%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT314^1 : 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 : n018.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 07:48:45 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT314^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 18:28:45 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.30 % (462730)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (462737)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2483386628:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (462737)Instruction limit reached!
% 0.21/0.30 % (462737)------------------------------
% 0.21/0.30 % (462737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (462737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (462737)CaDiCaL version: 2.1.3
% 0.21/0.30 % (462737)Termination reason: Instruction limit
% 0.21/0.30 % (462737)Termination phase: Saturation
% 0.21/0.30 % (462737)Time elapsed: 0.002 s
% 0.21/0.30 % (462737)Peak memory usage: 12 MB
% 0.21/0.30 % (462737)Instructions burned: 4 (million)
% 0.21/0.30 % (462735)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2498355631:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (462736)lrs+10_16_si=on:nwc=1.5:random_seed=941327644:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (462739)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3636040961:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (462738)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=2975374915: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)
% 0.21/0.30 % (462740)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1873337154:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (462741)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (462741)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
% 0.21/0.30 % (462741)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=3104593614:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (462736)Instruction limit reached!
% 0.21/0.30 % (462736)------------------------------
% 0.21/0.30 % (462736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (462736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (462736)CaDiCaL version: 2.1.3
% 0.21/0.30 % (462736)Termination reason: Instruction limit
% 0.21/0.30 % (462736)Termination phase: Saturation
% 0.21/0.30 % (462736)Time elapsed: 0.011 s
% 0.21/0.30 % (462736)Peak memory usage: 12 MB
% 0.21/0.30 % (462736)Instructions burned: 19 (million)
% 0.21/0.30 % (462743)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=223440706:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.30 % (462739)Instruction limit reached!
% 0.21/0.30 % (462739)------------------------------
% 0.21/0.30 % (462739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (462739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (462739)CaDiCaL version: 2.1.3
% 0.21/0.30 % (462739)Termination reason: Instruction limit
% 0.21/0.30 % (462739)Termination phase: Saturation
% 0.21/0.30 % (462739)Time elapsed: 0.015 s
% 0.21/0.30 % (462739)Peak memory usage: 12 MB
% 0.21/0.30 % (462739)Instructions burned: 25 (million)
% 0.21/0.30 % (462743)Instruction limit reached!
% 0.21/0.30 % (462743)------------------------------
% 0.21/0.30 % (462743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (462743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (462743)CaDiCaL version: 2.1.3
% 0.21/0.30 % (462743)Termination reason: Instruction limit
% 0.21/0.30 % (462743)Termination phase: Saturation
% 0.21/0.30 % (462743)Time elapsed: 0.004 s
% 0.21/0.30 % (462743)Peak memory usage: 12 MB
% 0.21/0.30 % (462743)Instructions burned: 5 (million)
% 0.21/0.30 % (462740)Instruction limit reached!
% 0.21/0.30 % (462740)------------------------------
% 0.21/0.30 % (462740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (462740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (462740)CaDiCaL version: 2.1.3
% 0.21/0.30 % (462740)Termination reason: Instruction limit
% 0.21/0.30 % (462740)Termination phase: Saturation
% 0.21/0.30 % (462740)Time elapsed: 0.022 s
% 0.21/0.30 % (462740)Peak memory usage: 12 MB
% 0.21/0.30 % (462740)Instructions burned: 76 (million)
% 0.21/0.30 % (462752)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.30 % (462735) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-462730-462735"...
% 0.21/0.30 % (462752)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1550133308:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.30 % (462735)...printing done.
% 0.21/0.30 % (462735)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% 0.21/0.30 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.21/0.30 thf(type_def_6, type, 'type/ind_types/list': $tType > $tType).
% 0.21/0.30 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.30 thf(type_def_8, type, sK0: $tType).
% 0.21/0.30 thf(func_def_0, type, 'const/nums/SUC': ('type/nums/num' > 'type/nums/num')).
% 0.21/0.30 thf(func_def_1, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.21/0.30 thf(func_def_2, type, 'const/nums/BIT1': ('type/nums/num' > 'type/nums/num')).
% 0.21/0.30 thf(func_def_3, type, 'const/nums/_0': 'type/nums/num').
% 0.21/0.30 thf(func_def_4, type, 'const/lists/TL': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.21/0.30 thf(func_def_5, type, 'const/lists/LENGTH': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/nums/num'))).
