%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU787_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:54:47 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU787_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 % Computer : n009.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 05:56:00 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 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
% 0.13/0.45 % (2769765)Will run a generic schedule for satisfiability detection.
% 0.13/0.45 % (2769771)% WARNING: option uhcvi not known.
% 0.13/0.45 % (2769771)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3010000474:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.45 % (2769771) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2769765-2769771"...
% 0.13/0.45 % (2769771)...printing done.
% 0.13/0.45 % (2769771)Refutation found. Thanks to Tanya!
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start Proof for theBenchmark
% 0.13/0.45 fof(f1,axiom,(
% 0.13/0.45 (breln1unionE = ! [X0,X1] : (breln1(X0,X1) => ! [X2] : (breln1(X0,X2) => ! [X3] : (in(X3,X0) => ! [X4] : (in(X4,X0) => (in(kpair(X3,X4),binunion(X1,X2)) => (in(kpair(X3,X4),X1) | in(kpair(X3,X4),X2))))))))),
% 0.13/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionE)).
% 0.13/0.45 fof(f2,conjecture,(
% 0.13/0.45 breln1unionE => ! [X0,X1] : (breln1(X0,X1) => ! [X2] : (breln1(X0,X2) => ! [X3] : (in(X3,X0) => ! [X4] : (in(X4,X0) => (in(kpair(X3,X4),binunion(X1,X2)) => ! [X5 : $o] : ((in(kpair(X3,X4),X1) => X5) => ((in(kpair(X3,X4),X2) => X5) => X5)))))))),
% 0.13/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionEcases)).
% 0.13/0.45 fof(f3,negated_conjecture,(
% 0.13/0.45 ~(breln1unionE => ! [X0,X1] : (breln1(X0,X1) => ! [X2] : (breln1(X0,X2) => ! [X3] : (in(X3,X0) => ! [X4] : (in(X4,X0) => (in(kpair(X3,X4),binunion(X1,X2)) => ! [X5 : $o] : ((in(kpair(X3,X4),X1) => X5) => ((in(kpair(X3,X4),X2) => X5) => X5))))))))),
% 0.13/0.45 inference(negated_conjecture,[status(cth)],[f2])).
% 0.13/0.45 fof(f4,plain,(
% 0.13/0.45 breln1unionE <=> ! [X0,X1] : (breln1(X0,X1) => ! [X2] : (breln1(X0,X2) => ! [X3] : (in(X3,X0) => ! [X4] : (in(X4,X0) => (in(kpair(X3,X4),binunion(X1,X2)) => (in(kpair(X3,X4),X1) | in(kpair(X3,X4),X2)))))))),
% 0.13/0.45 inference(flattening,[],[f1])).
% 0.13/0.45 fof(f5,plain,(
% 0.13/0.45 ~(breln1unionE => ! [X0,X1] : (breln1(X0,X1) => ! [X2] : (breln1(X0,X2) => ! [X3] : (in(X3,X0) => ! [X4] : (in(X4,X0) => (in(kpair(X3,X4),binunion(X1,X2)) => ! [X5 : $o] : ((in(kpair(X3,X4),X1) => X5) => ((in(kpair(X3,X4),X2) => X5) => X5))))))))),
% 0.13/0.45 inference(rectify,[],[f3])).
% 0.13/0.45 fof(f6,plain,(
% 0.13/0.45 breln1unionE => ! [X0,X1] : (breln1(X0,X1) => ! [X2] : (breln1(X0,X2) => ! [X3] : (in(X3,X0) => ! [X4] : (in(X4,X0) => (in(kpair(X3,X4),binunion(X1,X2)) => (in(kpair(X3,X4),X1) | in(kpair(X3,X4),X2)))))))),
% 0.13/0.45 inference(unused_predicate_definition_removal,[],[f4])).
