%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT023_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 : n002.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 09:47:58 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT023_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 00:08:23 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.08/0.24 % (908376)Will run a generic schedule for satisfiability detection.
% 0.08/0.24 % (908382)% WARNING: option uhcvi not known.
% 0.08/0.24 % (908382)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=279142094:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.24 % (908381)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1688217614_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.24 % (908381)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.08/0.24 % (908381)Terminated due to inappropriate strategy.
% 0.08/0.24 % (908381)------------------------------
% 0.08/0.24 % (908381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (908381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (908381)CaDiCaL version: 2.1.3
% 0.08/0.24 % (908381)Termination reason: Inappropriate
% 0.08/0.24 % (908381)Time elapsed: 0.001 s
% 0.08/0.24 % (908383)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2587879732:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.24 % (908384)dis+10_1_sil=32000:sp=arity:random_seed=4284556512:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.24 % (908385)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=243238862:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.24 % (908386)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2403837412:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.24 % (908381)Peak memory usage: 10 MB
% 0.08/0.24 % (908387)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3708679950:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.24 % (908381)------------------------------
% 0.08/0.24 % (908381)------------------------------
% 0.08/0.24 % (908386) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-908376-908386"...
% 0.08/0.24 % (908382) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-908376-908382"...
% 0.08/0.24 % (908386)...printing done.
% 0.08/0.24 % (908382)...printing done.
% 0.08/0.24 % (908382)Refutation found. Thanks to Tanya!
% 0.08/0.24 % SZS status Theorem for theBenchmark
% 0.08/0.24 % SZS output start Proof for theBenchmark
% 0.08/0.24 tff(type_def_5, type, collection: $tType).
% 0.08/0.24 tff(func_def_0, type, empty: collection).
% 0.08/0.24 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.08/0.24 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.08/0.24 tff(func_def_9, type, sK0: collection).
% 0.08/0.24 tff(func_def_10, type, sK1: collection).
% 0.08/0.24 tff(func_def_11, type, sK2: $int).
% 0.08/0.24 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.08/0.24 tff(f3,axiom,(
% 0.08/0.24 ! [X0 : $int,X1 : collection] : ~in(X0,remove(X0,X1))),
% 0.08/0.24 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax3)).
% 0.08/0.24 tff(f5,axiom,(
% 0.08/0.24 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) & X0 != X2) <=> in(X0,remove(X2,X1)))),
% 0.08/0.24 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax5)).
% 0.08/0.24 tff(f6,conjecture,(
% 0.08/0.24 ! [X0 : collection,X1 : collection] : ((! [X2 : $int] : (in(X2,X1) => $greater(X2,0)) & X0 = remove(4,remove(1,remove(2,X1)))) => ! [X3 : $int] : (in(X3,X0) => $greater(X3,2)))),
% 0.08/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1)).
% 0.08/0.24 tff(f7,negated_conjecture,(
% 0.08/0.24 ~ ! [X0 : collection,X1 : collection] : ((! [X2 : $int] : (in(X2,X1) => $greater(X2,0)) & X0 = remove(4,remove(1,remove(2,X1)))) => ! [X3 : $int] : (in(X3,X0) => $greater(X3,2)))),
% 0.08/0.24 inference(negated_conjecture,[status(cth)],[f6])).
% 0.08/0.24 tff(f8,plain,(
% 0.08/0.24 ~ ! [X0 : collection,X1 : collection] : ((! [X2 : $int] : (in(X2,X1) => $less(0,X2)) & X0 = remove(4,remove(1,remove(2,X1)))) => ! [X3 : $int] : (in(X3,X0) => $less(2,X3)))),
% 0.08/0.24 inference(theory_normalization,[],[f7])).
% 0.08/0.24 tff(f9,definition,(
% 0.08/0.24 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.08/0.24 introduced(theory,[tha_commutativity])).
% 0.08/0.24 tff(f10,definition,(
% 0.08/0.24 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.08/0.24 introduced(theory,[tha_associativity])).
