%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP004^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:07:37 AM UTC 2026
% Result : Theorem 0.23s 0.35s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP004^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 % Computer : n003.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 19:22:14 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.29 Running higher-order theorem proving
% 0.23/0.31 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
% 0.23/0.35 % (2938835)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.35 % (2938843)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=2304319797: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)
% 0.23/0.35 % (2938841)lrs+10_16_si=on:nwc=1.5:random_seed=2976526097:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.35 % (2938846)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.35 % (2938846)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
% 0.23/0.35 % (2938843) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2938835-2938843"...
% 0.23/0.35 % (2938842)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3612547013:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.35 % (2938840)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1204666983:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.35 % (2938844)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4254130532:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.35 % (2938843)...printing done.
% 0.23/0.35 % (2938845)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2723163194:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.35 % (2938846)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=3569149290:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.35 % (2938843)Refutation found. Thanks to Tanya!
% 0.23/0.35 % SZS status Theorem for theBenchmark
% 0.23/0.35 % SZS output start Proof for theBenchmark
% 0.23/0.35 thf(type_def_5, type, tyop_2Emin_2Ebool: $tType).
% 0.23/0.35 thf(type_def_6, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 0.23/0.35 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.35 thf(type_def_8, type, sK0: $tType).
% 0.23/0.35 thf(func_def_0, type, c_2Ebool_2E_21: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.35 thf(func_def_1, type, c_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 0.23/0.35 thf(func_def_2, type, c_2Emin_2E_3D: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.35 thf(func_def_3, type, c_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 0.23/0.35 thf(func_def_4, type, c_2Ebool_2E_3F: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.35 thf(func_def_5, type, c_2Epred__set_2ECHOICE: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.35 thf(func_def_6, type, c_2Epred__set_2EDELETE: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > $o))).
% 0.23/0.35 thf(func_def_7, type, c_2Ebool_2EIN: !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.23/0.35 thf(func_def_8, type, c_2Epred__set_2EREST: !>[X0: $tType]:(((X0 > $o) > X0 > $o))).
% 0.23/0.35 thf(func_def_9, type, c_2Epred__set_2ESUBSET: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.23/0.35 thf(func_def_10, type, c_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 0.23/0.35 thf(func_def_11, type, c_2Ebool_2E_7E: ($o > $o)).
% 0.23/0.35 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.23/0.35 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.35 thf(func_def_17, type, sK1: (sK0 > $o)).
% 0.23/0.35 thf(func_def_18, type, sK2: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.35 thf(func_def_19, type, sK3: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.23/0.35 thf(func_def_20, type, sK4: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.23/0.35 thf(f8,axiom,(
% 0.23/0.35 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) <=> ! [X3 : X0] : ((c_2Ebool_2EIN @ X0 @ X3 @ X1) => (c_2Ebool_2EIN @ X0 @ X3 @ X2)))),
% 0.23/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF)).
% 0.23/0.35 thf(f9,axiom,(
% 0.23/0.35 ! [X0 : $tType,X2 : X0,X1 : (X0 > $o),X3 : X0] : (((~ (X2 = X3)) & (c_2Ebool_2EIN @ X0 @ X2 @ X1)) <=> (c_2Ebool_2EIN @ X0 @ X2 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X3)))),
% 0.23/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DELETE)).
% 0.23/0.35 thf(f10,axiom,(
% 0.23/0.35 ! [X0 : $tType,X1 : (X0 > $o)] : (((c_2Epred__set_2EREST @ X0 @ X1)) = ((c_2Epred__set_2EDELETE @ X0 @ X1 @ (c_2Epred__set_2ECHOICE @ X0 @ X1))))),
% 0.23/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__DEF)).
% 0.23/0.36 thf(f11,conjecture,(
% 0.23/0.36 ! [X0 : $tType,X1 : (X0 > $o)] : (c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X1) @ X1)),
% 0.23/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__SUBSET)).
% 0.23/0.36 thf(f12,negated_conjecture,(
% 0.23/0.36 ~ ! [X0 : $tType,X1 : (X0 > $o)] : (c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X1) @ X1)),
% 0.23/0.36 inference(negated_conjecture,[status(cth)],[f11])).
