%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV085^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV085^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 15:12:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.26 % (1367174)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (1367183)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1546856595:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.26 % (1367183)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.26 % (1367180)% WARNING: option uhcvi not known.
% 0.19/0.26 % (1367179)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2616022360_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.26 % (1367180)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2080745626:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.26 % (1367181)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1756344940:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.26 % (1367182)dis+10_1_sil=32000:sp=arity:random_seed=2974917309:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.26 % (1367180)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.26 % Exception at run slice level
% 0.19/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.26 % (1367184)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=941094732:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.26 % (1367185)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3370717294:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.26 % (1367180)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.26 % (1367182) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1367174-1367182"...
% 0.19/0.26 % (1367184) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1367174-1367184"...
% 0.19/0.26 % (1367182)...printing done.
% 0.19/0.26 % (1367182)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% 0.19/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.26 thf(func_def_3, type, sK0: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.26 thf(func_def_4, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.26 thf(func_def_5, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.26 thf(func_def_6, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.19/0.26 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.19/0.26 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.26 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.26 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.26 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.26 thf(f1,conjecture,(
% 0.19/0.26 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X5 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o)] : (((X0 @ X6 @ X7) & (X0 @ X5 @ X6)) => (X0 @ X5 @ X7)) & ! [X5 : ($i > $o)] : (X0 @ X5 @ X5) & ? [X3 : ($i > $o),X4 : ($i > $o)] : ~(X0 @ X3 @ X4) & ? [X1 : ($i > $o),X2 : ($i > $o)] : (X0 @ X1 @ X2))),
% 0.19/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120_2_pme)).
% 0.19/0.26 thf(f2,negated_conjecture,(
% 0.19/0.26 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X5 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o)] : (((X0 @ X6 @ X7) & (X0 @ X5 @ X6)) => (X0 @ X5 @ X7)) & ! [X5 : ($i > $o)] : (X0 @ X5 @ X5) & ? [X3 : ($i > $o),X4 : ($i > $o)] : ~(X0 @ X3 @ X4) & ? [X1 : ($i > $o),X2 : ($i > $o)] : (X0 @ X1 @ X2))),
% 0.19/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.26 thf(f3,plain,(
% 0.19/0.26 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)) & ! [X4 : ($i > $o)] : (X0 @ X4 @ X4) & ? [X5 : ($i > $o),X6 : ($i > $o)] : ~(X0 @ X5 @ X6) & ? [X7 : ($i > $o),X8 : ($i > $o)] : (X0 @ X7 @ X8))),
% 0.19/0.26 inference(rectify,[],[f2])).
% 0.19/0.26 thf(f4,plain,(
% 0.19/0.26 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((((X0 @ X2 @ X3)) = $true) & (((X0 @ X1 @ X2)) = $true)) => (((X0 @ X1 @ X3)) = $true)) & ! [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) = $true) & ? [X5 : ($i > $o),X6 : ($i > $o)] : ~ (((X0 @ X5 @ X6)) = $true) & ? [X7 : ($i > $o),X8 : ($i > $o)] : (((X0 @ X7 @ X8)) = $true))),
% 0.19/0.26 inference(fool_elimination,[],[f3])).
% 0.19/0.26 thf(f5,plain,(
% 0.19/0.26 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : (((((X0 @ X2 @ X3)) = $true) & (((X0 @ X1 @ X2)) = $true)) => (((X0 @ X1 @ X3)) = $true)) & ! [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) = $true) & ? [X5 : ($i > $o),X6 : ($i > $o)] : (((X0 @ X5 @ X6)) != $true) & ? [X7 : ($i > $o),X8 : ($i > $o)] : (((X0 @ X7 @ X8)) = $true))),
% 0.19/0.26 inference(flattening,[],[f4])).
% 0.19/0.26 thf(f6,plain,(
% 0.19/0.26 ! [X0 : (($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)) = $true))) | ? [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) != $true) | ! [X5 : ($i > $o),X6 : ($i > $o)] : (((X0 @ X5 @ X6)) = $true) | ! [X7 : ($i > $o),X8 : ($i > $o)] : (((X0 @ X7 @ X8)) != $true))),
% 0.19/0.26 inference(ennf_transformation,[],[f5])).
% 0.19/0.26 thf(f7,plain,(
% 0.19/0.26 ! [X0 : (($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)) = $true)) | ? [X4 : ($i > $o)] : (((X0 @ X4 @ X4)) != $true) | ! [X5 : ($i > $o),X6 : ($i > $o)] : (((X0 @ X5 @ X6)) = $true) | ! [X7 : ($i > $o),X8 : ($i > $o)] : (((X0 @ X7 @ X8)) != $true))),
% 0.19/0.26 inference(flattening,[],[f6])).