% 0.21/0.30 thf(func_def_6, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.21/0.30 thf(func_def_7, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.21/0.30 thf(func_def_8, type, 'const/arith/-': ('type/nums/num' > 'type/nums/num' > 'type/nums/num')).
% 0.21/0.30 thf(func_def_12, type, sK1: 'type/ind_types/list' @ sK0).
% 0.21/0.30 thf(func_def_13, type, sK2: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > X0))).
% 0.21/0.30 thf(func_def_14, type, sK3: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0))).
% 0.21/0.30 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.21/0.30 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.30 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_18, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.30 thf(f1,axiom,(
% 0.21/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X3 : 'type/ind_types/list' @ X0,X2 : X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_')).
% 0.21/0.30 thf(f2,axiom,(
% 0.21/0.30 ! [X0 : 'type/nums/num'] : ((('const/arith/-' @ ('const/nums/SUC' @ X0) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = X0)),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/SUC_SUB1_')).
% 0.21/0.30 thf(f3,axiom,(
% 0.21/0.30 ! [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))))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/LENGTH_1')).
% 0.21/0.30 thf(f4,axiom,(
% 0.21/0.30 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = X2)),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/TL_')).
% 0.21/0.30 thf(f8,conjecture,(
% 0.21/0.30 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 != 'const/ind_types/NIL' @ X0) => ((('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) = (('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/LENGTH_TL_')).
% 0.21/0.30 thf(f9,negated_conjecture,(
% 0.21/0.30 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 != 'const/ind_types/NIL' @ X0) => ((('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) = (('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))),
% 0.21/0.30 inference(negated_conjecture,[status(cth)],[f8])).
% 0.21/0.30 thf(f10,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : 'type/ind_types/list' @ X0,X3 : X0] : ((X1 @ X2) => (X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2)))) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 0.21/0.30 inference(rectify,[],[f1])).
% 0.21/0.30 thf(f11,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((((X1 @ 'const/ind_types/NIL' @ X0)) = $true) & ! [X3 : X0,X2 : 'type/ind_types/list' @ X0] : ((((X1 @ X2)) = $true) => (((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2))) = $true))) => ! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true))),
% 0.21/0.30 inference(fool_elimination,[],[f10])).
% 0.21/0.30 thf(f12,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0] : ((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1))) = X1)),
% 0.21/0.30 inference(rectify,[],[f4])).
% 0.21/0.30 thf(f13,plain,(
% 0.21/0.30 ! [X0 : $tType,X2 : X0,X1 : 'type/ind_types/list' @ X0] : ((('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1))) = (('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X1))))),
% 0.21/0.30 inference(rectify,[],[f3])).
% 0.21/0.30 thf(f14,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true) | ((((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ? [X3 : X0,X2 : 'type/ind_types/list' @ X0] : ((((X1 @ X2)) = $true) & (((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2))) != $true))))),
% 0.21/0.30 inference(ennf_transformation,[],[f11])).
% 0.21/0.30 thf(f15,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true) | ? [X3 : X0,X2 : 'type/ind_types/list' @ X0] : ((((X1 @ X2)) = $true) & (((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2))) != $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 0.21/0.30 inference(flattening,[],[f14])).
% 0.21/0.30 thf(f16,plain,(
% 0.21/0.30 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) != (('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) & (X1 != 'const/ind_types/NIL' @ X0))),
% 0.21/0.30 inference(ennf_transformation,[],[f9])).
% 0.21/0.30 thf(f17,plain,(
% 0.21/0.30 ! [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))))),
% 0.21/0.30 inference(rectify,[],[f13])).
% 0.21/0.30 thf(f18,plain,(
% 0.21/0.30 ((('const/lists/LENGTH' @ sK0 @ ('const/lists/TL' @ sK0 @ sK1))) != (('const/arith/-' @ ('const/lists/LENGTH' @ sK0 @ sK1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) & (sK1 != 'const/ind_types/NIL' @ sK0)),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16])).
% 0.21/0.30 thf(f19,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | ? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : ((((X1 @ X4)) = $true) & ($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4))))) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 0.21/0.30 inference(rectify,[],[f15])).
% 0.21/0.30 thf(f20,plain,(
% 0.21/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | ((((X1 @ (sK3 @ X0 @ X1))) = $true) & ($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1)))))) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK3 @ X0 @ X1),skolemize(X4,sK3 @ X0 @ X1)],[f19])).
