%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT028_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 : n017.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 09:47:59 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT028_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n017.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 : Tue Sep 29 00:01:21 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.21/0.29 % (4146589)Will run a generic schedule for satisfiability detection.
% 0.21/0.29 % (4146598)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2740846238:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.29 % (4146595)% WARNING: option uhcvi not known.
% 0.21/0.29 % (4146594)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1465695130_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.29 % (4146596)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2077106048:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.29 % (4146597)dis+10_1_sil=32000:sp=arity:random_seed=1466052110:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.29 % (4146595)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=62756191:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.29 % (4146594)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.29 % (4146594)Terminated due to inappropriate strategy.
% 0.21/0.29 % (4146594)------------------------------
% 0.21/0.29 % (4146594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (4146594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (4146594)CaDiCaL version: 2.1.3
% 0.21/0.29 % (4146594)Termination reason: Inappropriate
% 0.21/0.29 % (4146594)Time elapsed: 0.001 s
% 0.21/0.29 % (4146594)Peak memory usage: 10 MB
% 0.21/0.29 % (4146600)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3459007433:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.29 % (4146599)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3422292840:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.29 % (4146594)------------------------------
% 0.21/0.29 % (4146594)------------------------------
% 0.21/0.29 % (4146600) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4146589-4146600"...
% 0.21/0.29 % (4146600)...printing done.
% 0.21/0.29 % (4146600)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 tff(type_def_5, type, collection: $tType).
% 0.21/0.29 tff(func_def_0, type, empty: collection).
% 0.21/0.29 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.21/0.29 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.21/0.29 tff(func_def_7, type, sK0: collection).
% 0.21/0.29 tff(func_def_8, type, sK1: collection).
% 0.21/0.29 tff(func_def_9, type, sK2: $int).
% 0.21/0.29 tff(func_def_10, type, sK3: $int > $int).
% 0.21/0.29 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.21/0.29 tff(f6,conjecture,(
% 0.21/0.29 ! [X0 : collection,X1 : collection] : ((! [X2 : $int] : (in(X2,X1) => $greater(X2,0)) & ! [X3 : $int] : (in(X3,X0) => ? [X4 : $int] : (in(X4,X1) & $greater(X3,X4)))) => ! [X5 : $int] : (in(X5,X0) => $greater(X5,1)))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1)).
% 0.21/0.29 tff(f7,negated_conjecture,(
% 0.21/0.29 ~ ! [X0 : collection,X1 : collection] : ((! [X2 : $int] : (in(X2,X1) => $greater(X2,0)) & ! [X3 : $int] : (in(X3,X0) => ? [X4 : $int] : (in(X4,X1) & $greater(X3,X4)))) => ! [X5 : $int] : (in(X5,X0) => $greater(X5,1)))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f6])).
% 0.21/0.29 tff(f8,plain,(
% 0.21/0.29 ~ ! [X0 : collection,X1 : collection] : ((! [X2 : $int] : (in(X2,X1) => $less(0,X2)) & ! [X3 : $int] : (in(X3,X0) => ? [X4 : $int] : (in(X4,X1) & $less(X4,X3)))) => ! [X5 : $int] : (in(X5,X0) => $less(1,X5)))),
% 0.21/0.29 inference(theory_normalization,[],[f7])).
% 0.21/0.29 tff(f9,definition,(
% 0.21/0.29 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.21/0.29 introduced(theory,[tha_commutativity])).
% 0.21/0.29 tff(f11,definition,(
% 0.21/0.29 ( ! [X0 : $int] : ($sum(X0,0) = X0) )),
% 0.21/0.29 introduced(theory,[tha_right_identity])).
% 0.21/0.29 tff(f15,definition,(
% 0.21/0.29 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less(X0,X2) | ~$less(X1,X2) | ~$less(X0,X1)) )),
% 0.21/0.29 introduced(theory,[tha_transitivity])).
% 0.21/0.29 tff(f16,definition,(
% 0.21/0.29 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 0.21/0.29 introduced(theory,[tha_order_totality])).
% 0.21/0.29 tff(f18,definition,(
% 0.21/0.29 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 0.21/0.29 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.21/0.29 tff(f20,definition,(
% 0.21/0.29 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,$sum(X0,1))) )),
% 0.21/0.29 introduced(theory,[tha_extra_integer_ordering])).
% 0.21/0.29 tff(f21,plain,(
% 0.21/0.29 ? [X0 : collection,X1 : collection] : (? [X5 : $int] : (~$less(1,X5) & in(X5,X0)) & (! [X2 : $int] : ($less(0,X2) | ~in(X2,X1)) & ! [X3 : $int] : (? [X4 : $int] : (in(X4,X1) & $less(X4,X3)) | ~in(X3,X0))))),
% 0.21/0.29 inference(ennf_transformation,[],[f8])).
