 0.21/0.47 inference(rectify,[],[f244])).
% 0.21/0.47 tff(f244,plain,(
% 0.21/0.47 ! [X0 : atom] : (? [X6 : int,X7 : int,X8 : list(int)] : nDvd(X6,X7,X8) = X0 | ? [X3 : int,X4 : int,X5 : list(int)] : dvd(X3,X4,X5) = X0 | ? [X1 : int,X2 : list(int)] : c_PresArith_Oatom_OLe(X1,X2) = X0)),
% 0.21/0.47 inference(flattening,[],[f243])).
% 0.21/0.47 tff(f243,plain,(
% 0.21/0.47 ! [X0 : atom] : ((? [X6 : int,X7 : int,X8 : list(int)] : nDvd(X6,X7,X8) = X0 | ? [X3 : int,X4 : int,X5 : list(int)] : dvd(X3,X4,X5) = X0) | ? [X1 : int,X2 : list(int)] : c_PresArith_Oatom_OLe(X1,X2) = X0)),
% 0.21/0.47 inference(ennf_transformation,[],[f143])).
% 0.21/0.47 tff(f143,plain,(
% 0.21/0.47 ! [X0 : atom] : (! [X1 : int,X2 : list(int)] : c_PresArith_Oatom_OLe(X1,X2) != X0 => (! [X3 : int,X4 : int,X5 : list(int)] : dvd(X3,X4,X5) != X0 => ~! [X6 : int,X7 : int,X8 : list(int)] : nDvd(X6,X7,X8) != X0))),
% 0.21/0.47 inference(rectify,[],[f79])).
% 0.21/0.47 tff(f79,axiom,(
% 0.21/0.47 ! [X13 : atom] : (! [X54 : int,X37 : list(int)] : c_PresArith_Oatom_OLe(X54,X37) != X13 => (! [X55 : int,X56 : int,X37 : list(int)] : dvd(X55,X56,X37) != X13 => ~! [X55 : int,X56 : int,X37 : list(int)] : nDvd(X55,X56,X37) != X13))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_atom_Oexhaust)).
% 0.21/0.47 tff(f1412,plain,(
% 0.21/0.47 spl22_145),
% 0.21/0.47 inference(avatar_split_clause,[],[f463,f1410])).
% 0.21/0.47 tff(f1410,plain,(
% 0.21/0.47 spl22_145 <=> ! [X1 : $tType,X0 : $tType,X5 : X0,X4 : fun(X1,fun(list(X1),X0)),X3 : X1,X2 : list(X1)] : list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_145])])).
% 0.21/0.47 tff(f463,plain,(
% 0.21/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,fun(list(X1),X0)),X5 : X0] : (list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f220])).
% 0.21/0.47 tff(f220,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : list(X1),X3 : X1,X4 : fun(X1,fun(list(X1),X0)),X5 : X0] : list_case(X0,X1,X5,X4,cons(X1,X3,X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2)),
% 0.21/0.47 inference(rectify,[],[f8])).
% 0.21/0.47 tff(f8,axiom,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X6 : list(X1),X7 : X1,X10 : fun(X1,fun(list(X1),X0)),X11 : X0] : list_case(X0,X1,X11,X10,cons(X1,X7,X6)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X10,X7),X6)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_list_Osimps_I5_J)).
% 0.21/0.47 tff(f1353,plain,(
% 0.21/0.47 spl22_144),
% 0.21/0.47 inference(avatar_split_clause,[],[f462,f1351])).
% 0.21/0.47 tff(f1351,plain,(
% 0.21/0.47 spl22_144 <=> ! [X0 : $tType,X5 : fun(int,fun(list(int),X0)),X4 : fun(int,fun(int,fun(list(int),X0))),X3 : fun(int,fun(int,fun(list(int),X0))),X2 : int,X1 : list(int)] : aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) = atom_rec(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_144])])).
% 0.21/0.47 tff(f462,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : int,X3 : fun(int,fun(int,fun(list(int),X0))),X1 : list(int),X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(list(int),X0))] : (aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) = atom_rec(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f219])).
% 0.21/0.47 tff(f219,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(int),X2 : int,X3 : fun(int,fun(int,fun(list(int),X0))),X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(list(int),X0))] : aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1) = atom_rec(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1))),
% 0.21/0.47 inference(rectify,[],[f86])).
% 0.21/0.47 tff(f86,axiom,(
% 0.21/0.47 ! [X0 : $tType,X6 : list(int),X22 : int,X23 : fun(int,fun(int,fun(list(int),X0))),X10 : fun(int,fun(int,fun(list(int),X0))),X11 : fun(int,fun(list(int),X0))] : aa(list(int),X0,aa(int,fun(list(int),X0),X11,X22),X6) = atom_rec(X0,X11,X10,X23,c_PresArith_Oatom_OLe(X22,X6))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_atom_Orecs_I1_J)).
% 0.21/0.47 tff(f1349,plain,(
% 0.21/0.47 spl22_143),
% 0.21/0.47 inference(avatar_split_clause,[],[f461,f1347])).
% 0.21/0.47 tff(f461,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : int,X3 : fun(int,fun(int,fun(list(int),X0))),X1 : list(int),X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(list(int),X0))] : (atom_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f218])).
% 0.21/0.47 tff(f218,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(int),X2 : int,X3 : fun(int,fun(int,fun(list(int),X0))),X4 : fun(int,fun(int,fun(list(int),X0))),X5 : fun(int,fun(list(int),X0))] : atom_case(X0,X5,X4,X3,c_PresArith_Oatom_OLe(X2,X1)) = aa(list(int),X0,aa(int,fun(list(int),X0),X5,X2),X1)),
% 0.21/0.47 inference(rectify,[],[f17])).
% 0.21/0.47 tff(f17,axiom,(
% 0.21/0.47 ! [X0 : $tType,X6 : list(int),X22 : int,X23 : fun(int,fun(int,fun(list(int),X0))),X10 : fun(int,fun(int,fun(list(int),X0))),X11 : fun(int,fun(list(int),X0))] : atom_case(X0,X11,X10,X23,c_PresArith_Oatom_OLe(X22,X6)) = aa(list(int),X0,aa(int,fun(list(int),X0),X11,X22),X6)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_atom_Osimps_I10_J)).
% 0.21/0.47 tff(f1345,plain,(
% 0.21/0.47 spl22_142),
% 0.21/0.47 inference(avatar_split_clause,[],[f454,f1343])).
% 0.21/0.47 tff(f1343,plain,(
% 0.21/0.47 spl22_142 <=> ! [X0 : $tType,X4 : X0,X3 : list(X0),X2 : X0,X1 : list(X0)] : splice(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,X4,cons(X0,X2,splice(X0,X3,X1)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_142])])).
% 0.21/0.47 tff(f454,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (splice(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,X4,cons(X0,X2,splice(X0,X3,X1)))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f213])).
% 0.21/0.47 tff(f213,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : splice(X0,cons(X0,X4,X3),cons(X0,X2,X1)) = cons(X0,X4,cons(X0,X2,splice(X0,X3,X1)))),
% 0.21/0.47 inference(rectify,[],[f9])).
% 0.21/0.47 tff(f9,axiom,(
% 0.21/0.47 ! [X0 : $tType,X12 : list(X0),X13 : X0,X9 : list(X0),X8 : X0] : splice(X0,cons(X0,X8,X9),cons(X0,X13,X12)) = cons(X0,X8,cons(X0,X13,splice(X0,X9,X12)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_splice_Osimps_I3_J)).
% 0.21/0.47 tff(f1338,plain,(
% 0.21/0.47 spl22_141),
% 0.21/0.47 inference(avatar_split_clause,[],[f423,f1336])).
% 0.21/0.47 tff(f1336,plain,(
% 0.21/0.47 spl22_141 <=> ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (sP0(X0,X1,X2) | cons(X0,sK20(X0,X1,X2),sK21(X0,X1,X2)) = X1 | ~listMem(X0,X2,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_141])])).
% 0.21/0.47 tff(f423,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (sP0(X0,X1,X2) | cons(X0,sK20(X0,X1,X2),sK21(X0,X1,X2)) = X1 | ~listMem(X0,X2,X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f295])).
% 0.21/0.47 tff(f295,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : ((listMem(X0,X2,X1) | (~sP0(X0,X1,X2) & ! [X3 : X0,X4 : list(X0)] : (cons(X0,X3,X4) != X1 | X2 != X3))) & (sP0(X0,X1,X2) | (cons(X0,sK20(X0,X1,X2),sK21(X0,X1,X2)) = X1 & sK20(X0,X1,X2) = X2) | ~listMem(X0,X2,X1)))),
% 0.21/0.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f293,f294])).
% 0.21/0.47 tff(f294,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : (? [X5 : X0,X6 : list(X0)] : (cons(X0,X5,X6) = X1 & X2 = X5) => (cons(X0,sK20(X0,X1,X2),sK21(X0,X1,X2)) = X1 & sK20(X0,X1,X2) = X2))),
% 0.21/0.47 introduced(choice_axiom,[])).
% 0.21/0.47 tff(f293,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : ((listMem(X0,X2,X1) | (~sP0(X0,X1,X2) & ! [X3 : X0,X4 : list(X0)] : (cons(X0,X3,X4) != X1 | X2 != X3))) & (sP0(X0,X1,X2) | ? [X5 : X0,X6 : list(X0)] : (cons(X0,X5,X6) = X1 & X2 = X5) | ~listMem(X0,X2,X1)))),
% 0.21/0.47 inference(rectify,[],[f292])).
% 0.21/0.47 tff(f292,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : ((listMem(X0,X2,X1) | (~sP0(X0,X1,X2) & ! [X6 : X0,X7 : list(X0)] : (cons(X0,X6,X7) != X1 | X2 != X6))) & (sP0(X0,X1,X2) | ? [X6 : X0,X7 : list(X0)] : (cons(X0,X6,X7) = X1 & X2 = X6) | ~listMem(X0,X2,X1)))),
% 0.21/0.47 inference(flattening,[],[f291])).
% 0.21/0.47 tff(f291,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : ((listMem(X0,X2,X1) | (~sP0(X0,X1,X2) & ! [X6 : X0,X7 : list(X0)] : (cons(X0,X6,X7) != X1 | X2 != X6))) & ((sP0(X0,X1,X2) | ? [X6 : X0,X7 : list(X0)] : (cons(X0,X6,X7) = X1 & X2 = X6)) | ~listMem(X0,X2,X1)))),
% 0.21/0.47 inference(nnf_transformation,[],[f261])).
% 0.21/0.47 tff(f261,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : (listMem(X0,X2,X1) <=> (sP0(X0,X1,X2) | ? [X6 : X0,X7 : list(X0)] : (cons(X0,X6,X7) = X1 & X2 = X6)))),
% 0.21/0.47 inference(definition_folding,[],[f198,f260])).
% 0.21/0.47 tff(f260,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : (sP0(X0,X1,X2) <=> ? [X3 : X0,X4 : list(X0),X5 : X0] : (listMem(X0,X3,X4) & cons(X0,X5,X4) = X1 & X2 = X3))),
% 0.21/0.47 introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])).
% 0.21/0.47 tff(f198,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : (listMem(X0,X2,X1) <=> (? [X3 : X0,X4 : list(X0),X5 : X0] : (listMem(X0,X3,X4) & cons(X0,X5,X4) = X1 & X2 = X3) | ? [X6 : X0,X7 : list(X0)] : (cons(X0,X6,X7) = X1 & X2 = X6)))),
% 0.21/0.47 inference(rectify,[],[f20])).
% 0.21/0.47 tff(f20,axiom,(
% 0.21/0.47 ! [X0 : $tType,X26 : list(X0),X27 : X0] : (listMem(X0,X27,X26) <=> (? [X28 : X0,X29 : list(X0),X30 : X0] : (listMem(X0,X28,X29) & cons(X0,X30,X29) = X26 & X27 = X28) | ? [X28 : X0,X29 : list(X0)] : (cons(X0,X28,X29) = X26 & X27 = X28)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_ListMem_Osimps)).
% 0.21/0.47 tff(f1332,plain,(
% 0.21/0.47 spl22_140 | ~spl22_37 | ~spl22_139),
% 0.21/0.47 inference(avatar_split_clause,[],[f1311,f1308,f674,f1330])).
% 0.21/0.47 tff(f1330,plain,(
% 0.21/0.47 spl22_140 <=> ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (~member(nat,atom_size(a),X2) | insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_140])])).
% 0.21/0.47 tff(f1308,plain,(
% 0.21/0.47 spl22_139 <=> ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2) | ~member(nat,zero_zero(nat),X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_139])])).
% 0.21/0.47 tff(f1311,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (~member(nat,atom_size(a),X2) | insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2)) ) | (~spl22_37 | ~spl22_139)),
% 0.21/0.47 inference(forward_demodulation,[],[f1309,f676])).
% 0.21/0.47 tff(f1309,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2) | ~member(nat,zero_zero(nat),X2)) ) | ~spl22_139),
% 0.21/0.47 inference(avatar_component_clause,[],[f1308])).
% 0.21/0.47 tff(f1310,plain,(
% 0.21/0.47 spl22_139),
% 0.21/0.47 inference(avatar_split_clause,[],[f504,f1308])).
% 0.21/0.47 tff(f504,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2) | ~member(nat,zero_zero(nat),X2)) )),
% 0.21/0.47 inference(forward_demodulation,[],[f403,f367])).
% 0.21/0.47 tff(f403,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2) | ~member(nat,zero_zero(nat),X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f246])).
% 0.21/0.47 tff(f246,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0,X2 : fun(nat,bool)] : ((nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2) | member(nat,zero_zero(nat),X2)) & (cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2) | ~member(nat,zero_zero(nat),X2)))),
% 0.21/0.47 inference(ennf_transformation,[],[f188])).
% 0.21/0.47 tff(f188,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0,X2 : fun(nat,bool)] : ((~member(nat,zero_zero(nat),X2) => nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2)) & (member(nat,zero_zero(nat),X2) => cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2)))),
% 0.21/0.47 inference(rectify,[],[f59])).
% 0.21/0.47 tff(f59,axiom,(
% 0.21/0.47 ! [X0 : $tType,X17 : X0,X44 : fun(nat,bool)] : ((~member(nat,zero_zero(nat),X44) => nil(X0) = sublist(X0,cons(X0,X17,nil(X0)),X44)) & (member(nat,zero_zero(nat),X44) => cons(X0,X17,nil(X0)) = sublist(X0,cons(X0,X17,nil(X0)),X44)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_sublist__singleton)).
% 0.21/0.47 tff(f1306,plain,(
% 0.21/0.47 spl22_138),
% 0.21/0.47 inference(avatar_split_clause,[],[f460,f1304])).
% 0.21/0.47 tff(f1304,plain,(
% 0.21/0.47 spl22_138 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X5 : fun(X1,X0),X4 : fun(X2,X1),X3 : X2] : aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_138])])).
% 0.21/0.47 tff(f460,plain,(
% 0.21/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X1,X0)] : (aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f217])).
% 0.21/0.47 tff(f217,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2,X4 : fun(X2,X1),X5 : fun(X1,X0)] : aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3))),
% 0.21/0.47 inference(rectify,[],[f112])).
% 0.21/0.47 tff(f112,axiom,(
% 0.21/0.47 ! [X2 : $tType,X1 : $tType,X0 : $tType,X64 : X0,X65 : fun(X0,X1),X63 : fun(X1,X2)] : aa(X0,X2,combb(X1,X2,X0,X63,X65),X64) = aa(X1,X2,X63,aa(X0,X1,X65,X64))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U)).
% 0.21/0.47 tff(f1302,plain,(
% 0.21/0.47 spl22_137 | ~spl22_37 | ~spl22_135),
% 0.21/0.47 inference(avatar_split_clause,[],[f1286,f1283,f674,f1300])).
% 0.21/0.47 tff(f1300,plain,(
% 0.21/0.47 spl22_137 <=> ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (member(nat,atom_size(a),X2) | nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_137])])).
% 0.21/0.47 tff(f1283,plain,(
% 0.21/0.47 spl22_135 <=> ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2) | member(nat,zero_zero(nat),X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_135])])).
% 0.21/0.47 tff(f1286,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (member(nat,atom_size(a),X2) | nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2)) ) | (~spl22_37 | ~spl22_135)),
% 0.21/0.47 inference(forward_demodulation,[],[f1284,f676])).
% 0.21/0.47 tff(f1284,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2) | member(nat,zero_zero(nat),X2)) ) | ~spl22_135),
% 0.21/0.47 inference(avatar_component_clause,[],[f1283])).
% 0.21/0.47 tff(f1292,plain,(
% 0.21/0.47 spl22_136 | ~spl22_22 | ~spl22_92),
% 0.21/0.47 inference(avatar_split_clause,[],[f1010,f967,f607,f1290])).
% 0.21/0.47 tff(f1290,plain,(
% 0.21/0.47 spl22_136 <=> ! [X0 : $tType,X1 : X0] : ~null(X0,insert(X0,X1,nil(X0)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_136])])).
% 0.21/0.47 tff(f607,plain,(
% 0.21/0.47 spl22_22 <=> ! [X0 : $tType,X2 : X0,X1 : list(X0)] : ~null(X0,cons(X0,X2,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_22])])).
% 0.21/0.47 tff(f967,plain,(
% 0.21/0.47 spl22_92 <=> ! [X0 : $tType,X1 : X0] : insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_92])])).
% 0.21/0.47 tff(f1010,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : X0] : (~null(X0,insert(X0,X1,nil(X0)))) ) | (~spl22_22 | ~spl22_92)),
% 0.21/0.47 inference(superposition,[],[f608,f968])).
% 0.21/0.47 tff(f968,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : X0] : (insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0))) ) | ~spl22_92),
% 0.21/0.47 inference(avatar_component_clause,[],[f967])).
% 0.21/0.47 tff(f608,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (~null(X0,cons(X0,X2,X1))) ) | ~spl22_22),
% 0.21/0.47 inference(avatar_component_clause,[],[f607])).
% 0.21/0.47 tff(f1285,plain,(
% 0.21/0.47 spl22_135),
% 0.21/0.47 inference(avatar_split_clause,[],[f503,f1283])).
% 0.21/0.47 tff(f503,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2) | member(nat,zero_zero(nat),X2)) )),
% 0.21/0.47 inference(forward_demodulation,[],[f404,f367])).
% 0.21/0.47 tff(f404,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2) | member(nat,zero_zero(nat),X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f246])).
% 0.21/0.47 tff(f1281,plain,(
% 0.21/0.47 spl22_134),
% 0.21/0.47 inference(avatar_split_clause,[],[f449,f1279])).
% 0.21/0.47 tff(f1279,plain,(
% 0.21/0.47 spl22_134 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : X0,X1 : list(X0)] : (list_all(X0,X3,cons(X0,X2,X1)) | ~list_all(X0,X3,X1) | ~pp(aa(X0,bool,X3,X2)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_134])])).
% 0.21/0.47 tff(f449,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : list(X0)] : (list_all(X0,X3,cons(X0,X2,X1)) | ~list_all(X0,X3,X1) | ~pp(aa(X0,bool,X3,X2))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f306])).
% 0.21/0.47 tff(f306,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : fun(X0,bool)] : ((list_all(X0,X3,cons(X0,X2,X1)) | ~list_all(X0,X3,X1) | ~pp(aa(X0,bool,X3,X2))) & ((list_all(X0,X3,X1) & pp(aa(X0,bool,X3,X2))) | ~list_all(X0,X3,cons(X0,X2,X1))))),
% 0.21/0.47 inference(flattening,[],[f305])).
% 0.21/0.47 tff(f305,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : fun(X0,bool)] : ((list_all(X0,X3,cons(X0,X2,X1)) | (~list_all(X0,X3,X1) | ~pp(aa(X0,bool,X3,X2)))) & ((list_all(X0,X3,X1) & pp(aa(X0,bool,X3,X2))) | ~list_all(X0,X3,cons(X0,X2,X1))))),
% 0.21/0.47 inference(nnf_transformation,[],[f208])).
