%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU506^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:29:51 AM UTC 2026
% Result : Theorem 0.08s 0.28s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU506^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:49:11 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.28 % (92834)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.28 % (92840)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1813148135:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.28 % (92840) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-92834-92840"...
% 0.08/0.28 % (92840)...printing done.
% 0.08/0.28 % (92841)lrs+10_16_si=on:nwc=1.5:random_seed=1469204045:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.28 % (92844)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2258220860:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.28 % (92843)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=3037738556: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)
% 0.08/0.28 % (92840)Refutation found. Thanks to Tanya!
% 0.08/0.28 % SZS status Theorem for theBenchmark
% 0.08/0.28 % SZS output start Proof for theBenchmark
% 0.08/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.08/0.28 thf(func_def_2, type, emptysetE: $o).
% 0.08/0.28 thf(func_def_4, type, setext: $o).
% 0.08/0.28 thf(func_def_8, type, sK1: $o).
% 0.08/0.28 thf(func_def_10, type, sK3: ($i > $i > $i)).
% 0.08/0.28 thf(func_def_11, type, sK4: ($i > $i > $i)).
% 0.08/0.28 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.08/0.28 thf(f1,axiom,(
% 0.08/0.28 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 0.08/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)).
% 0.08/0.28 thf(f2,axiom,(
% 0.08/0.28 (setext = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))))),
% 0.08/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext)).
% 0.08/0.28 thf(f3,conjecture,(
% 0.08/0.28 emptysetE => (setext => ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
% 0.08/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI)).
% 0.08/0.28 thf(f4,negated_conjecture,(
% 0.08/0.28 ~(emptysetE => (setext => ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset))))),
% 0.08/0.28 inference(negated_conjecture,[status(cth)],[f3])).
% 0.08/0.28 thf(f5,plain,(
% 0.08/0.28 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))))),
% 0.08/0.28 inference(rectify,[],[f2])).
% 0.08/0.28 thf(f6,plain,(
% 0.08/0.28 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X1)) = $true)) => (X0 = X1))) <=> (setext = $true)),
% 0.08/0.28 inference(fool_elimination,[],[f5])).
% 0.08/0.28 thf(f7,plain,(
% 0.08/0.28 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 0.08/0.28 inference(rectify,[],[f1])).
% 0.08/0.28 thf(f8,plain,(
% 0.08/0.28 ! [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) => ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 0.08/0.28 inference(fool_elimination,[],[f7])).
% 0.08/0.28 thf(f9,plain,(
% 0.08/0.28 ~(emptysetE => (setext => ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset))))),
% 0.08/0.28 inference(rectify,[],[f4])).
% 0.08/0.28 thf(f10,plain,(
% 0.08/0.28 ~((emptysetE = $true) => ((setext = $true) => ! [X0 : $i] : (! [X1 : $i] : ~ (((in @ X1 @ X0)) = $true) => (emptyset = X0))))),
% 0.08/0.28 inference(fool_elimination,[],[f9])).
% 0.08/0.28 thf(f11,plain,(
% 0.08/0.28 ~((emptysetE = $true) => ((setext = $true) => ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) => (emptyset = X0))))),
% 0.08/0.28 inference(flattening,[],[f10])).
% 0.08/0.28 thf(f12,plain,(
% 0.08/0.28 (emptysetE = $true) <=> ! [X0 : $i] : (! [X1 : $o] : ($true = X1) | (((in @ X0 @ emptyset)) != $true))),
% 0.08/0.28 inference(ennf_transformation,[],[f8])).
% 0.08/0.28 thf(f13,plain,(
% 0.08/0.28 (? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true)) & (setext = $true)) & (emptysetE = $true)),
% 0.08/0.28 inference(ennf_transformation,[],[f11])).
% 0.08/0.28 thf(f14,plain,(
% 0.08/0.28 (emptysetE = $true) & (setext = $true) & ? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true))),
% 0.08/0.28 inference(flattening,[],[f13])).
% 0.08/0.28 thf(f15,plain,(
% 0.08/0.28 ! [X0 : $i,X1 : $i] : (((X0 = X1) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) != $true))) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) <=> (setext = $true)),
% 0.08/0.28 inference(ennf_transformation,[],[f6])).
% 0.08/0.28 thf(f16,plain,(
% 0.08/0.28 ! [X0 : $i,X1 : $i] : ((X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) != $true))) <=> (setext = $true)),
% 0.08/0.28 inference(flattening,[],[f15])).
% 0.08/0.28 thf(f17,plain,(
% 0.08/0.28 ((emptysetE = $true) | ? [X0 : $i] : (? [X1 : $o] : ($true != X1) & (((in @ X0 @ emptyset)) = $true))) & (! [X0 : $i] : (! [X1 : $o] : ($true = X1) | (((in @ X0 @ emptyset)) != $true)) | (emptysetE != $true))),
% 0.08/0.28 inference(nnf_transformation,[],[f12])).
