%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT025_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 : 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 09:47:59 AM UTC 2026
% Result : Theorem 0.12s 0.25s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT025_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.17 % Computer : n002.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 00:08:22 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.20 Running first-order model finding
% 0.12/0.20 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
% 0.12/0.25 % (908085)Will run a generic schedule for satisfiability detection.
% 0.12/0.25 % (908091)% WARNING: option uhcvi not known.
% 0.12/0.25 % (908091)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=911095988:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.25 % (908091) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-908085-908091"...
% 0.12/0.25 % (908091)...printing done.
% 0.12/0.25 % (908091)Refutation found. Thanks to Tanya!
% 0.12/0.25 % SZS status Theorem for theBenchmark
% 0.12/0.25 % SZS output start Proof for theBenchmark
% 0.12/0.25 tff(type_def_5, type, collection: $tType).
% 0.12/0.25 tff(func_def_0, type, empty: collection).
% 0.12/0.25 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.12/0.25 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.12/0.25 tff(func_def_8, type, sK0: collection).
% 0.12/0.25 tff(func_def_9, type, sK1: $int).
% 0.12/0.25 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.12/0.25 tff(f3,axiom,(
% 0.12/0.25 ! [X0 : $int,X1 : collection] : ~in(X0,remove(X0,X1))),
% 0.12/0.25 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax3)).
% 0.12/0.25 tff(f5,axiom,(
% 0.12/0.25 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) & X0 != X2) <=> in(X0,remove(X2,X1)))),
% 0.12/0.25 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax5)).
% 0.12/0.25 tff(f6,conjecture,(
% 0.12/0.25 ! [X0 : collection] : ((! [X1 : $int] : (in(X1,X0) => $greatereq(X1,0)) & ! [X2 : $int] : (in(X2,X0) <=> in(X2,remove(0,remove(1,X0))))) => ! [X3 : $int] : (in(X3,X0) => $greatereq(X3,2)))),
% 0.12/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 0.12/0.25 tff(f7,negated_conjecture,(
% 0.12/0.25 ~ ! [X0 : collection] : ((! [X1 : $int] : (in(X1,X0) => $greatereq(X1,0)) & ! [X2 : $int] : (in(X2,X0) <=> in(X2,remove(0,remove(1,X0))))) => ! [X3 : $int] : (in(X3,X0) => $greatereq(X3,2)))),
% 0.12/0.25 inference(negated_conjecture,[status(cth)],[f6])).
% 0.12/0.25 tff(f8,plain,(
% 0.12/0.25 ~ ! [X0 : collection] : ((! [X1 : $int] : (in(X1,X0) => ~$less(X1,0)) & ! [X2 : $int] : (in(X2,X0) <=> in(X2,remove(0,remove(1,X0))))) => ! [X3 : $int] : (in(X3,X0) => ~$less(X3,2)))),
% 0.12/0.25 inference(theory_normalization,[],[f7])).
% 0.12/0.25 tff(f9,definition,(
% 0.12/0.25 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.12/0.25 introduced(theory,[tha_commutativity])).
% 0.12/0.25 tff(f16,definition,(
% 0.12/0.25 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.12/0.25 introduced(theory,[tha_order_totality])).
% 0.12/0.25 tff(f20,definition,(
% 0.12/0.25 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 0.12/0.25 introduced(theory,[tha_extra_integer_ordering])).
% 0.12/0.25 tff(f21,plain,(
% 0.12/0.25 ? [X0 : collection] : (? [X3 : $int] : ($less(X3,2) & in(X3,X0)) & (! [X1 : $int] : (~$less(X1,0) | ~in(X1,X0)) & ! [X2 : $int] : (in(X2,X0) <=> in(X2,remove(0,remove(1,X0))))))),
% 0.12/0.25 inference(ennf_transformation,[],[f8])).
% 0.12/0.25 tff(f22,plain,(
% 0.12/0.25 ? [X0 : collection] : (? [X3 : $int] : ($less(X3,2) & in(X3,X0)) & ! [X1 : $int] : (~$less(X1,0) | ~in(X1,X0)) & ! [X2 : $int] : (in(X2,X0) <=> in(X2,remove(0,remove(1,X0)))))),
% 0.12/0.25 inference(flattening,[],[f21])).
% 0.12/0.25 tff(f25,plain,(
% 0.12/0.25 ( ! [X0 : $int,X1 : collection] : (~in(X0,remove(X0,X1))) )),
% 0.12/0.25 inference(cnf_transformation,[],[f3])).
% 0.12/0.25 tff(f31,plain,(
% 0.12/0.25 ( ! [X2 : $int,X0 : $int,X1 : collection] : (~in(X0,remove(X2,X1)) | in(X0,X1)) )),
% 0.12/0.25 inference(cnf_transformation,[],[f5])).