% 0.19/0.26 thf(f8,plain,(
% 0.19/0.26 ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((($true != ((X0 @ (sK0 @ X0) @ (sK2 @ X0)))) & ($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) & ($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0))))) | ($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ! [X5 : ($i > $o),X6 : ($i > $o)] : (((X0 @ X5 @ X6)) = $true) | ! [X7 : ($i > $o),X8 : ($i > $o)] : (((X0 @ X7 @ X8)) != $true))),
% 0.19/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0)],[f7])).
% 0.19/0.26 thf(f9,plain,(
% 0.19/0.26 ( ! [X0 : (($i > $o) > ($i > $o) > $o),X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : (($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | (((X0 @ X5 @ X6)) = $true) | (((X0 @ X7 @ X8)) != $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f8])).
% 0.19/0.26 thf(f10,plain,(
% 0.19/0.26 ( ! [X0 : (($i > $o) > ($i > $o) > $o),X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : (($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true = ((X0 @ (sK1 @ X0) @ (sK2 @ X0)))) | (((X0 @ X5 @ X6)) = $true) | (((X0 @ X7 @ X8)) != $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f8])).
% 0.19/0.26 thf(f11,plain,(
% 0.19/0.26 ( ! [X0 : (($i > $o) > ($i > $o) > $o),X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : (($true != ((X0 @ (sK3 @ X0) @ (sK3 @ X0)))) | ($true != ((X0 @ (sK0 @ X0) @ (sK2 @ X0)))) | (((X0 @ X5 @ X6)) = $true) | (((X0 @ X7 @ X8)) != $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f8])).
% 0.19/0.26 thf(f21,plain,(
% 0.19/0.26 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X5 @ X6))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X7 @ X8)))) )),
% 0.19/0.26 inference(primitive_instantiation,[],[f9])).
% 0.19/0.26 thf(f52,plain,(
% 0.19/0.26 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : (($true != (((sK3 @ =) = (sK3 @ =)))) | ($true = (((sK0 @ =) = (sK1 @ =)))) | ($true = ((X5 = X6))) | ($true != ((X7 = X8)))) )),
% 0.19/0.26 inference(beta-eta_normalization,[],[f21])).
% 0.19/0.26 thf(f53,plain,(
% 0.19/0.26 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | ($true = (((sK0 @ =) = (sK1 @ =)))) | ($true = ((X5 = X6))) | ($true != ((X7 = X8)))) )),
% 0.19/0.26 inference(equality_proxy_clausification,[],[f52])).
% 0.19/0.26 thf(f54,plain,(
% 0.19/0.26 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | (((sK1 @ =)) = ((sK0 @ =))) | ($true = ((X5 = X6))) | ($true != ((X7 = X8)))) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f53])).
% 0.19/0.27 thf(f55,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | (((sK1 @ =)) = ((sK0 @ =))) | (X5 = X6) | ($true != ((X7 = X8)))) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f54])).
% 0.19/0.27 thf(f56,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | (((sK1 @ =)) = ((sK0 @ =))) | (X5 = X6) | (X7 != X8)) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f55])).
% 0.19/0.27 thf(f57,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK1 @ =)) = ((sK0 @ =))) | (X5 = X6) | (X7 != X8)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f56])).
% 0.19/0.27 thf(f59,definition,(
% 0.19/0.27 spl4_1 <=> ! [X8 : ($i > $o),X7 : ($i > $o)] : (X7 != X8)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.19/0.27 thf(f60,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X7 : ($i > $o)] : ((X7 != X8)) ) | ~spl4_1),
% 0.19/0.27 inference(avatar_component_clause,[],[f59])).
% 0.19/0.27 thf(f62,definition,(
% 0.19/0.27 spl4_2 <=> ! [X6 : ($i > $o),X5 : ($i > $o)] : (X5 = X6)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.19/0.27 thf(f63,plain,(
% 0.19/0.27 ( ! [X6 : ($i > $o),X5 : ($i > $o)] : ((X5 = X6)) ) | ~spl4_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f62])).
% 0.19/0.27 thf(f65,definition,(
% 0.19/0.27 spl4_3 <=> (((sK1 @ =)) = ((sK0 @ =)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.19/0.27 thf(f67,plain,(
% 0.19/0.27 (((sK1 @ =)) = ((sK0 @ =))) | ~spl4_3),
% 0.19/0.27 inference(avatar_component_clause,[],[f65])).
% 0.19/0.27 thf(f68,plain,(
% 0.19/0.27 spl4_1 | spl4_2 | spl4_3),
% 0.19/0.27 inference(avatar_split_clause,[],[f57,f65,f62,f59])).
% 0.19/0.27 thf(f69,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X5 @ X6))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X7 @ X8)))) )),
% 0.19/0.27 inference(primitive_instantiation,[],[f10])).