% 0.08/0.28 thf(f18,plain,(
% 0.08/0.28 ((emptysetE = $true) | ? [X0 : $i] : (? [X1 : $o] : ($true != X1) & (((in @ X0 @ emptyset)) = $true))) & (! [X2 : $i] : (! [X3 : $o] : ($true = X3) | (((in @ X2 @ emptyset)) != $true)) | (emptysetE != $true))),
% 0.08/0.28 inference(rectify,[],[f17])).
% 0.08/0.28 thf(f19,plain,(
% 0.08/0.28 ((emptysetE = $true) | ((sK1 != $true) & (((in @ sK0 @ emptyset)) = $true))) & (! [X2 : $i] : (! [X3 : $o] : ($true = X3) | (((in @ X2 @ emptyset)) != $true)) | (emptysetE != $true))),
% 0.08/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f18])).
% 0.08/0.28 thf(f20,plain,(
% 0.08/0.28 (emptysetE = $true) & (setext = $true) & ((emptyset != sK2) & ! [X1 : $i] : (((in @ X1 @ sK2)) != $true))),
% 0.08/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f14])).
% 0.08/0.28 thf(f21,plain,(
% 0.08/0.28 (! [X0 : $i,X1 : $i] : ((X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) != $true))) | (setext != $true)) & ((setext = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) & ! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ X1)) = $true))))),
% 0.08/0.28 inference(nnf_transformation,[],[f16])).
% 0.08/0.28 thf(f22,plain,(
% 0.08/0.28 (! [X0 : $i,X1 : $i] : ((X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) != $true))) | (setext != $true)) & ((setext = $true) | ? [X4 : $i,X5 : $i] : ((X4 != X5) & ! [X6 : $i] : ((((in @ X6 @ X4)) = $true) | (((in @ X6 @ X5)) != $true)) & ! [X7 : $i] : ((((in @ X7 @ X4)) != $true) | (((in @ X7 @ X5)) = $true))))),
% 0.08/0.28 inference(rectify,[],[f21])).
% 0.08/0.28 thf(f23,plain,(
% 0.08/0.28 (! [X0 : $i,X1 : $i] : ((X0 = X1) | ((((in @ (sK3 @ X1 @ X0) @ X0)) != $true) & (((in @ (sK3 @ X1 @ X0) @ X1)) = $true)) | ((((in @ (sK4 @ X1 @ X0) @ X0)) = $true) & (((in @ (sK4 @ X1 @ X0) @ X1)) != $true))) | (setext != $true)) & ((setext = $true) | ((sK5 != sK6) & ! [X6 : $i] : ((((in @ X6 @ sK5)) = $true) | (((in @ X6 @ sK6)) != $true)) & ! [X7 : $i] : ((((in @ X7 @ sK5)) != $true) | (((in @ X7 @ sK6)) = $true))))),
% 0.08/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK5,sK6]),skolemize(X3,sK4 @ X1 @ X0),skolemize(X3,sK4 @ X1 @ X0),skolemize(X4,sK5),skolemize(X5,sK6)],[f22])).
% 0.08/0.28 thf(f24,plain,(
% 0.08/0.28 ( ! [X2 : $i,X3 : $o] : (($true = X3) | (((in @ X2 @ emptyset)) != $true) | (emptysetE != $true)) )),
% 0.08/0.28 inference(cnf_transformation,[],[f19])).
% 0.08/0.28 thf(f27,plain,(
% 0.08/0.28 ( ! [X1 : $i] : ((((in @ X1 @ sK2)) != $true)) )),
% 0.08/0.28 inference(cnf_transformation,[],[f20])).
% 0.08/0.28 thf(f28,plain,(
% 0.08/0.28 (emptyset != sK2)),
% 0.08/0.28 inference(cnf_transformation,[],[f20])).
% 0.08/0.28 thf(f29,plain,(
% 0.08/0.28 (setext = $true)),
% 0.08/0.28 inference(cnf_transformation,[],[f20])).
% 0.08/0.28 thf(f30,plain,(
% 0.08/0.28 (emptysetE = $true)),
% 0.08/0.28 inference(cnf_transformation,[],[f20])).
% 0.08/0.28 thf(f35,plain,(
% 0.08/0.28 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | (((in @ (sK3 @ X1 @ X0) @ X1)) = $true) | (((in @ (sK4 @ X1 @ X0) @ X0)) = $true) | (setext != $true)) )),
% 0.08/0.28 inference(cnf_transformation,[],[f23])).
% 0.08/0.28 thf(f42,plain,(
% 0.08/0.28 ( ! [X2 : $i,X3 : $o] : (($true = X3) | (((in @ X2 @ emptyset)) != $true) | ($true != $true)) )),
% 0.08/0.28 inference(definition_unfolding,[],[f24,f30])).
% 0.08/0.28 thf(f45,plain,(
% 0.08/0.28 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK4 @ X1 @ X0) @ X0)) = $true) | (X0 = X1) | (((in @ (sK3 @ X1 @ X0) @ X1)) = $true) | ($true != $true)) )),
% 0.08/0.28 inference(definition_unfolding,[],[f35,f29])).
