TSTP Solution File: LCL767_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL767_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 : n020.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 13:49:13 EDT 2024
% Result : Theorem 115.50s 16.83s
% Output : Refutation 115.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL767_5 : TPTP v8.1.2. Released v6.0.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 23:06:47 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (15253)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.39 % (15256)WARNING: value z3 for option sas not known
% 0.21/0.39 % (15254)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.39 % (15255)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.39 % (15257)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.39 % (15256)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)
% 0.21/0.39 % (15259)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)
% 0.21/0.39 % (15258)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)
% 0.21/0.39 % (15260)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)
% 0.21/0.40 % Exception at run slice level
% 0.21/0.40 % Exception at run slice level
% 0.21/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.40 % Exception at run slice level
% 0.21/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.40 % (15260)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.41 % (15261)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.41 % (15262)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 % (15263)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)
% 0.21/0.42 % (15261)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.42 % (15262)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.42 % Exception at run slice level
% 0.21/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.44 % (15264)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)
% 115.50/16.80 % (15259)First to succeed.
% 115.50/16.83 % (15259)Refutation found. Thanks to Tanya!
% 115.50/16.83 % SZS status Theorem for theBenchmark
% 115.50/16.83 % SZS output start Proof for theBenchmark
% 115.50/16.83 tff(type_def_5, type, bool: $tType).
% 115.50/16.83 tff(type_def_6, type, dB: $tType).
% 115.50/16.83 tff(type_def_7, type, list: $tType > $tType).
% 115.50/16.83 tff(type_def_8, type, nat: $tType).
% 115.50/16.83 tff(type_def_9, type, fun: ($tType * $tType) > $tType).
% 115.50/16.83 tff(func_def_0, type, combb: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,X1) * fun(X2,X0)) > fun(X2,X1))).
% 115.50/16.83 tff(func_def_1, type, combc: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2))) > fun(X1,fun(X0,X2)))).
% 115.50/16.83 tff(func_def_2, type, combs: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * fun(X0,X1)) > fun(X0,X2))).
% 115.50/16.83 tff(func_def_3, type, it: fun(dB,bool)).
% 115.50/16.83 tff(func_def_4, type, abs: dB > dB).
% 115.50/16.83 tff(func_def_5, type, app: fun(dB,fun(dB,dB))).
% 115.50/16.83 tff(func_def_6, type, var: nat > dB).
% 115.50/16.83 tff(func_def_7, type, dB_case: !>[X0: $tType]:((fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB) > X0)).
% 115.50/16.83 tff(func_def_8, type, append: !>[X0: $tType]:(fun(list(X0),fun(list(X0),list(X0))))).
% 115.50/16.83 tff(func_def_9, type, butlast: !>[X0: $tType]:((list(X0)) > list(X0))).
% 115.50/16.83 tff(func_def_10, type, foldl: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0)) * X0 * list(X1)) > X0)).
% 115.50/16.83 tff(func_def_11, type, insert: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 115.50/16.83 tff(func_def_12, type, last: !>[X0: $tType]:((list(X0)) > X0)).
% 115.50/16.83 tff(func_def_13, type, cons: !>[X0: $tType]:(fun(X0,fun(list(X0),list(X0))))).
% 115.50/16.83 tff(func_def_14, type, nil: !>[X0: $tType]:(list(X0))).
% 115.50/16.83 tff(func_def_15, type, list_case: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(list(X1),X0)) * list(X1)) > X0)).
% 115.50/16.83 tff(func_def_16, type, maps: !>[X0: $tType, X1: $tType]:((fun(X0,list(X1)) * list(X0)) > list(X1))).
% 115.50/16.83 tff(func_def_17, type, rev: !>[X0: $tType]:((list(X0)) > list(X0))).
% 115.50/16.83 tff(func_def_18, type, rotate1: !>[X0: $tType]:((list(X0)) > list(X0))).
% 115.50/16.83 tff(func_def_19, type, splice: !>[X0: $tType]:((list(X0) * list(X0)) > list(X0))).
% 115.50/16.83 tff(func_def_20, type, aa: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * X0) > X1)).
