%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n004.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 07:49:09 AM UTC 2026
% Result : Theorem 0.19s 0.32s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT290^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n004.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 18:23:47 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.32 % (1653519)Will run a generic schedule for satisfiability detection.
% 0.19/0.32 % (1653541)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4079481779:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.32 % (1653536)% WARNING: option uhcvi not known.
% 0.19/0.32 % (1653538)dis+10_1_sil=32000:sp=arity:random_seed=233351057:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.32 % (1653537)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=784797944:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.32 % (1653535)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=932363000_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.32 % (1653536)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=714549681:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.32 % (1653540)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=384750663:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.32 % (1653539)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2350525819:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.32 % (1653536)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.32 % (1653539)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.32 % Exception at run slice level
% 0.19/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.32 % (1653536)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.32 % (1653556)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=254796039:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.32 % Exception at run slice level
% 0.19/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.32 % (1653541)Instruction limit reached!
% 0.19/0.32 % (1653541)------------------------------
% 0.19/0.32 % (1653541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1653541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1653541)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1653541)Termination reason: Instruction limit
% 0.19/0.32 % (1653541)Termination phase: Saturation
% 0.19/0.32 % (1653541)Time elapsed: 0.043 s
% 0.19/0.32 % (1653541)Peak memory usage: 13 MB
% 0.19/0.32 % (1653541)Instructions burned: 162 (million)
% 0.19/0.32 % (1653561)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2131783791:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.32 % (1653540) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1653519-1653540"...
% 0.19/0.32 % (1653570)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3828397435:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.19/0.32 % (1653540)...printing done.
% 0.19/0.32 % (1653570)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.32 % (1653570)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.32 % (1653540)Refutation found. Thanks to Tanya!
% 0.19/0.32 % SZS status Theorem for theBenchmark
% 0.19/0.32 % SZS output start Proof for theBenchmark
% 0.19/0.32 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.19/0.32 thf(type_def_6, type, 'type/ind_types/list': $tType > $tType).
% 0.19/0.32 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.32 thf(type_def_8, type, sK2: $tType).
% 0.19/0.32 thf(func_def_0, type, 'const/nums/SUC': ('type/nums/num' > 'type/nums/num')).
% 0.19/0.32 thf(func_def_1, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.19/0.32 thf(func_def_2, type, 'const/nums/_0': 'type/nums/num').
% 0.19/0.32 thf(func_def_3, type, 'const/lists/LENGTH': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/nums/num'))).
% 0.19/0.32 thf(func_def_4, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.19/0.32 thf(func_def_5, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.19/0.32 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.32 thf(func_def_10, type, sK0: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > X0))).
% 0.19/0.32 thf(func_def_11, type, sK1: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0))).
% 0.19/0.32 thf(func_def_12, type, sK3: 'type/ind_types/list' @ sK2).
% 0.19/0.32 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.19/0.32 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.32 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.32 thf(func_def_17, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.32 thf(f1,axiom,(
% 0.19/0.32 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) & (X1 @ 'const/ind_types/NIL' @ X0)) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 0.19/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_')).
% 0.19/0.32 thf(f3,axiom,(
% 0.19/0.32 ! [X0 : 'type/nums/num'] : ((('const/nums/SUC' @ X0)) != (('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 0.19/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/nums/NOT_SUC_')).
% 0.19/0.32 thf(f4,axiom,(
% 0.19/0.32 ! [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))))),
% 0.19/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/LENGTH_1')).
% 0.19/0.32 thf(f5,axiom,(
% 0.19/0.32 ! [X0 : $tType] : ((('const/lists/LENGTH' @ X0 @ 'const/ind_types/NIL' @ X0)) = (('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 0.19/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/LENGTH_0')).
% 0.19/0.32 thf(f6,conjecture,(
% 0.19/0.32 ! [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))),
% 0.19/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/LENGTH_EQ_NIL_')).
