TSTP Solution File: LCL789_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL789_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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:49:23 EDT 2024
% Result : Theorem 0.15s 0.41s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL789_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n005.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 : Mon Apr 29 22:48:56 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (31932)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (31933)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (31935)WARNING: value z3 for option sas not known
% 0.15/0.39 % (31934)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 % (31936)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (31935)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)
% 0.15/0.39 % (31937)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)
% 0.15/0.39 % (31938)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)
% 0.15/0.39 % (31939)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)
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % (31939)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 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
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % (31940)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.41 % (31937)First to succeed.
% 0.15/0.41 % (31940)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.41 % Exception at run slice level
% 0.15/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.41 % (31938)Also succeeded, but the first one will report.
% 0.15/0.41 % (31941)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)
% 0.15/0.41 % (31937)Refutation found. Thanks to Tanya!
% 0.15/0.41 % SZS status Theorem for theBenchmark
% 0.15/0.41 % SZS output start Proof for theBenchmark
% 0.15/0.41 tff(type_def_5, type, bool: $tType).
% 0.15/0.41 tff(type_def_6, type, dB: $tType).
% 0.15/0.41 tff(type_def_7, type, list: $tType > $tType).
% 0.15/0.41 tff(type_def_8, type, nat: $tType).
% 0.15/0.41 tff(type_def_9, type, type: $tType).
% 0.15/0.41 tff(type_def_10, type, fun1: ($tType * $tType) > $tType).
% 0.15/0.41 tff(func_def_0, type, combb: !>[X0: $tType, X1: $tType, X2: $tType]:(fun1(fun1(X0,X1),fun1(fun1(X2,X0),fun1(X2,X1))))).
% 0.15/0.41 tff(func_def_1, type, combc: !>[X0: $tType, X1: $tType, X2: $tType]:((fun1(X0,fun1(X1,X2)) * X1) > fun1(X0,X2))).
% 0.15/0.41 tff(func_def_2, type, combi: !>[X0: $tType]:(fun1(X0,X0))).
% 0.15/0.41 tff(func_def_3, type, combs: !>[X0: $tType, X1: $tType, X2: $tType]:((fun1(X0,fun1(X1,X2)) * fun1(X0,X1)) > fun1(X0,X2))).
% 0.15/0.41 tff(func_def_4, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.15/0.41 tff(func_def_5, type, it: fun1(dB,bool)).
% 0.15/0.41 tff(func_def_6, type, app: fun1(dB,fun1(dB,dB))).
% 0.15/0.41 tff(func_def_7, type, var: nat > dB).
% 0.15/0.41 tff(func_def_8, type, dB_size: dB > nat).
% 0.15/0.41 tff(func_def_9, type, lift: fun1(dB,fun1(nat,dB))).
% 0.15/0.41 tff(func_def_10, type, subst: fun1(dB,fun1(dB,fun1(nat,dB)))).
% 0.15/0.41 tff(func_def_11, type, foldl: !>[X0: $tType, X1: $tType]:((fun1(X0,fun1(X1,X0)) * X0 * list(X1)) > X0)).
% 0.15/0.41 tff(func_def_12, type, foldr: !>[X0: $tType, X1: $tType]:((fun1(X0,fun1(X1,X1)) * list(X0) * X1) > X1)).
% 0.15/0.41 tff(func_def_13, type, cons: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 0.15/0.41 tff(func_def_14, type, nil: !>[X0: $tType]:(list(X0))).
% 0.15/0.41 tff(func_def_15, type, list_case: !>[X0: $tType, X1: $tType]:((X0 * fun1(X1,fun1(list(X1),X0)) * list(X1)) > X0)).
% 0.15/0.41 tff(func_def_16, type, map: !>[X0: $tType, X1: $tType]:((fun1(X0,X1) * list(X0)) > list(X1))).
% 0.15/0.41 tff(func_def_17, type, splice: !>[X0: $tType]:((list(X0) * list(X0)) > list(X0))).
% 0.15/0.41 tff(func_def_18, type, size_size: !>[X0: $tType]:((X0) > nat)).
% 0.15/0.41 tff(func_def_19, type, shift: !>[X0: $tType]:((fun1(nat,X0) * nat * X0) > fun1(nat,X0))).
% 0.15/0.41 tff(func_def_20, type, atom: nat > type).
% 0.15/0.41 tff(func_def_21, type, fun: fun1(type,fun1(type,type))).
% 0.15/0.41 tff(func_def_22, type, type_case: !>[X0: $tType]:((fun1(nat,X0) * fun1(type,fun1(type,X0)) * type) > X0)).
% 0.15/0.41 tff(func_def_23, type, type_rec: !>[X0: $tType]:((fun1(nat,X0) * fun1(type,fun1(type,fun1(X0,fun1(X0,X0)))) * type) > X0)).
% 0.15/0.41 tff(func_def_24, type, type_size: type > nat).
% 0.15/0.41 tff(func_def_25, type, typing: fun1(nat,type) > fun1(dB,fun1(type,bool))).
% 0.15/0.41 tff(func_def_26, type, typings: (fun1(nat,type) * list(dB)) > fun1(list(type),bool)).
% 0.15/0.41 tff(func_def_27, type, aa: !>[X0: $tType, X1: $tType]:((fun1(X0,X1) * X0) > X1)).
% 0.15/0.41 tff(func_def_28, type, fEx: !>[X0: $tType]:(fun1(fun1(X0,bool),bool))).
% 0.15/0.41 tff(func_def_29, type, fFalse: bool).
% 0.15/0.41 tff(func_def_30, type, fTrue: bool).
% 0.15/0.41 tff(func_def_31, type, fconj: fun1(bool,fun1(bool,bool))).
% 0.15/0.41 tff(func_def_32, type, t1: type).
% 0.15/0.41 tff(func_def_33, type, t: type).
% 0.15/0.41 tff(func_def_34, type, t_a: type).
% 0.15/0.41 tff(func_def_35, type, t2: type).
% 0.15/0.41 tff(func_def_36, type, ts: list(type)).
% 0.15/0.41 tff(func_def_37, type, a: dB).
% 0.15/0.41 tff(func_def_38, type, as: list(dB)).
% 0.15/0.41 tff(func_def_39, type, e: fun1(nat,type)).
% 0.15/0.41 tff(func_def_40, type, ea: fun1(nat,type)).
% 0.15/0.41 tff(func_def_41, type, i: nat).
% 0.15/0.41 tff(func_def_42, type, ia: nat).
% 0.15/0.41 tff(func_def_43, type, n: nat).
% 0.15/0.41 tff(func_def_44, type, rs: list(dB)).
% 0.15/0.41 tff(func_def_45, type, t3: dB).
% 0.15/0.41 tff(func_def_46, type, u: dB).
% 0.15/0.41 tff(func_def_47, type, ua: dB).
% 0.15/0.41 tff(func_def_48, type, sK1: type).
% 0.15/0.41 tff(func_def_49, type, sK2: list(type)).
% 0.15/0.41 tff(func_def_50, type, sK3: type > type).
% 0.15/0.41 tff(func_def_51, type, sK4: type > type).
% 0.15/0.41 tff(func_def_52, type, sK5: type > nat).
% 0.15/0.41 tff(func_def_53, type, sK6: !>[X0: $tType]:((list(X0)) > X0)).
% 0.15/0.41 tff(func_def_54, type, sK7: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.15/0.41 tff(func_def_55, type, sK8: !>[X0: $tType]:((list(X0)) > X0)).
