%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT033_1 : TPTP v9.3.1. Released v5.0.0.
% 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 : Tue Sep 29 09:48:00 AM UTC 2026
% Result : Theorem 0.38s 0.29s
% Output : Refutation 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT033_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 00:05:53 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.38/0.29 % (913235)Will run a generic schedule for satisfiability detection.
% 0.38/0.29 % (913241)% WARNING: option uhcvi not known.
% 0.38/0.29 % (913240)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1260630300_3000 on theBenchmark for (3000ds/0Mi)
% 0.38/0.29 % (913240)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.38/0.29 % (913240)Terminated due to inappropriate strategy.
% 0.38/0.29 % (913240)------------------------------
% 0.38/0.29 % (913240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.29 % (913240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.29 % (913240)CaDiCaL version: 2.1.3
% 0.38/0.29 % (913240)Termination reason: Inappropriate
% 0.38/0.29 % (913240)Time elapsed: 0.0000 s
% 0.38/0.29 % (913240)Peak memory usage: 11 MB
% 0.38/0.29 % (913240)Instructions burned: 1 (million)
% 0.38/0.29 % (913242)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=762144526:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.38/0.29 % (913240)------------------------------
% 0.38/0.29 % (913240)------------------------------
% 0.38/0.29 % (913245)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=642991368:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.38/0.29 % (913243)dis+10_1_sil=32000:sp=arity:random_seed=793236989:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.38/0.29 % (913244)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2211808417:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.38/0.29 % (913246)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=22705613:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.38/0.29 % (913241)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3987570682:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.38/0.29 % (913251)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3111365058:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.38/0.29 % (913251)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.38/0.29 % (913251)Terminated due to inappropriate strategy.
% 0.38/0.29 % (913251)------------------------------
% 0.38/0.29 % (913251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.29 % (913251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.29 % (913251)CaDiCaL version: 2.1.3
% 0.38/0.29 % (913251)Termination reason: Inappropriate
% 0.38/0.29 % (913251)Time elapsed: 0.0000 s
% 0.38/0.29 % (913251)Peak memory usage: 10 MB
% 0.38/0.29 % (913251)Instructions burned: 1 (million)
% 0.38/0.29 % (913251)------------------------------
% 0.38/0.29 % (913251)------------------------------
% 0.38/0.29 % (913256)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1415091335:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.38/0.29 % (913241) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-913235-913241"...
% 0.38/0.29 % (913241)...printing done.
% 0.38/0.29 % (913241)Refutation found. Thanks to Tanya!
% 0.38/0.29 % SZS status Theorem for theBenchmark
% 0.38/0.29 % SZS output start Proof for theBenchmark
% 0.38/0.29 tff(type_def_5, type, collection: $tType).
% 0.38/0.29 tff(func_def_0, type, empty: collection).
% 0.38/0.29 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.38/0.29 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.38/0.29 tff(func_def_3, type, count: collection > $int).
% 0.38/0.29 tff(func_def_11, type, sK0: collection).
% 0.38/0.29 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.38/0.29 tff(f9,axiom,(
% 0.38/0.29 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(add(X0,X1)) = count(X1))),
% 0.38/0.29 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax4)).
% 0.38/0.29 tff(f10,axiom,(
% 0.38/0.29 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $difference(count(X1),1))),
% 0.38/0.29 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax5)).
% 0.38/0.29 tff(f11,axiom,(
% 0.38/0.29 ! [X0 : $int,X1 : collection] : (~in(X0,X1) <=> count(remove(X0,X1)) = count(X1))),
% 0.38/0.29 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax6)).
% 0.38/0.29 tff(f13,conjecture,(
% 0.38/0.29 ! [X0 : collection] : (count(add(5,X0)) = count(add(3,X0)) => count(remove(5,X0)) = count(remove(3,X0)))),
% 0.38/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1)).
% 0.38/0.29 tff(f14,negated_conjecture,(
% 0.38/0.29 ~ ! [X0 : collection] : (count(add(5,X0)) = count(add(3,X0)) => count(remove(5,X0)) = count(remove(3,X0)))),
% 0.38/0.29 inference(negated_conjecture,[status(cth)],[f13])).
% 0.38/0.29 tff(f16,plain,(
% 0.38/0.29 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $sum(count(X1),$uminus(1)))),
% 0.38/0.29 inference(theory_normalization,[],[f10])).