% 0.21/0.47 tff(f208,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : fun(X0,bool)] : (list_all(X0,X3,cons(X0,X2,X1)) <=> (list_all(X0,X3,X1) & pp(aa(X0,bool,X3,X2))))),
% 0.21/0.47 inference(rectify,[],[f55])).
% 0.21/0.47 tff(f55,axiom,(
% 0.21/0.47 ! [X0 : $tType,X16 : list(X0),X17 : X0,X38 : fun(X0,bool)] : (list_all(X0,X38,cons(X0,X17,X16)) <=> (list_all(X0,X38,X16) & pp(aa(X0,bool,X38,X17))))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_list__all__simps_I1_J)).
% 0.21/0.47 tff(f1277,plain,(
% 0.21/0.47 spl22_133),
% 0.21/0.47 inference(avatar_split_clause,[],[f419,f1275])).
% 0.21/0.47 tff(f1275,plain,(
% 0.21/0.47 spl22_133 <=> ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (cons(X0,sK19(X0,X1,X2),sK18(X0,X1,X2)) = X1 | ~sP0(X0,X1,X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_133])])).
% 0.21/0.47 tff(f419,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (cons(X0,sK19(X0,X1,X2),sK18(X0,X1,X2)) = X1 | ~sP0(X0,X1,X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f290])).
% 0.21/0.47 tff(f290,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : ((sP0(X0,X1,X2) | ! [X3 : X0,X4 : list(X0),X5 : X0] : (~listMem(X0,X3,X4) | cons(X0,X5,X4) != X1 | X2 != X3)) & ((listMem(X0,sK17(X0,X1,X2),sK18(X0,X1,X2)) & cons(X0,sK19(X0,X1,X2),sK18(X0,X1,X2)) = X1 & sK17(X0,X1,X2) = X2) | ~sP0(X0,X1,X2)))),
% 0.21/0.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f288,f289])).
% 0.21/0.47 tff(f289,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : (? [X6 : X0,X7 : list(X0),X8 : X0] : (listMem(X0,X6,X7) & cons(X0,X8,X7) = X1 & X2 = X6) => (listMem(X0,sK17(X0,X1,X2),sK18(X0,X1,X2)) & cons(X0,sK19(X0,X1,X2),sK18(X0,X1,X2)) = X1 & sK17(X0,X1,X2) = X2))),
% 0.21/0.47 introduced(choice_axiom,[])).
% 0.21/0.47 tff(f288,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : ((sP0(X0,X1,X2) | ! [X3 : X0,X4 : list(X0),X5 : X0] : (~listMem(X0,X3,X4) | cons(X0,X5,X4) != X1 | X2 != X3)) & (? [X6 : X0,X7 : list(X0),X8 : X0] : (listMem(X0,X6,X7) & cons(X0,X8,X7) = X1 & X2 = X6) | ~sP0(X0,X1,X2)))),
% 0.21/0.47 inference(rectify,[],[f287])).
% 0.21/0.47 tff(f287,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : ((sP0(X0,X1,X2) | ! [X3 : X0,X4 : list(X0),X5 : X0] : (~listMem(X0,X3,X4) | cons(X0,X5,X4) != X1 | X2 != X3)) & (? [X3 : X0,X4 : list(X0),X5 : X0] : (listMem(X0,X3,X4) & cons(X0,X5,X4) = X1 & X2 = X3) | ~sP0(X0,X1,X2)))),
% 0.21/0.47 inference(nnf_transformation,[],[f260])).
% 0.21/0.47 tff(f1273,plain,(
% 0.21/0.47 spl22_132),
% 0.21/0.47 inference(avatar_split_clause,[],[f412,f1271])).
% 0.21/0.47 tff(f1271,plain,(
% 0.21/0.47 spl22_132 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : fun(X1,fun(X0,X2))] : (nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) | ~zero(X0) | ~zero(X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_132])])).
% 0.21/0.47 tff(f412,plain,(
% 0.21/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : fun(X1,fun(X0,X2))] : (nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) | ~zero(X0) | ~zero(X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f251])).
% 0.21/0.47 tff(f251,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : fun(X1,fun(X0,X2))] : nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) | ~zero(X0) | ~zero(X1))),
% 0.21/0.47 inference(flattening,[],[f250])).
% 0.21/0.47 tff(f250,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (! [X3 : fun(X1,fun(X0,X2))] : nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) | (~zero(X0) | ~zero(X1)))),
% 0.21/0.47 inference(ennf_transformation,[],[f193])).
% 0.21/0.47 tff(f193,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((zero(X0) & zero(X1)) => ! [X3 : fun(X1,fun(X0,X2))] : nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)))),
% 0.21/0.47 inference(rectify,[],[f23])).
% 0.21/0.47 tff(f23,axiom,(
% 0.21/0.47 ! [X2 : $tType,X1 : $tType,X0 : $tType] : ((zero(X2) & zero(X1)) => ! [X18 : fun(X1,fun(X2,X0))] : nil(X0) = zipwith0(X1,X2,X0,X18,nil(X1),nil(X2)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_zipwith0_Osimps_I1_J)).
% 0.21/0.47 tff(f1207,plain,(
% 0.21/0.47 spl22_131 | ~spl22_7 | ~spl22_37 | ~spl22_57),
% 0.21/0.47 inference(avatar_split_clause,[],[f826,f768,f674,f539,f1205])).
% 0.21/0.47 tff(f1205,plain,(
% 0.21/0.47 spl22_131 <=> ! [X0 : nat] : div_mod(nat,X0,atom_size(a)) = X0),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_131])])).
% 0.21/0.47 tff(f539,plain,(
% 0.21/0.47 spl22_7 <=> semiring_div(nat)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_7])])).
% 0.21/0.47 tff(f768,plain,(
% 0.21/0.47 spl22_57 <=> ! [X0 : $tType,X1 : X0] : (div_mod(X0,X1,zero_zero(X0)) = X1 | ~semiring_div(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_57])])).
% 0.21/0.47 tff(f826,plain,(
% 0.21/0.47 ( ! [X0 : nat] : (div_mod(nat,X0,atom_size(a)) = X0) ) | (~spl22_7 | ~spl22_37 | ~spl22_57)),
% 0.21/0.47 inference(forward_demodulation,[],[f824,f676])).
% 0.21/0.47 tff(f824,plain,(
% 0.21/0.47 ( ! [X0 : nat] : (div_mod(nat,X0,zero_zero(nat)) = X0) ) | (~spl22_7 | ~spl22_57)),
% 0.21/0.47 inference(resolution,[],[f769,f541])).
% 0.21/0.47 tff(f541,plain,(
% 0.21/0.47 semiring_div(nat) | ~spl22_7),
% 0.21/0.47 inference(avatar_component_clause,[],[f539])).
% 0.21/0.47 tff(f769,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : X0] : (~semiring_div(X0) | div_mod(X0,X1,zero_zero(X0)) = X1) ) | ~spl22_57),
% 0.21/0.47 inference(avatar_component_clause,[],[f768])).
% 0.21/0.47 tff(f1203,plain,(
% 0.21/0.47 spl22_130),
% 0.21/0.47 inference(avatar_split_clause,[],[f402,f1201])).
% 0.21/0.47 tff(f1201,plain,(
% 0.21/0.47 spl22_130 <=> ! [X2 : int,X0 : list(int),X1 : int] : list_case(int,int,zero_zero(int),combk(int,list(int)),X0) = hd_coeff(nDvd(X2,X1,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_130])])).
% 0.21/0.47 tff(f402,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (list_case(int,int,zero_zero(int),combk(int,list(int)),X0) = hd_coeff(nDvd(X2,X1,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f187])).
% 0.21/0.47 tff(f187,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int] : list_case(int,int,zero_zero(int),combk(int,list(int)),X0) = hd_coeff(nDvd(X2,X1,X0))),
% 0.21/0.47 inference(rectify,[],[f57])).
% 0.21/0.47 tff(f57,axiom,(
% 0.21/0.47 ! [X39 : list(int),X40 : int,X43 : int] : list_case(int,int,zero_zero(int),combk(int,list(int)),X39) = hd_coeff(nDvd(X43,X40,X39))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_hd__coeff_Osimps_I3_J)).
% 0.21/0.47 tff(f1199,plain,(
% 0.21/0.47 spl22_129),
% 0.21/0.47 inference(avatar_split_clause,[],[f401,f1197])).
% 0.21/0.47 tff(f1197,plain,(
% 0.21/0.47 spl22_129 <=> ! [X2 : int,X0 : list(int),X1 : int] : list_case(int,int,zero_zero(int),combk(int,list(int)),X0) = hd_coeff(dvd(X2,X1,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_129])])).
% 0.21/0.47 tff(f401,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (list_case(int,int,zero_zero(int),combk(int,list(int)),X0) = hd_coeff(dvd(X2,X1,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f186])).
% 0.21/0.47 tff(f186,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int] : list_case(int,int,zero_zero(int),combk(int,list(int)),X0) = hd_coeff(dvd(X2,X1,X0))),
% 0.21/0.47 inference(rectify,[],[f58])).
% 0.21/0.47 tff(f58,axiom,(
% 0.21/0.47 ! [X39 : list(int),X40 : int,X43 : int] : list_case(int,int,zero_zero(int),combk(int,list(int)),X39) = hd_coeff(dvd(X43,X40,X39))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_hd__coeff_Osimps_I2_J)).
% 0.21/0.47 tff(f1195,plain,(
% 0.21/0.47 spl22_128),
% 0.21/0.47 inference(avatar_split_clause,[],[f375,f1193])).
% 0.21/0.47 tff(f1193,plain,(
% 0.21/0.47 spl22_128 <=> ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK12(X0,X1),sK13(X0,X1)) = X1 | nil(X0) = X1)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_128])])).
% 0.21/0.47 tff(f375,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK12(X0,X1),sK13(X0,X1)) = X1 | nil(X0) = X1) )),
% 0.21/0.47 inference(cnf_transformation,[],[f278])).
% 0.21/0.47 tff(f278,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : ((nil(X0) != X1 | ! [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) != X1) & (cons(X0,sK12(X0,X1),sK13(X0,X1)) = X1 | nil(X0) = X1))),
% 0.21/0.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f276,f277])).
% 0.21/0.47 tff(f277,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : (? [X4 : X0,X5 : list(X0)] : cons(X0,X4,X5) = X1 => cons(X0,sK12(X0,X1),sK13(X0,X1)) = X1)),
% 0.21/0.47 introduced(choice_axiom,[])).
% 0.21/0.47 tff(f276,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : ((nil(X0) != X1 | ! [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) != X1) & (? [X4 : X0,X5 : list(X0)] : cons(X0,X4,X5) = X1 | nil(X0) = X1))),
% 0.21/0.47 inference(rectify,[],[f275])).
% 0.21/0.47 tff(f275,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : ((nil(X0) != X1 | ! [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) != X1) & (? [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) = X1 | nil(X0) = X1))),
% 0.21/0.47 inference(nnf_transformation,[],[f163])).
% 0.21/0.47 tff(f163,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : (nil(X0) != X1 <=> ? [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) = X1)),
% 0.21/0.47 inference(rectify,[],[f34])).
% 0.21/0.47 tff(f34,axiom,(
% 0.21/0.47 ! [X0 : $tType,X16 : list(X0)] : (nil(X0) != X16 <=> ? [X30 : X0,X35 : list(X0)] : cons(X0,X30,X35) = X16)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_neq__Nil__conv)).
% 0.21/0.47 tff(f1191,plain,(
% 0.21/0.47 spl22_127),
% 0.21/0.47 inference(avatar_split_clause,[],[f372,f1189])).
% 0.21/0.47 tff(f1189,plain,(
% 0.21/0.47 spl22_127 <=> ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK10(X0,X1),sK11(X0,X1)) = X1 | nil(X0) = X1)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_127])])).
% 0.21/0.47 tff(f372,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK10(X0,X1),sK11(X0,X1)) = X1 | nil(X0) = X1) )),
% 0.21/0.47 inference(cnf_transformation,[],[f273])).
% 0.21/0.47 tff(f273,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK10(X0,X1),sK11(X0,X1)) = X1 | nil(X0) = X1)),
% 0.21/0.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f245,f272])).
% 0.21/0.47 tff(f272,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : (? [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) = X1 => cons(X0,sK10(X0,X1),sK11(X0,X1)) = X1)),
% 0.21/0.47 introduced(choice_axiom,[])).
% 0.21/0.47 tff(f245,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : (? [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) = X1 | nil(X0) = X1)),
% 0.21/0.47 inference(ennf_transformation,[],[f161])).
% 0.21/0.47 tff(f161,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : (nil(X0) != X1 => ~! [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) != X1)),
% 0.21/0.47 inference(rectify,[],[f35])).
% 0.21/0.47 tff(f35,axiom,(
% 0.21/0.47 ! [X0 : $tType,X13 : list(X0)] : (nil(X0) != X13 => ~! [X36 : X0,X37 : list(X0)] : cons(X0,X36,X37) != X13)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_list_Oexhaust)).
% 0.21/0.47 tff(f1187,plain,(
% 0.21/0.47 spl22_126),
% 0.21/0.47 inference(avatar_split_clause,[],[f371,f1185])).
% 0.21/0.47 tff(f1185,plain,(
% 0.21/0.47 spl22_126 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_126])])).
% 0.21/0.47 tff(f371,plain,(
% 0.21/0.47 ( ! [X0 : bool,X1 : bool] : (pp(X0) | pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f160])).
% 0.21/0.47 tff(f160,plain,(
% 0.21/0.47 ! [X0 : bool,X1 : bool] : (pp(X0) | pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)))),
% 0.21/0.47 inference(rectify,[],[f119])).
% 0.21/0.47 tff(f119,axiom,(
% 0.21/0.47 ! [X65 : bool,X63 : bool] : (pp(X65) | pp(X63) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X63),X65)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U)).
% 0.21/0.47 tff(f1183,plain,(
% 0.21/0.47 spl22_125),
% 0.21/0.47 inference(avatar_split_clause,[],[f353,f1181])).
% 0.21/0.47 tff(f1181,plain,(
% 0.21/0.47 spl22_125 <=> ! [X0 : atom] : (zero_zero(int) != divisor(decr_Z(X0)) | zero_zero(int) = divisor(X0) | zero_zero(int) != hd_coeff(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_125])])).
% 0.21/0.47 tff(f353,plain,(
% 0.21/0.47 ( ! [X0 : atom] : (zero_zero(int) != divisor(decr_Z(X0)) | zero_zero(int) = divisor(X0) | zero_zero(int) != hd_coeff(X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f242])).
% 0.21/0.47 tff(f242,plain,(
% 0.21/0.47 ! [X0 : atom] : (zero_zero(int) != divisor(decr_Z(X0)) | zero_zero(int) = divisor(X0) | zero_zero(int) != hd_coeff(X0))),
% 0.21/0.47 inference(flattening,[],[f241])).
% 0.21/0.47 tff(f241,plain,(
% 0.21/0.47 ! [X0 : atom] : ((zero_zero(int) != divisor(decr_Z(X0)) | zero_zero(int) = divisor(X0)) | zero_zero(int) != hd_coeff(X0))),
% 0.21/0.47 inference(ennf_transformation,[],[f142])).
% 0.21/0.47 tff(f142,plain,(
% 0.21/0.47 ! [X0 : atom] : (zero_zero(int) = hd_coeff(X0) => (zero_zero(int) != divisor(X0) => zero_zero(int) != divisor(decr_Z(X0))))),
% 0.21/0.47 inference(rectify,[],[f81])).
% 0.21/0.47 tff(f81,axiom,(
% 0.21/0.47 ! [X25 : atom] : (zero_zero(int) = hd_coeff(X25) => (zero_zero(int) != divisor(X25) => zero_zero(int) != divisor(decr_Z(X25))))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Z_Oanormal__decr)).
% 0.21/0.47 tff(f1169,plain,(
% 0.21/0.47 spl22_124 | ~spl22_8 | ~spl22_57),
% 0.21/0.47 inference(avatar_split_clause,[],[f825,f768,f544,f1167])).
% 0.21/0.47 tff(f1167,plain,(
% 0.21/0.47 spl22_124 <=> ! [X0 : int] : div_mod(int,X0,zero_zero(int)) = X0),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_124])])).
% 0.21/0.47 tff(f544,plain,(
% 0.21/0.47 spl22_8 <=> semiring_div(int)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_8])])).
% 0.21/0.47 tff(f825,plain,(
% 0.21/0.47 ( ! [X0 : int] : (div_mod(int,X0,zero_zero(int)) = X0) ) | (~spl22_8 | ~spl22_57)),
% 0.21/0.47 inference(resolution,[],[f769,f546])).
% 0.21/0.47 tff(f546,plain,(
% 0.21/0.47 semiring_div(int) | ~spl22_8),
% 0.21/0.47 inference(avatar_component_clause,[],[f544])).
% 0.21/0.47 tff(f1159,plain,(
% 0.21/0.47 spl22_123),
% 0.21/0.47 inference(avatar_split_clause,[],[f440,f1157])).
% 0.21/0.47 tff(f1157,plain,(
% 0.21/0.47 spl22_123 <=> ! [X2 : $tType,X0 : list(X2),X3 : X2,X1 : fun(X2,bool)] : (sP1(X2,X0,X1,X3) | ~list_ex1(X2,X1,X0) | pp(aa(X2,bool,X1,X3)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_123])])).
% 0.21/0.47 tff(f440,plain,(
% 0.21/0.47 ( ! [X2 : $tType,X3 : X2,X0 : list(X2),X1 : fun(X2,bool)] : (sP1(X2,X0,X1,X3) | ~list_ex1(X2,X1,X0) | pp(aa(X2,bool,X1,X3))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f301])).
% 0.21/0.47 tff(f1155,plain,(
% 0.21/0.47 spl22_122),
% 0.21/0.47 inference(avatar_split_clause,[],[f437,f1153])).
% 0.21/0.47 tff(f1153,plain,(
% 0.21/0.47 spl22_122 <=> ! [X2 : $tType,X0 : list(X2),X3 : X2,X1 : fun(X2,bool)] : (list_ex1(X2,X1,X0) | pp(aa(X2,bool,X1,X3)) | ~sP1(X2,X0,X1,X3))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_122])])).
% 0.21/0.47 tff(f437,plain,(
% 0.21/0.47 ( ! [X2 : $tType,X3 : X2,X0 : list(X2),X1 : fun(X2,bool)] : (list_ex1(X2,X1,X0) | pp(aa(X2,bool,X1,X3)) | ~sP1(X2,X0,X1,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f301])).
% 0.21/0.47 tff(f1151,plain,(
% 0.21/0.47 spl22_121),
% 0.21/0.47 inference(avatar_split_clause,[],[f431,f1149])).
% 0.21/0.47 tff(f431,plain,(
% 0.21/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : (aa(X0,X1,aa(X1,fun(X0,X1),combk(X1,X0),X3),X2) = X3) )),
% 0.21/0.47 inference(cnf_transformation,[],[f203])).
% 0.21/0.47 tff(f203,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1] : aa(X0,X1,aa(X1,fun(X0,X1),combk(X1,X0),X3),X2) = X3),
% 0.21/0.47 inference(rectify,[],[f113])).
% 0.21/0.47 tff(f113,axiom,(
% 0.21/0.47 ! [X1 : $tType,X0 : $tType,X65 : X1,X63 : X0] : aa(X1,X0,aa(X0,fun(X1,X0),combk(X0,X1),X63),X65) = X63),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U)).
% 0.21/0.47 tff(f1147,plain,(
% 0.21/0.47 spl22_120),
% 0.21/0.47 inference(avatar_split_clause,[],[f411,f1145])).
% 0.21/0.47 tff(f1145,plain,(
% 0.21/0.47 spl22_120 <=> ! [X2 : atom,X0 : list(int),X1 : int] : (i_Z(X2,cons(int,X1,X0)) | ~i_Z(decr_Z(X2),X0) | zero_zero(int) != hd_coeff(X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_120])])).