% 0.21/0.29 tff(f22,plain,(
% 0.21/0.29 ? [X0 : collection,X1 : collection] : (? [X5 : $int] : (~$less(1,X5) & in(X5,X0)) & ! [X2 : $int] : ($less(0,X2) | ~in(X2,X1)) & ! [X3 : $int] : (? [X4 : $int] : (in(X4,X1) & $less(X4,X3)) | ~in(X3,X0)))),
% 0.21/0.29 inference(flattening,[],[f21])).
% 0.21/0.29 tff(f27,plain,(
% 0.21/0.29 ? [X0 : collection,X1 : collection] : (? [X2 : $int] : (~$less(1,X2) & in(X2,X0)) & ! [X3 : $int] : ($less(0,X3) | ~in(X3,X1)) & ! [X4 : $int] : (? [X5 : $int] : (in(X5,X1) & $less(X5,X4)) | ~in(X4,X0)))),
% 0.21/0.29 inference(rectify,[],[f22])).
% 0.21/0.29 tff(f28,plain,(
% 0.21/0.29 (~$less(1,sK2) & in(sK2,sK0)) & ! [X3 : $int] : ($less(0,X3) | ~in(X3,sK1)) & ! [X4 : $int] : ((in(sK3(X4),sK1) & $less(sK3(X4),X4)) | ~in(X4,sK0))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X5,sK3(X4))],[f27])).
% 0.21/0.29 tff(f38,plain,(
% 0.21/0.29 ( ! [X4 : $int] : ($less(sK3(X4),X4) | ~in(X4,sK0)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f28])).
% 0.21/0.29 tff(f39,plain,(
% 0.21/0.29 ( ! [X4 : $int] : (in(sK3(X4),sK1) | ~in(X4,sK0)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f28])).
% 0.21/0.29 tff(f40,plain,(
% 0.21/0.29 ( ! [X3 : $int] : ($less(0,X3) | ~in(X3,sK1)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f28])).
% 0.21/0.29 tff(f41,plain,(
% 0.21/0.29 in(sK2,sK0)),
% 0.21/0.29 inference(cnf_transformation,[],[f28])).
% 0.21/0.29 tff(f42,plain,(
% 0.21/0.29 ~$less(1,sK2)),
% 0.21/0.29 inference(cnf_transformation,[],[f28])).
% 0.21/0.29 tff(f70,plain,(
% 0.21/0.29 ( ! [X0 : $int] : (~$less(X0,$sum(0,1)) | ~in(X0,sK1)) )),
% 0.21/0.29 inference(resolution,[],[f20,f40])).
% 0.21/0.29 tff(f71,plain,(
% 0.21/0.29 ( ! [X0 : $int] : (~in(X0,sK0) | ~$less(X0,$sum(sK3(X0),1))) )),
% 0.21/0.29 inference(resolution,[],[f20,f38])).
% 0.21/0.29 tff(f77,plain,(
% 0.21/0.29 ( ! [X0 : $int] : (~in($sum(X0,1),sK0) | ~$less(X0,sK3($sum(X0,1)))) )),
% 0.21/0.29 inference(resolution,[],[f20,f38])).
% 0.21/0.29 tff(f82,plain,(
% 0.21/0.29 ( ! [X0 : $int] : (~in(X0,sK1) | ~$less(X0,1)) )),
% 0.21/0.29 inference(evaluation,[],[f70])).
% 0.21/0.29 tff(f83,plain,(
% 0.21/0.29 ( ! [X0 : $int] : (~in(X0,sK0) | ~$less(sK3(X0),1)) )),
% 0.21/0.29 inference(resolution,[],[f82,f39])).
% 0.21/0.29 tff(f84,plain,(
% 0.21/0.29 ~$less(sK3(sK2),1)),
% 0.21/0.29 inference(resolution,[],[f83,f41])).
% 0.21/0.29 tff(f94,plain,(
% 0.21/0.29 ~$less(sK2,$sum(sK3(sK2),1))),
% 0.21/0.29 inference(resolution,[],[f71,f41])).
% 0.21/0.29 tff(f95,plain,(
% 0.21/0.29 $less(sK3(sK2),sK2)),
% 0.21/0.29 inference(resolution,[],[f94,f18])).
% 0.21/0.29 tff(f100,plain,(
% 0.21/0.29 ( ! [X0 : $int] : (~in($sum(1,X0),sK0) | ~$less(X0,sK3($sum(1,X0)))) )),
% 0.21/0.29 inference(superposition,[],[f77,f9])).
% 0.21/0.29 tff(f112,plain,(
% 0.21/0.29 ~in(1,sK0) | ~$less(0,sK3(1))),
% 0.21/0.29 inference(superposition,[],[f100,f11])).
% 0.21/0.29 tff(f118,definition,(
% 0.21/0.29 spl4_3 <=> $less(0,sK3(1))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.21/0.29 tff(f120,plain,(
% 0.21/0.29 ~$less(0,sK3(1)) | spl4_3),
% 0.21/0.29 inference(avatar_component_clause,[],[f118])).