% 115.50/16.83 tff(func_def_21, type, fFalse: bool).
% 115.50/16.83 tff(func_def_22, type, fNot: fun(bool,bool)).
% 115.50/16.83 tff(func_def_23, type, fTrue: bool).
% 115.50/16.83 tff(func_def_24, type, fconj: fun(bool,fun(bool,bool))).
% 115.50/16.83 tff(func_def_25, type, fdisj: fun(bool,fun(bool,bool))).
% 115.50/16.83 tff(func_def_26, type, fequal: !>[X0: $tType]:((X0) > fun(X0,bool))).
% 115.50/16.83 tff(func_def_27, type, i: nat).
% 115.50/16.83 tff(func_def_28, type, n: nat).
% 115.50/16.83 tff(func_def_29, type, rs: list(dB)).
% 115.50/16.83 tff(func_def_30, type, sK6: dB > dB).
% 115.50/16.83 tff(func_def_31, type, sK7: dB > dB).
% 115.50/16.83 tff(func_def_32, type, sK8: dB > dB).
% 115.50/16.83 tff(func_def_33, type, sK9: dB > nat).
% 115.50/16.83 tff(func_def_34, type, sK10: dB > list(dB)).
% 115.50/16.83 tff(func_def_35, type, sK11: dB > dB).
% 115.50/16.83 tff(func_def_36, type, sK12: dB > dB).
% 115.50/16.83 tff(func_def_37, type, sK13: dB > nat).
% 115.50/16.83 tff(func_def_38, type, sK14: !>[X0: $tType]:((list(X0)) > X0)).
% 115.50/16.83 tff(func_def_39, type, sK15: !>[X0: $tType]:((list(X0)) > list(X0))).
% 115.50/16.83 tff(func_def_40, type, sK16: !>[X0: $tType]:((list(X0)) > list(X0))).
% 115.50/16.83 tff(func_def_41, type, sK17: !>[X0: $tType]:((list(X0)) > X0)).
% 115.50/16.83 tff(func_def_42, type, sK18: !>[X0: $tType]:((list(X0)) > list(X0))).
% 115.50/16.83 tff(func_def_43, type, sK19: !>[X0: $tType]:((list(X0)) > X0)).
% 115.50/16.83 tff(func_def_44, type, sK20: !>[X0: $tType]:((list(X0)) > X0)).
% 115.50/16.83 tff(func_def_45, type, sK21: !>[X0: $tType]:((list(X0)) > list(X0))).
% 115.50/16.83 tff(func_def_46, type, sK22: !>[X0: $tType]:((fun(list(X0),bool)) > X0)).
% 115.50/16.83 tff(func_def_47, type, sK23: !>[X0: $tType]:((fun(list(X0),bool)) > list(X0))).
% 115.50/16.83 tff(func_def_48, type, sK24: !>[X0: $tType]:((fun(list(X0),bool)) > X0)).
% 115.50/16.83 tff(func_def_49, type, sK25: !>[X0: $tType]:((fun(list(X0),bool)) > X0)).
% 115.50/16.83 tff(func_def_50, type, sK26: !>[X0: $tType]:((fun(list(X0),bool)) > list(X0))).
% 115.50/16.83 tff(func_def_51, type, sK27: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > X0)).
% 115.50/16.83 tff(func_def_52, type, sK28: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > list(X0))).
% 115.50/16.83 tff(func_def_53, type, sK29: !>[X0: $tType, X1: $tType]:((fun(X1,X0) * fun(X1,X0)) > X1)).
% 115.50/16.83 tff(func_def_54, type, sK30: (dB * dB * list(dB) * dB) > list(dB)).
% 115.50/16.83 tff(func_def_55, type, sK31: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > list(X0))).
% 115.50/16.83 tff(func_def_56, type, sK32: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > list(X0))).
% 115.50/16.83 tff(func_def_57, type, sK33: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * list(X0)) > list(X0))).
% 115.50/16.83 tff(func_def_58, type, sK34: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 115.50/16.83 tff(func_def_59, type, sK35: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 115.50/16.83 tff(func_def_60, type, sK36: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X0)).