% 0.19/0.27 thf(f100,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : (($true != (((sK3 @ =) = (sK3 @ =)))) | ($true = (((sK1 @ =) = (sK2 @ =)))) | ($true = ((X5 = X6))) | ($true != ((X7 = X8)))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f69])).
% 0.19/0.27 thf(f101,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | ($true = (((sK1 @ =) = (sK2 @ =)))) | ($true = ((X5 = X6))) | ($true != ((X7 = X8)))) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f100])).
% 0.19/0.27 thf(f102,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | (((sK1 @ =)) = ((sK2 @ =))) | ($true = ((X5 = X6))) | ($true != ((X7 = X8)))) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f101])).
% 0.19/0.27 thf(f103,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | (((sK1 @ =)) = ((sK2 @ =))) | (X5 = X6) | ($true != ((X7 = X8)))) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f102])).
% 0.19/0.27 thf(f104,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | (((sK1 @ =)) = ((sK2 @ =))) | (X5 = X6) | (X7 != X8)) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f103])).
% 0.19/0.27 thf(f105,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK1 @ =)) = ((sK2 @ =))) | (X5 = X6) | (X7 != X8)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f104])).
% 0.19/0.27 thf(f107,definition,(
% 0.19/0.27 spl4_4 <=> (((sK1 @ =)) = ((sK2 @ =)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.19/0.27 thf(f109,plain,(
% 0.19/0.27 (((sK1 @ =)) = ((sK2 @ =))) | ~spl4_4),
% 0.19/0.27 inference(avatar_component_clause,[],[f107])).
% 0.19/0.27 thf(f110,plain,(
% 0.19/0.27 spl4_1 | spl4_2 | spl4_4),
% 0.19/0.27 inference(avatar_split_clause,[],[f105,f107,f62,f59])).
% 0.19/0.27 thf(f111,plain,(
% 0.19/0.27 ( ! [X6 : ($i > $o),X7 : $i,X5 : ($i > $o)] : ((((X5 @ X7)) = ((X6 @ X7)))) ) | ~spl4_2),
% 0.19/0.27 inference(argument_congruence,[],[f63])).
% 0.19/0.27 thf(f116,plain,(
% 0.19/0.27 ( ! [X6 : ($i > $o),X7 : $i,X5 : ($i > $o)] : (($true = ((X5 @ X7))) | ($false = ((X6 @ X7)))) ) | ~spl4_2),
% 0.19/0.27 inference(iff_proxy_clausification,[],[f111])).
% 0.19/0.27 thf(f118,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : (($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X5 @ X6))) | ($true != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ X7 @ X8)))) )),
% 0.19/0.27 inference(primitive_instantiation,[],[f11])).
% 0.19/0.27 thf(f151,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : (($true != (((sK3 @ =) = (sK3 @ =)))) | ($true != (((sK0 @ =) = (sK2 @ =)))) | ($true = ((X5 = X6))) | ($true != ((X7 = X8)))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f118])).
% 0.19/0.27 thf(f152,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | ($true != (((sK0 @ =) = (sK2 @ =)))) | ($true = ((X5 = X6))) | ($true != ((X7 = X8)))) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f151])).
% 0.19/0.27 thf(f153,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | (((sK0 @ =)) != ((sK2 @ =))) | ($true = ((X5 = X6))) | ($true != ((X7 = X8)))) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f152])).
% 0.19/0.27 thf(f154,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | (((sK0 @ =)) != ((sK2 @ =))) | (X5 = X6) | ($true != ((X7 = X8)))) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f153])).
% 0.19/0.27 thf(f155,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK3 @ =)) != ((sK3 @ =))) | (((sK0 @ =)) != ((sK2 @ =))) | (X5 = X6) | (X7 != X8)) )),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f154])).
% 0.19/0.27 thf(f156,plain,(
% 0.19/0.27 ( ! [X8 : ($i > $o),X6 : ($i > $o),X7 : ($i > $o),X5 : ($i > $o)] : ((((sK0 @ =)) != ((sK2 @ =))) | (X5 = X6) | (X7 != X8)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f155])).
% 0.19/0.27 thf(f160,plain,(
% 0.19/0.27 ( ! [X7 : $i,X5 : ($i > $o)] : (($true = ((X5 @ X7))) | ($false = (((^[Y0 : $i]: ($true)) @ X7)))) ) | ~spl4_2),
% 0.19/0.27 inference(primitive_instantiation,[],[f116])).
% 0.19/0.27 thf(f219,plain,(
% 0.19/0.27 ( ! [X7 : $i,X5 : ($i > $o)] : (($true = ((X5 @ X7))) | ($true = $false)) ) | ~spl4_2),
% 0.19/0.27 inference(beta-eta_normalization,[],[f160])).