% 0.21/0.47 tff(f411,plain,(
% 0.21/0.47 ( ! [X2 : atom,X0 : list(int),X1 : int] : (i_Z(X2,cons(int,X1,X0)) | ~i_Z(decr_Z(X2),X0) | zero_zero(int) != hd_coeff(X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f285])).
% 0.21/0.47 tff(f285,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : atom] : (((i_Z(X2,cons(int,X1,X0)) | ~i_Z(decr_Z(X2),X0)) & (i_Z(decr_Z(X2),X0) | ~i_Z(X2,cons(int,X1,X0)))) | zero_zero(int) != hd_coeff(X2))),
% 0.21/0.47 inference(nnf_transformation,[],[f249])).
% 0.21/0.47 tff(f249,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : atom] : ((i_Z(X2,cons(int,X1,X0)) <=> i_Z(decr_Z(X2),X0)) | zero_zero(int) != hd_coeff(X2))),
% 0.21/0.47 inference(ennf_transformation,[],[f192])).
% 0.21/0.47 tff(f192,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : atom] : (zero_zero(int) = hd_coeff(X2) => (i_Z(X2,cons(int,X1,X0)) <=> i_Z(decr_Z(X2),X0)))),
% 0.21/0.47 inference(rectify,[],[f78])).
% 0.21/0.47 tff(f78,axiom,(
% 0.21/0.47 ! [X16 : list(int),X17 : int,X7 : atom] : (zero_zero(int) = hd_coeff(X7) => (i_Z(X7,cons(int,X17,X16)) <=> i_Z(decr_Z(X7),X16)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Z_Onot__dep__decr)).
% 0.21/0.47 tff(f1143,plain,(
% 0.21/0.47 spl22_119),
% 0.21/0.47 inference(avatar_split_clause,[],[f410,f1141])).
% 0.21/0.47 tff(f1141,plain,(
% 0.21/0.47 spl22_119 <=> ! [X2 : atom,X0 : list(int),X1 : int] : (i_Z(decr_Z(X2),X0) | ~i_Z(X2,cons(int,X1,X0)) | zero_zero(int) != hd_coeff(X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_119])])).
% 0.21/0.47 tff(f410,plain,(
% 0.21/0.47 ( ! [X2 : atom,X0 : list(int),X1 : int] : (i_Z(decr_Z(X2),X0) | ~i_Z(X2,cons(int,X1,X0)) | zero_zero(int) != hd_coeff(X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f285])).
% 0.21/0.47 tff(f1139,plain,(
% 0.21/0.47 spl22_118),
% 0.21/0.47 inference(avatar_split_clause,[],[f368,f1137])).
% 0.21/0.47 tff(f1137,plain,(
% 0.21/0.47 spl22_118 <=> ! [X0 : list(int),X1 : int] : hd_coeff(c_PresArith_Oatom_OLe(X1,X0)) = list_case(int,int,zero_zero(int),combk(int,list(int)),X0)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_118])])).
% 0.21/0.47 tff(f368,plain,(
% 0.21/0.47 ( ! [X0 : list(int),X1 : int] : (hd_coeff(c_PresArith_Oatom_OLe(X1,X0)) = list_case(int,int,zero_zero(int),combk(int,list(int)),X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f157])).
% 0.21/0.47 tff(f157,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int] : hd_coeff(c_PresArith_Oatom_OLe(X1,X0)) = list_case(int,int,zero_zero(int),combk(int,list(int)),X0)),
% 0.21/0.47 inference(rectify,[],[f45])).
% 0.21/0.47 tff(f45,axiom,(
% 0.21/0.47 ! [X39 : list(int),X40 : int] : hd_coeff(c_PresArith_Oatom_OLe(X40,X39)) = list_case(int,int,zero_zero(int),combk(int,list(int)),X39)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_hd__coeff_Osimps_I1_J)).
% 0.21/0.47 tff(f1132,plain,(
% 0.21/0.47 spl22_117 | ~spl22_7 | ~spl22_37 | ~spl22_56),
% 0.21/0.47 inference(avatar_split_clause,[],[f823,f764,f674,f539,f1130])).
% 0.21/0.47 tff(f1130,plain,(
% 0.21/0.47 spl22_117 <=> ! [X0 : nat] : atom_size(a) = div_mod(nat,X0,X0)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_117])])).
% 0.21/0.47 tff(f764,plain,(
% 0.21/0.47 spl22_56 <=> ! [X0 : $tType,X1 : X0] : (zero_zero(X0) = div_mod(X0,X1,X1) | ~semiring_div(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_56])])).
% 0.21/0.47 tff(f823,plain,(
% 0.21/0.47 ( ! [X0 : nat] : (atom_size(a) = div_mod(nat,X0,X0)) ) | (~spl22_7 | ~spl22_37 | ~spl22_56)),
% 0.21/0.47 inference(forward_demodulation,[],[f821,f676])).
% 0.21/0.47 tff(f821,plain,(
% 0.21/0.47 ( ! [X0 : nat] : (zero_zero(nat) = div_mod(nat,X0,X0)) ) | (~spl22_7 | ~spl22_56)),
% 0.21/0.47 inference(resolution,[],[f765,f541])).
% 0.21/0.47 tff(f765,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : X0] : (~semiring_div(X0) | zero_zero(X0) = div_mod(X0,X1,X1)) ) | ~spl22_56),
% 0.21/0.47 inference(avatar_component_clause,[],[f764])).
% 0.21/0.47 tff(f1115,plain,(
% 0.21/0.47 spl22_116),
% 0.21/0.47 inference(avatar_split_clause,[],[f456,f1113])).
% 0.21/0.47 tff(f1113,plain,(
% 0.21/0.47 spl22_116 <=> ! [X0 : $tType,X2 : X0,X4 : X0,X3 : list(X0),X1 : list(X0)] : (X1 = X3 | cons(X0,X2,X1) != cons(X0,X4,X3))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_116])])).
% 0.21/0.47 tff(f456,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (X1 = X3 | cons(X0,X2,X1) != cons(X0,X4,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f308])).
% 0.21/0.47 tff(f308,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : ((cons(X0,X2,X1) = cons(X0,X4,X3) | X1 != X3 | X2 != X4) & ((X1 = X3 & X2 = X4) | cons(X0,X2,X1) != cons(X0,X4,X3)))),
% 0.21/0.47 inference(flattening,[],[f307])).
% 0.21/0.47 tff(f307,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : ((cons(X0,X2,X1) = cons(X0,X4,X3) | (X1 != X3 | X2 != X4)) & ((X1 = X3 & X2 = X4) | cons(X0,X2,X1) != cons(X0,X4,X3)))),
% 0.21/0.47 inference(nnf_transformation,[],[f214])).
% 0.21/0.47 tff(f214,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : (cons(X0,X2,X1) = cons(X0,X4,X3) <=> (X1 = X3 & X2 = X4))),
% 0.21/0.47 inference(rectify,[],[f3])).
% 0.21/0.47 tff(f3,axiom,(
% 0.21/0.47 ! [X0 : $tType,X4 : list(X0),X5 : X0,X6 : list(X0),X7 : X0] : (cons(X0,X7,X6) = cons(X0,X5,X4) <=> (X4 = X6 & X5 = X7))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_list_Oinject)).
% 0.21/0.47 tff(f1111,plain,(
% 0.21/0.47 spl22_115),
% 0.21/0.47 inference(avatar_split_clause,[],[f444,f1109])).
% 0.21/0.47 tff(f1109,plain,(
% 0.21/0.47 spl22_115 <=> ! [X0 : $tType,X3 : X0,X2 : list(X0),X1 : X0] : (member1(X0,X2,X1) | X1 = X3 | ~member1(X0,cons(X0,X3,X2),X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_115])])).
% 0.21/0.47 tff(f444,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X3 : X0,X1 : X0] : (member1(X0,X2,X1) | X1 = X3 | ~member1(X0,cons(X0,X3,X2),X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f304])).
% 0.21/0.47 tff(f304,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0,X2 : list(X0),X3 : X0] : ((member1(X0,cons(X0,X3,X2),X1) | (~member1(X0,X2,X1) & X1 != X3)) & (member1(X0,X2,X1) | X1 = X3 | ~member1(X0,cons(X0,X3,X2),X1)))),
% 0.21/0.47 inference(flattening,[],[f303])).
% 0.21/0.47 tff(f303,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0,X2 : list(X0),X3 : X0] : ((member1(X0,cons(X0,X3,X2),X1) | (~member1(X0,X2,X1) & X1 != X3)) & ((member1(X0,X2,X1) | X1 = X3) | ~member1(X0,cons(X0,X3,X2),X1)))),
% 0.21/0.47 inference(nnf_transformation,[],[f207])).
% 0.21/0.47 tff(f207,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0,X2 : list(X0),X3 : X0] : (member1(X0,cons(X0,X3,X2),X1) <=> (member1(X0,X2,X1) | X1 = X3))),
% 0.21/0.47 inference(rectify,[],[f21])).
% 0.21/0.47 tff(f21,axiom,(
% 0.21/0.47 ! [X0 : $tType,X15 : X0,X16 : list(X0),X17 : X0] : (member1(X0,cons(X0,X17,X16),X15) <=> (member1(X0,X16,X15) | X15 = X17))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_member__rec_I1_J)).
% 0.21/0.47 tff(f1107,plain,(
% 0.21/0.47 spl22_114),
% 0.21/0.47 inference(avatar_split_clause,[],[f430,f1105])).
% 0.21/0.47 tff(f1105,plain,(
% 0.21/0.47 spl22_114 <=> ! [X0 : int,X3 : int,X2 : list(int),X1 : int] : nDvd(X1,X0,nil(int)) = asubst(X3,X2,nDvd(X1,X0,nil(int)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_114])])).
% 0.21/0.47 tff(f430,plain,(
% 0.21/0.47 ( ! [X2 : list(int),X3 : int,X0 : int,X1 : int] : (nDvd(X1,X0,nil(int)) = asubst(X3,X2,nDvd(X1,X0,nil(int)))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f202])).
% 0.21/0.47 tff(f202,plain,(
% 0.21/0.47 ! [X0 : int,X1 : int,X2 : list(int),X3 : int] : nDvd(X1,X0,nil(int)) = asubst(X3,X2,nDvd(X1,X0,nil(int)))),
% 0.21/0.47 inference(rectify,[],[f93])).
% 0.21/0.47 tff(f93,axiom,(
% 0.21/0.47 ! [X31 : int,X32 : int,X60 : list(int),X61 : int] : nDvd(X32,X31,nil(int)) = asubst(X61,X60,nDvd(X32,X31,nil(int)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_asubst_Osimps_I6_J)).
% 0.21/0.47 tff(f1103,plain,(
% 0.21/0.47 spl22_113),
% 0.21/0.47 inference(avatar_split_clause,[],[f422,f1101])).
% 0.21/0.47 tff(f1101,plain,(
% 0.21/0.47 spl22_113 <=> ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (sP0(X0,X1,X2) | sK20(X0,X1,X2) = X2 | ~listMem(X0,X2,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_113])])).
% 0.21/0.47 tff(f422,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (sP0(X0,X1,X2) | sK20(X0,X1,X2) = X2 | ~listMem(X0,X2,X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f295])).
% 0.21/0.47 tff(f1099,plain,(
% 0.21/0.47 spl22_112),
% 0.21/0.47 inference(avatar_split_clause,[],[f420,f1097])).
% 0.21/0.47 tff(f1097,plain,(
% 0.21/0.47 spl22_112 <=> ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (listMem(X0,sK17(X0,X1,X2),sK18(X0,X1,X2)) | ~sP0(X0,X1,X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_112])])).
% 0.21/0.47 tff(f420,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (listMem(X0,sK17(X0,X1,X2),sK18(X0,X1,X2)) | ~sP0(X0,X1,X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f290])).
% 0.21/0.47 tff(f1095,plain,(
% 0.21/0.47 spl22_111),
% 0.21/0.47 inference(avatar_split_clause,[],[f370,f1093])).
% 0.21/0.47 tff(f1093,plain,(
% 0.21/0.47 spl22_111 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | ~pp(X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_111])])).
% 0.21/0.47 tff(f370,plain,(
% 0.21/0.47 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | ~pp(X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f159])).
% 0.21/0.47 tff(f159,plain,(
% 0.21/0.47 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X1),X0)) | ~pp(X1))),
% 0.21/0.47 inference(rectify,[],[f117])).
% 0.21/0.47 tff(f117,axiom,(
% 0.21/0.47 ! [X65 : bool,X63 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X63),X65)) | ~pp(X63))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U)).
% 0.21/0.47 tff(f1091,plain,(
% 0.21/0.47 spl22_110),
% 0.21/0.47 inference(avatar_split_clause,[],[f369,f1089])).
% 0.21/0.47 tff(f1089,plain,(
% 0.21/0.47 spl22_110 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | ~pp(X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_110])])).
% 0.21/0.47 tff(f369,plain,(
% 0.21/0.47 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | ~pp(X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f158])).
% 0.21/0.47 tff(f158,plain,(
% 0.21/0.47 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X0),X1)) | ~pp(X1))),
% 0.21/0.47 inference(rectify,[],[f118])).
% 0.21/0.47 tff(f118,axiom,(
% 0.21/0.47 ! [X63 : bool,X65 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,X63),X65)) | ~pp(X65))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U)).
% 0.21/0.47 tff(f1087,plain,(
% 0.21/0.47 spl22_109),
% 0.21/0.47 inference(avatar_split_clause,[],[f350,f1085])).
% 0.21/0.47 tff(f1085,plain,(
% 0.21/0.47 spl22_109 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) | ~semiring_div(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_109])])).
% 0.21/0.47 tff(f350,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) | ~semiring_div(X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f239])).
% 0.21/0.47 tff(f239,plain,(
% 0.21/0.47 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1) | ~semiring_div(X0))),
% 0.21/0.47 inference(ennf_transformation,[],[f140])).
% 0.21/0.47 tff(f140,plain,(
% 0.21/0.47 ! [X0 : $tType] : (semiring_div(X0) => ! [X1 : X0,X2 : X0] : div_mod(X0,X2,X1) = div_mod(X0,div_mod(X0,X2,X1),X1))),
% 0.21/0.47 inference(rectify,[],[f18])).
% 0.21/0.47 tff(f18,axiom,(
% 0.21/0.47 ! [X0 : $tType] : (semiring_div(X0) => ! [X24 : X0,X25 : X0] : div_mod(X0,X25,X24) = div_mod(X0,div_mod(X0,X25,X24),X24))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_mod__mod__trivial)).
% 0.21/0.47 tff(f1072,plain,(
% 0.21/0.47 spl22_108),
% 0.21/0.47 inference(avatar_split_clause,[],[f472,f1070])).
% 0.21/0.47 tff(f1070,plain,(
% 0.21/0.47 spl22_108 <=> ! [X2 : int,X4 : int,X0 : list(int),X5 : int,X3 : list(int),X1 : int] : (X0 = X3 | nDvd(X2,X1,X0) != nDvd(X5,X4,X3))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_108])])).
% 0.21/0.47 tff(f472,plain,(
% 0.21/0.47 ( ! [X2 : int,X3 : list(int),X0 : list(int),X1 : int,X4 : int,X5 : int] : (X0 = X3 | nDvd(X2,X1,X0) != nDvd(X5,X4,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f312])).
% 0.21/0.47 tff(f312,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int,X3 : list(int),X4 : int,X5 : int] : ((nDvd(X2,X1,X0) = nDvd(X5,X4,X3) | X0 != X3 | X1 != X4 | X2 != X5) & ((X0 = X3 & X1 = X4 & X2 = X5) | nDvd(X2,X1,X0) != nDvd(X5,X4,X3)))),
% 0.21/0.47 inference(flattening,[],[f311])).
% 0.21/0.47 tff(f311,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int,X3 : list(int),X4 : int,X5 : int] : ((nDvd(X2,X1,X0) = nDvd(X5,X4,X3) | (X0 != X3 | X1 != X4 | X2 != X5)) & ((X0 = X3 & X1 = X4 & X2 = X5) | nDvd(X2,X1,X0) != nDvd(X5,X4,X3)))),
% 0.21/0.47 inference(nnf_transformation,[],[f224])).
% 0.21/0.47 tff(f224,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int,X3 : list(int),X4 : int,X5 : int] : (nDvd(X2,X1,X0) = nDvd(X5,X4,X3) <=> (X0 = X3 & X1 = X4 & X2 = X5))),
% 0.21/0.47 inference(rectify,[],[f61])).
% 0.21/0.47 tff(f61,axiom,(
% 0.21/0.47 ! [X4 : list(int),X45 : int,X46 : int,X6 : list(int),X47 : int,X48 : int] : (nDvd(X48,X47,X6) = nDvd(X46,X45,X4) <=> (X4 = X6 & X45 = X47 & X46 = X48))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_atom_Osimps_I3_J)).
% 0.21/0.47 tff(f1068,plain,(
% 0.21/0.47 spl22_107),
% 0.21/0.47 inference(avatar_split_clause,[],[f468,f1066])).
% 0.21/0.47 tff(f1066,plain,(
% 0.21/0.47 spl22_107 <=> ! [X2 : int,X4 : int,X0 : list(int),X5 : int,X3 : list(int),X1 : int] : (X0 = X3 | dvd(X2,X1,X0) != dvd(X5,X4,X3))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_107])])).
% 0.21/0.47 tff(f468,plain,(
% 0.21/0.47 ( ! [X2 : int,X3 : list(int),X0 : list(int),X1 : int,X4 : int,X5 : int] : (X0 = X3 | dvd(X2,X1,X0) != dvd(X5,X4,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f310])).
% 0.21/0.47 tff(f310,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int,X3 : list(int),X4 : int,X5 : int] : ((dvd(X2,X1,X0) = dvd(X5,X4,X3) | X0 != X3 | X1 != X4 | X2 != X5) & ((X0 = X3 & X1 = X4 & X2 = X5) | dvd(X2,X1,X0) != dvd(X5,X4,X3)))),
% 0.21/0.47 inference(flattening,[],[f309])).
% 0.21/0.47 tff(f309,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int,X3 : list(int),X4 : int,X5 : int] : ((dvd(X2,X1,X0) = dvd(X5,X4,X3) | (X0 != X3 | X1 != X4 | X2 != X5)) & ((X0 = X3 & X1 = X4 & X2 = X5) | dvd(X2,X1,X0) != dvd(X5,X4,X3)))),
% 0.21/0.47 inference(nnf_transformation,[],[f223])).
% 0.21/0.47 tff(f223,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int,X3 : list(int),X4 : int,X5 : int] : (dvd(X2,X1,X0) = dvd(X5,X4,X3) <=> (X0 = X3 & X1 = X4 & X2 = X5))),
% 0.21/0.47 inference(rectify,[],[f60])).
% 0.21/0.47 tff(f60,axiom,(
% 0.21/0.47 ! [X4 : list(int),X45 : int,X46 : int,X6 : list(int),X47 : int,X48 : int] : (dvd(X48,X47,X6) = dvd(X46,X45,X4) <=> (X4 = X6 & X45 = X47 & X46 = X48))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_atom_Osimps_I2_J)).
% 0.21/0.47 tff(f1064,plain,(
% 0.21/0.47 spl22_106),
% 0.21/0.47 inference(avatar_split_clause,[],[f455,f1062])).
% 0.21/0.47 tff(f1062,plain,(
% 0.21/0.47 spl22_106 <=> ! [X0 : $tType,X4 : X0,X3 : list(X0),X2 : X0,X1 : list(X0)] : (X2 = X4 | cons(X0,X2,X1) != cons(X0,X4,X3))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_106])])).
% 0.21/0.47 tff(f455,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (X2 = X4 | cons(X0,X2,X1) != cons(X0,X4,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f308])).
% 0.21/0.47 tff(f1060,plain,(
% 0.21/0.47 spl22_105),
% 0.21/0.47 inference(avatar_split_clause,[],[f447,f1058])).