% 115.50/16.83 tff(pred_def_1, type, list_all: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 115.50/16.83 tff(pred_def_2, type, list_ex1: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 115.50/16.83 tff(pred_def_3, type, listsp: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 115.50/16.83 tff(pred_def_4, type, pp: bool > $o).
% 115.50/16.83 tff(pred_def_5, type, sP0: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 115.50/16.83 tff(pred_def_6, type, sP1: (dB * dB * list(dB) * dB) > $o).
% 115.50/16.83 tff(pred_def_7, type, sP2: !>[X0: $tType]:((list(X0) * fun(X0,bool) * X0) > $o)).
% 115.50/16.83 tff(pred_def_8, type, sP3: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > $o)).
% 115.50/16.83 tff(pred_def_9, type, sP4: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > $o)).
% 115.50/16.83 tff(pred_def_10, type, sP5: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * list(X0)) > $o)).
% 115.50/16.83 tff(f134160,plain,(
% 115.50/16.83 $false),
% 115.50/16.83 inference(resolution,[],[f134158,f382])).
% 115.50/16.83 tff(f382,plain,(
% 115.50/16.83 ( ! [X0 : nat] : (pp(aa(dB,bool,it,var(X0)))) )),
% 115.50/16.83 inference(cnf_transformation,[],[f120])).
% 115.50/16.83 tff(f120,plain,(
% 115.50/16.83 ! [X0 : nat] : pp(aa(dB,bool,it,var(X0)))),
% 115.50/16.83 inference(rectify,[],[f1])).
% 115.50/16.83 tff(f1,axiom,(
% 115.50/16.83 ! [X4 : nat] : pp(aa(dB,bool,it,var(X4)))),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Var__IT)).
% 115.50/16.83 tff(f134158,plain,(
% 115.50/16.83 ~pp(aa(dB,bool,it,var(i)))),
% 115.50/16.83 inference(resolution,[],[f134156,f4700])).
% 115.50/16.83 tff(f4700,plain,(
% 115.50/16.83 listsp(dB,it,rs)),
% 115.50/16.83 inference(resolution,[],[f379,f504])).
% 115.50/16.83 tff(f504,plain,(
% 115.50/16.83 ( ! [X0 : $tType,X2 : fun(X0,bool),X3 : list(X0),X1 : fun(X0,bool)] : (~listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3) | listsp(X0,X2,X3)) )),
% 115.50/16.83 inference(cnf_transformation,[],[f331])).
% 115.50/16.83 tff(f331,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : list(X0)] : ((listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3) | ~listsp(X0,X1,X3) | ~listsp(X0,X2,X3)) & ((listsp(X0,X1,X3) & listsp(X0,X2,X3)) | ~listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3)))),
% 115.50/16.83 inference(flattening,[],[f330])).
% 115.50/16.83 tff(f330,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : list(X0)] : ((listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3) | (~listsp(X0,X1,X3) | ~listsp(X0,X2,X3))) & ((listsp(X0,X1,X3) & listsp(X0,X2,X3)) | ~listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3)))),
% 115.50/16.83 inference(nnf_transformation,[],[f203])).
% 115.50/16.83 tff(f203,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : fun(X0,bool),X2 : fun(X0,bool),X3 : list(X0)] : (listsp(X0,combs(X0,bool,bool,combb(bool,fun(bool,bool),X0,fconj,X2),X1),X3) <=> (listsp(X0,X1,X3) & listsp(X0,X2,X3)))),
% 115.50/16.83 inference(rectify,[],[f18])).
% 115.50/16.83 tff(f18,axiom,(
% 115.50/16.83 ! [X2 : $tType,X29 : fun(X2,bool),X19 : fun(X2,bool),X30 : list(X2)] : (listsp(X2,combs(X2,bool,bool,combb(bool,fun(bool,bool),X2,fconj,X19),X29),X30) <=> (listsp(X2,X29,X30) & listsp(X2,X19,X30)))),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_listsp__conj__eq)).
