%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT290^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:43 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT290^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 18:19:17 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.29 % (703578)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (703589)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (703589)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.29 % (703589)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2215896266:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (703589)Refutation not found, incomplete strategy
% 0.21/0.29 % (703589)------------------------------
% 0.21/0.29 % (703589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (703589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (703589)CaDiCaL version: 2.1.3
% 0.21/0.29 % (703589)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (703589)Time elapsed: 0.003 s
% 0.21/0.29 % (703589)Peak memory usage: 12 MB
% 0.21/0.29 % (703589)Instructions burned: 9 (million)
% 0.21/0.29 % (703589)------------------------------
% 0.21/0.29 % (703589)------------------------------
% 0.21/0.29 % (703585)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3575488793:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (703584)lrs+10_16_si=on:nwc=1.5:random_seed=433574452:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (703583)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=674773133:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (703586)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3101682582:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.29 % (703588)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3780903086:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (703587)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2387022293:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (703585)Instruction limit reached!
% 0.21/0.29 % (703585)------------------------------
% 0.21/0.29 % (703585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (703585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (703585)CaDiCaL version: 2.1.3
% 0.21/0.29 % (703585)Termination reason: Instruction limit
% 0.21/0.29 % (703585)Termination phase: Saturation
% 0.21/0.29 % (703585)Time elapsed: 0.003 s
% 0.21/0.29 % (703585)Peak memory usage: 12 MB
% 0.21/0.29 % (703585)Instructions burned: 4 (million)
% 0.21/0.29 % (703587) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-703578-703587"...
% 0.21/0.29 % (703587)...printing done.
% 0.21/0.29 % (703587)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.21/0.29 thf(type_def_6, type, 'type/ind_types/list': $tType > $tType).
% 0.21/0.29 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(type_def_8, type, sK0: $tType).
% 0.21/0.29 thf(func_def_0, type, 'const/nums/SUC': ('type/nums/num' > 'type/nums/num')).
% 0.21/0.29 thf(func_def_1, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.21/0.29 thf(func_def_2, type, 'const/nums/_0': 'type/nums/num').
% 0.21/0.29 thf(func_def_3, type, 'const/lists/LENGTH': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/nums/num'))).
% 0.21/0.29 thf(func_def_4, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.21/0.29 thf(func_def_5, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.21/0.29 thf(func_def_9, type, sK1: 'type/ind_types/list' @ sK0).
% 0.21/0.29 thf(func_def_10, type, sK2: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > X0))).
% 0.21/0.29 thf(func_def_11, type, sK3: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0))).
% 0.21/0.29 thf(func_def_12, type, vNOT: ($o > $o)).
% 0.21/0.29 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.29 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.29 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_')).
% 0.21/0.29 thf(f3,axiom,(
% 0.21/0.29 ! [X0 : 'type/nums/num'] : ((('const/nums/SUC' @ X0)) != (('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/nums/NOT_SUC_')).
% 0.21/0.29 thf(f4,axiom,(
% 0.21/0.29 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = (('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X2))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/LENGTH_1')).
% 0.21/0.29 thf(f5,axiom,(
% 0.21/0.29 ! [X0 : $tType] : ((('const/lists/LENGTH' @ X0 @ 'const/ind_types/NIL' @ X0)) = (('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/LENGTH_0')).
% 0.21/0.29 thf(f6,conjecture,(
% 0.21/0.29 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/LENGTH' @ X0 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) = (X1 = 'const/ind_types/NIL' @ X0))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/LENGTH_EQ_NIL_')).
% 0.21/0.29 thf(f7,negated_conjecture,(
% 0.21/0.29 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/LENGTH' @ X0 @ X1)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))) = (X1 = 'const/ind_types/NIL' @ X0))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((((X1 @ 'const/ind_types/NIL' @ X0)) = $true) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((((X1 @ X3)) = $true) => (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) = $true))) => ! [X4 : 'type/ind_types/list' @ X0] : ($true = ((X1 @ X4))))),
% 0.21/0.29 inference(fool_elimination,[],[f8])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) <=> ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ X0 @ X1))))),
% 0.21/0.29 inference(fool_elimination,[],[f7])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ! [X0 : $tType,X2 : X0,X1 : 'type/ind_types/list' @ X0] : ((('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X1))) = (('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1))))),
% 0.21/0.29 inference(rectify,[],[f4])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : ($true = ((X1 @ X4))) | ((((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((((X1 @ X3)) = $true) & (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) != $true))))),
% 0.21/0.29 inference(ennf_transformation,[],[f9])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : ($true = ((X1 @ X4))) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((((X1 @ X3)) = $true) & (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) != $true)))),
% 0.21/0.29 inference(flattening,[],[f12])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) <~> ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ X0 @ X1))))),
% 0.21/0.29 inference(ennf_transformation,[],[f10])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/lists/LENGTH' @ X0 @ X1))) | ('const/ind_types/NIL' @ X0 != X1)) & (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ X0 @ X1))) | ('const/ind_types/NIL' @ X0 = X1)))),
% 0.21/0.29 inference(nnf_transformation,[],[f14])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 (((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/lists/LENGTH' @ sK0 @ sK1))) | ('const/ind_types/NIL' @ sK0 != sK1)) & (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ sK0 @ sK1))) | ('const/ind_types/NIL' @ sK0 = sK1))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = (('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X2))))),
% 0.21/0.29 inference(rectify,[],[f11])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : (($true = ((X1 @ X4))) & ($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4))))))),
% 0.21/0.29 inference(rectify,[],[f13])).
