%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU502^2 : 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 : n007.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 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU502^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.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 13:44:41 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.29 % (3380568)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (3380573)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3910757278:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (3380573)Refutation not found, incomplete strategy
% 0.21/0.29 % (3380573)------------------------------
% 0.21/0.29 % (3380573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3380573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3380573)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3380573)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (3380573)Time elapsed: 0.001 s
% 0.21/0.29 % (3380573)Peak memory usage: 12 MB
% 0.21/0.29 % (3380573)Instructions burned: 1 (million)
% 0.21/0.29 % (3380573)------------------------------
% 0.21/0.29 % (3380573)------------------------------
% 0.21/0.29 % (3380579)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (3380579)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
% 0.21/0.29 % (3380574)lrs+10_16_si=on:nwc=1.5:random_seed=1663101480:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (3380575)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1077313241:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (3380579)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1172034111:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (3380577)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=147786912:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (3380576)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=3617206439: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)
% 0.21/0.29 % (3380578)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1216521331:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (3380575)Refutation not found, incomplete strategy
% 0.21/0.29 % (3380575)------------------------------
% 0.21/0.29 % (3380575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3380575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3380574)Refutation not found, incomplete strategy
% 0.21/0.29 % (3380574)------------------------------
% 0.21/0.29 % (3380574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3380575)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3380574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3380575)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (3380575)Time elapsed: 0.001 s
% 0.21/0.29 % (3380575)Peak memory usage: 12 MB
% 0.21/0.29 % (3380574)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3380574)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (3380574)Time elapsed: 0.001 s
% 0.21/0.29 % (3380574)Peak memory usage: 12 MB
% 0.21/0.29 % (3380577) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3380568-3380577"...
% 0.21/0.29 % (3380576)Refutation not found, incomplete strategy
% 0.21/0.29 % (3380576)------------------------------
% 0.21/0.29 % (3380576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3380576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3380576)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3380576)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (3380576)Time elapsed: 0.001 s
% 0.21/0.29 % (3380576)Peak memory usage: 12 MB
% 0.21/0.29 % (3380576)Instructions burned: 1 (million)
% 0.21/0.29 % (3380575)------------------------------
% 0.21/0.29 % (3380575)------------------------------
% 0.21/0.29 % (3380574)------------------------------
% 0.21/0.29 % (3380574)------------------------------
% 0.21/0.29 % (3380578) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3380568-3380578"...
% 0.21/0.29 % (3380576)------------------------------
% 0.21/0.29 % (3380576)------------------------------
% 0.21/0.29 % (3380579) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3380568-3380579"...
% 0.21/0.29 % (3380577)...printing done.
% 0.21/0.29 % (3380581)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1742648864:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.29 % (3380578)...printing done.
% 0.21/0.29 % (3380577)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.29 thf(func_def_2, type, emptysetE: $o).
% 0.21/0.29 thf(func_def_8, type, sK2: $o).
% 0.21/0.29 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)).
% 0.21/0.29 thf(f2,conjecture,(
% 0.21/0.29 emptysetE => ! [X0 : $i] : ((in @ X0 @ emptyset) => $false)),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse)).
% 0.21/0.29 thf(f3,negated_conjecture,(
% 0.21/0.29 ~(emptysetE => ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f2])).
% 0.21/0.29 thf(f4,plain,(
% 0.21/0.29 ~(emptysetE => ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 0.21/0.29 inference(rectify,[],[f3])).
% 0.21/0.29 thf(f5,plain,(
% 0.21/0.29 ~((emptysetE = $true) => ! [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) => $false))),
% 0.21/0.29 inference(fool_elimination,[],[f4])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ! [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) => ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ~((emptysetE = $true) => ! [X0 : $i] : ~ (((in @ X0 @ emptyset)) = $true))),
% 0.21/0.29 inference(true_and_false_elimination,[],[f5])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ~((emptysetE = $true) => ! [X0 : $i] : (((in @ X0 @ emptyset)) != $true))),
% 0.21/0.29 inference(flattening,[],[f8])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 (emptysetE = $true) <=> ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1))),
% 0.21/0.29 inference(ennf_transformation,[],[f7])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 (emptysetE = $true) & ? [X0 : $i] : (((in @ X0 @ emptyset)) = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f9])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 (emptysetE = $true) & ($true = ((in @ sK0 @ emptyset)))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f11])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 ((emptysetE = $true) | ? [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) & ? [X1 : $o] : ($true != X1))) & (! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f10])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 ((emptysetE = $true) | ? [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) & ? [X1 : $o] : ($true != X1))) & (! [X2 : $i] : (($true != ((in @ X2 @ emptyset))) | ! [X3 : $o] : ($true = X3)) | (emptysetE != $true))),
% 0.21/0.29 inference(rectify,[],[f13])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 ((emptysetE = $true) | (($true = ((in @ sK1 @ emptyset))) & ($true != sK2))) & (! [X2 : $i] : (($true != ((in @ X2 @ emptyset))) | ! [X3 : $o] : ($true = X3)) | (emptysetE != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f14])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 ($true = ((in @ sK0 @ emptyset)))),
% 0.21/0.29 inference(cnf_transformation,[],[f12])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 (emptysetE = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f12])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $o] : (($true = X3) | (emptysetE != $true) | ($true != ((in @ X2 @ emptyset)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f15])).
% 0.21/0.29 thf(f21,definition,(
% 0.21/0.29 ($true != $false)),
% 0.21/0.29 introduced(theory,[fool_distinctness_axiom])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $o] : (($true != ((in @ X2 @ emptyset))) | ($true = X3)) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f18,f17])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true != $true) | ($true = X0)) )),
% 0.21/0.29 inference(superposition,[],[f23,f16])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = X0)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f24])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 ( ! [X0 : $o] : (($false != X0)) )),
% 0.21/0.29 inference(superposition,[],[f21,f25])).
% 0.21/0.29 thf(f32,plain,(
% 0.21/0.29 ($false != $false)),
% 0.21/0.29 inference(imitation,[],[f27])).
% 0.21/0.29 thf(f34,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f32])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (3380577)------------------------------
% 0.21/0.29 % (3380577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3380577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3380577)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3380577)Termination reason: Refutation
% 0.21/0.29 % (3380577)Time elapsed: 0.002 s
% 0.21/0.29 % (3380577)Peak memory usage: 12 MB
% 0.21/0.29 % (3380577)Instructions burned: 1 (million)
% 0.21/0.29 % (3380568)Success in time 0.035 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------