TSTP Solution File: LCL784_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL784_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 : n013.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 13:49:17 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL784_5 : TPTP v8.1.2. Released v6.0.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon Apr 29 22:54:04 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (19316)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39 % (19321)WARNING: value z3 for option sas not known
% 0.16/0.39 % (19320)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.39 % (19319)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.39 % (19322)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.39 % (19321)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.39 % (19323)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.39 % (19324)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.39 % (19325)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.39 % (19325)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.40 % Exception at run slice level
% 0.16/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.40 % Exception at run slice level
% 0.16/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.40 % Exception at run slice level
% 0.16/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.40 % (19323)First to succeed.
% 0.22/0.40 % (19324)Also succeeded, but the first one will report.
% 0.22/0.40 % (19323)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% 0.22/0.40 tff(type_def_5, type, bool: $tType).
% 0.22/0.40 tff(type_def_6, type, dB: $tType).
% 0.22/0.40 tff(type_def_7, type, list: $tType > $tType).
% 0.22/0.40 tff(type_def_8, type, nat: $tType).
% 0.22/0.40 tff(type_def_9, type, type: $tType).
% 0.22/0.40 tff(type_def_10, type, fun: ($tType * $tType) > $tType).
% 0.22/0.40 tff(func_def_0, type, combb: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,X1) * fun(X2,X0)) > fun(X2,X1))).
% 0.22/0.40 tff(func_def_1, type, combs: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * fun(X0,X1)) > fun(X0,X2))).
% 0.22/0.40 tff(func_def_2, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.22/0.40 tff(func_def_3, type, it: fun(dB,bool)).
% 0.22/0.40 tff(func_def_4, type, beta: fun(dB,fun(dB,bool))).
% 0.22/0.40 tff(func_def_5, type, abs: dB > dB).
% 0.22/0.40 tff(func_def_6, type, app: fun(dB,fun(dB,dB))).
% 0.22/0.40 tff(func_def_7, type, var: nat > dB).
% 0.22/0.40 tff(func_def_8, type, dB_size: dB > nat).
% 0.22/0.40 tff(func_def_9, type, liftn: (nat * dB * nat) > dB).
% 0.22/0.40 tff(func_def_10, type, subst: (dB * dB * nat) > dB).
% 0.22/0.40 tff(func_def_11, type, substn: (dB * dB * nat) > dB).
% 0.22/0.40 tff(func_def_12, type, foldl: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0)) * X0 * list(X1)) > X0)).
% 0.22/0.40 tff(func_def_13, type, insert: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 0.22/0.40 tff(func_def_14, type, cons: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 0.22/0.40 tff(func_def_15, type, nil: !>[X0: $tType]:(list(X0))).
% 0.22/0.40 tff(func_def_16, type, list_case: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(list(X1),X0)) * list(X1)) > X0)).
% 0.22/0.40 tff(func_def_17, type, list_size: !>[X0: $tType]:((fun(X0,nat) * list(X0)) > nat)).
% 0.22/0.40 tff(func_def_18, type, size_size: !>[X0: $tType]:((X0) > nat)).
% 0.22/0.40 tff(func_def_19, type, shift: !>[X0: $tType]:((fun(nat,X0) * nat * X0) > fun(nat,X0))).
% 0.22/0.40 tff(func_def_20, type, atom: nat > type).
% 0.22/0.40 tff(func_def_21, type, fun1: (type * type) > type).
% 0.22/0.40 tff(func_def_22, type, type_case: !>[X0: $tType]:((fun(nat,X0) * fun(type,fun(type,X0)) * type) > X0)).
% 0.22/0.40 tff(func_def_23, type, type_size: type > nat).
% 0.22/0.40 tff(func_def_24, type, aa: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * X0) > X1)).
% 0.22/0.40 tff(func_def_25, type, fFalse: bool).
% 0.22/0.40 tff(func_def_26, type, fTrue: bool).
% 0.22/0.40 tff(func_def_27, type, fconj: fun(bool,fun(bool,bool))).
% 0.22/0.40 tff(func_def_28, type, t1: type).
