%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n005.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 08:38:58 AM UTC 2026
% Result : Theorem 0.35s 0.42s
% Output : Refutation 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV087^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.29 % Computer : n005.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Sep 29 15:07:01 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.29/0.34 Running first-order model finding
% 0.29/0.34 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/0.42 % (1780261)Will run a generic schedule for satisfiability detection.
% 0.35/0.42 % (1780266)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3553838626_2999 on theBenchmark for (2999ds/0Mi)
% 0.35/0.42 % Exception at run slice level
% 0.35/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.35/0.42 % (1780267)% WARNING: option uhcvi not known.
% 0.35/0.42 % (1780267)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1509121010:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.35/0.42 % (1780268)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=238160653:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.35/0.42 % (1780269)dis+10_1_sil=32000:sp=arity:random_seed=3525391689:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.35/0.42 % (1780270)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4258465226:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.35/0.42 % (1780272)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1655575183:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.35/0.42 % (1780267)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.35/0.42 % (1780270)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.35/0.42 % (1780267)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.35/0.42 % (1780271)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=611378078:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.35/0.42 % (1780274)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=449739021:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.35/0.42 % Exception at run slice level
% 0.35/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.35/0.42 % (1780271) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1780261-1780271"...
% 0.35/0.42 % (1780270) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1780261-1780270"...
% 0.35/0.42 % (1780271)...printing done.
% 0.35/0.42 % (1780270)...printing done.
% 0.35/0.42 % (1780271)Refutation found. Thanks to Tanya!
% 0.35/0.42 % SZS status Theorem for theBenchmark
% 0.35/0.42 % SZS output start Proof for theBenchmark
% 0.35/0.42 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.35/0.42 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.35/0.42 thf(func_def_4, type, sP0: ((($i > $o) > ($i > $o) > $o) > $o)).
% 0.35/0.42 thf(func_def_5, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.35/0.42 thf(func_def_6, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.35/0.42 thf(func_def_7, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.35/0.42 thf(func_def_8, type, sK4: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.35/0.42 thf(func_def_9, type, sK5: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.35/0.42 thf(func_def_10, type, sK6: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.35/0.42 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.35/0.42 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.35/0.42 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 0.35/0.42 thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.35/0.42 thf(func_def_16, type, db2: !>[X0: $tType]:(X0)).
% 0.35/0.42 thf(func_def_17, type, db3: !>[X0: $tType]:(X0)).
% 0.35/0.42 thf(func_def_18, type, db4: !>[X0: $tType]:(X0)).
% 0.35/0.42 thf(f1,conjecture,(
% 0.35/0.42 ? [X0 : (($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))))),
% 0.35/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120H_pme)).
% 0.35/0.42 thf(f2,negated_conjecture,(
% 0.35/0.42 ~ ? [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))))),
% 0.35/0.42 inference(negated_conjecture,[status(cth)],[f1])).
% 0.35/0.42 thf(f3,plain,(
% 0.35/0.42 ~ ? [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))))),
% 0.35/0.42 inference(rectify,[],[f2])).
% 0.35/0.42 thf(f4,plain,(
% 0.35/0.42 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (((((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true)) => (X1 = X2)) & ! [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true)) => (((X0 @ X3 @ X5)) = $true)) & ! [X6 : ($i > $o)] : (((X0 @ X6 @ X6)) = $true) & ~ ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.35/0.42 inference(fool_elimination,[],[f3])).
% 0.35/0.42 thf(f5,plain,(
% 0.35/0.42 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (((((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true)) => (X1 = X2)) & ! [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : (((((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true)) => (((X0 @ X3 @ X5)) = $true)) & ! [X6 : ($i > $o)] : (((X0 @ X6 @ X6)) = $true) & ($true != ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.35/0.42 inference(flattening,[],[f4])).
% 0.35/0.42 thf(f6,plain,(
% 0.35/0.42 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : ((X1 != X2) & ((((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true))) | ? [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((((X0 @ X3 @ X5)) != $true) & ((((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true))) | ? [X6 : ($i > $o)] : (((X0 @ X6 @ X6)) != $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.35/0.42 inference(ennf_transformation,[],[f5])).
% 0.35/0.42 thf(f7,plain,(
% 0.35/0.42 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : ((X1 != X2) & (((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true)) | ? [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((((X0 @ X3 @ X5)) != $true) & (((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true)) | ? [X6 : ($i > $o)] : (((X0 @ X6 @ X6)) != $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.35/0.42 inference(flattening,[],[f6])).
% 0.35/0.42 thf(f8,definition,(
% 0.35/0.42 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((((X0 @ X3 @ X5)) != $true) & (((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true)) | ~ ($true = ((sP0 @ X0))))),
% 0.35/0.42 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.35/0.42 thf(f9,plain,(
% 0.35/0.42 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : ((X1 != X2) & (((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true)) | ($true = ((sP0 @ X0))) | ? [X6 : ($i > $o)] : (((X0 @ X6 @ X6)) != $true) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.35/0.42 inference(definition_folding,[],[f7,f8])).
