%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET593^5 : 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 : n016.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 08:23:39 AM UTC 2026
% Result : Theorem 0.11s 0.25s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET593^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.17 % Computer : n016.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 13:43:19 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.20 Running first-order model finding
% 0.11/0.20 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
% 0.11/0.25 % (359366)Will run a generic schedule for satisfiability detection.
% 0.11/0.25 % (359374)dis+10_1_sil=32000:sp=arity:random_seed=236514195:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.25 % (359372)% WARNING: option uhcvi not known.
% 0.11/0.25 % (359374) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-359366-359374"...
% 0.11/0.25 % (359372)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1310197736:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.25 % (359373)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4177605719:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.25 % (359375)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=216188309:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.25 % (359376)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1762609160:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.25 % (359372)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.25 % (359377)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2421508749:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.25 % (359375)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.25 % (359374)...printing done.
% 0.11/0.25 % (359372)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.11/0.25 % (359374)Refutation found. Thanks to Tanya!
% 0.11/0.25 % SZS status Theorem for theBenchmark
% 0.11/0.25 % SZS output start Proof for theBenchmark
% 0.11/0.25 thf(type_def_5, type, a: $tType).
% 0.11/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.11/0.25 thf(func_def_3, type, sP0: ((a > $o) > (a > $o) > (a > $o) > $o)).
% 0.11/0.25 thf(func_def_4, type, sK1: ((a > $o) > (a > $o) > (a > $o) > a)).
% 0.11/0.25 thf(func_def_5, type, sK2: (a > $o)).
% 0.11/0.25 thf(func_def_6, type, sK3: (a > $o)).
% 0.11/0.25 thf(func_def_7, type, sK4: (a > $o)).
% 0.11/0.25 thf(func_def_8, type, sK5: a).
% 0.11/0.25 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.11/0.25 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.11/0.25 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.11/0.25 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 0.11/0.25 thf(f1,conjecture,(
% 0.11/0.25 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (! [X3 : a] : ((X0 @ X3) => ((X2 @ X3) | (X1 @ X3))) => (! [X3 : a] : ((~(X2 @ X3) & (X0 @ X3)) => (X1 @ X3)) & ! [X3 : a] : ((~(X1 @ X3) & (X0 @ X3)) => (X2 @ X3))))),
% 0.11/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_52_pme)).
% 0.11/0.25 thf(f2,negated_conjecture,(
% 0.11/0.25 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (! [X3 : a] : ((X0 @ X3) => ((X2 @ X3) | (X1 @ X3))) => (! [X3 : a] : ((~(X2 @ X3) & (X0 @ X3)) => (X1 @ X3)) & ! [X3 : a] : ((~(X1 @ X3) & (X0 @ X3)) => (X2 @ X3))))),
% 0.11/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.11/0.25 thf(f3,plain,(
% 0.11/0.25 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (! [X3 : a] : ((X0 @ X3) => ((X2 @ X3) | (X1 @ X3))) => (! [X4 : a] : ((~(X2 @ X4) & (X0 @ X4)) => (X1 @ X4)) & ! [X5 : a] : ((~(X1 @ X5) & (X0 @ X5)) => (X2 @ X5))))),
% 0.11/0.25 inference(rectify,[],[f2])).
% 0.11/0.25 thf(f4,plain,(
% 0.11/0.25 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (! [X3 : a] : ((((X0 @ X3)) = $true) => ((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true))) => (! [X4 : a] : ((~ (((X2 @ X4)) = $true) & (((X0 @ X4)) = $true)) => (((X1 @ X4)) = $true)) & ! [X5 : a] : ((~ (((X1 @ X5)) = $true) & (((X0 @ X5)) = $true)) => (((X2 @ X5)) = $true))))),
% 0.11/0.25 inference(fool_elimination,[],[f3])).