% 0.12/0.25 tff(f32,plain,(
% 0.12/0.25 in(sK1,sK0)),
% 0.12/0.25 inference(cnf_transformation,[],[f22])).
% 0.12/0.25 tff(f33,plain,(
% 0.12/0.25 $less(sK1,2)),
% 0.12/0.25 inference(cnf_transformation,[],[f22])).
% 0.12/0.25 tff(f34,plain,(
% 0.12/0.25 ( ! [X1 : $int] : (~in(X1,sK0) | ~$less(X1,0)) )),
% 0.12/0.25 inference(cnf_transformation,[],[f22])).
% 0.12/0.25 tff(f36,plain,(
% 0.12/0.25 ( ! [X2 : $int] : (in(X2,remove(0,remove(1,sK0))) | ~in(X2,sK0)) )),
% 0.12/0.25 inference(cnf_transformation,[],[f22])).
% 0.12/0.25 tff(f41,plain,(
% 0.12/0.25 ( ! [X0 : $int,X1 : collection] : (in(X0,remove(X0,X1))) )),
% 0.12/0.25 inference(consistent_polarity_flipping,[],[f25])).
% 0.12/0.25 tff(f45,plain,(
% 0.12/0.25 ( ! [X2 : $int,X0 : $int,X1 : collection] : (in(X0,remove(X2,X1)) | ~in(X0,X1)) )),
% 0.12/0.25 inference(consistent_polarity_flipping,[],[f31])).
% 0.12/0.25 tff(f48,plain,(
% 0.12/0.25 ( ! [X2 : $int] : (~in(X2,remove(0,remove(1,sK0))) | in(X2,sK0)) )),
% 0.12/0.25 inference(consistent_polarity_flipping,[],[f36])).
% 0.12/0.25 tff(f50,plain,(
% 0.12/0.25 ( ! [X1 : $int] : (~$less(X1,0) | in(X1,sK0)) )),
% 0.12/0.25 inference(consistent_polarity_flipping,[],[f34])).
% 0.12/0.25 tff(f51,plain,(
% 0.12/0.25 ~in(sK1,sK0)),
% 0.12/0.25 inference(consistent_polarity_flipping,[],[f32])).
% 0.12/0.25 tff(f53,plain,(
% 0.12/0.25 in(0,sK0)),
% 0.12/0.25 inference(resolution,[],[f41,f48])).
% 0.12/0.25 tff(f66,plain,(
% 0.12/0.25 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,$sum(1,X0))) )),
% 0.12/0.25 inference(superposition,[],[f20,f9])).
% 0.12/0.25 tff(f73,plain,(
% 0.12/0.25 ( ! [X0 : $int] : (~in(X0,remove(1,sK0)) | in(X0,sK0)) )),
% 0.12/0.25 inference(resolution,[],[f45,f48])).
% 0.12/0.25 tff(f78,plain,(
% 0.12/0.25 in(1,sK0)),
% 0.12/0.25 inference(resolution,[],[f73,f41])).
% 0.12/0.25 tff(f81,plain,(
% 0.12/0.25 ( ! [X0 : $int] : (in(X0,sK0) | 0 = X0 | $less(0,X0)) )),
% 0.12/0.25 inference(resolution,[],[f16,f50])).
% 0.12/0.25 tff(f150,plain,(
% 0.12/0.25 0 = sK1 | $less(0,sK1)),
% 0.12/0.25 inference(resolution,[],[f81,f51])).
% 0.12/0.25 tff(f152,definition,(
% 0.12/0.25 spl2_1 <=> $less(0,sK1)),
% 0.12/0.25 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.12/0.25 tff(f154,plain,(
% 0.12/0.25 $less(0,sK1) | ~spl2_1),
% 0.12/0.25 inference(avatar_component_clause,[],[f152])).
% 0.12/0.25 tff(f156,definition,(
% 0.12/0.25 spl2_2 <=> 0 = sK1),
% 0.12/0.25 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.12/0.25 tff(f158,plain,(
% 0.12/0.25 0 = sK1 | ~spl2_2),
% 0.12/0.25 inference(avatar_component_clause,[],[f156])).
% 0.12/0.25 tff(f159,plain,(
% 0.12/0.25 spl2_1 | spl2_2),
% 0.12/0.25 inference(avatar_split_clause,[],[f150,f156,f152])).
% 0.12/0.25 tff(f162,plain,(
% 0.12/0.25 ~in(0,sK0) | ~spl2_2),
% 0.12/0.25 inference(superposition,[],[f51,f158])).
% 0.12/0.25 tff(f165,plain,(
% 0.12/0.25 $false | ~spl2_2),
% 0.12/0.25 inference(forward_subsumption_resolution,[],[f162,f53])).
