%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV235^5 : 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 : 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 08:39:11 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV235^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % 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 15:26:50 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.19/0.28 % (216888)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (216899)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1797739617:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (216894)% WARNING: option uhcvi not known.
% 0.19/0.28 % (216893)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=430580290_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (216898)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2502459825:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (216894)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1793436058:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (216895)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2385675538:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (216896)dis+10_1_sil=32000:sp=arity:random_seed=406797194:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (216897)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=988223186:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (216894)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (216897)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (216894)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % (216898) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-216888-216898"...
% 0.19/0.28 % (216898)...printing done.
% 0.19/0.28 % (216907)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4157618832:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.28 % (216899) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-216888-216899"...
% 0.19/0.28 % (216898)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% 0.19/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.28 thf(func_def_0, type, cE: ($i > $o)).
% 0.19/0.28 thf(func_def_1, type, cD: ($i > $o)).
% 0.19/0.28 thf(func_def_5, type, sP0: (($i > $o) > $o)).
% 0.19/0.28 thf(func_def_6, type, sK1: (($i > $o) > $i)).
% 0.19/0.28 thf(func_def_7, type, sK2: (($i > $o) > $i)).
% 0.19/0.28 thf(func_def_8, type, sK3: ($i > $o)).
% 0.19/0.28 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.19/0.28 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.28 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(f1,conjecture,(
% 0.19/0.28 ! [X0 : ($i > $o)] : (! [X1 : $i] : ((X0 @ X1) => ((cE @ X1) & (cD @ X1))) <=> (! [X1 : $i] : ((X0 @ X1) => (cE @ X1)) & ! [X1 : $i] : ((X0 @ X1) => (cD @ X1))))),
% 0.19/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM46A_pme)).
% 0.19/0.28 thf(f2,negated_conjecture,(
% 0.19/0.28 ~ ! [X0 : ($i > $o)] : (! [X1 : $i] : ((X0 @ X1) => ((cE @ X1) & (cD @ X1))) <=> (! [X1 : $i] : ((X0 @ X1) => (cE @ X1)) & ! [X1 : $i] : ((X0 @ X1) => (cD @ X1))))),
% 0.19/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.28 thf(f3,plain,(
% 0.19/0.28 ~ ! [X0 : ($i > $o)] : (! [X1 : $i] : ((X0 @ X1) => ((cE @ X1) & (cD @ X1))) <=> (! [X2 : $i] : ((X0 @ X2) => (cE @ X2)) & ! [X3 : $i] : ((X0 @ X3) => (cD @ X3))))),
% 0.19/0.28 inference(rectify,[],[f2])).
% 0.19/0.28 thf(f4,plain,(
% 0.19/0.28 ~ ! [X0 : ($i > $o)] : (! [X1 : $i] : ((((X0 @ X1)) = $true) => ((((cE @ X1)) = $true) & (((cD @ X1)) = $true))) <=> (! [X2 : $i] : ((((X0 @ X2)) = $true) => (((cE @ X2)) = $true)) & ! [X3 : $i] : ((((X0 @ X3)) = $true) => (((cD @ X3)) = $true))))),
% 0.19/0.28 inference(fool_elimination,[],[f3])).
% 0.19/0.28 thf(f5,plain,(
% 0.19/0.28 ? [X0 : ($i > $o)] : (! [X1 : $i] : (((((cE @ X1)) = $true) & (((cD @ X1)) = $true)) | (((X0 @ X1)) != $true)) <~> (! [X2 : $i] : ((((cE @ X2)) = $true) | (((X0 @ X2)) != $true)) & ! [X3 : $i] : ((((cD @ X3)) = $true) | (((X0 @ X3)) != $true))))),
% 0.19/0.28 inference(ennf_transformation,[],[f4])).
% 0.19/0.28 thf(f6,definition,(
% 0.19/0.28 ! [X0 : ($i > $o)] : (($true = ((sP0 @ X0))) <=> (! [X2 : $i] : ((((cE @ X2)) = $true) | (((X0 @ X2)) != $true)) & ! [X3 : $i] : ((((cD @ X3)) = $true) | (((X0 @ X3)) != $true))))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.19/0.28 thf(f7,plain,(
% 0.19/0.28 ? [X0 : ($i > $o)] : (! [X1 : $i] : (((((cE @ X1)) = $true) & (((cD @ X1)) = $true)) | (((X0 @ X1)) != $true)) <~> ($true = ((sP0 @ X0))))),
% 0.19/0.28 inference(definition_folding,[],[f5,f6])).
