%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT099_1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 : Tue Sep 29 09:48:07 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT099_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 00:09:09 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.22/0.28 % (2784758)Will run a generic schedule for satisfiability detection.
% 0.22/0.28 % (2784763)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1813571512_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.28 % (2784763)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.28 % (2784763)Terminated due to inappropriate strategy.
% 0.22/0.28 % (2784763)------------------------------
% 0.22/0.28 % (2784763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (2784763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (2784763)CaDiCaL version: 2.1.3
% 0.22/0.28 % (2784763)Termination reason: Inappropriate
% 0.22/0.28 % (2784763)Time elapsed: 0.0000 s
% 0.22/0.28 % (2784763)Peak memory usage: 10 MB
% 0.22/0.28 % (2784763)------------------------------
% 0.22/0.28 % (2784763)------------------------------
% 0.22/0.28 % (2784764)% WARNING: option uhcvi not known.
% 0.22/0.28 % (2784765)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=102775691:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.28 % (2784764)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=333138192:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.28 % (2784766)dis+10_1_sil=32000:sp=arity:random_seed=1644342321:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.28 % (2784767)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=249594383:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.28 % (2784768)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=296838077:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.28 % (2784769)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=988025918:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.28 % (2784771)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1257273481:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.28 % (2784771)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.28 % (2784771)Terminated due to inappropriate strategy.
% 0.22/0.28 % (2784771)------------------------------
% 0.22/0.28 % (2784771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (2784771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (2784771)CaDiCaL version: 2.1.3
% 0.22/0.28 % (2784771)Termination reason: Inappropriate
% 0.22/0.28 % (2784771)Time elapsed: 0.0000 s
% 0.22/0.28 % (2784771)Peak memory usage: 11 MB
% 0.22/0.28 % (2784771)------------------------------
% 0.22/0.28 % (2784771)------------------------------
% 0.22/0.28 % (2784767) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2784758-2784767"...
% 0.22/0.28 % (2784767)...printing done.
% 0.22/0.28 % (2784779)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=457413396:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.28 % (2784767)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 tff(type_def_5, type, list: $tType).
% 0.22/0.28 tff(func_def_0, type, nil: list).
% 0.22/0.28 tff(func_def_1, type, cons: ($int * list) > list).
% 0.22/0.28 tff(func_def_2, type, head: list > $int).
% 0.22/0.28 tff(func_def_3, type, tail: list > list).
% 0.22/0.28 tff(func_def_11, type, sK0: ($int * list) > $int).
% 0.22/0.28 tff(func_def_12, type, sK1: ($int * list) > list).
% 0.22/0.28 tff(func_def_13, type, sK2: $int).
% 0.22/0.28 tff(pred_def_1, type, inRange: ($int * list) > $o).
% 0.22/0.28 tff(f5,axiom,(
% 0.22/0.28 ! [X0 : $int,X1 : list] : (inRange(X0,X1) <=> (X1 = nil | ? [X2 : $int,X3 : list] : (X1 = cons(X2,X3) & $lesseq(0,X2) & $less(X2,X0) & inRange(X0,X3))))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inRange)).
% 0.22/0.28 tff(f6,conjecture,(
% 0.22/0.28 ! [X0 : $int] : ($greatereq(X0,4) => inRange(X0,cons(1,cons(3,cons(2,nil)))))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c)).
% 0.22/0.28 tff(f7,negated_conjecture,(
% 0.22/0.28 ~ ! [X0 : $int] : ($greatereq(X0,4) => inRange(X0,cons(1,cons(3,cons(2,nil)))))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f6])).
% 0.22/0.28 tff(f8,plain,(
% 0.22/0.28 ! [X0 : $int,X1 : list] : (inRange(X0,X1) <=> (X1 = nil | ? [X2 : $int,X3 : list] : (X1 = cons(X2,X3) & ~$less(X2,0) & $less(X2,X0) & inRange(X0,X3))))),
% 0.22/0.28 inference(theory_normalization,[],[f5])).
% 0.22/0.28 tff(f9,plain,(
% 0.22/0.28 ~ ! [X0 : $int] : (~$less(X0,4) => inRange(X0,cons(1,cons(3,cons(2,nil)))))),
% 0.22/0.28 inference(theory_normalization,[],[f7])).