% 0.21/0.47 tff(f1058,plain,(
% 0.21/0.47 spl22_105 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : X0,X1 : list(X0)] : (pp(aa(X0,bool,X3,X2)) | ~list_all(X0,X3,cons(X0,X2,X1)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_105])])).
% 0.21/0.47 tff(f447,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : list(X0)] : (pp(aa(X0,bool,X3,X2)) | ~list_all(X0,X3,cons(X0,X2,X1))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f306])).
% 0.21/0.47 tff(f1056,plain,(
% 0.21/0.47 spl22_104),
% 0.21/0.47 inference(avatar_split_clause,[],[f399,f1054])).
% 0.21/0.47 tff(f1054,plain,(
% 0.21/0.47 spl22_104 <=> ! [X2 : int,X0 : int,X1 : int] : nDvd(X1,X0,nil(int)) = hd_coeff1(X2,nDvd(X1,X0,nil(int)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_104])])).
% 0.21/0.47 tff(f399,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : int,X1 : int] : (nDvd(X1,X0,nil(int)) = hd_coeff1(X2,nDvd(X1,X0,nil(int)))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f184])).
% 0.21/0.47 tff(f184,plain,(
% 0.21/0.47 ! [X0 : int,X1 : int,X2 : int] : nDvd(X1,X0,nil(int)) = hd_coeff1(X2,nDvd(X1,X0,nil(int)))),
% 0.21/0.47 inference(rectify,[],[f94])).
% 0.21/0.47 tff(f94,axiom,(
% 0.21/0.47 ! [X31 : int,X32 : int,X62 : int] : nDvd(X32,X31,nil(int)) = hd_coeff1(X62,nDvd(X32,X31,nil(int)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_hd__coeff1_Osimps_I6_J)).
% 0.21/0.47 tff(f1052,plain,(
% 0.21/0.47 spl22_103),
% 0.21/0.47 inference(avatar_split_clause,[],[f398,f1050])).
% 0.21/0.47 tff(f1050,plain,(
% 0.21/0.47 spl22_103 <=> ! [X2 : int,X0 : int,X1 : int] : dvd(X1,X0,nil(int)) = hd_coeff1(X2,dvd(X1,X0,nil(int)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_103])])).
% 0.21/0.47 tff(f398,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : int,X1 : int] : (dvd(X1,X0,nil(int)) = hd_coeff1(X2,dvd(X1,X0,nil(int)))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f183])).
% 0.21/0.47 tff(f183,plain,(
% 0.21/0.47 ! [X0 : int,X1 : int,X2 : int] : dvd(X1,X0,nil(int)) = hd_coeff1(X2,dvd(X1,X0,nil(int)))),
% 0.21/0.47 inference(rectify,[],[f98])).
% 0.21/0.47 tff(f98,axiom,(
% 0.21/0.47 ! [X31 : int,X32 : int,X62 : int] : dvd(X32,X31,nil(int)) = hd_coeff1(X62,dvd(X32,X31,nil(int)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_hd__coeff1_Osimps_I5_J)).
% 0.21/0.47 tff(f1009,plain,(
% 0.21/0.47 spl22_102),
% 0.21/0.47 inference(avatar_split_clause,[],[f471,f1007])).
% 0.21/0.47 tff(f1007,plain,(
% 0.21/0.47 spl22_102 <=> ! [X2 : int,X3 : list(int),X4 : int,X0 : list(int),X5 : int,X1 : int] : (X1 = X4 | nDvd(X2,X1,X0) != nDvd(X5,X4,X3))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_102])])).
% 0.21/0.47 tff(f471,plain,(
% 0.21/0.47 ( ! [X2 : int,X3 : list(int),X0 : list(int),X1 : int,X4 : int,X5 : int] : (X1 = X4 | nDvd(X2,X1,X0) != nDvd(X5,X4,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f312])).
% 0.21/0.47 tff(f1005,plain,(
% 0.21/0.47 spl22_101),
% 0.21/0.47 inference(avatar_split_clause,[],[f470,f1003])).
% 0.21/0.47 tff(f1003,plain,(
% 0.21/0.47 spl22_101 <=> ! [X3 : list(int),X4 : int,X0 : list(int),X5 : int,X2 : int,X1 : int] : (X2 = X5 | nDvd(X2,X1,X0) != nDvd(X5,X4,X3))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_101])])).
% 0.21/0.47 tff(f470,plain,(
% 0.21/0.47 ( ! [X2 : int,X3 : list(int),X0 : list(int),X1 : int,X4 : int,X5 : int] : (X2 = X5 | nDvd(X2,X1,X0) != nDvd(X5,X4,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f312])).
% 0.21/0.47 tff(f1001,plain,(
% 0.21/0.47 spl22_100),
% 0.21/0.47 inference(avatar_split_clause,[],[f467,f999])).
% 0.21/0.47 tff(f999,plain,(
% 0.21/0.47 spl22_100 <=> ! [X2 : int,X3 : list(int),X4 : int,X0 : list(int),X5 : int,X1 : int] : (X1 = X4 | dvd(X2,X1,X0) != dvd(X5,X4,X3))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_100])])).
% 0.21/0.47 tff(f467,plain,(
% 0.21/0.47 ( ! [X2 : int,X3 : list(int),X0 : list(int),X1 : int,X4 : int,X5 : int] : (X1 = X4 | dvd(X2,X1,X0) != dvd(X5,X4,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f310])).
% 0.21/0.47 tff(f997,plain,(
% 0.21/0.47 spl22_99 | ~spl22_51 | ~spl22_79),
% 0.21/0.47 inference(avatar_split_clause,[],[f903,f872,f736,f995])).
% 0.21/0.47 tff(f995,plain,(
% 0.21/0.47 spl22_99 <=> ! [X0 : $tType,X1 : X0] : member(X0,X1,fequal(X0,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_99])])).
% 0.21/0.47 tff(f736,plain,(
% 0.21/0.47 spl22_51 <=> ! [X0 : $tType,X2 : X0] : pp(aa(X0,bool,fequal(X0,X2),X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_51])])).
% 0.21/0.47 tff(f872,plain,(
% 0.21/0.47 spl22_79 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (member(X0,X2,X1) | ~pp(aa(X0,bool,X1,X2)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_79])])).
% 0.21/0.47 tff(f903,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : X0] : (member(X0,X1,fequal(X0,X1))) ) | (~spl22_51 | ~spl22_79)),
% 0.21/0.47 inference(resolution,[],[f873,f737])).
% 0.21/0.47 tff(f737,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0] : (pp(aa(X0,bool,fequal(X0,X2),X2))) ) | ~spl22_51),
% 0.21/0.47 inference(avatar_component_clause,[],[f736])).
% 0.21/0.47 tff(f873,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | member(X0,X2,X1)) ) | ~spl22_79),
% 0.21/0.47 inference(avatar_component_clause,[],[f872])).
% 0.21/0.47 tff(f993,plain,(
% 0.21/0.47 spl22_98),
% 0.21/0.47 inference(avatar_split_clause,[],[f466,f991])).
% 0.21/0.47 tff(f991,plain,(
% 0.21/0.47 spl22_98 <=> ! [X3 : list(int),X4 : int,X0 : list(int),X5 : int,X2 : int,X1 : int] : (X2 = X5 | dvd(X2,X1,X0) != dvd(X5,X4,X3))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_98])])).
% 0.21/0.47 tff(f466,plain,(
% 0.21/0.47 ( ! [X2 : int,X3 : list(int),X0 : list(int),X1 : int,X4 : int,X5 : int] : (X2 = X5 | dvd(X2,X1,X0) != dvd(X5,X4,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f310])).
% 0.21/0.47 tff(f989,plain,(
% 0.21/0.47 spl22_97),
% 0.21/0.47 inference(avatar_split_clause,[],[f443,f987])).
% 0.21/0.47 tff(f987,plain,(
% 0.21/0.47 spl22_97 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : X0,X1 : list(X0)] : (list_ex1(X0,X3,cons(X0,X2,X1)) | ~sP1(X0,X1,X3,X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_97])])).
% 0.21/0.47 tff(f443,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : list(X0)] : (list_ex1(X0,X3,cons(X0,X2,X1)) | ~sP1(X0,X1,X3,X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f302])).
% 0.21/0.47 tff(f302,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : fun(X0,bool)] : ((list_ex1(X0,X3,cons(X0,X2,X1)) | ~sP1(X0,X1,X3,X2)) & (sP1(X0,X1,X3,X2) | ~list_ex1(X0,X3,cons(X0,X2,X1))))),
% 0.21/0.47 inference(nnf_transformation,[],[f263])).
% 0.21/0.47 tff(f263,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : fun(X0,bool)] : (list_ex1(X0,X3,cons(X0,X2,X1)) <=> sP1(X0,X1,X3,X2))),
% 0.21/0.47 inference(definition_folding,[],[f259,f262])).
% 0.21/0.47 tff(f259,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : fun(X0,bool)] : (list_ex1(X0,X3,cons(X0,X2,X1)) <=> ((list_ex1(X0,X3,X1) | pp(aa(X0,bool,X3,X2))) & (list_all(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combb(bool,bool,X0,fNot,X3)),fequal(X0,X2)),X1) | ~pp(aa(X0,bool,X3,X2)))))),
% 0.21/0.47 inference(ennf_transformation,[],[f206])).
% 0.21/0.47 tff(f206,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : fun(X0,bool)] : (list_ex1(X0,X3,cons(X0,X2,X1)) <=> ((~pp(aa(X0,bool,X3,X2)) => list_ex1(X0,X3,X1)) & (pp(aa(X0,bool,X3,X2)) => list_all(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combb(bool,bool,X0,fNot,X3)),fequal(X0,X2)),X1))))),
% 0.21/0.47 inference(rectify,[],[f54])).
% 0.21/0.47 tff(f54,axiom,(
% 0.21/0.47 ! [X0 : $tType,X16 : list(X0),X17 : X0,X38 : fun(X0,bool)] : (list_ex1(X0,X38,cons(X0,X17,X16)) <=> ((~pp(aa(X0,bool,X38,X17)) => list_ex1(X0,X38,X16)) & (pp(aa(X0,bool,X38,X17)) => list_all(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fdisj,combb(bool,bool,X0,fNot,X38)),fequal(X0,X17)),X16))))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_list__ex1__simps_I2_J)).
% 0.21/0.47 tff(f985,plain,(
% 0.21/0.47 spl22_96),
% 0.21/0.47 inference(avatar_split_clause,[],[f442,f983])).
% 0.21/0.47 tff(f983,plain,(
% 0.21/0.47 spl22_96 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : X0,X1 : list(X0)] : (sP1(X0,X1,X3,X2) | ~list_ex1(X0,X3,cons(X0,X2,X1)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_96])])).
% 0.21/0.47 tff(f442,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : list(X0)] : (sP1(X0,X1,X3,X2) | ~list_ex1(X0,X3,cons(X0,X2,X1))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f302])).
% 0.21/0.47 tff(f981,plain,(
% 0.21/0.47 spl22_95),
% 0.21/0.47 inference(avatar_split_clause,[],[f397,f979])).
% 0.21/0.47 tff(f979,plain,(
% 0.21/0.47 spl22_95 <=> ! [X2 : int,X0 : list(int),X1 : int] : decr_Z(nDvd(X2,X1,X0)) = nDvd(X2,X1,tl(int,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_95])])).
% 0.21/0.47 tff(f397,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (decr_Z(nDvd(X2,X1,X0)) = nDvd(X2,X1,tl(int,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f182])).
% 0.21/0.47 tff(f182,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int] : decr_Z(nDvd(X2,X1,X0)) = nDvd(X2,X1,tl(int,X0))),
% 0.21/0.47 inference(rectify,[],[f88])).
% 0.21/0.47 tff(f88,axiom,(
% 0.21/0.47 ! [X19 : list(int),X20 : int,X51 : int] : decr_Z(nDvd(X51,X20,X19)) = nDvd(X51,X20,tl(int,X19))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_decr_092_060_094isub_062Z_Osimps_I3_J)).
% 0.21/0.47 tff(f977,plain,(
% 0.21/0.47 spl22_94),
% 0.21/0.47 inference(avatar_split_clause,[],[f396,f975])).
% 0.21/0.47 tff(f975,plain,(
% 0.21/0.47 spl22_94 <=> ! [X2 : int,X0 : list(int),X1 : int] : decr_Z(dvd(X2,X1,X0)) = dvd(X2,X1,tl(int,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_94])])).
% 0.21/0.47 tff(f396,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (decr_Z(dvd(X2,X1,X0)) = dvd(X2,X1,tl(int,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f181])).
% 0.21/0.47 tff(f181,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int] : decr_Z(dvd(X2,X1,X0)) = dvd(X2,X1,tl(int,X0))),
% 0.21/0.47 inference(rectify,[],[f91])).
% 0.21/0.47 tff(f91,axiom,(
% 0.21/0.47 ! [X19 : list(int),X20 : int,X51 : int] : decr_Z(dvd(X51,X20,X19)) = dvd(X51,X20,tl(int,X19))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_decr_092_060_094isub_062Z_Osimps_I2_J)).
% 0.21/0.47 tff(f973,plain,(
% 0.21/0.47 spl22_93),
% 0.21/0.47 inference(avatar_split_clause,[],[f395,f971])).
% 0.21/0.47 tff(f971,plain,(
% 0.21/0.47 spl22_93 <=> ! [X2 : int,X0 : int,X1 : list(int)] : c_PresArith_Oatom_OLe(X0,nil(int)) = asubst(X2,X1,c_PresArith_Oatom_OLe(X0,nil(int)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_93])])).
% 0.21/0.47 tff(f395,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : int,X1 : list(int)] : (c_PresArith_Oatom_OLe(X0,nil(int)) = asubst(X2,X1,c_PresArith_Oatom_OLe(X0,nil(int)))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f180])).
% 0.21/0.47 tff(f180,plain,(
% 0.21/0.47 ! [X0 : int,X1 : list(int),X2 : int] : c_PresArith_Oatom_OLe(X0,nil(int)) = asubst(X2,X1,c_PresArith_Oatom_OLe(X0,nil(int)))),
% 0.21/0.47 inference(rectify,[],[f97])).
% 0.21/0.47 tff(f97,axiom,(
% 0.21/0.47 ! [X32 : int,X60 : list(int),X61 : int] : c_PresArith_Oatom_OLe(X32,nil(int)) = asubst(X61,X60,c_PresArith_Oatom_OLe(X32,nil(int)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_asubst_Osimps_I4_J)).
% 0.21/0.47 tff(f969,plain,(
% 0.21/0.47 spl22_92),
% 0.21/0.47 inference(avatar_split_clause,[],[f367,f967])).
% 0.21/0.47 tff(f963,plain,(
% 0.21/0.47 spl22_91 | ~spl22_35 | ~spl22_79),
% 0.21/0.47 inference(avatar_split_clause,[],[f902,f872,f666,f961])).
% 0.21/0.47 tff(f961,plain,(
% 0.21/0.47 spl22_91 <=> ! [X0 : bool] : (member(bool,X0,fNot) | pp(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_91])])).
% 0.21/0.47 tff(f666,plain,(
% 0.21/0.47 spl22_35 <=> ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_35])])).
% 0.21/0.47 tff(f902,plain,(
% 0.21/0.47 ( ! [X0 : bool] : (member(bool,X0,fNot) | pp(X0)) ) | (~spl22_35 | ~spl22_79)),
% 0.21/0.47 inference(resolution,[],[f873,f667])).
% 0.21/0.47 tff(f667,plain,(
% 0.21/0.47 ( ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0)) ) | ~spl22_35),
% 0.21/0.47 inference(avatar_component_clause,[],[f666])).
% 0.21/0.47 tff(f950,plain,(
% 0.21/0.47 spl22_90),
% 0.21/0.47 inference(avatar_split_clause,[],[f487,f948])).
% 0.21/0.47 tff(f948,plain,(
% 0.21/0.47 spl22_90 <=> ! [X0 : $tType,X4 : list(X0),X5 : X0,X3 : X0] : (sP0(X0,cons(X0,X5,X4),X3) | ~listMem(X0,X3,X4))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_90])])).
% 0.21/0.47 tff(f487,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X3 : X0,X4 : list(X0),X5 : X0] : (sP0(X0,cons(X0,X5,X4),X3) | ~listMem(X0,X3,X4)) )),
% 0.21/0.47 inference(equality_resolution,[],[f486])).
% 0.21/0.47 tff(f486,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : list(X0),X5 : X0] : (sP0(X0,cons(X0,X5,X4),X2) | ~listMem(X0,X3,X4) | X2 != X3) )),
% 0.21/0.47 inference(equality_resolution,[],[f421])).
% 0.21/0.47 tff(f421,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : list(X0),X4 : list(X0),X5 : X0] : (sP0(X0,X1,X2) | ~listMem(X0,X3,X4) | cons(X0,X5,X4) != X1 | X2 != X3) )),
% 0.21/0.47 inference(cnf_transformation,[],[f290])).
% 0.21/0.47 tff(f946,plain,(
% 0.21/0.47 spl22_89),
% 0.21/0.47 inference(avatar_split_clause,[],[f448,f944])).
% 0.21/0.47 tff(f944,plain,(
% 0.21/0.47 spl22_89 <=> ! [X0 : $tType,X3 : fun(X0,bool),X2 : X0,X1 : list(X0)] : (list_all(X0,X3,X1) | ~list_all(X0,X3,cons(X0,X2,X1)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_89])])).
% 0.21/0.47 tff(f448,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : fun(X0,bool),X1 : list(X0)] : (list_all(X0,X3,X1) | ~list_all(X0,X3,cons(X0,X2,X1))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f306])).
% 0.21/0.47 tff(f942,plain,(
% 0.21/0.47 spl22_88),
% 0.21/0.47 inference(avatar_split_clause,[],[f446,f940])).
% 0.21/0.47 tff(f940,plain,(
% 0.21/0.47 spl22_88 <=> ! [X0 : $tType,X3 : X0,X2 : list(X0),X1 : X0] : (member1(X0,cons(X0,X3,X2),X1) | ~member1(X0,X2,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_88])])).
% 0.21/0.47 tff(f446,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X3 : X0,X1 : X0] : (member1(X0,cons(X0,X3,X2),X1) | ~member1(X0,X2,X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f304])).
% 0.21/0.47 tff(f938,plain,(
% 0.21/0.47 spl22_87),
% 0.21/0.47 inference(avatar_split_clause,[],[f434,f936])).
% 0.21/0.47 tff(f936,plain,(
% 0.21/0.47 spl22_87 <=> ! [X2 : list(int),X0 : list(int),X1 : int,X3 : int] : (X0 = X2 | c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_87])])).
% 0.21/0.47 tff(f434,plain,(
% 0.21/0.47 ( ! [X2 : list(int),X3 : int,X0 : list(int),X1 : int] : (X0 = X2 | c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f298])).
% 0.21/0.47 tff(f298,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : list(int),X3 : int] : ((c_PresArith_Oatom_OLe(X1,X0) = c_PresArith_Oatom_OLe(X3,X2) | X0 != X2 | X1 != X3) & ((X0 = X2 & X1 = X3) | c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2)))),
% 0.21/0.47 inference(flattening,[],[f297])).
% 0.21/0.47 tff(f297,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : list(int),X3 : int] : ((c_PresArith_Oatom_OLe(X1,X0) = c_PresArith_Oatom_OLe(X3,X2) | (X0 != X2 | X1 != X3)) & ((X0 = X2 & X1 = X3) | c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2)))),
% 0.21/0.47 inference(nnf_transformation,[],[f205])).
% 0.21/0.47 tff(f205,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : list(int),X3 : int] : (c_PresArith_Oatom_OLe(X1,X0) = c_PresArith_Oatom_OLe(X3,X2) <=> (X0 = X2 & X1 = X3))),
% 0.21/0.47 inference(rectify,[],[f16])).
