%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT024_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 09:47:58 AM UTC 2026
% Result : Theorem 0.17s 0.26s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT024_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.18 % Computer : n010.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 00:06:02 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.26 % (2478417)Will run a generic schedule for satisfiability detection.
% 0.17/0.26 % (2478422)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3704200004_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.26 % (2478422)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.17/0.26 % (2478422)Terminated due to inappropriate strategy.
% 0.17/0.26 % (2478422)------------------------------
% 0.17/0.26 % (2478422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.26 % (2478422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.26 % (2478422)CaDiCaL version: 2.1.3
% 0.17/0.26 % (2478422)Termination reason: Inappropriate
% 0.17/0.26 % (2478422)Time elapsed: 0.0000 s
% 0.17/0.26 % (2478422)Peak memory usage: 10 MB
% 0.17/0.26 % (2478422)------------------------------
% 0.17/0.26 % (2478422)------------------------------
% 0.17/0.26 % (2478423)% WARNING: option uhcvi not known.
% 0.17/0.26 % (2478423)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1884902285:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.26 % (2478426)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2963623609:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.26 % (2478424)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3191853687:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.26 % (2478425)dis+10_1_sil=32000:sp=arity:random_seed=2653987630:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.26 % (2478430)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1000495885:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.26 % (2478430)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.17/0.26 % (2478430)Terminated due to inappropriate strategy.
% 0.17/0.26 % (2478430)------------------------------
% 0.17/0.26 % (2478430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.26 % (2478430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.26 % (2478430)CaDiCaL version: 2.1.3
% 0.17/0.26 % (2478430)Termination reason: Inappropriate
% 0.17/0.26 % (2478430)Time elapsed: 0.0000 s
% 0.17/0.26 % (2478430)Peak memory usage: 10 MB
% 0.17/0.26 % (2478430)------------------------------
% 0.17/0.26 % (2478430)------------------------------
% 0.17/0.26 % (2478423) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2478417-2478423"...
% 0.17/0.26 % (2478423)...printing done.
% 0.17/0.26 % (2478423)Refutation found. Thanks to Tanya!
% 0.17/0.26 % SZS status Theorem for theBenchmark
% 0.17/0.26 % SZS output start Proof for theBenchmark
% 0.17/0.26 tff(type_def_5, type, collection: $tType).
% 0.17/0.26 tff(func_def_0, type, empty: collection).
% 0.17/0.26 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.17/0.26 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.17/0.26 tff(func_def_8, type, sK0: collection).
% 0.17/0.26 tff(func_def_9, type, sK1: $int).
% 0.17/0.26 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.17/0.26 tff(f6,conjecture,(
% 0.17/0.26 ! [X0 : collection] : ((! [X1 : $int] : (in(X1,X0) => $greatereq(X1,0)) & ~in(0,X0) & ~in(1,X0)) => ! [X2 : $int] : (in(X2,X0) => $greatereq(X2,2)))),
% 0.17/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 0.17/0.26 tff(f7,negated_conjecture,(
% 0.17/0.26 ~ ! [X0 : collection] : ((! [X1 : $int] : (in(X1,X0) => $greatereq(X1,0)) & ~in(0,X0) & ~in(1,X0)) => ! [X2 : $int] : (in(X2,X0) => $greatereq(X2,2)))),
% 0.17/0.26 inference(negated_conjecture,[status(cth)],[f6])).
% 0.17/0.26 tff(f8,plain,(
% 0.17/0.26 ~ ! [X0 : collection] : ((! [X1 : $int] : (in(X1,X0) => ~$less(X1,0)) & ~in(0,X0) & ~in(1,X0)) => ! [X2 : $int] : (in(X2,X0) => ~$less(X2,2)))),
% 0.17/0.26 inference(theory_normalization,[],[f7])).
% 0.17/0.26 tff(f9,definition,(
% 0.17/0.26 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.17/0.26 introduced(theory,[tha_commutativity])).
% 0.17/0.26 tff(f16,definition,(
% 0.17/0.26 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.17/0.26 introduced(theory,[tha_order_totality])).
% 0.17/0.26 tff(f20,definition,(
% 0.17/0.26 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 0.17/0.26 introduced(theory,[tha_extra_integer_ordering])).