% 0.22/0.28 tff(f16,definition,(
% 0.22/0.28 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,X2) | $less(X0,X2)) )),
% 0.22/0.28 introduced(theory,[tha_transitivity])).
% 0.22/0.28 tff(f17,definition,(
% 0.22/0.28 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.22/0.28 introduced(theory,[tha_order_totality])).
% 0.22/0.28 tff(f22,plain,(
% 0.22/0.28 ? [X0 : $int] : (~inRange(X0,cons(1,cons(3,cons(2,nil)))) & ~$less(X0,4))),
% 0.22/0.28 inference(ennf_transformation,[],[f9])).
% 0.22/0.28 tff(f27,plain,(
% 0.22/0.28 ( ! [X2 : $int,X3 : list,X0 : $int,X1 : list] : (~inRange(X0,X3) | ~$less(X2,X0) | $less(X2,0) | cons(X2,X3) != X1 | inRange(X0,X1)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 tff(f32,plain,(
% 0.22/0.28 ( ! [X0 : $int,X1 : list] : (nil != X1 | inRange(X0,X1)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 tff(f33,plain,(
% 0.22/0.28 ~$less(sK2,4)),
% 0.22/0.28 inference(cnf_transformation,[],[f22])).
% 0.22/0.28 tff(f34,plain,(
% 0.22/0.28 ~inRange(sK2,cons(1,cons(3,cons(2,nil))))),
% 0.22/0.28 inference(cnf_transformation,[],[f22])).
% 0.22/0.28 tff(f35,plain,(
% 0.22/0.28 ( ! [X0 : $int] : (inRange(X0,nil)) )),
% 0.22/0.28 inference(equality_resolution,[],[f32])).
% 0.22/0.28 tff(f36,plain,(
% 0.22/0.28 ( ! [X2 : $int,X3 : list,X0 : $int] : (inRange(X0,cons(X2,X3)) | ~$less(X2,X0) | $less(X2,0) | ~inRange(X0,X3)) )),
% 0.22/0.28 inference(equality_resolution,[],[f27])).
% 0.22/0.28 tff(f72,plain,(
% 0.22/0.28 $less(4,sK2) | 4 = sK2),
% 0.22/0.28 inference(resolution,[],[f17,f33])).
% 0.22/0.28 tff(f86,definition,(
% 0.22/0.28 spl3_1 <=> 4 = sK2),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.22/0.28 tff(f88,plain,(
% 0.22/0.28 4 = sK2 | ~spl3_1),
% 0.22/0.28 inference(avatar_component_clause,[],[f86])).
% 0.22/0.28 tff(f90,definition,(
% 0.22/0.28 spl3_2 <=> $less(4,sK2)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.22/0.28 tff(f92,plain,(
% 0.22/0.28 $less(4,sK2) | ~spl3_2),
% 0.22/0.28 inference(avatar_component_clause,[],[f90])).
% 0.22/0.28 tff(f94,plain,(
% 0.22/0.28 spl3_1 | spl3_2),
% 0.22/0.28 inference(avatar_split_clause,[],[f72,f90,f86])).
% 0.22/0.28 tff(f95,plain,(
% 0.22/0.28 ( ! [X0 : $int] : ($less(X0,sK2) | ~$less(X0,4)) ) | ~spl3_2),
% 0.22/0.28 inference(resolution,[],[f92,f16])).
% 0.22/0.28 tff(f235,plain,(
% 0.22/0.28 ~$less(1,sK2) | $less(1,0) | ~inRange(sK2,cons(3,cons(2,nil)))),
% 0.22/0.28 inference(resolution,[],[f36,f34])).
% 0.22/0.28 tff(f239,plain,(
% 0.22/0.28 ~$less(1,sK2) | ~inRange(sK2,cons(3,cons(2,nil)))),
% 0.22/0.28 inference(evaluation,[],[f235])).
% 0.22/0.28 tff(f276,definition,(
% 0.22/0.28 spl3_7 <=> inRange(sK2,cons(3,cons(2,nil)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition])).
% 0.22/0.28 tff(f278,plain,(
% 0.22/0.28 ~inRange(sK2,cons(3,cons(2,nil))) | spl3_7),
% 0.22/0.28 inference(avatar_component_clause,[],[f276])).
% 0.22/0.28 tff(f280,definition,(
% 0.22/0.28 spl3_8 <=> $less(1,sK2)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition])).