% 0.21/0.47 tff(f16,axiom,(
% 0.21/0.47 ! [X4 : list(int),X21 : int,X6 : list(int),X22 : int] : (c_PresArith_Oatom_OLe(X22,X6) = c_PresArith_Oatom_OLe(X21,X4) <=> (X4 = X6 & X21 = X22))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_atom_Osimps_I1_J)).
% 0.21/0.47 tff(f934,plain,(
% 0.21/0.47 spl22_86),
% 0.21/0.47 inference(avatar_split_clause,[],[f432,f932])).
% 0.21/0.47 tff(f932,plain,(
% 0.21/0.47 spl22_86 <=> ! [X0 : $tType,X3 : X0,X2 : list(X0),X1 : X0] : (listMem(X0,X3,cons(X0,X1,X2)) | ~listMem(X0,X3,X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_86])])).
% 0.21/0.47 tff(f432,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X3 : X0,X1 : X0] : (listMem(X0,X3,cons(X0,X1,X2)) | ~listMem(X0,X3,X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f258])).
% 0.21/0.47 tff(f258,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0,X2 : list(X0),X3 : X0] : (listMem(X0,X3,cons(X0,X1,X2)) | ~listMem(X0,X3,X2))),
% 0.21/0.47 inference(ennf_transformation,[],[f204])).
% 0.21/0.47 tff(f204,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0,X2 : list(X0),X3 : X0] : (listMem(X0,X3,X2) => listMem(X0,X3,cons(X0,X1,X2)))),
% 0.21/0.47 inference(rectify,[],[f14])).
% 0.21/0.47 tff(f14,axiom,(
% 0.21/0.47 ! [X0 : $tType,X13 : X0,X9 : list(X0),X8 : X0] : (listMem(X0,X8,X9) => listMem(X0,X8,cons(X0,X13,X9)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_insert)).
% 0.21/0.47 tff(f930,plain,(
% 0.21/0.47 spl22_85),
% 0.21/0.47 inference(avatar_split_clause,[],[f406,f928])).
% 0.21/0.47 tff(f928,plain,(
% 0.21/0.47 spl22_85 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | ~pp(aa(X0,bool,fequal(X0,X2),X1)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_85])])).
% 0.21/0.47 tff(f406,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (X1 = X2 | ~pp(aa(X0,bool,fequal(X0,X2),X1))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f190])).
% 0.21/0.47 tff(f190,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0,X2 : X0] : (X1 = X2 | ~pp(aa(X0,bool,fequal(X0,X2),X1)))),
% 0.21/0.47 inference(rectify,[],[f122])).
% 0.21/0.47 tff(f122,axiom,(
% 0.21/0.47 ! [X0 : $tType,X13 : X0,X8 : X0] : (X8 = X13 | ~pp(aa(X0,bool,fequal(X0,X8),X13)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T)).
% 0.21/0.47 tff(f926,plain,(
% 0.21/0.47 spl22_84 | ~spl22_36 | ~spl22_78),
% 0.21/0.47 inference(avatar_split_clause,[],[f900,f868,f670,f924])).
% 0.21/0.47 tff(f924,plain,(
% 0.21/0.47 spl22_84 <=> ! [X0 : bool] : (~member(bool,X0,fNot) | ~pp(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_84])])).
% 0.21/0.47 tff(f670,plain,(
% 0.21/0.47 spl22_36 <=> ! [X0 : bool] : (~pp(X0) | ~pp(aa(bool,bool,fNot,X0)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_36])])).
% 0.21/0.47 tff(f868,plain,(
% 0.21/0.47 spl22_78 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,X2)) | ~member(X0,X2,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_78])])).
% 0.21/0.47 tff(f900,plain,(
% 0.21/0.47 ( ! [X0 : bool] : (~member(bool,X0,fNot) | ~pp(X0)) ) | (~spl22_36 | ~spl22_78)),
% 0.21/0.47 inference(resolution,[],[f869,f671])).
% 0.21/0.47 tff(f671,plain,(
% 0.21/0.47 ( ! [X0 : bool] : (~pp(aa(bool,bool,fNot,X0)) | ~pp(X0)) ) | ~spl22_36),
% 0.21/0.47 inference(avatar_component_clause,[],[f670])).
% 0.21/0.47 tff(f869,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,X2)) | ~member(X0,X2,X1)) ) | ~spl22_78),
% 0.21/0.47 inference(avatar_component_clause,[],[f868])).
% 0.21/0.47 tff(f922,plain,(
% 0.21/0.47 spl22_83),
% 0.21/0.47 inference(avatar_split_clause,[],[f366,f920])).
% 0.21/0.47 tff(f920,plain,(
% 0.21/0.47 spl22_83 <=> ! [X0 : int,X1 : int] : c_PresArith_Oatom_OLe(X0,nil(int)) = hd_coeff1(X1,c_PresArith_Oatom_OLe(X0,nil(int)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_83])])).
% 0.21/0.47 tff(f366,plain,(
% 0.21/0.47 ( ! [X0 : int,X1 : int] : (c_PresArith_Oatom_OLe(X0,nil(int)) = hd_coeff1(X1,c_PresArith_Oatom_OLe(X0,nil(int)))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f155])).
% 0.21/0.47 tff(f155,plain,(
% 0.21/0.47 ! [X0 : int,X1 : int] : c_PresArith_Oatom_OLe(X0,nil(int)) = hd_coeff1(X1,c_PresArith_Oatom_OLe(X0,nil(int)))),
% 0.21/0.47 inference(rectify,[],[f96])).
% 0.21/0.47 tff(f96,axiom,(
% 0.21/0.47 ! [X32 : int,X62 : int] : c_PresArith_Oatom_OLe(X32,nil(int)) = hd_coeff1(X62,c_PresArith_Oatom_OLe(X32,nil(int)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_hd__coeff1_Osimps_I4_J)).
% 0.21/0.47 tff(f916,plain,(
% 0.21/0.47 spl22_82),
% 0.21/0.47 inference(avatar_split_clause,[],[f330,f913])).
% 0.21/0.47 tff(f913,plain,(
% 0.21/0.47 spl22_82 <=> div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_82])])).
% 0.21/0.47 tff(f330,plain,(
% 0.21/0.47 div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a))),
% 0.21/0.47 inference(cnf_transformation,[],[f2])).
% 0.21/0.47 tff(f2,axiom,(
% 0.21/0.47 div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I3_J)).
% 0.21/0.47 tff(f882,plain,(
% 0.21/0.47 spl22_81),
% 0.21/0.47 inference(avatar_split_clause,[],[f433,f880])).
% 0.21/0.47 tff(f880,plain,(
% 0.21/0.47 spl22_81 <=> ! [X0 : list(int),X3 : int,X2 : list(int),X1 : int] : (X1 = X3 | c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_81])])).
% 0.21/0.47 tff(f433,plain,(
% 0.21/0.47 ( ! [X2 : list(int),X3 : int,X0 : list(int),X1 : int] : (X1 = X3 | c_PresArith_Oatom_OLe(X1,X0) != c_PresArith_Oatom_OLe(X3,X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f298])).
% 0.21/0.47 tff(f878,plain,(
% 0.21/0.47 spl22_80),
% 0.21/0.47 inference(avatar_split_clause,[],[f418,f876])).
% 0.21/0.47 tff(f876,plain,(
% 0.21/0.47 spl22_80 <=> ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (sK17(X0,X1,X2) = X2 | ~sP0(X0,X1,X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_80])])).
% 0.21/0.47 tff(f418,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (sK17(X0,X1,X2) = X2 | ~sP0(X0,X1,X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f290])).
% 0.21/0.47 tff(f874,plain,(
% 0.21/0.47 spl22_79),
% 0.21/0.47 inference(avatar_split_clause,[],[f417,f872])).
% 0.21/0.47 tff(f417,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (member(X0,X2,X1) | ~pp(aa(X0,bool,X1,X2))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f286])).
% 0.21/0.47 tff(f286,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : ((member(X0,X2,X1) | ~pp(aa(X0,bool,X1,X2))) & (pp(aa(X0,bool,X1,X2)) | ~member(X0,X2,X1)))),
% 0.21/0.47 inference(nnf_transformation,[],[f197])).
% 0.21/0.47 tff(f197,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (member(X0,X2,X1) <=> pp(aa(X0,bool,X1,X2)))),
% 0.21/0.47 inference(rectify,[],[f74])).
% 0.21/0.47 tff(f74,axiom,(
% 0.21/0.47 ! [X0 : $tType,X44 : fun(X0,bool),X17 : X0] : (member(X0,X17,X44) <=> pp(aa(X0,bool,X44,X17)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_mem__def)).
% 0.21/0.47 tff(f870,plain,(
% 0.21/0.47 spl22_78),
% 0.21/0.47 inference(avatar_split_clause,[],[f416,f868])).
% 0.21/0.47 tff(f416,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,X2)) | ~member(X0,X2,X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f286])).
% 0.21/0.47 tff(f866,plain,(
% 0.21/0.47 spl22_77),
% 0.21/0.47 inference(avatar_split_clause,[],[f365,f864])).
% 0.21/0.47 tff(f864,plain,(
% 0.21/0.47 spl22_77 <=> ! [X0 : list(int),X1 : int] : decr_Z(c_PresArith_Oatom_OLe(X1,X0)) = c_PresArith_Oatom_OLe(X1,tl(int,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_77])])).
% 0.21/0.47 tff(f365,plain,(
% 0.21/0.47 ( ! [X0 : list(int),X1 : int] : (decr_Z(c_PresArith_Oatom_OLe(X1,X0)) = c_PresArith_Oatom_OLe(X1,tl(int,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f154])).
% 0.21/0.47 tff(f154,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int] : decr_Z(c_PresArith_Oatom_OLe(X1,X0)) = c_PresArith_Oatom_OLe(X1,tl(int,X0))),
% 0.21/0.47 inference(rectify,[],[f90])).
% 0.21/0.47 tff(f90,axiom,(
% 0.21/0.47 ! [X19 : list(int),X20 : int] : decr_Z(c_PresArith_Oatom_OLe(X20,X19)) = c_PresArith_Oatom_OLe(X20,tl(int,X19))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_decr_092_060_094isub_062Z_Osimps_I1_J)).
% 0.21/0.47 tff(f862,plain,(
% 0.21/0.47 spl22_76),
% 0.21/0.47 inference(avatar_split_clause,[],[f349,f860])).
% 0.21/0.47 tff(f860,plain,(
% 0.21/0.47 spl22_76 <=> ! [X0 : $tType,X1 : X0] : (zero_zero(X0) = div_mod(X0,zero_zero(X0),X1) | ~semiring_div(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_76])])).
% 0.21/0.47 tff(f349,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : X0] : (zero_zero(X0) = div_mod(X0,zero_zero(X0),X1) | ~semiring_div(X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f238])).
% 0.21/0.47 tff(f238,plain,(
% 0.21/0.47 ! [X0 : $tType] : (! [X1 : X0] : zero_zero(X0) = div_mod(X0,zero_zero(X0),X1) | ~semiring_div(X0))),
% 0.21/0.47 inference(ennf_transformation,[],[f139])).
% 0.21/0.47 tff(f139,plain,(
% 0.21/0.47 ! [X0 : $tType] : (semiring_div(X0) => ! [X1 : X0] : zero_zero(X0) = div_mod(X0,zero_zero(X0),X1))),
% 0.21/0.47 inference(rectify,[],[f43])).
% 0.21/0.47 tff(f43,axiom,(
% 0.21/0.47 ! [X0 : $tType] : (semiring_div(X0) => ! [X25 : X0] : zero_zero(X0) = div_mod(X0,zero_zero(X0),X25))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mod__0)).
% 0.21/0.47 tff(f858,plain,(
% 0.21/0.47 spl22_75),
% 0.21/0.47 inference(avatar_split_clause,[],[f348,f856])).
% 0.21/0.47 tff(f856,plain,(
% 0.21/0.47 spl22_75 <=> ! [X0 : $tType,X1 : X0] : (zero_zero(X0) = div_mod(X0,X1,one_one(X0)) | ~semiring_div(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_75])])).
% 0.21/0.47 tff(f348,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : X0] : (zero_zero(X0) = div_mod(X0,X1,one_one(X0)) | ~semiring_div(X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f237])).
% 0.21/0.47 tff(f237,plain,(
% 0.21/0.47 ! [X0 : $tType] : (! [X1 : X0] : zero_zero(X0) = div_mod(X0,X1,one_one(X0)) | ~semiring_div(X0))),
% 0.21/0.47 inference(ennf_transformation,[],[f138])).
% 0.21/0.47 tff(f138,plain,(
% 0.21/0.47 ! [X0 : $tType] : (semiring_div(X0) => ! [X1 : X0] : zero_zero(X0) = div_mod(X0,X1,one_one(X0)))),
% 0.21/0.47 inference(rectify,[],[f46])).
% 0.21/0.47 tff(f46,axiom,(
% 0.21/0.47 ! [X0 : $tType] : (semiring_div(X0) => ! [X25 : X0] : zero_zero(X0) = div_mod(X0,X25,one_one(X0)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mod__by__1)).
% 0.21/0.47 tff(f854,plain,(
% 0.21/0.47 spl22_74),
% 0.21/0.47 inference(avatar_split_clause,[],[f341,f852])).
% 0.21/0.47 tff(f852,plain,(
% 0.21/0.47 spl22_74 <=> ! [X0 : $tType,X1 : list(X0)] : (zero_zero(X0) = iprod(X0,nil(X0),X1) | ~ring(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_74])])).
% 0.21/0.47 tff(f341,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : list(X0)] : (zero_zero(X0) = iprod(X0,nil(X0),X1) | ~ring(X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f231])).
% 0.21/0.47 tff(f231,plain,(
% 0.21/0.47 ! [X0 : $tType] : (! [X1 : list(X0)] : zero_zero(X0) = iprod(X0,nil(X0),X1) | ~ring(X0))),
% 0.21/0.47 inference(ennf_transformation,[],[f134])).
% 0.21/0.47 tff(f134,plain,(
% 0.21/0.47 ! [X0 : $tType] : (ring(X0) => ! [X1 : list(X0)] : zero_zero(X0) = iprod(X0,nil(X0),X1))),
% 0.21/0.47 inference(rectify,[],[f83])).
% 0.21/0.47 tff(f83,axiom,(
% 0.21/0.47 ! [X0 : $tType] : (ring(X0) => ! [X12 : list(X0)] : zero_zero(X0) = iprod(X0,nil(X0),X12))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_iprod__Nil)).
% 0.21/0.47 tff(f850,plain,(
% 0.21/0.47 spl22_73),
% 0.21/0.47 inference(avatar_split_clause,[],[f340,f848])).
% 0.21/0.47 tff(f848,plain,(
% 0.21/0.47 spl22_73 <=> ! [X0 : $tType,X1 : list(X0)] : (zero_zero(X0) = iprod(X0,X1,nil(X0)) | ~ring(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_73])])).
% 0.21/0.47 tff(f340,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : list(X0)] : (zero_zero(X0) = iprod(X0,X1,nil(X0)) | ~ring(X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f230])).
% 0.21/0.47 tff(f230,plain,(
% 0.21/0.47 ! [X0 : $tType] : (! [X1 : list(X0)] : zero_zero(X0) = iprod(X0,X1,nil(X0)) | ~ring(X0))),
% 0.21/0.47 inference(ennf_transformation,[],[f133])).
% 0.21/0.47 tff(f133,plain,(
% 0.21/0.47 ! [X0 : $tType] : (ring(X0) => ! [X1 : list(X0)] : zero_zero(X0) = iprod(X0,X1,nil(X0)))),
% 0.21/0.47 inference(rectify,[],[f82])).
% 0.21/0.47 tff(f82,axiom,(
% 0.21/0.47 ! [X0 : $tType] : (ring(X0) => ! [X9 : list(X0)] : zero_zero(X0) = iprod(X0,X9,nil(X0)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_iprod__Nil2)).
% 0.21/0.47 tff(f846,plain,(
% 0.21/0.47 spl22_72 | ~spl22_15 | ~spl22_52),
% 0.21/0.47 inference(avatar_split_clause,[],[f762,f744,f577,f843])).
% 0.21/0.47 tff(f843,plain,(
% 0.21/0.47 spl22_72 <=> atom_size(a) = size_size(atom,a)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_72])])).
% 0.21/0.47 tff(f744,plain,(
% 0.21/0.47 spl22_52 <=> ! [X0 : list(int),X1 : int] : size_size(atom,c_PresArith_Oatom_OLe(X1,X0)) = atom_size(a)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_52])])).
% 0.21/0.47 tff(f762,plain,(
% 0.21/0.47 atom_size(a) = size_size(atom,a) | (~spl22_15 | ~spl22_52)),
% 0.21/0.47 inference(superposition,[],[f745,f579])).
% 0.21/0.47 tff(f745,plain,(
% 0.21/0.47 ( ! [X0 : list(int),X1 : int] : (size_size(atom,c_PresArith_Oatom_OLe(X1,X0)) = atom_size(a)) ) | ~spl22_52),
% 0.21/0.47 inference(avatar_component_clause,[],[f744])).
% 0.21/0.47 tff(f837,plain,(
% 0.21/0.47 spl22_71 | ~spl22_37 | ~spl22_64),
% 0.21/0.47 inference(avatar_split_clause,[],[f800,f797,f674,f835])).
% 0.21/0.47 tff(f835,plain,(
% 0.21/0.47 spl22_71 <=> ! [X2 : int,X0 : list(int),X1 : int] : size_size(atom,nDvd(X2,X1,X0)) = atom_size(a)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_71])])).
% 0.21/0.47 tff(f797,plain,(
% 0.21/0.47 spl22_64 <=> ! [X2 : int,X0 : list(int),X1 : int] : zero_zero(nat) = size_size(atom,nDvd(X2,X1,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_64])])).
% 0.21/0.47 tff(f800,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (size_size(atom,nDvd(X2,X1,X0)) = atom_size(a)) ) | (~spl22_37 | ~spl22_64)),
% 0.21/0.47 inference(forward_demodulation,[],[f798,f676])).
% 0.21/0.47 tff(f798,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (zero_zero(nat) = size_size(atom,nDvd(X2,X1,X0))) ) | ~spl22_64),
% 0.21/0.47 inference(avatar_component_clause,[],[f797])).
% 0.21/0.47 tff(f833,plain,(
% 0.21/0.47 spl22_70 | ~spl22_37 | ~spl22_61),
% 0.21/0.47 inference(avatar_split_clause,[],[f787,f784,f674,f831])).
% 0.21/0.47 tff(f831,plain,(
% 0.21/0.47 spl22_70 <=> ! [X2 : int,X0 : list(int),X1 : int] : size_size(atom,dvd(X2,X1,X0)) = atom_size(a)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_70])])).
% 0.21/0.47 tff(f784,plain,(
% 0.21/0.47 spl22_61 <=> ! [X2 : int,X0 : list(int),X1 : int] : zero_zero(nat) = size_size(atom,dvd(X2,X1,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_61])])).
% 0.21/0.47 tff(f787,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (size_size(atom,dvd(X2,X1,X0)) = atom_size(a)) ) | (~spl22_37 | ~spl22_61)),
% 0.21/0.47 inference(forward_demodulation,[],[f785,f676])).
% 0.21/0.47 tff(f785,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (zero_zero(nat) = size_size(atom,dvd(X2,X1,X0))) ) | ~spl22_61),
% 0.21/0.47 inference(avatar_component_clause,[],[f784])).
% 0.21/0.47 tff(f820,plain,(
% 0.21/0.47 spl22_69),
% 0.21/0.47 inference(avatar_split_clause,[],[f458,f818])).
% 0.21/0.47 tff(f818,plain,(
% 0.21/0.47 spl22_69 <=> ! [X2 : int,X4 : int,X0 : list(int),X5 : int,X3 : list(int),X1 : int] : dvd(X2,X1,X0) != nDvd(X5,X4,X3)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_69])])).