% 115.50/16.83 tff(f379,plain,(
% 115.50/16.83 listsp(dB,combs(dB,bool,bool,combb(bool,fun(bool,bool),dB,fconj,it),combb(dB,bool,dB,it,aa(dB,fun(dB,dB),combc(dB,dB,dB,app),var(i)))),rs)),
% 115.50/16.83 inference(cnf_transformation,[],[f116])).
% 115.50/16.83 tff(f116,axiom,(
% 115.50/16.83 listsp(dB,combs(dB,bool,bool,combb(bool,fun(bool,bool),dB,fconj,it),combb(dB,bool,dB,it,aa(dB,fun(dB,dB),combc(dB,dB,dB,app),var(i)))),rs)),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 115.50/16.83 tff(f134156,plain,(
% 115.50/16.83 ~listsp(dB,it,rs) | ~pp(aa(dB,bool,it,var(i)))),
% 115.50/16.83 inference(resolution,[],[f134150,f395])).
% 115.50/16.83 tff(f395,plain,(
% 115.50/16.83 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (listsp(X0,X1,nil(X0))) )),
% 115.50/16.83 inference(cnf_transformation,[],[f132])).
% 115.50/16.83 tff(f132,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : fun(X0,bool)] : listsp(X0,X1,nil(X0))),
% 115.50/16.83 inference(rectify,[],[f9])).
% 115.50/16.83 tff(f9,axiom,(
% 115.50/16.83 ! [X2 : $tType,X19 : fun(X2,bool)] : listsp(X2,X19,nil(X2))),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_listsp_ONil)).
% 115.50/16.83 tff(f134150,plain,(
% 115.50/16.83 ~listsp(dB,it,nil(dB)) | ~listsp(dB,it,rs) | ~pp(aa(dB,bool,it,var(i)))),
% 115.50/16.83 inference(resolution,[],[f134121,f4332])).
% 115.50/16.83 tff(f4332,plain,(
% 115.50/16.83 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (sP0(X0,X2,insert(X0,X1,nil(X0))) | ~listsp(X0,X2,nil(X0)) | ~pp(aa(X0,bool,X2,X1))) )),
% 115.50/16.83 inference(superposition,[],[f602,f400])).
% 115.50/16.83 tff(f400,plain,(
% 115.50/16.83 ( ! [X0 : $tType,X1 : X0] : (insert(X0,X1,nil(X0)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0))) )),
% 115.50/16.83 inference(cnf_transformation,[],[f137])).
% 115.50/16.83 tff(f137,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : X0] : insert(X0,X1,nil(X0)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X1),nil(X0))),
% 115.50/16.83 inference(rectify,[],[f47])).
% 115.50/16.83 tff(f47,axiom,(
% 115.50/16.83 ! [X2 : $tType,X31 : X2] : insert(X2,X31,nil(X2)) = aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X31),nil(X2))),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_insert__Nil)).
% 115.50/16.83 tff(f602,plain,(
% 115.50/16.83 ( ! [X1 : $tType,X3 : X1,X0 : fun(X1,bool),X4 : list(X1)] : (sP0(X1,X0,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X4)) | ~listsp(X1,X0,X4) | ~pp(aa(X1,bool,X0,X3))) )),
% 115.50/16.83 inference(equality_resolution,[],[f459])).
% 115.50/16.83 tff(f459,plain,(
% 115.50/16.83 ( ! [X1 : $tType,X2 : list(X1),X3 : X1,X0 : fun(X1,bool),X4 : list(X1)] : (sP0(X1,X0,X2) | ~listsp(X1,X0,X4) | ~pp(aa(X1,bool,X0,X3)) | aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X4) != X2) )),
% 115.50/16.83 inference(cnf_transformation,[],[f306])).
% 115.50/16.83 tff(f306,plain,(
% 115.50/16.83 ! [X0 : fun(X1,bool),X1 : $tType,X2 : list(X1)] : ((sP0(X1,X0,X2) | (! [X3 : X1,X4 : list(X1)] : (~listsp(X1,X0,X4) | ~pp(aa(X1,bool,X0,X3)) | aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X4) != X2) & nil(X1) != X2)) & ((listsp(X1,X0,sK28(X1,X0,X2)) & pp(aa(X1,bool,X0,sK27(X1,X0,X2))) & aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK27(X1,X0,X2)),sK28(X1,X0,X2)) = X2) | nil(X1) = X2 | ~sP0(X1,X0,X2)))),
% 115.50/16.83 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f304,f305])).