% 0.22/0.40 tff(func_def_29, type, t_a: type).
% 0.22/0.40 tff(func_def_30, type, t: type).
% 0.22/0.40 tff(func_def_31, type, e: fun(nat,type)).
% 0.22/0.40 tff(func_def_32, type, ea: fun(nat,type)).
% 0.22/0.40 tff(func_def_33, type, i: nat).
% 0.22/0.40 tff(func_def_34, type, ia: nat).
% 0.22/0.40 tff(func_def_35, type, n: nat).
% 0.22/0.40 tff(func_def_36, type, rs: list(dB)).
% 0.22/0.40 tff(func_def_37, type, t2: dB).
% 0.22/0.40 tff(func_def_38, type, u: dB).
% 0.22/0.40 tff(func_def_39, type, ua: dB).
% 0.22/0.40 tff(func_def_40, type, sK6: dB > dB).
% 0.22/0.40 tff(func_def_41, type, sK7: dB > list(dB)).
% 0.22/0.40 tff(func_def_42, type, sK8: dB > nat).
% 0.22/0.40 tff(func_def_43, type, sK9: dB > dB).
% 0.22/0.40 tff(func_def_44, type, sK10: dB > dB).
% 0.22/0.40 tff(func_def_45, type, sK11: dB > list(dB)).
% 0.22/0.40 tff(func_def_46, type, sK12: !>[X0: $tType]:((list(X0)) > X0)).
% 0.22/0.40 tff(func_def_47, type, sK13: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.22/0.40 tff(func_def_48, type, sK14: (dB * dB) > dB).
% 0.22/0.40 tff(func_def_49, type, sK15: !>[X0: $tType]:((list(X0)) > X0)).
% 0.22/0.40 tff(func_def_50, type, sK16: !>[X0: $tType]:((list(X0)) > list(X0))).
% 0.22/0.40 tff(func_def_51, type, sK17: (dB * fun(nat,type)) > type).
% 0.22/0.40 tff(func_def_52, type, sK18: (dB * fun(nat,type)) > type).
% 0.22/0.40 tff(func_def_53, type, sK19: (type * dB * fun(nat,type)) > type).
% 0.22/0.40 tff(func_def_54, type, sK20: (type * dB * fun(nat,type)) > type).
% 0.22/0.40 tff(func_def_55, type, sK21: (dB * list(dB) * dB) > dB).
% 0.22/0.40 tff(func_def_56, type, sK22: (dB * list(dB) * dB) > dB).
% 0.22/0.40 tff(func_def_57, type, sK23: (dB * list(dB) * dB) > list(dB)).
% 0.22/0.40 tff(func_def_58, type, sK24: (dB * list(dB) * dB) > list(dB)).
% 0.22/0.40 tff(func_def_59, type, sK25: (dB * list(dB) * dB) > dB).
% 0.22/0.40 tff(func_def_60, type, sK26: (dB * list(dB) * nat) > list(dB)).
% 0.22/0.40 tff(func_def_61, type, sK27: (dB * dB * dB) > dB).
% 0.22/0.40 tff(func_def_62, type, sK28: (dB * dB * dB) > dB).
% 0.22/0.40 tff(func_def_63, type, sK29: (dB * dB * dB) > dB).
% 0.22/0.40 tff(func_def_64, type, sK30: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > X0)).
% 0.22/0.40 tff(func_def_65, type, sK31: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > list(X0))).
% 0.22/0.40 tff(func_def_66, type, sK32: (type * dB * dB * fun(nat,type)) > type).
% 0.22/0.40 tff(func_def_67, type, sK33: !>[X0: $tType, X1: $tType]:((fun(X1,X0) * fun(X1,X0)) > X1)).
% 0.22/0.40 tff(func_def_68, type, sK34: !>[X0: $tType]:((list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool))) > list(X0))).
% 0.22/0.40 tff(func_def_69, type, sK35: !>[X0: $tType]:((list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool))) > X0)).
% 0.22/0.40 tff(func_def_70, type, sK36: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 0.22/0.40 tff(func_def_71, type, sK37: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 0.22/0.40 tff(func_def_72, type, sK38: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X0)).