% 0.22/0.28 tff(f282,plain,(
% 0.22/0.28 ~$less(1,sK2) | spl3_8),
% 0.22/0.28 inference(avatar_component_clause,[],[f280])).
% 0.22/0.28 tff(f283,plain,(
% 0.22/0.28 ~spl3_7 | ~spl3_8),
% 0.22/0.28 inference(avatar_split_clause,[],[f239,f280,f276])).
% 0.22/0.28 tff(f284,plain,(
% 0.22/0.28 ~$less(3,sK2) | $less(3,0) | ~inRange(sK2,cons(2,nil)) | spl3_7),
% 0.22/0.28 inference(resolution,[],[f278,f36])).
% 0.22/0.28 tff(f285,plain,(
% 0.22/0.28 ~$less(3,sK2) | ~inRange(sK2,cons(2,nil)) | spl3_7),
% 0.22/0.28 inference(evaluation,[],[f284])).
% 0.22/0.28 tff(f287,definition,(
% 0.22/0.28 spl3_9 <=> inRange(sK2,cons(2,nil))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition])).
% 0.22/0.28 tff(f289,plain,(
% 0.22/0.28 ~inRange(sK2,cons(2,nil)) | spl3_9),
% 0.22/0.28 inference(avatar_component_clause,[],[f287])).
% 0.22/0.28 tff(f291,definition,(
% 0.22/0.28 spl3_10 <=> $less(3,sK2)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition])).
% 0.22/0.28 tff(f293,plain,(
% 0.22/0.28 ~$less(3,sK2) | spl3_10),
% 0.22/0.28 inference(avatar_component_clause,[],[f291])).
% 0.22/0.28 tff(f294,plain,(
% 0.22/0.28 ~spl3_9 | ~spl3_10 | spl3_7),
% 0.22/0.28 inference(avatar_split_clause,[],[f285,f276,f291,f287])).
% 0.22/0.28 tff(f321,plain,(
% 0.22/0.28 ~$less(2,sK2) | $less(2,0) | ~inRange(sK2,nil) | spl3_9),
% 0.22/0.28 inference(resolution,[],[f289,f36])).
% 0.22/0.28 tff(f322,plain,(
% 0.22/0.28 ~$less(2,sK2) | ~inRange(sK2,nil) | spl3_9),
% 0.22/0.28 inference(evaluation,[],[f321])).
% 0.22/0.28 tff(f323,plain,(
% 0.22/0.28 ~$less(2,sK2) | spl3_9),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f322,f35])).
% 0.22/0.28 tff(f346,plain,(
% 0.22/0.28 ~$less(2,4) | (~spl3_2 | spl3_9)),
% 0.22/0.28 inference(resolution,[],[f323,f95])).
% 0.22/0.28 tff(f348,plain,(
% 0.22/0.28 $false | (~spl3_2 | spl3_9)),
% 0.22/0.28 inference(evaluation,[],[f346])).
% 0.22/0.28 tff(f349,plain,(
% 0.22/0.28 ~spl3_2 | spl3_9),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f348])).
% 0.22/0.28 tff(f359,plain,(
% 0.22/0.28 ~$less(3,4) | (~spl3_2 | spl3_10)),
% 0.22/0.28 inference(resolution,[],[f293,f95])).
% 0.22/0.28 tff(f361,plain,(
% 0.22/0.28 $false | (~spl3_2 | spl3_10)),
% 0.22/0.28 inference(evaluation,[],[f359])).
% 0.22/0.28 tff(f362,plain,(
% 0.22/0.28 ~spl3_2 | spl3_10),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f361])).
% 0.22/0.28 tff(f365,plain,(
% 0.22/0.28 ~$less(2,4) | (~spl3_1 | spl3_9)),
% 0.22/0.28 inference(forward_demodulation,[],[f323,f88])).
% 0.22/0.28 tff(f366,plain,(
% 0.22/0.28 $false | (~spl3_1 | spl3_9)),
% 0.22/0.28 inference(evaluation,[],[f365])).
% 0.22/0.28 tff(f367,plain,(
% 0.22/0.28 ~spl3_1 | spl3_9),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f366])).
% 0.22/0.28 tff(f373,plain,(
% 0.22/0.28 ~$less(1,4) | (~spl3_1 | spl3_8)),
% 0.22/0.28 inference(forward_demodulation,[],[f282,f88])).