% 0.35/0.42 thf(f10,plain,(
% 0.35/0.42 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X3 : ($i > $o),X4 : ($i > $o),X5 : ($i > $o)] : ((((X0 @ X3 @ X5)) != $true) & (((X0 @ X4 @ X5)) = $true) & (((X0 @ X3 @ X4)) = $true)) | ($true != ((sP0 @ X0))))),
% 0.35/0.43 inference(nnf_transformation,[],[f8])).
% 0.35/0.43 thf(f11,plain,(
% 0.35/0.43 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X1 @ X3)) != $true) & (((X0 @ X2 @ X3)) = $true) & (((X0 @ X1 @ X2)) = $true)) | ($true != ((sP0 @ X0))))),
% 0.35/0.43 inference(rectify,[],[f10])).
% 0.35/0.43 thf(f12,plain,(
% 0.35/0.43 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((($true != ((X0 @ (sK1 @ X0) @ (sK3 @ X0)))) & ($true = ((X0 @ (sK2 @ X0) @ (sK3 @ X0)))) & ($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0))))) | ($true != ((sP0 @ X0))))),
% 0.35/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f11])).
% 0.35/0.43 thf(f13,plain,(
% 0.35/0.43 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o)] : ((X1 != X2) & (((X0 @ X2 @ X1)) = $true) & (((X0 @ X1 @ X2)) = $true)) | ($true = ((sP0 @ X0))) | ? [X3 : ($i > $o)] : ($true != ((X0 @ X3 @ X3))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.35/0.43 inference(rectify,[],[f9])).
% 0.35/0.43 thf(f14,plain,(
% 0.35/0.43 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (((((sK4 @ X0)) != ((sK5 @ X0))) & ($true = ((X0 @ (sK5 @ X0) @ (sK4 @ X0)))) & ($true = ((X0 @ (sK4 @ X0) @ (sK5 @ X0))))) | ($true = ((sP0 @ X0))) | ($true != ((X0 @ (sK6 @ X0) @ (sK6 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false))))))),
% 0.35/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f13])).
% 0.35/0.43 thf(f15,plain,(
% 0.35/0.43 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0))))) )),
% 0.35/0.43 inference(cnf_transformation,[],[f12])).
% 0.35/0.43 thf(f16,plain,(
% 0.35/0.43 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((sP0 @ X0))) | ($true = ((X0 @ (sK2 @ X0) @ (sK3 @ X0))))) )),
% 0.35/0.43 inference(cnf_transformation,[],[f12])).
% 0.35/0.43 thf(f17,plain,(
% 0.35/0.43 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK1 @ X0) @ (sK3 @ X0)))) | ($true != ((sP0 @ X0)))) )),
% 0.35/0.43 inference(cnf_transformation,[],[f12])).
% 0.35/0.43 thf(f18,plain,(
% 0.35/0.43 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK6 @ X0) @ (sK6 @ X0)))) | ($true = ((sP0 @ X0))) | ($true = ((X0 @ (sK4 @ X0) @ (sK5 @ X0)))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))))) )),
% 0.35/0.43 inference(cnf_transformation,[],[f14])).
% 0.35/0.43 thf(f20,plain,(
% 0.35/0.43 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK6 @ X0) @ (sK6 @ X0)))) | ($true = ((sP0 @ X0))) | (((sK4 @ X0)) != ((sK5 @ X0))) | ($true = ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))))) )),
% 0.35/0.43 inference(cnf_transformation,[],[f14])).
% 0.35/0.43 thf(f30,plain,(
% 0.35/0.43 ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))) != ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))))),
% 0.35/0.43 inference(primitive_instantiation,[],[f20])).
% 0.35/0.43 thf(f51,plain,(
% 0.35/0.43 ($true != (((sK6 @ =) = (sK6 @ =)))) | ($true = ((sP0 @ =))) | (((sK4 @ =)) != ((sK5 @ =))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.35/0.43 inference(beta-eta_normalization,[],[f30])).
% 0.35/0.43 thf(f52,plain,(
% 0.35/0.43 (((sK6 @ =)) != ((sK6 @ =))) | ($true = ((sP0 @ =))) | (((sK4 @ =)) != ((sK5 @ =))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.35/0.43 inference(equality_proxy_clausification,[],[f51])).
% 0.35/0.43 thf(f53,plain,(
% 0.35/0.43 (((sK6 @ =)) != ((sK6 @ =))) | ($true = ((sP0 @ =))) | (((sK4 @ =)) != ((sK5 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.35/0.43 inference(equality_proxy_clausification,[],[f52])).