% 0.22/0.40 tff(pred_def_1, type, zero: !>[X0: $tType]:($o)).
% 0.22/0.40 tff(pred_def_2, type, step1: !>[X0: $tType]:((fun(X0,fun(X0,bool)) * list(X0) * list(X0)) > $o)).
% 0.22/0.40 tff(pred_def_3, type, list_ex1: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 0.22/0.40 tff(pred_def_4, type, listsp: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 0.22/0.40 tff(pred_def_5, type, typing: (fun(nat,type) * dB * type) > $o).
% 0.22/0.40 tff(pred_def_6, type, pp: bool > $o).
% 0.22/0.40 tff(pred_def_7, type, sP0: dB > $o).
% 0.22/0.40 tff(pred_def_8, type, sP1: dB > $o).
% 0.22/0.40 tff(pred_def_9, type, sP2: (dB * list(dB) * dB) > $o).
% 0.22/0.40 tff(pred_def_10, type, sP3: (dB * dB * dB) > $o).
% 0.22/0.40 tff(pred_def_11, type, sP4: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 0.22/0.40 tff(pred_def_12, type, sP5: !>[X0: $tType]:((list(X0) * list(X0) * fun(X0,fun(X0,bool)) * X0 * X0) > $o)).
% 0.22/0.40 tff(f640,plain,(
% 0.22/0.40 $false),
% 0.22/0.40 inference(avatar_sat_refutation,[],[f569,f574,f579,f584,f591,f596,f601,f605,f610,f614,f618,f622,f628,f633,f638,f639])).
% 0.22/0.40 tff(f639,plain,(
% 0.22/0.40 spl39_5),
% 0.22/0.40 inference(avatar_split_clause,[],[f356,f588])).
% 0.22/0.40 tff(f588,plain,(
% 0.22/0.40 spl39_5 <=> pp(aa(dB,bool,it,u))),
% 0.22/0.40 introduced(avatar_definition,[new_symbols(naming,[spl39_5])])).
% 0.22/0.40 tff(f356,plain,(
% 0.22/0.40 pp(aa(dB,bool,it,u))),
% 0.22/0.40 inference(cnf_transformation,[],[f4])).
% 0.22/0.40 tff(f4,axiom,(
% 0.22/0.40 pp(aa(dB,bool,it,u))),
% 0.22/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uIT)).
% 0.22/0.40 tff(f638,plain,(
% 0.22/0.40 spl39_15),
% 0.22/0.40 inference(avatar_split_clause,[],[f355,f635])).
% 0.22/0.40 tff(f635,plain,(
% 0.22/0.41 spl39_15 <=> pp(aa(dB,bool,it,ua))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_15])])).
% 0.22/0.41 tff(f355,plain,(
% 0.22/0.41 pp(aa(dB,bool,it,ua))),
% 0.22/0.41 inference(cnf_transformation,[],[f2])).
% 0.22/0.41 tff(f2,axiom,(
% 0.22/0.41 pp(aa(dB,bool,it,ua))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Var_I3_J)).
% 0.22/0.41 tff(f633,plain,(
% 0.22/0.41 spl39_14),
% 0.22/0.41 inference(avatar_split_clause,[],[f354,f630])).
% 0.22/0.41 tff(f630,plain,(
% 0.22/0.41 spl39_14 <=> pp(aa(dB,bool,it,t2))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_14])])).
% 0.22/0.41 tff(f354,plain,(
% 0.22/0.41 pp(aa(dB,bool,it,t2))),
% 0.22/0.41 inference(cnf_transformation,[],[f1])).
% 0.22/0.41 tff(f1,axiom,(
% 0.22/0.41 pp(aa(dB,bool,it,t2))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096IT_At_096)).
% 0.22/0.41 tff(f628,plain,(
% 0.22/0.41 spl39_13 | ~spl39_9 | ~spl39_11),
% 0.22/0.41 inference(avatar_split_clause,[],[f623,f616,f607,f626])).
