TSTP Solution File: LCL769_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL769_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.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 May 21 00:34:08 EDT 2024
% Result : Theorem 1.43s 0.55s
% Output : Refutation 1.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL769_5 : TPTP v8.2.0. Released v6.0.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 01:31:56 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (24440)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (24443)WARNING: value z3 for option sas not known
% 0.21/0.38 % (24445)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)
% 0.21/0.38 % (24442)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (24441)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (24446)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)
% 0.21/0.38 % (24447)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)
% 0.21/0.38 % (24444)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (24443)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 % Exception at run slice level
% 0.21/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.39 % (24447)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.39 % Exception at run slice level
% 0.21/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.39 % Exception at run slice level
% 0.21/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.41 % (24448)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.41 % (24449)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 % (24450)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.41 % (24448)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.41 % (24449)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.41 % Exception at run slice level
% 0.21/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43 % (24451)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)
% 1.32/0.55 % (24450)First to succeed.
% 1.43/0.55 % (24450)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-24440"
% 1.43/0.55 % (24450)Refutation found. Thanks to Tanya!
% 1.43/0.55 % SZS status Theorem for theBenchmark
% 1.43/0.55 % SZS output start Proof for theBenchmark
% 1.43/0.55 tff(type_def_5, type, bool: $tType).
% 1.43/0.55 tff(type_def_6, type, dB: $tType).
% 1.43/0.55 tff(type_def_7, type, list: $tType > $tType).
% 1.43/0.55 tff(type_def_8, type, nat: $tType).
% 1.43/0.55 tff(type_def_9, type, fun: ($tType * $tType) > $tType).
% 1.43/0.55 tff(func_def_0, type, combb: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,X1) * fun(X2,X0)) > fun(X2,X1))).
% 1.43/0.55 tff(func_def_1, type, combc: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2))) > fun(X1,fun(X0,X2)))).
% 1.43/0.55 tff(func_def_2, type, combs: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * fun(X0,X1)) > fun(X0,X2))).
% 1.43/0.55 tff(func_def_3, type, it: fun(dB,bool)).
% 1.43/0.55 tff(func_def_4, type, abs: dB > dB).
% 1.43/0.55 tff(func_def_5, type, app: fun(dB,fun(dB,dB))).
% 1.43/0.55 tff(func_def_6, type, var: nat > dB).
% 1.43/0.55 tff(func_def_7, type, dB_case: !>[X0: $tType]:((fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB) > X0)).
% 1.43/0.55 tff(func_def_8, type, append: !>[X0: $tType]:(fun(list(X0),fun(list(X0),list(X0))))).
% 1.43/0.55 tff(func_def_9, type, butlast: !>[X0: $tType]:((list(X0)) > list(X0))).
% 1.43/0.55 tff(func_def_10, type, foldl: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0)) * X0 * list(X1)) > X0)).
% 1.43/0.55 tff(func_def_11, type, insert: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 1.43/0.55 tff(func_def_12, type, last: !>[X0: $tType]:((list(X0)) > X0)).
% 1.43/0.55 tff(func_def_13, type, cons: !>[X0: $tType]:(fun(X0,fun(list(X0),list(X0))))).
% 1.43/0.55 tff(func_def_14, type, nil: !>[X0: $tType]:(list(X0))).
% 1.43/0.55 tff(func_def_15, type, list_case: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(list(X1),X0)) * list(X1)) > X0)).
% 1.43/0.55 tff(func_def_16, type, maps: !>[X0: $tType, X1: $tType]:((fun(X0,list(X1)) * list(X0)) > list(X1))).
% 1.43/0.55 tff(func_def_17, type, rev: !>[X0: $tType]:((list(X0)) > list(X0))).
% 1.43/0.55 tff(func_def_18, type, rotate1: !>[X0: $tType]:((list(X0)) > list(X0))).
% 1.43/0.55 tff(func_def_19, type, splice: !>[X0: $tType]:((list(X0) * list(X0)) > list(X0))).
% 1.43/0.55 tff(func_def_20, type, aa: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * X0) > X1)).
% 1.43/0.55 tff(func_def_21, type, fFalse: bool).