% 0.11/0.25 thf(f5,plain,(
% 0.11/0.25 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (! [X3 : a] : ((((X0 @ X3)) = $true) => ((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true))) => (! [X4 : a] : (((((X2 @ X4)) != $true) & (((X0 @ X4)) = $true)) => (((X1 @ X4)) = $true)) & ! [X5 : a] : (((((X1 @ X5)) != $true) & (((X0 @ X5)) = $true)) => (((X2 @ X5)) = $true))))),
% 0.11/0.25 inference(flattening,[],[f4])).
% 0.11/0.25 thf(f6,plain,(
% 0.11/0.25 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((? [X4 : a] : ((((X1 @ X4)) != $true) & ((((X2 @ X4)) != $true) & (((X0 @ X4)) = $true))) | ? [X5 : a] : ((((X2 @ X5)) != $true) & ((((X1 @ X5)) != $true) & (((X0 @ X5)) = $true)))) & ! [X3 : a] : (((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true)) | (((X0 @ X3)) != $true)))),
% 0.11/0.25 inference(ennf_transformation,[],[f5])).
% 0.11/0.25 thf(f7,plain,(
% 0.11/0.25 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((? [X4 : a] : ((((X1 @ X4)) != $true) & (((X2 @ X4)) != $true) & (((X0 @ X4)) = $true)) | ? [X5 : a] : ((((X2 @ X5)) != $true) & (((X1 @ X5)) != $true) & (((X0 @ X5)) = $true))) & ! [X3 : a] : ((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true) | (((X0 @ X3)) != $true)))),
% 0.11/0.25 inference(flattening,[],[f6])).
% 0.11/0.25 thf(f8,definition,(
% 0.11/0.25 ! [X2 : (a > $o),X1 : (a > $o),X0 : (a > $o)] : (? [X5 : a] : ((((X2 @ X5)) != $true) & (((X1 @ X5)) != $true) & (((X0 @ X5)) = $true)) | ~ ($true = ((sP0 @ X0 @ X1 @ X2))))),
% 0.11/0.25 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.11/0.25 thf(f9,plain,(
% 0.11/0.25 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((? [X4 : a] : ((((X1 @ X4)) != $true) & (((X2 @ X4)) != $true) & (((X0 @ X4)) = $true)) | ($true = ((sP0 @ X0 @ X1 @ X2)))) & ! [X3 : a] : ((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true) | (((X0 @ X3)) != $true)))),
% 0.11/0.25 inference(definition_folding,[],[f7,f8])).
% 0.11/0.25 thf(f10,plain,(
% 0.11/0.25 ! [X2 : (a > $o),X1 : (a > $o),X0 : (a > $o)] : (? [X5 : a] : ((((X2 @ X5)) != $true) & (((X1 @ X5)) != $true) & (((X0 @ X5)) = $true)) | ($true != ((sP0 @ X0 @ X1 @ X2))))),
% 0.11/0.25 inference(nnf_transformation,[],[f8])).
% 0.11/0.25 thf(f11,plain,(
% 0.11/0.25 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (? [X3 : a] : ((((X0 @ X3)) != $true) & (((X1 @ X3)) != $true) & (((X2 @ X3)) = $true)) | ($true != ((sP0 @ X2 @ X1 @ X0))))),
% 0.11/0.25 inference(rectify,[],[f10])).
% 0.11/0.25 thf(f12,plain,(
% 0.11/0.25 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((($true != ((X0 @ (sK1 @ X2 @ X1 @ X0)))) & ($true != ((X1 @ (sK1 @ X2 @ X1 @ X0)))) & ($true = ((X2 @ (sK1 @ X2 @ X1 @ X0))))) | ($true != ((sP0 @ X2 @ X1 @ X0))))),
% 0.11/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK1 @ X2 @ X1 @ X0)],[f11])).