% 0.22/0.41 tff(f626,plain,(
% 0.22/0.41 spl39_13 <=> ! [X0 : fun(dB,bool)] : listsp(dB,X0,rs)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_13])])).
% 0.22/0.41 tff(f607,plain,(
% 0.22/0.41 spl39_9 <=> rs = nil(dB)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_9])])).
% 0.22/0.41 tff(f616,plain,(
% 0.22/0.41 spl39_11 <=> ! [X0 : $tType,X1 : fun(X0,bool)] : listsp(X0,X1,nil(X0))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_11])])).
% 0.22/0.41 tff(f623,plain,(
% 0.22/0.41 ( ! [X0 : fun(dB,bool)] : (listsp(dB,X0,rs)) ) | (~spl39_9 | ~spl39_11)),
% 0.22/0.41 inference(superposition,[],[f617,f609])).
% 0.22/0.41 tff(f609,plain,(
% 0.22/0.41 rs = nil(dB) | ~spl39_9),
% 0.22/0.41 inference(avatar_component_clause,[],[f607])).
% 0.22/0.41 tff(f617,plain,(
% 0.22/0.41 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (listsp(X0,X1,nil(X0))) ) | ~spl39_11),
% 0.22/0.41 inference(avatar_component_clause,[],[f616])).
% 0.22/0.41 tff(f622,plain,(
% 0.22/0.41 spl39_12),
% 0.22/0.41 inference(avatar_split_clause,[],[f536,f620])).
% 0.22/0.41 tff(f620,plain,(
% 0.22/0.41 spl39_12 <=> ! [X1 : $tType,X0 : fun(X1,bool)] : sP4(X1,X0,nil(X1))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_12])])).
% 0.22/0.41 tff(f536,plain,(
% 0.22/0.41 ( ! [X1 : $tType,X0 : fun(X1,bool)] : (sP4(X1,X0,nil(X1))) )),
% 0.22/0.41 inference(equality_resolution,[],[f449])).
% 0.22/0.41 tff(f449,plain,(
% 0.22/0.41 ( ! [X1 : $tType,X2 : list(X1),X0 : fun(X1,bool)] : (sP4(X1,X0,X2) | nil(X1) != X2) )),
% 0.22/0.41 inference(cnf_transformation,[],[f311])).
% 0.22/0.41 tff(f311,plain,(
% 0.22/0.41 ! [X0 : fun(X1,bool),X1 : $tType,X2 : list(X1)] : ((sP4(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,sK31(X1,X0,X2)) & pp(aa(X1,bool,X0,sK30(X1,X0,X2))) & cons(X1,sK30(X1,X0,X2),sK31(X1,X0,X2)) = X2) | nil(X1) = X2 | ~sP4(X1,X0,X2)))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31])],[f309,f310])).
% 0.22/0.41 tff(f310,plain,(
% 0.22/0.41 ! [X1 : $tType,X0 : fun(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,sK31(X1,X0,X2)) & pp(aa(X1,bool,X0,sK30(X1,X0,X2))) & cons(X1,sK30(X1,X0,X2),sK31(X1,X0,X2)) = X2))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 tff(f309,plain,(
% 0.22/0.41 ! [X0 : fun(X1,bool),X1 : $tType,X2 : list(X1)] : ((sP4(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 | ~sP4(X1,X0,X2)))),
% 0.22/0.41 inference(rectify,[],[f308])).
% 0.22/0.41 tff(f308,plain,(
% 0.22/0.41 ! [X2 : fun(X0,bool),X0 : $tType,X1 : list(X0)] : ((sP4(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 | ~sP4(X0,X2,X1)))),
% 0.22/0.41 inference(flattening,[],[f307])).
% 0.22/0.41 tff(f307,plain,(
% 0.22/0.41 ! [X2 : fun(X0,bool),X0 : $tType,X1 : list(X0)] : ((sP4(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) | ~sP4(X0,X2,X1)))),
% 0.22/0.41 inference(nnf_transformation,[],[f257])).
% 0.22/0.41 tff(f257,plain,(
% 0.22/0.41 ! [X2 : fun(X0,bool),X0 : $tType,X1 : list(X0)] : (sP4(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))),
% 0.22/0.41 introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])])).
