%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT035_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 : n018.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 0.18s 0.31s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT035_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 00:08:26 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.18/0.31 % (3911003)Will run a generic schedule for satisfiability detection.
% 0.18/0.31 % (3911018)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=77710460:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.31 % (3911015)% WARNING: option uhcvi not known.
% 0.18/0.31 % (3911014)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2577420355_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.31 % (3911015)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2096503079:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.31 % (3911017)dis+10_1_sil=32000:sp=arity:random_seed=2697948405:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.31 % (3911016)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3701989148:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.31 % (3911014)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.31 % (3911019)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1161992809:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.31 % (3911014)Terminated due to inappropriate strategy.
% 0.18/0.31 % (3911014)------------------------------
% 0.18/0.31 % (3911014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (3911014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (3911014)CaDiCaL version: 2.1.3
% 0.18/0.31 % (3911014)Termination reason: Inappropriate
% 0.18/0.31 % (3911014)Time elapsed: 0.001 s
% 0.18/0.31 % (3911014)Peak memory usage: 10 MB
% 0.18/0.31 % (3911014)Instructions burned: 1 (million)
% 0.18/0.31 % (3911020)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=201043289:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.31 % (3911014)------------------------------
% 0.18/0.31 % (3911014)------------------------------
% 0.18/0.31 % (3911034)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2362699237:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.31 % (3911034)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.31 % (3911034)Terminated due to inappropriate strategy.
% 0.18/0.31 % (3911034)------------------------------
% 0.18/0.31 % (3911034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (3911034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (3911034)CaDiCaL version: 2.1.3
% 0.18/0.31 % (3911034)Termination reason: Inappropriate
% 0.18/0.31 % (3911034)Time elapsed: 0.001 s
% 0.18/0.31 % (3911034)Peak memory usage: 10 MB
% 0.18/0.31 % (3911034)Instructions burned: 1 (million)
% 0.18/0.31 % (3911034)------------------------------
% 0.18/0.31 % (3911034)------------------------------
% 0.18/0.31 % (3911018)Instruction limit reached!
% 0.18/0.31 % (3911018)------------------------------
% 0.18/0.31 % (3911018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (3911018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (3911018)CaDiCaL version: 2.1.3
% 0.18/0.31 % (3911018)Termination reason: Instruction limit
% 0.18/0.31 % (3911018)Termination phase: Saturation
% 0.18/0.31 % (3911018)Time elapsed: 0.039 s
% 0.18/0.31 % (3911018)Peak memory usage: 12 MB
% 0.18/0.31 % (3911018)Instructions burned: 116 (million)
% 0.18/0.31 % (3911045)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1305352422:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.31 % (3911049)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3149440662:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.18/0.31 % (3911015) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3911003-3911015"...
% 0.18/0.31 % (3911015)...printing done.
% 0.18/0.31 % (3911015)Refutation found. Thanks to Tanya!
% 0.18/0.31 % SZS status Theorem for theBenchmark
% 0.18/0.31 % SZS output start Proof for theBenchmark
% 0.18/0.31 tff(type_def_5, type, collection: $tType).
% 0.18/0.31 tff(func_def_0, type, empty: collection).
% 0.18/0.31 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.18/0.31 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.18/0.31 tff(func_def_3, type, count: collection > $int).
% 0.18/0.31 tff(func_def_9, type, sK0: collection).
% 0.18/0.31 tff(func_def_10, type, sK1: $int).
% 0.18/0.31 tff(func_def_11, type, sK2: $int).
% 0.18/0.31 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.18/0.31 tff(f8,axiom,(
% 0.18/0.31 ! [X0 : $int,X1 : collection] : (~in(X0,X1) <=> count(add(X0,X1)) = $sum(count(X1),1))),
% 0.18/0.31 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax3)).
% 0.18/0.31 tff(f9,axiom,(
% 0.18/0.31 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(add(X0,X1)) = count(X1))),
% 0.18/0.31 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax4)).