% 0.08/0.24 tff(f13,definition,(
% 0.08/0.24 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.08/0.24 introduced(theory,[tha_inverse_op_unit])).
% 0.08/0.24 tff(f16,definition,(
% 0.08/0.24 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.08/0.24 introduced(theory,[tha_order_totality])).
% 0.08/0.24 tff(f17,definition,(
% 0.08/0.24 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | $less($sum(X0,X2),$sum(X1,X2))) )),
% 0.08/0.24 introduced(theory,[tha_order_monotonicity])).
% 0.08/0.24 tff(f19,definition,(
% 0.08/0.24 ( ! [X0 : $int] : ($uminus($uminus(X0)) = X0) )),
% 0.08/0.24 introduced(theory,[tha_minus_minus_x])).
% 0.08/0.24 tff(f20,definition,(
% 0.08/0.24 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 0.08/0.24 introduced(theory,[tha_extra_integer_ordering])).
% 0.08/0.24 tff(f21,plain,(
% 0.08/0.24 ? [X0 : collection,X1 : collection] : (? [X3 : $int] : (~$less(2,X3) & in(X3,X0)) & (! [X2 : $int] : ($less(0,X2) | ~in(X2,X1)) & X0 = remove(4,remove(1,remove(2,X1)))))),
% 0.08/0.24 inference(ennf_transformation,[],[f8])).
% 0.08/0.24 tff(f22,plain,(
% 0.08/0.24 ? [X0 : collection,X1 : collection] : (? [X3 : $int] : (~$less(2,X3) & in(X3,X0)) & ! [X2 : $int] : ($less(0,X2) | ~in(X2,X1)) & X0 = remove(4,remove(1,remove(2,X1))))),
% 0.08/0.24 inference(flattening,[],[f21])).
% 0.08/0.24 tff(f25,plain,(
% 0.08/0.24 ( ! [X0 : $int,X1 : collection] : (~in(X0,remove(X0,X1))) )),
% 0.08/0.24 inference(cnf_transformation,[],[f3])).
% 0.08/0.24 tff(f31,plain,(
% 0.08/0.24 ( ! [X2 : $int,X0 : $int,X1 : collection] : (~in(X0,remove(X2,X1)) | in(X0,X1)) )),
% 0.08/0.24 inference(cnf_transformation,[],[f5])).
% 0.08/0.24 tff(f32,plain,(
% 0.08/0.24 in(sK2,sK0)),
% 0.08/0.24 inference(cnf_transformation,[],[f22])).
% 0.08/0.24 tff(f33,plain,(
% 0.08/0.24 ~$less(2,sK2)),
% 0.08/0.24 inference(cnf_transformation,[],[f22])).
% 0.08/0.24 tff(f34,plain,(
% 0.08/0.24 ( ! [X2 : $int] : (~in(X2,sK1) | $less(0,X2)) )),
% 0.08/0.24 inference(cnf_transformation,[],[f22])).
% 0.08/0.24 tff(f35,plain,(
% 0.08/0.24 sK0 = remove(4,remove(1,remove(2,sK1)))),
% 0.08/0.24 inference(cnf_transformation,[],[f22])).
% 0.08/0.24 tff(f39,plain,(
% 0.08/0.24 ( ! [X0 : $int] : (0 = $sum($uminus(X0),X0)) )),
% 0.08/0.24 inference(superposition,[],[f13,f19])).
% 0.08/0.24 tff(f71,plain,(
% 0.08/0.24 ( ! [X0 : $int] : (~in(X0,sK0) | in(X0,remove(1,remove(2,sK1)))) )),
% 0.08/0.24 inference(superposition,[],[f31,f35])).
% 0.08/0.24 tff(f77,plain,(
% 0.08/0.24 ( ! [X0 : $int,X1 : $int] : ($less($sum(X1,1),X0) | $sum(X1,1) = X0 | ~$less(X1,X0)) )),
% 0.08/0.24 inference(resolution,[],[f16,f20])).