% 0.21/0.47 tff(f458,plain,(
% 0.21/0.47 ( ! [X2 : int,X3 : list(int),X0 : list(int),X1 : int,X4 : int,X5 : int] : (dvd(X2,X1,X0) != nDvd(X5,X4,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f215])).
% 0.21/0.47 tff(f215,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int,X3 : list(int),X4 : int,X5 : int] : dvd(X2,X1,X0) != nDvd(X5,X4,X3)),
% 0.21/0.47 inference(rectify,[],[f69])).
% 0.21/0.47 tff(f69,axiom,(
% 0.21/0.47 ! [X41 : list(int),X49 : int,X50 : int,X33 : list(int),X52 : int,X53 : int] : dvd(X50,X49,X41) != nDvd(X53,X52,X33)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_atom_Osimps_I9_J)).
% 0.21/0.47 tff(f816,plain,(
% 0.21/0.47 spl22_68),
% 0.21/0.47 inference(avatar_split_clause,[],[f429,f814])).
% 0.21/0.47 tff(f814,plain,(
% 0.21/0.47 spl22_68 <=> ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X1] : list_case(X1,X0,X3,X2,nil(X0)) = X3),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_68])])).
% 0.21/0.47 tff(f429,plain,(
% 0.21/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X1] : (list_case(X1,X0,X3,X2,nil(X0)) = X3) )),
% 0.21/0.47 inference(cnf_transformation,[],[f201])).
% 0.21/0.47 tff(f201,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X1] : list_case(X1,X0,X3,X2,nil(X0)) = X3),
% 0.21/0.47 inference(rectify,[],[f27])).
% 0.21/0.47 tff(f27,axiom,(
% 0.21/0.47 ! [X1 : $tType,X0 : $tType,X10 : fun(X1,fun(list(X1),X0)),X11 : X0] : list_case(X0,X1,X11,X10,nil(X1)) = X11),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_list_Osimps_I4_J)).
% 0.21/0.47 tff(f812,plain,(
% 0.21/0.47 spl22_67),
% 0.21/0.47 inference(avatar_split_clause,[],[f428,f810])).
% 0.21/0.47 tff(f810,plain,(
% 0.21/0.47 spl22_67 <=> ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),fun(X1,X1))),X3 : X1] : list_rec(X1,X0,X3,X2,nil(X0)) = X3),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_67])])).
% 0.21/0.47 tff(f428,plain,(
% 0.21/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),fun(X1,X1))),X3 : X1] : (list_rec(X1,X0,X3,X2,nil(X0)) = X3) )),
% 0.21/0.47 inference(cnf_transformation,[],[f200])).
% 0.21/0.47 tff(f200,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : $tType,X2 : fun(X0,fun(list(X0),fun(X1,X1))),X3 : X1] : list_rec(X1,X0,X3,X2,nil(X0)) = X3),
% 0.21/0.47 inference(rectify,[],[f33])).
% 0.21/0.47 tff(f33,axiom,(
% 0.21/0.47 ! [X1 : $tType,X0 : $tType,X10 : fun(X1,fun(list(X1),fun(X0,X0))),X11 : X0] : list_rec(X0,X1,X11,X10,nil(X1)) = X11),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_list_Orecs_I1_J)).
% 0.21/0.47 tff(f808,plain,(
% 0.21/0.47 spl22_66),
% 0.21/0.47 inference(avatar_split_clause,[],[f426,f806])).
% 0.21/0.47 tff(f806,plain,(
% 0.21/0.47 spl22_66 <=> ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (X1 = X2 | ~equal_equal(list(X0),X2,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_66])])).
% 0.21/0.47 tff(f426,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (X1 = X2 | ~equal_equal(list(X0),X2,X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f296])).
% 0.21/0.47 tff(f296,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : list(X0)] : ((equal_equal(list(X0),X2,X1) | X1 != X2) & (X1 = X2 | ~equal_equal(list(X0),X2,X1)))),
% 0.21/0.47 inference(nnf_transformation,[],[f199])).
% 0.21/0.47 tff(f199,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : list(X0)] : (equal_equal(list(X0),X2,X1) <=> X1 = X2)),
% 0.21/0.47 inference(rectify,[],[f48])).
% 0.21/0.47 tff(f48,axiom,(
% 0.21/0.47 ! [X0 : $tType,X15 : list(X0),X17 : list(X0)] : (equal_equal(list(X0),X17,X15) <=> X15 = X17)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_equal__list__def)).
% 0.21/0.47 tff(f804,plain,(
% 0.21/0.47 spl22_65),
% 0.21/0.47 inference(avatar_split_clause,[],[f394,f802])).
% 0.21/0.47 tff(f802,plain,(
% 0.21/0.47 spl22_65 <=> ! [X0 : $tType,X2 : X0,X1 : list(X0)] : tl(X0,cons(X0,X2,X1)) = X1),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_65])])).
% 0.21/0.47 tff(f394,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (tl(X0,cons(X0,X2,X1)) = X1) )),
% 0.21/0.47 inference(cnf_transformation,[],[f179])).
% 0.21/0.47 tff(f179,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : tl(X0,cons(X0,X2,X1)) = X1),
% 0.21/0.47 inference(rectify,[],[f92])).
% 0.21/0.47 tff(f92,axiom,(
% 0.21/0.47 ! [X0 : $tType,X9 : list(X0),X8 : X0] : tl(X0,cons(X0,X8,X9)) = X9),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_tl_Osimps_I2_J)).
% 0.21/0.47 tff(f799,plain,(
% 0.21/0.47 spl22_64),
% 0.21/0.47 inference(avatar_split_clause,[],[f393,f797])).
% 0.21/0.47 tff(f393,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (zero_zero(nat) = size_size(atom,nDvd(X2,X1,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f178])).
% 0.21/0.47 tff(f178,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int] : zero_zero(nat) = size_size(atom,nDvd(X2,X1,X0))),
% 0.21/0.47 inference(rectify,[],[f65])).
% 0.21/0.47 tff(f65,axiom,(
% 0.21/0.47 ! [X41 : list(int),X49 : int,X50 : int] : zero_zero(nat) = size_size(atom,nDvd(X50,X49,X41))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_atom_Osize_I6_J)).
% 0.21/0.47 tff(f795,plain,(
% 0.21/0.47 spl22_62 | ~spl22_63 | ~spl22_21),
% 0.21/0.47 inference(avatar_split_clause,[],[f612,f603,f792,f789])).
% 0.21/0.47 tff(f789,plain,(
% 0.21/0.47 spl22_62 <=> ! [X0 : bool] : fFalse = X0),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_62])])).
% 0.21/0.47 tff(f792,plain,(
% 0.21/0.47 spl22_63 <=> fFalse = fTrue),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_63])])).
% 0.21/0.47 tff(f603,plain,(
% 0.21/0.47 spl22_21 <=> ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_21])])).
% 0.21/0.47 tff(f612,plain,(
% 0.21/0.47 ( ! [X0 : bool] : (fFalse != fTrue | fFalse = X0) ) | ~spl22_21),
% 0.21/0.47 inference(equality_factoring,[],[f604])).
% 0.21/0.47 tff(f604,plain,(
% 0.21/0.47 ( ! [X0 : bool] : (fTrue = X0 | fFalse = X0) ) | ~spl22_21),
% 0.21/0.47 inference(avatar_component_clause,[],[f603])).
% 0.21/0.47 tff(f786,plain,(
% 0.21/0.47 spl22_61),
% 0.21/0.47 inference(avatar_split_clause,[],[f392,f784])).
% 0.21/0.47 tff(f392,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (zero_zero(nat) = size_size(atom,dvd(X2,X1,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f177])).
% 0.21/0.47 tff(f177,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int] : zero_zero(nat) = size_size(atom,dvd(X2,X1,X0))),
% 0.21/0.47 inference(rectify,[],[f63])).
% 0.21/0.47 tff(f63,axiom,(
% 0.21/0.47 ! [X41 : list(int),X49 : int,X50 : int] : zero_zero(nat) = size_size(atom,dvd(X50,X49,X41))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_atom_Osize_I5_J)).
% 0.21/0.47 tff(f782,plain,(
% 0.21/0.47 spl22_60),
% 0.21/0.47 inference(avatar_split_clause,[],[f380,f780])).
% 0.21/0.47 tff(f780,plain,(
% 0.21/0.47 spl22_60 <=> ! [X0 : $tType,X1 : list(X0)] : (equal_equal(list(X0),X1,nil(X0)) | ~null(X0,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_60])])).
% 0.21/0.47 tff(f380,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : list(X0)] : (equal_equal(list(X0),X1,nil(X0)) | ~null(X0,X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f280])).
% 0.21/0.47 tff(f280,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : ((equal_equal(list(X0),X1,nil(X0)) | ~null(X0,X1)) & (null(X0,X1) | ~equal_equal(list(X0),X1,nil(X0))))),
% 0.21/0.47 inference(nnf_transformation,[],[f165])).
% 0.21/0.47 tff(f165,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : (equal_equal(list(X0),X1,nil(X0)) <=> null(X0,X1))),
% 0.21/0.47 inference(rectify,[],[f37])).
% 0.21/0.47 tff(f37,axiom,(
% 0.21/0.47 ! [X0 : $tType,X16 : list(X0)] : (equal_equal(list(X0),X16,nil(X0)) <=> null(X0,X16))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_equal__Nil__null)).
% 0.21/0.47 tff(f778,plain,(
% 0.21/0.47 spl22_59),
% 0.21/0.47 inference(avatar_split_clause,[],[f379,f776])).
% 0.21/0.47 tff(f776,plain,(
% 0.21/0.47 spl22_59 <=> ! [X0 : $tType,X1 : list(X0)] : (null(X0,X1) | ~equal_equal(list(X0),X1,nil(X0)))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_59])])).
% 0.21/0.47 tff(f379,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : list(X0)] : (null(X0,X1) | ~equal_equal(list(X0),X1,nil(X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f280])).
% 0.21/0.47 tff(f774,plain,(
% 0.21/0.47 spl22_58),
% 0.21/0.47 inference(avatar_split_clause,[],[f364,f772])).
% 0.21/0.47 tff(f772,plain,(
% 0.21/0.47 spl22_58 <=> ! [X0 : $tType,X1 : fun(nat,bool)] : nil(X0) = sublist(X0,nil(X0),X1)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_58])])).
% 0.21/0.47 tff(f364,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : fun(nat,bool)] : (nil(X0) = sublist(X0,nil(X0),X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f153])).
% 0.21/0.47 tff(f153,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(nat,bool)] : nil(X0) = sublist(X0,nil(X0),X1)),
% 0.21/0.47 inference(rectify,[],[f62])).
% 0.21/0.47 tff(f62,axiom,(
% 0.21/0.47 ! [X0 : $tType,X44 : fun(nat,bool)] : nil(X0) = sublist(X0,nil(X0),X44)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_sublist__nil)).
% 0.21/0.47 tff(f770,plain,(
% 0.21/0.47 spl22_57),
% 0.21/0.47 inference(avatar_split_clause,[],[f347,f768])).
% 0.21/0.47 tff(f347,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : X0] : (div_mod(X0,X1,zero_zero(X0)) = X1 | ~semiring_div(X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f236])).
% 0.21/0.47 tff(f236,plain,(
% 0.21/0.47 ! [X0 : $tType] : (! [X1 : X0] : div_mod(X0,X1,zero_zero(X0)) = X1 | ~semiring_div(X0))),
% 0.21/0.47 inference(ennf_transformation,[],[f137])).
% 0.21/0.47 tff(f137,plain,(
% 0.21/0.47 ! [X0 : $tType] : (semiring_div(X0) => ! [X1 : X0] : div_mod(X0,X1,zero_zero(X0)) = X1)),
% 0.21/0.47 inference(rectify,[],[f49])).
% 0.21/0.47 tff(f49,axiom,(
% 0.21/0.47 ! [X0 : $tType] : (semiring_div(X0) => ! [X25 : X0] : div_mod(X0,X25,zero_zero(X0)) = X25)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_mod__by__0)).
% 0.21/0.47 tff(f766,plain,(
% 0.21/0.47 spl22_56),
% 0.21/0.47 inference(avatar_split_clause,[],[f346,f764])).
% 0.21/0.47 tff(f346,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : X0] : (zero_zero(X0) = div_mod(X0,X1,X1) | ~semiring_div(X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f235])).
% 0.21/0.47 tff(f235,plain,(
% 0.21/0.47 ! [X0 : $tType] : (! [X1 : X0] : zero_zero(X0) = div_mod(X0,X1,X1) | ~semiring_div(X0))),
% 0.21/0.47 inference(ennf_transformation,[],[f136])).
% 0.21/0.47 tff(f136,plain,(
% 0.21/0.47 ! [X0 : $tType] : (semiring_div(X0) => ! [X1 : X0] : zero_zero(X0) = div_mod(X0,X1,X1))),
% 0.21/0.47 inference(rectify,[],[f44])).
% 0.21/0.47 tff(f44,axiom,(
% 0.21/0.47 ! [X0 : $tType] : (semiring_div(X0) => ! [X25 : X0] : zero_zero(X0) = div_mod(X0,X25,X25))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_mod__self)).
% 0.21/0.47 tff(f760,plain,(
% 0.21/0.47 spl22_55 | ~spl22_37 | ~spl22_44),
% 0.21/0.47 inference(avatar_split_clause,[],[f709,f706,f674,f758])).
% 0.21/0.47 tff(f758,plain,(
% 0.21/0.47 spl22_55 <=> ! [X2 : int,X0 : list(int),X1 : int] : atom_size(nDvd(X2,X1,X0)) = atom_size(a)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_55])])).
% 0.21/0.47 tff(f706,plain,(
% 0.21/0.47 spl22_44 <=> ! [X2 : int,X0 : list(int),X1 : int] : zero_zero(nat) = atom_size(nDvd(X2,X1,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_44])])).
% 0.21/0.47 tff(f709,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (atom_size(nDvd(X2,X1,X0)) = atom_size(a)) ) | (~spl22_37 | ~spl22_44)),
% 0.21/0.47 inference(forward_demodulation,[],[f707,f676])).
% 0.21/0.47 tff(f707,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (zero_zero(nat) = atom_size(nDvd(X2,X1,X0))) ) | ~spl22_44),
% 0.21/0.47 inference(avatar_component_clause,[],[f706])).
% 0.21/0.47 tff(f756,plain,(
% 0.21/0.47 spl22_54 | ~spl22_37 | ~spl22_43),
% 0.21/0.47 inference(avatar_split_clause,[],[f704,f701,f674,f754])).
% 0.21/0.47 tff(f754,plain,(
% 0.21/0.47 spl22_54 <=> ! [X2 : int,X0 : list(int),X1 : int] : atom_size(dvd(X2,X1,X0)) = atom_size(a)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_54])])).
% 0.21/0.47 tff(f701,plain,(
% 0.21/0.47 spl22_43 <=> ! [X2 : int,X0 : list(int),X1 : int] : zero_zero(nat) = atom_size(dvd(X2,X1,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_43])])).
% 0.21/0.47 tff(f704,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (atom_size(dvd(X2,X1,X0)) = atom_size(a)) ) | (~spl22_37 | ~spl22_43)),
% 0.21/0.47 inference(forward_demodulation,[],[f702,f676])).
% 0.21/0.47 tff(f702,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (zero_zero(nat) = atom_size(dvd(X2,X1,X0))) ) | ~spl22_43),
% 0.21/0.47 inference(avatar_component_clause,[],[f701])).
% 0.21/0.47 tff(f750,plain,(
% 0.21/0.47 spl22_53 | ~spl22_37 | ~spl22_39),
% 0.21/0.47 inference(avatar_split_clause,[],[f687,f684,f674,f748])).
% 0.21/0.47 tff(f748,plain,(
% 0.21/0.47 spl22_53 <=> ! [X0 : $tType,X1 : fun(X0,nat)] : list_size(X0,X1,nil(X0)) = atom_size(a)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_53])])).
% 0.21/0.47 tff(f684,plain,(
% 0.21/0.47 spl22_39 <=> ! [X0 : $tType,X1 : fun(X0,nat)] : zero_zero(nat) = list_size(X0,X1,nil(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_39])])).
% 0.21/0.47 tff(f687,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : fun(X0,nat)] : (list_size(X0,X1,nil(X0)) = atom_size(a)) ) | (~spl22_37 | ~spl22_39)),
% 0.21/0.47 inference(forward_demodulation,[],[f685,f676])).
% 0.21/0.47 tff(f685,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : fun(X0,nat)] : (zero_zero(nat) = list_size(X0,X1,nil(X0))) ) | ~spl22_39),
% 0.21/0.47 inference(avatar_component_clause,[],[f684])).
% 0.21/0.47 tff(f746,plain,(
% 0.21/0.47 spl22_52 | ~spl22_37 | ~spl22_38),
% 0.21/0.47 inference(avatar_split_clause,[],[f682,f679,f674,f744])).
% 0.21/0.47 tff(f679,plain,(
% 0.21/0.47 spl22_38 <=> ! [X0 : list(int),X1 : int] : zero_zero(nat) = size_size(atom,c_PresArith_Oatom_OLe(X1,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_38])])).
% 0.21/0.47 tff(f682,plain,(
% 0.21/0.47 ( ! [X0 : list(int),X1 : int] : (size_size(atom,c_PresArith_Oatom_OLe(X1,X0)) = atom_size(a)) ) | (~spl22_37 | ~spl22_38)),
% 0.21/0.47 inference(forward_demodulation,[],[f680,f676])).
% 0.21/0.47 tff(f680,plain,(
% 0.21/0.47 ( ! [X0 : list(int),X1 : int] : (zero_zero(nat) = size_size(atom,c_PresArith_Oatom_OLe(X1,X0))) ) | ~spl22_38),
% 0.21/0.47 inference(avatar_component_clause,[],[f679])).
% 0.21/0.47 tff(f738,plain,(
% 0.21/0.47 spl22_51),
% 0.21/0.47 inference(avatar_split_clause,[],[f485,f736])).
% 0.21/0.47 tff(f485,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0] : (pp(aa(X0,bool,fequal(X0,X2),X2))) )),
% 0.21/0.47 inference(equality_resolution,[],[f405])).
% 0.21/0.47 tff(f405,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (pp(aa(X0,bool,fequal(X0,X2),X1)) | X1 != X2) )),
% 0.21/0.47 inference(cnf_transformation,[],[f189])).
% 0.21/0.47 tff(f189,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0,X2 : X0] : (pp(aa(X0,bool,fequal(X0,X2),X1)) | X1 != X2)),
% 0.21/0.47 inference(rectify,[],[f123])).
% 0.21/0.47 tff(f123,axiom,(
% 0.21/0.47 ! [X0 : $tType,X13 : X0,X8 : X0] : (pp(aa(X0,bool,fequal(X0,X8),X13)) | X8 != X13)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T)).
% 0.21/0.47 tff(f734,plain,(
% 0.21/0.47 spl22_50),
% 0.21/0.47 inference(avatar_split_clause,[],[f483,f732])).
% 0.21/0.47 tff(f732,plain,(
% 0.21/0.47 spl22_50 <=> ! [X0 : $tType,X2 : X0,X3 : list(X0)] : nil(X0) != cons(X0,X2,X3)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_50])])).
% 0.21/0.47 tff(f483,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : list(X0)] : (nil(X0) != cons(X0,X2,X3)) )),
% 0.21/0.47 inference(equality_resolution,[],[f376])).
% 0.21/0.47 tff(f376,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0)] : (nil(X0) != X1 | cons(X0,X2,X3) != X1) )),
% 0.21/0.47 inference(cnf_transformation,[],[f278])).
% 0.21/0.47 tff(f730,plain,(
% 0.21/0.47 spl22_49),
% 0.21/0.47 inference(avatar_split_clause,[],[f452,f728])).
% 0.21/0.47 tff(f728,plain,(
% 0.21/0.47 spl22_49 <=> ! [X4 : int,X0 : list(int),X3 : int,X2 : list(int),X1 : int] : c_PresArith_Oatom_OLe(X1,X0) != nDvd(X4,X3,X2)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_49])])).
