%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU899^5 : 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 : n018.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 08:34:22 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU899^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:46:41 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.22/0.29 % (177583)Will run a generic schedule for satisfiability detection.
% 0.22/0.29 % (177593)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3219748169:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.29 % (177590)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2335286583:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.29 % (177588)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3085318679_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.29 % (177591)dis+10_1_sil=32000:sp=arity:random_seed=1958874715:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.29 % Exception at run slice level
% 0.22/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.29 % (177594)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1714341322:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.29 % (177593) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-177583-177593"...
% 0.22/0.29 % (177591) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-177583-177591"...
% 0.22/0.29 % (177593)...printing done.
% 0.22/0.29 % (177593)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% 0.22/0.29 thf(type_def_5, type, b: $tType).
% 0.22/0.29 thf(type_def_6, type, a: $tType).
% 0.22/0.29 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.29 thf(func_def_0, type, cF: (b > a)).
% 0.22/0.29 thf(func_def_1, type, cS: (b > $o)).
% 0.22/0.29 thf(func_def_2, type, cR: (b > $o)).
% 0.22/0.29 thf(func_def_6, type, sP0: (a > $o)).
% 0.22/0.29 thf(func_def_7, type, sK1: (a > b)).
% 0.22/0.29 thf(func_def_8, type, sK2: (a > b)).
% 0.22/0.29 thf(func_def_9, type, sK3: a).
% 0.22/0.29 thf(func_def_10, type, sK4: b).
% 0.22/0.29 thf(f1,conjecture,(
% 0.22/0.29 ! [X0 : a] : (? [X1 : b] : ((X0 = ((cF @ X1))) & ((cS @ X1) | (cR @ X1))) <=> (? [X1 : b] : ((X0 = ((cF @ X1))) & (cS @ X1)) | ? [X1 : b] : ((X0 = ((cF @ X1))) & (cR @ X1))))),
% 0.22/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM34_pme)).
% 0.22/0.29 thf(f2,negated_conjecture,(
% 0.22/0.29 ~ ! [X0 : a] : (? [X1 : b] : ((X0 = ((cF @ X1))) & ((cS @ X1) | (cR @ X1))) <=> (? [X1 : b] : ((X0 = ((cF @ X1))) & (cS @ X1)) | ? [X1 : b] : ((X0 = ((cF @ X1))) & (cR @ X1))))),
% 0.22/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.29 thf(f3,plain,(
% 0.22/0.29 ~ ! [X0 : a] : (? [X1 : b] : ((X0 = ((cF @ X1))) & ((cS @ X1) | (cR @ X1))) <=> (? [X2 : b] : ((((cF @ X2)) = X0) & (cS @ X2)) | ? [X3 : b] : ((((cF @ X3)) = X0) & (cR @ X3))))),
% 0.22/0.29 inference(rectify,[],[f2])).
% 0.22/0.29 thf(f4,plain,(
% 0.22/0.29 ~ ! [X0 : a] : (? [X1 : b] : ((((cF @ X1)) = X0) & ((((cS @ X1)) = $true) | (((cR @ X1)) = $true))) <=> (? [X2 : b] : ((((cF @ X2)) = X0) & (((cS @ X2)) = $true)) | ? [X3 : b] : ((((cF @ X3)) = X0) & (((cR @ X3)) = $true))))),
% 0.22/0.29 inference(fool_elimination,[],[f3])).
% 0.22/0.29 thf(f5,plain,(
% 0.22/0.29 ? [X0 : a] : (? [X1 : b] : ((((cF @ X1)) = X0) & ((((cS @ X1)) = $true) | (((cR @ X1)) = $true))) <~> (? [X2 : b] : ((((cF @ X2)) = X0) & (((cS @ X2)) = $true)) | ? [X3 : b] : ((((cF @ X3)) = X0) & (((cR @ X3)) = $true))))),
% 0.22/0.29 inference(ennf_transformation,[],[f4])).