% 0.08/0.24 tff(f98,plain,(
% 0.08/0.24 in(sK2,remove(1,remove(2,sK1)))),
% 0.08/0.24 inference(resolution,[],[f71,f32])).
% 0.08/0.24 tff(f99,plain,(
% 0.08/0.24 in(sK2,remove(2,sK1))),
% 0.08/0.24 inference(resolution,[],[f98,f31])).
% 0.08/0.24 tff(f112,plain,(
% 0.08/0.24 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum($uminus(X0),$sum(X0,X1))) )),
% 0.08/0.24 inference(superposition,[],[f10,f39])).
% 0.08/0.24 tff(f122,plain,(
% 0.08/0.24 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X2,$sum(X0,$sum(X1,1))) | ~$less($sum(X0,X1),X2)) )),
% 0.08/0.24 inference(superposition,[],[f20,f10])).
% 0.08/0.24 tff(f126,plain,(
% 0.08/0.24 ( ! [X0 : $int,X1 : $int] : ($sum($uminus(X0),$sum(X0,X1)) = X1) )),
% 0.08/0.24 inference(evaluation,[],[f112])).
% 0.08/0.24 tff(f130,plain,(
% 0.08/0.24 in(sK2,sK1)),
% 0.08/0.24 inference(resolution,[],[f99,f31])).
% 0.08/0.24 tff(f131,plain,(
% 0.08/0.24 $less(0,sK2)),
% 0.08/0.24 inference(resolution,[],[f130,f34])).
% 0.08/0.24 tff(f132,plain,(
% 0.08/0.24 ( ! [X0 : $int] : ($less($sum(0,X0),$sum(sK2,X0))) )),
% 0.08/0.24 inference(resolution,[],[f131,f17])).
% 0.08/0.24 tff(f134,plain,(
% 0.08/0.24 ( ! [X0 : $int] : ($less(X0,$sum(sK2,X0))) )),
% 0.08/0.24 inference(evaluation,[],[f132])).
% 0.08/0.24 tff(f153,definition,(
% 0.08/0.24 spl3_1 <=> 1 = sK2),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.08/0.24 tff(f155,plain,(
% 0.08/0.24 1 = sK2 | ~spl3_1),
% 0.08/0.24 inference(avatar_component_clause,[],[f153])).
% 0.08/0.24 tff(f592,plain,(
% 0.08/0.24 ( ! [X0 : $int] : (~$less($sum(sK2,X0),$sum(X0,1))) )),
% 0.08/0.24 inference(resolution,[],[f122,f134])).
% 0.08/0.24 tff(f709,plain,(
% 0.08/0.24 $sum(sK2,1) = $sum(1,1) | ~$less(sK2,$sum(1,1))),
% 0.08/0.24 inference(resolution,[],[f592,f77])).
% 0.08/0.24 tff(f729,plain,(
% 0.08/0.24 2 = $sum(sK2,1) | ~$less(sK2,2)),
% 0.08/0.24 inference(evaluation,[],[f709])).
% 0.08/0.24 tff(f736,plain,(
% 0.08/0.24 2 = $sum(1,sK2) | ~$less(sK2,2)),
% 0.08/0.24 inference(forward_demodulation,[],[f729,f9])).
% 0.08/0.24 tff(f738,definition,(
% 0.08/0.24 spl3_3 <=> $less(sK2,2)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.08/0.24 tff(f740,plain,(
% 0.08/0.24 ~$less(sK2,2) | spl3_3),
% 0.08/0.24 inference(avatar_component_clause,[],[f738])).
% 0.08/0.24 tff(f742,definition,(
% 0.08/0.24 spl3_4 <=> 2 = $sum(1,sK2)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.08/0.24 tff(f744,plain,(
% 0.08/0.24 2 = $sum(1,sK2) | ~spl3_4),
% 0.08/0.24 inference(avatar_component_clause,[],[f742])).