% 0.19/0.28 thf(f8,plain,(
% 0.19/0.28 ! [X0 : ($i > $o)] : ((($true = ((sP0 @ X0))) | (? [X2 : $i] : ((((cE @ X2)) != $true) & (((X0 @ X2)) = $true)) | ? [X3 : $i] : ((((cD @ X3)) != $true) & (((X0 @ X3)) = $true)))) & ((! [X2 : $i] : ((((cE @ X2)) = $true) | (((X0 @ X2)) != $true)) & ! [X3 : $i] : ((((cD @ X3)) = $true) | (((X0 @ X3)) != $true))) | ($true != ((sP0 @ X0)))))),
% 0.19/0.28 inference(nnf_transformation,[],[f6])).
% 0.19/0.28 thf(f9,plain,(
% 0.19/0.28 ! [X0 : ($i > $o)] : ((($true = ((sP0 @ X0))) | ? [X2 : $i] : ((((cE @ X2)) != $true) & (((X0 @ X2)) = $true)) | ? [X3 : $i] : ((((cD @ X3)) != $true) & (((X0 @ X3)) = $true))) & ((! [X2 : $i] : ((((cE @ X2)) = $true) | (((X0 @ X2)) != $true)) & ! [X3 : $i] : ((((cD @ X3)) = $true) | (((X0 @ X3)) != $true))) | ($true != ((sP0 @ X0)))))),
% 0.19/0.28 inference(flattening,[],[f8])).
% 0.19/0.28 thf(f10,plain,(
% 0.19/0.28 ! [X0 : ($i > $o)] : ((($true = ((sP0 @ X0))) | ? [X1 : $i] : ((((cE @ X1)) != $true) & (((X0 @ X1)) = $true)) | ? [X2 : $i] : (($true != ((cD @ X2))) & (((X0 @ X2)) = $true))) & ((! [X3 : $i] : (($true = ((cE @ X3))) | (((X0 @ X3)) != $true)) & ! [X4 : $i] : (($true = ((cD @ X4))) | ($true != ((X0 @ X4))))) | ($true != ((sP0 @ X0)))))),
% 0.19/0.28 inference(rectify,[],[f9])).
% 0.19/0.28 thf(f11,plain,(
% 0.19/0.28 ! [X0 : ($i > $o)] : ((($true = ((sP0 @ X0))) | (($true != ((cE @ (sK1 @ X0)))) & ($true = ((X0 @ (sK1 @ X0))))) | (($true != ((cD @ (sK2 @ X0)))) & ($true = ((X0 @ (sK2 @ X0)))))) & ((! [X3 : $i] : (($true = ((cE @ X3))) | (((X0 @ X3)) != $true)) & ! [X4 : $i] : (($true = ((cD @ X4))) | ($true != ((X0 @ X4))))) | ($true != ((sP0 @ X0)))))),
% 0.19/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X2,sK2 @ X0),skolemize(X2,sK2 @ X0)],[f10])).
% 0.19/0.28 thf(f12,plain,(
% 0.19/0.28 ? [X0 : ($i > $o)] : ((($true != ((sP0 @ X0))) | ? [X1 : $i] : (((((cE @ X1)) != $true) | (((cD @ X1)) != $true)) & (((X0 @ X1)) = $true))) & (($true = ((sP0 @ X0))) | ! [X1 : $i] : (((((cE @ X1)) = $true) & (((cD @ X1)) = $true)) | (((X0 @ X1)) != $true))))),
% 0.19/0.28 inference(nnf_transformation,[],[f7])).
% 0.19/0.28 thf(f13,plain,(
% 0.19/0.28 ? [X0 : ($i > $o)] : ((($true != ((sP0 @ X0))) | ? [X1 : $i] : (((((cE @ X1)) != $true) | (((cD @ X1)) != $true)) & (((X0 @ X1)) = $true))) & (($true = ((sP0 @ X0))) | ! [X2 : $i] : (((((cE @ X2)) = $true) & ($true = ((cD @ X2)))) | (((X0 @ X2)) != $true))))),
% 0.19/0.28 inference(rectify,[],[f12])).