% 0.22/0.28 tff(f374,plain,(
% 0.22/0.28 $false | (~spl3_1 | spl3_8)),
% 0.22/0.28 inference(evaluation,[],[f373])).
% 0.22/0.28 tff(f375,plain,(
% 0.22/0.28 ~spl3_1 | spl3_8),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f374])).
% 0.22/0.28 tff(f379,plain,(
% 0.22/0.28 ~$less(3,4) | (~spl3_1 | spl3_10)),
% 0.22/0.28 inference(forward_demodulation,[],[f293,f88])).
% 0.22/0.28 tff(f380,plain,(
% 0.22/0.28 $false | (~spl3_1 | spl3_10)),
% 0.22/0.28 inference(evaluation,[],[f379])).
% 0.22/0.28 tff(f381,plain,(
% 0.22/0.28 ~spl3_1 | spl3_10),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f380])).
% 0.22/0.28 tff(f382,plain,(
% 0.22/0.28 ( ! [X0 : $int] : ($less(X0,sK2) | ~$less(X0,4)) ) | ~spl3_2),
% 0.22/0.28 inference(resolution,[],[f92,f16])).
% 0.22/0.28 tff(f416,plain,(
% 0.22/0.28 ~$less(1,4) | (~spl3_2 | spl3_8)),
% 0.22/0.28 inference(resolution,[],[f382,f282])).
% 0.22/0.28 tff(f420,plain,(
% 0.22/0.28 $false | (~spl3_2 | spl3_8)),
% 0.22/0.28 inference(evaluation,[],[f416])).
% 0.22/0.28 tff(f421,plain,(
% 0.22/0.28 ~spl3_2 | spl3_8),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f420])).
% 0.22/0.28 cnf(s2, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f94])).
% 0.22/0.28 cnf(s12, plain, ~spl3_7 | ~spl3_8, inference(sat_conversion,[],[f283])).
% 0.22/0.28 cnf(s13, plain, spl3_7 | ~spl3_9 | ~spl3_10, inference(sat_conversion,[],[f294])).
% 0.22/0.28 cnf(s14, plain, ~spl3_2 | spl3_9, inference(sat_conversion,[],[f349])).
% 0.22/0.28 cnf(s15, plain, ~spl3_2 | spl3_10, inference(sat_conversion,[],[f362])).
% 0.22/0.28 cnf(s16, plain, ~spl3_1 | spl3_9, inference(sat_conversion,[],[f367])).
% 0.22/0.28 cnf(s17, plain, ~spl3_1 | spl3_8, inference(sat_conversion,[],[f375])).
% 0.22/0.28 cnf(s18, plain, ~spl3_1 | spl3_10, inference(sat_conversion,[],[f381])).
% 0.22/0.28 cnf(s19, plain, ~spl3_2 | spl3_8, inference(sat_conversion,[],[f421])).
% 0.22/0.28 cnf(s22, plain, ~spl3_2, inference(rat,[],[s13,s12,s14,s15,s19])).
% 0.22/0.28 cnf(s23, plain, spl3_1, inference(rat,[],[s2,s22])).
% 0.22/0.28 cnf(s24, plain, spl3_10, inference(rat,[],[s18,s23])).
% 0.22/0.28 cnf(s25, plain, spl3_8, inference(rat,[],[s17,s23])).
% 0.22/0.28 cnf(s26, plain, spl3_9, inference(rat,[],[s16,s23])).
% 0.22/0.28 cnf(s27, plain, ~spl3_7, inference(rat,[],[s12,s25])).
% 0.22/0.28 cnf(s28, plain, $false, inference(rat,[],[s13,s24,s27,s26])).
% 0.22/0.28 tff(f422,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(avatar_sat_refutation,[],[s28])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (2784767)------------------------------
% 0.22/0.28 % (2784767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (2784767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (2784767)CaDiCaL version: 2.1.3
% 0.22/0.28 % (2784767)Termination reason: Refutation
% 0.22/0.28 % (2784767)Time elapsed: 0.013 s
% 0.22/0.28 % (2784767)Peak memory usage: 13 MB
% 0.22/0.28 % (2784767)Instructions burned: 17 (million)
% 0.22/0.28 % (2784758)Success in time 0.053 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------