%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU897^5 : 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 : n008.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 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU897^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:45:25 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.19/0.27 % (3257236)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (3257245)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3711813915:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (3257245)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (3257242)% WARNING: option uhcvi not known.
% 0.19/0.27 % (3257245) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3257236-3257245"...
% 0.19/0.27 % (3257243)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3825455938:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (3257241)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=763888091_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (3257242)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1615327648:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (3257244)dis+10_1_sil=32000:sp=arity:random_seed=1314895197:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (3257246)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3295788201:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (3257242)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % Exception at run slice level
% 0.19/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.27 % (3257247)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=23062024:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (3257245)...printing done.
% 0.19/0.27 % (3257242)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.27 % (3257245)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, a: $tType).
% 0.19/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, cS: (a > $o)).
% 0.19/0.27 thf(func_def_1, type, cR: (a > $o)).
% 0.19/0.27 thf(func_def_5, type, sK0: (a > a)).
% 0.19/0.27 thf(func_def_6, type, sK1: a).
% 0.19/0.27 thf(func_def_7, type, sK2: a).
% 0.19/0.27 thf(func_def_8, type, sK3: a).
% 0.19/0.27 thf(func_def_9, type, sK4: (a > (a > a) > a)).
% 0.19/0.27 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.19/0.27 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.27 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(f1,conjecture,(
% 0.19/0.27 ! [X0 : a] : ((cR @ X0) => (cS @ X0)) <=> ! [X1 : (a > a),X0 : a] : (? [X2 : a] : ((X0 = ((X1 @ X2))) & (cR @ X2)) => ? [X2 : a] : ((X0 = ((X1 @ X2))) & (cS @ X2)))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM30_pme)).
% 0.19/0.27 thf(f2,negated_conjecture,(
% 0.19/0.27 ~(! [X0 : a] : ((cR @ X0) => (cS @ X0)) <=> ! [X1 : (a > a),X0 : a] : (? [X2 : a] : ((X0 = ((X1 @ X2))) & (cR @ X2)) => ? [X2 : a] : ((X0 = ((X1 @ X2))) & (cS @ X2))))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.27 thf(f3,plain,(
% 0.19/0.27 ~(! [X0 : a] : ((cR @ X0) => (cS @ X0)) <=> ! [X1 : (a > a),X2 : a] : (? [X3 : a] : ((((X1 @ X3)) = X2) & (cR @ X3)) => ? [X4 : a] : ((((X1 @ X4)) = X2) & (cS @ X4))))),
% 0.19/0.27 inference(rectify,[],[f2])).
% 0.19/0.27 thf(f4,plain,(
% 0.19/0.27 ~(! [X0 : a] : ((((cR @ X0)) = $true) => (((cS @ X0)) = $true)) <=> ! [X1 : (a > a),X2 : a] : (? [X3 : a] : ((((X1 @ X3)) = X2) & (((cR @ X3)) = $true)) => ? [X4 : a] : ((((X1 @ X4)) = X2) & (((cS @ X4)) = $true))))),
% 0.19/0.27 inference(fool_elimination,[],[f3])).
% 0.19/0.27 thf(f5,plain,(
% 0.19/0.27 ! [X0 : a] : ((((cS @ X0)) = $true) | (((cR @ X0)) != $true)) <~> ! [X1 : (a > a),X2 : a] : (? [X4 : a] : ((((X1 @ X4)) = X2) & (((cS @ X4)) = $true)) | ! [X3 : a] : ((((X1 @ X3)) != X2) | (((cR @ X3)) != $true)))),
% 0.19/0.27 inference(ennf_transformation,[],[f4])).
% 0.19/0.27 thf(f6,plain,(
% 0.19/0.27 (? [X1 : (a > a),X2 : a] : (! [X4 : a] : ((((X1 @ X4)) != X2) | (((cS @ X4)) != $true)) & ? [X3 : a] : ((((X1 @ X3)) = X2) & (((cR @ X3)) = $true))) | ? [X0 : a] : ((((cS @ X0)) != $true) & (((cR @ X0)) = $true))) & (! [X1 : (a > a),X2 : a] : (? [X4 : a] : ((((X1 @ X4)) = X2) & (((cS @ X4)) = $true)) | ! [X3 : a] : ((((X1 @ X3)) != X2) | (((cR @ X3)) != $true))) | ! [X0 : a] : ((((cS @ X0)) = $true) | (((cR @ X0)) != $true)))),
% 0.19/0.27 inference(nnf_transformation,[],[f5])).