% 0.12/0.25 tff(f166,plain,(
% 0.12/0.25 ~spl2_2),
% 0.12/0.25 inference(avatar_contradiction_clause,[],[f165])).
% 0.12/0.25 tff(f205,plain,(
% 0.12/0.25 ~$less(sK1,$sum(1,0)) | ~spl2_1),
% 0.12/0.25 inference(resolution,[],[f66,f154])).
% 0.12/0.25 tff(f208,plain,(
% 0.12/0.25 ~$less(sK1,1) | ~spl2_1),
% 0.12/0.25 inference(evaluation,[],[f205])).
% 0.12/0.25 tff(f209,plain,(
% 0.12/0.25 $less(1,sK1) | 1 = sK1 | ~spl2_1),
% 0.12/0.25 inference(resolution,[],[f208,f16])).
% 0.12/0.25 tff(f212,definition,(
% 0.12/0.25 spl2_3 <=> 1 = sK1),
% 0.12/0.25 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.12/0.25 tff(f214,plain,(
% 0.12/0.25 1 = sK1 | ~spl2_3),
% 0.12/0.25 inference(avatar_component_clause,[],[f212])).
% 0.12/0.25 tff(f216,definition,(
% 0.12/0.25 spl2_4 <=> $less(1,sK1)),
% 0.12/0.25 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.12/0.25 tff(f218,plain,(
% 0.12/0.25 $less(1,sK1) | ~spl2_4),
% 0.12/0.25 inference(avatar_component_clause,[],[f216])).
% 0.12/0.25 tff(f220,plain,(
% 0.12/0.25 spl2_3 | spl2_4 | ~spl2_1),
% 0.12/0.25 inference(avatar_split_clause,[],[f209,f152,f216,f212])).
% 0.12/0.25 tff(f222,plain,(
% 0.12/0.25 ~$less(sK1,$sum(1,1)) | ~spl2_4),
% 0.12/0.25 inference(resolution,[],[f218,f66])).
% 0.12/0.25 tff(f225,plain,(
% 0.12/0.25 ~$less(sK1,2) | ~spl2_4),
% 0.12/0.25 inference(evaluation,[],[f222])).
% 0.12/0.25 tff(f226,plain,(
% 0.12/0.25 $false | ~spl2_4),
% 0.12/0.25 inference(forward_subsumption_resolution,[],[f225,f33])).
% 0.12/0.25 tff(f227,plain,(
% 0.12/0.25 ~spl2_4),
% 0.12/0.25 inference(avatar_contradiction_clause,[],[f226])).
% 0.12/0.25 tff(f248,plain,(
% 0.12/0.25 ~in(1,sK0) | ~spl2_3),
% 0.12/0.25 inference(superposition,[],[f51,f214])).
% 0.12/0.25 tff(f254,plain,(
% 0.12/0.25 $false | ~spl2_3),
% 0.12/0.25 inference(forward_subsumption_resolution,[],[f248,f78])).
% 0.12/0.25 tff(f255,plain,(
% 0.12/0.25 ~spl2_3),
% 0.12/0.25 inference(avatar_contradiction_clause,[],[f254])).
% 0.12/0.25 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f159])).
% 0.12/0.25 cnf(s2, plain, ~spl2_2, inference(sat_conversion,[],[f166])).
% 0.12/0.25 cnf(s4, plain, ~spl2_1 | spl2_3 | spl2_4, inference(sat_conversion,[],[f220])).
% 0.12/0.25 cnf(s5, plain, ~spl2_4, inference(sat_conversion,[],[f227])).
% 0.12/0.25 cnf(s6, plain, ~spl2_3, inference(sat_conversion,[],[f255])).
% 0.12/0.25 cnf(s7, plain, ~spl2_1, inference(rat,[],[s4,s5,s6])).
% 0.12/0.25 cnf(s8, plain, $false, inference(rat,[],[s1,s2,s7])).
% 0.12/0.25 tff(f256,plain,(
% 0.12/0.25 $false),
% 0.12/0.25 inference(avatar_sat_refutation,[],[s8])).
% 0.12/0.25 % SZS output end Proof for theBenchmark
% 0.12/0.25 % (908091)------------------------------
% 0.12/0.25 % (908091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.25 % (908091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.25 % (908091)CaDiCaL version: 2.1.3
% 0.12/0.25 % (908091)Termination reason: Refutation
% 0.12/0.25 % (908091)Time elapsed: 0.005 s
% 0.12/0.25 % (908091)Peak memory usage: 12 MB
% 0.12/0.25 % (908091)Instructions burned: 9 (million)
% 0.12/0.25 % (908085)Success in time 0.036 s
% 0.12/0.25 % Vampire exiting
%------------------------------------------------------------------------------