% 0.19/0.28 thf(f14,plain,(
% 0.19/0.28 (($true != ((sP0 @ sK3))) | ((($true != ((cE @ sK4))) | ($true != ((cD @ sK4)))) & ($true = ((sK3 @ sK4))))) & (($true = ((sP0 @ sK3))) | ! [X2 : $i] : (((((cE @ X2)) = $true) & ($true = ((cD @ X2)))) | ($true != ((sK3 @ X2)))))),
% 0.19/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f13])).
% 0.19/0.28 thf(f15,plain,(
% 0.19/0.28 ( ! [X0 : ($i > $o),X4 : $i] : (($true != ((X0 @ X4))) | ($true = ((cD @ X4))) | ($true != ((sP0 @ X0)))) )),
% 0.19/0.28 inference(cnf_transformation,[],[f11])).
% 0.19/0.28 thf(f16,plain,(
% 0.19/0.28 ( ! [X3 : $i,X0 : ($i > $o)] : ((((X0 @ X3)) != $true) | ($true = ((cE @ X3))) | ($true != ((sP0 @ X0)))) )),
% 0.19/0.28 inference(cnf_transformation,[],[f11])).
% 0.19/0.28 thf(f17,plain,(
% 0.19/0.28 ( ! [X0 : ($i > $o)] : (($true = ((sP0 @ X0))) | ($true = ((X0 @ (sK2 @ X0)))) | ($true = ((X0 @ (sK1 @ X0))))) )),
% 0.19/0.28 inference(cnf_transformation,[],[f11])).
% 0.19/0.28 thf(f18,plain,(
% 0.19/0.28 ( ! [X0 : ($i > $o)] : (($true != ((cD @ (sK2 @ X0)))) | ($true = ((X0 @ (sK1 @ X0)))) | ($true = ((sP0 @ X0)))) )),
% 0.19/0.28 inference(cnf_transformation,[],[f11])).
% 0.19/0.28 thf(f19,plain,(
% 0.19/0.28 ( ! [X0 : ($i > $o)] : (($true != ((cE @ (sK1 @ X0)))) | ($true = ((sP0 @ X0))) | ($true = ((X0 @ (sK2 @ X0))))) )),
% 0.19/0.28 inference(cnf_transformation,[],[f11])).
% 0.19/0.28 thf(f20,plain,(
% 0.19/0.28 ( ! [X0 : ($i > $o)] : (($true != ((cD @ (sK2 @ X0)))) | ($true != ((cE @ (sK1 @ X0)))) | ($true = ((sP0 @ X0)))) )),
% 0.19/0.28 inference(cnf_transformation,[],[f11])).
% 0.19/0.28 thf(f21,plain,(
% 0.19/0.28 ( ! [X2 : $i] : (($true = ((sP0 @ sK3))) | ($true = ((cD @ X2))) | ($true != ((sK3 @ X2)))) )),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f22,plain,(
% 0.19/0.28 ( ! [X2 : $i] : (($true = ((sP0 @ sK3))) | (((cE @ X2)) = $true) | ($true != ((sK3 @ X2)))) )),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f23,plain,(
% 0.19/0.28 ($true != ((sP0 @ sK3))) | ($true = ((sK3 @ sK4)))),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f24,plain,(
% 0.19/0.28 ($true != ((sP0 @ sK3))) | ($true != ((cE @ sK4))) | ($true != ((cD @ sK4)))),
% 0.19/0.28 inference(cnf_transformation,[],[f14])).
% 0.19/0.28 thf(f26,definition,(
% 0.19/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.28 thf(f28,definition,(
% 0.19/0.28 spl5_1 <=> ! [X2 : $i] : (($true = ((cD @ X2))) | ($true != ((sK3 @ X2))))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.19/0.28 thf(f29,plain,(
% 0.19/0.28 ( ! [X2 : $i] : (($true != ((sK3 @ X2))) | ($true = ((cD @ X2)))) ) | ~spl5_1),
% 0.19/0.28 inference(avatar_component_clause,[],[f28])).