% 0.22/0.41 tff(f618,plain,(
% 0.22/0.41 spl39_11),
% 0.22/0.41 inference(avatar_split_clause,[],[f382,f616])).
% 0.22/0.41 tff(f382,plain,(
% 0.22/0.41 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (listsp(X0,X1,nil(X0))) )),
% 0.22/0.41 inference(cnf_transformation,[],[f122])).
% 0.22/0.41 tff(f122,plain,(
% 0.22/0.41 ! [X0 : $tType,X1 : fun(X0,bool)] : listsp(X0,X1,nil(X0))),
% 0.22/0.41 inference(rectify,[],[f25])).
% 0.22/0.41 tff(f25,axiom,(
% 0.22/0.41 ! [X0 : $tType,X37 : fun(X0,bool)] : listsp(X0,X37,nil(X0))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_listsp_ONil)).
% 0.22/0.41 tff(f614,plain,(
% 0.22/0.41 spl39_10),
% 0.22/0.41 inference(avatar_split_clause,[],[f380,f612])).
% 0.22/0.41 tff(f612,plain,(
% 0.22/0.41 spl39_10 <=> ! [X0 : dB,X1 : nat] : abs(X0) != var(X1)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_10])])).
% 0.22/0.41 tff(f380,plain,(
% 0.22/0.41 ( ! [X0 : dB,X1 : nat] : (abs(X0) != var(X1)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f119])).
% 0.22/0.41 tff(f119,plain,(
% 0.22/0.41 ! [X0 : dB,X1 : nat] : abs(X0) != var(X1)),
% 0.22/0.41 inference(rectify,[],[f45])).
% 0.22/0.41 tff(f45,axiom,(
% 0.22/0.41 ! [X58 : dB,X27 : nat] : var(X27) != abs(X58)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_dB_Osimps_I6_J)).
% 0.22/0.41 tff(f610,plain,(
% 0.22/0.41 spl39_9),
% 0.22/0.41 inference(avatar_split_clause,[],[f353,f607])).
% 0.22/0.41 tff(f353,plain,(
% 0.22/0.41 rs = nil(dB)),
% 0.22/0.41 inference(cnf_transformation,[],[f3])).
% 0.22/0.41 tff(f3,axiom,(
% 0.22/0.41 rs = nil(dB)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Nil)).
% 0.22/0.41 tff(f605,plain,(
% 0.22/0.41 spl39_8),
% 0.22/0.41 inference(avatar_split_clause,[],[f373,f603])).
% 0.22/0.41 tff(f603,plain,(
% 0.22/0.41 spl39_8 <=> ! [X0 : dB] : (sP1(X0) | ~sP0(X0))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_8])])).
% 0.22/0.41 tff(f373,plain,(
% 0.22/0.41 ( ! [X0 : dB] : (sP1(X0) | ~sP0(X0)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f267])).
% 0.22/0.41 tff(f267,plain,(
% 0.22/0.41 ! [X0 : dB] : ((sP1(X0) | (~sP0(X0) & ! [X1 : dB] : (~pp(aa(dB,bool,it,X1)) | abs(X1) != X0) & ! [X2 : list(dB),X3 : nat] : (~listsp(dB,it,X2) | foldl(dB,dB,app,var(X3),X2) != X0))) & (sP0(X0) | (pp(aa(dB,bool,it,sK6(X0))) & abs(sK6(X0)) = X0) | (listsp(dB,it,sK7(X0)) & foldl(dB,dB,app,var(sK8(X0)),sK7(X0)) = X0) | ~sP1(X0)))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f264,f266,f265])).