% 0.19/0.32 thf(f7,negated_conjecture,(
% 0.19/0.32 ~ ! [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))),
% 0.19/0.32 inference(negated_conjecture,[status(cth)],[f6])).
% 0.19/0.32 thf(f8,plain,(
% 0.19/0.32 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) & (X1 @ 'const/ind_types/NIL' @ X0)) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 0.19/0.32 inference(rectify,[],[f1])).
% 0.19/0.32 thf(f9,plain,(
% 0.19/0.32 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((((X1 @ X3)) = $true) => (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) = $true)) & (((X1 @ 'const/ind_types/NIL' @ X0)) = $true)) => ! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true))),
% 0.19/0.32 inference(fool_elimination,[],[f8])).
% 0.19/0.32 thf(f10,plain,(
% 0.19/0.32 ~ ! [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)))),
% 0.19/0.32 inference(fool_elimination,[],[f7])).
% 0.19/0.32 thf(f11,plain,(
% 0.19/0.32 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true) | (? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) != $true) & (((X1 @ X3)) = $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true)))),
% 0.19/0.32 inference(ennf_transformation,[],[f9])).
% 0.19/0.32 thf(f12,plain,(
% 0.19/0.32 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true) | ? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) != $true) & (((X1 @ X3)) = $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 0.19/0.32 inference(flattening,[],[f11])).
% 0.19/0.32 thf(f13,plain,(
% 0.19/0.32 ? [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)))),
% 0.19/0.32 inference(ennf_transformation,[],[f10])).
% 0.19/0.32 thf(f14,plain,(
% 0.19/0.32 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | ? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4)))) & (((X1 @ X4)) = $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 0.19/0.32 inference(rectify,[],[f12])).
% 0.19/0.32 thf(f15,plain,(
% 0.19/0.32 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))))) & ($true = ((X1 @ (sK1 @ X0 @ X1))))) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 0.19/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK1 @ X0 @ X1),skolemize(X4,sK1 @ X0 @ X1)],[f14])).
% 0.19/0.32 thf(f16,plain,(
% 0.19/0.32 (((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3))) != (('const/ind_types/NIL' @ sK2 = sK3)))),
% 0.19/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f13])).
% 0.19/0.32 thf(f18,plain,(
% 0.19/0.32 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : ('type/ind_types/list' @ X0 > $o)] : (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))))) | (((X1 @ X2)) = $true) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true)) )),
% 0.19/0.32 inference(cnf_transformation,[],[f15])).
% 0.19/0.32 thf(f20,plain,(
% 0.19/0.32 ( ! [X0 : 'type/nums/num'] : (((('const/nums/SUC' @ X0)) != (('const/nums/NUMERAL' @ 'const/nums/_0')))) )),
% 0.19/0.32 inference(cnf_transformation,[],[f3])).
% 0.19/0.32 thf(f21,plain,(
% 0.19/0.32 ( ! [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))))) )),
% 0.19/0.32 inference(cnf_transformation,[],[f4])).
% 0.19/0.32 thf(f22,plain,(
% 0.19/0.32 ( ! [X0 : $tType] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ X0 @ 'const/ind_types/NIL' @ X0)))) )),
% 0.19/0.32 inference(cnf_transformation,[],[f5])).
% 0.19/0.32 thf(f23,plain,(
% 0.19/0.32 (((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3))) != (('const/ind_types/NIL' @ sK2 = sK3)))),
% 0.19/0.32 inference(cnf_transformation,[],[f16])).
% 0.19/0.32 thf(f26,plain,(
% 0.19/0.32 ($true = ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3)))) | ($true = (('const/ind_types/NIL' @ sK2 = sK3)))),
% 0.19/0.32 inference(xor_proxy_clausification,[],[f23])).
