%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV081^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:37:36 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV081^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:07:02 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.19/0.27 % (196585)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (196596)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.27 % (196596)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
% 0.19/0.27 % (196596)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=2848944744:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.27 % (196596)Refutation not found, incomplete strategy
% 0.19/0.27 % (196596)------------------------------
% 0.19/0.27 % (196596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (196596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (196596)CaDiCaL version: 2.1.3
% 0.19/0.27 % (196596)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.27 % (196596)Time elapsed: 0.003 s
% 0.19/0.27 % (196596)Peak memory usage: 12 MB
% 0.19/0.27 % (196596)Instructions burned: 8 (million)
% 0.19/0.27 % (196596)------------------------------
% 0.19/0.27 % (196596)------------------------------
% 0.19/0.27 % (196591)lrs+10_16_si=on:nwc=1.5:random_seed=2208445870:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.27 % (196594)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2621359734:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.27 % (196590)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4052386766:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.27 % (196592)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2120276288:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.27 % (196593)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=3640476335: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)
% 0.19/0.27 % (196595)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=530658346:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.27 % (196591) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-196585-196591"...
% 0.19/0.27 % (196592) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-196585-196592"...
% 0.19/0.27 % (196594) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-196585-196594"...
% 0.19/0.27 % (196590) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-196585-196590"...
% 0.19/0.27 % (196595) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-196585-196595"...
% 0.19/0.27 % (196591)...printing done.
% 0.19/0.27 % (196592)...printing done.
% 0.19/0.27 % (196594)...printing done.
% 0.19/0.27 % (196593) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-196585-196593"...
% 0.19/0.27 % (196590)...printing done.
% 0.19/0.27 % (196592)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_3, type, sK0: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.27 thf(func_def_4, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.27 thf(func_def_5, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.27 thf(func_def_6, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.27 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.19/0.27 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.27 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.27 thf(f1,conjecture,(
% 0.19/0.27 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X3 : ($i > $o)] : (X0 @ X3 @ X3) & ? [X1 : ($i > $o),X2 : ($i > $o)] : (X0 @ X1 @ X2) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (((X0 @ X4 @ X5) & (X0 @ X3 @ X4)) => (X0 @ X3 @ X5)))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120_1_pme)).
% 0.19/0.27 thf(f2,negated_conjecture,(
% 0.19/0.27 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X3 : ($i > $o)] : (X0 @ X3 @ X3) & ? [X1 : ($i > $o),X2 : ($i > $o)] : (X0 @ X1 @ X2) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (((X0 @ X4 @ X5) & (X0 @ X3 @ X4)) => (X0 @ X3 @ X5)))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.27 thf(f3,plain,(
% 0.19/0.27 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ? [X2 : ($i > $o),X3 : ($i > $o)] : (X0 @ X2 @ X3) & ! [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : (((X0 @ X6 @ X5) & (X0 @ X4 @ X6)) => (X0 @ X4 @ X5)))),
% 0.19/0.27 inference(rectify,[],[f2])).
% 0.19/0.27 thf(f4,plain,(
% 0.19/0.27 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X3 : ($i > $o),X2 : ($i > $o)] : ($true = ((X0 @ X2 @ X3))) & ! [X6 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X4 @ X6)) = $true) & (((X0 @ X6 @ X5)) = $true)) => (((X0 @ X4 @ X5)) = $true)) & ! [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) = $true))),
% 0.19/0.27 inference(fool_elimination,[],[f3])).
% 0.19/0.27 thf(f5,plain,(
% 0.19/0.27 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X3 : ($i > $o),X2 : ($i > $o)] : ($true != ((X0 @ X2 @ X3))) | ? [X6 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((((X0 @ X4 @ X5)) != $true) & ((((X0 @ X4 @ X6)) = $true) & (((X0 @ X6 @ X5)) = $true))) | ? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true))),
% 0.19/0.27 inference(ennf_transformation,[],[f4])).
% 0.19/0.27 thf(f6,plain,(
% 0.19/0.27 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X5 : ($i > $o),X4 : ($i > $o),X6 : ($i > $o)] : ((((X0 @ X6 @ X5)) = $true) & (((X0 @ X4 @ X6)) = $true) & (((X0 @ X4 @ X5)) != $true)) | ! [X3 : ($i > $o),X2 : ($i > $o)] : ($true != ((X0 @ X2 @ X3))) | ? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true))),
% 0.19/0.27 inference(flattening,[],[f5])).
% 0.19/0.27 thf(f7,plain,(
% 0.19/0.27 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X3 @ X1)) = $true) & ($true = ((X0 @ X2 @ X3))) & (((X0 @ X2 @ X1)) != $true)) | ! [X4 : ($i > $o),X5 : ($i > $o)] : ($true != ((X0 @ X5 @ X4))) | ? [X6 : ($i > $o)] : ($true != ((X0 @ X6 @ X6))))),
% 0.19/0.27 inference(rectify,[],[f6])).
% 0.19/0.27 thf(f8,plain,(
% 0.19/0.27 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((($true = ((X0 @ (sK2 @ X0) @ (sK0 @ X0)))) & (((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $true) & (((X0 @ (sK1 @ X0) @ (sK0 @ X0))) != $true)) | ! [X4 : ($i > $o),X5 : ($i > $o)] : ($true != ((X0 @ X5 @ X4))) | (((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true))),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X6,sK3 @ X0),skolemize(X6,sK3 @ X0),skolemize(X6,sK3 @ X0),skolemize(X6,sK3 @ X0)],[f7])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 ( ! [X0 : (($i > $o) > ($i > $o) > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true) | (((X0 @ (sK1 @ X0) @ (sK0 @ X0))) != $true) | ($true != ((X0 @ X5 @ X4)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))) != $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ X5 @ X4)) != $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))) != $true)) )),
% 0.19/0.27 inference(primitive_instantiation,[],[f9])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 ($true != $true) | ($true != $true) | ($true != $true)),
% 0.19/0.27 inference(beta-eta_normalization,[],[f16])).
% 0.19/0.27 thf(f21,plain,(
% 0.19/0.27 ($true != $true)),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f20])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f21])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (196592)------------------------------
% 0.19/0.27 % (196592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (196592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (196592)CaDiCaL version: 2.1.3
% 0.19/0.27 % (196592)Termination reason: Refutation
% 0.19/0.27 % (196592)Time elapsed: 0.002 s
% 0.19/0.27 % (196592)Peak memory usage: 12 MB
% 0.19/0.27 % (196592)Instructions burned: 2 (million)
% 0.19/0.27 % (196585)Success in time 0.034 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------