% 0.11/0.25 thf(f13,plain,(
% 0.11/0.25 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((? [X3 : a] : ((((X1 @ X3)) != $true) & (((X2 @ X3)) != $true) & (((X0 @ X3)) = $true)) | ($true = ((sP0 @ X0 @ X1 @ X2)))) & ! [X4 : a] : ((((X2 @ X4)) = $true) | (((X1 @ X4)) = $true) | (((X0 @ X4)) != $true)))),
% 0.11/0.25 inference(rectify,[],[f9])).
% 0.11/0.25 thf(f14,plain,(
% 0.11/0.25 ((($true != ((sK3 @ sK5))) & ($true != ((sK4 @ sK5))) & ($true = ((sK2 @ sK5)))) | ($true = ((sP0 @ sK2 @ sK3 @ sK4)))) & ! [X4 : a] : (($true = ((sK4 @ X4))) | ($true = ((sK3 @ X4))) | ($true != ((sK2 @ X4))))),
% 0.11/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f13])).
% 0.11/0.25 thf(f15,plain,(
% 0.11/0.25 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | ($true = ((X2 @ (sK1 @ X2 @ X1 @ X0))))) )),
% 0.11/0.25 inference(cnf_transformation,[],[f12])).
% 0.11/0.25 thf(f16,plain,(
% 0.11/0.25 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != ((X1 @ (sK1 @ X2 @ X1 @ X0)))) | ($true != ((sP0 @ X2 @ X1 @ X0)))) )),
% 0.11/0.25 inference(cnf_transformation,[],[f12])).
% 0.11/0.25 thf(f17,plain,(
% 0.11/0.25 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != ((X0 @ (sK1 @ X2 @ X1 @ X0)))) | ($true != ((sP0 @ X2 @ X1 @ X0)))) )),
% 0.11/0.25 inference(cnf_transformation,[],[f12])).
% 0.11/0.25 thf(f18,plain,(
% 0.11/0.25 ( ! [X4 : a] : (($true != ((sK2 @ X4))) | ($true = ((sK3 @ X4))) | ($true = ((sK4 @ X4)))) )),
% 0.11/0.25 inference(cnf_transformation,[],[f14])).
% 0.11/0.25 thf(f19,plain,(
% 0.11/0.25 ($true = ((sK2 @ sK5))) | ($true = ((sP0 @ sK2 @ sK3 @ sK4)))),
% 0.11/0.25 inference(cnf_transformation,[],[f14])).
% 0.11/0.25 thf(f20,plain,(
% 0.11/0.25 ($true != ((sK4 @ sK5))) | ($true = ((sP0 @ sK2 @ sK3 @ sK4)))),
% 0.11/0.25 inference(cnf_transformation,[],[f14])).
% 0.11/0.25 thf(f21,plain,(
% 0.11/0.25 ($true != ((sK3 @ sK5))) | ($true = ((sP0 @ sK2 @ sK3 @ sK4)))),
% 0.11/0.25 inference(cnf_transformation,[],[f14])).
% 0.11/0.25 thf(f23,definition,(
% 0.11/0.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.11/0.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.11/0.25 thf(f25,definition,(
% 0.11/0.25 spl6_1 <=> ($true = ((sP0 @ sK2 @ sK3 @ sK4)))),
% 0.11/0.25 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.11/0.25 thf(f27,plain,(
% 0.11/0.25 ($true = ((sP0 @ sK2 @ sK3 @ sK4))) | ~spl6_1),
% 0.11/0.25 inference(avatar_component_clause,[],[f25])).
% 0.11/0.25 thf(f29,definition,(
% 0.11/0.25 spl6_2 <=> ($true = ((sK2 @ sK5)))),
% 0.11/0.25 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.11/0.25 thf(f31,plain,(
% 0.11/0.25 ($true = ((sK2 @ sK5))) | ~spl6_2),
% 0.11/0.25 inference(avatar_component_clause,[],[f29])).
% 0.11/0.25 thf(f32,plain,(
% 0.11/0.25 spl6_1 | spl6_2),
% 0.11/0.25 inference(avatar_split_clause,[],[f19,f29,f25])).
