%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT034_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 : n007.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 0.52s 0.47s
% Output : Refutation 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT034_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.27 % Computer : n007.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 00:04:11 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.32 Running first-order model finding
% 0.26/0.32 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
% 0.52/0.47 % (2986606)Will run a generic schedule for satisfiability detection.
% 0.52/0.47 % (2986615)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=365231192:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.52/0.47 % (2986612)% WARNING: option uhcvi not known.
% 0.52/0.47 % (2986612)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=437928408:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.52/0.47 % (2986611)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=932025091_2999 on theBenchmark for (2999ds/0Mi)
% 0.52/0.47 % (2986611)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.52/0.47 % (2986611)Terminated due to inappropriate strategy.
% 0.52/0.47 % (2986611)------------------------------
% 0.52/0.47 % (2986611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.47 % (2986611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.47 % (2986613)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=405256293:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.52/0.47 % (2986611)CaDiCaL version: 2.1.3
% 0.52/0.47 % (2986611)Termination reason: Inappropriate
% 0.52/0.47 % (2986611)Time elapsed: 0.002 s
% 0.52/0.47 % (2986611)Peak memory usage: 11 MB
% 0.52/0.47 % (2986611)Instructions burned: 1 (million)
% 0.52/0.47 % (2986614)dis+10_1_sil=32000:sp=arity:random_seed=3741816898:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.52/0.47 % (2986616)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1357973145:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.52/0.47 % (2986611)------------------------------
% 0.52/0.47 % (2986611)------------------------------
% 0.52/0.47 % (2986617)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2109484644:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.52/0.47 % (2986625)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1639527192:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.52/0.47 % (2986625)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.52/0.47 % (2986625)Terminated due to inappropriate strategy.
% 0.52/0.47 % (2986625)------------------------------
% 0.52/0.47 % (2986625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.47 % (2986625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.47 % (2986625)CaDiCaL version: 2.1.3
% 0.52/0.47 % (2986625)Termination reason: Inappropriate
% 0.52/0.47 % (2986625)Time elapsed: 0.002 s
% 0.52/0.47 % (2986625)Peak memory usage: 10 MB
% 0.52/0.47 % (2986625)Instructions burned: 1 (million)
% 0.52/0.47 % (2986625)------------------------------
% 0.52/0.47 % (2986625)------------------------------
% 0.52/0.47 % (2986615)Instruction limit reached!
% 0.52/0.47 % (2986615)------------------------------
% 0.52/0.47 % (2986615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.47 % (2986615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.47 % (2986615)CaDiCaL version: 2.1.3
% 0.52/0.47 % (2986615)Termination reason: Instruction limit
% 0.52/0.47 % (2986615)Termination phase: Saturation
% 0.52/0.47 % (2986615)Time elapsed: 0.065 s
% 0.52/0.47 % (2986615)Peak memory usage: 13 MB
% 0.52/0.47 % (2986612) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2986606-2986612"...
% 0.52/0.47 % (2986615)Instructions burned: 122 (million)
% 0.52/0.47 % (2986614) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2986606-2986614"...
% 0.52/0.47 % (2986627)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3576257683:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.52/0.47 % (2986628)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=1261156626:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.52/0.47 % (2986612)...printing done.
% 0.52/0.47 % (2986614)...printing done.
% 0.52/0.47 % (2986612)Refutation found. Thanks to Tanya!
% 0.52/0.47 % SZS status Theorem for theBenchmark
% 0.52/0.47 % SZS output start Proof for theBenchmark
% 0.52/0.47 tff(type_def_5, type, collection: $tType).
% 0.52/0.47 tff(func_def_0, type, empty: collection).
% 0.52/0.47 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.52/0.47 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.52/0.47 tff(func_def_3, type, count: collection > $int).
% 0.52/0.47 tff(func_def_9, type, sK0: collection).
% 0.52/0.47 tff(func_def_10, type, sK1: $int).
% 0.52/0.47 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.52/0.47 tff(f8,axiom,(
% 0.52/0.47 ! [X0 : $int,X1 : collection] : (~in(X0,X1) <=> count(add(X0,X1)) = $sum(count(X1),1))),
% 0.52/0.47 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax3)).
% 0.52/0.47 tff(f9,axiom,(
% 0.52/0.47 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(add(X0,X1)) = count(X1))),
% 0.52/0.47 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax4)).