% 1.43/0.55 tff(func_def_22, type, fNot: fun(bool,bool)).
% 1.43/0.55 tff(func_def_23, type, fTrue: bool).
% 1.43/0.55 tff(func_def_24, type, fconj: fun(bool,fun(bool,bool))).
% 1.43/0.55 tff(func_def_25, type, fdisj: fun(bool,fun(bool,bool))).
% 1.43/0.55 tff(func_def_26, type, fequal: !>[X0: $tType]:((X0) > fun(X0,bool))).
% 1.43/0.55 tff(func_def_27, type, i: nat).
% 1.43/0.55 tff(func_def_28, type, rs: list(dB)).
% 1.43/0.55 tff(func_def_29, type, sK6: dB > dB).
% 1.43/0.55 tff(func_def_30, type, sK7: dB > dB).
% 1.43/0.55 tff(func_def_31, type, sK8: dB > dB).
% 1.43/0.55 tff(func_def_32, type, sK9: dB > nat).
% 1.43/0.55 tff(func_def_33, type, sK10: dB > list(dB)).
% 1.43/0.55 tff(func_def_34, type, sK11: dB > dB).
% 1.43/0.55 tff(func_def_35, type, sK12: dB > dB).
% 1.43/0.55 tff(func_def_36, type, sK13: dB > nat).
% 1.43/0.55 tff(func_def_37, type, sK14: !>[X0: $tType]:((list(X0)) > X0)).
% 1.43/0.55 tff(func_def_38, type, sK15: !>[X0: $tType]:((list(X0)) > list(X0))).
% 1.43/0.55 tff(func_def_39, type, sK16: !>[X0: $tType]:((list(X0)) > list(X0))).
% 1.43/0.55 tff(func_def_40, type, sK17: !>[X0: $tType]:((list(X0)) > X0)).
% 1.43/0.55 tff(func_def_41, type, sK18: !>[X0: $tType]:((list(X0)) > list(X0))).
% 1.43/0.55 tff(func_def_42, type, sK19: !>[X0: $tType]:((list(X0)) > X0)).
% 1.43/0.55 tff(func_def_43, type, sK20: !>[X0: $tType]:((list(X0)) > X0)).
% 1.43/0.55 tff(func_def_44, type, sK21: !>[X0: $tType]:((list(X0)) > list(X0))).
% 1.43/0.55 tff(func_def_45, type, sK22: !>[X0: $tType]:((fun(list(X0),bool)) > X0)).
% 1.43/0.55 tff(func_def_46, type, sK23: !>[X0: $tType]:((fun(list(X0),bool)) > list(X0))).
% 1.43/0.55 tff(func_def_47, type, sK24: !>[X0: $tType]:((fun(list(X0),bool)) > X0)).
% 1.43/0.55 tff(func_def_48, type, sK25: !>[X0: $tType]:((fun(list(X0),bool)) > X0)).
% 1.43/0.55 tff(func_def_49, type, sK26: !>[X0: $tType]:((fun(list(X0),bool)) > list(X0))).
% 1.43/0.55 tff(func_def_50, type, sK27: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > X0)).
% 1.43/0.55 tff(func_def_51, type, sK28: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > list(X0))).
% 1.43/0.55 tff(func_def_52, type, sK29: !>[X0: $tType, X1: $tType]:((fun(X1,X0) * fun(X1,X0)) > X1)).
% 1.43/0.55 tff(func_def_53, type, sK30: (dB * dB * list(dB) * dB) > list(dB)).
% 1.43/0.55 tff(func_def_54, type, sK31: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > list(X0))).
% 1.43/0.55 tff(func_def_55, type, sK32: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > list(X0))).
% 1.43/0.55 tff(func_def_56, type, sK33: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * list(X0)) > list(X0))).
% 1.43/0.55 tff(func_def_57, type, sK34: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 1.43/0.55 tff(func_def_58, type, sK35: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 1.43/0.55 tff(func_def_59, type, sK36: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X0)).