% 0.11/0.25 thf(f34,definition,(
% 0.11/0.25 spl6_3 <=> ($true = ((sK4 @ sK5)))),
% 0.11/0.25 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 0.11/0.25 thf(f36,plain,(
% 0.11/0.25 ($true != ((sK4 @ sK5))) | spl6_3),
% 0.11/0.25 inference(avatar_component_clause,[],[f34])).
% 0.11/0.25 thf(f37,plain,(
% 0.11/0.25 spl6_1 | ~spl6_3),
% 0.11/0.25 inference(avatar_split_clause,[],[f20,f34,f25])).
% 0.11/0.25 thf(f39,definition,(
% 0.11/0.25 spl6_4 <=> ($true = ((sK3 @ sK5)))),
% 0.11/0.25 introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition])).
% 0.11/0.25 thf(f41,plain,(
% 0.11/0.25 ($true != ((sK3 @ sK5))) | spl6_4),
% 0.11/0.25 inference(avatar_component_clause,[],[f39])).
% 0.11/0.25 thf(f42,plain,(
% 0.11/0.25 spl6_1 | ~spl6_4),
% 0.11/0.25 inference(avatar_split_clause,[],[f21,f39,f25])).
% 0.11/0.25 thf(f43,plain,(
% 0.11/0.25 ($true != $true) | ($true = ((sK3 @ sK5))) | ($true = ((sK4 @ sK5))) | ~spl6_2),
% 0.11/0.25 inference(constrained_superposition,[],[f18,f31])).
% 0.11/0.25 thf(f44,plain,(
% 0.11/0.25 ($true = ((sK3 @ sK5))) | ($true = ((sK4 @ sK5))) | ~spl6_2),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f43])).
% 0.11/0.25 thf(f45,plain,(
% 0.11/0.25 ($true = ((sK4 @ sK5))) | (~spl6_2 | spl6_4)),
% 0.11/0.25 inference(forward_subsumption_resolution,[],[f44,f41])).
% 0.11/0.25 thf(f46,plain,(
% 0.11/0.25 $false | (~spl6_2 | spl6_3 | spl6_4)),
% 0.11/0.25 inference(forward_subsumption_resolution,[],[f45,f36])).
% 0.11/0.25 thf(f47,plain,(
% 0.11/0.25 ~spl6_2 | spl6_3 | spl6_4),
% 0.11/0.25 inference(avatar_contradiction_clause,[],[f46])).
% 0.11/0.25 thf(f53,plain,(
% 0.11/0.25 ( ! [X0 : a] : (($true != $true) | ($true = ((sK3 @ X0))) | ($true = ((sK4 @ X0))) | ($false = ((sK2 @ X0)))) )),
% 0.11/0.25 inference(constrained_superposition,[],[f18,f23])).
% 0.11/0.25 thf(f55,plain,(
% 0.11/0.25 ( ! [X0 : a] : (($true = ((sK4 @ X0))) | ($true = ((sK3 @ X0))) | ($false = ((sK2 @ X0)))) )),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f53])).
% 0.11/0.25 thf(f67,plain,(
% 0.11/0.25 ($true != $true) | ($true = ((sK2 @ (sK1 @ sK2 @ sK3 @ sK4)))) | ~spl6_1),
% 0.11/0.25 inference(constrained_superposition,[],[f15,f27])).
% 0.11/0.25 thf(f70,plain,(
% 0.11/0.25 ($true = ((sK2 @ (sK1 @ sK2 @ sK3 @ sK4)))) | ~spl6_1),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f67])).
% 0.11/0.25 thf(f179,definition,(
% 0.11/0.25 spl6_8 <=> ($true = ((sK4 @ (sK1 @ sK2 @ sK3 @ sK4))))),
% 0.11/0.25 introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition])).
% 0.11/0.25 thf(f180,plain,(
% 0.11/0.25 ($true != ((sK4 @ (sK1 @ sK2 @ sK3 @ sK4)))) | spl6_8),
% 0.11/0.25 inference(avatar_component_clause,[],[f179])).