% 0.19/0.27 thf(f7,plain,(
% 0.19/0.27 (? [X0 : (a > a),X1 : a] : (! [X2 : a] : ((((X0 @ X2)) != X1) | (((cS @ X2)) != $true)) & ? [X3 : a] : ((((X0 @ X3)) = X1) & (((cR @ X3)) = $true))) | ? [X4 : a] : ((((cS @ X4)) != $true) & ($true = ((cR @ X4))))) & (! [X5 : (a > a),X6 : a] : (? [X7 : a] : ((((X5 @ X7)) = X6) & ($true = ((cS @ X7)))) | ! [X8 : a] : ((((X5 @ X8)) != X6) | ($true != ((cR @ X8))))) | ! [X9 : a] : (($true = ((cS @ X9))) | ($true != ((cR @ X9)))))),
% 0.19/0.27 inference(rectify,[],[f6])).
% 0.19/0.27 thf(f8,plain,(
% 0.19/0.27 ((! [X2 : a] : ((sK1 != ((sK0 @ X2))) | (((cS @ X2)) != $true)) & ((sK1 = ((sK0 @ sK2))) & ($true = ((cR @ sK2))))) | (($true != ((cS @ sK3))) & ($true = ((cR @ sK3))))) & (! [X5 : (a > a),X6 : a] : (((((X5 @ (sK4 @ X6 @ X5))) = X6) & ($true = ((cS @ (sK4 @ X6 @ X5))))) | ! [X8 : a] : ((((X5 @ X8)) != X6) | ($true != ((cR @ X8))))) | ! [X9 : a] : (($true = ((cS @ X9))) | ($true != ((cR @ X9)))))),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2),skolemize(X4,sK3),skolemize(X7,sK4 @ X6 @ X5)],[f7])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 ( ! [X8 : a,X6 : a,X9 : a,X5 : (a > a)] : (($true = ((cS @ (sK4 @ X6 @ X5)))) | (((X5 @ X8)) != X6) | ($true != ((cR @ X8))) | ($true = ((cS @ X9))) | ($true != ((cR @ X9)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 ( ! [X8 : a,X6 : a,X9 : a,X5 : (a > a)] : ((((X5 @ (sK4 @ X6 @ X5))) = X6) | (((X5 @ X8)) != X6) | ($true != ((cR @ X8))) | ($true = ((cS @ X9))) | ($true != ((cR @ X9)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f11,plain,(
% 0.19/0.27 ($true = ((cR @ sK2))) | ($true = ((cR @ sK3)))),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f12,plain,(
% 0.19/0.27 ($true = ((cR @ sK2))) | ($true != ((cS @ sK3)))),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f13,plain,(
% 0.19/0.27 (sK1 = ((sK0 @ sK2))) | ($true = ((cR @ sK3)))),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 (sK1 = ((sK0 @ sK2))) | ($true != ((cS @ sK3)))),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 ( ! [X2 : a] : ((sK1 != ((sK0 @ X2))) | (((cS @ X2)) != $true) | ($true = ((cR @ sK3)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 ( ! [X2 : a] : ((sK1 != ((sK0 @ X2))) | (((cS @ X2)) != $true) | ($true != ((cS @ sK3)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f18,definition,(
% 0.19/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.27 thf(f19,plain,(
% 0.19/0.27 ( ! [X8 : a,X9 : a,X5 : (a > a)] : ((((X5 @ X8)) = ((X5 @ (sK4 @ (X5 @ X8) @ X5)))) | ($true != ((cR @ X8))) | ($true = ((cS @ X9))) | ($true != ((cR @ X9)))) )),
% 0.19/0.27 inference(equality_resolution,[],[f10])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 ( ! [X8 : a,X9 : a,X5 : (a > a)] : (($true = ((cS @ (sK4 @ (X5 @ X8) @ X5)))) | ($true != ((cR @ X8))) | ($true = ((cS @ X9))) | ($true != ((cR @ X9)))) )),
% 0.19/0.27 inference(equality_resolution,[],[f9])).
% 0.19/0.27 thf(f22,definition,(
% 0.19/0.27 spl5_1 <=> ! [X9 : a] : (($true = ((cS @ X9))) | ($true != ((cR @ X9))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.19/0.27 thf(f23,plain,(
% 0.19/0.27 ( ! [X9 : a] : (($true = ((cS @ X9))) | ($true != ((cR @ X9)))) ) | ~spl5_1),
% 0.19/0.27 inference(avatar_component_clause,[],[f22])).
