%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV087^5 : 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 : 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 08:37:37 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV087^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 15:07:16 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.20/0.26 % (197432)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.26 % (197437)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3767042866:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.26 % (197443)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.26 % (197443)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
% 0.20/0.26 % (197437) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-197432-197437"...
% 0.20/0.26 % (197438)lrs+10_16_si=on:nwc=1.5:random_seed=2931775376:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.26 % (197439)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2182988069:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.26 % (197440)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=3139051696: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)
% 0.20/0.26 % (197442)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=206977435:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.26 % (197441)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3325559336:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.26 % (197437)...printing done.
% 0.20/0.26 % (197443)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=370969581:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.26 % (197437)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% 0.20/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.26 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.26 thf(func_def_4, type, sP0: ((($i > $o) > ($i > $o) > $o) > $o)).
% 0.20/0.26 thf(func_def_5, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_6, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_7, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_8, type, sK4: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_9, type, sK5: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_10, type, sK6: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.20/0.26 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.26 thf(func_def_17, type, sK9: ((($i > $o) > ($i > $o) > $o) > $i)).
% 0.20/0.26 thf(func_def_18, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(f1,conjecture,(
% 0.20/0.26 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X4 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => (X4 = X5)) & ! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))))),
% 0.20/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120H_pme)).
% 0.20/0.26 thf(f2,negated_conjecture,(
% 0.20/0.26 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X4 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => (X4 = X5)) & ! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ~(X0 @ (^[X1 : $i] : ($true)) @ (^[X1 : $i] : ($false))))),
% 0.20/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.26 thf(f3,plain,(
% 0.20/0.26 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X2)) => (X1 = X2)) & ! [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (((X0 @ X4 @ X5) & (X0 @ X3 @ X4)) => (X0 @ X3 @ X5)) & ! [X6 : ($i > $o)] : (X0 @ X6 @ X6) & ~(X0 @ (^[X7 : $i] : ($true)) @ (^[X8 : $i] : ($false))))),
% 0.20/0.26 inference(rectify,[],[f2])).
% 0.20/0.26 thf(f4,plain,(
% 0.20/0.26 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (((((X0 @ X1 @ X2)) = $true) & (((X0 @ X2 @ X1)) = $true)) => (X1 = X2)) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (((((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true)) => ($true = ((X0 @ X3 @ X5)))) & ! [X6 : ($i > $o)] : ($true = ((X0 @ X6 @ X6))) & ~ ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.20/0.26 inference(fool_elimination,[],[f3])).
% 0.20/0.26 thf(f5,plain,(
% 0.20/0.26 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X6 : ($i > $o)] : ($true = ((X0 @ X6 @ X6))) & ($true != ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))) & ! [X1 : ($i > $o),X2 : ($i > $o)] : (((((X0 @ X1 @ X2)) = $true) & (((X0 @ X2 @ X1)) = $true)) => (X1 = X2)) & ! [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (((((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true)) => ($true = ((X0 @ X3 @ X5)))))),
% 0.20/0.26 inference(flattening,[],[f4])).
% 0.20/0.26 thf(f6,plain,(
% 0.20/0.26 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X6 : ($i > $o)] : ($true != ((X0 @ X6 @ X6))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))) | ? [X1 : ($i > $o),X2 : ($i > $o)] : ((X1 != X2) & ((((X0 @ X1 @ X2)) = $true) & (((X0 @ X2 @ X1)) = $true))) | ? [X3 : ($i > $o),X5 : ($i > $o),X4 : ($i > $o)] : (($true != ((X0 @ X3 @ X5))) & ((((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true))))),
% 0.20/0.26 inference(ennf_transformation,[],[f5])).
% 0.20/0.26 thf(f7,plain,(
% 0.20/0.26 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X6 : ($i > $o)] : ($true != ((X0 @ X6 @ X6))) | ? [X1 : ($i > $o),X2 : ($i > $o)] : ((X1 != X2) & (((X0 @ X1 @ X2)) = $true) & (((X0 @ X2 @ X1)) = $true)) | ? [X4 : ($i > $o),X5 : ($i > $o),X3 : ($i > $o)] : (($true != ((X0 @ X3 @ X5))) & (((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true)) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.20/0.26 inference(flattening,[],[f6])).