% 0.15/0.41 tff(func_def_56, type, sK9: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.15/0.41 tff(func_def_57, type, sK10: !>[X0: $tType]:((fun1(X0,bool) * list(X0)) > X0)).
% 0.15/0.41 tff(func_def_58, type, sK11: !>[X0: $tType]:((fun1(X0,bool) * list(X0)) > list(X0))).
% 0.15/0.41 tff(func_def_59, type, sK12: (type * list(dB) * dB * fun1(nat,type)) > list(type)).
% 0.15/0.41 tff(func_def_60, type, sK13: (type * list(dB) * dB * fun1(nat,type)) > list(type)).
% 0.15/0.41 tff(func_def_61, type, sK14: (type * list(dB) * nat * fun1(nat,type)) > list(type)).
% 0.15/0.41 tff(func_def_62, type, sK15: (type * dB * dB * fun1(nat,type)) > type).
% 0.15/0.41 tff(func_def_63, type, sK16: !>[X0: $tType, X1: $tType]:((fun1(X1,X0) * fun1(X1,X0)) > X1)).
% 0.15/0.41 tff(func_def_64, type, sK17: !>[X0: $tType, X1: $tType]:((fun1(X0,fun1(X1,X0))) > X1)).
% 0.15/0.41 tff(func_def_65, type, sK18: !>[X0: $tType, X1: $tType]:((fun1(X0,fun1(X1,X0))) > X1)).
% 0.15/0.41 tff(func_def_66, type, sK19: !>[X0: $tType, X1: $tType]:((fun1(X0,fun1(X1,X0))) > X0)).
% 0.15/0.41 tff(func_def_67, type, sK20: !>[X0: $tType, X1: $tType]:((list(X1) * fun1(X1,X0) * list(X0) * X0) > X1)).
% 0.15/0.41 tff(func_def_68, type, sK21: !>[X0: $tType, X1: $tType]:((list(X1) * fun1(X1,X0) * list(X0) * X0) > list(X1))).
% 0.15/0.41 tff(func_def_69, type, sK22: !>[X0: $tType, X1: $tType]:((list(X1) * X1 * list(X0) * fun1(X0,X1)) > X0)).
% 0.15/0.41 tff(func_def_70, type, sK23: !>[X0: $tType, X1: $tType]:((list(X1) * X1 * list(X0) * fun1(X0,X1)) > list(X0))).
% 0.15/0.41 tff(func_def_71, type, sK24: (type * type * list(dB) * fun1(nat,type)) > list(type)).
% 0.15/0.41 tff(pred_def_1, type, zero: !>[X0: $tType]:($o)).
% 0.15/0.41 tff(pred_def_2, type, listsp: !>[X0: $tType]:((fun1(X0,bool) * list(X0)) > $o)).
% 0.15/0.41 tff(pred_def_3, type, pp: bool > $o).
% 0.15/0.41 tff(pred_def_4, type, sP0: !>[X0: $tType]:((fun1(X0,bool) * list(X0)) > $o)).
% 0.15/0.41 tff(f725,plain,(
% 0.15/0.41 $false),
% 0.15/0.41 inference(avatar_sat_refutation,[],[f527,f532,f537,f541,f545,f550,f555,f560,f564,f568,f572,f583,f590,f596,f600,f604,f608,f614,f619,f623,f627,f631,f635,f639,f643,f647,f657,f661,f665,f669,f673,f680,f684,f688,f694,f699,f703,f710,f716,f722,f724])).
% 0.15/0.41 tff(f724,plain,(
% 0.15/0.41 spl25_13 | ~spl25_40),
% 0.15/0.41 inference(avatar_split_clause,[],[f723,f719,f587])).
% 0.15/0.41 tff(f587,plain,(
% 0.15/0.41 spl25_13 <=> pp(aa(dB,bool,combc(dB,type,bool,typing(e),t2),u))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_13])])).
% 0.15/0.41 tff(f719,plain,(
% 0.15/0.41 spl25_40 <=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t2))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_40])])).
% 0.15/0.41 tff(f723,plain,(
% 0.15/0.41 pp(aa(dB,bool,combc(dB,type,bool,typing(e),t2),u)) | ~spl25_40),
% 0.15/0.41 inference(forward_demodulation,[],[f721,f442])).
% 0.15/0.41 tff(f442,plain,(
% 0.15/0.41 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun1(X0,fun1(X2,X1))] : (aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4)) )),
% 0.15/0.41 inference(cnf_transformation,[],[f194])).
% 0.15/0.41 tff(f194,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0,X4 : X2,X5 : fun1(X0,fun1(X2,X1))] : aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun1(X2,X1),X5,X3),X4)),
% 0.15/0.41 inference(rectify,[],[f105])).
% 0.15/0.41 tff(f105,axiom,(
% 0.15/0.41 ! [X0 : $tType,X2 : $tType,X1 : $tType,X89 : X0,X90 : X1,X88 : fun1(X0,fun1(X1,X2))] : aa(X0,X2,combc(X0,X1,X2,X88,X90),X89) = aa(X1,X2,aa(X0,fun1(X1,X2),X88,X89),X90)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U)).
% 0.15/0.41 tff(f721,plain,(
% 0.15/0.41 pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t2)) | ~spl25_40),
% 0.15/0.41 inference(avatar_component_clause,[],[f719])).
% 0.15/0.41 tff(f722,plain,(
% 0.15/0.41 spl25_40),
% 0.15/0.41 inference(avatar_split_clause,[],[f322,f719])).
% 0.15/0.41 tff(f322,plain,(
% 0.15/0.41 pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t2))),
% 0.15/0.41 inference(cnf_transformation,[],[f2])).
% 0.15/0.41 tff(f2,axiom,(
% 0.15/0.41 pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),t2))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_uT)).
% 0.15/0.41 tff(f716,plain,(
% 0.15/0.41 spl25_39 | ~spl25_38),
% 0.15/0.41 inference(avatar_split_clause,[],[f711,f707,f713])).
% 0.15/0.41 tff(f713,plain,(
% 0.15/0.41 spl25_39 <=> pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t2),ua))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_39])])).
% 0.15/0.41 tff(f707,plain,(
% 0.15/0.41 spl25_38 <=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t2))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_38])])).
% 0.15/0.41 tff(f711,plain,(
% 0.15/0.41 pp(aa(dB,bool,combc(dB,type,bool,typing(ea),t2),ua)) | ~spl25_38),
% 0.15/0.41 inference(forward_demodulation,[],[f709,f442])).
% 0.15/0.41 tff(f709,plain,(
% 0.15/0.41 pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t2)) | ~spl25_38),
% 0.15/0.41 inference(avatar_component_clause,[],[f707])).
% 0.15/0.41 tff(f710,plain,(
% 0.15/0.41 spl25_38),
% 0.15/0.41 inference(avatar_split_clause,[],[f321,f707])).
% 0.15/0.41 tff(f321,plain,(
% 0.15/0.41 pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t2))),
% 0.15/0.41 inference(cnf_transformation,[],[f53])).
% 0.15/0.41 tff(f53,axiom,(
% 0.15/0.41 pp(aa(type,bool,aa(dB,fun1(type,bool),typing(ea),ua),t2))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Var_I4_J)).
% 0.15/0.41 tff(f703,plain,(
% 0.15/0.41 spl25_37),
% 0.15/0.41 inference(avatar_split_clause,[],[f399,f701])).
% 0.15/0.41 tff(f701,plain,(
% 0.15/0.41 spl25_37 <=> ! [X0 : $tType,X3 : fun1(nat,X0),X2 : fun1(type,fun1(type,fun1(X0,fun1(X0,X0)))),X1 : nat] : aa(nat,X0,X3,X1) = type_rec(X0,X3,X2,atom(X1))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_37])])).