% 0.17/0.26 tff(f21,plain,(
% 0.17/0.26 ? [X0 : collection] : (? [X2 : $int] : ($less(X2,2) & in(X2,X0)) & (! [X1 : $int] : (~$less(X1,0) | ~in(X1,X0)) & ~in(0,X0) & ~in(1,X0)))),
% 0.17/0.26 inference(ennf_transformation,[],[f8])).
% 0.17/0.26 tff(f22,plain,(
% 0.17/0.26 ? [X0 : collection] : (? [X2 : $int] : ($less(X2,2) & in(X2,X0)) & ! [X1 : $int] : (~$less(X1,0) | ~in(X1,X0)) & ~in(0,X0) & ~in(1,X0))),
% 0.17/0.26 inference(flattening,[],[f21])).
% 0.17/0.26 tff(f32,plain,(
% 0.17/0.26 in(sK1,sK0)),
% 0.17/0.26 inference(cnf_transformation,[],[f22])).
% 0.17/0.26 tff(f33,plain,(
% 0.17/0.26 $less(sK1,2)),
% 0.17/0.26 inference(cnf_transformation,[],[f22])).
% 0.17/0.26 tff(f34,plain,(
% 0.17/0.26 ( ! [X1 : $int] : (~$less(X1,0) | ~in(X1,sK0)) )),
% 0.17/0.26 inference(cnf_transformation,[],[f22])).
% 0.17/0.26 tff(f35,plain,(
% 0.17/0.26 ~in(1,sK0)),
% 0.17/0.26 inference(cnf_transformation,[],[f22])).
% 0.17/0.26 tff(f36,plain,(
% 0.17/0.26 ~in(0,sK0)),
% 0.17/0.26 inference(cnf_transformation,[],[f22])).
% 0.17/0.26 tff(f48,plain,(
% 0.17/0.26 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,$sum(1,X0))) )),
% 0.17/0.26 inference(superposition,[],[f20,f9])).
% 0.17/0.26 tff(f53,plain,(
% 0.17/0.26 ( ! [X0 : $int] : (~in(X0,sK0) | 0 = X0 | $less(0,X0)) )),
% 0.17/0.26 inference(resolution,[],[f16,f34])).
% 0.17/0.26 tff(f123,plain,(
% 0.17/0.26 0 = sK1 | $less(0,sK1)),
% 0.17/0.26 inference(resolution,[],[f53,f32])).
% 0.17/0.26 tff(f125,definition,(
% 0.17/0.26 spl2_1 <=> $less(0,sK1)),
% 0.17/0.26 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.17/0.26 tff(f127,plain,(
% 0.17/0.26 $less(0,sK1) | ~spl2_1),
% 0.17/0.26 inference(avatar_component_clause,[],[f125])).
% 0.17/0.26 tff(f129,definition,(
% 0.17/0.26 spl2_2 <=> 0 = sK1),
% 0.17/0.26 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.17/0.26 tff(f131,plain,(
% 0.17/0.26 0 = sK1 | ~spl2_2),
% 0.17/0.26 inference(avatar_component_clause,[],[f129])).
% 0.17/0.26 tff(f132,plain,(
% 0.17/0.26 spl2_1 | spl2_2),
% 0.17/0.26 inference(avatar_split_clause,[],[f123,f129,f125])).
% 0.17/0.26 tff(f137,plain,(
% 0.17/0.26 in(0,sK0) | ~spl2_2),
% 0.17/0.26 inference(superposition,[],[f32,f131])).
% 0.17/0.26 tff(f139,plain,(
% 0.17/0.26 $false | ~spl2_2),
% 0.17/0.26 inference(forward_subsumption_resolution,[],[f137,f36])).
% 0.17/0.26 tff(f140,plain,(
% 0.17/0.26 ~spl2_2),
% 0.17/0.26 inference(avatar_contradiction_clause,[],[f139])).
% 0.17/0.26 tff(f202,plain,(
% 0.17/0.26 ~$less(sK1,$sum(1,0)) | ~spl2_1),
% 0.17/0.26 inference(resolution,[],[f127,f48])).
% 0.17/0.26 tff(f206,plain,(
% 0.17/0.26 ~$less(sK1,1) | ~spl2_1),
% 0.17/0.26 inference(evaluation,[],[f202])).