% 0.20/0.26 thf(f8,definition,(
% 0.20/0.26 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X4 : ($i > $o),X5 : ($i > $o),X3 : ($i > $o)] : (($true != ((X0 @ X3 @ X5))) & (((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true)) | ~ ($true = ((sP0 @ X0))))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.20/0.26 thf(f9,plain,(
% 0.20/0.26 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X6 : ($i > $o)] : ($true != ((X0 @ X6 @ X6))) | ? [X1 : ($i > $o),X2 : ($i > $o)] : ((X1 != X2) & (((X0 @ X1 @ X2)) = $true) & (((X0 @ X2 @ X1)) = $true)) | ($true = ((sP0 @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.20/0.26 inference(definition_folding,[],[f7,f8])).
% 0.20/0.26 thf(f10,plain,(
% 0.20/0.26 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X4 : ($i > $o),X5 : ($i > $o),X3 : ($i > $o)] : (($true != ((X0 @ X3 @ X5))) & (((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true)) | ($true != ((sP0 @ X0))))),
% 0.20/0.26 inference(nnf_transformation,[],[f8])).
% 0.20/0.26 thf(f11,plain,(
% 0.20/0.26 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (($true != ((X0 @ X3 @ X2))) & (((X0 @ X1 @ X2)) = $true) & ($true = ((X0 @ X3 @ X1)))) | ($true != ((sP0 @ X0))))),
% 0.20/0.26 inference(rectify,[],[f10])).
% 0.20/0.26 thf(f12,plain,(
% 0.20/0.26 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((($true != ((X0 @ (sK3 @ X0) @ (sK2 @ X0)))) & ($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) & ($true = ((X0 @ (sK3 @ X0) @ (sK1 @ X0))))) | ($true != ((sP0 @ X0))))),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f11])).
% 0.20/0.26 thf(f13,plain,(
% 0.20/0.26 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true) | ? [X2 : ($i > $o),X3 : ($i > $o)] : ((X2 != X3) & (((X0 @ X2 @ X3)) = $true) & ($true = ((X0 @ X3 @ X2)))) | ($true = ((sP0 @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.20/0.26 inference(rectify,[],[f9])).
% 0.20/0.26 thf(f14,plain,(
% 0.20/0.26 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK4 @ X0) @ (sK4 @ X0))) != $true) | ((((sK5 @ X0)) != ((sK6 @ X0))) & ($true = ((X0 @ (sK5 @ X0) @ (sK6 @ X0)))) & ($true = ((X0 @ (sK6 @ X0) @ (sK5 @ X0))))) | ($true = ((sP0 @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f13])).
% 0.20/0.27 thf(f15,plain,(
% 0.20/0.27 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((X0 @ (sK3 @ X0) @ (sK1 @ X0))))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f12])).
% 0.20/0.27 thf(f16,plain,(
% 0.20/0.27 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0))))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f12])).
% 0.20/0.27 thf(f17,plain,(
% 0.20/0.27 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK3 @ X0) @ (sK2 @ X0)))) | ($true != ((sP0 @ X0)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f12])).
% 0.20/0.27 thf(f18,plain,(
% 0.20/0.27 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK4 @ X0) @ (sK4 @ X0))) != $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))) | ($true = ((X0 @ (sK6 @ X0) @ (sK5 @ X0)))) | ($true = ((sP0 @ X0)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f14])).
% 0.20/0.27 thf(f20,plain,(
% 0.20/0.27 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK4 @ X0) @ (sK4 @ X0))) != $true) | (((sK5 @ X0)) != ((sK6 @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))) | ($true = ((sP0 @ X0)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f14])).
% 0.20/0.27 thf(f23,plain,(
% 0.20/0.27 ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) = $true) | (((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))),
% 0.20/0.27 inference(primitive_instantiation,[],[f20])).
% 0.20/0.27 thf(f39,plain,(
% 0.20/0.27 (((sK5 @ =)) != ((sK6 @ =))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true != (((sK4 @ =) = (sK4 @ =)))) | ($true = ((sP0 @ =)))),
% 0.20/0.27 inference(beta-eta_normalization,[],[f23])).
% 0.20/0.27 thf(f40,plain,(
% 0.20/0.27 ($true = ((sP0 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true != (((sK4 @ =) = (sK4 @ =)))) | (((sK5 @ =)) != ((sK6 @ =)))),
% 0.20/0.27 inference(equality_proxy_clausification,[],[f39])).