% 0.19/0.28 thf(f31,definition,(
% 0.19/0.28 spl5_2 <=> ($true = ((sP0 @ sK3)))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.19/0.28 thf(f32,plain,(
% 0.19/0.28 ($true != ((sP0 @ sK3))) | spl5_2),
% 0.19/0.28 inference(avatar_component_clause,[],[f31])).
% 0.19/0.28 thf(f33,plain,(
% 0.19/0.28 ($true = ((sP0 @ sK3))) | ~spl5_2),
% 0.19/0.28 inference(avatar_component_clause,[],[f31])).
% 0.19/0.28 thf(f34,plain,(
% 0.19/0.28 spl5_1 | spl5_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f21,f31,f28])).
% 0.19/0.28 thf(f36,definition,(
% 0.19/0.28 spl5_3 <=> ! [X2 : $i] : ((((cE @ X2)) = $true) | ($true != ((sK3 @ X2))))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.19/0.28 thf(f37,plain,(
% 0.19/0.28 ( ! [X2 : $i] : (($true != ((sK3 @ X2))) | (((cE @ X2)) = $true)) ) | ~spl5_3),
% 0.19/0.28 inference(avatar_component_clause,[],[f36])).
% 0.19/0.28 thf(f38,plain,(
% 0.19/0.28 spl5_3 | spl5_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f22,f31,f36])).
% 0.19/0.28 thf(f40,definition,(
% 0.19/0.28 spl5_4 <=> ($true = ((sK3 @ sK4)))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.19/0.28 thf(f42,plain,(
% 0.19/0.28 ($true = ((sK3 @ sK4))) | ~spl5_4),
% 0.19/0.28 inference(avatar_component_clause,[],[f40])).
% 0.19/0.28 thf(f43,plain,(
% 0.19/0.28 spl5_4 | ~spl5_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f23,f31,f40])).
% 0.19/0.28 thf(f45,definition,(
% 0.19/0.28 spl5_5 <=> ($true = ((cD @ sK4)))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.19/0.28 thf(f49,definition,(
% 0.19/0.28 spl5_6 <=> ($true = ((cE @ sK4)))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.19/0.28 thf(f51,plain,(
% 0.19/0.28 ($true != ((cE @ sK4))) | spl5_6),
% 0.19/0.28 inference(avatar_component_clause,[],[f49])).
% 0.19/0.28 thf(f52,plain,(
% 0.19/0.28 ~spl5_5 | ~spl5_6 | ~spl5_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f24,f31,f49,f45])).
% 0.19/0.28 thf(f65,plain,(
% 0.19/0.28 ( ! [X0 : $i] : (($true != $true) | ($true = ((cD @ X0))) | ($true != ((sP0 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0)))))) | (sK4 != X0)) ) | ~spl5_4),
% 0.19/0.28 inference(constrained_superposition,[],[f15,f42])).
% 0.19/0.28 thf(f76,plain,(
% 0.19/0.28 ( ! [X0 : $i] : (($true = ((cD @ X0))) | ($true != ((sP0 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0)))))) | (sK4 != X0)) ) | ~spl5_4),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f65])).
% 0.19/0.28 thf(f77,plain,(
% 0.19/0.28 ( ! [X0 : $i] : (($true = ((cD @ X0))) | ($true != ((sP0 @ sK3))) | (sK4 != X0)) ) | ~spl5_4),
% 0.19/0.28 inference(beta-eta_normalization,[],[f76])).
% 0.19/0.28 thf(f97,plain,(
% 0.19/0.28 ( ! [X0 : $i] : ((sK4 != X0) | ($true = ((cD @ X0)))) ) | (~spl5_2 | ~spl5_4)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f77,f33])).
% 0.19/0.28 thf(f113,plain,(
% 0.19/0.28 ( ! [X0 : $i] : (($true != $true) | ($true = ((cE @ X0))) | ($true != ((sP0 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0)))))) | (sK4 != X0)) ) | ~spl5_4),
% 0.19/0.28 inference(constrained_superposition,[],[f16,f42])).
% 0.19/0.28 thf(f128,plain,(
% 0.19/0.28 ( ! [X0 : $i] : (($true = ((cE @ X0))) | ($true != ((sP0 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0)))))) | (sK4 != X0)) ) | ~spl5_4),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f113])).