% 0.11/0.25 thf(f181,plain,(
% 0.11/0.25 ($true = ((sK4 @ (sK1 @ sK2 @ sK3 @ sK4)))) | ~spl6_8),
% 0.11/0.25 inference(avatar_component_clause,[],[f179])).
% 0.11/0.25 thf(f183,definition,(
% 0.11/0.25 spl6_9 <=> ($true = ((sK3 @ (sK1 @ sK2 @ sK3 @ sK4))))),
% 0.11/0.25 introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition])).
% 0.11/0.25 thf(f185,plain,(
% 0.11/0.25 ($true = ((sK3 @ (sK1 @ sK2 @ sK3 @ sK4)))) | ~spl6_9),
% 0.11/0.25 inference(avatar_component_clause,[],[f183])).
% 0.11/0.25 thf(f189,plain,(
% 0.11/0.25 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true != $true) | ($true != ((sP0 @ X0 @ X1 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) | (sK3 != X1) | (sK2 != X0)) ) | ~spl6_8),
% 0.11/0.25 inference(constrained_superposition,[],[f17,f181])).
% 0.11/0.25 thf(f193,plain,(
% 0.11/0.25 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true != ((sP0 @ X0 @ X1 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) | (sK3 != X1) | (sK2 != X0)) ) | ~spl6_8),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f189])).
% 0.11/0.25 thf(f194,plain,(
% 0.11/0.25 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true != ((sP0 @ X0 @ X1 @ sK4))) | (sK3 != X1) | (sK2 != X0)) ) | ~spl6_8),
% 0.11/0.25 inference(beta-eta_normalization,[],[f193])).
% 0.11/0.25 thf(f198,plain,(
% 0.11/0.25 ($true != $true) | (sK3 != sK3) | (sK2 != sK2) | (~spl6_1 | ~spl6_8)),
% 0.11/0.25 inference(constrained_superposition,[],[f194,f27])).
% 0.11/0.25 thf(f199,plain,(
% 0.11/0.25 $false | (~spl6_1 | ~spl6_8)),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f198])).
% 0.11/0.25 thf(f200,plain,(
% 0.11/0.25 ~spl6_1 | ~spl6_8),
% 0.11/0.25 inference(avatar_contradiction_clause,[],[f199])).
% 0.11/0.25 thf(f205,plain,(
% 0.11/0.25 ($true != $true) | ($true = ((sK3 @ (sK1 @ sK2 @ sK3 @ sK4)))) | ($false = ((sK2 @ (sK1 @ sK2 @ sK3 @ sK4)))) | spl6_8),
% 0.11/0.25 inference(constrained_superposition,[],[f180,f55])).
% 0.11/0.25 thf(f206,plain,(
% 0.11/0.25 ($true = ((sK3 @ (sK1 @ sK2 @ sK3 @ sK4)))) | ($false = ((sK2 @ (sK1 @ sK2 @ sK3 @ sK4)))) | spl6_8),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f205])).
% 0.11/0.25 thf(f208,plain,(
% 0.11/0.25 ($true = $false) | ($true = ((sK3 @ (sK1 @ sK2 @ sK3 @ sK4)))) | (~spl6_1 | spl6_8)),
% 0.11/0.25 inference(forward_demodulation,[],[f206,f70])).
% 0.11/0.25 thf(f209,plain,(
% 0.11/0.25 ($true = ((sK3 @ (sK1 @ sK2 @ sK3 @ sK4)))) | (~spl6_1 | spl6_8)),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f208])).
% 0.11/0.25 thf(f210,plain,(
% 0.11/0.25 spl6_9 | ~spl6_1 | spl6_8),
% 0.11/0.25 inference(avatar_split_clause,[],[f209,f179,f25,f183])).