% 115.50/16.83 tff(f305,plain,(
% 115.50/16.83 ! [X1 : $tType,X0 : fun(X1,bool),X2 : list(X1)] : (? [X5 : X1,X6 : list(X1)] : (listsp(X1,X0,X6) & pp(aa(X1,bool,X0,X5)) & aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X5),X6) = X2) => (listsp(X1,X0,sK28(X1,X0,X2)) & pp(aa(X1,bool,X0,sK27(X1,X0,X2))) & aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK27(X1,X0,X2)),sK28(X1,X0,X2)) = X2))),
% 115.50/16.83 introduced(choice_axiom,[])).
% 115.50/16.83 tff(f304,plain,(
% 115.50/16.83 ! [X0 : fun(X1,bool),X1 : $tType,X2 : list(X1)] : ((sP0(X1,X0,X2) | (! [X3 : X1,X4 : list(X1)] : (~listsp(X1,X0,X4) | ~pp(aa(X1,bool,X0,X3)) | aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X4) != X2) & nil(X1) != X2)) & (? [X5 : X1,X6 : list(X1)] : (listsp(X1,X0,X6) & pp(aa(X1,bool,X0,X5)) & aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X5),X6) = X2) | nil(X1) = X2 | ~sP0(X1,X0,X2)))),
% 115.50/16.83 inference(rectify,[],[f303])).
% 115.50/16.83 tff(f303,plain,(
% 115.50/16.83 ! [X2 : fun(X0,bool),X0 : $tType,X1 : list(X0)] : ((sP0(X0,X2,X1) | (! [X3 : X0,X4 : list(X0)] : (~listsp(X0,X2,X4) | ~pp(aa(X0,bool,X2,X3)) | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1) & nil(X0) != X1)) & (? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) = X1) | nil(X0) = X1 | ~sP0(X0,X2,X1)))),
% 115.50/16.83 inference(flattening,[],[f302])).
% 115.50/16.83 tff(f302,plain,(
% 115.50/16.83 ! [X2 : fun(X0,bool),X0 : $tType,X1 : list(X0)] : ((sP0(X0,X2,X1) | (! [X3 : X0,X4 : list(X0)] : (~listsp(X0,X2,X4) | ~pp(aa(X0,bool,X2,X3)) | aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1) & nil(X0) != X1)) & ((? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) = X1) | nil(X0) = X1) | ~sP0(X0,X2,X1)))),
% 115.50/16.83 inference(nnf_transformation,[],[f262])).
% 115.50/16.83 tff(f262,plain,(
% 115.50/16.83 ! [X2 : fun(X0,bool),X0 : $tType,X1 : list(X0)] : (sP0(X0,X2,X1) <=> (? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) = X1) | nil(X0) = X1))),
% 115.50/16.83 introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])).
% 115.50/16.83 tff(f134121,plain,(
% 115.50/16.83 ~sP0(dB,it,insert(dB,var(i),nil(dB))) | ~listsp(dB,it,rs)),
% 115.50/16.83 inference(resolution,[],[f134080,f461])).
% 115.50/16.83 tff(f461,plain,(
% 115.50/16.83 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : list(X0)] : (listsp(X0,X2,X1) | ~sP0(X0,X2,X1)) )),
% 115.50/16.83 inference(cnf_transformation,[],[f307])).
% 115.50/16.83 tff(f307,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : list(X0),X2 : fun(X0,bool)] : ((listsp(X0,X2,X1) | ~sP0(X0,X2,X1)) & (sP0(X0,X2,X1) | ~listsp(X0,X2,X1)))),
% 115.50/16.83 inference(nnf_transformation,[],[f263])).