% 0.22/0.29 thf(f6,definition,(
% 0.22/0.29 ! [X0 : a] : (($true = ((sP0 @ X0))) <=> (? [X2 : b] : ((((cF @ X2)) = X0) & (((cS @ X2)) = $true)) | ? [X3 : b] : ((((cF @ X3)) = X0) & (((cR @ X3)) = $true))))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.22/0.29 thf(f7,plain,(
% 0.22/0.29 ? [X0 : a] : (? [X1 : b] : ((((cF @ X1)) = X0) & ((((cS @ X1)) = $true) | (((cR @ X1)) = $true))) <~> ($true = ((sP0 @ X0))))),
% 0.22/0.29 inference(definition_folding,[],[f5,f6])).
% 0.22/0.29 thf(f8,plain,(
% 0.22/0.29 ! [X0 : a] : ((($true = ((sP0 @ X0))) | (! [X2 : b] : ((((cF @ X2)) != X0) | (((cS @ X2)) != $true)) & ! [X3 : b] : ((((cF @ X3)) != X0) | (((cR @ X3)) != $true)))) & ((? [X2 : b] : ((((cF @ X2)) = X0) & (((cS @ X2)) = $true)) | ? [X3 : b] : ((((cF @ X3)) = X0) & (((cR @ X3)) = $true))) | ($true != ((sP0 @ X0)))))),
% 0.22/0.29 inference(nnf_transformation,[],[f6])).
% 0.22/0.29 thf(f9,plain,(
% 0.22/0.29 ! [X0 : a] : ((($true = ((sP0 @ X0))) | (! [X2 : b] : ((((cF @ X2)) != X0) | (((cS @ X2)) != $true)) & ! [X3 : b] : ((((cF @ X3)) != X0) | (((cR @ X3)) != $true)))) & (? [X2 : b] : ((((cF @ X2)) = X0) & (((cS @ X2)) = $true)) | ? [X3 : b] : ((((cF @ X3)) = X0) & (((cR @ X3)) = $true)) | ($true != ((sP0 @ X0)))))),
% 0.22/0.29 inference(flattening,[],[f8])).
% 0.22/0.29 thf(f10,plain,(
% 0.22/0.29 ! [X0 : a] : ((($true = ((sP0 @ X0))) | (! [X1 : b] : ((((cF @ X1)) != X0) | (((cS @ X1)) != $true)) & ! [X2 : b] : ((((cF @ X2)) != X0) | ($true != ((cR @ X2)))))) & (? [X3 : b] : ((((cF @ X3)) = X0) & ($true = ((cS @ X3)))) | ? [X4 : b] : ((((cF @ X4)) = X0) & ($true = ((cR @ X4)))) | ($true != ((sP0 @ X0)))))),
% 0.22/0.29 inference(rectify,[],[f9])).
% 0.22/0.29 thf(f11,plain,(
% 0.22/0.29 ! [X0 : a] : ((($true = ((sP0 @ X0))) | (! [X1 : b] : ((((cF @ X1)) != X0) | (((cS @ X1)) != $true)) & ! [X2 : b] : ((((cF @ X2)) != X0) | ($true != ((cR @ X2)))))) & (((((cF @ (sK1 @ X0))) = X0) & ($true = ((cS @ (sK1 @ X0))))) | ((((cF @ (sK2 @ X0))) = X0) & ($true = ((cR @ (sK2 @ X0))))) | ($true != ((sP0 @ X0)))))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK2 @ X0),skolemize(X4,sK2 @ X0)],[f10])).
% 0.22/0.29 thf(f12,plain,(
% 0.22/0.29 ? [X0 : a] : ((($true != ((sP0 @ X0))) | ! [X1 : b] : ((((cF @ X1)) != X0) | ((((cS @ X1)) != $true) & (((cR @ X1)) != $true)))) & (($true = ((sP0 @ X0))) | ? [X1 : b] : ((((cF @ X1)) = X0) & ((((cS @ X1)) = $true) | (((cR @ X1)) = $true)))))),
% 0.22/0.29 inference(nnf_transformation,[],[f7])).
