%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU503^2 : 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 : n016.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 08:29:50 AM UTC 2026
% Result : Theorem 0.24s 0.31s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU503^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n016.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:51:50 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.26 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
% 0.24/0.31 % (377383)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.31 % (377391)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=2222217423: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)
% 0.24/0.31 % (377390)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3047526472:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.31 % (377389)lrs+10_16_si=on:nwc=1.5:random_seed=2914657037:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.31 % (377391)Refutation not found, incomplete strategy
% 0.24/0.31 % (377391)------------------------------
% 0.24/0.31 % (377391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.31 % (377391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.31 % (377391)CaDiCaL version: 2.1.3
% 0.24/0.31 % (377391)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.31 % (377391)Time elapsed: 0.002 s
% 0.24/0.31 % (377391)Peak memory usage: 12 MB
% 0.24/0.31 % (377391)Instructions burned: 1 (million)
% 0.24/0.31 % (377390)Refutation not found, incomplete strategy
% 0.24/0.31 % (377390)------------------------------
% 0.24/0.31 % (377390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.31 % (377390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.31 % (377390)CaDiCaL version: 2.1.3
% 0.24/0.31 % (377390)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.31 % (377390)Time elapsed: 0.001 s
% 0.24/0.31 % (377390)Peak memory usage: 12 MB
% 0.24/0.31 % (377389)Refutation not found, incomplete strategy
% 0.24/0.31 % (377389)------------------------------
% 0.24/0.31 % (377389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.31 % (377389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.31 % (377389)CaDiCaL version: 2.1.3
% 0.24/0.31 % (377389)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.31 % (377389)Time elapsed: 0.001 s
% 0.24/0.31 % (377389)Peak memory usage: 12 MB
% 0.24/0.31 % (377391)------------------------------
% 0.24/0.31 % (377391)------------------------------
% 0.24/0.31 % (377390)------------------------------
% 0.24/0.31 % (377390)------------------------------
% 0.24/0.31 % (377389)------------------------------
% 0.24/0.31 % (377389)------------------------------
% 0.24/0.31 % (377393)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2982775927:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.31 % (377394)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.31 % (377394)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.24/0.31 % (377393) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-377383-377393"...
% 0.24/0.31 % (377393)...printing done.
% 0.24/0.31 % (377392)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=498046535:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.31 % (377393)Refutation found. Thanks to Tanya!
% 0.24/0.31 % SZS status Theorem for theBenchmark
% 0.24/0.31 % SZS output start Proof for theBenchmark
% 0.24/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.31 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.24/0.31 thf(func_def_2, type, emptysetE: $o).
% 0.24/0.31 thf(func_def_8, type, sK2: $o).
% 0.24/0.31 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.24/0.31 thf(f1,axiom,(
% 0.24/0.31 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.24/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE)).
% 0.24/0.31 thf(f2,conjecture,(
% 0.24/0.31 emptysetE => ! [X0 : $i] : ~(in @ X0 @ emptyset)),
% 0.24/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset)).
% 0.24/0.31 thf(f3,negated_conjecture,(
% 0.24/0.31 ~(emptysetE => ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 0.24/0.31 inference(negated_conjecture,[status(cth)],[f2])).
% 0.24/0.31 thf(f4,plain,(
% 0.24/0.31 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.24/0.31 inference(rectify,[],[f1])).
% 0.24/0.31 thf(f5,plain,(
% 0.24/0.31 ! [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) => ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 0.24/0.31 inference(fool_elimination,[],[f4])).
% 0.24/0.31 thf(f6,plain,(
% 0.24/0.31 ~(emptysetE => ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 0.24/0.31 inference(rectify,[],[f3])).
% 0.24/0.31 thf(f7,plain,(
% 0.24/0.31 ~((emptysetE = $true) => ! [X0 : $i] : ~ (((in @ X0 @ emptyset)) = $true))),
% 0.24/0.31 inference(fool_elimination,[],[f6])).
% 0.24/0.31 thf(f8,plain,(
% 0.24/0.31 ~((emptysetE = $true) => ! [X0 : $i] : (((in @ X0 @ emptyset)) != $true))),
% 0.24/0.31 inference(flattening,[],[f7])).
% 0.24/0.31 thf(f9,plain,(
% 0.24/0.31 (emptysetE = $true) <=> ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1))),
% 0.24/0.31 inference(ennf_transformation,[],[f5])).
% 0.24/0.31 thf(f10,plain,(
% 0.24/0.31 (emptysetE = $true) & ? [X0 : $i] : (((in @ X0 @ emptyset)) = $true)),
% 0.24/0.31 inference(ennf_transformation,[],[f8])).
% 0.24/0.31 thf(f11,plain,(
% 0.24/0.31 (emptysetE = $true) & (((in @ sK0 @ emptyset)) = $true)),
% 0.24/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f10])).
% 0.24/0.31 thf(f12,plain,(
% 0.24/0.31 ((emptysetE = $true) | ? [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) & ? [X1 : $o] : ($true != X1))) & (! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true))),
% 0.24/0.31 inference(nnf_transformation,[],[f9])).
% 0.24/0.31 thf(f13,plain,(
% 0.24/0.31 ((emptysetE = $true) | ? [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) & ? [X1 : $o] : ($true != X1))) & (! [X2 : $i] : ((((in @ X2 @ emptyset)) != $true) | ! [X3 : $o] : ($true = X3)) | (emptysetE != $true))),
% 0.24/0.31 inference(rectify,[],[f12])).