% 0.22/0.41 tff(f265,plain,(
% 0.22/0.41 ! [X0 : dB] : (? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) => (pp(aa(dB,bool,it,sK6(X0))) & abs(sK6(X0)) = X0))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 tff(f266,plain,(
% 0.22/0.41 ! [X0 : dB] : (? [X5 : list(dB),X6 : nat] : (listsp(dB,it,X5) & foldl(dB,dB,app,var(X6),X5) = X0) => (listsp(dB,it,sK7(X0)) & foldl(dB,dB,app,var(sK8(X0)),sK7(X0)) = X0))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 tff(f264,plain,(
% 0.22/0.41 ! [X0 : dB] : ((sP1(X0) | (~sP0(X0) & ! [X1 : dB] : (~pp(aa(dB,bool,it,X1)) | abs(X1) != X0) & ! [X2 : list(dB),X3 : nat] : (~listsp(dB,it,X2) | foldl(dB,dB,app,var(X3),X2) != X0))) & (sP0(X0) | ? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) | ? [X5 : list(dB),X6 : nat] : (listsp(dB,it,X5) & foldl(dB,dB,app,var(X6),X5) = X0) | ~sP1(X0)))),
% 0.22/0.41 inference(rectify,[],[f263])).
% 0.22/0.41 tff(f263,plain,(
% 0.22/0.41 ! [X0 : dB] : ((sP1(X0) | (~sP0(X0) & ! [X4 : dB] : (~pp(aa(dB,bool,it,X4)) | abs(X4) != X0) & ! [X5 : list(dB),X6 : nat] : (~listsp(dB,it,X5) | foldl(dB,dB,app,var(X6),X5) != X0))) & (sP0(X0) | ? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) | ? [X5 : list(dB),X6 : nat] : (listsp(dB,it,X5) & foldl(dB,dB,app,var(X6),X5) = X0) | ~sP1(X0)))),
% 0.22/0.41 inference(flattening,[],[f262])).
% 0.22/0.41 tff(f262,plain,(
% 0.22/0.41 ! [X0 : dB] : ((sP1(X0) | (~sP0(X0) & ! [X4 : dB] : (~pp(aa(dB,bool,it,X4)) | abs(X4) != X0) & ! [X5 : list(dB),X6 : nat] : (~listsp(dB,it,X5) | foldl(dB,dB,app,var(X6),X5) != X0))) & ((sP0(X0) | ? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) | ? [X5 : list(dB),X6 : nat] : (listsp(dB,it,X5) & foldl(dB,dB,app,var(X6),X5) = X0)) | ~sP1(X0)))),
% 0.22/0.41 inference(nnf_transformation,[],[f251])).
% 0.22/0.41 tff(f251,plain,(
% 0.22/0.41 ! [X0 : dB] : (sP1(X0) <=> (sP0(X0) | ? [X4 : dB] : (pp(aa(dB,bool,it,X4)) & abs(X4) = X0) | ? [X5 : list(dB),X6 : nat] : (listsp(dB,it,X5) & foldl(dB,dB,app,var(X6),X5) = X0)))),
% 0.22/0.41 introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])])).
% 0.22/0.41 tff(f601,plain,(
% 0.22/0.41 spl39_7),
% 0.22/0.41 inference(avatar_split_clause,[],[f352,f598])).
% 0.22/0.41 tff(f598,plain,(
% 0.22/0.41 spl39_7 <=> typing(e,u,t)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_7])])).
% 0.22/0.41 tff(f352,plain,(
% 0.22/0.41 typing(e,u,t)),
% 0.22/0.41 inference(cnf_transformation,[],[f20])).
% 0.22/0.41 tff(f20,axiom,(
% 0.22/0.41 typing(e,u,t)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_uT)).
% 0.22/0.41 tff(f596,plain,(
% 0.22/0.41 spl39_6),
% 0.22/0.41 inference(avatar_split_clause,[],[f351,f593])).
% 0.22/0.41 tff(f593,plain,(
% 0.22/0.41 spl39_6 <=> typing(ea,ua,t)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_6])])).
% 0.22/0.41 tff(f351,plain,(
% 0.22/0.41 typing(ea,ua,t)),
% 0.22/0.41 inference(cnf_transformation,[],[f38])).
% 0.22/0.41 tff(f38,axiom,(
% 0.22/0.41 typing(ea,ua,t)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Var_I4_J)).
% 0.22/0.41 tff(f591,plain,(
% 0.22/0.41 ~spl39_5 | spl39_4),
% 0.22/0.41 inference(avatar_split_clause,[],[f586,f581,f588])).