% 0.08/0.24 tff(f745,plain,(
% 0.08/0.24 ~spl3_3 | spl3_4),
% 0.08/0.24 inference(avatar_split_clause,[],[f736,f742,f738])).
% 0.08/0.24 tff(f786,plain,(
% 0.08/0.24 $less(2,sK2) | 2 = sK2 | spl3_3),
% 0.08/0.24 inference(resolution,[],[f740,f16])).
% 0.08/0.24 tff(f787,plain,(
% 0.08/0.24 2 = sK2 | spl3_3),
% 0.08/0.24 inference(forward_subsumption_resolution,[],[f786,f33])).
% 0.08/0.24 tff(f889,plain,(
% 0.08/0.24 in(2,remove(2,sK1)) | spl3_3),
% 0.08/0.24 inference(superposition,[],[f99,f787])).
% 0.08/0.24 tff(f912,plain,(
% 0.08/0.24 $false | spl3_3),
% 0.08/0.24 inference(forward_subsumption_resolution,[],[f889,f25])).
% 0.08/0.24 tff(f913,plain,(
% 0.08/0.24 spl3_3),
% 0.08/0.24 inference(avatar_contradiction_clause,[],[f912])).
% 0.08/0.24 tff(f1045,plain,(
% 0.08/0.24 sK2 = $sum($uminus(1),2) | ~spl3_4),
% 0.08/0.24 inference(superposition,[],[f126,f744])).
% 0.08/0.24 tff(f1081,plain,(
% 0.08/0.24 1 = sK2 | ~spl3_4),
% 0.08/0.24 inference(evaluation,[],[f1045])).
% 0.08/0.24 tff(f1095,plain,(
% 0.08/0.24 spl3_1 | ~spl3_4),
% 0.08/0.24 inference(avatar_split_clause,[],[f1081,f742,f153])).
% 0.08/0.24 tff(f1110,plain,(
% 0.08/0.24 in(1,remove(1,remove(2,sK1))) | ~spl3_1),
% 0.08/0.24 inference(superposition,[],[f98,f155])).
% 0.08/0.24 tff(f1142,plain,(
% 0.08/0.24 $false | ~spl3_1),
% 0.08/0.24 inference(forward_subsumption_resolution,[],[f1110,f25])).
% 0.08/0.24 tff(f1143,plain,(
% 0.08/0.24 ~spl3_1),
% 0.08/0.24 inference(avatar_contradiction_clause,[],[f1142])).
% 0.08/0.24 cnf(s3, plain, ~spl3_3 | spl3_4, inference(sat_conversion,[],[f745])).
% 0.08/0.24 cnf(s4, plain, spl3_3, inference(sat_conversion,[],[f913])).
% 0.08/0.24 cnf(s8, plain, spl3_1 | ~spl3_4, inference(sat_conversion,[],[f1095])).
% 0.08/0.24 cnf(s10, plain, ~spl3_1, inference(sat_conversion,[],[f1143])).
% 0.08/0.24 cnf(s11, plain, ~spl3_4, inference(rat,[],[s8,s10])).
% 0.08/0.24 cnf(s14, plain, $false, inference(rat,[],[s3,s11,s4])).
% 0.08/0.24 tff(f1144,plain,(
% 0.08/0.24 $false),
% 0.08/0.24 inference(avatar_sat_refutation,[],[s14])).
% 0.08/0.24 % SZS output end Proof for theBenchmark
% 0.08/0.24 % (908382)------------------------------
% 0.08/0.24 % (908382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (908382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (908382)CaDiCaL version: 2.1.3
% 0.08/0.24 % (908382)Termination reason: Refutation
% 0.08/0.24 % (908382)Time elapsed: 0.017 s
% 0.08/0.24 % (908382)Peak memory usage: 13 MB
% 0.08/0.24 % (908382)Instructions burned: 44 (million)
% 0.08/0.24 % (908376)Success in time 0.033 s
% 0.08/0.24 % Vampire exiting
%------------------------------------------------------------------------------