% 0.22/0.29 thf(f13,plain,(
% 0.22/0.29 ? [X0 : a] : ((($true != ((sP0 @ X0))) | ! [X1 : b] : ((((cF @ X1)) != X0) | ((((cS @ X1)) != $true) & (((cR @ X1)) != $true)))) & (($true = ((sP0 @ X0))) | ? [X2 : b] : ((((cF @ X2)) = X0) & ((((cS @ X2)) = $true) | ($true = ((cR @ X2)))))))),
% 0.22/0.29 inference(rectify,[],[f12])).
% 0.22/0.29 thf(f14,plain,(
% 0.22/0.29 (($true != ((sP0 @ sK3))) | ! [X1 : b] : ((((cF @ X1)) != sK3) | ((((cS @ X1)) != $true) & (((cR @ X1)) != $true)))) & (($true = ((sP0 @ sK3))) | ((sK3 = ((cF @ sK4))) & (($true = ((cS @ sK4))) | ($true = ((cR @ sK4))))))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X2,sK4)],[f13])).
% 0.22/0.29 thf(f15,plain,(
% 0.22/0.29 ( ! [X0 : a] : (($true != ((sP0 @ X0))) | ($true = ((cR @ (sK2 @ X0)))) | ($true = ((cS @ (sK1 @ X0))))) )),
% 0.22/0.29 inference(cnf_transformation,[],[f11])).
% 0.22/0.29 thf(f16,plain,(
% 0.22/0.29 ( ! [X0 : a] : (($true != ((sP0 @ X0))) | (((cF @ (sK2 @ X0))) = X0) | ($true = ((cS @ (sK1 @ X0))))) )),
% 0.22/0.29 inference(cnf_transformation,[],[f11])).
% 0.22/0.29 thf(f17,plain,(
% 0.22/0.29 ( ! [X0 : a] : (($true != ((sP0 @ X0))) | ($true = ((cR @ (sK2 @ X0)))) | (((cF @ (sK1 @ X0))) = X0)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f11])).
% 0.22/0.29 thf(f18,plain,(
% 0.22/0.29 ( ! [X0 : a] : (($true != ((sP0 @ X0))) | (((cF @ (sK2 @ X0))) = X0) | (((cF @ (sK1 @ X0))) = X0)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f11])).
% 0.22/0.29 thf(f19,plain,(
% 0.22/0.29 ( ! [X2 : b,X0 : a] : ((((cF @ X2)) != X0) | ($true = ((sP0 @ X0))) | ($true != ((cR @ X2)))) )),
% 0.22/0.29 inference(cnf_transformation,[],[f11])).
% 0.22/0.29 thf(f20,plain,(
% 0.22/0.29 ( ! [X0 : a,X1 : b] : ((((cF @ X1)) != X0) | ($true = ((sP0 @ X0))) | (((cS @ X1)) != $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f11])).
% 0.22/0.29 thf(f21,plain,(
% 0.22/0.29 ($true = ((sP0 @ sK3))) | ($true = ((cS @ sK4))) | ($true = ((cR @ sK4)))),
% 0.22/0.29 inference(cnf_transformation,[],[f14])).
% 0.22/0.29 thf(f22,plain,(
% 0.22/0.29 ($true = ((sP0 @ sK3))) | (sK3 = ((cF @ sK4)))),
% 0.22/0.29 inference(cnf_transformation,[],[f14])).
% 0.22/0.29 thf(f23,plain,(
% 0.22/0.29 ( ! [X1 : b] : (($true != ((sP0 @ sK3))) | (((cF @ X1)) != sK3) | (((cR @ X1)) != $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f14])).
% 0.22/0.29 thf(f24,plain,(
% 0.22/0.29 ( ! [X1 : b] : (($true != ((sP0 @ sK3))) | (((cF @ X1)) != sK3) | (((cS @ X1)) != $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f14])).