% 115.50/16.83 tff(f263,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : list(X0),X2 : fun(X0,bool)] : (listsp(X0,X2,X1) <=> sP0(X0,X2,X1))),
% 115.50/16.83 inference(definition_folding,[],[f181,f262])).
% 115.50/16.83 tff(f181,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : list(X0),X2 : fun(X0,bool)] : (listsp(X0,X2,X1) <=> (? [X3 : X0,X4 : list(X0)] : (listsp(X0,X2,X4) & pp(aa(X0,bool,X2,X3)) & aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) = X1) | nil(X0) = X1))),
% 115.50/16.83 inference(rectify,[],[f38])).
% 115.50/16.83 tff(f38,axiom,(
% 115.50/16.83 ! [X2 : $tType,X20 : list(X2),X19 : fun(X2,bool)] : (listsp(X2,X19,X20) <=> (? [X38 : X2,X39 : list(X2)] : (listsp(X2,X19,X39) & pp(aa(X2,bool,X19,X38)) & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X38),X39) = X20) | nil(X2) = X20))),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_listsp_Osimps)).
% 115.50/16.83 tff(f134080,plain,(
% 115.50/16.83 ~listsp(dB,it,insert(dB,var(i),nil(dB))) | ~listsp(dB,it,rs)),
% 115.50/16.83 inference(resolution,[],[f133658,f9038])).
% 115.50/16.83 tff(f9038,plain,(
% 115.50/16.83 ~pp(aa(dB,bool,it,foldl(dB,dB,app,foldl(dB,dB,app,var(n),rs),insert(dB,var(i),nil(dB)))))),
% 115.50/16.83 inference(superposition,[],[f669,f8667])).
% 115.50/16.83 tff(f8667,plain,(
% 115.50/16.83 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X0)),X3 : X0,X4 : X1] : (aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4) = foldl(X0,X1,X2,X3,insert(X1,X4,nil(X1)))) )),
% 115.50/16.83 inference(forward_demodulation,[],[f8434,f400])).
% 115.50/16.83 tff(f8434,plain,(
% 115.50/16.83 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X0)),X3 : X0,X4 : X1] : (aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4) = foldl(X0,X1,X2,X3,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X4),nil(X1)))) )),
% 115.50/16.83 inference(superposition,[],[f586,f490])).
% 115.50/16.83 tff(f490,plain,(
% 115.50/16.83 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X1,fun(X0,X1))] : (foldl(X1,X0,X3,X2,nil(X0)) = X2) )),
% 115.50/16.83 inference(cnf_transformation,[],[f194])).
% 115.50/16.83 tff(f194,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X1,fun(X0,X1))] : foldl(X1,X0,X3,X2,nil(X0)) = X2),
% 115.50/16.83 inference(rectify,[],[f35])).
% 115.50/16.83 tff(f35,axiom,(
% 115.50/16.83 ! [X0 : $tType,X2 : $tType,X20 : X2,X21 : fun(X2,fun(X0,X2))] : foldl(X2,X0,X21,X20,nil(X0)) = X20),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_foldl__Nil)).
% 115.50/16.83 tff(f586,plain,(
% 115.50/16.83 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : X1,X4 : X0,X5 : fun(X0,fun(X1,X0))] : (foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2)) )),
% 115.50/16.83 inference(cnf_transformation,[],[f229])).
% 115.50/16.83 tff(f229,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : $tType,X2 : list(X1),X3 : X1,X4 : X0,X5 : fun(X0,fun(X1,X0))] : foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2)),
% 115.50/16.83 inference(rectify,[],[f34])).
% 115.50/16.83 tff(f34,axiom,(
% 115.50/16.83 ! [X2 : $tType,X0 : $tType,X13 : list(X0),X12 : X0,X20 : X2,X21 : fun(X2,fun(X0,X2))] : foldl(X2,X0,X21,X20,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X12),X13)) = foldl(X2,X0,X21,aa(X0,X2,aa(X2,fun(X0,X2),X21,X20),X12),X13)),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_foldl__Cons)).
% 115.50/16.83 tff(f669,plain,(
% 115.50/16.83 ~pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,var(n),rs)),var(i))))),
% 115.50/16.83 inference(backward_demodulation,[],[f662,f668])).
