%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU526^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:29:55 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU526^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.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 13:48:18 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
% 0.22/0.28 % (791958)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (791966)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3246764214:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.28 % (791966) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-791958-791966"...
% 0.22/0.28 % (791966)...printing done.
% 0.22/0.28 % (791966)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.28 thf(func_def_2, type, emptysetE: $o).
% 0.22/0.28 thf(func_def_4, type, setext: $o).
% 0.22/0.28 thf(func_def_5, type, nonempty: ($i > $o)).
% 0.22/0.28 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.28 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.28 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.22/0.28 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.28 thf(func_def_13, type, sK1: $o).
% 0.22/0.28 thf(func_def_17, type, sK5: ($i > $i > $i)).
% 0.22/0.28 thf(func_def_18, type, sK6: ($i > $i > $i)).
% 0.22/0.28 thf(f1,axiom,(
% 0.22/0.28 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE)).
% 0.22/0.28 thf(f2,axiom,(
% 0.22/0.28 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext)).
% 0.22/0.28 thf(f3,axiom,(
% 0.22/0.28 (nonempty = (^[X0 : $i] : ((X0 != emptyset))))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty)).
% 0.22/0.28 thf(f4,conjecture,(
% 0.22/0.28 emptysetE => (setext => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((in @ X1 @ X0) & $true)))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness)).
% 0.22/0.28 thf(f5,negated_conjecture,(
% 0.22/0.28 ~(emptysetE => (setext => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((in @ X1 @ X0) & $true))))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.22/0.28 inference(fool_elimination,[],[f3])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))))),
% 0.22/0.28 inference(rectify,[],[f2])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (! [X3 : $i] : (($true = ((in @ X3 @ X1))) => ($true = ((in @ X3 @ X0)))) => (X0 = X1))) <=> (setext = $true)),
% 0.22/0.28 inference(fool_elimination,[],[f7])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.22/0.28 inference(rectify,[],[f1])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 ! [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) => ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 0.22/0.28 inference(fool_elimination,[],[f9])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 ~(emptysetE => (setext => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((in @ X1 @ X0) & $true))))),
% 0.22/0.28 inference(rectify,[],[f5])).
% 0.22/0.28 thf(f12,plain,(
% 0.22/0.28 ~((emptysetE = $true) => ((setext = $true) => ! [X0 : $i] : ((((nonempty @ X0)) = $true) => ? [X1 : $i] : ((((in @ X1 @ X0)) = $true) & $true))))),
% 0.22/0.28 inference(fool_elimination,[],[f11])).
% 0.22/0.28 thf(f13,plain,(
% 0.22/0.28 ~((emptysetE = $true) => ((setext = $true) => ! [X0 : $i] : ((((nonempty @ X0)) = $true) => ? [X1 : $i] : (((in @ X1 @ X0)) = $true))))),
% 0.22/0.28 inference(true_and_false_elimination,[],[f12])).
% 0.22/0.28 thf(f14,plain,(
% 0.22/0.28 (emptysetE = $true) <=> ! [X0 : $i] : (! [X1 : $o] : ($true = X1) | (((in @ X0 @ emptyset)) != $true))),
% 0.22/0.28 inference(ennf_transformation,[],[f10])).
% 0.22/0.28 thf(f15,plain,(
% 0.22/0.28 (? [X0 : $i] : ((((nonempty @ X0)) = $true) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true)) & (setext = $true)) & (emptysetE = $true)),
% 0.22/0.28 inference(ennf_transformation,[],[f13])).
% 0.22/0.28 thf(f16,plain,(
% 0.22/0.28 (setext = $true) & ? [X0 : $i] : ((((nonempty @ X0)) = $true) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true)) & (emptysetE = $true)),
% 0.22/0.28 inference(flattening,[],[f15])).
% 0.22/0.28 thf(f17,plain,(
% 0.22/0.28 ! [X1 : $i,X0 : $i] : (((X0 = X1) | ? [X3 : $i] : (($true != ((in @ X3 @ X0))) & ($true = ((in @ X3 @ X1))))) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) <=> (setext = $true)),
% 0.22/0.28 inference(ennf_transformation,[],[f8])).
% 0.22/0.28 thf(f18,plain,(
% 0.22/0.28 (setext = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)) | ? [X3 : $i] : (($true != ((in @ X3 @ X0))) & ($true = ((in @ X3 @ X1)))) | (X0 = X1))),
% 0.22/0.28 inference(flattening,[],[f17])).
% 0.22/0.28 thf(f19,plain,(
% 0.22/0.28 ((emptysetE = $true) | ? [X0 : $i] : (? [X1 : $o] : ($true != X1) & (((in @ X0 @ emptyset)) = $true))) & (! [X0 : $i] : (! [X1 : $o] : ($true = X1) | (((in @ X0 @ emptyset)) != $true)) | (emptysetE != $true))),
% 0.22/0.28 inference(nnf_transformation,[],[f14])).