% 0.15/0.41 tff(f399,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X2 : fun1(type,fun1(type,fun1(X0,fun1(X0,X0)))),X3 : fun1(nat,X0),X1 : nat] : (aa(nat,X0,X3,X1) = type_rec(X0,X3,X2,atom(X1))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f168])).
% 0.15/0.41 tff(f168,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : nat,X2 : fun1(type,fun1(type,fun1(X0,fun1(X0,X0)))),X3 : fun1(nat,X0)] : aa(nat,X0,X3,X1) = type_rec(X0,X3,X2,atom(X1))),
% 0.15/0.41 inference(rectify,[],[f23])).
% 0.15/0.41 tff(f23,axiom,(
% 0.15/0.41 ! [X0 : $tType,X23 : nat,X9 : fun1(type,fun1(type,fun1(X0,fun1(X0,X0)))),X10 : fun1(nat,X0)] : type_rec(X0,X10,X9,atom(X23)) = aa(nat,X0,X10,X23)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_type_Orecs_I1_J)).
% 0.15/0.41 tff(f699,plain,(
% 0.15/0.41 ~spl25_36 | ~spl25_14 | ~spl25_26),
% 0.15/0.41 inference(avatar_split_clause,[],[f653,f645,f593,f696])).
% 0.15/0.41 tff(f696,plain,(
% 0.15/0.41 spl25_36 <=> rs = nil(dB)),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_36])])).
% 0.15/0.41 tff(f593,plain,(
% 0.15/0.41 spl25_14 <=> rs = cons(dB,a,as)),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_14])])).
% 0.15/0.41 tff(f645,plain,(
% 0.15/0.41 spl25_26 <=> ! [X0 : $tType,X2 : X0,X3 : list(X0)] : nil(X0) != cons(X0,X2,X3)),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_26])])).
% 0.15/0.41 tff(f653,plain,(
% 0.15/0.41 rs != nil(dB) | (~spl25_14 | ~spl25_26)),
% 0.15/0.41 inference(superposition,[],[f646,f595])).
% 0.15/0.41 tff(f595,plain,(
% 0.15/0.41 rs = cons(dB,a,as) | ~spl25_14),
% 0.15/0.41 inference(avatar_component_clause,[],[f593])).
% 0.15/0.41 tff(f646,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X2 : X0,X3 : list(X0)] : (nil(X0) != cons(X0,X2,X3)) ) | ~spl25_26),
% 0.15/0.41 inference(avatar_component_clause,[],[f645])).
% 0.15/0.41 tff(f694,plain,(
% 0.15/0.41 spl25_35),
% 0.15/0.41 inference(avatar_split_clause,[],[f398,f692])).
% 0.15/0.41 tff(f692,plain,(
% 0.15/0.41 spl25_35 <=> ! [X0 : $tType,X3 : fun1(nat,X0),X2 : fun1(type,fun1(type,X0)),X1 : nat] : aa(nat,X0,X3,X1) = type_case(X0,X3,X2,atom(X1))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_35])])).
% 0.15/0.41 tff(f398,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X2 : fun1(type,fun1(type,X0)),X3 : fun1(nat,X0),X1 : nat] : (aa(nat,X0,X3,X1) = type_case(X0,X3,X2,atom(X1))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f167])).
% 0.15/0.41 tff(f167,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : nat,X2 : fun1(type,fun1(type,X0)),X3 : fun1(nat,X0)] : aa(nat,X0,X3,X1) = type_case(X0,X3,X2,atom(X1))),
% 0.15/0.41 inference(rectify,[],[f24])).
% 0.15/0.41 tff(f24,axiom,(
% 0.15/0.41 ! [X0 : $tType,X23 : nat,X9 : fun1(type,fun1(type,X0)),X10 : fun1(nat,X0)] : aa(nat,X0,X10,X23) = type_case(X0,X10,X9,atom(X23))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_type_Osimps_I5_J)).
% 0.15/0.41 tff(f688,plain,(
% 0.15/0.41 spl25_34),
% 0.15/0.41 inference(avatar_split_clause,[],[f494,f686])).
% 0.15/0.41 tff(f686,plain,(
% 0.15/0.41 spl25_34 <=> ! [X0 : $tType,X2 : fun1(nat,X0),X4 : nat,X1 : X0] : aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_34])])).
% 0.15/0.41 tff(f494,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X2 : fun1(nat,X0),X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1) )),
% 0.15/0.41 inference(equality_resolution,[],[f433])).
% 0.15/0.41 tff(f433,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X2 : fun1(nat,X0),X3 : nat,X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 | X3 != X4) )),
% 0.15/0.41 inference(cnf_transformation,[],[f227])).
% 0.15/0.41 tff(f227,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : X0,X2 : fun1(nat,X0),X3 : nat,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 | X3 != X4)),
% 0.15/0.41 inference(ennf_transformation,[],[f187])).
% 0.15/0.41 tff(f187,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : X0,X2 : fun1(nat,X0),X3 : nat,X4 : nat] : (X3 = X4 => aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1)),
% 0.15/0.41 inference(rectify,[],[f26])).
% 0.15/0.41 tff(f26,axiom,(
% 0.15/0.41 ! [X0 : $tType,X13 : X0,X17 : fun1(nat,X0),X30 : nat,X24 : nat] : (X24 = X30 => aa(nat,X0,shift(X0,X17,X24,X13),X30) = X13)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_shift__eq)).
% 0.15/0.41 tff(f684,plain,(
% 0.15/0.41 spl25_33),
% 0.15/0.41 inference(avatar_split_clause,[],[f479,f682])).
% 0.15/0.41 tff(f682,plain,(
% 0.15/0.41 spl25_33 <=> ! [X1 : fun1(nat,type)] : pp(aa(list(type),bool,typings(X1,nil(dB)),nil(type)))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_33])])).
% 0.15/0.41 tff(f479,plain,(
% 0.15/0.41 ( ! [X1 : fun1(nat,type)] : (pp(aa(list(type),bool,typings(X1,nil(dB)),nil(type)))) )),
% 0.15/0.41 inference(equality_resolution,[],[f364])).
% 0.15/0.41 tff(f364,plain,(
% 0.15/0.41 ( ! [X0 : list(type),X1 : fun1(nat,type)] : (pp(aa(list(type),bool,typings(X1,nil(dB)),X0)) | nil(type) != X0) )),
% 0.15/0.41 inference(cnf_transformation,[],[f266])).
% 0.15/0.41 tff(f266,plain,(
% 0.15/0.41 ! [X0 : list(type),X1 : fun1(nat,type)] : ((pp(aa(list(type),bool,typings(X1,nil(dB)),X0)) | nil(type) != X0) & (nil(type) = X0 | ~pp(aa(list(type),bool,typings(X1,nil(dB)),X0))))),
% 0.15/0.41 inference(nnf_transformation,[],[f142])).
% 0.15/0.41 tff(f142,plain,(
% 0.15/0.41 ! [X0 : list(type),X1 : fun1(nat,type)] : (pp(aa(list(type),bool,typings(X1,nil(dB)),X0)) <=> nil(type) = X0)),
% 0.15/0.41 inference(rectify,[],[f94])).
% 0.15/0.41 tff(f94,axiom,(
% 0.15/0.41 ! [X46 : list(type),X17 : fun1(nat,type)] : (pp(aa(list(type),bool,typings(X17,nil(dB)),X46)) <=> nil(type) = X46)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_typings_Osimps_I1_J)).