% 0.13/0.45 fof(f7,plain,(
% 0.13/0.45 ! [X0,X1] : (! [X2] : (! [X3] : (! [X4] : (((in(kpair(X3,X4),X1) | in(kpair(X3,X4),X2)) | ~in(kpair(X3,X4),binunion(X1,X2))) | ~in(X4,X0)) | ~in(X3,X0)) | ~breln1(X0,X2)) | ~breln1(X0,X1)) | ~breln1unionE),
% 0.13/0.45 inference(ennf_transformation,[],[f6])).
% 0.13/0.45 fof(f8,plain,(
% 0.13/0.45 ! [X0,X1] : (! [X2] : (! [X3] : (! [X4] : (in(kpair(X3,X4),X1) | in(kpair(X3,X4),X2) | ~in(kpair(X3,X4),binunion(X1,X2)) | ~in(X4,X0)) | ~in(X3,X0)) | ~breln1(X0,X2)) | ~breln1(X0,X1)) | ~breln1unionE),
% 0.13/0.45 inference(flattening,[],[f7])).
% 0.13/0.45 fof(f9,plain,(
% 0.13/0.45 ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : ((? [X5 : $o] : ((~X5 & (X5 | ~in(kpair(X3,X4),X2))) & (X5 | ~in(kpair(X3,X4),X1))) & in(kpair(X3,X4),binunion(X1,X2))) & in(X4,X0)) & in(X3,X0)) & breln1(X0,X2)) & breln1(X0,X1)) & breln1unionE),
% 0.13/0.45 inference(ennf_transformation,[],[f5])).
% 0.13/0.45 fof(f10,plain,(
% 0.13/0.45 ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (? [X5 : $o] : (~X5 & (X5 | ~in(kpair(X3,X4),X2)) & (X5 | ~in(kpair(X3,X4),X1))) & in(kpair(X3,X4),binunion(X1,X2)) & in(X4,X0)) & in(X3,X0)) & breln1(X0,X2)) & breln1(X0,X1)) & breln1unionE),
% 0.13/0.45 inference(flattening,[],[f9])).
% 0.13/0.45 fof(f11,plain,(
% 0.13/0.45 ( ! [X2,X3,X0,X1,X4] : (~breln1unionE | ~breln1(X0,X1) | ~breln1(X0,X2) | ~in(X3,X0) | ~in(X4,X0) | ~in(kpair(X3,X4),binunion(X1,X2)) | in(kpair(X3,X4),X2) | in(kpair(X3,X4),X1)) )),
% 0.13/0.45 inference(cnf_transformation,[],[f8])).
% 0.13/0.45 fof(f12,plain,(
% 0.13/0.45 sK5 | ~in(kpair(sK3,sK4),sK2)),
% 0.13/0.45 inference(cnf_transformation,[],[f10])).
% 0.13/0.45 fof(f13,plain,(
% 0.13/0.45 sK5 | ~in(kpair(sK3,sK4),sK1)),
% 0.13/0.45 inference(cnf_transformation,[],[f10])).
% 0.13/0.45 fof(f14,plain,(
% 0.13/0.45 ~sK5),
% 0.13/0.45 inference(cnf_transformation,[],[f10])).
% 0.13/0.45 fof(f15,plain,(
% 0.13/0.45 in(sK4,sK0)),
% 0.13/0.45 inference(cnf_transformation,[],[f10])).
% 0.13/0.45 fof(f16,plain,(
% 0.13/0.45 in(kpair(sK3,sK4),binunion(sK1,sK2))),
% 0.13/0.45 inference(cnf_transformation,[],[f10])).
% 0.13/0.45 fof(f17,plain,(
% 0.13/0.45 in(sK3,sK0)),
% 0.13/0.45 inference(cnf_transformation,[],[f10])).
% 0.13/0.45 fof(f18,plain,(
% 0.13/0.45 breln1(sK0,sK2)),
% 0.13/0.45 inference(cnf_transformation,[],[f10])).
% 0.13/0.45 fof(f19,plain,(
% 0.13/0.45 breln1(sK0,sK1)),
% 0.13/0.45 inference(cnf_transformation,[],[f10])).