% 0.21/0.29 tff(f122,definition,(
% 0.21/0.29 spl4_4 <=> in(1,sK0)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.21/0.29 tff(f125,plain,(
% 0.21/0.29 ~spl4_3 | ~spl4_4),
% 0.21/0.29 inference(avatar_split_clause,[],[f112,f122,f118])).
% 0.21/0.29 tff(f126,plain,(
% 0.21/0.29 ~in(sK3(1),sK1) | spl4_3),
% 0.21/0.29 inference(resolution,[],[f120,f40])).
% 0.21/0.29 tff(f127,plain,(
% 0.21/0.29 ~in(1,sK0) | spl4_3),
% 0.21/0.29 inference(resolution,[],[f126,f39])).
% 0.21/0.29 tff(f188,plain,(
% 0.21/0.29 ( ! [X0 : $int] : (~$less(X0,1) | ~$less(sK3(sK2),X0)) )),
% 0.21/0.29 inference(resolution,[],[f15,f84])).
% 0.21/0.29 tff(f214,plain,(
% 0.21/0.29 ~$less(sK2,1)),
% 0.21/0.29 inference(resolution,[],[f188,f95])).
% 0.21/0.29 tff(f282,plain,(
% 0.21/0.29 $less(sK2,1) | 1 = sK2),
% 0.21/0.29 inference(resolution,[],[f16,f42])).
% 0.21/0.29 tff(f367,definition,(
% 0.21/0.29 spl4_26 <=> 1 = sK2),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl4_26])],[avatar_definition])).
% 0.21/0.29 tff(f369,plain,(
% 0.21/0.29 1 = sK2 | ~spl4_26),
% 0.21/0.29 inference(avatar_component_clause,[],[f367])).
% 0.21/0.29 tff(f390,definition,(
% 0.21/0.29 spl4_31 <=> $less(sK2,1)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl4_31])],[avatar_definition])).
% 0.21/0.29 tff(f392,plain,(
% 0.21/0.29 $less(sK2,1) | ~spl4_31),
% 0.21/0.29 inference(avatar_component_clause,[],[f390])).
% 0.21/0.29 tff(f393,plain,(
% 0.21/0.29 spl4_26 | spl4_31),
% 0.21/0.29 inference(avatar_split_clause,[],[f282,f390,f367])).
% 0.21/0.29 tff(f448,plain,(
% 0.21/0.29 in(1,sK0) | ~spl4_26),
% 0.21/0.29 inference(superposition,[],[f41,f369])).
% 0.21/0.29 tff(f464,plain,(
% 0.21/0.29 spl4_4 | ~spl4_26),
% 0.21/0.29 inference(avatar_split_clause,[],[f448,f367,f122])).
% 0.21/0.29 tff(f465,plain,(
% 0.21/0.29 $false | ~spl4_31),
% 0.21/0.29 inference(resolution,[],[f392,f214])).
% 0.21/0.29 tff(f468,plain,(
% 0.21/0.29 ~spl4_31),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f465])).
% 0.21/0.29 tff(f469,plain,(
% 0.21/0.29 ~spl4_4 | spl4_3),
% 0.21/0.29 inference(avatar_split_clause,[],[f127,f118,f122])).
% 0.21/0.29 cnf(s2, plain, ~spl4_3 | ~spl4_4, inference(sat_conversion,[],[f125])).
% 0.21/0.29 cnf(s19, plain, spl4_26 | spl4_31, inference(sat_conversion,[],[f393])).
% 0.21/0.29 cnf(s27, plain, spl4_4 | ~spl4_26, inference(sat_conversion,[],[f464])).
% 0.21/0.29 cnf(s28, plain, ~spl4_31, inference(sat_conversion,[],[f468])).
% 0.21/0.29 cnf(s29, plain, spl4_3 | ~spl4_4, inference(sat_conversion,[],[f469])).
% 0.21/0.29 cnf(s31, plain, spl4_26, inference(rat,[],[s19,s28])).
% 0.21/0.29 cnf(s32, plain, spl4_4, inference(rat,[],[s27,s31])).
% 0.21/0.29 cnf(s33, plain, spl4_3, inference(rat,[],[s29,s32])).
% 0.21/0.29 cnf(s35, plain, $false, inference(rat,[],[s2,s32,s33])).
% 0.21/0.29 tff(f470,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(avatar_sat_refutation,[],[s35])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (4146600)------------------------------
% 0.21/0.29 % (4146600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (4146600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (4146600)CaDiCaL version: 2.1.3
% 0.21/0.29 % (4146600)Termination reason: Refutation
% 0.21/0.29 % (4146600)Time elapsed: 0.010 s
% 0.21/0.29 % (4146600)Peak memory usage: 13 MB
% 0.21/0.29 % (4146600)Instructions burned: 13 (million)
% 0.21/0.29 % (4146589)Success in time 0.05 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------