% 0.17/0.26 tff(f291,plain,(
% 0.17/0.26 $less(1,sK1) | 1 = sK1 | ~spl2_1),
% 0.17/0.26 inference(resolution,[],[f206,f16])).
% 0.17/0.26 tff(f294,definition,(
% 0.17/0.26 spl2_3 <=> 1 = sK1),
% 0.17/0.26 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.17/0.27 tff(f296,plain,(
% 0.17/0.27 1 = sK1 | ~spl2_3),
% 0.17/0.27 inference(avatar_component_clause,[],[f294])).
% 0.17/0.27 tff(f298,definition,(
% 0.17/0.27 spl2_4 <=> $less(1,sK1)),
% 0.17/0.27 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.17/0.27 tff(f300,plain,(
% 0.17/0.27 $less(1,sK1) | ~spl2_4),
% 0.17/0.27 inference(avatar_component_clause,[],[f298])).
% 0.17/0.27 tff(f302,plain,(
% 0.17/0.27 spl2_3 | spl2_4 | ~spl2_1),
% 0.17/0.27 inference(avatar_split_clause,[],[f291,f125,f298,f294])).
% 0.17/0.27 tff(f304,plain,(
% 0.17/0.27 ~$less(sK1,$sum(1,1)) | ~spl2_4),
% 0.17/0.27 inference(resolution,[],[f300,f48])).
% 0.17/0.27 tff(f307,plain,(
% 0.17/0.27 ~$less(sK1,2) | ~spl2_4),
% 0.17/0.27 inference(evaluation,[],[f304])).
% 0.17/0.27 tff(f308,plain,(
% 0.17/0.27 $false | ~spl2_4),
% 0.17/0.27 inference(forward_subsumption_resolution,[],[f307,f33])).
% 0.17/0.27 tff(f309,plain,(
% 0.17/0.27 ~spl2_4),
% 0.17/0.27 inference(avatar_contradiction_clause,[],[f308])).
% 0.17/0.27 tff(f310,plain,(
% 0.17/0.27 in(1,sK0) | ~spl2_3),
% 0.17/0.27 inference(superposition,[],[f32,f296])).
% 0.17/0.27 tff(f318,plain,(
% 0.17/0.27 $false | ~spl2_3),
% 0.17/0.27 inference(forward_subsumption_resolution,[],[f310,f35])).
% 0.17/0.27 tff(f319,plain,(
% 0.17/0.27 ~spl2_3),
% 0.17/0.27 inference(avatar_contradiction_clause,[],[f318])).
% 0.17/0.27 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f132])).
% 0.17/0.27 cnf(s2, plain, ~spl2_2, inference(sat_conversion,[],[f140])).
% 0.17/0.27 cnf(s4, plain, ~spl2_1 | spl2_3 | spl2_4, inference(sat_conversion,[],[f302])).
% 0.17/0.27 cnf(s5, plain, ~spl2_4, inference(sat_conversion,[],[f309])).
% 0.17/0.27 cnf(s6, plain, ~spl2_3, inference(sat_conversion,[],[f319])).
% 0.17/0.27 cnf(s7, plain, ~spl2_1, inference(rat,[],[s4,s5,s6])).
% 0.17/0.27 cnf(s8, plain, $false, inference(rat,[],[s1,s2,s7])).
% 0.17/0.27 tff(f320,plain,(
% 0.17/0.27 $false),
% 0.17/0.27 inference(avatar_sat_refutation,[],[s8])).
% 0.17/0.27 % SZS output end Proof for theBenchmark
% 0.17/0.27 % (2478423)------------------------------
% 0.17/0.27 % (2478423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.27 % (2478423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.27 % (2478423)CaDiCaL version: 2.1.3
% 0.17/0.27 % (2478423)Termination reason: Refutation
% 0.17/0.27 % (2478423)Time elapsed: 0.011 s
% 0.17/0.27 % (2478423)Peak memory usage: 12 MB
% 0.17/0.27 % (2478423)Instructions burned: 11 (million)
% 0.17/0.27 % (2478417)Success in time 0.054 s
% 0.17/0.27 % Vampire exiting
%------------------------------------------------------------------------------