% 0.22/0.41 tff(f581,plain,(
% 0.22/0.41 spl39_4 <=> pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(i),rs),u,i)))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_4])])).
% 0.22/0.41 tff(f586,plain,(
% 0.22/0.41 ~pp(aa(dB,bool,it,u)) | spl39_4),
% 0.22/0.41 inference(forward_demodulation,[],[f585,f384])).
% 0.22/0.41 tff(f384,plain,(
% 0.22/0.41 ( ! [X0 : dB,X1 : nat] : (subst(var(X1),X0,X1) = X0) )),
% 0.22/0.41 inference(cnf_transformation,[],[f124])).
% 0.22/0.41 tff(f124,plain,(
% 0.22/0.41 ! [X0 : dB,X1 : nat] : subst(var(X1),X0,X1) = X0),
% 0.22/0.41 inference(rectify,[],[f15])).
% 0.22/0.41 tff(f15,axiom,(
% 0.22/0.41 ! [X15 : dB,X13 : nat] : subst(var(X13),X15,X13) = X15),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_subst__eq)).
% 0.22/0.41 tff(f585,plain,(
% 0.22/0.41 ~pp(aa(dB,bool,it,subst(var(i),u,i))) | spl39_4),
% 0.22/0.41 inference(forward_demodulation,[],[f583,f558])).
% 0.22/0.41 tff(f558,plain,(
% 0.22/0.41 ( ! [X2 : nat] : (var(X2) = foldl(dB,dB,app,var(X2),rs)) )),
% 0.22/0.41 inference(forward_demodulation,[],[f538,f353])).
% 0.22/0.41 tff(f538,plain,(
% 0.22/0.41 ( ! [X2 : nat] : (var(X2) = foldl(dB,dB,app,var(X2),nil(dB))) )),
% 0.22/0.41 inference(equality_resolution,[],[f537])).
% 0.22/0.41 tff(f537,plain,(
% 0.22/0.41 ( ! [X2 : nat,X1 : dB] : (var(X2) = foldl(dB,dB,app,X1,nil(dB)) | var(X2) != X1) )),
% 0.22/0.41 inference(equality_resolution,[],[f455])).
% 0.22/0.41 tff(f455,plain,(
% 0.22/0.41 ( ! [X2 : nat,X0 : list(dB),X1 : dB] : (var(X2) = foldl(dB,dB,app,X1,X0) | nil(dB) != X0 | var(X2) != X1) )),
% 0.22/0.41 inference(cnf_transformation,[],[f314])).
% 0.22/0.41 tff(f314,plain,(
% 0.22/0.41 ! [X0 : list(dB),X1 : dB,X2 : nat] : ((var(X2) = foldl(dB,dB,app,X1,X0) | nil(dB) != X0 | var(X2) != X1) & ((nil(dB) = X0 & var(X2) = X1) | var(X2) != foldl(dB,dB,app,X1,X0)))),
% 0.22/0.41 inference(flattening,[],[f313])).
% 0.22/0.41 tff(f313,plain,(
% 0.22/0.41 ! [X0 : list(dB),X1 : dB,X2 : nat] : ((var(X2) = foldl(dB,dB,app,X1,X0) | (nil(dB) != X0 | var(X2) != X1)) & ((nil(dB) = X0 & var(X2) = X1) | var(X2) != foldl(dB,dB,app,X1,X0)))),
% 0.22/0.41 inference(nnf_transformation,[],[f169])).
% 0.22/0.41 tff(f169,plain,(
% 0.22/0.41 ! [X0 : list(dB),X1 : dB,X2 : nat] : (var(X2) = foldl(dB,dB,app,X1,X0) <=> (nil(dB) = X0 & var(X2) = X1))),
% 0.22/0.41 inference(rectify,[],[f14])).
% 0.22/0.41 tff(f14,axiom,(
% 0.22/0.41 ! [X9 : list(dB),X16 : dB,X12 : nat] : (var(X12) = foldl(dB,dB,app,X16,X9) <=> (nil(dB) = X9 & var(X12) = X16))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Var__eq__apps__conv)).
