%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT315^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT315^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n005.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 18:25:31 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.27 % (2028444)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (2028452)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=1504186090: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)
% 0.21/0.27 % (2028452) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2028444-2028452"...
% 0.21/0.27 % (2028452)...printing done.
% 0.21/0.27 % (2028452)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% 0.21/0.27 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.21/0.27 thf(type_def_6, type, 'type/ind_types/list': $tType > $tType).
% 0.21/0.27 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.27 thf(type_def_8, type, sK0: $tType).
% 0.21/0.27 thf(func_def_0, type, 'const/nums/SUC': ('type/nums/num' > 'type/nums/num')).
% 0.21/0.27 thf(func_def_1, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.21/0.27 thf(func_def_2, type, 'const/nums/BIT1': ('type/nums/num' > 'type/nums/num')).
% 0.21/0.27 thf(func_def_3, type, 'const/nums/_0': 'type/nums/num').
% 0.21/0.27 thf(func_def_4, type, 'const/lists/TL': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.21/0.27 thf(func_def_5, type, 'const/lists/EL': !>[X0: $tType]:(('type/nums/num' > 'type/ind_types/list' @ X0 > X0))).
% 0.21/0.27 thf(func_def_6, type, 'const/arith/+': ('type/nums/num' > 'type/nums/num' > 'type/nums/num')).
% 0.21/0.27 thf(func_def_8, type, sK1: 'type/nums/num').
% 0.21/0.27 thf(func_def_9, type, sK2: 'type/ind_types/list' @ sK0).
% 0.21/0.27 thf(f1,axiom,(
% 0.21/0.27 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/nums/num'] : ((('const/lists/EL' @ X0 @ ('const/nums/SUC' @ X1) @ X2)) = (('const/lists/EL' @ X0 @ X1 @ ('const/lists/TL' @ X0 @ X2))))),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/EL_1')).
% 0.21/0.27 thf(f2,axiom,(
% 0.21/0.27 ! [X0 : 'type/nums/num'] : ((('const/nums/SUC' @ X0)) = (('const/arith/+' @ X0 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/arith/ADD1_')).
% 0.21/0.27 thf(f3,conjecture,(
% 0.21/0.27 ! [X0 : $tType,X2 : 'type/nums/num',X1 : 'type/ind_types/list' @ X0] : ((('const/lists/EL' @ X0 @ X2 @ ('const/lists/TL' @ X0 @ X1))) = (('const/lists/EL' @ X0 @ ('const/arith/+' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X1)))),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/EL_TL_')).
% 0.21/0.27 thf(f4,negated_conjecture,(
% 0.21/0.27 ~ ! [X0 : $tType,X2 : 'type/nums/num',X1 : 'type/ind_types/list' @ X0] : ((('const/lists/EL' @ X0 @ X2 @ ('const/lists/TL' @ X0 @ X1))) = (('const/lists/EL' @ X0 @ ('const/arith/+' @ X2 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X1)))),
% 0.21/0.27 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.27 thf(f5,plain,(
% 0.21/0.27 ~ ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/nums/num'] : ((('const/lists/EL' @ X0 @ X1 @ ('const/lists/TL' @ X0 @ X2))) = (('const/lists/EL' @ X0 @ ('const/arith/+' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X2)))),
% 0.21/0.27 inference(rectify,[],[f4])).
% 0.21/0.27 thf(f6,plain,(
% 0.21/0.27 ? [X0 : $tType,X1 : 'type/nums/num',X2 : 'type/ind_types/list' @ X0] : ((('const/lists/EL' @ X0 @ X1 @ ('const/lists/TL' @ X0 @ X2))) != (('const/lists/EL' @ X0 @ ('const/arith/+' @ X1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ X2)))),
% 0.21/0.27 inference(ennf_transformation,[],[f5])).
% 0.21/0.27 thf(f7,plain,(
% 0.21/0.27 ((('const/lists/EL' @ sK0 @ ('const/arith/+' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ sK2)) != (('const/lists/EL' @ sK0 @ sK1 @ ('const/lists/TL' @ sK0 @ sK2))))),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6])).