% 0.23/0.36 thf(f13,plain,(
% 0.23/0.36 ! [X0 : $tType,X1 : X0,X2 : (X0 > $o),X3 : X0] : (((~ (X1 = X3)) & (c_2Ebool_2EIN @ X0 @ X1 @ X2)) <=> (c_2Ebool_2EIN @ X0 @ X1 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3)))),
% 0.23/0.36 inference(rectify,[],[f9])).
% 0.23/0.36 thf(f14,plain,(
% 0.23/0.36 ! [X0 : $tType,X3 : X0,X2 : (X0 > $o),X1 : X0] : (($true = ((c_2Ebool_2EIN @ X0 @ X1 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3)))) <=> (($true = ((c_2Ebool_2EIN @ X0 @ X1 @ X2))) & ($true = ((~ (X1 = X3))))))),
% 0.23/0.36 inference(fool_elimination,[],[f13])).
% 0.23/0.36 thf(f17,plain,(
% 0.23/0.36 ~ ! [X0 : $tType,X1 : (X0 > $o)] : (c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X1) @ X1)),
% 0.23/0.36 inference(rectify,[],[f12])).
% 0.23/0.36 thf(f18,plain,(
% 0.23/0.36 ~ ! [X0 : $tType,X1 : (X0 > $o)] : (((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X1) @ X1)) = $true)),
% 0.23/0.36 inference(fool_elimination,[],[f17])).
% 0.23/0.36 thf(f21,plain,(
% 0.23/0.36 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2) <=> ! [X3 : X0] : ((c_2Ebool_2EIN @ X0 @ X3 @ X1) => (c_2Ebool_2EIN @ X0 @ X3 @ X2)))),
% 0.23/0.36 inference(rectify,[],[f8])).
% 0.23/0.36 thf(f22,plain,(
% 0.23/0.36 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2)) = $true) <=> ! [X3 : X0] : ((((c_2Ebool_2EIN @ X0 @ X3 @ X1)) = $true) => (((c_2Ebool_2EIN @ X0 @ X3 @ X2)) = $true)))),
% 0.23/0.36 inference(fool_elimination,[],[f21])).
% 0.23/0.36 thf(f34,plain,(
% 0.23/0.36 ? [X0 : $tType,X1 : (X0 > $o)] : (((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X1) @ X1)) != $true)),
% 0.23/0.36 inference(ennf_transformation,[],[f18])).
% 0.23/0.36 thf(f35,plain,(
% 0.23/0.36 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2)) = $true) <=> ! [X3 : X0] : ((((c_2Ebool_2EIN @ X0 @ X3 @ X2)) = $true) | (((c_2Ebool_2EIN @ X0 @ X3 @ X1)) != $true)))),
% 0.23/0.36 inference(ennf_transformation,[],[f22])).
% 0.23/0.36 thf(f36,plain,(
% 0.23/0.36 (((c_2Epred__set_2ESUBSET @ sK0 @ (c_2Epred__set_2EREST @ sK0 @ sK1) @ sK1)) != $true)),
% 0.23/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f34])).
% 0.23/0.36 thf(f47,plain,(
% 0.23/0.36 ! [X0 : $tType,X3 : X0,X2 : (X0 > $o),X1 : X0] : ((($true = ((c_2Ebool_2EIN @ X0 @ X1 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3)))) | (($true != ((c_2Ebool_2EIN @ X0 @ X1 @ X2))) | ($true != ((~ (X1 = X3)))))) & ((($true = ((c_2Ebool_2EIN @ X0 @ X1 @ X2))) & ($true = ((~ (X1 = X3))))) | ($true != ((c_2Ebool_2EIN @ X0 @ X1 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3))))))),
% 0.23/0.36 inference(nnf_transformation,[],[f14])).
% 0.23/0.36 thf(f48,plain,(
% 0.23/0.36 ! [X0 : $tType,X3 : X0,X2 : (X0 > $o),X1 : X0] : ((($true = ((c_2Ebool_2EIN @ X0 @ X1 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3)))) | ($true != ((c_2Ebool_2EIN @ X0 @ X1 @ X2))) | ($true != ((~ (X1 = X3))))) & ((($true = ((c_2Ebool_2EIN @ X0 @ X1 @ X2))) & ($true = ((~ (X1 = X3))))) | ($true != ((c_2Ebool_2EIN @ X0 @ X1 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3))))))),
% 0.23/0.36 inference(flattening,[],[f47])).