% 0.20/0.27 thf(f41,plain,(
% 0.20/0.27 (((sK5 @ =)) != ((sK6 @ =))) | ($true = ((sP0 @ =))) | (((sK4 @ =)) != ((sK4 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.20/0.27 inference(equality_proxy_clausification,[],[f40])).
% 0.20/0.27 thf(f42,plain,(
% 0.20/0.27 ($true = ((sP0 @ =))) | (((sK5 @ =)) != ((sK6 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f41])).
% 0.20/0.27 thf(f45,definition,(
% 0.20/0.27 spl7_1 <=> ($true = ((sP0 @ =)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.20/0.27 thf(f47,plain,(
% 0.20/0.27 ($true = ((sP0 @ =))) | ~spl7_1),
% 0.20/0.27 inference(avatar_component_clause,[],[f45])).
% 0.20/0.27 thf(f49,definition,(
% 0.20/0.27 spl7_2 <=> (((sK5 @ =)) = ((sK6 @ =)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.20/0.27 thf(f53,definition,(
% 0.20/0.27 spl7_3 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.20/0.27 thf(f55,plain,(
% 0.20/0.27 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl7_3),
% 0.20/0.27 inference(avatar_component_clause,[],[f53])).
% 0.20/0.27 thf(f56,plain,(
% 0.20/0.27 spl7_1 | ~spl7_2 | spl7_3),
% 0.20/0.27 inference(avatar_split_clause,[],[f42,f53,f49,f45])).
% 0.20/0.27 thf(f57,plain,(
% 0.20/0.27 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) = $true)),
% 0.20/0.27 inference(primitive_instantiation,[],[f18])).
% 0.20/0.27 thf(f72,plain,(
% 0.20/0.27 ($true = ((sP0 @ =))) | ((((sK6 @ =) = (sK5 @ =))) = $true) | ($true != (((sK4 @ =) = (sK4 @ =)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.20/0.27 inference(beta-eta_normalization,[],[f57])).
% 0.20/0.27 thf(f73,plain,(
% 0.20/0.27 ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))))) | ($true != (((sK4 @ =) = (sK4 @ =)))) | (((sK5 @ =)) = ((sK6 @ =))) | ($true = ((sP0 @ =)))),
% 0.20/0.27 inference(equality_proxy_clausification,[],[f72])).
% 0.20/0.27 thf(f74,plain,(
% 0.20/0.27 ($true = ((sP0 @ =))) | ($true != (((sK4 @ =) = (sK4 @ =)))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | (((sK5 @ =)) = ((sK6 @ =)))),
% 0.20/0.27 inference(equality_proxy_clausification,[],[f73])).
% 0.20/0.27 thf(f75,plain,(
% 0.20/0.27 (((sK5 @ =)) = ((sK6 @ =))) | (((sK4 @ =)) != ((sK4 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ($true = ((sP0 @ =)))),
% 0.20/0.27 inference(equality_proxy_clausification,[],[f74])).
% 0.20/0.27 thf(f76,plain,(
% 0.20/0.27 ($true = ((sP0 @ =))) | (((sK5 @ =)) = ((sK6 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f75])).
% 0.20/0.27 thf(f87,plain,(
% 0.20/0.27 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($false)) @ X1)) = (((^[Y0 : $i]: ($true)) @ X1)))) ) | ~spl7_3),
% 0.20/0.27 inference(argument_congruence,[],[f55])).
% 0.20/0.27 thf(f88,plain,(
% 0.20/0.27 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($false)) @ X1)) = $true) | ((((^[Y0 : $i]: ($true)) @ X1)) = $false)) ) | ~spl7_3),
% 0.20/0.27 inference(iff_proxy_clausification,[],[f87])).
% 0.20/0.27 thf(f91,plain,(
% 0.20/0.27 ($true = $false) | ($true = $false) | ~spl7_3),
% 0.20/0.27 inference(beta-eta_normalization,[],[f88])).
% 0.20/0.27 thf(f92,plain,(
% 0.20/0.27 ($true = $false) | ~spl7_3),
% 0.20/0.27 inference(duplicate_literal_removal,[],[f91])).
% 0.20/0.27 thf(f93,plain,(
% 0.20/0.27 $false | ~spl7_3),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f92])).
% 0.20/0.27 thf(f94,plain,(
% 0.20/0.27 ~spl7_3),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f93])).