% 0.52/0.47 tff(f13,conjecture,(
% 0.52/0.47 ! [X0 : collection,X1 : $int] : $greatereq($sum(count(X0),1),count(add(X1,X0)))),
% 0.52/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 0.52/0.47 tff(f14,negated_conjecture,(
% 0.52/0.47 ~ ! [X0 : collection,X1 : $int] : $greatereq($sum(count(X0),1),count(add(X1,X0)))),
% 0.52/0.47 inference(negated_conjecture,[status(cth)],[f13])).
% 0.52/0.47 tff(f17,plain,(
% 0.52/0.47 ~ ! [X0 : collection,X1 : $int] : ~$less($sum(count(X0),1),count(add(X1,X0)))),
% 0.52/0.47 inference(theory_normalization,[],[f14])).
% 0.52/0.47 tff(f18,definition,(
% 0.52/0.47 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.52/0.47 introduced(theory,[tha_commutativity])).
% 0.52/0.47 tff(f19,definition,(
% 0.52/0.47 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.52/0.47 introduced(theory,[tha_associativity])).
% 0.52/0.47 tff(f22,definition,(
% 0.52/0.47 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.52/0.47 introduced(theory,[tha_inverse_op_unit])).
% 0.52/0.47 tff(f26,definition,(
% 0.52/0.47 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | $less($sum(X0,X2),$sum(X1,X2))) )),
% 0.52/0.47 introduced(theory,[tha_order_monotonicity])).
% 0.52/0.47 tff(f31,plain,(
% 0.52/0.47 ? [X0 : collection,X1 : $int] : $less($sum(count(X0),1),count(add(X1,X0)))),
% 0.52/0.47 inference(ennf_transformation,[],[f17])).
% 0.52/0.47 tff(f45,plain,(
% 0.52/0.47 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(count(X1),1) | in(X0,X1)) )),
% 0.52/0.47 inference(cnf_transformation,[],[f8])).
% 0.52/0.47 tff(f47,plain,(
% 0.52/0.47 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = count(X1) | ~in(X0,X1)) )),
% 0.52/0.47 inference(cnf_transformation,[],[f9])).
% 0.52/0.47 tff(f53,plain,(
% 0.52/0.47 $less($sum(count(sK0),1),count(add(sK1,sK0)))),
% 0.52/0.47 inference(cnf_transformation,[],[f31])).
% 0.52/0.47 tff(f66,plain,(
% 0.52/0.47 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(count(X1),1) | ~in(X0,X1)) )),
% 0.52/0.47 inference(consistent_polarity_flipping,[],[f45])).
% 0.52/0.47 tff(f68,plain,(
% 0.52/0.47 ( ! [X0 : $int,X1 : collection] : (in(X0,X1) | count(add(X0,X1)) = count(X1)) )),
% 0.52/0.47 inference(consistent_polarity_flipping,[],[f47])).
% 0.52/0.47 tff(f118,plain,(
% 0.52/0.47 ( ! [X0 : $int] : ($less($sum($sum(count(sK0),1),X0),$sum(count(add(sK1,sK0)),X0))) )),
% 0.52/0.47 inference(resolution,[],[f26,f53])).
% 0.52/0.47 tff(f124,plain,(
% 0.52/0.47 ( ! [X0 : $int] : ($less($sum($sum(1,count(sK0)),X0),$sum(count(add(sK1,sK0)),X0))) )),
% 0.52/0.47 inference(forward_demodulation,[],[f118,f18])).
% 0.52/0.47 tff(f145,plain,(
% 0.52/0.47 ( ! [X0 : $int,X1 : $int] : (0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1))))) )),
% 0.52/0.47 inference(superposition,[],[f19,f22])).
% 0.52/0.47 tff(f167,plain,(
% 0.52/0.47 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(add(X0,X1)) = $sum(1,count(X1))) )),
% 0.52/0.47 inference(forward_demodulation,[],[f66,f18])).
% 0.52/0.47 tff(f169,plain,(
% 0.52/0.47 ( ! [X0 : $int] : ($less($sum(1,$sum(count(sK0),X0)),$sum(count(add(sK1,sK0)),X0))) )),
% 0.52/0.47 inference(forward_demodulation,[],[f124,f19])).
% 0.52/0.47 tff(f173,plain,(
% 0.52/0.47 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(1,count(X1)) | count(add(X0,X1)) = count(X1)) )),
% 0.52/0.47 inference(resolution,[],[f167,f68])).
% 0.52/0.47 tff(f189,plain,(
% 0.52/0.47 $less($sum(1,0),$sum(count(add(sK1,sK0)),$uminus(count(sK0))))),
% 0.52/0.47 inference(superposition,[],[f169,f22])).