% 0.38/0.29 tff(f17,definition,(
% 0.38/0.29 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.38/0.29 introduced(theory,[tha_commutativity])).
% 0.38/0.29 tff(f30,plain,(
% 0.38/0.29 ? [X0 : collection] : (count(remove(5,X0)) != count(remove(3,X0)) & count(add(5,X0)) = count(add(3,X0)))),
% 0.38/0.29 inference(ennf_transformation,[],[f14])).
% 0.38/0.29 tff(f45,plain,(
% 0.38/0.29 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) != count(X1) | in(X0,X1)) )),
% 0.38/0.29 inference(cnf_transformation,[],[f9])).
% 0.38/0.29 tff(f46,plain,(
% 0.38/0.29 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(add(X0,X1)) = count(X1)) )),
% 0.38/0.29 inference(cnf_transformation,[],[f9])).
% 0.38/0.29 tff(f48,plain,(
% 0.38/0.29 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)) )),
% 0.38/0.29 inference(cnf_transformation,[],[f16])).
% 0.38/0.29 tff(f50,plain,(
% 0.38/0.29 ( ! [X0 : $int,X1 : collection] : (in(X0,X1) | count(X1) = count(remove(X0,X1))) )),
% 0.38/0.29 inference(cnf_transformation,[],[f11])).
% 0.38/0.29 tff(f52,plain,(
% 0.38/0.29 count(add(5,sK0)) = count(add(3,sK0))),
% 0.38/0.29 inference(cnf_transformation,[],[f30])).
% 0.38/0.29 tff(f53,plain,(
% 0.38/0.29 count(remove(5,sK0)) != count(remove(3,sK0))),
% 0.38/0.29 inference(cnf_transformation,[],[f30])).
% 0.38/0.29 tff(f58,plain,(
% 0.38/0.29 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),-1) | ~in(X0,X1)) )),
% 0.38/0.29 inference(evaluation,[],[f48])).
% 0.38/0.29 tff(f120,plain,(
% 0.38/0.29 count(add(3,sK0)) != count(sK0) | in(5,sK0)),
% 0.38/0.29 inference(superposition,[],[f45,f52])).
% 0.38/0.29 tff(f122,definition,(
% 0.38/0.29 spl1_3 <=> in(5,sK0)),
% 0.38/0.29 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.38/0.29 tff(f124,plain,(
% 0.38/0.29 in(5,sK0) | ~spl1_3),
% 0.38/0.29 inference(avatar_component_clause,[],[f122])).
% 0.38/0.29 tff(f126,definition,(
% 0.38/0.29 spl1_4 <=> count(add(3,sK0)) = count(sK0)),
% 0.38/0.29 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.38/0.29 tff(f127,plain,(
% 0.38/0.29 count(add(3,sK0)) = count(sK0) | ~spl1_4),
% 0.38/0.29 inference(avatar_component_clause,[],[f126])).
% 0.38/0.29 tff(f129,plain,(
% 0.38/0.29 spl1_3 | ~spl1_4),
% 0.38/0.29 inference(avatar_split_clause,[],[f120,f126,f122])).
% 0.38/0.29 tff(f141,plain,(
% 0.38/0.29 ( ! [X0 : collection,X1 : $int] : (count(X0) = count(remove(X1,X0)) | count(X0) = count(add(X1,X0))) )),
% 0.38/0.29 inference(resolution,[],[f50,f46])).
% 0.38/0.29 tff(f184,plain,(
% 0.38/0.29 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(remove(X0,X1)) = $sum(-1,count(X1))) )),
% 0.38/0.29 inference(forward_demodulation,[],[f58,f17])).
% 0.38/0.29 tff(f249,plain,(
% 0.38/0.29 count(remove(5,sK0)) = $sum(-1,count(sK0)) | ~spl1_3),
% 0.38/0.29 inference(resolution,[],[f124,f184])).
% 0.38/0.29 tff(f275,plain,(
% 0.38/0.29 count(sK0) != count(sK0) | in(3,sK0) | ~spl1_4),
% 0.38/0.29 inference(superposition,[],[f45,f127])).
% 0.38/0.29 tff(f278,plain,(
% 0.38/0.29 in(3,sK0) | ~spl1_4),
% 0.38/0.29 inference(trivial_inequality_removal,[],[f275])).
% 0.38/0.29 tff(f280,definition,(
% 0.38/0.29 spl1_9 <=> in(3,sK0)),
% 0.38/0.29 introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition])).