% 0.21/0.27 thf(f8,plain,(
% 0.21/0.27 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : 'type/nums/num'] : ((('const/lists/EL' @ X0 @ X2 @ ('const/lists/TL' @ X0 @ X1))) = (('const/lists/EL' @ X0 @ ('const/nums/SUC' @ X2) @ X1)))),
% 0.21/0.27 inference(rectify,[],[f1])).
% 0.21/0.27 thf(f9,plain,(
% 0.21/0.27 ((('const/lists/EL' @ sK0 @ ('const/arith/+' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ sK2)) != (('const/lists/EL' @ sK0 @ sK1 @ ('const/lists/TL' @ sK0 @ sK2))))),
% 0.21/0.27 inference(cnf_transformation,[],[f7])).
% 0.21/0.27 thf(f10,plain,(
% 0.21/0.27 ( ! [X0 : 'type/nums/num'] : (((('const/nums/SUC' @ X0)) = (('const/arith/+' @ X0 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) )),
% 0.21/0.27 inference(cnf_transformation,[],[f2])).
% 0.21/0.27 thf(f11,plain,(
% 0.21/0.27 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : 'type/ind_types/list' @ X0] : (((('const/lists/EL' @ X0 @ X2 @ ('const/lists/TL' @ X0 @ X1))) = (('const/lists/EL' @ X0 @ ('const/nums/SUC' @ X2) @ X1)))) )),
% 0.21/0.27 inference(cnf_transformation,[],[f8])).
% 0.21/0.27 thf(f13,definition,(
% 0.21/0.27 spl3_1 <=> ((('const/lists/EL' @ sK0 @ ('const/arith/+' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ sK2)) = (('const/lists/EL' @ sK0 @ sK1 @ ('const/lists/TL' @ sK0 @ sK2))))),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.21/0.27 thf(f15,plain,(
% 0.21/0.27 ((('const/lists/EL' @ sK0 @ ('const/arith/+' @ sK1 @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))) @ sK2)) != (('const/lists/EL' @ sK0 @ sK1 @ ('const/lists/TL' @ sK0 @ sK2)))) | spl3_1),
% 0.21/0.27 inference(avatar_component_clause,[],[f13])).
% 0.21/0.27 thf(f16,plain,(
% 0.21/0.27 ~spl3_1),
% 0.21/0.27 inference(avatar_split_clause,[],[f9,f13])).
% 0.21/0.27 thf(f34,plain,(
% 0.21/0.27 ((('const/lists/EL' @ sK0 @ sK1 @ ('const/lists/TL' @ sK0 @ sK2))) != (('const/lists/EL' @ sK0 @ ('const/nums/SUC' @ sK1) @ sK2))) | spl3_1),
% 0.21/0.27 inference(forward_demodulation,[],[f15,f10])).
% 0.21/0.27 thf(f35,plain,(
% 0.21/0.27 $false | spl3_1),
% 0.21/0.27 inference(forward_subsumption_resolution,[],[f34,f11])).
% 0.21/0.27 thf(f36,plain,(
% 0.21/0.27 spl3_1),
% 0.21/0.27 inference(avatar_contradiction_clause,[],[f35])).
% 0.21/0.27 cnf(s1, plain, ~spl3_1, inference(sat_conversion,[],[f16])).
% 0.21/0.27 cnf(s2, plain, spl3_1, inference(sat_conversion,[],[f36])).
% 0.21/0.27 cnf(s3, plain, $false, inference(rat,[],[s1,s2])).
% 0.21/0.27 thf(f37,plain,(
% 0.21/0.27 $false),
% 0.21/0.27 inference(avatar_sat_refutation,[],[s3])).
% 0.21/0.27 % SZS output end Proof for theBenchmark
% 0.21/0.27 % (2028452)------------------------------
% 0.21/0.27 % (2028452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2028452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2028452)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2028452)Termination reason: Refutation
% 0.21/0.27 % (2028452)Time elapsed: 0.003 s
% 0.21/0.27 % (2028452)Peak memory usage: 13 MB
% 0.21/0.27 % (2028452)Instructions burned: 5 (million)
% 0.21/0.27 % (2028444)Success in time 0.04 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------