% 0.19/0.27 thf(f25,definition,(
% 0.19/0.27 spl5_2 <=> ! [X5 : (a > a),X8 : a] : (($true = ((cS @ (sK4 @ (X5 @ X8) @ X5)))) | ($true != ((cR @ X8))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.19/0.27 thf(f26,plain,(
% 0.19/0.27 ( ! [X8 : a,X5 : (a > a)] : (($true = ((cS @ (sK4 @ (X5 @ X8) @ X5)))) | ($true != ((cR @ X8)))) ) | ~spl5_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f25])).
% 0.19/0.27 thf(f27,plain,(
% 0.19/0.27 spl5_1 | spl5_2),
% 0.19/0.27 inference(avatar_split_clause,[],[f20,f25,f22])).
% 0.19/0.27 thf(f29,definition,(
% 0.19/0.27 spl5_3 <=> ! [X5 : (a > a),X8 : a] : ((((X5 @ X8)) = ((X5 @ (sK4 @ (X5 @ X8) @ X5)))) | ($true != ((cR @ X8))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.19/0.27 thf(f30,plain,(
% 0.19/0.27 ( ! [X8 : a,X5 : (a > a)] : ((((X5 @ X8)) = ((X5 @ (sK4 @ (X5 @ X8) @ X5)))) | ($true != ((cR @ X8)))) ) | ~spl5_3),
% 0.19/0.27 inference(avatar_component_clause,[],[f29])).
% 0.19/0.27 thf(f31,plain,(
% 0.19/0.27 spl5_1 | spl5_3),
% 0.19/0.27 inference(avatar_split_clause,[],[f19,f29,f22])).
% 0.19/0.27 thf(f33,definition,(
% 0.19/0.27 spl5_4 <=> ($true = ((cR @ sK3)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.19/0.27 thf(f35,plain,(
% 0.19/0.27 ($true = ((cR @ sK3))) | ~spl5_4),
% 0.19/0.27 inference(avatar_component_clause,[],[f33])).
% 0.19/0.27 thf(f37,definition,(
% 0.19/0.27 spl5_5 <=> ($true = ((cR @ sK2)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.19/0.27 thf(f39,plain,(
% 0.19/0.27 ($true = ((cR @ sK2))) | ~spl5_5),
% 0.19/0.27 inference(avatar_component_clause,[],[f37])).
% 0.19/0.27 thf(f40,plain,(
% 0.19/0.27 spl5_4 | spl5_5),
% 0.19/0.27 inference(avatar_split_clause,[],[f11,f37,f33])).
% 0.19/0.27 thf(f42,definition,(
% 0.19/0.27 spl5_6 <=> ($true = ((cS @ sK3)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.19/0.27 thf(f44,plain,(
% 0.19/0.27 ($true != ((cS @ sK3))) | spl5_6),
% 0.19/0.27 inference(avatar_component_clause,[],[f42])).
% 0.19/0.27 thf(f45,plain,(
% 0.19/0.27 ~spl5_6 | spl5_5),
% 0.19/0.27 inference(avatar_split_clause,[],[f12,f37,f42])).
% 0.19/0.27 thf(f47,definition,(
% 0.19/0.27 spl5_7 <=> (sK1 = ((sK0 @ sK2)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 0.19/0.27 thf(f49,plain,(
% 0.19/0.27 (sK1 = ((sK0 @ sK2))) | ~spl5_7),
% 0.19/0.27 inference(avatar_component_clause,[],[f47])).
% 0.19/0.27 thf(f50,plain,(
% 0.19/0.27 spl5_4 | spl5_7),
% 0.19/0.27 inference(avatar_split_clause,[],[f13,f47,f33])).
% 0.19/0.27 thf(f51,plain,(
% 0.19/0.27 ~spl5_6 | spl5_7),
% 0.19/0.27 inference(avatar_split_clause,[],[f14,f47,f42])).
% 0.19/0.27 thf(f53,definition,(
% 0.19/0.27 spl5_8 <=> ! [X2 : a] : ((sK1 != ((sK0 @ X2))) | (((cS @ X2)) != $true))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.19/0.27 thf(f54,plain,(
% 0.19/0.27 ( ! [X2 : a] : ((sK1 != ((sK0 @ X2))) | (((cS @ X2)) != $true)) ) | ~spl5_8),
% 0.19/0.27 inference(avatar_component_clause,[],[f53])).
% 0.19/0.27 thf(f55,plain,(
% 0.19/0.27 spl5_4 | spl5_8),
% 0.19/0.27 inference(avatar_split_clause,[],[f15,f53,f33])).