% 0.38/0.29 tff(f281,plain,(
% 0.38/0.29 in(3,sK0) | ~spl1_9),
% 0.38/0.29 inference(avatar_component_clause,[],[f280])).
% 0.38/0.29 tff(f305,plain,(
% 0.38/0.29 spl1_9 | ~spl1_4),
% 0.38/0.29 inference(avatar_split_clause,[],[f278,f126,f280])).
% 0.38/0.29 tff(f335,plain,(
% 0.38/0.29 count(remove(3,sK0)) = $sum(-1,count(sK0)) | ~spl1_9),
% 0.38/0.29 inference(resolution,[],[f281,f184])).
% 0.38/0.29 tff(f882,plain,(
% 0.38/0.29 count(remove(3,sK0)) != $sum(-1,count(sK0)) | ~spl1_3),
% 0.38/0.29 inference(superposition,[],[f53,f249])).
% 0.38/0.29 tff(f972,plain,(
% 0.38/0.29 count(remove(3,sK0)) != count(sK0) | count(add(5,sK0)) = count(sK0)),
% 0.38/0.29 inference(superposition,[],[f53,f141])).
% 0.38/0.29 tff(f1197,definition,(
% 0.38/0.29 spl1_15 <=> count(remove(3,sK0)) = $sum(-1,count(sK0))),
% 0.38/0.29 introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition])).
% 0.38/0.29 tff(f1226,plain,(
% 0.38/0.29 count(add(3,sK0)) = count(sK0) | count(remove(3,sK0)) != count(sK0)),
% 0.38/0.29 inference(forward_demodulation,[],[f972,f52])).
% 0.38/0.29 tff(f1232,plain,(
% 0.38/0.29 count(add(3,sK0)) = count(sK0)),
% 0.38/0.29 inference(forward_subsumption_resolution,[],[f1226,f141])).
% 0.38/0.29 tff(f1233,plain,(
% 0.38/0.29 spl1_4),
% 0.38/0.29 inference(avatar_split_clause,[],[f1232,f126])).
% 0.38/0.29 tff(f1247,plain,(
% 0.38/0.29 ~spl1_15 | ~spl1_3),
% 0.38/0.29 inference(avatar_split_clause,[],[f882,f122,f1197])).
% 0.38/0.29 tff(f1252,plain,(
% 0.38/0.29 spl1_15 | ~spl1_9),
% 0.38/0.29 inference(avatar_split_clause,[],[f335,f280,f1197])).
% 0.38/0.29 cnf(s2, plain, spl1_3 | ~spl1_4, inference(sat_conversion,[],[f129])).
% 0.38/0.29 cnf(s14, plain, ~spl1_4 | spl1_9, inference(sat_conversion,[],[f305])).
% 0.38/0.29 cnf(s60, plain, spl1_4, inference(sat_conversion,[],[f1233])).
% 0.38/0.29 cnf(s67, plain, ~spl1_3 | ~spl1_15, inference(sat_conversion,[],[f1247])).
% 0.38/0.29 cnf(s79, plain, ~spl1_9 | spl1_15, inference(sat_conversion,[],[f1252])).
% 0.38/0.29 cnf(s93, plain, spl1_9, inference(rat,[],[s14,s60])).
% 0.38/0.29 cnf(s94, plain, spl1_15, inference(rat,[],[s79,s93])).
% 0.38/0.29 cnf(s97, plain, ~spl1_3, inference(rat,[],[s67,s94])).
% 0.38/0.29 cnf(s103, plain, $false, inference(rat,[],[s2,s60,s97])).
% 0.38/0.29 tff(f1257,plain,(
% 0.38/0.29 $false),
% 0.38/0.29 inference(avatar_sat_refutation,[],[s103])).
% 0.38/0.29 % SZS output end Proof for theBenchmark
% 0.38/0.29 % (913241)------------------------------
% 0.38/0.29 % (913241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.29 % (913241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.29 % (913241)CaDiCaL version: 2.1.3
% 0.38/0.29 % (913241)Termination reason: Refutation
% 0.38/0.29 % (913241)Time elapsed: 0.039 s
% 0.38/0.29 % (913241)Peak memory usage: 13 MB
% 0.38/0.29 % (913241)Instructions burned: 58 (million)
% 0.38/0.29 % (913235)Success in time 0.064 s
% 0.38/0.29 % Vampire exiting
%------------------------------------------------------------------------------