% 0.15/0.41 tff(f680,plain,(
% 0.15/0.41 spl25_32),
% 0.15/0.41 inference(avatar_split_clause,[],[f369,f678])).
% 0.15/0.41 tff(f678,plain,(
% 0.15/0.41 spl25_32 <=> ! [X1 : $tType,X0 : $tType,X2 : fun1(X0,X1)] : nil(X1) = map(X0,X1,X2,nil(X0))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_32])])).
% 0.15/0.41 tff(f369,plain,(
% 0.15/0.41 ( ! [X1 : $tType,X0 : $tType,X2 : fun1(X0,X1)] : (nil(X1) = map(X0,X1,X2,nil(X0))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f147])).
% 0.15/0.41 tff(f147,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : $tType,X2 : fun1(X0,X1)] : nil(X1) = map(X0,X1,X2,nil(X0))),
% 0.15/0.41 inference(rectify,[],[f81])).
% 0.15/0.41 tff(f81,axiom,(
% 0.15/0.41 ! [X1 : $tType,X0 : $tType,X59 : fun1(X1,X0)] : nil(X0) = map(X1,X0,X59,nil(X1))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_map_Osimps_I1_J)).
% 0.15/0.41 tff(f673,plain,(
% 0.15/0.41 spl25_31 | spl25_1 | ~spl25_11),
% 0.15/0.41 inference(avatar_split_clause,[],[f574,f570,f524,f671])).
% 0.15/0.41 tff(f671,plain,(
% 0.15/0.41 spl25_31 <=> ! [X0 : bool] : (~pp(X0) | fTrue = X0)),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_31])])).
% 0.15/0.41 tff(f524,plain,(
% 0.15/0.41 spl25_1 <=> pp(fFalse)),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_1])])).
% 0.15/0.41 tff(f570,plain,(
% 0.15/0.41 spl25_11 <=> ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_11])])).
% 0.15/0.41 tff(f574,plain,(
% 0.15/0.41 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | (spl25_1 | ~spl25_11)),
% 0.15/0.41 inference(superposition,[],[f526,f571])).
% 0.15/0.41 tff(f571,plain,(
% 0.15/0.41 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) ) | ~spl25_11),
% 0.15/0.41 inference(avatar_component_clause,[],[f570])).
% 0.15/0.41 tff(f526,plain,(
% 0.15/0.41 ~pp(fFalse) | spl25_1),
% 0.15/0.41 inference(avatar_component_clause,[],[f524])).
% 0.15/0.41 tff(f669,plain,(
% 0.15/0.41 spl25_30),
% 0.15/0.41 inference(avatar_split_clause,[],[f397,f667])).
% 0.15/0.41 tff(f667,plain,(
% 0.15/0.41 spl25_30 <=> ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun1(X1,fun1(X0,X1))] : foldl(X1,X0,X3,X2,nil(X0)) = X2),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_30])])).
% 0.15/0.41 tff(f397,plain,(
% 0.15/0.41 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun1(X1,fun1(X0,X1))] : (foldl(X1,X0,X3,X2,nil(X0)) = X2) )),
% 0.15/0.41 inference(cnf_transformation,[],[f166])).
% 0.15/0.41 tff(f166,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun1(X1,fun1(X0,X1))] : foldl(X1,X0,X3,X2,nil(X0)) = X2),
% 0.15/0.41 inference(rectify,[],[f85])).
% 0.15/0.41 tff(f85,axiom,(
% 0.15/0.41 ! [X1 : $tType,X0 : $tType,X57 : X0,X59 : fun1(X0,fun1(X1,X0))] : foldl(X0,X1,X59,X57,nil(X1)) = X57),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_foldl__Nil)).
% 0.15/0.41 tff(f665,plain,(
% 0.15/0.41 spl25_29),
% 0.15/0.41 inference(avatar_split_clause,[],[f396,f663])).
% 0.15/0.41 tff(f663,plain,(
% 0.15/0.41 spl25_29 <=> ! [X1 : $tType,X0 : $tType,X3 : fun1(X0,fun1(X1,X1)),X2 : X1] : foldr(X0,X1,X3,nil(X0),X2) = X2),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_29])])).
% 0.15/0.41 tff(f396,plain,(
% 0.15/0.41 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun1(X0,fun1(X1,X1))] : (foldr(X0,X1,X3,nil(X0),X2) = X2) )),
% 0.15/0.41 inference(cnf_transformation,[],[f165])).
% 0.15/0.41 tff(f165,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun1(X0,fun1(X1,X1))] : foldr(X0,X1,X3,nil(X0),X2) = X2),
% 0.15/0.41 inference(rectify,[],[f88])).
% 0.15/0.41 tff(f88,axiom,(
% 0.15/0.41 ! [X1 : $tType,X0 : $tType,X57 : X0,X59 : fun1(X1,fun1(X0,X0))] : foldr(X1,X0,X59,nil(X1),X57) = X57),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_foldr_Osimps_I1_J)).
% 0.15/0.41 tff(f661,plain,(
% 0.15/0.41 spl25_28),
% 0.15/0.41 inference(avatar_split_clause,[],[f395,f659])).
% 0.15/0.41 tff(f659,plain,(
% 0.15/0.41 spl25_28 <=> ! [X1 : $tType,X0 : $tType,X2 : fun1(X0,fun1(list(X0),X1)),X3 : X1] : list_case(X1,X0,X3,X2,nil(X0)) = X3),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_28])])).
% 0.15/0.41 tff(f395,plain,(
% 0.15/0.41 ( ! [X1 : $tType,X0 : $tType,X2 : fun1(X0,fun1(list(X0),X1)),X3 : X1] : (list_case(X1,X0,X3,X2,nil(X0)) = X3) )),
% 0.15/0.41 inference(cnf_transformation,[],[f164])).
% 0.15/0.41 tff(f164,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : $tType,X2 : fun1(X0,fun1(list(X0),X1)),X3 : X1] : list_case(X1,X0,X3,X2,nil(X0)) = X3),
% 0.15/0.41 inference(rectify,[],[f84])).
% 0.15/0.41 tff(f84,axiom,(
% 0.15/0.41 ! [X1 : $tType,X0 : $tType,X9 : fun1(X1,fun1(list(X1),X0)),X10 : X0] : list_case(X0,X1,X10,X9,nil(X1)) = X10),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_list_Osimps_I4_J)).
% 0.15/0.41 tff(f657,plain,(
% 0.15/0.41 spl25_27),
% 0.15/0.41 inference(avatar_split_clause,[],[f348,f655])).
% 0.15/0.41 tff(f655,plain,(
% 0.15/0.41 spl25_27 <=> ! [X0 : $tType,X1 : list(X0)] : map(X0,X0,combi(X0),X1) = X1),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_27])])).
% 0.15/0.41 tff(f348,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X1 : list(X0)] : (map(X0,X0,combi(X0),X1) = X1) )),
% 0.15/0.41 inference(cnf_transformation,[],[f130])).
% 0.15/0.41 tff(f130,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : list(X0)] : map(X0,X0,combi(X0),X1) = X1),
% 0.15/0.41 inference(rectify,[],[f63])).
% 0.15/0.41 tff(f63,axiom,(
% 0.15/0.41 ! [X0 : $tType,X70 : list(X0)] : map(X0,X0,combi(X0),X70) = X70),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_map__ident)).
% 0.15/0.41 tff(f647,plain,(
% 0.15/0.41 spl25_26),
% 0.15/0.41 inference(avatar_split_clause,[],[f476,f645])).
% 0.15/0.41 tff(f476,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X2 : X0,X3 : list(X0)] : (nil(X0) != cons(X0,X2,X3)) )),
% 0.15/0.41 inference(equality_resolution,[],[f358])).