% 0.22/0.29 thf(f28,definition,(
% 0.22/0.29 spl5_1 <=> ($true = ((cR @ sK4)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.22/0.29 thf(f32,definition,(
% 0.22/0.29 spl5_2 <=> ($true = ((cS @ sK4)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.22/0.29 thf(f34,plain,(
% 0.22/0.29 ($true = ((cS @ sK4))) | ~spl5_2),
% 0.22/0.29 inference(avatar_component_clause,[],[f32])).
% 0.22/0.29 thf(f36,definition,(
% 0.22/0.29 spl5_3 <=> ($true = ((sP0 @ sK3)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.22/0.29 thf(f37,plain,(
% 0.22/0.29 ($true != ((sP0 @ sK3))) | spl5_3),
% 0.22/0.29 inference(avatar_component_clause,[],[f36])).
% 0.22/0.29 thf(f38,plain,(
% 0.22/0.29 ($true = ((sP0 @ sK3))) | ~spl5_3),
% 0.22/0.29 inference(avatar_component_clause,[],[f36])).
% 0.22/0.29 thf(f39,plain,(
% 0.22/0.29 spl5_1 | spl5_2 | spl5_3),
% 0.22/0.29 inference(avatar_split_clause,[],[f21,f36,f32,f28])).
% 0.22/0.29 thf(f41,definition,(
% 0.22/0.29 spl5_4 <=> (sK3 = ((cF @ sK4)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.22/0.29 thf(f43,plain,(
% 0.22/0.29 (sK3 = ((cF @ sK4))) | ~spl5_4),
% 0.22/0.29 inference(avatar_component_clause,[],[f41])).
% 0.22/0.29 thf(f44,plain,(
% 0.22/0.29 spl5_4 | spl5_3),
% 0.22/0.29 inference(avatar_split_clause,[],[f22,f36,f41])).
% 0.22/0.29 thf(f46,definition,(
% 0.22/0.29 spl5_5 <=> ! [X1 : b] : ((((cF @ X1)) != sK3) | (((cR @ X1)) != $true))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.22/0.29 thf(f47,plain,(
% 0.22/0.29 ( ! [X1 : b] : ((((cF @ X1)) != sK3) | (((cR @ X1)) != $true)) ) | ~spl5_5),
% 0.22/0.29 inference(avatar_component_clause,[],[f46])).
% 0.22/0.29 thf(f48,plain,(
% 0.22/0.29 spl5_5 | ~spl5_3),
% 0.22/0.29 inference(avatar_split_clause,[],[f23,f36,f46])).
% 0.22/0.29 thf(f50,definition,(
% 0.22/0.29 spl5_6 <=> ! [X1 : b] : ((((cF @ X1)) != sK3) | (((cS @ X1)) != $true))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.22/0.29 thf(f51,plain,(
% 0.22/0.29 ( ! [X1 : b] : ((((cF @ X1)) != sK3) | (((cS @ X1)) != $true)) ) | ~spl5_6),
% 0.22/0.29 inference(avatar_component_clause,[],[f50])).
% 0.22/0.29 thf(f52,plain,(
% 0.22/0.29 spl5_6 | ~spl5_3),
% 0.22/0.29 inference(avatar_split_clause,[],[f24,f36,f50])).
% 0.22/0.29 thf(f62,plain,(
% 0.22/0.29 ( ! [X0 : a] : ((sK3 != X0) | ($true = ((sP0 @ X0))) | ($true != ((cR @ sK4)))) ) | ~spl5_4),
% 0.22/0.29 inference(constrained_superposition,[],[f19,f43])).
% 0.22/0.29 thf(f65,definition,(
% 0.22/0.29 spl5_7 <=> ! [X0 : a] : ((sK3 != X0) | ($true = ((sP0 @ X0))))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 0.22/0.29 thf(f66,plain,(
% 0.22/0.29 ( ! [X0 : a] : ((sK3 != X0) | ($true = ((sP0 @ X0)))) ) | ~spl5_7),
% 0.22/0.29 inference(avatar_component_clause,[],[f65])).