% 0.23/0.36 thf(f49,plain,(
% 0.23/0.36 ! [X0 : $tType,X1 : X0,X2 : (X0 > $o),X3 : X0] : ((($true = ((c_2Ebool_2EIN @ X0 @ X3 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X1)))) | (((c_2Ebool_2EIN @ X0 @ X3 @ X2)) != $true) | (((~ (X3 = X1))) != $true)) & (((((c_2Ebool_2EIN @ X0 @ X3 @ X2)) = $true) & (((~ (X3 = X1))) = $true)) | ($true != ((c_2Ebool_2EIN @ X0 @ X3 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X1))))))),
% 0.23/0.36 inference(rectify,[],[f48])).
% 0.23/0.36 thf(f50,plain,(
% 0.23/0.36 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2)) = $true) | ? [X3 : X0] : ((((c_2Ebool_2EIN @ X0 @ X3 @ X2)) != $true) & (((c_2Ebool_2EIN @ X0 @ X3 @ X1)) = $true))) & (! [X3 : X0] : ((((c_2Ebool_2EIN @ X0 @ X3 @ X2)) = $true) | (((c_2Ebool_2EIN @ X0 @ X3 @ X1)) != $true)) | (((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2)) != $true)))),
% 0.23/0.36 inference(nnf_transformation,[],[f35])).
% 0.23/0.36 thf(f51,plain,(
% 0.23/0.36 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2)) = $true) | ? [X3 : X0] : ((((c_2Ebool_2EIN @ X0 @ X3 @ X2)) != $true) & (((c_2Ebool_2EIN @ X0 @ X3 @ X1)) = $true))) & (! [X4 : X0] : (($true = ((c_2Ebool_2EIN @ X0 @ X4 @ X2))) | (((c_2Ebool_2EIN @ X0 @ X4 @ X1)) != $true)) | (((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2)) != $true)))),
% 0.23/0.36 inference(rectify,[],[f50])).
% 0.23/0.36 thf(f52,plain,(
% 0.23/0.36 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2)) = $true) | (($true != ((c_2Ebool_2EIN @ X0 @ (sK3 @ X0 @ X2 @ X1) @ X2))) & ($true = ((c_2Ebool_2EIN @ X0 @ (sK3 @ X0 @ X2 @ X1) @ X1))))) & (! [X4 : X0] : (($true = ((c_2Ebool_2EIN @ X0 @ X4 @ X2))) | (((c_2Ebool_2EIN @ X0 @ X4 @ X1)) != $true)) | (((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2)) != $true)))),
% 0.23/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK2 @ X0 @ X1)],[f51])).
% 0.23/0.36 thf(f59,plain,(
% 0.23/0.36 (((c_2Epred__set_2ESUBSET @ sK0 @ (c_2Epred__set_2EREST @ sK0 @ sK1) @ sK1)) != $true)),
% 0.23/0.36 inference(cnf_transformation,[],[f36])).
% 0.23/0.36 thf(f71,plain,(
% 0.23/0.36 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : X0] : (($true != ((c_2Ebool_2EIN @ X0 @ X3 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X1)))) | (((c_2Ebool_2EIN @ X0 @ X3 @ X2)) = $true)) )),
% 0.23/0.36 inference(cnf_transformation,[],[f49])).
% 0.23/0.36 thf(f74,plain,(
% 0.23/0.36 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (($true = ((c_2Ebool_2EIN @ X0 @ (sK3 @ X0 @ X2 @ X1) @ X1))) | (((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2)) = $true)) )),
% 0.23/0.36 inference(cnf_transformation,[],[f52])).
% 0.23/0.36 thf(f75,plain,(
% 0.23/0.36 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (($true != ((c_2Ebool_2EIN @ X0 @ (sK3 @ X0 @ X2 @ X1) @ X2))) | (((c_2Epred__set_2ESUBSET @ X0 @ X1 @ X2)) = $true)) )),
% 0.23/0.36 inference(cnf_transformation,[],[f52])).
% 0.23/0.36 thf(f76,plain,(
% 0.23/0.36 ( ! [X0 : $tType,X1 : (X0 > $o)] : ((((c_2Epred__set_2EREST @ X0 @ X1)) = ((c_2Epred__set_2EDELETE @ X0 @ X1 @ (c_2Epred__set_2ECHOICE @ X0 @ X1))))) )),
% 0.23/0.36 inference(cnf_transformation,[],[f10])).