% 0.19/0.28 thf(f129,plain,(
% 0.19/0.28 ( ! [X0 : $i] : (($true = ((cE @ X0))) | ($true != ((sP0 @ sK3))) | (sK4 != X0)) ) | ~spl5_4),
% 0.19/0.28 inference(beta-eta_normalization,[],[f128])).
% 0.19/0.28 thf(f136,plain,(
% 0.19/0.28 ($true = ((cD @ sK4))) | (~spl5_2 | ~spl5_4)),
% 0.19/0.28 inference(equality_resolution,[],[f97])).
% 0.19/0.28 thf(f137,plain,(
% 0.19/0.28 spl5_5 | ~spl5_2 | ~spl5_4),
% 0.19/0.28 inference(avatar_split_clause,[],[f136,f40,f31,f45])).
% 0.19/0.28 thf(f138,plain,(
% 0.19/0.28 ($true != $true) | (((sP0 @ sK3)) = $false) | spl5_2),
% 0.19/0.28 inference(constrained_superposition,[],[f32,f26])).
% 0.19/0.28 thf(f139,plain,(
% 0.19/0.28 (((sP0 @ sK3)) = $false) | spl5_2),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f138])).
% 0.19/0.28 thf(f182,definition,(
% 0.19/0.28 spl5_15 <=> ! [X0 : $i] : (($true = ((cE @ X0))) | (sK4 != X0))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_15])],[avatar_definition])).
% 0.19/0.28 thf(f183,plain,(
% 0.19/0.28 ( ! [X0 : $i] : ((sK4 != X0) | ($true = ((cE @ X0)))) ) | ~spl5_15),
% 0.19/0.28 inference(avatar_component_clause,[],[f182])).
% 0.19/0.28 thf(f218,plain,(
% 0.19/0.28 ($true = $false) | ($true = ((sK3 @ (sK2 @ sK3)))) | ($true = ((sK3 @ (sK1 @ sK3)))) | spl5_2),
% 0.19/0.28 inference(constrained_superposition,[],[f17,f139])).
% 0.19/0.28 thf(f263,plain,(
% 0.19/0.28 ($true = ((sK3 @ (sK2 @ sK3)))) | ($true = ((sK3 @ (sK1 @ sK3)))) | spl5_2),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f218])).
% 0.19/0.28 thf(f275,definition,(
% 0.19/0.28 spl5_18 <=> ($true = ((sK3 @ (sK1 @ sK3))))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_18])],[avatar_definition])).
% 0.19/0.28 thf(f276,plain,(
% 0.19/0.28 ($true != ((sK3 @ (sK1 @ sK3)))) | spl5_18),
% 0.19/0.28 inference(avatar_component_clause,[],[f275])).
% 0.19/0.28 thf(f277,plain,(
% 0.19/0.28 ($true = ((sK3 @ (sK1 @ sK3)))) | ~spl5_18),
% 0.19/0.28 inference(avatar_component_clause,[],[f275])).
% 0.19/0.28 thf(f279,definition,(
% 0.19/0.28 spl5_19 <=> ($true = ((sK3 @ (sK2 @ sK3))))),
% 0.19/0.28 introduced(definition,[new_symbols(definition,[spl5_19])],[avatar_definition])).
% 0.19/0.28 thf(f281,plain,(
% 0.19/0.28 ($true = ((sK3 @ (sK2 @ sK3)))) | ~spl5_19),
% 0.19/0.28 inference(avatar_component_clause,[],[f279])).
% 0.19/0.28 thf(f284,plain,(
% 0.19/0.28 spl5_18 | spl5_19 | spl5_2),
% 0.19/0.28 inference(avatar_split_clause,[],[f263,f31,f279,f275])).
% 0.19/0.28 thf(f309,plain,(
% 0.19/0.28 ($true != $true) | ($true = ((cE @ (sK1 @ sK3)))) | (~spl5_3 | ~spl5_18)),
% 0.19/0.28 inference(constrained_superposition,[],[f37,f277])).
% 0.19/0.28 thf(f324,plain,(
% 0.19/0.28 ($true = ((cE @ (sK1 @ sK3)))) | (~spl5_3 | ~spl5_18)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f309])).
