%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI601_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 09:34:56 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI601_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 20:56:32 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.19/0.27 % (3007682)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (3007694)% WARNING: option uhcvi not known.
% 0.19/0.27 % (3007694)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=737840134:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (3007693)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2489783451_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (3007695)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2760267199:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (3007696)dis+10_1_sil=32000:sp=arity:random_seed=3668261334:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (3007693)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.27 % (3007693)Terminated due to inappropriate strategy.
% 0.19/0.27 % (3007693)------------------------------
% 0.19/0.27 % (3007693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3007693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3007697)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3952340404:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (3007693)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3007693)Termination reason: Inappropriate
% 0.19/0.27 % (3007693)Time elapsed: 0.0000 s
% 0.19/0.27 % (3007693)Peak memory usage: 10 MB
% 0.19/0.27 % (3007699)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=960911086:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (3007698)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=491709325:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (3007693)------------------------------
% 0.19/0.27 % (3007693)------------------------------
% 0.19/0.27 % (3007694) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3007682-3007694"...
% 0.19/0.27 % (3007694)...printing done.
% 0.19/0.27 % (3007694)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 tff(func_def_0, type, a: $int).
% 0.19/0.27 tff(func_def_1, type, f: $int > $int).
% 0.19/0.27 tff(f1,conjecture,(
% 0.19/0.27 ! [X0 : $int] : $greater(f(X0),X0) => ($less(3,a) => $less(4,f($sum(a,1))))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fX_gt_X_implies_ineq)).
% 0.19/0.27 tff(f2,negated_conjecture,(
% 0.19/0.27 ~(! [X0 : $int] : $greater(f(X0),X0) => ($less(3,a) => $less(4,f($sum(a,1)))))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.27 tff(f3,plain,(
% 0.19/0.27 ~(! [X0 : $int] : $less(X0,f(X0)) => ($less(3,a) => $less(4,f($sum(a,1)))))),
% 0.19/0.27 inference(theory_normalization,[],[f2])).
% 0.19/0.27 tff(f4,definition,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.19/0.27 introduced(theory,[tha_commutativity])).
% 0.19/0.27 tff(f10,definition,(
% 0.19/0.27 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 0.19/0.27 introduced(theory,[tha_transitivity])).
% 0.19/0.27 tff(f12,definition,(
% 0.19/0.27 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
% 0.19/0.27 introduced(theory,[tha_order_monotonicity])).
% 0.19/0.27 tff(f13,definition,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 0.19/0.27 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.19/0.27 tff(f15,definition,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 0.19/0.27 introduced(theory,[tha_extra_integer_ordering])).
% 0.19/0.27 tff(f16,plain,(
% 0.19/0.27 (~$less(4,f($sum(a,1))) & $less(3,a)) & ! [X0 : $int] : $less(X0,f(X0))),
% 0.19/0.27 inference(ennf_transformation,[],[f3])).
% 0.19/0.27 tff(f17,plain,(
% 0.19/0.27 ~$less(4,f($sum(a,1))) & $less(3,a) & ! [X0 : $int] : $less(X0,f(X0))),
% 0.19/0.27 inference(flattening,[],[f16])).
% 0.19/0.27 tff(f18,plain,(
% 0.19/0.27 ( ! [X0 : $int] : ($less(X0,f(X0))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f17])).
% 0.19/0.27 tff(f19,plain,(
% 0.19/0.27 $less(3,a)),
% 0.19/0.27 inference(cnf_transformation,[],[f17])).
% 0.19/0.27 tff(f20,plain,(
% 0.19/0.27 ~$less(4,f($sum(a,1)))),
% 0.19/0.27 inference(cnf_transformation,[],[f17])).
% 0.19/0.27 tff(f24,plain,(
% 0.19/0.27 ~$less(4,f($sum(1,a)))),
% 0.19/0.27 inference(superposition,[],[f20,f4])).
% 0.19/0.27 tff(f29,plain,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(1,X0)) | $less(X0,X1)) )),
% 0.19/0.27 inference(superposition,[],[f13,f4])).
% 0.19/0.27 tff(f35,plain,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : ($less(X0,f(X1)) | ~$less(X0,X1)) )),
% 0.19/0.27 inference(resolution,[],[f10,f18])).
% 0.19/0.27 tff(f59,plain,(
% 0.19/0.27 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | $less($sum(X0,X1),$sum(X2,X0))) )),
% 0.19/0.27 inference(superposition,[],[f12,f4])).
% 0.19/0.27 tff(f93,plain,(
% 0.19/0.27 ~$less(4,$sum(1,a))),
% 0.19/0.27 inference(resolution,[],[f35,f24])).
% 0.19/0.27 tff(f224,plain,(
% 0.19/0.27 $less(a,4)),
% 0.19/0.27 inference(resolution,[],[f93,f29])).
% 0.19/0.27 tff(f304,plain,(
% 0.19/0.27 ( ! [X0 : $int] : ($less($sum(X0,3),$sum(a,X0))) )),
% 0.19/0.27 inference(resolution,[],[f59,f19])).
% 0.19/0.27 tff(f962,plain,(
% 0.19/0.27 ~$less(a,$sum(1,3))),
% 0.19/0.27 inference(resolution,[],[f304,f15])).
% 0.19/0.27 tff(f986,plain,(
% 0.19/0.27 ~$less(a,4)),
% 0.19/0.27 inference(evaluation,[],[f962])).
% 0.19/0.27 tff(f998,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f986,f224])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (3007694)------------------------------
% 0.19/0.27 % (3007694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3007694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3007694)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3007694)Termination reason: Refutation
% 0.19/0.27 % (3007694)Time elapsed: 0.014 s
% 0.19/0.27 % (3007694)Peak memory usage: 12 MB
% 0.19/0.27 % (3007694)Instructions burned: 40 (million)
% 0.19/0.27 % (3007682)Success in time 0.045 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------