% 0.23/0.36 thf(f99,definition,(
% 0.23/0.36 spl5_1 <=> (((c_2Epred__set_2ESUBSET @ sK0 @ (c_2Epred__set_2EREST @ sK0 @ sK1) @ sK1)) = $true)),
% 0.23/0.36 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.23/0.36 thf(f101,plain,(
% 0.23/0.36 (((c_2Epred__set_2ESUBSET @ sK0 @ (c_2Epred__set_2EREST @ sK0 @ sK1) @ sK1)) != $true) | spl5_1),
% 0.23/0.36 inference(avatar_component_clause,[],[f99])).
% 0.23/0.36 thf(f102,plain,(
% 0.23/0.36 ~spl5_1),
% 0.23/0.36 inference(avatar_split_clause,[],[f59,f99])).
% 0.23/0.36 thf(f112,plain,(
% 0.23/0.36 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (($true != $true) | (((c_2Ebool_2EIN @ X0 @ (sK3 @ X0 @ X1 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3)) @ X2)) = $true) | (((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3) @ X1)) = $true)) )),
% 0.23/0.36 inference(superposition,[],[f71,f74])).
% 0.23/0.36 thf(f113,plain,(
% 0.23/0.36 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : ((((c_2Ebool_2EIN @ X0 @ (sK3 @ X0 @ X1 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3)) @ X2)) = $true) | (((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X2 @ X3) @ X1)) = $true)) )),
% 0.23/0.36 inference(trivial_inequality_removal,[],[f112])).
% 0.23/0.36 thf(f139,plain,(
% 0.23/0.36 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (($true = ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X2) @ X1))) | ($true != $true) | ($true = ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X2) @ X1)))) )),
% 0.23/0.36 inference(superposition,[],[f75,f113])).
% 0.23/0.36 thf(f143,plain,(
% 0.23/0.36 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (($true = ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X2) @ X1))) | ($true != $true)) )),
% 0.23/0.36 inference(duplicate_literal_removal,[],[f139])).
% 0.23/0.36 thf(f144,plain,(
% 0.23/0.36 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (($true = ((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EDELETE @ X0 @ X1 @ X2) @ X1)))) )),
% 0.23/0.36 inference(trivial_inequality_removal,[],[f143])).
% 0.23/0.36 thf(f159,plain,(
% 0.23/0.36 ( ! [X0 : $tType,X1 : (X0 > $o)] : ((((c_2Epred__set_2ESUBSET @ X0 @ (c_2Epred__set_2EREST @ X0 @ X1) @ X1)) = $true)) )),
% 0.23/0.36 inference(superposition,[],[f144,f76])).
% 0.23/0.36 thf(f172,plain,(
% 0.23/0.36 ($true != $true) | spl5_1),
% 0.23/0.36 inference(superposition,[],[f101,f159])).
% 0.23/0.36 thf(f174,plain,(
% 0.23/0.36 $false | spl5_1),
% 0.23/0.36 inference(trivial_inequality_removal,[],[f172])).
% 0.23/0.36 thf(f175,plain,(
% 0.23/0.36 spl5_1),
% 0.23/0.36 inference(avatar_contradiction_clause,[],[f174])).
% 0.23/0.36 cnf(s1, plain, ~spl5_1, inference(sat_conversion,[],[f102])).
% 0.23/0.36 cnf(s3, plain, spl5_1, inference(sat_conversion,[],[f175])).
% 0.23/0.36 cnf(s4, plain, $false, inference(rat,[],[s1,s3])).
% 0.23/0.36 thf(f177,plain,(
% 0.23/0.36 $false),
% 0.23/0.36 inference(avatar_sat_refutation,[],[s4])).
% 0.23/0.36 % SZS output end Proof for theBenchmark
% 0.23/0.36 % (2938843)------------------------------
% 0.23/0.36 % (2938843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (2938843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (2938843)CaDiCaL version: 2.1.3
% 0.23/0.36 % (2938843)Termination reason: Refutation
% 0.23/0.36 % (2938843)Time elapsed: 0.012 s
% 0.23/0.36 % (2938843)Peak memory usage: 13 MB
% 0.23/0.36 % (2938843)Instructions burned: 19 (million)
% 0.23/0.36 % (2938835)Success in time 0.038 s
% 0.23/0.36 % Vampire exiting
%------------------------------------------------------------------------------