% 0.18/0.31 tff(f13,conjecture,(
% 0.18/0.31 ! [X0 : collection,X1 : $int,X2 : $int] : ($greater(X2,0) => $greatereq($sum(count(X0),X2),count(add(X1,X0))))),
% 0.18/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 0.18/0.31 tff(f14,negated_conjecture,(
% 0.18/0.31 ~ ! [X0 : collection,X1 : $int,X2 : $int] : ($greater(X2,0) => $greatereq($sum(count(X0),X2),count(add(X1,X0))))),
% 0.18/0.31 inference(negated_conjecture,[status(cth)],[f13])).
% 0.18/0.31 tff(f17,plain,(
% 0.18/0.31 ~ ! [X0 : collection,X1 : $int,X2 : $int] : ($less(0,X2) => ~$less($sum(count(X0),X2),count(add(X1,X0))))),
% 0.18/0.31 inference(theory_normalization,[],[f14])).
% 0.18/0.31 tff(f18,definition,(
% 0.18/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.18/0.31 introduced(theory,[tha_commutativity])).
% 0.18/0.31 tff(f23,definition,(
% 0.18/0.31 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 0.18/0.31 introduced(theory,[tha_non-reflexivity])).
% 0.18/0.31 tff(f24,definition,(
% 0.18/0.31 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 0.18/0.31 introduced(theory,[tha_transitivity])).
% 0.18/0.31 tff(f25,definition,(
% 0.18/0.31 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.18/0.31 introduced(theory,[tha_order_totality])).
% 0.18/0.31 tff(f26,definition,(
% 0.18/0.31 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | $less($sum(X0,X2),$sum(X1,X2))) )),
% 0.18/0.31 introduced(theory,[tha_order_monotonicity])).
% 0.18/0.31 tff(f29,definition,(
% 0.18/0.31 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 0.18/0.31 introduced(theory,[tha_extra_integer_ordering])).
% 0.18/0.31 tff(f31,plain,(
% 0.18/0.31 ? [X0 : collection,X1 : $int,X2 : $int] : ($less($sum(count(X0),X2),count(add(X1,X0))) & $less(0,X2))),
% 0.18/0.31 inference(ennf_transformation,[],[f17])).
% 0.18/0.31 tff(f45,plain,(
% 0.18/0.31 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(count(X1),1) | in(X0,X1)) )),
% 0.18/0.31 inference(cnf_transformation,[],[f8])).
% 0.18/0.31 tff(f47,plain,(
% 0.18/0.31 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(add(X0,X1)) = count(X1)) )),
% 0.18/0.31 inference(cnf_transformation,[],[f9])).
% 0.18/0.31 tff(f53,plain,(
% 0.18/0.31 $less(0,sK2)),
% 0.18/0.31 inference(cnf_transformation,[],[f31])).
% 0.18/0.31 tff(f54,plain,(
% 0.18/0.31 $less($sum(count(sK0),sK2),count(add(sK1,sK0)))),
% 0.18/0.31 inference(cnf_transformation,[],[f31])).
% 0.18/0.31 tff(f95,plain,(
% 0.18/0.31 ( ! [X0 : $int] : (~$less(X0,$sum(count(sK0),sK2)) | $less(X0,count(add(sK1,sK0)))) )),
% 0.18/0.31 inference(resolution,[],[f24,f54])).
% 0.18/0.31 tff(f100,plain,(
% 0.18/0.31 ( ! [X0 : $int] : ($less(X0,count(add(sK1,sK0))) | ~$less(X0,$sum(sK2,count(sK0)))) )),
% 0.18/0.31 inference(forward_demodulation,[],[f95,f18])).
% 0.18/0.31 tff(f101,plain,(
% 0.18/0.31 ~$less(count(add(sK1,sK0)),$sum(sK2,count(sK0)))),
% 0.18/0.31 inference(resolution,[],[f100,f23])).
% 0.18/0.31 tff(f130,plain,(
% 0.18/0.31 ( ! [X0 : $int] : ($less($sum(0,X0),$sum(sK2,X0))) )),
% 0.18/0.31 inference(resolution,[],[f26,f53])).