% 0.13/0.45 fof(f20,plain,(
% 0.13/0.45 breln1unionE),
% 0.13/0.45 inference(cnf_transformation,[],[f10])).
% 0.13/0.45 fof(f22,definition,(
% 0.13/0.45 spl6_1 <=> in(kpair(sK3,sK4),sK2)),
% 0.13/0.45 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.13/0.45 fof(f24,plain,(
% 0.13/0.45 ~in(kpair(sK3,sK4),sK2) | spl6_1),
% 0.13/0.45 inference(avatar_component_clause,[],[f22])).
% 0.13/0.45 fof(f26,definition,(
% 0.13/0.45 spl6_2 <=> sK5),
% 0.13/0.45 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.13/0.45 fof(f29,plain,(
% 0.13/0.45 ~spl6_1 | spl6_2),
% 0.13/0.45 inference(avatar_split_clause,[],[f12,f26,f22])).
% 0.13/0.45 fof(f31,definition,(
% 0.13/0.45 spl6_3 <=> in(kpair(sK3,sK4),sK1)),
% 0.13/0.45 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 0.13/0.45 fof(f33,plain,(
% 0.13/0.45 ~in(kpair(sK3,sK4),sK1) | spl6_3),
% 0.13/0.45 inference(avatar_component_clause,[],[f31])).
% 0.13/0.45 fof(f34,plain,(
% 0.13/0.45 ~spl6_3 | spl6_2),
% 0.13/0.45 inference(avatar_split_clause,[],[f13,f26,f31])).
% 0.13/0.45 fof(f35,plain,(
% 0.13/0.45 ~spl6_2),
% 0.13/0.45 inference(avatar_split_clause,[],[f14,f26])).
% 0.13/0.45 fof(f37,definition,(
% 0.13/0.45 spl6_4 <=> ! [X2,X4,X0,X3,X1] : (~breln1(X0,X1) | in(kpair(X3,X4),X1) | in(kpair(X3,X4),X2) | ~in(kpair(X3,X4),binunion(X1,X2)) | ~in(X4,X0) | ~in(X3,X0) | ~breln1(X0,X2))),
% 0.13/0.45 introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition])).
% 0.13/0.45 fof(f38,plain,(
% 0.13/0.45 ( ! [X2,X3,X0,X1,X4] : (~in(kpair(X3,X4),binunion(X1,X2)) | in(kpair(X3,X4),X1) | in(kpair(X3,X4),X2) | ~breln1(X0,X1) | ~in(X4,X0) | ~in(X3,X0) | ~breln1(X0,X2)) ) | ~spl6_4),
% 0.13/0.45 inference(avatar_component_clause,[],[f37])).
% 0.13/0.45 fof(f40,definition,(
% 0.13/0.45 spl6_5 <=> breln1unionE),
% 0.13/0.45 introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition])).
% 0.13/0.45 fof(f43,plain,(
% 0.13/0.45 spl6_4 | ~spl6_5),
% 0.13/0.45 inference(avatar_split_clause,[],[f11,f40,f37])).
% 0.13/0.45 fof(f44,plain,(
% 0.13/0.45 spl6_5),
% 0.13/0.45 inference(avatar_split_clause,[],[f20,f40])).
% 0.13/0.45 fof(f45,plain,(
% 0.13/0.45 ( ! [X0] : (in(kpair(sK3,sK4),sK1) | in(kpair(sK3,sK4),sK2) | ~breln1(X0,sK1) | ~in(sK4,X0) | ~in(sK3,X0) | ~breln1(X0,sK2)) ) | ~spl6_4),
% 0.13/0.45 inference(resolution,[],[f38,f16])).
% 0.13/0.45 fof(f46,plain,(
% 0.13/0.45 ( ! [X0] : (in(kpair(sK3,sK4),sK2) | ~breln1(X0,sK1) | ~in(sK4,X0) | ~in(sK3,X0) | ~breln1(X0,sK2)) ) | (spl6_3 | ~spl6_4)),
% 0.13/0.45 inference(forward_subsumption_resolution,[],[f45,f33])).