% 0.15/0.41 tff(f358,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0)] : (nil(X0) != X1 | cons(X0,X2,X3) != X1) )),
% 0.15/0.41 inference(cnf_transformation,[],[f263])).
% 0.15/0.41 tff(f263,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : list(X0)] : ((nil(X0) != X1 | ! [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) != X1) & (cons(X0,sK8(X0,X1),sK9(X0,X1)) = X1 | nil(X0) = X1))),
% 0.15/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f261,f262])).
% 0.15/0.41 tff(f262,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : list(X0)] : (? [X4 : X0,X5 : list(X0)] : cons(X0,X4,X5) = X1 => cons(X0,sK8(X0,X1),sK9(X0,X1)) = X1)),
% 0.15/0.41 introduced(choice_axiom,[])).
% 0.15/0.41 tff(f261,plain,(
% 0.15/0.41 ! [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))),
% 0.15/0.41 inference(rectify,[],[f260])).
% 0.15/0.41 tff(f260,plain,(
% 0.15/0.41 ! [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))),
% 0.15/0.41 inference(nnf_transformation,[],[f139])).
% 0.15/0.41 tff(f139,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : list(X0)] : (nil(X0) != X1 <=> ? [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) = X1)),
% 0.15/0.41 inference(rectify,[],[f98])).
% 0.15/0.41 tff(f98,axiom,(
% 0.15/0.41 ! [X0 : $tType,X58 : list(X0)] : (nil(X0) != X58 <=> ? [X86 : X0,X87 : list(X0)] : cons(X0,X86,X87) = X58)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_neq__Nil__conv)).
% 0.15/0.41 tff(f643,plain,(
% 0.15/0.41 spl25_25),
% 0.15/0.41 inference(avatar_split_clause,[],[f389,f641])).
% 0.15/0.41 tff(f641,plain,(
% 0.15/0.41 spl25_25 <=> ! [X0 : $tType,X2 : fun1(X0,bool),X1 : list(X0)] : (listsp(X0,X2,X1) | ~sP0(X0,X2,X1))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_25])])).
% 0.15/0.41 tff(f389,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X2 : fun1(X0,bool),X1 : list(X0)] : (listsp(X0,X2,X1) | ~sP0(X0,X2,X1)) )),
% 0.15/0.41 inference(cnf_transformation,[],[f272])).
% 0.15/0.41 tff(f272,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : list(X0),X2 : fun1(X0,bool)] : ((listsp(X0,X2,X1) | ~sP0(X0,X2,X1)) & (sP0(X0,X2,X1) | ~listsp(X0,X2,X1)))),
% 0.15/0.41 inference(nnf_transformation,[],[f248])).
% 0.15/0.41 tff(f248,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : list(X0),X2 : fun1(X0,bool)] : (listsp(X0,X2,X1) <=> sP0(X0,X2,X1))),
% 0.15/0.41 inference(definition_folding,[],[f161,f247])).
% 0.15/0.41 tff(f247,plain,(
% 0.15/0.41 ! [X2 : fun1(X0,bool),X0 : $tType,X1 : list(X0)] : (sP0(X0,X2,X1) <=> (? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & cons(X0,X3,X4) = X1) | nil(X0) = X1))),
% 0.15/0.41 introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])).
% 0.15/0.41 tff(f161,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : list(X0),X2 : fun1(X0,bool)] : (listsp(X0,X2,X1) <=> (? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & cons(X0,X3,X4) = X1) | nil(X0) = X1))),
% 0.15/0.41 inference(rectify,[],[f92])).
% 0.15/0.41 tff(f92,axiom,(
% 0.15/0.41 ! [X0 : $tType,X57 : list(X0),X72 : fun1(X0,bool)] : (listsp(X0,X72,X57) <=> (? [X82 : X0,X83 : list(X0)] : (listsp(X0,X72,X83) & pp(aa(X0,bool,X72,X82)) & cons(X0,X82,X83) = X57) | nil(X0) = X57))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_listsp_Osimps)).
% 0.15/0.41 tff(f639,plain,(
% 0.15/0.41 spl25_24),
% 0.15/0.41 inference(avatar_split_clause,[],[f388,f637])).
% 0.15/0.41 tff(f637,plain,(
% 0.15/0.41 spl25_24 <=> ! [X0 : $tType,X2 : fun1(X0,bool),X1 : list(X0)] : (sP0(X0,X2,X1) | ~listsp(X0,X2,X1))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_24])])).
% 0.15/0.41 tff(f388,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X2 : fun1(X0,bool),X1 : list(X0)] : (sP0(X0,X2,X1) | ~listsp(X0,X2,X1)) )),
% 0.15/0.41 inference(cnf_transformation,[],[f272])).
% 0.15/0.41 tff(f635,plain,(
% 0.15/0.41 spl25_23),
% 0.15/0.41 inference(avatar_split_clause,[],[f361,f633])).
% 0.15/0.41 tff(f633,plain,(
% 0.15/0.41 spl25_23 <=> ! [X0 : nat,X1 : nat] : (X0 = X1 | var(X0) != var(X1))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_23])])).
% 0.15/0.41 tff(f361,plain,(
% 0.15/0.41 ( ! [X0 : nat,X1 : nat] : (X0 = X1 | var(X0) != var(X1)) )),
% 0.15/0.41 inference(cnf_transformation,[],[f265])).
% 0.15/0.41 tff(f265,plain,(
% 0.15/0.41 ! [X0 : nat,X1 : nat] : ((var(X0) = var(X1) | X0 != X1) & (X0 = X1 | var(X0) != var(X1)))),
% 0.15/0.41 inference(nnf_transformation,[],[f141])).
% 0.15/0.41 tff(f141,plain,(
% 0.15/0.41 ! [X0 : nat,X1 : nat] : (var(X0) = var(X1) <=> X0 = X1)),
% 0.15/0.41 inference(rectify,[],[f33])).
% 0.15/0.41 tff(f33,axiom,(
% 0.15/0.41 ! [X22 : nat,X23 : nat] : (var(X23) = var(X22) <=> X22 = X23)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_dB_Osimps_I1_J)).
% 0.15/0.41 tff(f631,plain,(
% 0.15/0.41 spl25_22),
% 0.15/0.41 inference(avatar_split_clause,[],[f359,f629])).
% 0.15/0.41 tff(f629,plain,(
% 0.15/0.41 spl25_22 <=> ! [X0 : nat,X1 : nat] : (X0 = X1 | atom(X0) != atom(X1))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_22])])).
% 0.15/0.41 tff(f359,plain,(
% 0.15/0.41 ( ! [X0 : nat,X1 : nat] : (X0 = X1 | atom(X0) != atom(X1)) )),
% 0.15/0.41 inference(cnf_transformation,[],[f264])).
% 0.15/0.41 tff(f264,plain,(
% 0.15/0.41 ! [X0 : nat,X1 : nat] : ((atom(X0) = atom(X1) | X0 != X1) & (X0 = X1 | atom(X0) != atom(X1)))),
% 0.15/0.41 inference(nnf_transformation,[],[f140])).
% 0.15/0.41 tff(f140,plain,(
% 0.15/0.41 ! [X0 : nat,X1 : nat] : (atom(X0) = atom(X1) <=> X0 = X1)),
% 0.15/0.41 inference(rectify,[],[f18])).
% 0.15/0.41 tff(f18,axiom,(
% 0.15/0.41 ! [X22 : nat,X23 : nat] : (atom(X23) = atom(X22) <=> X22 = X23)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_type_Osimps_I1_J)).
