%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV257^5 : 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 : 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 08:38:08 AM UTC 2026
% Result : Theorem 0.25s 0.36s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV257^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n007.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 15:25:56 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running higher-order theorem proving
% 0.25/0.30 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
% 0.25/0.36 % (3503495)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.36 % (3503503)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=917801734: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)
% 0.25/0.36 % (3503503)Refutation not found, incomplete strategy
% 0.25/0.36 % (3503503)------------------------------
% 0.25/0.36 % (3503503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (3503503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (3503503)CaDiCaL version: 2.1.3
% 0.25/0.36 % (3503503)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.36 % (3503503)Time elapsed: 0.002 s
% 0.25/0.36 % (3503503)Peak memory usage: 12 MB
% 0.25/0.36 % (3503503)Instructions burned: 2 (million)
% 0.25/0.36 % (3503503)------------------------------
% 0.25/0.36 % (3503503)------------------------------
% 0.25/0.36 % (3503506)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.36 % (3503506)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
% 0.25/0.36 % (3503501)lrs+10_16_si=on:nwc=1.5:random_seed=3005242806:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.36 % (3503500)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2501412400:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.36 % (3503502)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1268683190:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.36 % (3503504)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3071930195:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.36 % (3503505)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=939443950:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.36 % (3503506)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=3447384121:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.36 % (3503504)Refutation not found, incomplete strategy
% 0.25/0.36 % (3503504)------------------------------
% 0.25/0.36 % (3503504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (3503504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (3503504)CaDiCaL version: 2.1.3
% 0.25/0.36 % (3503504)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.36 % (3503504)Time elapsed: 0.004 s
% 0.25/0.36 % (3503504)Peak memory usage: 12 MB
% 0.25/0.36 % (3503504)Instructions burned: 3 (million)
% 0.25/0.36 % (3503502)Instruction limit reached!
% 0.25/0.36 % (3503502)------------------------------
% 0.25/0.36 % (3503502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (3503502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (3503502)CaDiCaL version: 2.1.3
% 0.25/0.36 % (3503502)Termination reason: Instruction limit
% 0.25/0.36 % (3503502)Termination phase: Saturation
% 0.25/0.36 % (3503502)Time elapsed: 0.004 s
% 0.25/0.36 % (3503502)Peak memory usage: 12 MB
% 0.25/0.36 % (3503502)Instructions burned: 3 (million)
% 0.25/0.36 % (3503504)------------------------------
% 0.25/0.36 % (3503504)------------------------------
% 0.25/0.36 % (3503508)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1272127341:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.25/0.36 % (3503501) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3503495-3503501"...
% 0.25/0.36 % (3503508)Instruction limit reached!
% 0.25/0.36 % (3503508)------------------------------
% 0.25/0.36 % (3503508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (3503508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (3503508)CaDiCaL version: 2.1.3
% 0.25/0.36 % (3503508)Termination reason: Instruction limit
% 0.25/0.36 % (3503508)Termination phase: Saturation
% 0.25/0.36 % (3503508)Time elapsed: 0.002 s
% 0.25/0.36 % (3503508)Peak memory usage: 12 MB
% 0.25/0.36 % (3503508)Instructions burned: 3 (million)
% 0.25/0.36 % (3503501)...printing done.
% 0.25/0.36 % (3503506)Refutation not found, incomplete strategy
% 0.25/0.36 % (3503506)------------------------------
% 0.25/0.36 % (3503506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (3503501)Refutation found. Thanks to Tanya!
% 0.25/0.36 % SZS status Theorem for theBenchmark
% 0.25/0.36 % SZS output start Proof for theBenchmark
% 0.25/0.36 thf(type_def_5, type, a: $tType).
% 0.25/0.36 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.25/0.36 thf(func_def_0, type, cOPEN: ((a > $o) > $o)).
% 0.25/0.36 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.25/0.36 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.25/0.36 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.25/0.36 thf(func_def_7, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.25/0.36 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.25/0.36 thf(func_def_9, type, sK0: (((a > $o) > $o) > a > $o)).
% 0.25/0.36 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.25/0.36 thf(func_def_11, type, sK1: a).
% 0.25/0.36 thf(func_def_12, type, sK2: (((a > $o) > $o) > a)).
% 0.25/0.36 thf(func_def_13, type, sK3: a).
% 0.25/0.36 thf(func_def_14, type, sK4: (a > $o)).
% 0.25/0.36 thf(f1,conjecture,(
% 0.25/0.36 (! [X1 : ((a > $o) > $o)] : (! [X2 : (a > $o)] : ((X1 @ X2) => (cOPEN @ X2)) => (cOPEN @ (^[X2 : a] : (? [X3 : (a > $o)] : ((X1 @ X3) & (X3 @ X2)))))) & ! [X5 : (a > $o),X4 : (a > $o)] : (((cOPEN @ X5) & (cOPEN @ X4)) => (cOPEN @ (^[X2 : a] : ((X5 @ X2) & (X4 @ X2))))) & (cOPEN @ (^[X0 : a] : ($true)))) => (cOPEN @ (^[X0 : a] : ($false)))),
% 0.25/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM625_pme)).