% 0.21/0.29 thf(f19,plain,(
% 0.21/0.29 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | (($true = ((X1 @ (sK3 @ X0 @ X1)))) & ($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1)))))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK3 @ X0 @ X1),skolemize(X4,sK3 @ X0 @ X1)],[f18])).
% 0.21/0.29 thf(f21,plain,(
% 0.21/0.29 ( ! [X0 : $tType] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ X0 @ 'const/ind_types/NIL' @ X0)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f5])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ sK0 @ sK1))) | ('const/ind_types/NIL' @ sK0 = sK1)),
% 0.21/0.29 inference(cnf_transformation,[],[f16])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/lists/LENGTH' @ sK0 @ sK1))) | ('const/ind_types/NIL' @ sK0 != sK1)),
% 0.21/0.29 inference(cnf_transformation,[],[f16])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = (('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X2))))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f17])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 ( ! [X0 : 'type/nums/num'] : (((('const/nums/SUC' @ X0)) != (('const/nums/NUMERAL' @ 'const/nums/_0')))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f3])).
% 0.21/0.29 thf(f26,plain,(
% 0.21/0.29 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : ('type/ind_types/list' @ X0 > $o)] : (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1))))) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | (((X1 @ X2)) = $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f19])).
% 0.21/0.29 thf(f64,plain,(
% 0.21/0.29 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ($true != (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ 'const/ind_types/NIL' @ X0)))) )),
% 0.21/0.29 inference(leibniz_equality_elimination,[],[f26])).
% 0.21/0.29 thf(f74,plain,(
% 0.21/0.29 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (($true != ((~ ('const/ind_types/NIL' @ X0 = X1)))) | ((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1)) )),
% 0.21/0.29 inference(beta-eta_normalization,[],[f64])).
% 0.21/0.29 thf(f75,plain,(
% 0.21/0.29 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (($true = (('const/ind_types/NIL' @ X0 = X1))) | ((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1)) )),
% 0.21/0.29 inference(not_proxy_clausification,[],[f74])).
% 0.21/0.29 thf(f76,plain,(
% 0.21/0.29 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.21/0.29 inference(equality_proxy_clausification,[],[f75])).
% 0.21/0.29 thf(f280,plain,(
% 0.21/0.29 ( ! [X1 : $tType,X0 : 'type/ind_types/list' @ X1] : (((('const/lists/LENGTH' @ X1 @ X0)) = (('const/nums/SUC' @ ('const/lists/LENGTH' @ X1 @ (sK3 @ X1 @ (^[Y0 : 'type/ind_types/list' @ X1]: (~ (Y0 = X0)))))))) | ('const/ind_types/NIL' @ X1 = X0)) )),
% 0.21/0.29 inference(superposition,[],[f24,f76])).
% 0.21/0.29 thf(f370,plain,(
% 0.21/0.29 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/lists/LENGTH' @ X0 @ X1))) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.21/0.29 inference(superposition,[],[f25,f280])).
% 0.21/0.29 thf(f371,plain,(
% 0.21/0.29 ('const/ind_types/NIL' @ sK0 = sK1) | ('const/ind_types/NIL' @ sK0 = sK1) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 0.21/0.29 inference(superposition,[],[f370,f22])).
% 0.21/0.29 thf(f373,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ('const/ind_types/NIL' @ sK0 = sK1)),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f371])).
% 0.21/0.29 thf(f374,plain,(
% 0.21/0.29 ('const/ind_types/NIL' @ sK0 = sK1)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f373])).
% 0.21/0.29 thf(f404,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ sK0 @ sK1)))),
% 0.21/0.29 inference(superposition,[],[f21,f374])).
% 0.21/0.29 thf(f405,plain,(
% 0.21/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ('const/ind_types/NIL' @ sK0 != sK1)),
% 0.21/0.29 inference(superposition,[],[f23,f404])).
% 0.21/0.29 thf(f408,plain,(
% 0.21/0.29 ('const/ind_types/NIL' @ sK0 != sK1)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f405])).
% 0.21/0.29 thf(f409,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f408,f374])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (703587)------------------------------
% 0.21/0.29 % (703587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (703587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (703587)CaDiCaL version: 2.1.3
% 0.21/0.29 % (703587)Termination reason: Refutation
% 0.21/0.29 % (703587)Time elapsed: 0.008 s
% 0.21/0.29 % (703587)Peak memory usage: 12 MB
% 0.21/0.29 % (703587)Instructions burned: 24 (million)
% 0.21/0.29 % (703578)Success in time 0.047 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------