% 0.21/0.30 thf(f21,plain,(
% 0.21/0.30 ( ! [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))))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f17])).
% 0.21/0.30 thf(f22,plain,(
% 0.21/0.30 ( ! [X0 : 'type/nums/num'] : (((('const/arith/-' @ ('const/nums/SUC' @ X0) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = X0)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f2])).
% 0.21/0.30 thf(f23,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : X0,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1))) = X1)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f12])).
% 0.21/0.30 thf(f26,plain,(
% 0.21/0.30 (sK1 != 'const/ind_types/NIL' @ sK0)),
% 0.21/0.30 inference(cnf_transformation,[],[f18])).
% 0.21/0.30 thf(f27,plain,(
% 0.21/0.30 ((('const/lists/LENGTH' @ sK0 @ ('const/lists/TL' @ sK0 @ sK1))) != (('const/arith/-' @ ('const/lists/LENGTH' @ sK0 @ sK1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),
% 0.21/0.30 inference(cnf_transformation,[],[f18])).
% 0.21/0.30 thf(f29,plain,(
% 0.21/0.30 ( ! [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)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f176,definition,(
% 0.21/0.30 spl4_1 <=> ! [X0 : 'type/ind_types/list' @ sK0] : (sK1 != X0)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.21/0.30 thf(f177,plain,(
% 0.21/0.30 ( ! [X0 : 'type/ind_types/list' @ sK0] : ((sK1 != X0)) ) | ~spl4_1),
% 0.21/0.30 inference(avatar_component_clause,[],[f176])).
% 0.21/0.30 thf(f207,plain,(
% 0.21/0.30 ( ! [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)))) )),
% 0.21/0.30 inference(leibniz_equality_elimination,[],[f29])).
% 0.21/0.30 thf(f235,plain,(
% 0.21/0.30 ( ! [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)) )),
% 0.21/0.30 inference(beta-eta_normalization,[],[f207])).
% 0.21/0.30 thf(f236,plain,(
% 0.21/0.30 ( ! [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 = (('const/ind_types/NIL' @ X0 = X1)))) )),
% 0.21/0.30 inference(not_proxy_clausification,[],[f235])).
% 0.21/0.30 thf(f237,plain,(
% 0.21/0.30 ( ! [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)) )),
% 0.21/0.30 inference(equality_proxy_clausification,[],[f236])).
% 0.21/0.30 thf(f601,plain,(
% 0.21/0.30 ( ! [X1 : $tType,X0 : 'type/ind_types/list' @ X1] : ((((sK3 @ X1 @ (^[Y0 : 'type/ind_types/list' @ X1]: (~ (Y0 = X0))))) = (('const/lists/TL' @ X1 @ X0))) | ('const/ind_types/NIL' @ X1 = X0)) )),
% 0.21/0.30 inference(constrained_superposition,[],[f23,f237])).
% 0.21/0.30 thf(f627,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | ((((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1)))) != $true) | ($true != (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ 'const/ind_types/NIL' @ X0))) | ($true = (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ X2)))) )),
% 0.21/0.30 inference(constrained_superposition,[],[f29,f601])).
% 0.21/0.30 thf(f630,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (($true != ((~ ('const/ind_types/NIL' @ X0 = X1)))) | ('const/ind_types/NIL' @ X0 = X1) | (((~ (X2 = X1))) = $true) | (((~ (('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1)) = X1))) != $true)) )),
% 0.21/0.30 inference(beta-eta_normalization,[],[f627])).
% 0.21/0.30 thf(f631,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : ((((~ (X2 = X1))) = $true) | ('const/ind_types/NIL' @ X0 = X1) | ($true = (('const/ind_types/NIL' @ X0 = X1))) | (((~ (('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1)) = X1))) != $true)) )),
% 0.21/0.30 inference(not_proxy_clausification,[],[f630])).
% 0.21/0.30 thf(f632,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : ((((X2 = X1)) = $false) | ('const/ind_types/NIL' @ X0 = X1) | ($true = (('const/ind_types/NIL' @ X0 = X1))) | (((~ (('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1)) = X1))) != $true)) )),
% 0.21/0.30 inference(not_proxy_clausification,[],[f631])).