% 0.11/0.25 thf(f212,plain,(
% 0.11/0.25 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true != $true) | ($true != ((sP0 @ X0 @ (^[Y0 : a]: (sK3 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X1))) | (sK2 != X0) | (sK4 != X1)) ) | ~spl6_9),
% 0.11/0.25 inference(constrained_superposition,[],[f16,f185])).
% 0.11/0.25 thf(f219,plain,(
% 0.11/0.25 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true != ((sP0 @ X0 @ (^[Y0 : a]: (sK3 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X1))) | (sK2 != X0) | (sK4 != X1)) ) | ~spl6_9),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f212])).
% 0.11/0.25 thf(f220,plain,(
% 0.11/0.25 ( ! [X0 : (a > $o),X1 : (a > $o)] : (($true != ((sP0 @ X0 @ sK3 @ X1))) | (sK2 != X0) | (sK4 != X1)) ) | ~spl6_9),
% 0.11/0.25 inference(beta-eta_normalization,[],[f219])).
% 0.11/0.25 thf(f237,plain,(
% 0.11/0.25 ($true != $true) | (sK2 != sK2) | (sK4 != sK4) | (~spl6_1 | ~spl6_9)),
% 0.11/0.25 inference(constrained_superposition,[],[f220,f27])).
% 0.11/0.25 thf(f238,plain,(
% 0.11/0.25 $false | (~spl6_1 | ~spl6_9)),
% 0.11/0.25 inference(trivial_inequality_removal,[],[f237])).
% 0.11/0.25 thf(f239,plain,(
% 0.11/0.25 ~spl6_1 | ~spl6_9),
% 0.11/0.25 inference(avatar_contradiction_clause,[],[f238])).
% 0.11/0.25 cnf(s1, plain, spl6_1 | spl6_2, inference(sat_conversion,[],[f32])).
% 0.11/0.25 cnf(s2, plain, spl6_1 | ~spl6_3, inference(sat_conversion,[],[f37])).
% 0.11/0.25 cnf(s3, plain, spl6_1 | ~spl6_4, inference(sat_conversion,[],[f42])).
% 0.11/0.25 cnf(s4, plain, ~spl6_2 | spl6_3 | spl6_4, inference(sat_conversion,[],[f47])).
% 0.11/0.25 cnf(s12, plain, ~spl6_1 | ~spl6_8, inference(sat_conversion,[],[f200])).
% 0.11/0.25 cnf(s13, plain, ~spl6_1 | spl6_8 | spl6_9, inference(sat_conversion,[],[f210])).
% 0.11/0.25 cnf(s16, plain, ~spl6_1 | ~spl6_9, inference(sat_conversion,[],[f239])).
% 0.11/0.25 cnf(s17, plain, spl6_1, inference(rat,[],[s4,s1,s2,s3])).
% 0.11/0.25 cnf(s18, plain, ~spl6_9, inference(rat,[],[s16,s17])).
% 0.11/0.25 cnf(s19, plain, spl6_8, inference(rat,[],[s13,s18,s17])).
% 0.11/0.25 cnf(s20, plain, $false, inference(rat,[],[s12,s19,s17])).
% 0.11/0.25 thf(f241,plain,(
% 0.11/0.25 $false),
% 0.11/0.25 inference(avatar_sat_refutation,[],[s20])).
% 0.11/0.25 % SZS output end Proof for theBenchmark
% 0.11/0.25 % (359374)------------------------------
% 0.11/0.25 % (359374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.25 % (359374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.25 % (359374)CaDiCaL version: 2.1.3
% 0.11/0.25 % (359374)Termination reason: Refutation
% 0.11/0.25 % (359374)Time elapsed: 0.007 s
% 0.11/0.25 % (359374)Peak memory usage: 12 MB
% 0.11/0.25 % (359374)Instructions burned: 20 (million)
% 0.11/0.25 % (359366)Success in time 0.041 s
% 0.11/0.25 % Vampire exiting
%------------------------------------------------------------------------------