% 0.15/0.41 tff(f627,plain,(
% 0.15/0.41 spl25_21),
% 0.15/0.41 inference(avatar_split_clause,[],[f347,f625])).
% 0.15/0.41 tff(f625,plain,(
% 0.15/0.41 spl25_21 <=> ! [X0 : $tType,X1 : X0] : aa(X0,X0,combi(X0),X1) = X1),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_21])])).
% 0.15/0.41 tff(f347,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X1 : X0] : (aa(X0,X0,combi(X0),X1) = X1) )),
% 0.15/0.41 inference(cnf_transformation,[],[f129])).
% 0.15/0.41 tff(f129,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : X0] : aa(X0,X0,combi(X0),X1) = X1),
% 0.15/0.41 inference(rectify,[],[f106])).
% 0.15/0.41 tff(f106,axiom,(
% 0.15/0.41 ! [X0 : $tType,X88 : X0] : aa(X0,X0,combi(X0),X88) = X88),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U)).
% 0.15/0.41 tff(f623,plain,(
% 0.15/0.41 spl25_20),
% 0.15/0.41 inference(avatar_split_clause,[],[f346,f621])).
% 0.15/0.41 tff(f621,plain,(
% 0.15/0.41 spl25_20 <=> ! [X0 : $tType,X1 : list(X0)] : splice(X0,nil(X0),X1) = X1),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_20])])).
% 0.15/0.41 tff(f346,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X1 : list(X0)] : (splice(X0,nil(X0),X1) = X1) )),
% 0.15/0.41 inference(cnf_transformation,[],[f128])).
% 0.15/0.41 tff(f128,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : list(X0)] : splice(X0,nil(X0),X1) = X1),
% 0.15/0.41 inference(rectify,[],[f90])).
% 0.15/0.41 tff(f90,axiom,(
% 0.15/0.41 ! [X0 : $tType,X69 : list(X0)] : splice(X0,nil(X0),X69) = X69),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_splice_Osimps_I1_J)).
% 0.15/0.41 tff(f619,plain,(
% 0.15/0.41 ~spl25_19 | ~spl25_14 | ~spl25_17),
% 0.15/0.41 inference(avatar_split_clause,[],[f610,f606,f593,f616])).
% 0.15/0.41 tff(f616,plain,(
% 0.15/0.41 spl25_19 <=> as = rs),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_19])])).
% 0.15/0.41 tff(f606,plain,(
% 0.15/0.41 spl25_17 <=> ! [X0 : $tType,X2 : list(X0),X1 : X0] : cons(X0,X1,X2) != X2),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_17])])).
% 0.15/0.41 tff(f610,plain,(
% 0.15/0.41 as != rs | (~spl25_14 | ~spl25_17)),
% 0.15/0.41 inference(superposition,[],[f607,f595])).
% 0.15/0.41 tff(f607,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X2 : list(X0),X1 : X0] : (cons(X0,X1,X2) != X2) ) | ~spl25_17),
% 0.15/0.41 inference(avatar_component_clause,[],[f606])).
% 0.15/0.41 tff(f614,plain,(
% 0.15/0.41 spl25_18),
% 0.15/0.41 inference(avatar_split_clause,[],[f345,f612])).
% 0.15/0.41 tff(f612,plain,(
% 0.15/0.41 spl25_18 <=> ! [X0 : $tType,X1 : list(X0)] : splice(X0,X1,nil(X0)) = X1),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_18])])).
% 0.15/0.41 tff(f345,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X1 : list(X0)] : (splice(X0,X1,nil(X0)) = X1) )),
% 0.15/0.41 inference(cnf_transformation,[],[f127])).
% 0.15/0.41 tff(f127,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : list(X0)] : splice(X0,X1,nil(X0)) = X1),
% 0.15/0.41 inference(rectify,[],[f89])).
% 0.15/0.41 tff(f89,axiom,(
% 0.15/0.41 ! [X0 : $tType,X60 : list(X0)] : splice(X0,X60,nil(X0)) = X60),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_splice__Nil2)).
% 0.15/0.41 tff(f608,plain,(
% 0.15/0.41 spl25_17),
% 0.15/0.41 inference(avatar_split_clause,[],[f365,f606])).
% 0.15/0.41 tff(f365,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X2 : list(X0),X1 : X0] : (cons(X0,X1,X2) != X2) )),
% 0.15/0.41 inference(cnf_transformation,[],[f143])).
% 0.15/0.41 tff(f143,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : X0,X2 : list(X0)] : cons(X0,X1,X2) != X2),
% 0.15/0.41 inference(rectify,[],[f55])).
% 0.15/0.41 tff(f55,axiom,(
% 0.15/0.41 ! [X0 : $tType,X61 : X0,X60 : list(X0)] : cons(X0,X61,X60) != X60),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_not__Cons__self)).
% 0.15/0.41 tff(f604,plain,(
% 0.15/0.41 spl25_16),
% 0.15/0.41 inference(avatar_split_clause,[],[f338,f602])).
% 0.15/0.41 tff(f602,plain,(
% 0.15/0.41 spl25_16 <=> ! [X0 : nat] : pp(aa(dB,bool,it,var(X0)))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_16])])).
% 0.15/0.41 tff(f338,plain,(
% 0.15/0.41 ( ! [X0 : nat] : (pp(aa(dB,bool,it,var(X0)))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f121])).
% 0.15/0.41 tff(f121,plain,(
% 0.15/0.41 ! [X0 : nat] : pp(aa(dB,bool,it,var(X0)))),
% 0.15/0.41 inference(rectify,[],[f22])).
% 0.15/0.41 tff(f22,axiom,(
% 0.15/0.41 ! [X27 : nat] : pp(aa(dB,bool,it,var(X27)))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Var__IT)).
% 0.15/0.41 tff(f600,plain,(
% 0.15/0.41 spl25_15),
% 0.15/0.41 inference(avatar_split_clause,[],[f337,f598])).
% 0.15/0.41 tff(f598,plain,(
% 0.15/0.41 spl25_15 <=> ! [X0 : nat] : zero_zero(nat) = size_size(type,atom(X0))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_15])])).
% 0.15/0.41 tff(f337,plain,(
% 0.15/0.41 ( ! [X0 : nat] : (zero_zero(nat) = size_size(type,atom(X0))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f120])).
% 0.15/0.41 tff(f120,plain,(
% 0.15/0.41 ! [X0 : nat] : zero_zero(nat) = size_size(type,atom(X0))),
% 0.15/0.41 inference(rectify,[],[f95])).
% 0.15/0.41 tff(f95,axiom,(
% 0.15/0.41 ! [X21 : nat] : zero_zero(nat) = size_size(type,atom(X21))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_type_Osize_I3_J)).
% 0.15/0.41 tff(f596,plain,(
% 0.15/0.41 spl25_14),
% 0.15/0.41 inference(avatar_split_clause,[],[f320,f593])).
% 0.15/0.41 tff(f320,plain,(
% 0.15/0.41 rs = cons(dB,a,as)),
% 0.15/0.41 inference(cnf_transformation,[],[f32])).
% 0.15/0.41 tff(f32,axiom,(
% 0.15/0.41 rs = cons(dB,a,as)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Cons)).
% 0.15/0.41 tff(f590,plain,(
% 0.15/0.41 ~spl25_13 | spl25_12),
% 0.15/0.41 inference(avatar_split_clause,[],[f585,f580,f587])).
% 0.15/0.41 tff(f580,plain,(
% 0.15/0.41 spl25_12 <=> pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),aa(type,type,aa(type,fun1(type,type),fun,t1),foldr(type,type,fun,ts,t))))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_12])])).