% 0.19/0.27 thf(f56,plain,(
% 0.19/0.27 ~spl5_6 | spl5_8),
% 0.19/0.27 inference(avatar_split_clause,[],[f16,f53,f42])).
% 0.19/0.27 thf(f62,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : a] : (($true = ((cS @ ((^[Y0 : a]: (Y0)) @ X0)))) | ($true != ((cR @ X1))) | (((cR @ X0)) != $true) | (X0 != X1)) ) | (~spl5_2 | ~spl5_3)),
% 0.19/0.27 inference(constrained_superposition,[],[f26,f30])).
% 0.19/0.27 thf(f65,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : a] : ((((cS @ X0)) = $true) | ($true != ((cR @ X1))) | (((cR @ X0)) != $true) | (X0 != X1)) ) | (~spl5_2 | ~spl5_3)),
% 0.19/0.27 inference(beta-eta_normalization,[],[f62])).
% 0.19/0.27 thf(f70,plain,(
% 0.19/0.27 ($true != $true) | (((cS @ sK3)) = $false) | spl5_6),
% 0.19/0.27 inference(constrained_superposition,[],[f44,f18])).
% 0.19/0.27 thf(f72,plain,(
% 0.19/0.27 (((cS @ sK3)) = $false) | spl5_6),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f70])).
% 0.19/0.27 thf(f83,plain,(
% 0.19/0.27 ( ! [X0 : a] : (($true != $true) | (((cR @ X0)) != $true) | ($true != ((cR @ sK3))) | (sK3 != X0)) ) | (~spl5_2 | ~spl5_3 | spl5_6)),
% 0.19/0.27 inference(constrained_superposition,[],[f44,f65])).
% 0.19/0.27 thf(f84,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((((cR @ X0)) != $true) | ($true != ((cR @ sK3))) | (sK3 != X0)) ) | (~spl5_2 | ~spl5_3 | spl5_6)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f83])).
% 0.19/0.27 thf(f88,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((((cR @ X0)) != $true) | (sK3 != X0)) ) | (~spl5_2 | ~spl5_3 | ~spl5_4 | spl5_6)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f84,f35])).
% 0.19/0.27 thf(f91,plain,(
% 0.19/0.27 ($true != $true) | (sK3 != sK3) | (~spl5_2 | ~spl5_3 | ~spl5_4 | spl5_6)),
% 0.19/0.27 inference(constrained_superposition,[],[f88,f35])).
% 0.19/0.27 thf(f94,plain,(
% 0.19/0.27 $false | (~spl5_2 | ~spl5_3 | ~spl5_4 | spl5_6)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f91])).
% 0.19/0.27 thf(f95,plain,(
% 0.19/0.27 ~spl5_2 | ~spl5_3 | ~spl5_4 | spl5_6),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f94])).
% 0.19/0.27 thf(f96,plain,(
% 0.19/0.27 ($true = $false) | ($true != ((cR @ sK3))) | (~spl5_1 | spl5_6)),
% 0.19/0.27 inference(constrained_superposition,[],[f23,f72])).
% 0.19/0.27 thf(f101,plain,(
% 0.19/0.27 ($true != ((cR @ sK3))) | (~spl5_1 | spl5_6)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f96])).
% 0.19/0.27 thf(f106,plain,(
% 0.19/0.27 $false | (~spl5_1 | ~spl5_4 | spl5_6)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f101,f35])).
% 0.19/0.27 thf(f107,plain,(
% 0.19/0.27 ~spl5_1 | ~spl5_4 | spl5_6),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f106])).
% 0.19/0.27 thf(f109,plain,(
% 0.19/0.27 ( ! [X1 : a] : ((sK1 = (((^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK4 @ sK1 @ (^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true != ((cR @ X1))) | (sK2 != X1)) ) | (~spl5_3 | ~spl5_7)),
% 0.19/0.27 inference(constrained_superposition,[],[f30,f49])).
% 0.19/0.27 thf(f114,plain,(
% 0.19/0.27 ( ! [X1 : a] : ((sK1 = ((sK0 @ (sK4 @ sK1 @ sK0)))) | ($true != ((cR @ X1))) | (sK2 != X1)) ) | (~spl5_3 | ~spl5_7)),
% 0.19/0.27 inference(beta-eta_normalization,[],[f109])).
% 0.19/0.27 thf(f117,definition,(
% 0.19/0.27 spl5_9 <=> ! [X1 : a] : (($true != ((cR @ X1))) | (sK2 != X1))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition])).
