%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU924^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 : Wed Sep 30 08:31:57 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU924^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.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 14:48:14 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.27 % (2606947)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (2606955)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=587528066:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.27 % (2606955) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2606947-2606955"...
% 0.22/0.27 % (2606955)...printing done.
% 0.22/0.27 % (2606955)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% 0.22/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.27 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.27 thf(func_def_4, type, sK0: ($i > $i)).
% 0.22/0.27 thf(func_def_7, type, sK3: ((($i > $i) > $o) > $i > $i)).
% 0.22/0.27 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.22/0.27 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.27 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.27 thf(f1,conjecture,(
% 0.22/0.27 ! [X1 : ($i > $i),X0 : $i] : (! [X2 : (($i > $i) > $o)] : (((X2 @ (^[X3 : $i] : (X0))) & ! [X4 : ($i > $i)] : ((X2 @ X4) => (X2 @ (^[X3 : $i] : (X0))))) => (X2 @ X1)) => ! [X3 : $i] : (((X1 @ X3)) = X0))),
% 0.22/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM134_pme)).
% 0.22/0.27 thf(f2,negated_conjecture,(
% 0.22/0.27 ~ ! [X1 : ($i > $i),X0 : $i] : (! [X2 : (($i > $i) > $o)] : (((X2 @ (^[X3 : $i] : (X0))) & ! [X4 : ($i > $i)] : ((X2 @ X4) => (X2 @ (^[X3 : $i] : (X0))))) => (X2 @ X1)) => ! [X3 : $i] : (((X1 @ X3)) = X0))),
% 0.22/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.27 thf(f3,plain,(
% 0.22/0.27 ~ ! [X0 : ($i > $i),X1 : $i] : (! [X2 : (($i > $i) > $o)] : (((X2 @ (^[X3 : $i] : (X1))) & ! [X4 : ($i > $i)] : ((X2 @ X4) => (X2 @ (^[X5 : $i] : (X1))))) => (X2 @ X0)) => ! [X6 : $i] : (((X0 @ X6)) = X1))),
% 0.22/0.27 inference(rectify,[],[f2])).
% 0.22/0.27 thf(f4,plain,(
% 0.22/0.27 ~ ! [X0 : ($i > $i),X1 : $i] : (! [X2 : (($i > $i) > $o)] : ((($true = ((X2 @ (^[Y0 : $i]: (X1))))) & ! [X4 : ($i > $i)] : ((((X2 @ X4)) = $true) => ($true = ((X2 @ (^[Y0 : $i]: (X1))))))) => ($true = ((X2 @ X0)))) => ! [X6 : $i] : (((X0 @ X6)) = X1))),
% 0.22/0.27 inference(fool_elimination,[],[f3])).
% 0.22/0.27 thf(f5,plain,(
% 0.22/0.27 ~ ! [X1 : $i,X0 : ($i > $i)] : (! [X2 : (($i > $i) > $o)] : ((! [X3 : ($i > $i)] : (($true = ((X2 @ X3))) => ($true = ((X2 @ (^[Y0 : $i]: (X1)))))) & ($true = ((X2 @ (^[Y0 : $i]: (X1)))))) => ($true = ((X2 @ X0)))) => ! [X4 : $i] : (((X0 @ X4)) = X1))),
% 0.22/0.27 inference(rectify,[],[f4])).
% 0.22/0.27 thf(f6,plain,(
% 0.22/0.27 ? [X1 : $i,X0 : ($i > $i)] : (? [X4 : $i] : (((X0 @ X4)) != X1) & ! [X2 : (($i > $i) > $o)] : (($true = ((X2 @ X0))) | (? [X3 : ($i > $i)] : (($true != ((X2 @ (^[Y0 : $i]: (X1))))) & ($true = ((X2 @ X3)))) | ($true != ((X2 @ (^[Y0 : $i]: (X1))))))))),
% 0.22/0.27 inference(ennf_transformation,[],[f5])).
% 0.22/0.27 thf(f7,plain,(
% 0.22/0.27 ? [X0 : ($i > $i),X1 : $i] : (? [X4 : $i] : (((X0 @ X4)) != X1) & ! [X2 : (($i > $i) > $o)] : (($true = ((X2 @ X0))) | ? [X3 : ($i > $i)] : (($true != ((X2 @ (^[Y0 : $i]: (X1))))) & ($true = ((X2 @ X3)))) | ($true != ((X2 @ (^[Y0 : $i]: (X1)))))))),
% 0.22/0.27 inference(flattening,[],[f6])).
% 0.22/0.27 thf(f8,plain,(
% 0.22/0.27 ? [X0 : ($i > $i),X1 : $i] : (? [X2 : $i] : (((X0 @ X2)) != X1) & ! [X3 : (($i > $i) > $o)] : (($true = ((X3 @ X0))) | ? [X4 : ($i > $i)] : (($true != ((X3 @ (^[Y0 : $i]: (X1))))) & ($true = ((X3 @ X4)))) | ($true != ((X3 @ (^[Y0 : $i]: (X1)))))))),
% 0.22/0.27 inference(rectify,[],[f7])).