% 0.22/0.28 thf(f20,plain,(
% 0.22/0.28 ((emptysetE = $true) | ? [X0 : $i] : (? [X1 : $o] : ($true != X1) & (((in @ X0 @ emptyset)) = $true))) & (! [X2 : $i] : (! [X3 : $o] : ($true = X3) | ($true != ((in @ X2 @ emptyset)))) | (emptysetE != $true))),
% 0.22/0.28 inference(rectify,[],[f19])).
% 0.22/0.28 thf(f21,plain,(
% 0.22/0.28 ((emptysetE = $true) | (($true != sK1) & ($true = ((in @ sK0 @ emptyset))))) & (! [X2 : $i] : (! [X3 : $o] : ($true = X3) | ($true != ((in @ X2 @ emptyset)))) | (emptysetE != $true))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20])).
% 0.22/0.28 thf(f22,plain,(
% 0.22/0.28 (setext = $true) & (($true = ((nonempty @ sK2))) & ! [X1 : $i] : ($true != ((in @ X1 @ sK2)))) & (emptysetE = $true)),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f16])).
% 0.22/0.28 thf(f23,plain,(
% 0.22/0.28 ((setext = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true)) & ! [X3 : $i] : (($true = ((in @ X3 @ X0))) | ($true != ((in @ X3 @ X1)))) & (X0 != X1))) & (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)) | ? [X3 : $i] : (($true != ((in @ X3 @ X0))) & ($true = ((in @ X3 @ X1)))) | (X0 = X1)) | (setext != $true))),
% 0.22/0.28 inference(nnf_transformation,[],[f18])).
% 0.22/0.28 thf(f24,plain,(
% 0.22/0.28 ((setext = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) & ! [X3 : $i] : (($true = ((in @ X3 @ X1))) | ($true != ((in @ X3 @ X0)))) & (X0 != X1))) & (! [X4 : $i,X5 : $i] : (? [X6 : $i] : (($true = ((in @ X6 @ X5))) & ($true != ((in @ X6 @ X4)))) | ? [X7 : $i] : (($true != ((in @ X7 @ X5))) & ($true = ((in @ X7 @ X4)))) | (X4 = X5)) | (setext != $true))),
% 0.22/0.28 inference(rectify,[],[f23])).
% 0.22/0.28 thf(f25,plain,(
% 0.22/0.28 ((setext = $true) | (! [X2 : $i] : (($true != ((in @ X2 @ sK4))) | ($true = ((in @ X2 @ sK3)))) & ! [X3 : $i] : (($true = ((in @ X3 @ sK4))) | ($true != ((in @ X3 @ sK3)))) & (sK4 != sK3))) & (! [X4 : $i,X5 : $i] : ((($true = ((in @ (sK5 @ X5 @ X4) @ X5))) & (((in @ (sK5 @ X5 @ X4) @ X4)) != $true)) | (($true != ((in @ (sK6 @ X5 @ X4) @ X5))) & ($true = ((in @ (sK6 @ X5 @ X4) @ X4)))) | (X4 = X5)) | (setext != $true))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,vAPP,vAPP]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X7,sK6 @ X5 @ X4),skolemize(X7,sK6 @ X5 @ X4)],[f24])).
% 0.22/0.28 thf(f26,plain,(
% 0.22/0.28 ( ! [X2 : $i,X3 : $o] : (($true = X3) | ($true != ((in @ X2 @ emptyset))) | (emptysetE != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f21])).
% 0.22/0.28 thf(f29,plain,(
% 0.22/0.28 (emptysetE = $true)),
% 0.22/0.28 inference(cnf_transformation,[],[f22])).
% 0.22/0.28 thf(f30,plain,(
% 0.22/0.28 ( ! [X1 : $i] : (($true != ((in @ X1 @ sK2)))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f22])).
% 0.22/0.28 thf(f31,plain,(
% 0.22/0.28 ($true = ((nonempty @ sK2)))),
% 0.22/0.28 inference(cnf_transformation,[],[f22])).
% 0.22/0.28 thf(f32,plain,(
% 0.22/0.28 (setext = $true)),
% 0.22/0.28 inference(cnf_transformation,[],[f22])).
% 0.22/0.28 thf(f33,plain,(
% 0.22/0.28 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.22/0.28 inference(cnf_transformation,[],[f6])).
% 0.22/0.28 thf(f36,plain,(
% 0.22/0.28 ( ! [X4 : $i,X5 : $i] : (($true = ((in @ (sK5 @ X5 @ X4) @ X5))) | ($true = ((in @ (sK6 @ X5 @ X4) @ X4))) | (X4 = X5) | (setext != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f25])).
% 0.22/0.28 thf(f45,plain,(
% 0.22/0.28 ( ! [X2 : $i,X3 : $o] : (($true != ((in @ X2 @ emptyset))) | ($true != $true) | ($true = X3)) )),
% 0.22/0.28 inference(definition_unfolding,[],[f26,f29])).
% 0.22/0.28 thf(f46,plain,(
% 0.22/0.28 ($true = (((^[Y0 : $i]: (~ (emptyset = Y0))) @ sK2)))),
% 0.22/0.28 inference(definition_unfolding,[],[f31,f33])).