% 0.19/0.27 thf(f118,plain,(
% 0.19/0.27 ( ! [X1 : a] : (($true != ((cR @ X1))) | (sK2 != X1)) ) | ~spl5_9),
% 0.19/0.27 inference(avatar_component_clause,[],[f117])).
% 0.19/0.27 thf(f120,definition,(
% 0.19/0.27 spl5_10 <=> (sK1 = ((sK0 @ (sK4 @ sK1 @ sK0))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition])).
% 0.19/0.27 thf(f122,plain,(
% 0.19/0.27 (sK1 = ((sK0 @ (sK4 @ sK1 @ sK0)))) | ~spl5_10),
% 0.19/0.27 inference(avatar_component_clause,[],[f120])).
% 0.19/0.27 thf(f123,plain,(
% 0.19/0.27 spl5_9 | spl5_10 | ~spl5_3 | ~spl5_7),
% 0.19/0.27 inference(avatar_split_clause,[],[f114,f47,f29,f120,f117])).
% 0.19/0.27 thf(f133,plain,(
% 0.19/0.27 (sK1 != sK1) | ($true != ((cS @ sK2))) | (~spl5_7 | ~spl5_8)),
% 0.19/0.27 inference(constrained_superposition,[],[f54,f49])).
% 0.19/0.27 thf(f134,plain,(
% 0.19/0.27 ($true != ((cS @ sK2))) | (~spl5_7 | ~spl5_8)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f133])).
% 0.19/0.27 thf(f136,plain,(
% 0.19/0.27 ($true != $true) | ($true != ((cR @ sK2))) | (~spl5_1 | ~spl5_7 | ~spl5_8)),
% 0.19/0.27 inference(constrained_superposition,[],[f134,f23])).
% 0.19/0.27 thf(f139,plain,(
% 0.19/0.27 ($true != ((cR @ sK2))) | (~spl5_1 | ~spl5_7 | ~spl5_8)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f136])).
% 0.19/0.27 thf(f140,plain,(
% 0.19/0.27 $false | (~spl5_1 | ~spl5_5 | ~spl5_7 | ~spl5_8)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f139,f39])).
% 0.19/0.27 thf(f141,plain,(
% 0.19/0.27 ~spl5_1 | ~spl5_5 | ~spl5_7 | ~spl5_8),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f140])).
% 0.19/0.27 thf(f146,plain,(
% 0.19/0.27 ( ! [X1 : a] : (($true = ((cS @ (sK4 @ sK1 @ (^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ($true != ((cR @ X1))) | (sK2 != X1)) ) | (~spl5_2 | ~spl5_7)),
% 0.19/0.27 inference(constrained_superposition,[],[f26,f49])).
% 0.19/0.27 thf(f153,plain,(
% 0.19/0.27 ( ! [X1 : a] : (($true = ((cS @ (sK4 @ sK1 @ sK0)))) | ($true != ((cR @ X1))) | (sK2 != X1)) ) | (~spl5_2 | ~spl5_7)),
% 0.19/0.27 inference(beta-eta_normalization,[],[f146])).
% 0.19/0.27 thf(f171,plain,(
% 0.19/0.27 ($true != $true) | (sK2 != sK2) | (~spl5_5 | ~spl5_9)),
% 0.19/0.27 inference(constrained_superposition,[],[f118,f39])).
% 0.19/0.27 thf(f174,plain,(
% 0.19/0.27 $false | (~spl5_5 | ~spl5_9)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f171])).
% 0.19/0.27 thf(f175,plain,(
% 0.19/0.27 ~spl5_5 | ~spl5_9),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f174])).
% 0.19/0.27 thf(f178,definition,(
% 0.19/0.27 spl5_15 <=> ($true = ((cS @ (sK4 @ sK1 @ sK0))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl5_15])],[avatar_definition])).
% 0.19/0.27 thf(f180,plain,(
% 0.19/0.27 ($true = ((cS @ (sK4 @ sK1 @ sK0)))) | ~spl5_15),
% 0.19/0.27 inference(avatar_component_clause,[],[f178])).
% 0.19/0.27 thf(f181,plain,(
% 0.19/0.27 spl5_9 | spl5_15 | ~spl5_2 | ~spl5_7),
% 0.19/0.27 inference(avatar_split_clause,[],[f153,f47,f25,f178,f117])).