% 0.15/0.41 tff(f585,plain,(
% 0.15/0.41 ~pp(aa(dB,bool,combc(dB,type,bool,typing(e),t2),u)) | spl25_12),
% 0.15/0.41 inference(forward_demodulation,[],[f584,f325])).
% 0.15/0.41 tff(f325,plain,(
% 0.15/0.41 t2 = aa(type,type,aa(type,fun1(type,type),fun,t1),foldr(type,type,fun,ts,t))),
% 0.15/0.41 inference(cnf_transformation,[],[f3])).
% 0.15/0.41 tff(f3,axiom,(
% 0.15/0.41 t2 = aa(type,type,aa(type,fun1(type,type),fun,t1),foldr(type,type,fun,ts,t))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_T)).
% 0.15/0.41 tff(f584,plain,(
% 0.15/0.41 ~pp(aa(dB,bool,combc(dB,type,bool,typing(e),aa(type,type,aa(type,fun1(type,type),fun,t1),foldr(type,type,fun,ts,t))),u)) | spl25_12),
% 0.15/0.41 inference(forward_demodulation,[],[f582,f442])).
% 0.15/0.41 tff(f582,plain,(
% 0.15/0.41 ~pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),aa(type,type,aa(type,fun1(type,type),fun,t1),foldr(type,type,fun,ts,t)))) | spl25_12),
% 0.15/0.41 inference(avatar_component_clause,[],[f580])).
% 0.15/0.41 tff(f583,plain,(
% 0.15/0.41 ~spl25_12),
% 0.15/0.41 inference(avatar_split_clause,[],[f311,f580])).
% 0.15/0.41 tff(f311,plain,(
% 0.15/0.41 ~pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),aa(type,type,aa(type,fun1(type,type),fun,t1),foldr(type,type,fun,ts,t))))),
% 0.15/0.41 inference(cnf_transformation,[],[f115])).
% 0.15/0.41 tff(f115,plain,(
% 0.15/0.41 ~pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),aa(type,type,aa(type,fun1(type,type),fun,t1),foldr(type,type,fun,ts,t))))),
% 0.15/0.41 inference(flattening,[],[f114])).
% 0.15/0.41 tff(f114,negated_conjecture,(
% 0.15/0.41 ~pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),aa(type,type,aa(type,fun1(type,type),fun,t1),foldr(type,type,fun,ts,t))))),
% 0.15/0.41 inference(negated_conjecture,[],[f113])).
% 0.15/0.41 tff(f113,conjecture,(
% 0.15/0.41 pp(aa(type,bool,aa(dB,fun1(type,bool),typing(e),u),aa(type,type,aa(type,fun1(type,type),fun,t1),foldr(type,type,fun,ts,t))))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.15/0.41 tff(f572,plain,(
% 0.15/0.41 spl25_11),
% 0.15/0.41 inference(avatar_split_clause,[],[f339,f570])).
% 0.15/0.41 tff(f339,plain,(
% 0.15/0.41 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) )),
% 0.15/0.41 inference(cnf_transformation,[],[f122])).
% 0.15/0.41 tff(f122,plain,(
% 0.15/0.41 ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 0.15/0.41 inference(rectify,[],[f112])).
% 0.15/0.41 tff(f112,axiom,(
% 0.15/0.41 ! [X88 : bool] : (fFalse = X88 | fTrue = X88)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T)).
% 0.15/0.41 tff(f568,plain,(
% 0.15/0.41 spl25_10),
% 0.15/0.41 inference(avatar_split_clause,[],[f336,f566])).
% 0.15/0.41 tff(f566,plain,(
% 0.15/0.41 spl25_10 <=> ! [X0 : nat] : zero_zero(nat) = dB_size(var(X0))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_10])])).
% 0.15/0.41 tff(f336,plain,(
% 0.15/0.41 ( ! [X0 : nat] : (zero_zero(nat) = dB_size(var(X0))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f119])).
% 0.15/0.41 tff(f119,plain,(
% 0.15/0.41 ! [X0 : nat] : zero_zero(nat) = dB_size(var(X0))),
% 0.15/0.41 inference(rectify,[],[f99])).
% 0.15/0.41 tff(f99,axiom,(
% 0.15/0.41 ! [X21 : nat] : zero_zero(nat) = dB_size(var(X21))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_dB_Osize_I1_J)).
% 0.15/0.41 tff(f564,plain,(
% 0.15/0.41 spl25_9),
% 0.15/0.41 inference(avatar_split_clause,[],[f335,f562])).
% 0.15/0.41 tff(f562,plain,(
% 0.15/0.41 spl25_9 <=> ! [X0 : nat] : zero_zero(nat) = type_size(atom(X0))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_9])])).
% 0.15/0.41 tff(f335,plain,(
% 0.15/0.41 ( ! [X0 : nat] : (zero_zero(nat) = type_size(atom(X0))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f118])).
% 0.15/0.41 tff(f118,plain,(
% 0.15/0.41 ! [X0 : nat] : zero_zero(nat) = type_size(atom(X0))),
% 0.15/0.41 inference(rectify,[],[f93])).
% 0.15/0.41 tff(f93,axiom,(
% 0.15/0.41 ! [X21 : nat] : zero_zero(nat) = type_size(atom(X21))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_type_Osize_I1_J)).
% 0.15/0.41 tff(f560,plain,(
% 0.15/0.41 spl25_8),
% 0.15/0.41 inference(avatar_split_clause,[],[f319,f557])).
% 0.15/0.41 tff(f557,plain,(
% 0.15/0.41 spl25_8 <=> pp(aa(dB,bool,it,u))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_8])])).
% 0.15/0.41 tff(f319,plain,(
% 0.15/0.41 pp(aa(dB,bool,it,u))),
% 0.15/0.41 inference(cnf_transformation,[],[f4])).
% 0.15/0.41 tff(f4,axiom,(
% 0.15/0.41 pp(aa(dB,bool,it,u))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uIT)).
% 0.15/0.41 tff(f555,plain,(
% 0.15/0.41 spl25_7),
% 0.15/0.41 inference(avatar_split_clause,[],[f318,f552])).
% 0.15/0.41 tff(f552,plain,(
% 0.15/0.41 spl25_7 <=> pp(aa(dB,bool,it,ua))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_7])])).
% 0.15/0.41 tff(f318,plain,(
% 0.15/0.41 pp(aa(dB,bool,it,ua))),
% 0.15/0.41 inference(cnf_transformation,[],[f6])).
% 0.15/0.41 tff(f6,axiom,(
% 0.15/0.41 pp(aa(dB,bool,it,ua))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Var_I3_J)).
% 0.15/0.41 tff(f550,plain,(
% 0.15/0.41 spl25_6),
% 0.15/0.41 inference(avatar_split_clause,[],[f317,f547])).
% 0.15/0.41 tff(f547,plain,(
% 0.15/0.41 spl25_6 <=> pp(aa(dB,bool,it,t3))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_6])])).
% 0.15/0.41 tff(f317,plain,(
% 0.15/0.41 pp(aa(dB,bool,it,t3))),
% 0.15/0.41 inference(cnf_transformation,[],[f1])).
% 0.15/0.41 tff(f1,axiom,(
% 0.15/0.41 pp(aa(dB,bool,it,t3))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096IT_At_096)).
% 0.15/0.41 tff(f545,plain,(
% 0.15/0.41 spl25_5),
% 0.15/0.41 inference(avatar_split_clause,[],[f482,f543])).