% 0.20/0.27 thf(f95,plain,(
% 0.20/0.27 spl7_3 | spl7_1 | spl7_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f76,f49,f45,f53])).
% 0.20/0.27 thf(f376,plain,(
% 0.20/0.27 ($true = (((sK3 @ =) = (sK1 @ =)))) | ($true != $true) | ~spl7_1),
% 0.20/0.27 inference(constrained_superposition,[],[f15,f47])).
% 0.20/0.27 thf(f377,plain,(
% 0.20/0.27 ($true != $true) | (((sK3 @ =)) = ((sK1 @ =))) | ~spl7_1),
% 0.20/0.27 inference(equality_proxy_clausification,[],[f376])).
% 0.20/0.27 thf(f378,plain,(
% 0.20/0.27 (((sK3 @ =)) = ((sK1 @ =))) | ~spl7_1),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f377])).
% 0.20/0.27 thf(f384,plain,(
% 0.20/0.27 ($true != $true) | ($true = (((sK1 @ =) = (sK2 @ =)))) | ~spl7_1),
% 0.20/0.27 inference(constrained_superposition,[],[f16,f47])).
% 0.20/0.27 thf(f385,plain,(
% 0.20/0.27 (((sK2 @ =)) = ((sK1 @ =))) | ($true != $true) | ~spl7_1),
% 0.20/0.27 inference(equality_proxy_clausification,[],[f384])).
% 0.20/0.27 thf(f386,plain,(
% 0.20/0.27 (((sK2 @ =)) = ((sK1 @ =))) | ~spl7_1),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f385])).
% 0.20/0.27 thf(f392,plain,(
% 0.20/0.27 ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | (((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) != $true)),
% 0.20/0.27 inference(primitive_instantiation,[],[f17])).
% 0.20/0.27 thf(f412,plain,(
% 0.20/0.27 ($true != ((sP0 @ =))) | ($true != (((sK3 @ =) = (sK2 @ =))))),
% 0.20/0.27 inference(beta-eta_normalization,[],[f392])).
% 0.20/0.27 thf(f413,plain,(
% 0.20/0.27 (((sK3 @ =)) != ((sK2 @ =))) | ($true != ((sP0 @ =)))),
% 0.20/0.27 inference(equality_proxy_clausification,[],[f412])).
% 0.20/0.27 thf(f425,plain,(
% 0.20/0.27 (((sK3 @ =)) != ((sK2 @ =))) | ~spl7_1),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f413,f47])).
% 0.20/0.27 thf(f430,plain,(
% 0.20/0.27 (((sK3 @ =)) != ((sK1 @ =))) | ~spl7_1),
% 0.20/0.27 inference(forward_demodulation,[],[f425,f386])).
% 0.20/0.27 thf(f431,plain,(
% 0.20/0.27 $false | ~spl7_1),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f430,f378])).
% 0.20/0.27 thf(f432,plain,(
% 0.20/0.27 ~spl7_1),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f431])).
% 0.20/0.27 cnf(s1, plain, spl7_1 | ~spl7_2 | spl7_3, inference(sat_conversion,[],[f56])).
% 0.20/0.27 cnf(s3, plain, ~spl7_3, inference(sat_conversion,[],[f94])).
% 0.20/0.27 cnf(s4, plain, spl7_1 | spl7_2 | spl7_3, inference(sat_conversion,[],[f95])).
% 0.20/0.27 cnf(s8, plain, ~spl7_1, inference(sat_conversion,[],[f432])).
% 0.20/0.27 cnf(s9, plain, spl7_2 | spl7_3, inference(rat,[],[s4,s8])).
% 0.20/0.27 cnf(s10, plain, spl7_2, inference(rat,[],[s9,s3])).
% 0.20/0.27 cnf(s11, plain, $false, inference(rat,[],[s1,s3,s10,s8])).
% 0.20/0.27 thf(f433,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(avatar_sat_refutation,[],[s11])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (197437)------------------------------
% 0.20/0.27 % (197437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (197437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (197437)CaDiCaL version: 2.1.3
% 0.20/0.27 % (197437)Termination reason: Refutation
% 0.20/0.27 % (197437)Time elapsed: 0.008 s
% 0.20/0.27 % (197437)Peak memory usage: 13 MB
% 0.20/0.27 % (197437)Instructions burned: 27 (million)
% 0.20/0.27 % (197432)Success in time 0.033 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------