% 0.35/0.43 thf(f54,plain,(
% 0.35/0.43 ($true = ((sP0 @ =))) | (((sK4 @ =)) != ((sK5 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.35/0.43 inference(trivial_inequality_removal,[],[f53])).
% 0.35/0.43 thf(f56,definition,(
% 0.35/0.43 spl7_1 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.35/0.43 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.35/0.43 thf(f58,plain,(
% 0.35/0.43 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl7_1),
% 0.35/0.43 inference(avatar_component_clause,[],[f56])).
% 0.35/0.43 thf(f60,definition,(
% 0.35/0.43 spl7_2 <=> (((sK4 @ =)) = ((sK5 @ =)))),
% 0.35/0.43 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.35/0.43 thf(f62,plain,(
% 0.35/0.43 (((sK4 @ =)) != ((sK5 @ =))) | spl7_2),
% 0.35/0.43 inference(avatar_component_clause,[],[f60])).
% 0.35/0.43 thf(f64,definition,(
% 0.35/0.43 spl7_3 <=> ($true = ((sP0 @ =)))),
% 0.35/0.43 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.35/0.43 thf(f66,plain,(
% 0.35/0.43 ($true = ((sP0 @ =))) | ~spl7_3),
% 0.35/0.43 inference(avatar_component_clause,[],[f64])).
% 0.35/0.43 thf(f67,plain,(
% 0.35/0.43 spl7_1 | ~spl7_2 | spl7_3),
% 0.35/0.43 inference(avatar_split_clause,[],[f54,f64,f60,f56])).
% 0.35/0.43 thf(f68,plain,(
% 0.35/0.43 ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))))),
% 0.35/0.43 inference(primitive_instantiation,[],[f18])).
% 0.35/0.43 thf(f96,plain,(
% 0.35/0.43 ($true != (((sK6 @ =) = (sK6 @ =)))) | ($true = ((sP0 @ =))) | ($true = (((sK4 @ =) = (sK5 @ =)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.35/0.43 inference(beta-eta_normalization,[],[f68])).
% 0.35/0.43 thf(f97,plain,(
% 0.35/0.43 (((sK6 @ =)) != ((sK6 @ =))) | ($true = ((sP0 @ =))) | ($true = (((sK4 @ =) = (sK5 @ =)))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.35/0.43 inference(equality_proxy_clausification,[],[f96])).
% 0.35/0.43 thf(f98,plain,(
% 0.35/0.43 (((sK6 @ =)) != ((sK6 @ =))) | ($true = ((sP0 @ =))) | (((sK4 @ =)) = ((sK5 @ =))) | ($true = (((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))))),
% 0.35/0.43 inference(equality_proxy_clausification,[],[f97])).
% 0.35/0.43 thf(f99,plain,(
% 0.35/0.43 (((sK6 @ =)) != ((sK6 @ =))) | ($true = ((sP0 @ =))) | (((sK4 @ =)) = ((sK5 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.35/0.43 inference(equality_proxy_clausification,[],[f98])).
% 0.35/0.43 thf(f100,plain,(
% 0.35/0.43 ($true = ((sP0 @ =))) | (((sK4 @ =)) = ((sK5 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.35/0.43 inference(trivial_inequality_removal,[],[f99])).
% 0.35/0.43 thf(f101,plain,(
% 0.35/0.43 ($true = ((sP0 @ =))) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl7_2),
% 0.35/0.43 inference(forward_subsumption_resolution,[],[f100,f62])).
% 0.35/0.43 thf(f102,plain,(
% 0.35/0.43 spl7_1 | spl7_3 | spl7_2),
% 0.35/0.43 inference(avatar_split_clause,[],[f101,f60,f64,f56])).
% 0.35/0.43 thf(f167,plain,(
% 0.35/0.43 ($true != $true) | ($true = (((sK1 @ =) = (sK2 @ =)))) | ~spl7_3),
% 0.35/0.43 inference(constrained_superposition,[],[f15,f66])).
% 0.35/0.43 thf(f168,plain,(
% 0.35/0.43 ($true != $true) | (((sK1 @ =)) = ((sK2 @ =))) | ~spl7_3),
% 0.35/0.43 inference(equality_proxy_clausification,[],[f167])).
% 0.35/0.43 thf(f169,plain,(
% 0.35/0.43 (((sK1 @ =)) = ((sK2 @ =))) | ~spl7_3),
% 0.35/0.43 inference(trivial_inequality_removal,[],[f168])).
% 0.35/0.43 thf(f175,plain,(
% 0.35/0.43 ($true != $true) | ($true = (((sK2 @ =) = (sK3 @ =)))) | ~spl7_3),
% 0.35/0.43 inference(constrained_superposition,[],[f16,f66])).