% 0.21/0.30 thf(f633,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : ((((~ (('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1)) = X1))) != $true) | ($true = (('const/ind_types/NIL' @ X0 = X1))) | ('const/ind_types/NIL' @ X0 = X1) | (X1 != X2)) )),
% 0.21/0.30 inference(equality_proxy_clausification,[],[f632])).
% 0.21/0.30 thf(f634,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | (X1 != X2) | ($true = (('const/ind_types/NIL' @ X0 = X1))) | (((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1)) = X1)) = $true)) )),
% 0.21/0.30 inference(not_proxy_clausification,[],[f633])).
% 0.21/0.30 thf(f635,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | (X1 != X2) | (((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1)) = X1)) = $true) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.21/0.30 inference(equality_proxy_clausification,[],[f634])).
% 0.21/0.30 thf(f636,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | ((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1))) = X1) | (X1 != X2) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.21/0.30 inference(equality_proxy_clausification,[],[f635])).
% 0.21/0.30 thf(f637,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1))) = X1) | ('const/ind_types/NIL' @ X0 = X1) | (X1 != X2)) )),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f636])).
% 0.21/0.30 thf(f704,plain,(
% 0.21/0.30 ( ! [X1 : $tType,X2 : 'type/ind_types/list' @ X1,X0 : 'type/ind_types/list' @ X1] : (((('const/lists/LENGTH' @ X1 @ X0)) = (('const/nums/SUC' @ ('const/lists/LENGTH' @ X1 @ ('const/lists/TL' @ X1 @ X0))))) | ('const/ind_types/NIL' @ X1 = X0) | (X0 != X2)) )),
% 0.21/0.30 inference(constrained_superposition,[],[f21,f637])).
% 0.21/0.30 thf(f714,plain,(
% 0.21/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) = (('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) | ('const/ind_types/NIL' @ X0 = X1) | (X1 != X2)) )),
% 0.21/0.30 inference(constrained_superposition,[],[f22,f704])).
% 0.21/0.30 thf(f726,plain,(
% 0.21/0.30 ( ! [X0 : 'type/ind_types/list' @ sK0] : (((('const/lists/LENGTH' @ sK0 @ ('const/lists/TL' @ sK0 @ sK1))) != (('const/lists/LENGTH' @ sK0 @ ('const/lists/TL' @ sK0 @ sK1)))) | (sK1 = 'const/ind_types/NIL' @ sK0) | (sK1 != X0)) )),
% 0.21/0.30 inference(constrained_superposition,[],[f27,f714])).
% 0.21/0.30 thf(f728,plain,(
% 0.21/0.30 ( ! [X0 : 'type/ind_types/list' @ sK0] : ((sK1 != X0) | (sK1 = 'const/ind_types/NIL' @ sK0)) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f726])).
% 0.21/0.30 thf(f731,plain,(
% 0.21/0.30 ( ! [X0 : 'type/ind_types/list' @ sK0] : ((sK1 != X0)) )),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f728,f26])).
% 0.21/0.30 thf(f732,plain,(
% 0.21/0.30 spl4_1),
% 0.21/0.30 inference(avatar_split_clause,[],[f731,f176])).
% 0.21/0.30 thf(f733,plain,(
% 0.21/0.30 (sK1 != sK1) | ~spl4_1),
% 0.21/0.30 inference(imitation,[],[f177])).
% 0.21/0.30 thf(f736,plain,(
% 0.21/0.30 $false | ~spl4_1),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f733])).
% 0.21/0.30 thf(f737,plain,(
% 0.21/0.30 ~spl4_1),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f736])).
% 0.21/0.30 cnf(s2, plain, spl4_1, inference(sat_conversion,[],[f732])).
% 0.21/0.30 cnf(s4, plain, ~spl4_1, inference(sat_conversion,[],[f737])).
% 0.21/0.30 cnf(s5, plain, $false, inference(rat,[],[s2,s4])).
% 0.21/0.30 thf(f738,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(avatar_sat_refutation,[],[s5])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (462735)------------------------------
% 0.21/0.30 % (462735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (462735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (462735)CaDiCaL version: 2.1.3
% 0.21/0.30 % (462735)Termination reason: Refutation
% 0.21/0.30 % (462735)Time elapsed: 0.033 s
% 0.21/0.30 % (462735)Peak memory usage: 13 MB
% 0.21/0.30 % (462735)Instructions burned: 60 (million)
% 0.21/0.30 % (462730)Success in time 0.064 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------