% 0.22/0.28 thf(f51,plain,(
% 0.22/0.28 ( ! [X4 : $i,X5 : $i] : (($true = ((in @ (sK6 @ X5 @ X4) @ X4))) | (X4 = X5) | ($true = ((in @ (sK5 @ X5 @ X4) @ X5))) | ($true != $true)) )),
% 0.22/0.28 inference(definition_unfolding,[],[f36,f32])).
% 0.22/0.28 thf(f56,plain,(
% 0.22/0.28 ($true = ((~ (emptyset = sK2))))),
% 0.22/0.28 inference(beta-eta_normalization,[],[f46])).
% 0.22/0.28 thf(f57,plain,(
% 0.22/0.28 (((emptyset = sK2)) = $false)),
% 0.22/0.28 inference(not_proxy_clausification,[],[f56])).
% 0.22/0.28 thf(f58,plain,(
% 0.22/0.28 (emptyset != sK2)),
% 0.22/0.28 inference(equality_proxy_clausification,[],[f57])).
% 0.22/0.28 thf(f59,plain,(
% 0.22/0.28 ( ! [X4 : $i,X5 : $i] : (($true = ((in @ (sK6 @ X5 @ X4) @ X4))) | ($true = ((in @ (sK5 @ X5 @ X4) @ X5))) | (X4 = X5)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f51])).
% 0.22/0.28 thf(f60,plain,(
% 0.22/0.28 ( ! [X2 : $i,X3 : $o] : (($true = X3) | ($true != ((in @ X2 @ emptyset)))) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f45])).
% 0.22/0.28 thf(f63,definition,(
% 0.22/0.28 spl7_1 <=> ! [X2 : $i] : ($true != ((in @ X2 @ emptyset)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.22/0.28 thf(f64,plain,(
% 0.22/0.28 ( ! [X2 : $i] : (($true != ((in @ X2 @ emptyset)))) ) | ~spl7_1),
% 0.22/0.28 inference(avatar_component_clause,[],[f63])).
% 0.22/0.28 thf(f66,definition,(
% 0.22/0.28 spl7_2 <=> ! [X3 : $o] : ($true = X3)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.22/0.28 thf(f67,plain,(
% 0.22/0.28 ( ! [X3 : $o] : (($true = X3)) ) | ~spl7_2),
% 0.22/0.28 inference(avatar_component_clause,[],[f66])).
% 0.22/0.28 thf(f68,plain,(
% 0.22/0.28 spl7_1 | spl7_2),
% 0.22/0.28 inference(avatar_split_clause,[],[f60,f66,f63])).
% 0.22/0.28 thf(f72,plain,(
% 0.22/0.28 ($true != $true) | ~spl7_2),
% 0.22/0.28 inference(constrained_superposition,[],[f30,f67])).
% 0.22/0.28 thf(f73,plain,(
% 0.22/0.28 $false | ~spl7_2),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f72])).
% 0.22/0.28 thf(f74,plain,(
% 0.22/0.28 ~spl7_2),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f73])).
% 0.22/0.28 thf(f76,plain,(
% 0.22/0.28 ( ! [X0 : $i] : ((((in @ (sK5 @ X0 @ emptyset) @ X0)) = $true) | ($true != $true) | (emptyset = X0)) ) | ~spl7_1),
% 0.22/0.28 inference(constrained_superposition,[],[f64,f59])).
% 0.22/0.28 thf(f77,plain,(
% 0.22/0.28 ( ! [X0 : $i] : ((((in @ (sK5 @ X0 @ emptyset) @ X0)) = $true) | (emptyset = X0)) ) | ~spl7_1),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f76])).
% 0.22/0.28 thf(f79,plain,(
% 0.22/0.28 (emptyset = sK2) | ($true != $true) | ~spl7_1),
% 0.22/0.28 inference(constrained_superposition,[],[f30,f77])).
% 0.22/0.28 thf(f80,plain,(
% 0.22/0.28 (emptyset = sK2) | ~spl7_1),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f79])).
% 0.22/0.28 thf(f81,plain,(
% 0.22/0.28 $false | ~spl7_1),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f80,f58])).
% 0.22/0.28 thf(f82,plain,(
% 0.22/0.28 ~spl7_1),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f81])).
% 0.22/0.28 cnf(s1, plain, spl7_1 | spl7_2, inference(sat_conversion,[],[f68])).
% 0.22/0.28 cnf(s2, plain, ~spl7_2, inference(sat_conversion,[],[f74])).
% 0.22/0.28 cnf(s3, plain, ~spl7_1, inference(sat_conversion,[],[f82])).
% 0.22/0.28 cnf(s4, plain, $false, inference(rat,[],[s1,s2,s3])).
% 0.22/0.28 thf(f83,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(avatar_sat_refutation,[],[s4])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (791966)------------------------------
% 0.22/0.28 % (791966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (791966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (791966)CaDiCaL version: 2.1.3
% 0.22/0.28 % (791966)Termination reason: Refutation
% 0.22/0.28 % (791966)Time elapsed: 0.003 s
% 0.22/0.28 % (791966)Peak memory usage: 13 MB
% 0.22/0.28 % (791966)Instructions burned: 6 (million)
% 0.22/0.28 % (791958)Success in time 0.031 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------