%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI183_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 09:34:09 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI183_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n010.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 : Mon Sep 28 20:44:47 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.19/0.28 % (2298797)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (2298806)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1745352004:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (2298803)% WARNING: option uhcvi not known.
% 0.19/0.28 % (2298802)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1031608672_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (2298803)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3434425236:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (2298804)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1191089949:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (2298805)dis+10_1_sil=32000:sp=arity:random_seed=49434506:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (2298802)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.28 % (2298802)Terminated due to inappropriate strategy.
% 0.19/0.28 % (2298802)------------------------------
% 0.19/0.28 % (2298802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (2298808)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=552962485:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (2298802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (2298807)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4262288809:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (2298802)CaDiCaL version: 2.1.3
% 0.19/0.28 % (2298802)Termination reason: Inappropriate
% 0.19/0.28 % (2298802)Time elapsed: 0.0000 s
% 0.19/0.28 % (2298802)Peak memory usage: 10 MB
% 0.19/0.28 % (2298802)------------------------------
% 0.19/0.28 % (2298802)------------------------------
% 0.19/0.28 % (2298805) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2298797-2298805"...
% 0.19/0.28 % (2298805)...printing done.
% 0.19/0.28 % (2298816)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3275394803:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.28 % (2298805)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% 0.19/0.28 tff(func_def_0, type, f: $int > $int).
% 0.19/0.28 tff(func_def_6, type, sK0: $int).
% 0.19/0.28 tff(f1,conjecture,(
% 0.19/0.28 ! [X0 : $int,X1 : $int] : ($less(X0,X1) => $less(f(X0),f(X1))) => ! [X2 : $int] : $greater(f($sum(f(X2),2)),f(f(X2)))),
% 0.19/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 0.19/0.28 tff(f2,negated_conjecture,(
% 0.19/0.28 ~(! [X0 : $int,X1 : $int] : ($less(X0,X1) => $less(f(X0),f(X1))) => ! [X2 : $int] : $greater(f($sum(f(X2),2)),f(f(X2))))),
% 0.19/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.28 tff(f3,plain,(
% 0.19/0.28 ~(! [X0 : $int,X1 : $int] : ($less(X0,X1) => $less(f(X0),f(X1))) => ! [X2 : $int] : $less(f(f(X2)),f($sum(f(X2),2))))),
% 0.19/0.28 inference(theory_normalization,[],[f2])).
% 0.19/0.28 tff(f4,definition,(
% 0.19/0.28 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.19/0.28 introduced(theory,[tha_commutativity])).
% 0.19/0.28 tff(f5,definition,(
% 0.19/0.28 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.19/0.28 introduced(theory,[tha_associativity])).
% 0.19/0.28 tff(f9,definition,(
% 0.19/0.28 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 0.19/0.28 introduced(theory,[tha_non-reflexivity])).
% 0.19/0.28 tff(f10,definition,(
% 0.19/0.28 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 0.19/0.28 introduced(theory,[tha_transitivity])).
% 0.19/0.28 tff(f13,definition,(
% 0.19/0.28 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 0.19/0.28 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.19/0.28 tff(f16,plain,(
% 0.19/0.28 ? [X2 : $int] : ~$less(f(f(X2)),f($sum(f(X2),2))) & ! [X0 : $int,X1 : $int] : ($less(f(X0),f(X1)) | ~$less(X0,X1))),
% 0.19/0.28 inference(ennf_transformation,[],[f3])).
% 0.19/0.28 tff(f17,plain,(
% 0.19/0.28 ? [X0 : $int] : ~$less(f(f(X0)),f($sum(f(X0),2))) & ! [X1 : $int,X2 : $int] : ($less(f(X1),f(X2)) | ~$less(X1,X2))),
% 0.19/0.28 inference(rectify,[],[f16])).
% 0.19/0.28 tff(f18,plain,(
% 0.19/0.28 ~$less(f(f(sK0)),f($sum(f(sK0),2))) & ! [X1 : $int,X2 : $int] : ($less(f(X1),f(X2)) | ~$less(X1,X2))),
% 0.19/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f17])).