% 0.22/0.29 thf(f67,plain,(
% 0.22/0.29 ~spl5_1 | spl5_7 | ~spl5_4),
% 0.22/0.29 inference(avatar_split_clause,[],[f62,f41,f65,f28])).
% 0.22/0.29 thf(f70,plain,(
% 0.22/0.29 ( ! [X0 : a] : ((sK3 != X0) | ($true = ((sP0 @ X0))) | ($true != ((cS @ sK4)))) ) | ~spl5_4),
% 0.22/0.29 inference(constrained_superposition,[],[f20,f43])).
% 0.22/0.29 thf(f72,plain,(
% 0.22/0.29 ( ! [X0 : a] : ((sK3 != X0) | ($true = ((sP0 @ X0)))) ) | (~spl5_2 | ~spl5_4)),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f70,f34])).
% 0.22/0.29 thf(f73,plain,(
% 0.22/0.29 spl5_7 | ~spl5_2 | ~spl5_4),
% 0.22/0.29 inference(avatar_split_clause,[],[f72,f41,f32,f65])).
% 0.22/0.29 thf(f83,plain,(
% 0.22/0.29 ($true = ((sP0 @ sK3))) | ~spl5_7),
% 0.22/0.29 inference(equality_resolution,[],[f66])).
% 0.22/0.29 thf(f84,plain,(
% 0.22/0.29 $false | (spl5_3 | ~spl5_7)),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f83,f37])).
% 0.22/0.29 thf(f85,plain,(
% 0.22/0.29 spl5_3 | ~spl5_7),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f84])).
% 0.22/0.29 thf(f86,plain,(
% 0.22/0.29 ($true != $true) | (sK3 = ((cF @ (sK2 @ sK3)))) | ($true = ((cS @ (sK1 @ sK3)))) | ~spl5_3),
% 0.22/0.29 inference(constrained_superposition,[],[f16,f38])).
% 0.22/0.29 thf(f87,plain,(
% 0.22/0.29 ($true != $true) | ($true = ((cR @ (sK2 @ sK3)))) | ($true = ((cS @ (sK1 @ sK3)))) | ~spl5_3),
% 0.22/0.29 inference(constrained_superposition,[],[f15,f38])).
% 0.22/0.29 thf(f88,plain,(
% 0.22/0.29 ($true = ((cR @ (sK2 @ sK3)))) | ($true = ((cS @ (sK1 @ sK3)))) | ~spl5_3),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f87])).
% 0.22/0.29 thf(f89,plain,(
% 0.22/0.29 (sK3 = ((cF @ (sK2 @ sK3)))) | ($true = ((cS @ (sK1 @ sK3)))) | ~spl5_3),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f86])).
% 0.22/0.29 thf(f91,definition,(
% 0.22/0.29 spl5_8 <=> ($true = ((cS @ (sK1 @ sK3))))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.22/0.29 thf(f93,plain,(
% 0.22/0.29 ($true = ((cS @ (sK1 @ sK3)))) | ~spl5_8),
% 0.22/0.29 inference(avatar_component_clause,[],[f91])).
% 0.22/0.29 thf(f95,definition,(
% 0.22/0.29 spl5_9 <=> ($true = ((cR @ (sK2 @ sK3))))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition])).
% 0.22/0.29 thf(f97,plain,(
% 0.22/0.29 ($true = ((cR @ (sK2 @ sK3)))) | ~spl5_9),
% 0.22/0.29 inference(avatar_component_clause,[],[f95])).
% 0.22/0.29 thf(f98,plain,(
% 0.22/0.29 spl5_8 | spl5_9 | ~spl5_3),
% 0.22/0.29 inference(avatar_split_clause,[],[f88,f36,f95,f91])).