% 115.50/16.83 tff(f668,plain,(
% 115.50/16.83 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X1),insert(dB,X0,nil(dB))))) )),
% 115.50/16.83 inference(forward_demodulation,[],[f433,f400])).
% 115.50/16.83 tff(f433,plain,(
% 115.50/16.83 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X1),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),nil(dB))))) )),
% 115.50/16.83 inference(cnf_transformation,[],[f166])).
% 115.50/16.83 tff(f166,plain,(
% 115.50/16.83 ! [X0 : dB,X1 : list(dB),X2 : dB] : aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X1),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X0),nil(dB))))),
% 115.50/16.83 inference(rectify,[],[f7])).
% 115.50/16.83 tff(f7,axiom,(
% 115.50/16.83 ! [X18 : dB,X14 : list(dB),X15 : dB] : aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X15,X14)),X18) = foldl(dB,dB,app,X15,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X14),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X18),nil(dB))))),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_app__last)).
% 115.50/16.83 tff(f662,plain,(
% 115.50/16.83 ~pp(aa(dB,bool,it,foldl(dB,dB,app,var(n),aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),insert(dB,var(i),nil(dB))))))),
% 115.50/16.83 inference(backward_demodulation,[],[f378,f400])).
% 115.50/16.83 tff(f378,plain,(
% 115.50/16.83 ~pp(aa(dB,bool,it,foldl(dB,dB,app,var(n),aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB))))))),
% 115.50/16.83 inference(cnf_transformation,[],[f119])).
% 115.50/16.83 tff(f119,plain,(
% 115.50/16.83 ~pp(aa(dB,bool,it,foldl(dB,dB,app,var(n),aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB))))))),
% 115.50/16.83 inference(flattening,[],[f118])).
% 115.50/16.83 tff(f118,negated_conjecture,(
% 115.50/16.83 ~pp(aa(dB,bool,it,foldl(dB,dB,app,var(n),aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB))))))),
% 115.50/16.83 inference(negated_conjecture,[],[f117])).
% 115.50/16.83 tff(f117,conjecture,(
% 115.50/16.83 pp(aa(dB,bool,it,foldl(dB,dB,app,var(n),aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),rs),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB))))))),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 115.50/16.83 tff(f133658,plain,(
% 115.50/16.83 ( ! [X2 : list(dB),X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,foldl(dB,dB,app,var(X0),X1),X2))) | ~listsp(dB,it,X2) | ~listsp(dB,it,X1)) )),
% 115.50/16.83 inference(resolution,[],[f6196,f532])).
% 115.50/16.83 tff(f532,plain,(
% 115.50/16.83 ( ! [X0 : $tType,X2 : list(X0),X3 : fun(X0,bool),X1 : list(X0)] : (listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) | ~listsp(X0,X3,X1) | ~listsp(X0,X3,X2)) )),
% 115.50/16.83 inference(cnf_transformation,[],[f347])).
% 115.50/16.83 tff(f347,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : fun(X0,bool)] : ((listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) | ~listsp(X0,X3,X1) | ~listsp(X0,X3,X2)) & ((listsp(X0,X3,X1) & listsp(X0,X3,X2)) | ~listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))))),
% 115.50/16.83 inference(flattening,[],[f346])).
% 115.50/16.83 tff(f346,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : fun(X0,bool)] : ((listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) | (~listsp(X0,X3,X1) | ~listsp(X0,X3,X2))) & ((listsp(X0,X3,X1) & listsp(X0,X3,X2)) | ~listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1))))),
% 115.50/16.83 inference(nnf_transformation,[],[f208])).
% 115.50/16.83 tff(f208,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : list(X0),X2 : list(X0),X3 : fun(X0,bool)] : (listsp(X0,X3,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X2),X1)) <=> (listsp(X0,X3,X1) & listsp(X0,X3,X2)))),
% 115.50/16.83 inference(rectify,[],[f8])).