% 1.43/0.55 tff(pred_def_1, type, list_all: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 1.43/0.55 tff(pred_def_2, type, list_ex1: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 1.43/0.55 tff(pred_def_3, type, listsp: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 1.43/0.55 tff(pred_def_4, type, pp: bool > $o).
% 1.43/0.55 tff(pred_def_5, type, sP0: !>[X0: $tType]:((fun(X0,bool) * list(X0)) > $o)).
% 1.43/0.55 tff(pred_def_6, type, sP1: (dB * dB * list(dB) * dB) > $o).
% 1.43/0.55 tff(pred_def_7, type, sP2: !>[X0: $tType]:((list(X0) * fun(X0,bool) * X0) > $o)).
% 1.43/0.55 tff(pred_def_8, type, sP3: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > $o)).
% 1.43/0.55 tff(pred_def_9, type, sP4: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * X0) > $o)).
% 1.43/0.55 tff(pred_def_10, type, sP5: !>[X0: $tType]:((list(X0) * list(X0) * list(X0) * list(X0)) > $o)).
% 1.43/0.55 tff(f2782,plain,(
% 1.43/0.55 $false),
% 1.43/0.55 inference(subsumption_resolution,[],[f2718,f384])).
% 1.43/0.55 tff(f384,plain,(
% 1.43/0.55 ( ! [X0 : nat] : (pp(aa(dB,bool,it,var(X0)))) )),
% 1.43/0.55 inference(cnf_transformation,[],[f120])).
% 1.43/0.55 tff(f120,plain,(
% 1.43/0.55 ! [X0 : nat] : pp(aa(dB,bool,it,var(X0)))),
% 1.43/0.55 inference(rectify,[],[f1])).
% 1.43/0.55 tff(f1,axiom,(
% 1.43/0.55 ! [X4 : nat] : pp(aa(dB,bool,it,var(X4)))),
% 1.43/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Var__IT)).
% 1.43/0.55 tff(f2718,plain,(
% 1.43/0.55 ~pp(aa(dB,bool,it,var(i)))),
% 1.43/0.55 inference(resolution,[],[f1633,f710])).
% 1.43/0.55 tff(f710,plain,(
% 1.43/0.55 ~sP0(dB,it,insert(dB,var(i),nil(dB)))),
% 1.43/0.55 inference(resolution,[],[f464,f666])).
% 1.43/0.55 tff(f666,plain,(
% 1.43/0.55 ~listsp(dB,it,insert(dB,var(i),nil(dB)))),
% 1.43/0.55 inference(backward_demodulation,[],[f379,f401])).
% 1.43/0.55 tff(f401,plain,(
% 1.43/0.55 ( ! [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))) )),
% 1.43/0.55 inference(cnf_transformation,[],[f136])).
% 1.43/0.55 tff(f136,plain,(
% 1.43/0.55 ! [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))),
% 1.43/0.55 inference(rectify,[],[f22])).
% 1.43/0.55 tff(f22,axiom,(
% 1.43/0.55 ! [X2 : $tType,X33 : X2] : insert(X2,X33,nil(X2)) = aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X33),nil(X2))),
% 1.43/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_insert__Nil)).
% 1.43/0.55 tff(f379,plain,(
% 1.43/0.55 ~listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
% 1.43/0.55 inference(cnf_transformation,[],[f119])).
% 1.43/0.55 tff(f119,plain,(
% 1.43/0.55 ~listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
% 1.43/0.55 inference(flattening,[],[f118])).
% 1.43/0.55 tff(f118,negated_conjecture,(
% 1.43/0.55 ~listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
% 1.43/0.55 inference(negated_conjecture,[],[f117])).
% 1.43/0.55 tff(f117,conjecture,(
% 1.43/0.55 listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB)))),
% 1.43/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 1.43/0.55 tff(f464,plain,(
% 1.43/0.55 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : list(X0)] : (listsp(X0,X2,X1) | ~sP0(X0,X2,X1)) )),
% 1.43/0.55 inference(cnf_transformation,[],[f308])).
% 1.43/0.55 tff(f308,plain,(
% 1.43/0.55 ! [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)))),
% 1.43/0.55 inference(nnf_transformation,[],[f263])).