% 0.18/0.31 tff(f139,plain,(
% 0.18/0.31 ( ! [X0 : $int] : ($less(X0,$sum(sK2,X0))) )),
% 0.18/0.31 inference(evaluation,[],[f130])).
% 0.18/0.31 tff(f143,plain,(
% 0.18/0.31 ~$less(sK2,1)),
% 0.18/0.31 inference(resolution,[],[f139,f29])).
% 0.18/0.31 tff(f150,plain,(
% 0.18/0.31 $less(1,sK2) | 1 = sK2),
% 0.18/0.31 inference(resolution,[],[f143,f25])).
% 0.18/0.31 tff(f153,definition,(
% 0.18/0.31 spl3_1 <=> 1 = sK2),
% 0.18/0.31 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.18/0.31 tff(f155,plain,(
% 0.18/0.31 1 = sK2 | ~spl3_1),
% 0.18/0.31 inference(avatar_component_clause,[],[f153])).
% 0.18/0.31 tff(f157,definition,(
% 0.18/0.31 spl3_2 <=> $less(1,sK2)),
% 0.18/0.31 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.18/0.31 tff(f159,plain,(
% 0.18/0.31 $less(1,sK2) | ~spl3_2),
% 0.18/0.31 inference(avatar_component_clause,[],[f157])).
% 0.18/0.31 tff(f161,plain,(
% 0.18/0.31 spl3_1 | spl3_2),
% 0.18/0.31 inference(avatar_split_clause,[],[f150,f157,f153])).
% 0.18/0.31 tff(f192,plain,(
% 0.18/0.31 ( ! [X0 : $int] : ($less($sum(1,X0),$sum(sK2,X0))) ) | ~spl3_2),
% 0.18/0.31 inference(resolution,[],[f159,f26])).
% 0.18/0.31 tff(f207,plain,(
% 0.18/0.31 ( ! [X0 : $int,X1 : collection] : (in(X0,X1) | count(add(X0,X1)) = $sum(1,count(X1))) )),
% 0.18/0.31 inference(forward_demodulation,[],[f45,f18])).
% 0.18/0.31 tff(f249,plain,(
% 0.18/0.31 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(1,count(X1)) | count(add(X0,X1)) = count(X1)) )),
% 0.18/0.31 inference(resolution,[],[f207,f47])).
% 0.18/0.31 tff(f1313,plain,(
% 0.18/0.31 ~$less($sum(1,count(sK0)),$sum(sK2,count(sK0))) | count(sK0) = count(add(sK1,sK0))),
% 0.18/0.31 inference(superposition,[],[f101,f249])).
% 0.18/0.31 tff(f1316,plain,(
% 0.18/0.31 $less($sum(count(sK0),sK2),$sum(1,count(sK0))) | count(sK0) = count(add(sK1,sK0))),
% 0.18/0.31 inference(superposition,[],[f54,f249])).
% 0.18/0.31 tff(f1329,plain,(
% 0.18/0.31 $less($sum(sK2,count(sK0)),$sum(1,count(sK0))) | count(sK0) = count(add(sK1,sK0))),
% 0.18/0.31 inference(forward_demodulation,[],[f1316,f18])).
% 0.18/0.31 tff(f1332,plain,(
% 0.18/0.31 count(sK0) = count(add(sK1,sK0)) | ~spl3_2),
% 0.18/0.31 inference(forward_subsumption_resolution,[],[f1313,f192])).
% 0.18/0.31 tff(f1338,definition,(
% 0.18/0.31 spl3_5 <=> count(sK0) = count(add(sK1,sK0))),
% 0.18/0.31 introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition])).
% 0.18/0.31 tff(f1340,plain,(
% 0.18/0.31 count(sK0) = count(add(sK1,sK0)) | ~spl3_5),
% 0.18/0.31 inference(avatar_component_clause,[],[f1338])).
% 0.18/0.31 tff(f1350,plain,(
% 0.18/0.31 spl3_5 | ~spl3_2),
% 0.18/0.31 inference(avatar_split_clause,[],[f1332,f157,f1338])).