% 0.22/0.41 tff(f583,plain,(
% 0.22/0.41 ~pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(i),rs),u,i))) | spl39_4),
% 0.22/0.41 inference(avatar_component_clause,[],[f581])).
% 0.22/0.41 tff(f584,plain,(
% 0.22/0.41 ~spl39_4),
% 0.22/0.41 inference(avatar_split_clause,[],[f520,f581])).
% 0.22/0.41 tff(f520,plain,(
% 0.22/0.41 ~pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(i),rs),u,i)))),
% 0.22/0.41 inference(definition_unfolding,[],[f346,f350])).
% 0.22/0.41 tff(f350,plain,(
% 0.22/0.41 n = i),
% 0.22/0.41 inference(cnf_transformation,[],[f5])).
% 0.22/0.41 tff(f5,axiom,(
% 0.22/0.41 n = i),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_True)).
% 0.22/0.41 tff(f346,plain,(
% 0.22/0.41 ~pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(n),rs),u,i)))),
% 0.22/0.41 inference(cnf_transformation,[],[f110])).
% 0.22/0.41 tff(f110,plain,(
% 0.22/0.41 ~pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(n),rs),u,i)))),
% 0.22/0.41 inference(flattening,[],[f109])).
% 0.22/0.41 tff(f109,negated_conjecture,(
% 0.22/0.41 ~pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(n),rs),u,i)))),
% 0.22/0.41 inference(negated_conjecture,[],[f108])).
% 0.22/0.41 tff(f108,conjecture,(
% 0.22/0.41 pp(aa(dB,bool,it,subst(foldl(dB,dB,app,var(n),rs),u,i)))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.22/0.41 tff(f579,plain,(
% 0.22/0.41 spl39_3),
% 0.22/0.41 inference(avatar_split_clause,[],[f349,f576])).
% 0.22/0.41 tff(f576,plain,(
% 0.22/0.41 spl39_3 <=> pp(fTrue)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_3])])).
% 0.22/0.41 tff(f349,plain,(
% 0.22/0.41 pp(fTrue)),
% 0.22/0.41 inference(cnf_transformation,[],[f102])).
% 0.22/0.41 tff(f102,axiom,(
% 0.22/0.41 pp(fTrue)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U)).
% 0.22/0.41 tff(f574,plain,(
% 0.22/0.41 spl39_2),
% 0.22/0.41 inference(avatar_split_clause,[],[f348,f571])).
% 0.22/0.41 tff(f571,plain,(
% 0.22/0.41 spl39_2 <=> zero(nat)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_2])])).
% 0.22/0.41 tff(f348,plain,(
% 0.22/0.41 zero(nat)),
% 0.22/0.41 inference(cnf_transformation,[],[f100])).
% 0.22/0.41 tff(f100,axiom,(
% 0.22/0.41 zero(nat)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero)).
% 0.22/0.41 tff(f569,plain,(
% 0.22/0.41 ~spl39_1),
% 0.22/0.41 inference(avatar_split_clause,[],[f347,f566])).
% 0.22/0.41 tff(f566,plain,(
% 0.22/0.41 spl39_1 <=> pp(fFalse)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl39_1])])).
% 0.22/0.41 tff(f347,plain,(
% 0.22/0.41 ~pp(fFalse)),
% 0.22/0.41 inference(cnf_transformation,[],[f101])).
% 0.22/0.41 tff(f101,axiom,(
% 0.22/0.41 ~pp(fFalse)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U)).
% 0.22/0.41 % SZS output end Proof for theBenchmark
% 0.22/0.41 % (19323)------------------------------
% 0.22/0.41 % (19323)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.41 % (19323)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (19323)Memory used [KB]: 1210
% 0.22/0.41 % (19323)Time elapsed: 0.016 s
% 0.22/0.41 % (19323)Instructions burned: 26 (million)
% 0.22/0.41 % (19323)------------------------------
% 0.22/0.41 % (19323)------------------------------
% 0.22/0.41 % (19316)Success in time 0.038 s
%------------------------------------------------------------------------------