% 0.08/0.28 thf(f51,plain,(
% 0.08/0.28 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK4 @ X1 @ X0) @ X0)) = $true) | (((in @ (sK3 @ X1 @ X0) @ X1)) = $true) | (X0 = X1)) )),
% 0.08/0.28 inference(trivial_inequality_removal,[],[f45])).
% 0.08/0.28 thf(f52,plain,(
% 0.08/0.28 ( ! [X2 : $i,X3 : $o] : ((((in @ X2 @ emptyset)) != $true) | ($true = X3)) )),
% 0.08/0.28 inference(trivial_inequality_removal,[],[f42])).
% 0.08/0.28 thf(f56,definition,(
% 0.08/0.28 spl7_1 <=> ! [X3 : $o] : ($true = X3)),
% 0.08/0.28 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.08/0.28 thf(f57,plain,(
% 0.08/0.28 ( ! [X3 : $o] : (($true = X3)) ) | ~spl7_1),
% 0.08/0.28 inference(avatar_component_clause,[],[f56])).
% 0.08/0.28 thf(f59,definition,(
% 0.08/0.28 spl7_2 <=> ! [X2 : $i] : (((in @ X2 @ emptyset)) != $true)),
% 0.08/0.28 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.08/0.28 thf(f60,plain,(
% 0.08/0.28 ( ! [X2 : $i] : ((((in @ X2 @ emptyset)) != $true)) ) | ~spl7_2),
% 0.08/0.28 inference(avatar_component_clause,[],[f59])).
% 0.08/0.28 thf(f61,plain,(
% 0.08/0.28 spl7_1 | spl7_2),
% 0.08/0.28 inference(avatar_split_clause,[],[f52,f59,f56])).
% 0.08/0.28 thf(f62,plain,(
% 0.08/0.28 ( ! [X0 : $i] : (($true != $true) | (((in @ (sK4 @ sK2 @ X0) @ X0)) = $true) | (sK2 = X0)) )),
% 0.08/0.28 inference(constrained_superposition,[],[f27,f51])).
% 0.08/0.28 thf(f64,plain,(
% 0.08/0.28 ( ! [X0 : $i] : ((((in @ (sK4 @ sK2 @ X0) @ X0)) = $true) | (sK2 = X0)) )),
% 0.08/0.28 inference(trivial_inequality_removal,[],[f62])).
% 0.08/0.28 thf(f66,plain,(
% 0.08/0.28 (emptyset = sK2) | ($true != $true) | ~spl7_2),
% 0.08/0.28 inference(constrained_superposition,[],[f60,f64])).
% 0.08/0.28 thf(f67,plain,(
% 0.08/0.28 (emptyset = sK2) | ~spl7_2),
% 0.08/0.28 inference(trivial_inequality_removal,[],[f66])).
% 0.08/0.28 thf(f68,plain,(
% 0.08/0.28 $false | ~spl7_2),
% 0.08/0.28 inference(forward_subsumption_resolution,[],[f67,f28])).
% 0.08/0.28 thf(f69,plain,(
% 0.08/0.28 ~spl7_2),
% 0.08/0.28 inference(avatar_contradiction_clause,[],[f68])).
% 0.08/0.28 thf(f71,plain,(
% 0.08/0.28 ($true != $true) | ~spl7_1),
% 0.08/0.28 inference(constrained_superposition,[],[f27,f57])).
% 0.08/0.28 thf(f73,plain,(
% 0.08/0.28 $false | ~spl7_1),
% 0.08/0.28 inference(trivial_inequality_removal,[],[f71])).
% 0.08/0.28 thf(f74,plain,(
% 0.08/0.28 ~spl7_1),
% 0.08/0.28 inference(avatar_contradiction_clause,[],[f73])).
% 0.08/0.28 cnf(s1, plain, spl7_1 | spl7_2, inference(sat_conversion,[],[f61])).
% 0.08/0.28 cnf(s2, plain, ~spl7_2, inference(sat_conversion,[],[f69])).
% 0.08/0.28 cnf(s3, plain, ~spl7_1, inference(sat_conversion,[],[f74])).
% 0.08/0.28 cnf(s4, plain, $false, inference(rat,[],[s1,s2,s3])).
% 0.08/0.28 thf(f78,plain,(
% 0.08/0.28 $false),
% 0.08/0.28 inference(avatar_sat_refutation,[],[s4])).
% 0.08/0.28 % SZS output end Proof for theBenchmark
% 0.08/0.28 % (92840)------------------------------
% 0.08/0.28 % (92840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.28 % (92840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.28 % (92840)CaDiCaL version: 2.1.3
% 0.08/0.28 % (92840)Termination reason: Refutation
% 0.08/0.28 % (92840)Time elapsed: 0.003 s
% 0.08/0.28 % (92840)Peak memory usage: 13 MB
% 0.08/0.28 % (92840)Instructions burned: 5 (million)
% 0.08/0.28 % (92834)Success in time 0.036 s
% 0.08/0.28 % Vampire exiting
%------------------------------------------------------------------------------