% 0.19/0.28 tff(f19,plain,(
% 0.19/0.28 ( ! [X2 : $int,X1 : $int] : ($less(f(X1),f(X2)) | ~$less(X1,X2)) )),
% 0.19/0.28 inference(cnf_transformation,[],[f18])).
% 0.19/0.28 tff(f20,plain,(
% 0.19/0.28 ~$less(f(f(sK0)),f($sum(f(sK0),2)))),
% 0.19/0.28 inference(cnf_transformation,[],[f18])).
% 0.19/0.28 tff(f21,plain,(
% 0.19/0.28 ~$less(f(sK0),$sum(f(sK0),2))),
% 0.19/0.28 inference(resolution,[],[f20,f19])).
% 0.19/0.28 tff(f32,plain,(
% 0.19/0.28 ( ! [X0 : $int] : ($less(X0,$sum(X0,1))) )),
% 0.19/0.28 inference(resolution,[],[f13,f9])).
% 0.19/0.28 tff(f33,plain,(
% 0.19/0.28 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(1,X0)) | $less(X0,X1)) )),
% 0.19/0.28 inference(superposition,[],[f13,f4])).
% 0.19/0.28 tff(f39,plain,(
% 0.19/0.28 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,f(X1)) | $less(X0,f(X2)) | ~$less(X1,X2)) )),
% 0.19/0.28 inference(resolution,[],[f10,f19])).
% 0.19/0.28 tff(f46,plain,(
% 0.19/0.28 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X2,X1) | $less(f(X0),f(X1)) | ~$less(X0,X2)) )),
% 0.19/0.28 inference(resolution,[],[f39,f19])).
% 0.19/0.28 tff(f92,plain,(
% 0.19/0.28 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum(X1,$sum(X2,X0))) )),
% 0.19/0.28 inference(superposition,[],[f5,f4])).
% 0.19/0.28 tff(f112,plain,(
% 0.19/0.28 ( ! [X0 : $int,X1 : $int] : ($less(f(X0),f($sum(X1,1))) | ~$less(X0,X1)) )),
% 0.19/0.28 inference(resolution,[],[f32,f46])).
% 0.19/0.28 tff(f119,plain,(
% 0.19/0.28 ( ! [X0 : $int] : (~$less($sum(X0,1),X0)) )),
% 0.19/0.28 inference(resolution,[],[f112,f9])).
% 0.19/0.28 tff(f140,plain,(
% 0.19/0.28 ( ! [X0 : $int] : ($less(X0,$sum($sum(1,X0),1))) )),
% 0.19/0.28 inference(resolution,[],[f33,f119])).
% 0.19/0.28 tff(f146,plain,(
% 0.19/0.28 ( ! [X0 : $int] : ($less(X0,$sum(1,$sum(1,X0)))) )),
% 0.19/0.28 inference(forward_demodulation,[],[f140,f4])).
% 0.19/0.28 tff(f642,plain,(
% 0.19/0.28 ( ! [X0 : $int] : ($less(X0,$sum(X0,$sum(1,1)))) )),
% 0.19/0.28 inference(superposition,[],[f146,f92])).
% 0.19/0.28 tff(f657,plain,(
% 0.19/0.28 ( ! [X0 : $int] : ($less(X0,$sum(X0,2))) )),
% 0.19/0.28 inference(evaluation,[],[f642])).
% 0.19/0.28 tff(f708,plain,(
% 0.19/0.28 $false),
% 0.19/0.28 inference(resolution,[],[f657,f21])).
% 0.19/0.28 % SZS output end Proof for theBenchmark
% 0.19/0.28 % (2298805)------------------------------
% 0.19/0.28 % (2298805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (2298805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (2298805)CaDiCaL version: 2.1.3
% 0.19/0.28 % (2298805)Termination reason: Refutation
% 0.19/0.28 % (2298805)Time elapsed: 0.019 s
% 0.19/0.28 % (2298805)Peak memory usage: 12 MB
% 0.19/0.28 % (2298805)Instructions burned: 29 (million)
% 0.19/0.28 % (2298797)Success in time 0.058 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------