% 0.52/0.47 tff(f197,plain,(
% 0.52/0.47 $less(1,$sum(count(add(sK1,sK0)),$uminus(count(sK0))))),
% 0.52/0.47 inference(evaluation,[],[f189])).
% 0.52/0.47 tff(f199,plain,(
% 0.52/0.47 $less(1,$sum($uminus(count(sK0)),count(add(sK1,sK0))))),
% 0.52/0.47 inference(forward_demodulation,[],[f197,f18])).
% 0.52/0.47 tff(f394,plain,(
% 0.52/0.47 $less(0,$sum(count(add(sK1,sK0)),$uminus($sum(1,count(sK0)))))),
% 0.52/0.47 inference(superposition,[],[f169,f145])).
% 0.52/0.47 tff(f1092,plain,(
% 0.52/0.47 $less(0,$sum($sum(1,count(sK0)),$uminus($sum(1,count(sK0))))) | count(sK0) = count(add(sK1,sK0))),
% 0.52/0.47 inference(superposition,[],[f394,f173])).
% 0.52/0.47 tff(f1112,definition,(
% 0.52/0.47 spl2_1 <=> count(sK0) = count(add(sK1,sK0))),
% 0.52/0.47 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.52/0.47 tff(f1114,plain,(
% 0.52/0.47 count(sK0) = count(add(sK1,sK0)) | ~spl2_1),
% 0.52/0.47 inference(avatar_component_clause,[],[f1112])).
% 0.52/0.47 tff(f1134,plain,(
% 0.52/0.47 $less(0,0) | count(sK0) = count(add(sK1,sK0))),
% 0.52/0.47 inference(forward_demodulation,[],[f1092,f22])).
% 0.52/0.47 tff(f1135,plain,(
% 0.52/0.47 count(sK0) = count(add(sK1,sK0))),
% 0.52/0.47 inference(evaluation,[],[f1134])).
% 0.52/0.47 tff(f1169,plain,(
% 0.52/0.47 spl2_1),
% 0.52/0.47 inference(avatar_split_clause,[],[f1135,f1112])).
% 0.52/0.47 tff(f1229,plain,(
% 0.52/0.47 $less(1,$sum($uminus(count(sK0)),count(sK0))) | ~spl2_1),
% 0.52/0.47 inference(superposition,[],[f199,f1114])).
% 0.52/0.47 tff(f1276,plain,(
% 0.52/0.47 $less(1,$sum(count(sK0),$uminus(count(sK0)))) | ~spl2_1),
% 0.52/0.47 inference(forward_demodulation,[],[f1229,f18])).
% 0.52/0.47 tff(f1286,plain,(
% 0.52/0.47 $less(1,0) | ~spl2_1),
% 0.52/0.47 inference(forward_demodulation,[],[f1276,f22])).
% 0.52/0.47 tff(f1287,plain,(
% 0.52/0.47 $false | ~spl2_1),
% 0.52/0.47 inference(evaluation,[],[f1286])).
% 0.52/0.47 tff(f1288,plain,(
% 0.52/0.47 ~spl2_1),
% 0.52/0.47 inference(avatar_contradiction_clause,[],[f1287])).
% 0.52/0.47 cnf(s10, plain, spl2_1, inference(sat_conversion,[],[f1169])).
% 0.52/0.47 cnf(s27, plain, ~spl2_1, inference(sat_conversion,[],[f1288])).
% 0.52/0.47 cnf(s30, plain, $false, inference(rat,[],[s10,s27])).
% 0.52/0.47 tff(f1289,plain,(
% 0.52/0.47 $false),
% 0.52/0.47 inference(avatar_sat_refutation,[],[s30])).
% 0.52/0.47 % SZS output end Proof for theBenchmark
% 0.52/0.47 % (2986612)------------------------------
% 0.52/0.47 % (2986612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.47 % (2986612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.47 % (2986612)CaDiCaL version: 2.1.3
% 0.52/0.47 % (2986612)Termination reason: Refutation
% 0.52/0.47 % (2986612)Time elapsed: 0.101 s
% 0.52/0.47 % (2986612)Peak memory usage: 13 MB
% 0.52/0.47 % (2986612)Instructions burned: 53 (million)
% 0.52/0.47 % (2986606)Success in time 0.138 s
% 0.52/0.47 % Vampire exiting
%------------------------------------------------------------------------------