% 0.24/0.31 thf(f14,plain,(
% 0.24/0.31 ((emptysetE = $true) | ((((in @ sK1 @ emptyset)) = $true) & (sK2 != $true))) & (! [X2 : $i] : ((((in @ X2 @ emptyset)) != $true) | ! [X3 : $o] : ($true = X3)) | (emptysetE != $true))),
% 0.24/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f13])).
% 0.24/0.31 thf(f15,plain,(
% 0.24/0.31 (((in @ sK0 @ emptyset)) = $true)),
% 0.24/0.31 inference(cnf_transformation,[],[f11])).
% 0.24/0.31 thf(f16,plain,(
% 0.24/0.31 (emptysetE = $true)),
% 0.24/0.31 inference(cnf_transformation,[],[f11])).
% 0.24/0.31 thf(f17,plain,(
% 0.24/0.31 ( ! [X2 : $i,X3 : $o] : ((((in @ X2 @ emptyset)) != $true) | ($true = X3) | (emptysetE != $true)) )),
% 0.24/0.31 inference(cnf_transformation,[],[f14])).
% 0.24/0.31 thf(f20,definition,(
% 0.24/0.31 ($false != $true)),
% 0.24/0.31 introduced(theory,[fool_distinctness_axiom])).
% 0.24/0.31 thf(f24,plain,(
% 0.24/0.31 ( ! [X2 : $i,X3 : $o] : ((((in @ X2 @ emptyset)) != $true) | ($true = X3) | ($true != $true)) )),
% 0.24/0.31 inference(definition_unfolding,[],[f17,f16])).
% 0.24/0.31 thf(f25,plain,(
% 0.24/0.31 ( ! [X2 : $i,X3 : $o] : ((((in @ X2 @ emptyset)) != $true) | ($true = X3)) )),
% 0.24/0.31 inference(trivial_inequality_removal,[],[f24])).
% 0.24/0.31 thf(f27,definition,(
% 0.24/0.31 spl3_1 <=> ! [X3 : $o] : ($true = X3)),
% 0.24/0.31 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.24/0.31 thf(f28,plain,(
% 0.24/0.31 ( ! [X3 : $o] : (($true = X3)) ) | ~spl3_1),
% 0.24/0.31 inference(avatar_component_clause,[],[f27])).
% 0.24/0.31 thf(f30,definition,(
% 0.24/0.31 spl3_2 <=> ! [X2 : $i] : (((in @ X2 @ emptyset)) != $true)),
% 0.24/0.31 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.24/0.31 thf(f31,plain,(
% 0.24/0.31 ( ! [X2 : $i] : ((((in @ X2 @ emptyset)) != $true)) ) | ~spl3_2),
% 0.24/0.31 inference(avatar_component_clause,[],[f30])).
% 0.24/0.31 thf(f32,plain,(
% 0.24/0.31 spl3_1 | spl3_2),
% 0.24/0.31 inference(avatar_split_clause,[],[f25,f30,f27])).
% 0.24/0.31 thf(f33,plain,(
% 0.24/0.31 ($true != $true) | ~spl3_2),
% 0.24/0.31 inference(constrained_superposition,[],[f31,f15])).
% 0.24/0.31 thf(f34,plain,(
% 0.24/0.31 $false | ~spl3_2),
% 0.24/0.31 inference(trivial_inequality_removal,[],[f33])).
% 0.24/0.31 thf(f35,plain,(
% 0.24/0.31 ~spl3_2),
% 0.24/0.31 inference(avatar_contradiction_clause,[],[f34])).
% 0.24/0.31 thf(f39,plain,(
% 0.24/0.31 ( ! [X0 : $o] : (($false != X0)) ) | ~spl3_1),
% 0.24/0.31 inference(constrained_superposition,[],[f20,f28])).
% 0.24/0.31 thf(f40,plain,(
% 0.24/0.31 $false | ~spl3_1),
% 0.24/0.31 inference(equality_resolution,[],[f39])).
% 0.24/0.31 thf(f41,plain,(
% 0.24/0.31 ~spl3_1),
% 0.24/0.31 inference(avatar_contradiction_clause,[],[f40])).
% 0.24/0.31 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f32])).
% 0.24/0.31 cnf(s2, plain, ~spl3_2, inference(sat_conversion,[],[f35])).
% 0.24/0.31 cnf(s3, plain, ~spl3_1, inference(sat_conversion,[],[f41])).
% 0.24/0.31 cnf(s4, plain, $false, inference(rat,[],[s1,s2,s3])).
% 0.24/0.31 thf(f42,plain,(
% 0.24/0.31 $false),
% 0.24/0.31 inference(avatar_sat_refutation,[],[s4])).
% 0.24/0.31 % SZS output end Proof for theBenchmark
% 0.24/0.31 % (377393)------------------------------
% 0.24/0.31 % (377393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.31 % (377393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.31 % (377393)CaDiCaL version: 2.1.3
% 0.24/0.31 % (377393)Termination reason: Refutation
% 0.24/0.31 % (377393)Time elapsed: 0.003 s
% 0.24/0.31 % (377393)Peak memory usage: 13 MB
% 0.24/0.31 % (377393)Instructions burned: 2 (million)
% 0.24/0.31 % (377383)Success in time 0.043 s
% 0.24/0.31 % Vampire exiting
%------------------------------------------------------------------------------