% 0.22/0.29 thf(f100,definition,(
% 0.22/0.29 spl5_10 <=> (sK3 = ((cF @ (sK2 @ sK3))))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition])).
% 0.22/0.29 thf(f102,plain,(
% 0.22/0.29 (sK3 = ((cF @ (sK2 @ sK3)))) | ~spl5_10),
% 0.22/0.29 inference(avatar_component_clause,[],[f100])).
% 0.22/0.29 thf(f103,plain,(
% 0.22/0.29 spl5_8 | spl5_10 | ~spl5_3),
% 0.22/0.29 inference(avatar_split_clause,[],[f89,f36,f100,f91])).
% 0.22/0.29 thf(f112,plain,(
% 0.22/0.29 ($true != $true) | ($true = ((cR @ (sK2 @ sK3)))) | (sK3 = ((cF @ (sK1 @ sK3)))) | ~spl5_3),
% 0.22/0.29 inference(constrained_superposition,[],[f17,f38])).
% 0.22/0.29 thf(f115,plain,(
% 0.22/0.29 ($true = ((cR @ (sK2 @ sK3)))) | (sK3 = ((cF @ (sK1 @ sK3)))) | ~spl5_3),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f112])).
% 0.22/0.29 thf(f117,definition,(
% 0.22/0.29 spl5_11 <=> (sK3 = ((cF @ (sK1 @ sK3))))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition])).
% 0.22/0.29 thf(f119,plain,(
% 0.22/0.29 (sK3 = ((cF @ (sK1 @ sK3)))) | ~spl5_11),
% 0.22/0.29 inference(avatar_component_clause,[],[f117])).
% 0.22/0.29 thf(f120,plain,(
% 0.22/0.29 spl5_11 | spl5_9 | ~spl5_3),
% 0.22/0.29 inference(avatar_split_clause,[],[f115,f36,f95,f117])).
% 0.22/0.29 thf(f123,plain,(
% 0.22/0.29 ($true != $true) | (sK3 = ((cF @ (sK2 @ sK3)))) | (sK3 = ((cF @ (sK1 @ sK3)))) | ~spl5_3),
% 0.22/0.29 inference(constrained_superposition,[],[f18,f38])).
% 0.22/0.29 thf(f126,plain,(
% 0.22/0.29 (sK3 = ((cF @ (sK2 @ sK3)))) | (sK3 = ((cF @ (sK1 @ sK3)))) | ~spl5_3),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f123])).
% 0.22/0.29 thf(f127,plain,(
% 0.22/0.29 spl5_11 | spl5_10 | ~spl5_3),
% 0.22/0.29 inference(avatar_split_clause,[],[f126,f36,f100,f117])).
% 0.22/0.29 thf(f128,plain,(
% 0.22/0.29 (sK3 != sK3) | ($true != ((cS @ (sK1 @ sK3)))) | (~spl5_6 | ~spl5_11)),
% 0.22/0.29 inference(constrained_superposition,[],[f51,f119])).
% 0.22/0.29 thf(f133,plain,(
% 0.22/0.29 ($true != ((cS @ (sK1 @ sK3)))) | (~spl5_6 | ~spl5_11)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f128])).
% 0.22/0.29 thf(f134,plain,(
% 0.22/0.29 $false | (~spl5_6 | ~spl5_8 | ~spl5_11)),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f133,f93])).
% 0.22/0.29 thf(f135,plain,(
% 0.22/0.29 ~spl5_6 | ~spl5_8 | ~spl5_11),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f134])).
% 0.22/0.29 thf(f139,plain,(
% 0.22/0.29 (sK3 != sK3) | ($true != ((cR @ (sK2 @ sK3)))) | (~spl5_5 | ~spl5_10)),
% 0.22/0.29 inference(constrained_superposition,[],[f47,f102])).
% 0.22/0.29 thf(f142,plain,(
% 0.22/0.29 ($true != ((cR @ (sK2 @ sK3)))) | (~spl5_5 | ~spl5_10)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f139])).