% 0.35/0.43 thf(f176,plain,(
% 0.35/0.43 ($true != $true) | (((sK2 @ =)) = ((sK3 @ =))) | ~spl7_3),
% 0.35/0.43 inference(equality_proxy_clausification,[],[f175])).
% 0.35/0.43 thf(f177,plain,(
% 0.35/0.43 (((sK2 @ =)) = ((sK3 @ =))) | ~spl7_3),
% 0.35/0.43 inference(trivial_inequality_removal,[],[f176])).
% 0.35/0.43 thf(f179,plain,(
% 0.35/0.43 (((sK1 @ =)) = ((sK3 @ =))) | ~spl7_3),
% 0.35/0.43 inference(forward_demodulation,[],[f177,f169])).
% 0.35/0.43 thf(f183,plain,(
% 0.35/0.43 ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true != ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))),
% 0.35/0.43 inference(primitive_instantiation,[],[f17])).
% 0.35/0.43 thf(f203,plain,(
% 0.35/0.43 ($true != (((sK1 @ =) = (sK3 @ =)))) | ($true != ((sP0 @ =)))),
% 0.35/0.43 inference(beta-eta_normalization,[],[f183])).
% 0.35/0.43 thf(f204,plain,(
% 0.35/0.43 (((sK1 @ =)) != ((sK3 @ =))) | ($true != ((sP0 @ =)))),
% 0.35/0.43 inference(equality_proxy_clausification,[],[f203])).
% 0.35/0.43 thf(f214,plain,(
% 0.35/0.43 ($true != ((sP0 @ =))) | ~spl7_3),
% 0.35/0.43 inference(forward_subsumption_resolution,[],[f204,f179])).
% 0.35/0.43 thf(f215,plain,(
% 0.35/0.43 $false | ~spl7_3),
% 0.35/0.43 inference(forward_subsumption_resolution,[],[f214,f66])).
% 0.35/0.43 thf(f216,plain,(
% 0.35/0.43 ~spl7_3),
% 0.35/0.43 inference(avatar_contradiction_clause,[],[f215])).
% 0.35/0.43 thf(f217,plain,(
% 0.35/0.43 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl7_1),
% 0.35/0.43 inference(argument_congruence,[],[f58])).
% 0.35/0.43 thf(f219,plain,(
% 0.35/0.43 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ($true)) @ X1))) | ($true = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl7_1),
% 0.35/0.43 inference(iff_proxy_clausification,[],[f217])).
% 0.35/0.43 thf(f220,plain,(
% 0.35/0.43 ($true = $false) | ($true = $false) | ~spl7_1),
% 0.35/0.43 inference(beta-eta_normalization,[],[f219])).
% 0.35/0.43 thf(f221,plain,(
% 0.35/0.43 ($true = $false) | ~spl7_1),
% 0.35/0.43 inference(duplicate_literal_removal,[],[f220])).
% 0.35/0.43 thf(f222,plain,(
% 0.35/0.43 $false | ~spl7_1),
% 0.35/0.43 inference(trivial_inequality_removal,[],[f221])).
% 0.35/0.43 thf(f223,plain,(
% 0.35/0.43 ~spl7_1),
% 0.35/0.43 inference(avatar_contradiction_clause,[],[f222])).
% 0.35/0.43 cnf(s1, plain, spl7_1 | ~spl7_2 | spl7_3, inference(sat_conversion,[],[f67])).
% 0.35/0.43 cnf(s2, plain, spl7_1 | spl7_2 | spl7_3, inference(sat_conversion,[],[f102])).
% 0.35/0.43 cnf(s6, plain, ~spl7_3, inference(sat_conversion,[],[f216])).
% 0.35/0.43 cnf(s7, plain, ~spl7_1, inference(sat_conversion,[],[f223])).
% 0.35/0.43 cnf(s8, plain, spl7_2, inference(rat,[],[s2,s6,s7])).
% 0.35/0.43 cnf(s9, plain, $false, inference(rat,[],[s1,s6,s8,s7])).
% 0.35/0.43 thf(f225,plain,(
% 0.35/0.43 $false),
% 0.35/0.43 inference(avatar_sat_refutation,[],[s9])).
% 0.35/0.43 % SZS output end Proof for theBenchmark
% 0.35/0.43 % (1780271)------------------------------
% 0.35/0.43 % (1780271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.43 % (1780271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.43 % (1780271)CaDiCaL version: 2.1.3
% 0.35/0.43 % (1780271)Termination reason: Refutation
% 0.35/0.43 % (1780271)Time elapsed: 0.023 s
% 0.35/0.43 % (1780271)Peak memory usage: 13 MB
% 0.35/0.43 % (1780271)Instructions burned: 23 (million)
% 0.35/0.43 % (1780261)Success in time 0.074 s
% 0.35/0.43 % Vampire exiting
%------------------------------------------------------------------------------