% 0.19/0.32 thf(f27,plain,(
% 0.19/0.32 (((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/lists/LENGTH' @ sK2 @ sK3))) = $false) | ((('const/ind_types/NIL' @ sK2 = sK3)) = $false)),
% 0.19/0.32 inference(xor_proxy_clausification,[],[f23])).
% 0.19/0.32 thf(f28,plain,(
% 0.19/0.32 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/lists/LENGTH' @ sK2 @ sK3))) | ((('const/ind_types/NIL' @ sK2 = sK3)) = $false)),
% 0.19/0.32 inference(equality_proxy_clausification,[],[f27])).
% 0.19/0.32 thf(f29,plain,(
% 0.19/0.32 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/lists/LENGTH' @ sK2 @ sK3))) | (sK3 != 'const/ind_types/NIL' @ sK2)),
% 0.19/0.32 inference(equality_proxy_clausification,[],[f28])).
% 0.19/0.32 thf(f30,plain,(
% 0.19/0.32 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ sK2 @ sK3))) | ($true = (('const/ind_types/NIL' @ sK2 = sK3)))),
% 0.19/0.32 inference(equality_proxy_clausification,[],[f26])).
% 0.19/0.32 thf(f31,plain,(
% 0.19/0.32 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ sK2 @ sK3))) | (sK3 = 'const/ind_types/NIL' @ sK2)),
% 0.19/0.32 inference(equality_proxy_clausification,[],[f30])).
% 0.19/0.32 thf(f33,definition,(
% 0.19/0.32 spl4_1 <=> (sK3 = 'const/ind_types/NIL' @ sK2)),
% 0.19/0.32 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.19/0.32 thf(f34,plain,(
% 0.19/0.32 (sK3 = 'const/ind_types/NIL' @ sK2) | ~spl4_1),
% 0.19/0.32 inference(avatar_component_clause,[],[f33])).
% 0.19/0.32 thf(f35,plain,(
% 0.19/0.32 (sK3 != 'const/ind_types/NIL' @ sK2) | spl4_1),
% 0.19/0.32 inference(avatar_component_clause,[],[f33])).
% 0.19/0.32 thf(f37,definition,(
% 0.19/0.32 spl4_2 <=> ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ sK2 @ sK3)))),
% 0.19/0.32 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.19/0.32 thf(f38,plain,(
% 0.19/0.32 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/lists/LENGTH' @ sK2 @ sK3))) | ~spl4_2),
% 0.19/0.32 inference(avatar_component_clause,[],[f37])).
% 0.19/0.32 thf(f39,plain,(
% 0.19/0.32 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/lists/LENGTH' @ sK2 @ sK3))) | spl4_2),
% 0.19/0.32 inference(avatar_component_clause,[],[f37])).
% 0.19/0.32 thf(f40,plain,(
% 0.19/0.32 ~spl4_1 | ~spl4_2),
% 0.19/0.32 inference(avatar_split_clause,[],[f29,f37,f33])).
% 0.19/0.32 thf(f41,plain,(
% 0.19/0.32 spl4_1 | spl4_2),
% 0.19/0.32 inference(avatar_split_clause,[],[f31,f37,f33])).
% 0.19/0.32 thf(f106,plain,(
% 0.19/0.32 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))))) )),
% 0.19/0.32 inference(constrained_superposition,[],[f20,f21])).
% 0.19/0.32 thf(f108,plain,(
% 0.19/0.32 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ($true != (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ 'const/ind_types/NIL' @ X0)))) )),
% 0.19/0.32 inference(leibniz_equality_elimination,[],[f18])).
% 0.19/0.32 thf(f141,plain,(
% 0.19/0.32 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ($true != ((~ ('const/ind_types/NIL' @ X0 = X1))))) )),
% 0.19/0.32 inference(beta-eta_normalization,[],[f108])).
% 0.19/0.32 thf(f142,plain,(
% 0.19/0.32 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ($true = (('const/ind_types/NIL' @ X0 = X1)))) )),
% 0.19/0.32 inference(not_proxy_clausification,[],[f141])).