% 115.50/16.83 tff(f8,axiom,(
% 115.50/16.83 ! [X2 : $tType,X11 : list(X2),X13 : list(X2),X19 : fun(X2,bool)] : (listsp(X2,X19,aa(list(X2),list(X2),aa(list(X2),fun(list(X2),list(X2)),append(X2),X13),X11)) <=> (listsp(X2,X19,X11) & listsp(X2,X19,X13)))),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_append__in__listsp__conv)).
% 115.50/16.83 tff(f6196,plain,(
% 115.50/16.83 ( ! [X2 : list(dB),X0 : nat,X1 : list(dB)] : (~listsp(dB,it,aa(list(dB),list(dB),aa(list(dB),fun(list(dB),list(dB)),append(dB),X1),X2)) | pp(aa(dB,bool,it,foldl(dB,dB,app,foldl(dB,dB,app,var(X0),X1),X2)))) )),
% 115.50/16.83 inference(superposition,[],[f408,f584])).
% 115.50/16.83 tff(f584,plain,(
% 115.50/16.83 ( ! [X1 : $tType,X0 : $tType,X2 : list(X1),X3 : list(X1),X4 : X0,X5 : fun(X0,fun(X1,X0))] : (foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(list(X1),fun(list(X1),list(X1)),append(X1),X3),X2)) = foldl(X0,X1,X5,foldl(X0,X1,X5,X4,X3),X2)) )),
% 115.50/16.83 inference(cnf_transformation,[],[f227])).
% 115.50/16.83 tff(f227,plain,(
% 115.50/16.83 ! [X0 : $tType,X1 : $tType,X2 : list(X1),X3 : list(X1),X4 : X0,X5 : fun(X0,fun(X1,X0))] : foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(list(X1),fun(list(X1),list(X1)),append(X1),X3),X2)) = foldl(X0,X1,X5,foldl(X0,X1,X5,X4,X3),X2)),
% 115.50/16.83 inference(rectify,[],[f11])).
% 115.50/16.83 tff(f11,axiom,(
% 115.50/16.83 ! [X2 : $tType,X0 : $tType,X11 : list(X0),X13 : list(X0),X20 : X2,X21 : fun(X2,fun(X0,X2))] : foldl(X2,X0,X21,X20,aa(list(X0),list(X0),aa(list(X0),fun(list(X0),list(X0)),append(X0),X13),X11)) = foldl(X2,X0,X21,foldl(X2,X0,X21,X20,X13),X11)),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_foldl__append)).
% 115.50/16.83 tff(f408,plain,(
% 115.50/16.83 ( ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1)) )),
% 115.50/16.83 inference(cnf_transformation,[],[f236])).
% 115.50/16.83 tff(f236,plain,(
% 115.50/16.83 ! [X0 : nat,X1 : list(dB)] : (pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) | ~listsp(dB,it,X1))),
% 115.50/16.83 inference(ennf_transformation,[],[f145])).
% 115.50/16.83 tff(f145,plain,(
% 115.50/16.83 ! [X0 : nat,X1 : list(dB)] : (listsp(dB,it,X1) => pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))))),
% 115.50/16.83 inference(rectify,[],[f2])).
% 115.50/16.83 tff(f2,axiom,(
% 115.50/16.83 ! [X5 : nat,X6 : list(dB)] : (listsp(dB,it,X6) => pp(aa(dB,bool,it,foldl(dB,dB,app,var(X5),X6))))),
% 115.50/16.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_IT_OVar)).
% 115.50/16.83 % SZS output end Proof for theBenchmark
% 115.50/16.83 % (15259)------------------------------
% 115.50/16.83 % (15259)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 115.50/16.83 % (15259)Termination reason: Refutation
% 115.50/16.83
% 115.50/16.83 % (15259)Memory used [KB]: 57094
% 115.50/16.83 % (15259)Time elapsed: 16.429 s
% 115.50/16.83 % (15259)Instructions burned: 66611 (million)
% 115.50/16.83 % (15259)------------------------------
% 115.50/16.83 % (15259)------------------------------
% 115.50/16.83 % (15253)Success in time 16.349 s
%------------------------------------------------------------------------------