% 1.43/0.55 tff(f263,plain,(
% 1.43/0.55 ! [X0 : $tType,X1 : list(X0),X2 : fun(X0,bool)] : (listsp(X0,X2,X1) <=> sP0(X0,X2,X1))),
% 1.43/0.55 inference(definition_folding,[],[f181,f262])).
% 1.43/0.55 tff(f262,plain,(
% 1.43/0.55 ! [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))),
% 1.43/0.55 introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])).
% 1.43/0.55 tff(f181,plain,(
% 1.43/0.55 ! [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))),
% 1.43/0.55 inference(rectify,[],[f11])).
% 1.43/0.55 tff(f11,axiom,(
% 1.43/0.55 ! [X2 : $tType,X17 : list(X2),X5 : fun(X2,bool)] : (listsp(X2,X5,X17) <=> (? [X23 : X2,X24 : list(X2)] : (listsp(X2,X5,X24) & pp(aa(X2,bool,X5,X23)) & aa(list(X2),list(X2),aa(X2,fun(list(X2),list(X2)),cons(X2),X23),X24) = X17) | nil(X2) = X17))),
% 1.43/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_listsp_Osimps)).
% 1.43/0.55 tff(f1633,plain,(
% 1.43/0.55 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : X0] : (sP0(X0,X2,insert(X0,X1,nil(X0))) | ~pp(aa(X0,bool,X2,X1))) )),
% 1.43/0.55 inference(subsumption_resolution,[],[f1629,f396])).
% 1.43/0.55 tff(f396,plain,(
% 1.43/0.55 ( ! [X0 : $tType,X1 : fun(X0,bool)] : (listsp(X0,X1,nil(X0))) )),
% 1.43/0.55 inference(cnf_transformation,[],[f131])).
% 1.43/0.55 tff(f131,plain,(
% 1.43/0.55 ! [X0 : $tType,X1 : fun(X0,bool)] : listsp(X0,X1,nil(X0))),
% 1.43/0.55 inference(rectify,[],[f2])).
% 1.43/0.55 tff(f2,axiom,(
% 1.43/0.55 ! [X2 : $tType,X5 : fun(X2,bool)] : listsp(X2,X5,nil(X2))),
% 1.43/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_listsp_ONil)).
% 1.43/0.55 tff(f1629,plain,(
% 1.43/0.55 ( ! [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))) )),
% 1.43/0.55 inference(superposition,[],[f606,f401])).
% 1.43/0.55 tff(f606,plain,(
% 1.43/0.55 ( ! [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))) )),
% 1.43/0.55 inference(equality_resolution,[],[f462])).
% 1.43/0.55 tff(f462,plain,(
% 1.43/0.55 ( ! [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) )),
% 1.43/0.55 inference(cnf_transformation,[],[f307])).
% 1.43/0.55 tff(f307,plain,(
% 1.43/0.55 ! [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)))),
% 1.43/0.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f305,f306])).
% 1.43/0.55 tff(f306,plain,(
% 1.43/0.55 ! [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))),
% 1.43/0.55 introduced(choice_axiom,[])).
% 1.43/0.55 tff(f305,plain,(
% 1.43/0.55 ! [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)))),
% 1.43/0.55 inference(rectify,[],[f304])).
% 1.43/0.55 tff(f304,plain,(
% 1.43/0.55 ! [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)))),
% 1.43/0.55 inference(flattening,[],[f303])).
% 1.43/0.55 tff(f303,plain,(
% 1.43/0.55 ! [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)))),
% 1.43/0.55 inference(nnf_transformation,[],[f262])).
% 1.43/0.55 % SZS output end Proof for theBenchmark
% 1.43/0.55 % (24450)------------------------------
% 1.43/0.55 % (24450)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.43/0.55 % (24450)Termination reason: Refutation
% 1.43/0.55
% 1.43/0.55 % (24450)Memory used [KB]: 2610
% 1.43/0.55 % (24450)Time elapsed: 0.145 s
% 1.43/0.55 % (24450)Instructions burned: 350 (million)
% 1.43/0.55 % (24440)Success in time 0.186 s
%------------------------------------------------------------------------------