% 0.19/0.32 thf(f143,plain,(
% 0.19/0.32 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.19/0.32 inference(equality_proxy_clausification,[],[f142])).
% 0.19/0.32 thf(f1020,plain,(
% 0.19/0.32 ( ! [X1 : $tType,X0 : 'type/ind_types/list' @ X1] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/lists/LENGTH' @ X1 @ X0))) | ('const/ind_types/NIL' @ X1 = X0)) )),
% 0.19/0.32 inference(constrained_superposition,[],[f106,f143])).
% 0.19/0.32 thf(f1045,plain,(
% 0.19/0.32 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | (sK3 = 'const/ind_types/NIL' @ sK2) | ~spl4_2),
% 0.19/0.32 inference(constrained_superposition,[],[f1020,f38])).
% 0.19/0.32 thf(f1052,plain,(
% 0.19/0.32 (sK3 = 'const/ind_types/NIL' @ sK2) | ~spl4_2),
% 0.19/0.32 inference(trivial_inequality_removal,[],[f1045])).
% 0.19/0.32 thf(f1053,plain,(
% 0.19/0.32 $false | (spl4_1 | ~spl4_2)),
% 0.19/0.32 inference(forward_subsumption_resolution,[],[f1052,f35])).
% 0.19/0.32 thf(f1054,plain,(
% 0.19/0.32 spl4_1 | ~spl4_2),
% 0.19/0.32 inference(avatar_contradiction_clause,[],[f1053])).
% 0.19/0.32 thf(f1055,plain,(
% 0.19/0.32 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/lists/LENGTH' @ sK2 @ 'const/ind_types/NIL' @ sK2))) | (~spl4_1 | spl4_2)),
% 0.19/0.32 inference(forward_demodulation,[],[f39,f34])).
% 0.19/0.32 thf(f1056,plain,(
% 0.19/0.32 $false | (~spl4_1 | spl4_2)),
% 0.19/0.32 inference(forward_subsumption_resolution,[],[f1055,f22])).
% 0.19/0.32 thf(f1057,plain,(
% 0.19/0.32 ~spl4_1 | spl4_2),
% 0.19/0.32 inference(avatar_contradiction_clause,[],[f1056])).
% 0.19/0.32 cnf(s1, plain, ~spl4_1 | ~spl4_2, inference(sat_conversion,[],[f40])).
% 0.19/0.32 cnf(s2, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f41])).
% 0.19/0.32 cnf(s3, plain, spl4_1 | ~spl4_2, inference(sat_conversion,[],[f1054])).
% 0.19/0.32 cnf(s4, plain, ~spl4_1 | spl4_2, inference(sat_conversion,[],[f1057])).
% 0.19/0.32 cnf(s5, plain, spl4_1, inference(rat,[],[s2,s3])).
% 0.19/0.32 cnf(s6, plain, spl4_2, inference(rat,[],[s4,s5])).
% 0.19/0.32 cnf(s7, plain, $false, inference(rat,[],[s1,s6,s5])).
% 0.19/0.32 thf(f1058,plain,(
% 0.19/0.32 $false),
% 0.19/0.32 inference(avatar_sat_refutation,[],[s7])).
% 0.19/0.32 % SZS output end Proof for theBenchmark
% 0.19/0.32 % (1653540)------------------------------
% 0.19/0.32 % (1653540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (1653540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (1653540)CaDiCaL version: 2.1.3
% 0.19/0.32 % (1653540)Termination reason: Refutation
% 0.19/0.32 % (1653540)Time elapsed: 0.045 s
% 0.19/0.32 % (1653540)Peak memory usage: 13 MB
% 0.19/0.32 % (1653540)Instructions burned: 85 (million)
% 0.19/0.32 % (1653519)Success in time 0.088 s
% 0.19/0.32 % Vampire exiting
%------------------------------------------------------------------------------