% 0.18/0.31 tff(f1453,plain,(
% 0.18/0.31 ~$less(count(sK0),$sum(sK2,count(sK0))) | ~spl3_5),
% 0.18/0.31 inference(superposition,[],[f101,f1340])).
% 0.18/0.31 tff(f1484,plain,(
% 0.18/0.31 $false | ~spl3_5),
% 0.18/0.31 inference(forward_subsumption_resolution,[],[f1453,f139])).
% 0.18/0.31 tff(f1485,plain,(
% 0.18/0.31 ~spl3_5),
% 0.18/0.31 inference(avatar_contradiction_clause,[],[f1484])).
% 0.18/0.31 tff(f1498,definition,(
% 0.18/0.31 spl3_14 <=> $less($sum(sK2,count(sK0)),$sum(1,count(sK0)))),
% 0.18/0.31 introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition])).
% 0.18/0.31 tff(f1500,plain,(
% 0.18/0.31 $less($sum(sK2,count(sK0)),$sum(1,count(sK0))) | ~spl3_14),
% 0.18/0.31 inference(avatar_component_clause,[],[f1498])).
% 0.18/0.31 tff(f1506,plain,(
% 0.18/0.31 spl3_5 | spl3_14),
% 0.18/0.31 inference(avatar_split_clause,[],[f1329,f1498,f1338])).
% 0.18/0.31 tff(f1747,plain,(
% 0.18/0.31 $less($sum(1,count(sK0)),$sum(1,count(sK0))) | (~spl3_1 | ~spl3_14)),
% 0.18/0.31 inference(forward_demodulation,[],[f1500,f155])).
% 0.18/0.31 tff(f1748,plain,(
% 0.18/0.31 $false | (~spl3_1 | ~spl3_14)),
% 0.18/0.31 inference(forward_subsumption_resolution,[],[f1747,f23])).
% 0.18/0.31 tff(f1749,plain,(
% 0.18/0.31 ~spl3_1 | ~spl3_14),
% 0.18/0.31 inference(avatar_contradiction_clause,[],[f1748])).
% 0.18/0.31 cnf(s2, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f161])).
% 0.18/0.31 cnf(s7, plain, ~spl3_2 | spl3_5, inference(sat_conversion,[],[f1350])).
% 0.18/0.31 cnf(s12, plain, ~spl3_5, inference(sat_conversion,[],[f1485])).
% 0.18/0.31 cnf(s17, plain, spl3_5 | spl3_14, inference(sat_conversion,[],[f1506])).
% 0.18/0.31 cnf(s23, plain, ~spl3_1 | ~spl3_14, inference(sat_conversion,[],[f1749])).
% 0.18/0.31 cnf(s27, plain, spl3_14, inference(rat,[],[s17,s12])).
% 0.18/0.31 cnf(s29, plain, ~spl3_1, inference(rat,[],[s23,s27])).
% 0.18/0.31 cnf(s32, plain, ~spl3_2, inference(rat,[],[s7,s12])).
% 0.18/0.31 cnf(s34, plain, $false, inference(rat,[],[s2,s32,s29])).
% 0.18/0.31 tff(f1750,plain,(
% 0.18/0.31 $false),
% 0.18/0.31 inference(avatar_sat_refutation,[],[s34])).
% 0.18/0.31 % SZS output end Proof for theBenchmark
% 0.18/0.31 % (3911015)------------------------------
% 0.18/0.31 % (3911015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (3911015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (3911015)CaDiCaL version: 2.1.3
% 0.18/0.31 % (3911015)Termination reason: Refutation
% 0.18/0.31 % (3911015)Time elapsed: 0.048 s
% 0.18/0.31 % (3911015)Peak memory usage: 13 MB
% 0.18/0.31 % (3911015)Instructions burned: 71 (million)
% 0.18/0.31 % (3911003)Success in time 0.084 s
% 0.18/0.31 % Vampire exiting
%------------------------------------------------------------------------------