% 0.19/0.28 thf(f356,plain,(
% 0.19/0.28 ($true != $true) | ($true = ((sP0 @ sK3))) | ($true = ((sK3 @ (sK2 @ sK3)))) | (~spl5_3 | ~spl5_18)),
% 0.19/0.28 inference(constrained_superposition,[],[f19,f324])).
% 0.19/0.28 thf(f357,plain,(
% 0.19/0.28 ($true = ((sP0 @ sK3))) | ($true = ((sK3 @ (sK2 @ sK3)))) | (~spl5_3 | ~spl5_18)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f356])).
% 0.19/0.28 thf(f366,plain,(
% 0.19/0.28 ($true = ((sK3 @ (sK2 @ sK3)))) | (spl5_2 | ~spl5_3 | ~spl5_18)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f357,f32])).
% 0.19/0.28 thf(f367,plain,(
% 0.19/0.28 spl5_19 | spl5_2 | ~spl5_3 | ~spl5_18),
% 0.19/0.28 inference(avatar_split_clause,[],[f366,f275,f36,f31,f279])).
% 0.19/0.28 thf(f371,plain,(
% 0.19/0.28 ($true != $true) | ($true = ((cD @ (sK2 @ sK3)))) | (~spl5_1 | ~spl5_19)),
% 0.19/0.28 inference(constrained_superposition,[],[f29,f281])).
% 0.19/0.28 thf(f384,plain,(
% 0.19/0.28 ($true = ((cD @ (sK2 @ sK3)))) | (~spl5_1 | ~spl5_19)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f371])).
% 0.19/0.28 thf(f392,plain,(
% 0.19/0.28 ($true != $true) | ($true != ((cE @ (sK1 @ sK3)))) | ($true = ((sP0 @ sK3))) | (~spl5_1 | ~spl5_19)),
% 0.19/0.28 inference(constrained_superposition,[],[f20,f384])).
% 0.19/0.28 thf(f393,plain,(
% 0.19/0.28 ($true != $true) | ($true = ((sK3 @ (sK1 @ sK3)))) | ($true = ((sP0 @ sK3))) | (~spl5_1 | ~spl5_19)),
% 0.19/0.28 inference(constrained_superposition,[],[f18,f384])).
% 0.19/0.28 thf(f394,plain,(
% 0.19/0.28 ($true = ((sK3 @ (sK1 @ sK3)))) | ($true = ((sP0 @ sK3))) | (~spl5_1 | ~spl5_19)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f393])).
% 0.19/0.28 thf(f395,plain,(
% 0.19/0.28 ($true != ((cE @ (sK1 @ sK3)))) | ($true = ((sP0 @ sK3))) | (~spl5_1 | ~spl5_19)),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f392])).
% 0.19/0.28 thf(f404,plain,(
% 0.19/0.28 ($true = ((sP0 @ sK3))) | (~spl5_1 | ~spl5_3 | ~spl5_18 | ~spl5_19)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f395,f324])).
% 0.19/0.28 thf(f405,plain,(
% 0.19/0.28 $false | (~spl5_1 | spl5_2 | ~spl5_3 | ~spl5_18 | ~spl5_19)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f404,f32])).
% 0.19/0.28 thf(f406,plain,(
% 0.19/0.28 ~spl5_1 | spl5_2 | ~spl5_3 | ~spl5_18 | ~spl5_19),
% 0.19/0.28 inference(avatar_contradiction_clause,[],[f405])).
% 0.19/0.28 thf(f407,plain,(
% 0.19/0.28 ($true = ((sP0 @ sK3))) | (~spl5_1 | spl5_18 | ~spl5_19)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f394,f276])).
% 0.19/0.28 thf(f409,plain,(
% 0.19/0.28 $false | (~spl5_1 | spl5_2 | spl5_18 | ~spl5_19)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f407,f32])).
% 0.19/0.28 thf(f410,plain,(
% 0.19/0.28 ~spl5_1 | spl5_2 | spl5_18 | ~spl5_19),
% 0.19/0.28 inference(avatar_contradiction_clause,[],[f409])).