% 0.22/0.29 thf(f144,plain,(
% 0.22/0.29 $false | (~spl5_5 | ~spl5_9 | ~spl5_10)),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f142,f97])).
% 0.22/0.29 thf(f145,plain,(
% 0.22/0.29 ~spl5_5 | ~spl5_9 | ~spl5_10),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f144])).
% 0.22/0.29 cnf(s1, plain, spl5_1 | spl5_2 | spl5_3, inference(sat_conversion,[],[f39])).
% 0.22/0.29 cnf(s2, plain, spl5_3 | spl5_4, inference(sat_conversion,[],[f44])).
% 0.22/0.29 cnf(s3, plain, ~spl5_3 | spl5_5, inference(sat_conversion,[],[f48])).
% 0.22/0.29 cnf(s4, plain, ~spl5_3 | spl5_6, inference(sat_conversion,[],[f52])).
% 0.22/0.29 cnf(s5, plain, ~spl5_1 | ~spl5_4 | spl5_7, inference(sat_conversion,[],[f67])).
% 0.22/0.29 cnf(s6, plain, ~spl5_2 | ~spl5_4 | spl5_7, inference(sat_conversion,[],[f73])).
% 0.22/0.29 cnf(s7, plain, spl5_3 | ~spl5_7, inference(sat_conversion,[],[f85])).
% 0.22/0.29 cnf(s8, plain, ~spl5_3 | spl5_8 | spl5_9, inference(sat_conversion,[],[f98])).
% 0.22/0.29 cnf(s9, plain, ~spl5_3 | spl5_8 | spl5_10, inference(sat_conversion,[],[f103])).
% 0.22/0.29 cnf(s11, plain, ~spl5_3 | spl5_9 | spl5_11, inference(sat_conversion,[],[f120])).
% 0.22/0.29 cnf(s12, plain, ~spl5_3 | spl5_10 | spl5_11, inference(sat_conversion,[],[f127])).
% 0.22/0.29 cnf(s13, plain, ~spl5_6 | ~spl5_8 | ~spl5_11, inference(sat_conversion,[],[f135])).
% 0.22/0.29 cnf(s14, plain, ~spl5_5 | ~spl5_9 | ~spl5_10, inference(sat_conversion,[],[f145])).
% 0.22/0.29 cnf(s15, plain, spl5_8 | ~spl5_3, inference(rat,[],[s14,s9,s8,s3])).
% 0.22/0.29 cnf(s16, plain, ~spl5_3, inference(rat,[],[s14,s12,s11,s13,s15,s3,s4])).
% 0.22/0.29 cnf(s17, plain, ~spl5_7, inference(rat,[],[s7,s16])).
% 0.22/0.29 cnf(s18, plain, spl5_4, inference(rat,[],[s2,s16])).
% 0.22/0.29 cnf(s19, plain, ~spl5_2, inference(rat,[],[s6,s17,s18])).
% 0.22/0.29 cnf(s20, plain, ~spl5_1, inference(rat,[],[s5,s17,s18])).
% 0.22/0.29 cnf(s21, plain, $false, inference(rat,[],[s1,s16,s20,s19])).
% 0.22/0.29 thf(f146,plain,(
% 0.22/0.29 $false),
% 0.22/0.29 inference(avatar_sat_refutation,[],[s21])).
% 0.22/0.29 % SZS output end Proof for theBenchmark
% 0.22/0.29 % (177593)------------------------------
% 0.22/0.29 % (177593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (177593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (177593)CaDiCaL version: 2.1.3
% 0.22/0.29 % (177593)Termination reason: Refutation
% 0.22/0.29 % (177593)Time elapsed: 0.006 s
% 0.22/0.29 % (177593)Peak memory usage: 12 MB
% 0.22/0.29 % (177593)Instructions burned: 9 (million)
% 0.22/0.29 % (177583)Success in time 0.044 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------