% 0.19/0.27 thf(f220,plain,(
% 0.19/0.27 ( ! [X7 : $i,X5 : ($i > $o)] : (($true = ((X5 @ X7)))) ) | ~spl4_2),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f219])).
% 0.19/0.27 thf(f229,definition,(
% 0.19/0.27 spl4_5 <=> ! [X2 : ($i > $o),X1 : $i] : ($true = ((X2 @ X1)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.19/0.27 thf(f230,plain,(
% 0.19/0.27 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((X2 @ X1)))) ) | ~spl4_5),
% 0.19/0.27 inference(avatar_component_clause,[],[f229])).
% 0.19/0.27 thf(f254,plain,(
% 0.19/0.27 spl4_5 | ~spl4_2),
% 0.19/0.27 inference(avatar_split_clause,[],[f220,f62,f229])).
% 0.19/0.27 thf(f256,plain,(
% 0.19/0.27 $false | ~spl4_1),
% 0.19/0.27 inference(flex-flex_simplification,[],[f60])).
% 0.19/0.27 thf(f257,plain,(
% 0.19/0.27 ~spl4_1),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f256])).
% 0.19/0.27 thf(f259,definition,(
% 0.19/0.27 spl4_11 <=> (((sK0 @ =)) = ((sK2 @ =)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition])).
% 0.19/0.27 thf(f262,plain,(
% 0.19/0.27 spl4_1 | spl4_2 | ~spl4_11),
% 0.19/0.27 inference(avatar_split_clause,[],[f156,f259,f62,f59])).
% 0.19/0.27 thf(f266,plain,(
% 0.19/0.27 (((sK0 @ =)) = ((sK2 @ =))) | (~spl4_3 | ~spl4_4)),
% 0.19/0.27 inference(forward_demodulation,[],[f109,f67])).
% 0.19/0.27 thf(f267,plain,(
% 0.19/0.27 spl4_11 | ~spl4_3 | ~spl4_4),
% 0.19/0.27 inference(avatar_split_clause,[],[f266,f107,f65,f259])).
% 0.19/0.27 thf(f280,plain,(
% 0.19/0.27 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl4_5),
% 0.19/0.27 inference(primitive_instantiation,[],[f230])).
% 0.19/0.27 thf(f300,plain,(
% 0.19/0.27 ($true = $false) | ~spl4_5),
% 0.19/0.27 inference(beta-eta_normalization,[],[f280])).
% 0.19/0.27 thf(f301,plain,(
% 0.19/0.27 $false | ~spl4_5),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f300])).
% 0.19/0.27 thf(f302,plain,(
% 0.19/0.27 ~spl4_5),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f301])).
% 0.19/0.27 cnf(s1, plain, spl4_1 | spl4_2 | spl4_3, inference(sat_conversion,[],[f68])).
% 0.19/0.27 cnf(s2, plain, spl4_1 | spl4_2 | spl4_4, inference(sat_conversion,[],[f110])).
% 0.19/0.27 cnf(s8, plain, ~spl4_2 | spl4_5, inference(sat_conversion,[],[f254])).
% 0.19/0.27 cnf(s10, plain, ~spl4_1, inference(sat_conversion,[],[f257])).
% 0.19/0.27 cnf(s11, plain, spl4_1 | spl4_2 | ~spl4_11, inference(sat_conversion,[],[f262])).
% 0.19/0.27 cnf(s12, plain, ~spl4_3 | ~spl4_4 | spl4_11, inference(sat_conversion,[],[f267])).
% 0.19/0.27 cnf(s13, plain, ~spl4_5, inference(sat_conversion,[],[f302])).
% 0.19/0.27 cnf(s17, plain, ~spl4_2, inference(rat,[],[s8,s13])).
% 0.19/0.27 cnf(s18, plain, ~spl4_11, inference(rat,[],[s11,s10,s17])).
% 0.19/0.27 cnf(s19, plain, spl4_4, inference(rat,[],[s2,s17,s10])).
% 0.19/0.27 cnf(s20, plain, ~spl4_3, inference(rat,[],[s12,s18,s19])).
% 0.19/0.27 cnf(s21, plain, $false, inference(rat,[],[s1,s20,s17,s10])).
% 0.19/0.27 thf(f316,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s21])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (1367182)------------------------------
% 0.19/0.27 % (1367182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1367182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1367182)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1367182)Termination reason: Refutation
% 0.19/0.27 % (1367182)Time elapsed: 0.010 s
% 0.19/0.27 % (1367182)Peak memory usage: 12 MB
% 0.19/0.27 % (1367182)Instructions burned: 17 (million)
% 0.19/0.27 % (1367174)Success in time 0.045 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------