% 0.19/0.28 thf(f412,plain,(
% 0.19/0.28 ( ! [X0 : $i] : (($true = ((cE @ X0))) | (sK4 != X0)) ) | (~spl5_2 | ~spl5_4)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f129,f33])).
% 0.19/0.28 thf(f414,plain,(
% 0.19/0.28 spl5_15 | ~spl5_2 | ~spl5_4),
% 0.19/0.28 inference(avatar_split_clause,[],[f412,f40,f31,f182])).
% 0.19/0.28 thf(f435,plain,(
% 0.19/0.28 ($true = ((cE @ sK4))) | ~spl5_15),
% 0.19/0.28 inference(equality_resolution,[],[f183])).
% 0.19/0.28 thf(f436,plain,(
% 0.19/0.28 $false | (spl5_6 | ~spl5_15)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f435,f51])).
% 0.19/0.28 thf(f437,plain,(
% 0.19/0.28 spl5_6 | ~spl5_15),
% 0.19/0.28 inference(avatar_contradiction_clause,[],[f436])).
% 0.19/0.28 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f34])).
% 0.19/0.28 cnf(s2, plain, spl5_2 | spl5_3, inference(sat_conversion,[],[f38])).
% 0.19/0.28 cnf(s3, plain, ~spl5_2 | spl5_4, inference(sat_conversion,[],[f43])).
% 0.19/0.28 cnf(s4, plain, ~spl5_2 | ~spl5_5 | ~spl5_6, inference(sat_conversion,[],[f52])).
% 0.19/0.28 cnf(s9, plain, ~spl5_2 | ~spl5_4 | spl5_5, inference(sat_conversion,[],[f137])).
% 0.19/0.28 cnf(s22, plain, spl5_2 | spl5_18 | spl5_19, inference(sat_conversion,[],[f284])).
% 0.19/0.28 cnf(s23, plain, spl5_2 | ~spl5_3 | ~spl5_18 | spl5_19, inference(sat_conversion,[],[f367])).
% 0.19/0.28 cnf(s24, plain, ~spl5_1 | spl5_2 | ~spl5_3 | ~spl5_18 | ~spl5_19, inference(sat_conversion,[],[f406])).
% 0.19/0.28 cnf(s25, plain, ~spl5_1 | spl5_2 | spl5_18 | ~spl5_19, inference(sat_conversion,[],[f410])).
% 0.19/0.28 cnf(s27, plain, ~spl5_2 | ~spl5_4 | spl5_15, inference(sat_conversion,[],[f414])).
% 0.19/0.28 cnf(s28, plain, spl5_6 | ~spl5_15, inference(sat_conversion,[],[f437])).
% 0.19/0.28 cnf(s29, plain, ~spl5_4 | ~spl5_2, inference(rat,[],[s4,s28,s9,s27])).
% 0.19/0.28 cnf(s30, plain, ~spl5_2, inference(rat,[],[s29,s3])).
% 0.19/0.28 cnf(s31, plain, spl5_3, inference(rat,[],[s2,s30])).
% 0.19/0.28 cnf(s32, plain, spl5_1, inference(rat,[],[s1,s30])).
% 0.19/0.28 cnf(s33, plain, spl5_18, inference(rat,[],[s25,s22,s30,s32])).
% 0.19/0.28 cnf(s34, plain, spl5_19, inference(rat,[],[s23,s30,s31,s33])).
% 0.19/0.28 cnf(s35, plain, $false, inference(rat,[],[s24,s32,s31,s30,s34,s33])).
% 0.19/0.28 thf(f438,plain,(
% 0.19/0.28 $false),
% 0.19/0.28 inference(avatar_sat_refutation,[],[s35])).
% 0.19/0.28 % SZS output end Proof for theBenchmark
% 0.19/0.28 % (216898)------------------------------
% 0.19/0.28 % (216898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (216898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (216898)CaDiCaL version: 2.1.3
% 0.19/0.28 % (216898)Termination reason: Refutation
% 0.19/0.28 % (216898)Time elapsed: 0.018 s
% 0.19/0.28 % (216898)Peak memory usage: 12 MB
% 0.19/0.28 % (216898)Instructions burned: 29 (million)
% 0.19/0.28 % (216888)Success in time 0.053 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------