% 0.19/0.27 thf(f201,plain,(
% 0.19/0.27 (sK1 != sK1) | ($true != ((cS @ (sK4 @ sK1 @ sK0)))) | (~spl5_8 | ~spl5_10)),
% 0.19/0.27 inference(constrained_superposition,[],[f54,f122])).
% 0.19/0.27 thf(f202,plain,(
% 0.19/0.27 ($true != ((cS @ (sK4 @ sK1 @ sK0)))) | (~spl5_8 | ~spl5_10)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f201])).
% 0.19/0.27 thf(f209,plain,(
% 0.19/0.27 $false | (~spl5_8 | ~spl5_10 | ~spl5_15)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f202,f180])).
% 0.19/0.27 thf(f210,plain,(
% 0.19/0.27 ~spl5_8 | ~spl5_10 | ~spl5_15),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f209])).
% 0.19/0.27 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f27])).
% 0.19/0.27 cnf(s2, plain, spl5_1 | spl5_3, inference(sat_conversion,[],[f31])).
% 0.19/0.27 cnf(s3, plain, spl5_4 | spl5_5, inference(sat_conversion,[],[f40])).
% 0.19/0.27 cnf(s4, plain, spl5_5 | ~spl5_6, inference(sat_conversion,[],[f45])).
% 0.19/0.27 cnf(s5, plain, spl5_4 | spl5_7, inference(sat_conversion,[],[f50])).
% 0.19/0.27 cnf(s6, plain, ~spl5_6 | spl5_7, inference(sat_conversion,[],[f51])).
% 0.19/0.27 cnf(s7, plain, spl5_4 | spl5_8, inference(sat_conversion,[],[f55])).
% 0.19/0.27 cnf(s8, plain, ~spl5_6 | spl5_8, inference(sat_conversion,[],[f56])).
% 0.19/0.27 cnf(s9, plain, ~spl5_2 | ~spl5_3 | ~spl5_4 | spl5_6, inference(sat_conversion,[],[f95])).
% 0.19/0.27 cnf(s12, plain, ~spl5_1 | ~spl5_4 | spl5_6, inference(sat_conversion,[],[f107])).
% 0.19/0.27 cnf(s13, plain, ~spl5_3 | ~spl5_7 | spl5_9 | spl5_10, inference(sat_conversion,[],[f123])).
% 0.19/0.27 cnf(s15, plain, ~spl5_1 | ~spl5_5 | ~spl5_7 | ~spl5_8, inference(sat_conversion,[],[f141])).
% 0.19/0.27 cnf(s19, plain, ~spl5_5 | ~spl5_9, inference(sat_conversion,[],[f175])).
% 0.19/0.27 cnf(s20, plain, ~spl5_2 | ~spl5_7 | spl5_9 | spl5_15, inference(sat_conversion,[],[f181])).
% 0.19/0.27 cnf(s21, plain, ~spl5_8 | ~spl5_10 | ~spl5_15, inference(sat_conversion,[],[f210])).
% 0.19/0.27 cnf(s24, plain, spl5_4 | spl5_1, inference(rat,[],[s21,s20,s13,s19,s3,s5,s7,s2,s1])).
% 0.19/0.27 cnf(s25, plain, ~spl5_4 | ~spl5_2 | ~spl5_3, inference(rat,[],[s21,s20,s13,s19,s4,s6,s8,s9])).
% 0.19/0.27 cnf(s26, plain, spl5_1, inference(rat,[],[s25,s24,s1,s2])).
% 0.19/0.27 cnf(s27, plain, spl5_4, inference(rat,[],[s15,s3,s5,s7,s26])).
% 0.19/0.27 cnf(s29, plain, spl5_6, inference(rat,[],[s12,s26,s27])).
% 0.19/0.27 cnf(s30, plain, spl5_8, inference(rat,[],[s8,s29])).
% 0.19/0.27 cnf(s31, plain, spl5_7, inference(rat,[],[s6,s29])).
% 0.19/0.27 cnf(s32, plain, spl5_5, inference(rat,[],[s4,s29])).
% 0.19/0.27 cnf(s33, plain, $false, inference(rat,[],[s15,s30,s26,s31,s32])).
% 0.19/0.27 thf(f220,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s33])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (3257245)------------------------------
% 0.19/0.27 % (3257245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3257245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3257245)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3257245)Termination reason: Refutation
% 0.19/0.27 % (3257245)Time elapsed: 0.007 s
% 0.19/0.27 % (3257245)Peak memory usage: 12 MB
% 0.19/0.27 % (3257245)Instructions burned: 18 (million)
% 0.19/0.27 % (3257236)Success in time 0.033 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------