% 0.21/0.47 tff(f452,plain,(
% 0.21/0.47 ( ! [X2 : list(int),X3 : int,X0 : list(int),X1 : int,X4 : int] : (c_PresArith_Oatom_OLe(X1,X0) != nDvd(X4,X3,X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f211])).
% 0.21/0.47 tff(f211,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : list(int),X3 : int,X4 : int] : c_PresArith_Oatom_OLe(X1,X0) != nDvd(X4,X3,X2)),
% 0.21/0.47 inference(rectify,[],[f75])).
% 0.21/0.47 tff(f75,axiom,(
% 0.21/0.47 ! [X41 : list(int),X42 : int,X33 : list(int),X52 : int,X53 : int] : c_PresArith_Oatom_OLe(X42,X41) != nDvd(X53,X52,X33)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_atom_Osimps_I7_J)).
% 0.21/0.47 tff(f726,plain,(
% 0.21/0.47 spl22_48 | ~spl22_15 | ~spl22_32),
% 0.21/0.47 inference(avatar_split_clause,[],[f656,f650,f577,f723])).
% 0.21/0.47 tff(f723,plain,(
% 0.21/0.47 spl22_48 <=> divisor(a) = hd_coeff(a)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_48])])).
% 0.21/0.47 tff(f650,plain,(
% 0.21/0.47 spl22_32 <=> ! [X0 : list(int),X1 : int] : hd_coeff(a) = divisor(c_PresArith_Oatom_OLe(X1,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_32])])).
% 0.21/0.47 tff(f656,plain,(
% 0.21/0.47 divisor(a) = hd_coeff(a) | (~spl22_15 | ~spl22_32)),
% 0.21/0.47 inference(superposition,[],[f651,f579])).
% 0.21/0.47 tff(f651,plain,(
% 0.21/0.47 ( ! [X0 : list(int),X1 : int] : (hd_coeff(a) = divisor(c_PresArith_Oatom_OLe(X1,X0))) ) | ~spl22_32),
% 0.21/0.47 inference(avatar_component_clause,[],[f650])).
% 0.21/0.47 tff(f721,plain,(
% 0.21/0.47 spl22_47),
% 0.21/0.47 inference(avatar_split_clause,[],[f450,f719])).
% 0.21/0.47 tff(f719,plain,(
% 0.21/0.47 spl22_47 <=> ! [X2 : int,X4 : int,X0 : list(int),X3 : list(int),X1 : int] : dvd(X2,X1,X0) != c_PresArith_Oatom_OLe(X4,X3)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_47])])).
% 0.21/0.47 tff(f450,plain,(
% 0.21/0.47 ( ! [X2 : int,X3 : list(int),X0 : list(int),X1 : int,X4 : int] : (dvd(X2,X1,X0) != c_PresArith_Oatom_OLe(X4,X3)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f209])).
% 0.21/0.47 tff(f209,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int,X3 : list(int),X4 : int] : dvd(X2,X1,X0) != c_PresArith_Oatom_OLe(X4,X3)),
% 0.21/0.47 inference(rectify,[],[f71])).
% 0.21/0.47 tff(f71,axiom,(
% 0.21/0.47 ! [X33 : list(int),X52 : int,X53 : int,X41 : list(int),X42 : int] : c_PresArith_Oatom_OLe(X42,X41) != dvd(X53,X52,X33)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_atom_Osimps_I4_J)).
% 0.21/0.47 tff(f717,plain,(
% 0.21/0.47 spl22_46),
% 0.21/0.47 inference(avatar_split_clause,[],[f425,f715])).
% 0.21/0.47 tff(f715,plain,(
% 0.21/0.47 spl22_46 <=> ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (listMem(X0,X2,X1) | ~sP0(X0,X1,X2))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_46])])).
% 0.21/0.47 tff(f425,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (listMem(X0,X2,X1) | ~sP0(X0,X1,X2)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f295])).
% 0.21/0.47 tff(f713,plain,(
% 0.21/0.47 spl22_45),
% 0.21/0.47 inference(avatar_split_clause,[],[f391,f711])).
% 0.21/0.47 tff(f711,plain,(
% 0.21/0.47 spl22_45 <=> ! [X2 : int,X0 : atom,X1 : list(int)] : divisor(X0) = divisor(asubst(X2,X1,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_45])])).
% 0.21/0.47 tff(f391,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : atom,X1 : list(int)] : (divisor(X0) = divisor(asubst(X2,X1,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f176])).
% 0.21/0.47 tff(f176,plain,(
% 0.21/0.47 ! [X0 : atom,X1 : list(int),X2 : int] : divisor(X0) = divisor(asubst(X2,X1,X0))),
% 0.21/0.47 inference(rectify,[],[f95])).
% 0.21/0.47 tff(f95,axiom,(
% 0.21/0.47 ! [X25 : atom,X19 : list(int),X20 : int] : divisor(X25) = divisor(asubst(X20,X19,X25))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_divisor__asubst)).
% 0.21/0.47 tff(f708,plain,(
% 0.21/0.47 spl22_44),
% 0.21/0.47 inference(avatar_split_clause,[],[f390,f706])).
% 0.21/0.47 tff(f390,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (zero_zero(nat) = atom_size(nDvd(X2,X1,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f175])).
% 0.21/0.47 tff(f175,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int] : zero_zero(nat) = atom_size(nDvd(X2,X1,X0))),
% 0.21/0.47 inference(rectify,[],[f66])).
% 0.21/0.47 tff(f66,axiom,(
% 0.21/0.47 ! [X41 : list(int),X49 : int,X50 : int] : zero_zero(nat) = atom_size(nDvd(X50,X49,X41))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_atom_Osize_I3_J)).
% 0.21/0.47 tff(f703,plain,(
% 0.21/0.47 spl22_43),
% 0.21/0.47 inference(avatar_split_clause,[],[f389,f701])).
% 0.21/0.47 tff(f389,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (zero_zero(nat) = atom_size(dvd(X2,X1,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f174])).
% 0.21/0.47 tff(f174,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int] : zero_zero(nat) = atom_size(dvd(X2,X1,X0))),
% 0.21/0.47 inference(rectify,[],[f64])).
% 0.21/0.47 tff(f64,axiom,(
% 0.21/0.47 ! [X41 : list(int),X49 : int,X50 : int] : zero_zero(nat) = atom_size(dvd(X50,X49,X41))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_atom_Osize_I2_J)).
% 0.21/0.47 tff(f699,plain,(
% 0.21/0.47 spl22_42),
% 0.21/0.47 inference(avatar_split_clause,[],[f373,f697])).
% 0.21/0.47 tff(f697,plain,(
% 0.21/0.47 spl22_42 <=> ! [X0 : $tType,X1 : list(X0)] : (nil(X0) = X1 | ~null(X0,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_42])])).
% 0.21/0.47 tff(f373,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : list(X0)] : (nil(X0) = X1 | ~null(X0,X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f274])).
% 0.21/0.47 tff(f274,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : ((null(X0,X1) | nil(X0) != X1) & (nil(X0) = X1 | ~null(X0,X1)))),
% 0.21/0.47 inference(nnf_transformation,[],[f162])).
% 0.21/0.47 tff(f162,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : (null(X0,X1) <=> nil(X0) = X1)),
% 0.21/0.47 inference(rectify,[],[f31])).
% 0.21/0.47 tff(f31,axiom,(
% 0.21/0.47 ! [X0 : $tType,X16 : list(X0)] : (null(X0,X16) <=> nil(X0) = X16)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_List_Onull__def)).
% 0.21/0.47 tff(f695,plain,(
% 0.21/0.47 spl22_41),
% 0.21/0.47 inference(avatar_split_clause,[],[f363,f693])).
% 0.21/0.47 tff(f693,plain,(
% 0.21/0.47 spl22_41 <=> ! [X0 : $tType,X1 : list(X0)] : splice(X0,nil(X0),X1) = X1),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_41])])).
% 0.21/0.47 tff(f363,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : list(X0)] : (splice(X0,nil(X0),X1) = X1) )),
% 0.21/0.47 inference(cnf_transformation,[],[f152])).
% 0.21/0.47 tff(f152,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : splice(X0,nil(X0),X1) = X1),
% 0.21/0.47 inference(rectify,[],[f30])).
% 0.21/0.47 tff(f30,axiom,(
% 0.21/0.47 ! [X0 : $tType,X12 : list(X0)] : splice(X0,nil(X0),X12) = X12),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_splice_Osimps_I1_J)).
% 0.21/0.47 tff(f691,plain,(
% 0.21/0.47 spl22_40),
% 0.21/0.47 inference(avatar_split_clause,[],[f362,f689])).
% 0.21/0.47 tff(f689,plain,(
% 0.21/0.47 spl22_40 <=> ! [X0 : $tType,X1 : list(X0)] : splice(X0,X1,nil(X0)) = X1),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_40])])).
% 0.21/0.47 tff(f362,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : list(X0)] : (splice(X0,X1,nil(X0)) = X1) )),
% 0.21/0.47 inference(cnf_transformation,[],[f151])).
% 0.21/0.47 tff(f151,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0)] : splice(X0,X1,nil(X0)) = X1),
% 0.21/0.47 inference(rectify,[],[f29])).
% 0.21/0.47 tff(f29,axiom,(
% 0.21/0.47 ! [X0 : $tType,X9 : list(X0)] : splice(X0,X9,nil(X0)) = X9),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_splice__Nil2)).
% 0.21/0.47 tff(f686,plain,(
% 0.21/0.47 spl22_39),
% 0.21/0.47 inference(avatar_split_clause,[],[f361,f684])).
% 0.21/0.47 tff(f361,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : fun(X0,nat)] : (zero_zero(nat) = list_size(X0,X1,nil(X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f150])).
% 0.21/0.47 tff(f150,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(X0,nat)] : zero_zero(nat) = list_size(X0,X1,nil(X0))),
% 0.21/0.47 inference(rectify,[],[f80])).
% 0.21/0.47 tff(f80,axiom,(
% 0.21/0.47 ! [X0 : $tType,X57 : fun(X0,nat)] : zero_zero(nat) = list_size(X0,X57,nil(X0))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_list_Osize_I1_J)).
% 0.21/0.47 tff(f681,plain,(
% 0.21/0.47 spl22_38),
% 0.21/0.47 inference(avatar_split_clause,[],[f360,f679])).
% 0.21/0.47 tff(f360,plain,(
% 0.21/0.47 ( ! [X0 : list(int),X1 : int] : (zero_zero(nat) = size_size(atom,c_PresArith_Oatom_OLe(X1,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f149])).
% 0.21/0.47 tff(f149,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int] : zero_zero(nat) = size_size(atom,c_PresArith_Oatom_OLe(X1,X0))),
% 0.21/0.47 inference(rectify,[],[f51])).
% 0.21/0.47 tff(f51,axiom,(
% 0.21/0.47 ! [X41 : list(int),X42 : int] : zero_zero(nat) = size_size(atom,c_PresArith_Oatom_OLe(X42,X41))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_atom_Osize_I4_J)).
% 0.21/0.47 tff(f677,plain,(
% 0.21/0.47 spl22_37 | ~spl22_15 | ~spl22_26),
% 0.21/0.47 inference(avatar_split_clause,[],[f654,f626,f577,f674])).
% 0.21/0.47 tff(f626,plain,(
% 0.21/0.47 spl22_26 <=> ! [X0 : list(int),X1 : int] : zero_zero(nat) = atom_size(c_PresArith_Oatom_OLe(X1,X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_26])])).
% 0.21/0.47 tff(f654,plain,(
% 0.21/0.47 zero_zero(nat) = atom_size(a) | (~spl22_15 | ~spl22_26)),
% 0.21/0.47 inference(superposition,[],[f627,f579])).
% 0.21/0.47 tff(f627,plain,(
% 0.21/0.47 ( ! [X0 : list(int),X1 : int] : (zero_zero(nat) = atom_size(c_PresArith_Oatom_OLe(X1,X0))) ) | ~spl22_26),
% 0.21/0.47 inference(avatar_component_clause,[],[f626])).
% 0.21/0.47 tff(f672,plain,(
% 0.21/0.47 spl22_36),
% 0.21/0.47 inference(avatar_split_clause,[],[f339,f670])).
% 0.21/0.47 tff(f339,plain,(
% 0.21/0.47 ( ! [X0 : bool] : (~pp(X0) | ~pp(aa(bool,bool,fNot,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f132])).
% 0.21/0.47 tff(f132,plain,(
% 0.21/0.47 ! [X0 : bool] : (~pp(X0) | ~pp(aa(bool,bool,fNot,X0)))),
% 0.21/0.47 inference(rectify,[],[f110])).
% 0.21/0.47 tff(f110,axiom,(
% 0.21/0.47 ! [X63 : bool] : (~pp(X63) | ~pp(aa(bool,bool,fNot,X63)))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U)).
% 0.21/0.47 tff(f668,plain,(
% 0.21/0.47 spl22_35),
% 0.21/0.47 inference(avatar_split_clause,[],[f336,f666])).
% 0.21/0.47 tff(f336,plain,(
% 0.21/0.47 ( ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f129])).
% 0.21/0.47 tff(f129,plain,(
% 0.21/0.47 ! [X0 : bool] : (pp(aa(bool,bool,fNot,X0)) | pp(X0))),
% 0.21/0.47 inference(rectify,[],[f111])).
% 0.21/0.47 tff(f111,axiom,(
% 0.21/0.47 ! [X63 : bool] : (pp(aa(bool,bool,fNot,X63)) | pp(X63))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U)).
% 0.21/0.47 tff(f664,plain,(
% 0.21/0.47 spl22_34),
% 0.21/0.47 inference(avatar_split_clause,[],[f335,f662])).
% 0.21/0.47 tff(f662,plain,(
% 0.21/0.47 spl22_34 <=> ! [X0 : $tType] : nil(X0) = tl(X0,nil(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_34])])).
% 0.21/0.47 tff(f335,plain,(
% 0.21/0.47 ( ! [X0 : $tType] : (nil(X0) = tl(X0,nil(X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f89])).
% 0.21/0.47 tff(f89,axiom,(
% 0.21/0.47 ! [X0 : $tType] : nil(X0) = tl(X0,nil(X0))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_tl_Osimps_I1_J)).
% 0.21/0.47 tff(f660,plain,(
% 0.21/0.47 spl22_33),
% 0.21/0.47 inference(avatar_split_clause,[],[f334,f658])).
% 0.21/0.47 tff(f658,plain,(
% 0.21/0.47 spl22_33 <=> ! [X0 : int] : zero_zero(int) = div_mod(int,zero_zero(int),X0)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_33])])).
% 0.21/0.47 tff(f334,plain,(
% 0.21/0.47 ( ! [X0 : int] : (zero_zero(int) = div_mod(int,zero_zero(int),X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f128])).
% 0.21/0.47 tff(f128,plain,(
% 0.21/0.47 ! [X0 : int] : zero_zero(int) = div_mod(int,zero_zero(int),X0)),
% 0.21/0.47 inference(rectify,[],[f41])).
% 0.21/0.47 tff(f41,axiom,(
% 0.21/0.47 ! [X24 : int] : zero_zero(int) = div_mod(int,zero_zero(int),X24)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_zmod__zero)).
% 0.21/0.47 tff(f652,plain,(
% 0.21/0.47 spl22_32),
% 0.21/0.47 inference(avatar_split_clause,[],[f502,f650])).
% 0.21/0.47 tff(f502,plain,(
% 0.21/0.47 ( ! [X0 : list(int),X1 : int] : (hd_coeff(a) = divisor(c_PresArith_Oatom_OLe(X1,X0))) )),
% 0.21/0.47 inference(forward_demodulation,[],[f358,f329])).
% 0.21/0.47 tff(f329,plain,(
% 0.21/0.47 hd_coeff(a) = one_one(int)),
% 0.21/0.47 inference(cnf_transformation,[],[f5])).
% 0.21/0.47 tff(f5,axiom,(
% 0.21/0.47 hd_coeff(a) = one_one(int)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_assms_I2_J)).
% 0.21/0.47 tff(f358,plain,(
% 0.21/0.47 ( ! [X0 : list(int),X1 : int] : (one_one(int) = divisor(c_PresArith_Oatom_OLe(X1,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f147])).
% 0.21/0.47 tff(f147,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int] : one_one(int) = divisor(c_PresArith_Oatom_OLe(X1,X0))),
% 0.21/0.47 inference(rectify,[],[f15])).
% 0.21/0.47 tff(f15,axiom,(
% 0.21/0.47 ! [X19 : list(int),X20 : int] : one_one(int) = divisor(c_PresArith_Oatom_OLe(X20,X19))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_divisor_Osimps_I1_J)).
% 0.21/0.47 tff(f648,plain,(
% 0.21/0.47 spl22_31),
% 0.21/0.47 inference(avatar_split_clause,[],[f493,f646])).
% 0.21/0.47 tff(f646,plain,(
% 0.21/0.47 spl22_31 <=> ! [X0 : $tType,X2 : list(X0),X3 : X0] : member1(X0,cons(X0,X3,X2),X3)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_31])])).
% 0.21/0.47 tff(f493,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X3 : X0] : (member1(X0,cons(X0,X3,X2),X3)) )),
% 0.21/0.47 inference(equality_resolution,[],[f445])).
% 0.21/0.47 tff(f445,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X3 : X0,X1 : X0] : (member1(X0,cons(X0,X3,X2),X1) | X1 != X3) )),
% 0.21/0.47 inference(cnf_transformation,[],[f304])).
% 0.21/0.47 tff(f644,plain,(
% 0.21/0.47 spl22_30),
% 0.21/0.47 inference(avatar_split_clause,[],[f386,f642])).
% 0.21/0.47 tff(f642,plain,(
% 0.21/0.47 spl22_30 <=> ! [X0 : $tType,X2 : X0,X1 : list(X0)] : listMem(X0,X2,cons(X0,X2,X1))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_30])])).
% 0.21/0.47 tff(f386,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (listMem(X0,X2,cons(X0,X2,X1))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f171])).
% 0.21/0.47 tff(f171,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : listMem(X0,X2,cons(X0,X2,X1))),
% 0.21/0.47 inference(rectify,[],[f13])).
% 0.21/0.47 tff(f13,axiom,(
% 0.21/0.47 ! [X0 : $tType,X9 : list(X0),X8 : X0] : listMem(X0,X8,cons(X0,X8,X9))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_elem)).
% 0.21/0.47 tff(f640,plain,(
% 0.21/0.47 spl22_29),
% 0.21/0.47 inference(avatar_split_clause,[],[f385,f638])).
% 0.21/0.47 tff(f638,plain,(
% 0.21/0.47 spl22_29 <=> ! [X2 : int,X0 : list(int),X1 : int] : divisor(nDvd(X2,X1,X0)) = X2),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_29])])).
% 0.21/0.47 tff(f385,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (divisor(nDvd(X2,X1,X0)) = X2) )),
% 0.21/0.47 inference(cnf_transformation,[],[f170])).
% 0.21/0.47 tff(f170,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int] : divisor(nDvd(X2,X1,X0)) = X2),
% 0.21/0.47 inference(rectify,[],[f68])).
% 0.21/0.47 tff(f68,axiom,(
% 0.21/0.47 ! [X19 : list(int),X20 : int,X51 : int] : divisor(nDvd(X51,X20,X19)) = X51),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_divisor_Osimps_I3_J)).
% 0.21/0.47 tff(f636,plain,(
% 0.21/0.47 spl22_28),
% 0.21/0.47 inference(avatar_split_clause,[],[f384,f634])).
% 0.21/0.47 tff(f634,plain,(
% 0.21/0.47 spl22_28 <=> ! [X2 : int,X0 : list(int),X1 : int] : divisor(dvd(X2,X1,X0)) = X2),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_28])])).
% 0.21/0.47 tff(f384,plain,(
% 0.21/0.47 ( ! [X2 : int,X0 : list(int),X1 : int] : (divisor(dvd(X2,X1,X0)) = X2) )),
% 0.21/0.47 inference(cnf_transformation,[],[f169])).