% 0.22/0.27 thf(f9,plain,(
% 0.22/0.27 (((sK0 @ sK2)) != sK1) & ! [X3 : (($i > $i) > $o)] : (($true = ((X3 @ sK0))) | (($true != ((X3 @ (^[Y0 : $i]: (sK1))))) & ($true = ((X3 @ (sK3 @ X3))))) | ($true != ((X3 @ (^[Y0 : $i]: (sK1))))))),
% 0.22/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X4,sK3 @ X3)],[f8])).
% 0.22/0.27 thf(f11,plain,(
% 0.22/0.27 ( ! [X3 : (($i > $i) > $o)] : (($true != ((X3 @ (^[Y0 : $i]: (sK1))))) | ($true = ((X3 @ sK0))) | ($true != ((X3 @ (^[Y0 : $i]: (sK1)))))) )),
% 0.22/0.27 inference(cnf_transformation,[],[f9])).
% 0.22/0.27 thf(f12,plain,(
% 0.22/0.27 (((sK0 @ sK2)) != sK1)),
% 0.22/0.27 inference(cnf_transformation,[],[f9])).
% 0.22/0.27 thf(f14,plain,(
% 0.22/0.27 ( ! [X3 : (($i > $i) > $o)] : (($true != ((X3 @ (^[Y0 : $i]: (sK1))))) | ($true = ((X3 @ sK0)))) )),
% 0.22/0.27 inference(duplicate_literal_removal,[],[f11])).
% 0.22/0.27 thf(f16,definition,(
% 0.22/0.27 spl4_1 <=> (((sK0 @ sK2)) = sK1)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.22/0.27 thf(f18,plain,(
% 0.22/0.27 (((sK0 @ sK2)) != sK1) | spl4_1),
% 0.22/0.27 inference(avatar_component_clause,[],[f16])).
% 0.22/0.27 thf(f19,plain,(
% 0.22/0.27 ~spl4_1),
% 0.22/0.27 inference(avatar_split_clause,[],[f12,f16])).
% 0.22/0.27 thf(f21,plain,(
% 0.22/0.27 ((^[Y0 : $i]: (sK1)) = sK0)),
% 0.22/0.27 inference(leibniz_equality_elimination,[],[f14])).
% 0.22/0.27 thf(f33,definition,(
% 0.22/0.27 spl4_2 <=> ((^[Y0 : $i]: (sK1)) = sK0)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.22/0.27 thf(f35,plain,(
% 0.22/0.27 ((^[Y0 : $i]: (sK1)) = sK0) | ~spl4_2),
% 0.22/0.27 inference(avatar_component_clause,[],[f33])).
% 0.22/0.27 thf(f36,plain,(
% 0.22/0.27 spl4_2),
% 0.22/0.27 inference(avatar_split_clause,[],[f21,f33])).
% 0.22/0.27 thf(f37,plain,(
% 0.22/0.27 ( ! [X1 : $i] : (((((^[Y0 : $i]: (sK1)) @ X1)) = ((sK0 @ X1)))) ) | ~spl4_2),
% 0.22/0.27 inference(argument_congruence,[],[f35])).
% 0.22/0.28 thf(f39,plain,(
% 0.22/0.28 ( ! [X1 : $i] : ((sK1 = ((sK0 @ X1)))) ) | ~spl4_2),
% 0.22/0.28 inference(beta-eta_normalization,[],[f37])).
% 0.22/0.28 thf(f40,plain,(
% 0.22/0.28 (sK1 != sK1) | (spl4_1 | ~spl4_2)),
% 0.22/0.28 inference(superposition,[],[f18,f39])).
% 0.22/0.28 thf(f41,plain,(
% 0.22/0.28 $false | (spl4_1 | ~spl4_2)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f40])).
% 0.22/0.28 thf(f42,plain,(
% 0.22/0.28 spl4_1 | ~spl4_2),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f41])).
% 0.22/0.28 cnf(s1, plain, ~spl4_1, inference(sat_conversion,[],[f19])).
% 0.22/0.28 cnf(s2, plain, spl4_2, inference(sat_conversion,[],[f36])).
% 0.22/0.28 cnf(s4, plain, spl4_1 | ~spl4_2, inference(sat_conversion,[],[f42])).
% 0.22/0.28 cnf(s5, plain, spl4_1, inference(rat,[],[s4,s2])).
% 0.22/0.28 cnf(s6, plain, $false, inference(rat,[],[s1,s5])).
% 0.22/0.28 thf(f43,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(avatar_sat_refutation,[],[s6])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (2606955)------------------------------
% 0.22/0.28 % (2606955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (2606955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (2606955)CaDiCaL version: 2.1.3
% 0.22/0.28 % (2606955)Termination reason: Refutation
% 0.22/0.28 % (2606955)Time elapsed: 0.002 s
% 0.22/0.28 % (2606955)Peak memory usage: 13 MB
% 0.22/0.28 % (2606955)Instructions burned: 2 (million)
% 0.22/0.28 % (2606947)Success in time 0.025 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------