% 0.25/0.36 thf(f2,negated_conjecture,(
% 0.25/0.36 ~((! [X1 : ((a > $o) > $o)] : (! [X2 : (a > $o)] : ((X1 @ X2) => (cOPEN @ X2)) => (cOPEN @ (^[X2 : a] : (? [X3 : (a > $o)] : ((X1 @ X3) & (X3 @ X2)))))) & ! [X5 : (a > $o),X4 : (a > $o)] : (((cOPEN @ X5) & (cOPEN @ X4)) => (cOPEN @ (^[X2 : a] : ((X5 @ X2) & (X4 @ X2))))) & (cOPEN @ (^[X0 : a] : ($true)))) => (cOPEN @ (^[X0 : a] : ($false))))),
% 0.25/0.36 inference(negated_conjecture,[status(cth)],[f1])).
% 0.25/0.36 thf(f3,plain,(
% 0.25/0.36 ~((! [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : ((X0 @ X1) => (cOPEN @ X1)) => (cOPEN @ (^[X2 : a] : (? [X3 : (a > $o)] : ((X0 @ X3) & (X3 @ X2)))))) & ! [X4 : (a > $o),X5 : (a > $o)] : (((cOPEN @ X4) & (cOPEN @ X5)) => (cOPEN @ (^[X6 : a] : ((X4 @ X6) & (X5 @ X6))))) & (cOPEN @ (^[X7 : a] : ($true)))) => (cOPEN @ (^[X8 : a] : ($false))))),
% 0.25/0.36 inference(rectify,[],[f2])).
% 0.25/0.36 thf(f4,plain,(
% 0.25/0.36 ~((! [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : (($true = ((X0 @ X1))) => (((cOPEN @ X1)) = $true)) => ($true = ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1))))))))) & ! [X4 : (a > $o),X5 : (a > $o)] : (((((cOPEN @ X4)) = $true) & (((cOPEN @ X5)) = $true)) => ($true = ((cOPEN @ (^[Y0 : a]: ((X5 @ Y0) & (X4 @ Y0))))))) & ($true = ((cOPEN @ (^[Y0 : a]: ($true)))))) => ($true = ((cOPEN @ (^[Y0 : a]: ($false))))))),
% 0.25/0.36 inference(fool_elimination,[],[f3])).
% 0.25/0.36 thf(f5,plain,(
% 0.25/0.36 ~((! [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : (($true = ((X0 @ X1))) => (((cOPEN @ X1)) = $true)) => ($true = ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1))))))))) & ($true = ((cOPEN @ (^[Y0 : a]: ($true))))) & ! [X2 : (a > $o),X3 : (a > $o)] : (((((cOPEN @ X2)) = $true) & (((cOPEN @ X3)) = $true)) => ($true = ((cOPEN @ (^[Y0 : a]: ((X3 @ Y0) & (X2 @ Y0)))))))) => ($true = ((cOPEN @ (^[Y0 : a]: ($false))))))),
% 0.25/0.36 inference(rectify,[],[f4])).
% 0.25/0.36 thf(f6,plain,(
% 0.25/0.36 ($true != ((cOPEN @ (^[Y0 : a]: ($false))))) & (! [X0 : ((a > $o) > $o)] : (? [X1 : (a > $o)] : (($true = ((X0 @ X1))) & (((cOPEN @ X1)) != $true)) | ($true = ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1))))))))) & ($true = ((cOPEN @ (^[Y0 : a]: ($true))))) & ! [X2 : (a > $o),X3 : (a > $o)] : (($true = ((cOPEN @ (^[Y0 : a]: ((X3 @ Y0) & (X2 @ Y0)))))) | ((((cOPEN @ X2)) != $true) | (((cOPEN @ X3)) != $true))))),
% 0.25/0.36 inference(ennf_transformation,[],[f5])).
% 0.25/0.36 thf(f7,plain,(
% 0.25/0.36 ! [X3 : (a > $o),X2 : (a > $o)] : ((((cOPEN @ X3)) != $true) | (((cOPEN @ X2)) != $true) | ($true = ((cOPEN @ (^[Y0 : a]: ((X3 @ Y0) & (X2 @ Y0))))))) & ($true = ((cOPEN @ (^[Y0 : a]: ($true))))) & ! [X0 : ((a > $o) > $o)] : (? [X1 : (a > $o)] : (($true = ((X0 @ X1))) & (((cOPEN @ X1)) != $true)) | ($true = ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1))))))))) & ($true != ((cOPEN @ (^[Y0 : a]: ($false)))))),
% 0.25/0.36 inference(flattening,[],[f6])).
% 0.25/0.36 thf(f8,plain,(
% 0.25/0.36 ! [X0 : (a > $o),X1 : (a > $o)] : (($true != ((cOPEN @ X0))) | (((cOPEN @ X1)) != $true) | ($true = ((cOPEN @ (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))))))) & ($true = ((cOPEN @ (^[Y0 : a]: ($true))))) & ! [X2 : ((a > $o) > $o)] : (? [X3 : (a > $o)] : (($true = ((X2 @ X3))) & (((cOPEN @ X3)) != $true)) | ($true = ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X2 @ Y1))))))))) & ($true != ((cOPEN @ (^[Y0 : a]: ($false)))))),
% 0.25/0.36 inference(rectify,[],[f7])).