% 0.15/0.41 tff(f543,plain,(
% 0.15/0.41 spl25_5 <=> ! [X1 : $tType,X0 : fun1(X1,bool)] : sP0(X1,X0,nil(X1))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_5])])).
% 0.15/0.41 tff(f482,plain,(
% 0.15/0.41 ( ! [X1 : $tType,X0 : fun1(X1,bool)] : (sP0(X1,X0,nil(X1))) )),
% 0.15/0.41 inference(equality_resolution,[],[f386])).
% 0.15/0.41 tff(f386,plain,(
% 0.15/0.41 ( ! [X1 : $tType,X2 : list(X1),X0 : fun1(X1,bool)] : (sP0(X1,X0,X2) | nil(X1) != X2) )),
% 0.15/0.41 inference(cnf_transformation,[],[f271])).
% 0.15/0.41 tff(f271,plain,(
% 0.15/0.41 ! [X0 : fun1(X1,bool),X1 : $tType,X2 : list(X1)] : ((sP0(X1,X0,X2) | (! [X3 : X1,X4 : list(X1)] : (~listsp(X1,X0,X4) | ~pp(aa(X1,bool,X0,X3)) | cons(X1,X3,X4) != X2) & nil(X1) != X2)) & ((listsp(X1,X0,sK11(X1,X0,X2)) & pp(aa(X1,bool,X0,sK10(X1,X0,X2))) & cons(X1,sK10(X1,X0,X2),sK11(X1,X0,X2)) = X2) | nil(X1) = X2 | ~sP0(X1,X0,X2)))),
% 0.15/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f269,f270])).
% 0.15/0.41 tff(f270,plain,(
% 0.15/0.41 ! [X1 : $tType,X0 : fun1(X1,bool),X2 : list(X1)] : (? [X5 : X1,X6 : list(X1)] : (listsp(X1,X0,X6) & pp(aa(X1,bool,X0,X5)) & cons(X1,X5,X6) = X2) => (listsp(X1,X0,sK11(X1,X0,X2)) & pp(aa(X1,bool,X0,sK10(X1,X0,X2))) & cons(X1,sK10(X1,X0,X2),sK11(X1,X0,X2)) = X2))),
% 0.15/0.41 introduced(choice_axiom,[])).
% 0.15/0.41 tff(f269,plain,(
% 0.15/0.41 ! [X0 : fun1(X1,bool),X1 : $tType,X2 : list(X1)] : ((sP0(X1,X0,X2) | (! [X3 : X1,X4 : list(X1)] : (~listsp(X1,X0,X4) | ~pp(aa(X1,bool,X0,X3)) | cons(X1,X3,X4) != X2) & nil(X1) != X2)) & (? [X5 : X1,X6 : list(X1)] : (listsp(X1,X0,X6) & pp(aa(X1,bool,X0,X5)) & cons(X1,X5,X6) = X2) | nil(X1) = X2 | ~sP0(X1,X0,X2)))),
% 0.15/0.41 inference(rectify,[],[f268])).
% 0.15/0.41 tff(f268,plain,(
% 0.15/0.41 ! [X2 : fun1(X0,bool),X0 : $tType,X1 : list(X0)] : ((sP0(X0,X2,X1) | (! [X3 : X0,X4 : list(X0)] : (~listsp(X0,X2,X4) | ~pp(aa(X0,bool,X2,X3)) | cons(X0,X3,X4) != X1) & nil(X0) != X1)) & (? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & cons(X0,X3,X4) = X1) | nil(X0) = X1 | ~sP0(X0,X2,X1)))),
% 0.15/0.41 inference(flattening,[],[f267])).
% 0.15/0.41 tff(f267,plain,(
% 0.15/0.41 ! [X2 : fun1(X0,bool),X0 : $tType,X1 : list(X0)] : ((sP0(X0,X2,X1) | (! [X3 : X0,X4 : list(X0)] : (~listsp(X0,X2,X4) | ~pp(aa(X0,bool,X2,X3)) | cons(X0,X3,X4) != X1) & nil(X0) != X1)) & ((? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & cons(X0,X3,X4) = X1) | nil(X0) = X1) | ~sP0(X0,X2,X1)))),
% 0.15/0.41 inference(nnf_transformation,[],[f247])).
% 0.15/0.41 tff(f541,plain,(
% 0.15/0.41 spl25_4),
% 0.15/0.41 inference(avatar_split_clause,[],[f344,f539])).
% 0.15/0.41 tff(f539,plain,(
% 0.15/0.41 spl25_4 <=> ! [X0 : $tType,X1 : fun1(X0,bool)] : listsp(X0,X1,nil(X0))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_4])])).
% 0.15/0.41 tff(f344,plain,(
% 0.15/0.41 ( ! [X0 : $tType,X1 : fun1(X0,bool)] : (listsp(X0,X1,nil(X0))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f126])).
% 0.15/0.41 tff(f126,plain,(
% 0.15/0.41 ! [X0 : $tType,X1 : fun1(X0,bool)] : listsp(X0,X1,nil(X0))),
% 0.15/0.41 inference(rectify,[],[f83])).
% 0.15/0.41 tff(f83,axiom,(
% 0.15/0.41 ! [X0 : $tType,X72 : fun1(X0,bool)] : listsp(X0,X72,nil(X0))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_listsp_ONil)).
% 0.15/0.41 tff(f537,plain,(
% 0.15/0.41 spl25_3),
% 0.15/0.41 inference(avatar_split_clause,[],[f315,f534])).
% 0.15/0.41 tff(f534,plain,(
% 0.15/0.41 spl25_3 <=> pp(fTrue)),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_3])])).
% 0.15/0.41 tff(f315,plain,(
% 0.15/0.41 pp(fTrue)),
% 0.15/0.41 inference(cnf_transformation,[],[f102])).
% 0.15/0.41 tff(f102,axiom,(
% 0.15/0.41 pp(fTrue)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U)).
% 0.15/0.41 tff(f532,plain,(
% 0.15/0.41 spl25_2),
% 0.15/0.41 inference(avatar_split_clause,[],[f314,f529])).
% 0.15/0.41 tff(f529,plain,(
% 0.15/0.41 spl25_2 <=> zero(nat)),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl25_2])])).
% 0.15/0.41 tff(f314,plain,(
% 0.15/0.41 zero(nat)),
% 0.15/0.41 inference(cnf_transformation,[],[f100])).
% 0.15/0.41 tff(f100,axiom,(
% 0.15/0.41 zero(nat)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero)).
% 0.15/0.41 tff(f527,plain,(
% 0.15/0.41 ~spl25_1),
% 0.15/0.41 inference(avatar_split_clause,[],[f312,f524])).
% 0.15/0.41 tff(f312,plain,(
% 0.15/0.41 ~pp(fFalse)),
% 0.15/0.41 inference(cnf_transformation,[],[f111])).
% 0.15/0.41 tff(f111,axiom,(
% 0.15/0.41 ~pp(fFalse)),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U)).
% 0.15/0.41 % SZS output end Proof for theBenchmark
% 0.15/0.41 % (31937)------------------------------
% 0.15/0.41 % (31937)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.41 % (31937)Termination reason: Refutation
% 0.15/0.41
% 0.15/0.41 % (31937)Memory used [KB]: 1280
% 0.15/0.41 % (31937)Time elapsed: 0.023 s
% 0.15/0.41 % (31937)Instructions burned: 38 (million)
% 0.15/0.41 % (31937)------------------------------
% 0.15/0.41 % (31937)------------------------------
% 0.15/0.41 % (31932)Success in time 0.047 s
%------------------------------------------------------------------------------