% 0.13/0.45 fof(f47,plain,(
% 0.13/0.45 ( ! [X0] : (~breln1(X0,sK2) | ~in(sK4,X0) | ~in(sK3,X0) | ~breln1(X0,sK1)) ) | (spl6_1 | spl6_3 | ~spl6_4)),
% 0.13/0.45 inference(forward_subsumption_resolution,[],[f46,f24])).
% 0.13/0.45 fof(f48,plain,(
% 0.13/0.45 ~in(sK4,sK0) | ~in(sK3,sK0) | ~breln1(sK0,sK1) | (spl6_1 | spl6_3 | ~spl6_4)),
% 0.13/0.45 inference(resolution,[],[f47,f18])).
% 0.13/0.45 fof(f49,plain,(
% 0.13/0.45 ~in(sK3,sK0) | ~breln1(sK0,sK1) | (spl6_1 | spl6_3 | ~spl6_4)),
% 0.13/0.45 inference(forward_subsumption_resolution,[],[f48,f15])).
% 0.13/0.45 fof(f50,plain,(
% 0.13/0.45 ~breln1(sK0,sK1) | (spl6_1 | spl6_3 | ~spl6_4)),
% 0.13/0.45 inference(forward_subsumption_resolution,[],[f49,f17])).
% 0.13/0.45 fof(f51,plain,(
% 0.13/0.45 $false | (spl6_1 | spl6_3 | ~spl6_4)),
% 0.13/0.45 inference(forward_subsumption_resolution,[],[f50,f19])).
% 0.13/0.45 fof(f52,plain,(
% 0.13/0.45 spl6_1 | spl6_3 | ~spl6_4),
% 0.13/0.45 inference(avatar_contradiction_clause,[],[f51])).
% 0.13/0.45 cnf(s1, plain, ~spl6_1 | spl6_2, inference(sat_conversion,[],[f29])).
% 0.13/0.45 cnf(s2, plain, spl6_2 | ~spl6_3, inference(sat_conversion,[],[f34])).
% 0.13/0.45 cnf(s3, plain, ~spl6_2, inference(sat_conversion,[],[f35])).
% 0.13/0.45 cnf(s4, plain, spl6_4 | ~spl6_5, inference(sat_conversion,[],[f43])).
% 0.13/0.45 cnf(s5, plain, spl6_5, inference(sat_conversion,[],[f44])).
% 0.13/0.45 cnf(s6, plain, spl6_1 | spl6_3 | ~spl6_4, inference(sat_conversion,[],[f52])).
% 0.13/0.45 cnf(s7, plain, spl6_4, inference(rat,[],[s4,s5])).
% 0.13/0.45 cnf(s8, plain, ~spl6_3, inference(rat,[],[s2,s3])).
% 0.13/0.45 cnf(s9, plain, spl6_1, inference(rat,[],[s6,s7,s8])).
% 0.13/0.45 cnf(s10, plain, $false, inference(rat,[],[s1,s3,s9])).
% 0.13/0.45 fof(f53,plain,(
% 0.13/0.45 $false),
% 0.13/0.45 inference(avatar_sat_refutation,[],[s10])).
% 0.13/0.45 % SZS output end Proof for theBenchmark
% 0.13/0.45 % (2769771)------------------------------
% 0.13/0.45 % (2769771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.45 % (2769771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.45 % (2769771)CaDiCaL version: 2.1.3
% 0.13/0.45 % (2769771)Termination reason: Refutation
% 0.13/0.45 % (2769771)Time elapsed: 0.002 s
% 0.13/0.45 % (2769771)Peak memory usage: 12 MB
% 0.13/0.45 % (2769771)Instructions burned: 2 (million)
% 0.13/0.45 % (2769765)Success in time 0.029 s
% 0.13/0.45 % Vampire exiting
%------------------------------------------------------------------------------