% 0.21/0.47 tff(f169,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int,X2 : int] : divisor(dvd(X2,X1,X0)) = X2),
% 0.21/0.47 inference(rectify,[],[f67])).
% 0.21/0.47 tff(f67,axiom,(
% 0.21/0.47 ! [X19 : list(int),X20 : int,X51 : int] : divisor(dvd(X51,X20,X19)) = X51),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_divisor_Osimps_I2_J)).
% 0.21/0.47 tff(f632,plain,(
% 0.21/0.47 spl22_27),
% 0.21/0.47 inference(avatar_split_clause,[],[f382,f630])).
% 0.21/0.47 tff(f630,plain,(
% 0.21/0.47 spl22_27 <=> ! [X0 : $tType,X2 : list(X0),X1 : X0] : cons(X0,X1,X2) != X2),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_27])])).
% 0.21/0.47 tff(f382,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X1 : X0] : (cons(X0,X1,X2) != X2) )),
% 0.21/0.47 inference(cnf_transformation,[],[f167])).
% 0.21/0.47 tff(f167,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0,X2 : list(X0)] : cons(X0,X1,X2) != X2),
% 0.21/0.47 inference(rectify,[],[f6])).
% 0.21/0.47 tff(f6,axiom,(
% 0.21/0.47 ! [X0 : $tType,X8 : X0,X9 : list(X0)] : cons(X0,X8,X9) != X9),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_not__Cons__self)).
% 0.21/0.47 tff(f628,plain,(
% 0.21/0.47 spl22_26),
% 0.21/0.47 inference(avatar_split_clause,[],[f359,f626])).
% 0.21/0.47 tff(f359,plain,(
% 0.21/0.47 ( ! [X0 : list(int),X1 : int] : (zero_zero(nat) = atom_size(c_PresArith_Oatom_OLe(X1,X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f148])).
% 0.21/0.47 tff(f148,plain,(
% 0.21/0.47 ! [X0 : list(int),X1 : int] : zero_zero(nat) = atom_size(c_PresArith_Oatom_OLe(X1,X0))),
% 0.21/0.47 inference(rectify,[],[f50])).
% 0.21/0.47 tff(f50,axiom,(
% 0.21/0.47 ! [X41 : list(int),X42 : int] : atom_size(c_PresArith_Oatom_OLe(X42,X41)) = zero_zero(nat)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_atom_Osize_I1_J)).
% 0.21/0.47 tff(f624,plain,(
% 0.21/0.47 spl22_25 | ~spl22_11 | ~spl22_21),
% 0.21/0.47 inference(avatar_split_clause,[],[f611,f603,f559,f622])).
% 0.21/0.47 tff(f622,plain,(
% 0.21/0.47 spl22_25 <=> ! [X0 : bool] : (pp(X0) | fFalse = X0)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_25])])).
% 0.21/0.47 tff(f559,plain,(
% 0.21/0.47 spl22_11 <=> pp(fTrue)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_11])])).
% 0.21/0.47 tff(f611,plain,(
% 0.21/0.47 ( ! [X0 : bool] : (pp(X0) | fFalse = X0) ) | (~spl22_11 | ~spl22_21)),
% 0.21/0.47 inference(superposition,[],[f561,f604])).
% 0.21/0.47 tff(f561,plain,(
% 0.21/0.47 pp(fTrue) | ~spl22_11),
% 0.21/0.47 inference(avatar_component_clause,[],[f559])).
% 0.21/0.47 tff(f620,plain,(
% 0.21/0.47 spl22_24),
% 0.21/0.47 inference(avatar_split_clause,[],[f344,f618])).
% 0.21/0.47 tff(f344,plain,(
% 0.21/0.47 ( ! [X0 : $tType] : (one_one(X0) != zero_zero(X0) | ~zero_neq_one(X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f233])).
% 0.21/0.47 tff(f233,plain,(
% 0.21/0.47 ! [X0 : $tType] : (one_one(X0) != zero_zero(X0) | ~zero_neq_one(X0))),
% 0.21/0.47 inference(ennf_transformation,[],[f53])).
% 0.21/0.47 tff(f53,axiom,(
% 0.21/0.47 ! [X0 : $tType] : (zero_neq_one(X0) => one_one(X0) != zero_zero(X0))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_one__neq__zero)).
% 0.21/0.47 tff(f616,plain,(
% 0.21/0.47 spl22_23),
% 0.21/0.47 inference(avatar_split_clause,[],[f333,f614])).
% 0.21/0.47 tff(f614,plain,(
% 0.21/0.47 spl22_23 <=> ! [X0 : int] : zero_zero(int) = div_mod(int,X0,X0)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_23])])).
% 0.21/0.47 tff(f333,plain,(
% 0.21/0.47 ( ! [X0 : int] : (zero_zero(int) = div_mod(int,X0,X0)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f127])).
% 0.21/0.47 tff(f127,plain,(
% 0.21/0.47 ! [X0 : int] : zero_zero(int) = div_mod(int,X0,X0)),
% 0.21/0.47 inference(rectify,[],[f42])).
% 0.21/0.47 tff(f42,axiom,(
% 0.21/0.47 ! [X25 : int] : zero_zero(int) = div_mod(int,X25,X25)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_zmod__self)).
% 0.21/0.47 tff(f609,plain,(
% 0.21/0.47 spl22_22),
% 0.21/0.47 inference(avatar_split_clause,[],[f381,f607])).
% 0.21/0.47 tff(f381,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : X0,X1 : list(X0)] : (~null(X0,cons(X0,X2,X1))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f166])).
% 0.21/0.47 tff(f166,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : list(X0),X2 : X0] : ~null(X0,cons(X0,X2,X1))),
% 0.21/0.47 inference(rectify,[],[f11])).
% 0.21/0.47 tff(f11,axiom,(
% 0.21/0.47 ! [X0 : $tType,X9 : list(X0),X8 : X0] : ~null(X0,cons(X0,X8,X9))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_null__rec_I1_J)).
% 0.21/0.47 tff(f605,plain,(
% 0.21/0.47 spl22_21),
% 0.21/0.47 inference(avatar_split_clause,[],[f337,f603])).
% 0.21/0.47 tff(f337,plain,(
% 0.21/0.47 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) )),
% 0.21/0.47 inference(cnf_transformation,[],[f130])).
% 0.21/0.47 tff(f130,plain,(
% 0.21/0.47 ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 0.21/0.47 inference(rectify,[],[f121])).
% 0.21/0.47 tff(f121,axiom,(
% 0.21/0.47 ! [X63 : bool] : (fFalse = X63 | fTrue = X63)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T)).
% 0.21/0.47 tff(f601,plain,(
% 0.21/0.47 spl22_20),
% 0.21/0.47 inference(avatar_split_clause,[],[f490,f599])).
% 0.21/0.47 tff(f599,plain,(
% 0.21/0.47 spl22_20 <=> ! [X0 : $tType,X2 : list(X0)] : equal_equal(list(X0),X2,X2)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_20])])).
% 0.21/0.47 tff(f490,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0)] : (equal_equal(list(X0),X2,X2)) )),
% 0.21/0.47 inference(equality_resolution,[],[f427])).
% 0.21/0.47 tff(f427,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X2 : list(X0),X1 : list(X0)] : (equal_equal(list(X0),X2,X1) | X1 != X2) )),
% 0.21/0.47 inference(cnf_transformation,[],[f296])).
% 0.21/0.47 tff(f597,plain,(
% 0.21/0.47 spl22_19),
% 0.21/0.47 inference(avatar_split_clause,[],[f357,f595])).
% 0.21/0.47 tff(f595,plain,(
% 0.21/0.47 spl22_19 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : list_all(X0,X1,nil(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_19])])).
% 0.21/0.47 tff(f357,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (list_all(X0,X1,nil(X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f146])).
% 0.21/0.47 tff(f146,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(X0,bool)] : list_all(X0,X1,nil(X0))),
% 0.21/0.47 inference(rectify,[],[f56])).
% 0.21/0.47 tff(f56,axiom,(
% 0.21/0.47 ! [X0 : $tType,X38 : fun(X0,bool)] : list_all(X0,X38,nil(X0))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_list__all__simps_I2_J)).
% 0.21/0.47 tff(f593,plain,(
% 0.21/0.47 spl22_18),
% 0.21/0.47 inference(avatar_split_clause,[],[f356,f591])).
% 0.21/0.47 tff(f591,plain,(
% 0.21/0.47 spl22_18 <=> ! [X0 : $tType,X1 : X0] : ~member1(X0,nil(X0),X1)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_18])])).
% 0.21/0.47 tff(f356,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : X0] : (~member1(X0,nil(X0),X1)) )),
% 0.21/0.47 inference(cnf_transformation,[],[f145])).
% 0.21/0.47 tff(f145,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : X0] : ~member1(X0,nil(X0),X1)),
% 0.21/0.47 inference(rectify,[],[f24])).
% 0.21/0.47 tff(f24,axiom,(
% 0.21/0.47 ! [X0 : $tType,X13 : X0] : ~member1(X0,nil(X0),X13)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_member__rec_I2_J)).
% 0.21/0.47 tff(f589,plain,(
% 0.21/0.47 spl22_17),
% 0.21/0.47 inference(avatar_split_clause,[],[f355,f587])).
% 0.21/0.47 tff(f587,plain,(
% 0.21/0.47 spl22_17 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : ~list_ex1(X0,X1,nil(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_17])])).
% 0.21/0.47 tff(f355,plain,(
% 0.21/0.47 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (~list_ex1(X0,X1,nil(X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f144])).
% 0.21/0.47 tff(f144,plain,(
% 0.21/0.47 ! [X0 : $tType,X1 : fun(X0,bool)] : ~list_ex1(X0,X1,nil(X0))),
% 0.21/0.47 inference(rectify,[],[f40])).
% 0.21/0.47 tff(f40,axiom,(
% 0.21/0.47 ! [X0 : $tType,X38 : fun(X0,bool)] : ~list_ex1(X0,X38,nil(X0))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_list__ex1__simps_I1_J)).
% 0.21/0.47 tff(f585,plain,(
% 0.21/0.47 spl22_16),
% 0.21/0.47 inference(avatar_split_clause,[],[f329,f582])).
% 0.21/0.47 tff(f582,plain,(
% 0.21/0.47 spl22_16 <=> hd_coeff(a) = one_one(int)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_16])])).
% 0.21/0.47 tff(f580,plain,(
% 0.21/0.47 spl22_15),
% 0.21/0.47 inference(avatar_split_clause,[],[f328,f577])).
% 0.21/0.47 tff(f328,plain,(
% 0.21/0.47 a = c_PresArith_Oatom_OLe(int1,list1)),
% 0.21/0.47 inference(cnf_transformation,[],[f1])).
% 0.21/0.47 tff(f1,axiom,(
% 0.21/0.47 a = c_PresArith_Oatom_OLe(int1,list1)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Le)).
% 0.21/0.47 tff(f575,plain,(
% 0.21/0.47 spl22_14),
% 0.21/0.47 inference(avatar_split_clause,[],[f332,f573])).
% 0.21/0.47 tff(f573,plain,(
% 0.21/0.47 spl22_14 <=> ! [X0 : $tType] : null(X0,nil(X0))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_14])])).
% 0.21/0.47 tff(f332,plain,(
% 0.21/0.47 ( ! [X0 : $tType] : (null(X0,nil(X0))) )),
% 0.21/0.47 inference(cnf_transformation,[],[f126])).
% 0.21/0.47 tff(f126,plain,(
% 0.21/0.47 ! [X0 : $tType] : null(X0,nil(X0))),
% 0.21/0.47 inference(rectify,[],[f32])).
% 0.21/0.47 tff(f32,axiom,(
% 0.21/0.47 ! [X1 : $tType] : null(X1,nil(X1))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_null__rec_I2_J)).
% 0.21/0.47 tff(f571,plain,(
% 0.21/0.47 spl22_12 | spl22_13),
% 0.21/0.47 inference(avatar_split_clause,[],[f313,f568,f564])).
% 0.21/0.47 tff(f564,plain,(
% 0.21/0.47 spl22_12 <=> i_Z(a,cons(int,i,e))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_12])])).
% 0.21/0.47 tff(f568,plain,(
% 0.21/0.47 spl22_13 <=> i_Z(a,cons(int,j,e))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_13])])).
% 0.21/0.47 tff(f313,plain,(
% 0.21/0.47 i_Z(a,cons(int,j,e)) | i_Z(a,cons(int,i,e))),
% 0.21/0.47 inference(cnf_transformation,[],[f264])).
% 0.21/0.47 tff(f264,plain,(
% 0.21/0.47 (~i_Z(a,cons(int,j,e)) | ~i_Z(a,cons(int,i,e))) & (i_Z(a,cons(int,j,e)) | i_Z(a,cons(int,i,e)))),
% 0.21/0.47 inference(nnf_transformation,[],[f229])).
% 0.21/0.47 tff(f229,plain,(
% 0.21/0.47 i_Z(a,cons(int,i,e)) <~> i_Z(a,cons(int,j,e))),
% 0.21/0.47 inference(ennf_transformation,[],[f125])).
% 0.21/0.47 tff(f125,negated_conjecture,(
% 0.21/0.47 ~(i_Z(a,cons(int,i,e)) <=> i_Z(a,cons(int,j,e)))),
% 0.21/0.47 inference(negated_conjecture,[],[f124])).
% 0.21/0.47 tff(f124,conjecture,(
% 0.21/0.47 i_Z(a,cons(int,i,e)) <=> i_Z(a,cons(int,j,e))),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.21/0.47 tff(f562,plain,(
% 0.21/0.47 spl22_11),
% 0.21/0.47 inference(avatar_split_clause,[],[f326,f559])).
% 0.21/0.47 tff(f326,plain,(
% 0.21/0.47 pp(fTrue)),
% 0.21/0.47 inference(cnf_transformation,[],[f109])).
% 0.21/0.47 tff(f109,axiom,(
% 0.21/0.47 pp(fTrue)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U)).
% 0.21/0.47 tff(f557,plain,(
% 0.21/0.47 spl22_10),
% 0.21/0.47 inference(avatar_split_clause,[],[f325,f554])).
% 0.21/0.47 tff(f554,plain,(
% 0.21/0.47 spl22_10 <=> zero(int)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_10])])).
% 0.21/0.47 tff(f325,plain,(
% 0.21/0.47 zero(int)),
% 0.21/0.47 inference(cnf_transformation,[],[f101])).
% 0.21/0.47 tff(f101,axiom,(
% 0.21/0.47 zero(int)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero)).
% 0.21/0.47 tff(f552,plain,(
% 0.21/0.47 spl22_9),
% 0.21/0.47 inference(avatar_split_clause,[],[f324,f549])).
% 0.21/0.47 tff(f549,plain,(
% 0.21/0.47 spl22_9 <=> zero(nat)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_9])])).
% 0.21/0.47 tff(f324,plain,(
% 0.21/0.47 zero(nat)),
% 0.21/0.47 inference(cnf_transformation,[],[f106])).
% 0.21/0.47 tff(f106,axiom,(
% 0.21/0.47 zero(nat)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero)).
% 0.21/0.47 tff(f547,plain,(
% 0.21/0.47 spl22_8),
% 0.21/0.47 inference(avatar_split_clause,[],[f323,f544])).
% 0.21/0.47 tff(f323,plain,(
% 0.21/0.47 semiring_div(int)),
% 0.21/0.47 inference(cnf_transformation,[],[f99])).
% 0.21/0.47 tff(f99,axiom,(
% 0.21/0.47 semiring_div(int)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div)).
% 0.21/0.47 tff(f542,plain,(
% 0.21/0.47 spl22_7),
% 0.21/0.47 inference(avatar_split_clause,[],[f322,f539])).
% 0.21/0.47 tff(f322,plain,(
% 0.21/0.47 semiring_div(nat)),
% 0.21/0.47 inference(cnf_transformation,[],[f104])).
% 0.21/0.47 tff(f104,axiom,(
% 0.21/0.47 semiring_div(nat)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Divides_Osemiring__div)).
% 0.21/0.47 tff(f537,plain,(
% 0.21/0.47 spl22_6),
% 0.21/0.47 inference(avatar_split_clause,[],[f321,f534])).
% 0.21/0.47 tff(f534,plain,(
% 0.21/0.47 spl22_6 <=> zero_neq_one(int)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_6])])).
% 0.21/0.47 tff(f321,plain,(
% 0.21/0.47 zero_neq_one(int)),
% 0.21/0.47 inference(cnf_transformation,[],[f100])).
% 0.21/0.47 tff(f100,axiom,(
% 0.21/0.47 zero_neq_one(int)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one)).
% 0.21/0.47 tff(f532,plain,(
% 0.21/0.47 spl22_5),
% 0.21/0.47 inference(avatar_split_clause,[],[f320,f529])).
% 0.21/0.47 tff(f320,plain,(
% 0.21/0.47 zero_neq_one(nat)),
% 0.21/0.47 inference(cnf_transformation,[],[f105])).
% 0.21/0.47 tff(f105,axiom,(
% 0.21/0.47 zero_neq_one(nat)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one)).
% 0.21/0.47 tff(f527,plain,(
% 0.21/0.47 spl22_4),
% 0.21/0.47 inference(avatar_split_clause,[],[f319,f524])).
% 0.21/0.47 tff(f524,plain,(
% 0.21/0.47 spl22_4 <=> one(int)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_4])])).
% 0.21/0.47 tff(f319,plain,(
% 0.21/0.47 one(int)),
% 0.21/0.47 inference(cnf_transformation,[],[f103])).
% 0.21/0.47 tff(f103,axiom,(
% 0.21/0.47 one(int)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone)).
% 0.21/0.47 tff(f522,plain,(
% 0.21/0.47 spl22_3),
% 0.21/0.47 inference(avatar_split_clause,[],[f318,f519])).
% 0.21/0.47 tff(f519,plain,(
% 0.21/0.47 spl22_3 <=> one(nat)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_3])])).
% 0.21/0.47 tff(f318,plain,(
% 0.21/0.47 one(nat)),
% 0.21/0.47 inference(cnf_transformation,[],[f107])).
% 0.21/0.47 tff(f107,axiom,(
% 0.21/0.47 one(nat)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone)).
% 0.21/0.47 tff(f517,plain,(
% 0.21/0.47 spl22_2),
% 0.21/0.47 inference(avatar_split_clause,[],[f317,f514])).
% 0.21/0.47 tff(f514,plain,(
% 0.21/0.47 spl22_2 <=> ring(int)),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl22_2])])).
% 0.21/0.47 tff(f317,plain,(
% 0.21/0.47 ring(int)),
% 0.21/0.47 inference(cnf_transformation,[],[f102])).
% 0.21/0.47 tff(f102,axiom,(
% 0.21/0.47 ring(int)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring)).
% 0.21/0.47 tff(f512,plain,(
% 0.21/0.47 ~spl22_1),
% 0.21/0.47 inference(avatar_split_clause,[],[f315,f509])).
% 0.21/0.47 tff(f315,plain,(
% 0.21/0.47 ~pp(fFalse)),
% 0.21/0.47 inference(cnf_transformation,[],[f108])).
% 0.21/0.47 tff(f108,axiom,(
% 0.21/0.47 ~pp(fFalse)),
% 0.21/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U)).
% 0.21/0.47 % SZS output end Proof for theBenchmark
% 0.21/0.47 % (19711)------------------------------
% 0.21/0.47 % (19711)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.47 % (19711)Termination reason: Refutation
% 0.21/0.47
% 0.21/0.47 % (19711)Memory used [KB]: 1928
% 0.21/0.47 % (19711)Time elapsed: 0.082 s
% 0.21/0.47 % (19711)Instructions burned: 135 (million)
% 0.21/0.47 % (19711)------------------------------
% 0.21/0.47 % (19711)------------------------------
% 0.21/0.47 % (19706)Success in time 0.097 s
%------------------------------------------------------------------------------