%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT045_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 : n012.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 09:48:01 AM UTC 2026
% Result : Theorem 0.08s 0.17s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : DAT045_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 00:06:51 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.12 Running first-order model finding
% 0.08/0.12 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
% 0.08/0.17 % (3916856)Will run a generic schedule for satisfiability detection.
% 0.08/0.17 % (3916862)% WARNING: option uhcvi not known.
% 0.08/0.17 % (3916865)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3753500341:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.17 % (3916861)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=454063645_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.17 % (3916863)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1220649811:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.17 % (3916864)dis+10_1_sil=32000:sp=arity:random_seed=3700716813:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.17 % (3916862)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=399131284:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.17 % (3916866)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2758267304:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.17 % (3916867)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2456037719:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.17 % (3916861)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.08/0.17 % (3916861)Terminated due to inappropriate strategy.
% 0.08/0.17 % (3916861)------------------------------
% 0.08/0.17 % (3916861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (3916861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (3916861)CaDiCaL version: 2.1.3
% 0.08/0.17 % (3916861)Termination reason: Inappropriate
% 0.08/0.17 % (3916861)Time elapsed: 0.0000 s
% 0.08/0.17 % (3916861)Peak memory usage: 10 MB
% 0.08/0.17 % (3916861)Instructions burned: 1 (million)
% 0.08/0.17 % (3916861)------------------------------
% 0.08/0.17 % (3916861)------------------------------
% 0.08/0.17 % (3916862) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3916856-3916862"...
% 0.08/0.17 % (3916866) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3916856-3916866"...
% 0.08/0.17 % (3916862)...printing done.
% 0.08/0.17 % (3916862)Refutation found. Thanks to Tanya!
% 0.08/0.17 % SZS status Theorem for theBenchmark
% 0.08/0.17 % SZS output start Proof for theBenchmark
% 0.08/0.17 tff(type_def_5, type, collection: $tType).
% 0.08/0.17 tff(func_def_0, type, empty: collection).
% 0.08/0.17 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.08/0.17 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.08/0.17 tff(func_def_3, type, count: collection > $int).
% 0.08/0.17 tff(func_def_9, type, sK0: collection).
% 0.08/0.17 tff(func_def_10, type, sK1: $int).
% 0.08/0.17 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.08/0.17 tff(f8,axiom,(
% 0.08/0.17 ! [X0 : $int,X1 : collection] : (~in(X0,X1) <=> count(add(X0,X1)) = $sum(count(X1),1))),
% 0.08/0.17 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax3)).
% 0.08/0.17 tff(f13,conjecture,(
% 0.08/0.17 ! [X0 : collection,X1 : $int] : (! [X2 : $int] : (in(X2,X0) => $greater(X1,X2)) => $greater(count(add(X1,X0)),count(X0)))),
% 0.08/0.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1)).
% 0.08/0.17 tff(f14,negated_conjecture,(
% 0.08/0.17 ~ ! [X0 : collection,X1 : $int] : (! [X2 : $int] : (in(X2,X0) => $greater(X1,X2)) => $greater(count(add(X1,X0)),count(X0)))),
% 0.08/0.17 inference(negated_conjecture,[status(cth)],[f13])).
% 0.08/0.17 tff(f17,plain,(
% 0.08/0.17 ~ ! [X0 : collection,X1 : $int] : (! [X2 : $int] : (in(X2,X0) => $less(X2,X1)) => $less(count(X0),count(add(X1,X0))))),
% 0.08/0.17 inference(theory_normalization,[],[f14])).
% 0.08/0.17 tff(f18,definition,(
% 0.08/0.17 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.08/0.17 introduced(theory,[tha_commutativity])).
% 0.08/0.17 tff(f23,definition,(
% 0.08/0.17 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 0.08/0.17 introduced(theory,[tha_non-reflexivity])).
% 0.08/0.17 tff(f27,definition,(
% 0.08/0.17 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 0.08/0.17 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.08/0.17 tff(f31,plain,(
% 0.08/0.17 ? [X0 : collection,X1 : $int] : (~$less(count(X0),count(add(X1,X0))) & ! [X2 : $int] : ($less(X2,X1) | ~in(X2,X0)))),
% 0.08/0.17 inference(ennf_transformation,[],[f17])).
% 0.08/0.17 tff(f45,plain,(
% 0.08/0.17 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(count(X1),1) | in(X0,X1)) )),
% 0.08/0.17 inference(cnf_transformation,[],[f8])).
% 0.08/0.17 tff(f53,plain,(
% 0.08/0.17 ( ! [X2 : $int] : (~in(X2,sK0) | $less(X2,sK1)) )),
% 0.08/0.17 inference(cnf_transformation,[],[f31])).
% 0.08/0.17 tff(f54,plain,(
% 0.08/0.17 ~$less(count(sK0),count(add(sK1,sK0)))),
% 0.08/0.17 inference(cnf_transformation,[],[f31])).
% 0.08/0.17 tff(f73,plain,(
% 0.08/0.17 ( ! [X0 : $int] : ($less(X0,$sum(X0,1))) )),
% 0.08/0.17 inference(resolution,[],[f27,f23])).
% 0.08/0.17 tff(f84,plain,(
% 0.08/0.17 ( ! [X0 : $int] : ($less(X0,$sum(1,X0))) )),
% 0.08/0.17 inference(superposition,[],[f73,f18])).
% 0.08/0.17 tff(f198,plain,(
% 0.08/0.17 ( ! [X0 : $int,X1 : collection] : (in(X0,X1) | count(add(X0,X1)) = $sum(1,count(X1))) )),
% 0.08/0.17 inference(forward_demodulation,[],[f45,f18])).
% 0.08/0.17 tff(f222,plain,(
% 0.08/0.17 ( ! [X0 : $int] : ($less(X0,sK1) | count(add(X0,sK0)) = $sum(1,count(sK0))) )),
% 0.08/0.17 inference(resolution,[],[f198,f53])).
% 0.08/0.17 tff(f239,plain,(
% 0.08/0.17 count(add(sK1,sK0)) = $sum(1,count(sK0))),
% 0.08/0.17 inference(resolution,[],[f222,f23])).
% 0.08/0.17 tff(f271,plain,(
% 0.08/0.17 ~$less(count(sK0),$sum(1,count(sK0)))),
% 0.08/0.17 inference(superposition,[],[f54,f239])).
% 0.08/0.17 tff(f288,plain,(
% 0.08/0.17 $false),
% 0.08/0.17 inference(forward_subsumption_resolution,[],[f271,f84])).
% 0.08/0.17 % SZS output end Proof for theBenchmark
% 0.08/0.17 % (3916862)------------------------------
% 0.08/0.17 % (3916862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (3916862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (3916862)CaDiCaL version: 2.1.3
% 0.08/0.17 % (3916862)Termination reason: Refutation
% 0.08/0.17 % (3916862)Time elapsed: 0.005 s
% 0.08/0.17 % (3916862)Peak memory usage: 12 MB
% 0.08/0.17 % (3916862)Instructions burned: 11 (million)
% 0.08/0.17 % (3916856)Success in time 0.036 s
% 0.08/0.17 % Vampire exiting
%------------------------------------------------------------------------------