% 0.25/0.36 thf(f9,plain,(
% 0.25/0.36 ! [X0 : (a > $o),X1 : (a > $o)] : (($true != ((cOPEN @ X0))) | (((cOPEN @ X1)) != $true) | ($true = ((cOPEN @ (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))))))) & ($true = ((cOPEN @ (^[Y0 : a]: ($true))))) & ! [X2 : ((a > $o) > $o)] : ((($true = ((X2 @ (sK0 @ X2)))) & ($true != ((cOPEN @ (sK0 @ X2))))) | ($true = ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X2 @ Y1))))))))) & ($true != ((cOPEN @ (^[Y0 : a]: ($false)))))),
% 0.25/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X2)],[f8])).
% 0.25/0.36 thf(f10,plain,(
% 0.25/0.36 ($true != ((cOPEN @ (^[Y0 : a]: ($false)))))),
% 0.25/0.36 inference(cnf_transformation,[],[f9])).
% 0.25/0.36 thf(f12,plain,(
% 0.25/0.36 ( ! [X2 : ((a > $o) > $o)] : (($true = ((X2 @ (sK0 @ X2)))) | ($true = ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X2 @ Y1))))))))) )),
% 0.25/0.36 inference(cnf_transformation,[],[f9])).
% 0.25/0.36 thf(f38,plain,(
% 0.25/0.36 (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & ((^[Y2 : a > $o]: ($false)) @ Y1))))))) = $true) | ((((^[Y0 : a > $o]: ($false)) @ (sK0 @ (^[Y0 : a > $o]: ($false))))) = $true)),
% 0.25/0.36 inference(primitive_instantiation,[],[f12])).
% 0.25/0.36 thf(f60,plain,(
% 0.25/0.36 (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & $false)))))) = $true) | ($true = $false)),
% 0.25/0.36 inference(beta-eta_normalization,[],[f38])).
% 0.25/0.36 thf(f61,plain,(
% 0.25/0.36 (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & $false)))))) = $true)),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f60])).
% 0.25/0.36 thf(f62,plain,(
% 0.25/0.36 ($true = ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ($false)))))))),
% 0.25/0.36 inference(boolean_simplification,[],[f61])).
% 0.25/0.36 thf(f73,plain,(
% 0.25/0.36 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ($false))))) | ($true != $true)),
% 0.25/0.36 inference(constrained_superposition,[],[f10,f62])).
% 0.25/0.36 thf(f78,plain,(
% 0.25/0.36 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ($false)))))),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f73])).
% 0.25/0.36 thf(f80,plain,(
% 0.25/0.36 ((((^[Y0 : a]: ($false)) @ sK3)) != (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ($false)))) @ sK3)))),
% 0.25/0.36 inference(negative_extensionality,[],[f78])).
% 0.25/0.36 thf(f81,plain,(
% 0.25/0.36 ($true = (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ($false)))) @ sK3))) | ($true = (((^[Y0 : a]: ($false)) @ sK3)))),
% 0.25/0.36 inference(xor_proxy_clausification,[],[f80])).
% 0.25/0.36 thf(f85,plain,(
% 0.25/0.36 ($true = $false) | ($true = ((?? @ (a > $o) @ (^[Y0 : a > $o]: ($false)))))),
% 0.25/0.36 inference(beta-eta_normalization,[],[f81])).
% 0.25/0.36 thf(f86,plain,(
% 0.25/0.36 ($true = $false) | ($true = (((^[Y0 : a > $o]: ($false)) @ sK4)))),
% 0.25/0.36 inference(sigma_proxy_clausification,[],[f85])).
% 0.25/0.36 thf(f87,plain,(
% 0.25/0.36 ($true = (((^[Y0 : a > $o]: ($false)) @ sK4)))),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f86])).
% 0.25/0.36 thf(f88,plain,(
% 0.25/0.36 ($true = $false)),
% 0.25/0.36 inference(beta-eta_normalization,[],[f87])).
% 0.25/0.36 thf(f89,plain,(
% 0.25/0.36 $false),
% 0.25/0.36 inference(trivial_inequality_removal,[],[f88])).
% 0.25/0.36 % SZS output end Proof for theBenchmark
% 0.25/0.36 % (3503501)------------------------------
% 0.25/0.36 % (3503501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (3503501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (3503501)CaDiCaL version: 2.1.3
% 0.25/0.36 % (3503501)Termination reason: Refutation
% 0.25/0.36 % (3503501)Time elapsed: 0.011 s
% 0.25/0.36 % (3503501)Peak memory usage: 12 MB
% 0.25/0.36 % (3503501)Instructions burned: 10 (million)
% 0.25/0.36 % (3503495)Success in time 0.05 s
% 0.25/0.36 % Vampire exiting
%------------------------------------------------------------------------------